Autogun
An Autogun is a chemically-powered projectile throwing weapon (a slug thrower), that can be compared to late 20th century fire arms, though it is significantly more powerful, which is why it avoids the title of stubber (which have virtually no improvements on World War II firearms) which are even worse than lasguns (there is not a single part of a suit of flak armor that a rifle sized stubber can pierce at any range). Simply put these weapons use a propellant to accelerate a metal projectile to punch holes in things. It is a significantly older weapon than the Lasgun, and does not see quite as much use due to the Departmento Munitorium - Lasgun Power Packs weigh significantly less than autogun magazines and are far more sustainable (rechargeable via heat, light, or wall outlet). Lasguns are also significantly more accurate and require notably less maintenance than Autoguns, and have no recoil, meaning even the 8-year-old baby-faced kids and 98-year-old dusty seniors the Imperial Guard recruits can fire it straight, so a big reason that Autoguns were phased out was a matter of practicality. Though /tg/ rather enjoys musing that the main reason was cost (all that grimdark spent ammunition came from somewhere, after all). In spite of the ammunition problem, the Autogun still sees use throughout the Imperium, and it's removal from official service hasn't stopped it's development.
Variants
Autopistol
Most often a machine pistol or submachine gun, the Autopistol is a single-handed submachine gun (called the Uzi Autopistol) which is frequently used by Chaos heretics (and on occasion, traitor guardsmen) and cultists who don't particularly care about accuracy or expenses and wish to be able to make noise and cause death at a distance (the former is done better by an Autogun than a Lasgun) as they close in to use their swords.
Autogun
There are dozens of other Autogun models that have been created since, including more-advanced versions that use caseless ammunition. The most common variety is an assault-rifle sized version formerly used by Imperial Guard regiments, known as the Armageddon-Pattern Autogun. It can fire on semi-automatic, 5-round bursts, or on full-auto and holds 60 rounds in a triple-stacked magazine. Most versions are modded to fire specifically in 5-round bursts, allowing it to achieve 12 bursts per mag. Whilst the Autogun is not hugely damaging, its fire rate is extremely high, allowing it to quite literally chew through body armor at medium range. Autoguns are commonly employed by pirates, rebel groups, Chaos cultists, Kriegers, Planetary Defense Forces, Hive Gangers, Adeptus Arbites and low-tech civilisations that are too underdeveloped to create even a simple Lasgun, which puts into perspective just how poor these people are.
Autocannon
The Autocannon is the big-cheese of the Autogun family, firing enormous shells capable of tearing through bodies like a guillotine through a French aristocrat's neck. Most commonly mounted on vehicles, but also seeing use in Imperial Guard Heavy weapons teams, it possesses a worrying rate of fire, and good armour penetration, proving that even older tech can work when made sufficiently huge. It used to be much better, using what were approximately up-scaled Heavy Bolter shells to literally kill anything, but then grimdark happened and the Mechanicus forgot how to read. You know, business as usual.
The long-barreled Hydra variation is used on the Hydra Flak Tank, designed to serve as anti-air support but used to chew up any cocky infantry that gets too close. nowadays it give warning shots that may clip an enemy it that enemy is standing right in front of it and jumps up and down screaming "SHOOT ME"
Also comes in Reaper variant, which only the Chaos Space Marines get because Assault Cannons were discovered after the Horus Heresy, and everybody Imperial promptly thought they were cooler than the Reaper Autocannon. This is an infantry-portable, twin-linked Autocannon that wants to put its shells in your face at 36" or less. Scary for light vehicles and monsters, the Imperials were right (for once) to switch to the Assault Cannon for infantry fighting.
Assault Cannon
The Assault cannon is an Autogun with an outrageous rate of fire, meaning it has to have rotating barrels to stop them from melting. It also fires unique, diamond-hard rounds at significantly increased velocity, resulting in far greater stopping power and penetration. The upgraded weapons system was found post-Heresy, meaning that Chaos doesn't get these meat-eaters. Primarily used by Space Marines as anti-infantry weaponry on Terminators, Dreadnoughts, and various other vehicles and aircraft.
Punisher Gatling Cannon
The most dakka in the game. Able to churn out more shots than a squad of Tactical Marines at even greater strength, this baby will melt down any block of infantry it comes across and can even threaten Monstrous Creatures by the sheer volume of fire they put out.
Gatling Blaster
Strapped to the mighty Reaver Battle Titan and above, this is the weapon you field when you need the biggest dakka the Imperium of Man has to offer.
Gallery
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Autoguns - Better Than Your Crap Flashlights!
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A typical mass produced model.
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Traitor Guardsmen armed with Armageddon-pattern Autoguns and Autopistols. You know you want 'em.
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The Punisher Gatling Cannon and its tank. Sometimes you just need a little more gun.
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The Gatling Blaster. For when you need big dakka.