  Including the generalized CP symmetry, we have performed a comprehensive scan
of leptonic mixing patterns which can be obtained from finite discrete groups
with order less than 2000. Both the semidirect approach and its variant are
considered. The lepton mixing matrices which can admit a good agreement with
experimental data can be organized into eight different categories up to
possible row and column permutations. These viable mixing patterns can be
completely obtained from the discrete flavor groups $\Delta(6n^2)$,
$D^{(1)}_{9n,3n}$, $A_5$ and $\Sigma(168)$ combined with CP symmetry. We
perform a detailed analytical and numerical analysis for each possible mixing
pattern. The resulting predictions for lepton mixing parameter, neutrinoless
double decay and flavored leptogenesis are studied.
