The Jem'Hadar have a relatively simple system of rank with the leader of any unit known as the First. His second in command is known as the Second, his third in command is the Third and so on. (DS9: "Hippocratic Oath", "Rocks and Shoals")
In units that comprise of sub-units the First, Second and Third of the larger unit outrank the First, Second and Third of any sub-unit. The Fourth of the larger unit is considered equivalent in rank to the First of a sub-unit, the Firth with the Second of the sub-unit and so forth. (The Dominion War Sourcebook: The Fires of Armageddon)
The Vorta in charge of the unit has the power to assign Jem'Hadar at any position, promoting and demoting them as they see fit. If a First is killed the next Jem'Hadar in line usually would be promoted to First, however a Vorta can deny the Jem'Hadar the promotion if they feel they are undeserving of the position. (DS9: "Rocks and Shoals")
This honorific title is given to a Jem'Hadar who lives past the age of 20, which given the Jem'Hadar's sole purpose is a rare event. Taran'atar was an Honored Elder by 2376. (DS9: "To the Death", DS9 novel: Avatar)
The Vorta have a rank system separate from the Jem'Hadar they command. These ranks are split into two groups depending on whether the Vorta commands ground forces of fleet units. (The Dominion War Sourcebook: The Fires of Armageddon)
Vorta fleet ranksEdit
A Sadok'toran (translates as "supreme leader in the name of the Founders") is the highest fleet rank a Vorta can obtain. A Sadok'toran commands a division and as such are often the most experienced commanders in the Dominion military in some case with centuries of service. Equivalent to a high ranking Admiral.
A Chelek'toran commands Dominion strike fleets. A Vorta's performance as a Chelek'toran is essential to whether they are deserving to be promoted to Sadok'toran.
A Suba'toran commands a wing. In a wing there are usually several other Vorta who are qualified to hold this rank in case the Suba'toran is killed in action. These Vorta are not above backstabbing to get a Suba'toran out of the way to further their progression.
A Vara'toran commands a squadron. Given the small scale of squadrons the Vara'toran often limit themselves to broad strategic orders and leave the direction of the fighting to the Jem'Hadar.
A Rona'toran is a Vorta that is in command on any specific Dominion vessel. While the rank is somewhat equivalent to that of a captain its position in the Vorta military hierarchy is much lower then a captain would be in Starfleet for instance.
A Doko'toran is a junior Vorta who is given a position of authority on board a larger starship such as a battle cruiser or battleship. It serves in function like a lieutenant. Nalla was a fire control Doko'toran aboard Cerrein's dreadnaught during Operation Urrent Gar in the opening months of the Dominion War.(Extermination)
Vorta ground forces ranksEdit
Vorta ground force commanders use the same ranks as fleet Vorta but use the suffix -'atorn instead of -'toran. (The Dominion War Sourcebook: The Fires of Armageddon)
A Hentek'atorn commands a ground force division.
A Sadok'atorn commands a ground force brigade.
A Chelek'atorn commands a ground force regiment.
A Rona'atorn commands a ground force platoon.