  We study in this paper several properties concerning singularities of
foliations in $(\mathbb{C}^3,\mathbf{0})$ that are pull-back of dicritical
foliations in $(\mathbb{C}^2,\mathbf{0})$. Particularly, we will investigate
the existence of first integrals (holomorphic and meromorphic) and the
dicriticalness of such a foliation. In the study of meromorphic first integrals
we follow the same method used by R. Meziani and P. Sad in dimension two. While
the foliations we study are pull-back of foliations in
$(\mathbb{C}^2,\mathbf{0})$, the adaptations are not straightforward.
