  We prove that the target space of an extremal Fano contraction from a log
canonical pair has only log canonical singularities. We also treat some related
topics, for example, the finite generation of canonical rings for compact
K\"ahler manifolds, and so on. The main ingredient of this paper is the nefness
of the moduli parts of lc-trivial fibrations. We also give some observations on
the semi-ampleness of the moduli parts of lc-trivial fibrations. For the
reader's convenience, we discuss some examples of non-K\"ahler manifolds,
flopping contractions, and so on, in order to clarify our results.
