A holomorphic foliation $\mathcal {F}$ on a compact complex manifold $M$ is said to be an $\mathcal {L}$-foliation if there exists an action of a complex Lie group $G$ such that the generic leaf of $\mathcal {F}$ coincides with the generic orbit of $G$. We study $\mathcal {L}$-foliations of codimension one, in particular in projective space, in the spirit of ical invariant theory, but here the invariants are sometimes transcendental ones. We give a list of examples and general properties. Some classification results are obtained in low dimensions.