Open problems concerning all the finite groups What are the open problems concerning all the finite groups?
The references will be appreciated. Here are two examples:  


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*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.).

*K.S. Brown's problem (B2000 Q.4; SW2016 p.760): Let $G$ be a finite group, $\mu$ be the Möbius function of its subgroup lattice $L(G)$. Then the sum $\sum_{H \in L(G)}\mu(H,G)|G:H|$ is nonzero.
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.
 A: There are plenty of examples; the below are taken from the Kourovka Notebook, and include a fairly broad range of topics.

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*(4.55) Let $G$ be a finite group and $\mathbb{Z}_p$ the localization at $p$. Does the Krull-Schmidt theorem hold for projective $\mathbb{Z}_pG$-modules?

*(8.51) If $G$ is a finite group and $p$ a prime, let $m_p(G)$ denote the number of ordinary irreducible characters of $G$ whose degree is not divisible by $p$. Let $P$ be a Sylow $p$-subgroup of $G$. Is it true that $m_p(G) = m_p(N_G(P))$?

*(9.6) Is it true that an independent basis of quasiidentities of any finite group is finite?

A few other questions of a similar format to the questions you provided include (9.23), (11.17), (13.31), and (16.45).
The questions I picked are all of the form "Is $P$ true for all finite groups $G$?". There are many questions of the form "Characterize the finite groups $G$ for which $P$ holds", which to my ears has a slightly different ring to it than what you were asking for. There are also some questions regarding the class of finite groups, which again is a different interpretation.
Indeed, completely in line with Yves' comment, there is some ambiguity in what a problem for "all" finite groups should look like. Fortunately, there are enough problems in the Notebook to satisfy any interpretation, I should think.
