The Ur-Quan Hierarchy is a massive force controlled by the Ur-Quan Kzer-Za. The internal command structure of the hierarchy is not known, although there is speculation that an Ur-Quan Lord's number (i.e. Lord 999) may be equivalent to rank.
The external command structure is well-documented. The Ur-Quan are superior to any given race in the Heirarchy regardless of their station in Ur-Quan society (if one exists). After this, the Battle Thralls exist to fight for the Kzer-Za. They are governed by Ur-Quan slave laws, but retain some degree of autonomy. At the bottom of the chain are fallow slaves who chose not to fight for the Hierarchy and were slave-shielded on their home planets.
Hierarchy Battle Thralls During the First War (Star Control I):
The Thraddash claim to have been Battle Thralls at the time, told to "guard the rear". They are usually not included in such lists because there is no mention of the Thraddash in Star Control I.