On a holonomy flag of non-holonomic distributions

We give definition of a holonomy flag in subRiemannian geometry — a generalization of a Riemannian holonomy algebra — and calculate it for the 3D subRiemannian Lie groups. We rewrite and give new interpretation for the Codazzi equations for the $(2,3)$-distributions on the $SU(2)$ and the Heisenberg group.