On well $p$-embedded subgroups of finite groups

Let $G$ be a finite group, $H$ a subgroup of $G$ and $H_{s G}$ the subgroup of $H$ genarated by all those subgroups of $H$ which are $s$-permutable in $G$. Then we say that $H$ is well $p$-embedded in $G$ if $G$ has a quasinormal subgroup $T$ such that $HT=G$ and $T\cap H\leq H_{s G}$. In the present article we use the well $p$-embedded groups to obtain new characterizations for some class of finite soluble, supersoluble, metanilpotent and dispersive groups.