Of course there are the $p$-subgroups of a maximal torus, and in the case $G=PU_p$, there is an interesting non toral elementary p-subgroup considered by Vistoli in [this paper][1]. 

How many other cases are known? For example, how about $G=PU_n$ where $n$ is not a prime? 


  [1]: https://arxiv.org/abs/math/0505052