The effects of non-conservative forces and nonholonomic constraints on Lie symmetries and conserved quantities of a Hamiltonian system are studied. When non-conservative forces or nonholonomic constraints are inserted in the Hamiltonian system, we obtain the conditions under which Lie symmetries, structure equation and conserved quantities of the system will remain present. The famous Emden equation and Appell-Hamel model are taken as examples to illustrate the application of the results.