  A connected algebraic group Q defined over a field of characteristic zero is
quasi-reductive if there is an element of its dual of reductive type, that is
such that the quotient of its stabiliser by the centre of Q is a reductive
subgroup of GL(q), where q=Lie(Q). Due to results of M. Duflo, coadjoint
representation of a quasi-reductive Q possesses a so called maximal reductive
stabiliser and knowing this subgroup, defined up to a conjugation in Q, one can
describe all coadjoint orbits of reductive type. In this paper, we consider
quasi-reductive parabolic subalgebras of simple complex Lie algebras as well as
all seaweed subalgebras of gl(n) and describe the classes of their maximal
reductive stabilisers.
