  The submodule structure of general Specht modules in prime characteristic is
a difficult open problem. Kleshchev and Sheth [Journal of Algebra, 221(2),
pp.705-722] gave a combinatorial description of the submodule structure of
Specht modules labelled by $2$-part partitions in prime characteristic. Using
this result, as well as filtrations of Specht modules labelled by hook
partitions via $2$-part Specht modules in characteristic $2$, one can study the
submodule structure of hook Specht modules. In particular, we classify which of
these are uniserial.
