  Kirillov's orbit theory provides a powerful tool for the investigation of
irreducible unitary representations of many classes of Lie groups. In a
previous paper we used a modification hereof, called monomial linearisation, to
construct a monomial basis of the regular representation of $p$-Sylow subgroups
$U$ of the finite classical groups of untwisted type. In this sequel to this
article we determine the stabilizers of special orbit generators and show, that
for the groups of Lie type ${\mathfrak{B}}_n$ and ${\mathfrak{D}}_n$ a subclass
of the orbit modules decompose the $U$-modules affording the Andr\'{e}-Neto
supercharacters into a direct sum of submodules. Moreover these special orbit
modules are either isomorphic or have no irreducible constituent in common, and
each irreducible $U$ module is up to isomorphism constituent of precisely one
of these.
