On finite $\pi$-soluble groups with no wide subgroups

A subgroup $H$ of a finite group $G$ is said to be wide if each prime divisor of the order $G$ divides the order $H$. We obtain the description of finite $\pi$-soluble groups with no wide maximal subgroups with $\pi$-number indices. We also investigate groups with $\pi$-special subgroups.