The City Council shall have full power to try and determine all complaints against any member of said Department, and to remove them, or any of them summarily, or on conviction of insubordination, neglect of duty, incompetency, or violation of the rules, regulations, or ordinances governing said Department. The City Council shall also have the power, upon the recommendation of the Chief Engineer, to make such changes in the positions held by any member of the Department, either to remove him or her or place him or her in a subordinate position, as they may deem for the best interests of the Department.