Reduced fusion systems over $p$-groups with abelian subgroup of index   $p$: II
  Let $p$ be an odd prime, and let $S$ be a $p$-group with a unique elementary abelian subgroup $A$ of index $p$. We classify the simple fusion systems over all such groups $S$ in which $A$ is essential. The resulting list, which depends on the classification of finite simple groups, includes a large variety of new, exotic simple fusion systems. 
David A. Craven, Bob Oliver, Jason Semeraro
math.GR