The Crime Society's background is currently unknown, yet it is almost similar to the Crime Syndicate, and are the evil doppelgangers of the heroes of Earth-2. Also paralleling to that of the Justice Society is their larger roster (which is not strictly limited to the Justice Society counterparts).
The Society later encountered and fought the Challengers (consisted of Donna Troy, Jason Todd, Kyle Rayner, and Bob the Monitor) and the Jokester. After the Challengers and along with the Jokester escape to another universe, the Crime Society were then offered a place among the Monarch's trans-dimensional army. The Society then fought on Earth-51 and battle the Monitors. When Superboy Prime subsequently caused the destruction of Earth-51's reality, it is unknown if any of the Crime Society somehow survived the devastation.
and other unspecified counterparts.