  Given an integer $k\ge3$ and a group $G$ of odd order, if there exists a
$2$-$(v,k,1)$-design and if $v$ is sufficiently large, then there is such a
design whose automorphism group has a subgroup isomorphic to $G$. A weaker
result is proved when $|G|$ is even and $(k,|G|)=1$.
