gr.group theory - Highly transitive groups (without assuming the classification of finite simple groups)

Well, the theorem that $M_{11}$ and $M_{12}$ are the only sharply $k$-transitive groups for $k> 3$ is about 100 years older than the classification theorem...

Also, if $k>3$ (without the sharply hypothesis), $G$ must be simple, unless it is in $S_4$. Of course, that's why the classification is useful.