The Ur-Quan Hierarchy is a massive force controlled by the Ur-Quan Kzer-Za. The internal command structure of the heirarchy is not known, although there is speculation that and 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 Heirarchy and were slave-sheilded on their home planets.
Heirarchy Battle Thralls During the First War (Star Control I):
Heirarchy Battle Thralls At The Beginning of the Second War (Star Control II):