Solvability of finite coatomic groups (Q752178)

\textit{F. Menegazzo} [Atti Accad. Naz. Lincei., Rend., Cl. Sci. Fis. Mat. Nat., VIII. Ser. 48, 559-562 (1970; Zbl 0216.088)] introduced the class of IM-groups (they are also called coatomic groups), i.e. groups in which every proper subgroup is the intersection of some maximal subgroups. He also determined all finite solvable coatomic groups. Further \textit{F. Migliorini} [Matematiche 29, 231-248 (1974; Zbl 0336.20018)], \textit{M. Bianchi} and \textit{M. C. Tamburini Bellani} [Rend., Sci. Mat. Appl., A 111, 429-436 (1977; see the preceding review Zbl 0715.20011)] obtained criteria for nonsimplicity of the finite coatomic groups. The question of existence of finite nonsolvable coatomic groups remained open. In this paper it is proved the solvability of finite coatomic groups whose simple sections are known simple groups.