Towards the Classification of Finite Simple Groups with exactly Three or   Four Supercharacter Theories
  A supercharacter theory for a finite group $G$ is a set of superclasses each of which is a union of conjugacy classes together with a set of sums of irreducible characters called supercharacters that together satisfy certain compatibility conditions.The aim of this paper is to give a description of some finite simple groups with exactly three or four supercharacter theories. 
Ali Reza Ashrafi and Fatemeh Koorepazan-Moftakhar
math.GR