Regular orbits of finite primitive solvable groups, III

Suppose that a finite solvable group $G$ acts faithfully, irreducibly and quasi-primitively on a finite vector space $V$. Then $G$ has a uniquely determined normal subgroup $E$ which is a direct product of extraspecial $p$-groups for various $p$ and we denote $e=\sqrt{\mathrm{\mid }E\mathrm{/}\text{bZ}(E)\mathrm{\mid }}$. We prove that when $e=2,3,4,8,9,16$, $G$ will have regular orbits on $V$ when the corresponding vector space is not too small.