Not military police in the traditional use of the word the Military Police is actually the police force for the whole of the Elysian Celestial Empire. It is composed of members trained as Elysian Infantry with special training in urban warfare, backed up by forensics units and various pieces of special equipment - along with the wide spread knowledge that it is gods will to report a crime which means that Elysia has possibly the lowest crime rate amongst the three great civilizations. The jurisdiction of the Military Police includes violent crime, theft, property crime and the more 'physical side' - the other varieties of crime are normally dealt with by the Intelligence Agency. The Military Police is notoriously brutal with its criminals as a deterrent, and the prison system is a fate that most people would want to avoid - it often includes Soul Cleansing.
These units fall outside the normal heirachy and is a somewhat chaotic, although particularly effective, system.