I served in the 1st Logistical Command between 1968 and 1969. 1st Log was not a Division, Regiment, or Corps. It was a Command, established directly under the Department of the Army.
In Vietnam, it reported directly to USARV, the overall command for all forces in Vietnam. It was larger than a Division. There were several sub area commands under 1st Log. There were more support troops in Vietnam than there were combat troops.
Logistics services were not organized like combat units. Subsidiary organizations were called 'Sub Area Commands,' and operated within a geographic area. For example, my unit was included within the Cam Ranh Bay Sub Area Command. This sub command oversaw the operation of maintenance brigades, field hospitals, ammunition facilities, transportation units, and quartermaster supply organizations that operated within the II Corps Tactical Zone.