Let $G$ be a group (not necessarily finite). Can we say something about its structure if we suppose that all of its proper subgroups are abelian? Is there a difference between the finite case and the infinite case?
To put it in another way, is the class of such groups wild or do we control it? Naturally, abelian groups are part of it, but I am interested in the nonabelian case.
This question may sound quite open but I think it should be interesting to investigate it.