invariance and conserved quantities

aaaa202

Noethers theorem relates invariance in some way to the conservation of a quantity. Some common ones are rotational invariance, translational etc.
But after solving the hydrogen atom in QM I discovered that there can be hidden conserved quantities caused by more subtle invariances (the Runge-Lenz vector).
So my question is: Are there anything that tells us maximum amount of conserved quantites for a system with a given hamiltonian?