  We describe several exotic fusion systems related to the Sporadic simple
groups at odd primes. More generally, we classify saturated fusion systems
supported on Sylow $3$-subgroups of the Conway group $\mathrm{Co}_1$ and the
Thompson group $\mathrm{F}_3$, and a Sylow $5$-subgroup of the Monster
$\mathrm{M}$, as well as a particular maximal subgroup of the latter two
$p$-groups. This work is supported by computations in MAGMA.
