Geodesic
Influence of properties of maximal subgroups on the structure of a finite group
Matematičeskie zametki, Tome 11 (1972) no. 2, pp. 183-190 
V. S. Monakhov. Influence of properties of maximal subgroups on the structure of a finite group. Matematičeskie zametki, Tome 11 (1972) no. 2, pp. 183-190. http://geodesic.mathdoc.fr/item/MZM_1972_11_2_a7/
@article{MZM_1972_11_2_a7,
     author = {V. S. Monakhov},
     title = {Influence of properties of maximal subgroups on the structure of a finite group},
     journal = {Matemati\v{c}eskie zametki},
     pages = {183--190},
     year = {1972},
     volume = {11},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_11_2_a7/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We establish some tests for the solvability of finite groups and describe one class of unsolvable groups. We prove that an unsolvable group $G$ such that a maximal subgroup $M=P\times H$ is nilpotent and the 2-Sylow subgroup $P$ of $M$ is metacyclic has a normal series $G\supseteq G_0\supset T\supseteq\{1\}$ such that $T$ is contained in $M$, $G_0/T\simeq PSL(2,q)$, where $q$ is a power of a prime of the form $2^n\pm1$ and the index of $G_0$ in $G$ is not greater than 2.