  We study the local lifting problem of actions of semidirect products of a
cyclic $p$-group by a cyclic prime to $p$ group, where $p$ is the
characteristic of the special fibre. We give a criterion based on
Harbater-Katz-Gabber compactification of local actions, which allows us to
decide whether a local action lifts or not. In particular for the case of
dihedral group we give an example of dihedral local action that can not lift
and in this way we give a stronger obstruction than the KGB-obstruction.
