The director of rehabilitation and correction is the executive head of the department of rehabilitation and correction. All duties conferred on the various divisions and institutions of the department by law or by order of the director shall be performed under the rules and regulations that the director prescribes and shall be under the director’s control. Inmates committed to the department of rehabilitation and correction shall be under the legal custody of the director or the director’s designee, and the director or the director’s designee shall have power to control transfers of inmates between the several state institutions included under section 5120.05 of the Revised Code.