I study the interaction of two forces in the formation of social groups: the preference for high quality peers and the desire for status among one's peers. I present a characterization of fundamental properties of equilibrium group structures in a perfect information, simultaneous move game when group membership is priced uniformly and cannot directly depend on type. While equilibrium groups generally exhibit some form of assortative matching between individual type and peer quality, the presence of status concern reduces the potential degree of sorting and acts as a force for greater homogeneity across groups. I analyse the effect of status concern for the provision of groups under different market structures and particularly focus on the implications for segregation and social exclusion. I find that status concern reduces the potential for and benefit from segregation - both for a social planner and a monopolist - but the interaction of preference for rank and status can make the exclusion of some agents a second-best outcome.