On finite solvable groups with bicyclic cofactors of primary subgroups

Finite soluble groups with bicyclic cofactors of primary subgroups are investigated. It is proved that the derived length of $G/\Phi(G)$ is at most $6,$ the nilpotent length of $G$ is at most $4,$ $\{2,3\}'$-Hall subgroup of $G$ possesses an ordered Sylow tower of supersolvable type and normal in $G$.