19.54 (2018)

What are the chief factors of a finite group in which every 2-maximal subgroup is not $m$-maximal for any $m \geqslant 3$?

A subgroup $H$ of a group $G$ is said to be $m$-maximal if there is a chain of subgroups $H = H_0 < H_1 < \dots < H_{m-1} < H_m = G$ in which $H_i$ is maximal in $H_{i+1}$ for every $i$. Note that for every $m \geqslant 3$ there is a finite group in which some 2-maximal subgroup is $m$-maximal.