  We study irreducible restrictions from modules over symmetric groups to
subgroups. We get reduction results which substantially restrict the classes of
subgroups and modules for which this is possible. Such results are known when
the characteristic of the ground field is greater than $3$, but the small
characteristics cases require a substantially more delicate analysis and new
ideas. This work fits into the Aschbacher-Scott program on maximal subgroups of
finite classical groups.
