What are the open problems concerning all the finite groups?
The references will be appreciated. Here are two examples:
Aschbacher-Guralnick conjecture (AG1984 p.447): the number of conjugacy classes of maximal subgroups of a finite group is at most its class number (i.e. the number of conjugacy classes of elements, or the number of irreducible complex representations up to equiv.).
There are two types of problems, those involving an upper/lower bound (like Aschbacher-Guralnick conjecture) and those "exact", involving no bound (like K.S. Brown's problem). I guess the first type is much more abundant than the second, so for the first type, please restrict to the main problems.