Supersolvability of a finite group with $\mu X$-supplemented subgroups

Let $G$ be a finite group, $X$ – some non-empty subset of the group $G$. The subgroup $H$ of group $G$ is identified $\mu X$-supplemented in $G$ if there exists a subgroup $B$ such that $G = HB$ and for any maximal subgroup $H_1$ of $H$ there is $x \in X$ such that $H_1 B \ne G$ and $H_1 B^x = B^x H_1$. The $p$-supersolvability of a finite group with $\mu X$-supplemented Sylow $p$-subgroup for initial importance of the number $p$ are obtained. New conditions of the supersolvability finite groups is received.