Let
E
E
be an extraspecial-type group and
V
V
a faithful, absolutely irreducible
k
[
E
]
k[E]
-module, where
k
k
is a finite field. Let
G
G
be the normalizer in
G
L
(
V
)
GL(V)
of
E
E
. We show that, with few exceptions, there exists a
v
∈
V
v\in V
such that the restriction of
V
V
to
C
H
(
v
)
C_H(v)
is self-dual whenever
H
≤
G
H\le G
and
(
|
H
|
,
|
V
|
)
=
1
(\vert H\vert , \vert V\vert )=1
.