On finite groups with some primary subgroups satisfying partial $S$-$\Pi$-property

A $p$-subgroup $H$ of a finite group $G$ is said to satisfy partial $S$-$\Pi$-property in $G$ if $G$ has a chief series $\Gamma_{G}: 1=G_{0}finite groups with some primary subgroups satisfying partial $S$-$\Pi$-property.