"The bureaucracy is expanding to meet the needs of the expanding bureaucracy."
"If the populace knew with what idiocy they were ruled, they would revolt."
The Adeptus Administratum is the name of the pencil pushers of the Imperium of Man. Founded by Malcador the Sigillite back in the day the Emprah was strutting about, the Administratum is the bureaucratic division of the Adeptus Terra. They assess the tithes every world must pay to the Imperium, take census data, and maintain records. Unfortunately, a bureaucracy ten thousand years old and spanning most of the galaxy has created red tape that stretches for light years and inertia that can (and has) cost and caused wars. Imagine the Vogon equivalent of the Department of Motor Vehicles with all the grimdark of Warhammer 40,000 and half of the productivity, then multiplied by the number of planets in the Imperium. The Adepts of a department will keep going about their duties long after their department has become completely useless because they will likely be executed for abandoning their position if they were to stop. That's the Administratum. It's run by the aptly named Master of the Administratum, who is the most powerful of the High Lords of Terra (because he can threaten to get anyone so bogged down in red tape they will never see the end of it in the span of their lives).
Life for the average Administratum paper pusher is safer than that of a guardsman or a factory serf toiling away on an assembly line for 14 hours a day in a factory complex on a world where 'safety codes' are a thing of legend and possibly considered borderline heresy by the nobility, but is not easy or pleasant by any means. Posts are generally hereditary and the standards of living are monastic baring the necessities to make more adepts (Administrandum courtships involves both parties making careful inspection of each other's request forms). The general policy is that servants of the Imperium should have no loyalty to anything besides the Imperium and frivolities are discouraged as distraction, though there are those who get around it especially among the higher ups. Mostly what Administratum Adepts do is process what papers come their way for twelve hours between eating, washing and sleeping. This is before the fact that there is a complex web of departments, sub departments and so forth, which has in at least one case led to a war when the Administratum ran out of space in a solar system to put all their paperwork and couldn't decide what to do about it that rages on to this very day.
This environment can produce a number of amazing administrative savants such that if you dropped one of them with her trusty portable cogitator and pens in a mob of a million starved refugees with nothing but the clothes on their back, in a year she'll have organized them to the point that they've built a new city better than the ones they fled (these guys come up in The Black Library's books). The problem is that said environment also produces plenty of sapped office drones who are incapable of doing anything but their likely pointless task, petty tyrants whose only joy in life is lording what power their office has have over others, corrupt jerks who can do their jobs well but only do so when a few Imperials are slipped under the table, and general morons who might be able to spell their name with only one letter out of place on the third try but nevertheless have positions of power because of their dad and remain in his job because the paperwork to remove him gets lost and forgotten (possibly deliberately by one of the previously mentioned corrupt jerks).
It should be noted however that the Administratum is an Imperial institution handling Imperial scale affairs often on the scale of hundreds of worlds at best, millions at worst, and efficiency tends to slow when the system is just that massive. Planets mostly govern themselves and their local governments have their own bureaucracies to execute the wills of the governor and his associates. As said governors are largely free to set up their systems and are not bound by Administratum rules, this can make things more difficult or more efficient depending on the planet in question.
The rest of the Imperium routinely despises the Administratum; even the Adeptus Arbites and the Inquisition admit they are highly inefficient (in fact there's a whole Ordo with the sole role to cut as much red tape as possible). The Astartes and Guard are more straightforward in their thoughts, thinking that more than a few wars could be won if they gave each Admin adept a lasgun and sent them to the front lines. However, as much as they are disliked, all other departments need the Administratum, as they won't know where to go to start ordering basic supplies even if they were desperate enough to try. In the far grim future, the ordering form is a dark and mystical document that requires much ritual and mediation before it can be filled in- and Emperor help you if you make a mistake on said form.
These are the various departments that we know exist however the fluff is kinda patchy and much of what we know comes from old, throwaway fluff written without much thought and as much grimdark as is humanly possible so it's kinda debatable how accurate any of it is these days, and remember, they only handle galactic matters, and very rarely interfere with planetary affairs unless it involves them in a way big enough to be bothered over it. They will gladly overlook genocidal interplanetary wars as long as those wars do not disrupt the tithe to the Imperium.
- Departmento Munitorum: The branch of the Administratum charged with running the Imperial Guard. Their duties encompass aspects ranging from estimating and managing manpower, weaponry, and supplies of the Imperial Guard, but the Guard is so massive that it's rare for the Munitorum NOT to make constant fuck-ups at the least convenient times (You needed some more lasgun power packs? Too bad, you're getting dress clothes for Ogryn instead.), and trying to requisition anything beyond your standard kit is an exercise in futility. The Munitorum also decides which planets have met their tithe requirements or not, but on a few occasions rounding errors or misspellings have resulted in worlds being declared traitors or wiped out regiments being sentenced to death posthumously.
- Estate Imperium: Charged with maintaining the records of the Imperium. The Chancellor of the Estate Imperium can occasionally get a spot on the High Lords of Terra. Well, were he not doped-up on anti-depressants to deal his raging OCD, anyway (that's fine though as the only thing he does is provide the Master of the Administratum with an extra vote).
- Historical Revision Unit: The propaganda branch of the Imperium, charged with making sure Imperial history makes the Emperor and the Imperium look perfect and eliminating all knowledge of traitors. Because the Imperium wasn't grimdark enough, they cut/paste the Ministry of Truth into one of their foundational institutions. However, they must have done it with Linux, because they didn't manage to get enough of in to really affect the universe. Although... there has been a shit ton of 'revisions' to a wide variety of things to make various institutions look so unrealistically good that it defies sanity, and yet it has become 'fact'... Well played GW... On the other hand. This lack of knowledge of the very existence of traitors could be very useful in...other ways (Rebellious types still show up but it's much less likely to spread when most of society thinks that it's good that society is as fucked as it is.)
- Officio Agricultae: The department charged with overseeing agriculture in the Imperium, serving to determine the tithes of the various agri-worlds that litter the Imperium, and making sure that that there is enough food to feed the people of the Imperium. Food will still not be distributed equally, however, and pretty much only the nobles and the Imperial Guard gets priority over food while civilians get whatever scraps are left. Food riots ensue. Or so the fluff says. But if you think about it there's no way food can be so scarce. It's been ten thousands years. If everyone is starving they would be dead by now. Sure there might be late shipments or whatever but it's really hard to create hive world with billions of people that last for millennia without a reliable food supply. Every society is three meals away from revolution, so unless future humans can subsist on algae this has to be wrong. It sounds real grimdark to say 'no food for you peasants because we are transparently evil dicks who need it for our huge blobs of cannon fodder' but it stops being practical ten seconds later. If the Imperium can manage the production lines for a billion lasguns they can manage to get corn to the next generation of guardsmen. (But then again this is considered 'British' humor).
- Officio Medicae: The department charged with medical affairs of the Imperium. Unless you're a noble, Guardsman, or Inquisitor, you won't be getting access to any meaningful medical assistance ( the middle probably won't be able to live long enough for that to matter anyway) without visiting a dread-inducing back alley doc, who is always located in the underhive, smells of Obscura, and whose services cost an arm and a leg. Sometimes literally. If you do fall under the aforementioned categories, you are eligible for drugs and cybernetics that can keep you alive and kicking for a few centuries. Although certain Ecclesiarchal charities and missions do still provide medical treatment for the common citizens of the Imperium, just provided that they do not suspect anyone in your area of heresy, which can turn a humble medical mission into a crusade to burn your district or even your entire planet into ash.