In this article we study several classes of ‘small’
2
2
-groups: we complete the classification, started by Stancu, of all saturated fusion systems on metacyclic
p
p
-groups for all primes
p
p
. We consider Suzuki
2
2
-groups, and classify all center-free saturated fusion systems on
2
2
-groups of
2
2
-rank
2
2
. We end by classifying all possible
F
\mathcal {F}
-centric,
F
\mathcal {F}
-radical subgroups in saturated fusion systems on
2
2
-groups of
2
2
-rank
2
2
.