Should a dishwasher be on a GFCI outlet?
Likewise, is a GFCI required for a dishwasher?
The dishwasher GFCI protection was adopted in the 2014 NEC. Also GFCI outlets are required to be readily accessible so they no longer can be located under the sink. The dishwasher also has to be AFCI protected so most are installing "dual purpose" AFCI/GFCI circuit breakers.
Besides, can a dishwasher be plugged into a normal outlet?
Dishwashers can be either hardwired, or cord-and-plug connected. Because of this, a receptacle installed in a location that requires the removal of the dishwasher is not code compliant. i.e. If you can't find where the dishwasher is plugged in, it's likely hardwired.
A GFCI is not required but the fact it trips a GFCI indicates there may be a fault in the dishwasher. If left un-repaired there may be an increasing danger to persons using it. It should be checked by an appliance repair person.