The Catholic Church is very specific in this. They are ok with secret societies depending on what they stand for.
Also remember, secret societies and fraternities are slightly different. Secret Societies you dont know who is a member or what they are called...yada yada yada.
Anyway, I am also Catholic and greek and the literature I have looked at seems to support fraternities. Anyway there are several Jesuit and Catholic schools that have greek systems !!
Hope this helps...
