On Some Maximal Subgroups Having No Prime Power Index of Finite Groups

In this paper, we will further characterize the structure of nonsolvable groups by combining the properties of the second maximal subgroups related to $$\operatorname{Max}^{\overline{p^{\alpha}}}(G)$$ , where $$\operatorname{Max}^{\overline{p^{\alpha}}}(G)=\bigl\{M\lessdot G\mid |G\colon M|\neq p^{\alpha}, p \ \ \text{is prime and} \ \ \alpha\geq 1\bigr\}.$$