I really think that their should be a way to see what clan someone belongs to on their Call Of Duty Elite Profile.  They are already doing this with what groups someone belongs to which is ok, but I think it would make more sense to show their clan.  That way if you played with someone and wanted to invite them to your clan you could go to their profile and see if they already belong to a clan before sending them an invite.  Or if you were looking to join a clan you could see if they belonged to a clan and which one it is so you could attempt to join it.