We extend the Tanaka theory to the context of supergeometry and obtain an upper bound on the supersymmetry dimension of geometric structures related to strongly regular bracket-generating distributions on supermanifolds and their structure related to strongly regular bracket-generating distributions on supermanifolds and their structure reductions. Several examples will be demonstrated, including distributions with at most simple Lie superalgerbas as maximum symmetry. The talk is based on joint works with Andrea Santi, Dennis The and Andreu Llabres.