A novel maize variety designated PHEGW and seed, plants and plant parts thereof. Methods for producing a maize plant that comprise crossing maize variety PHEGW with another maize plant. Methods for producing a maize plant containing in its genetic material one or more traits introgressed into PHEGW through backcross conversion and/or transformation, and to the maize seed, plant and plant part produced thereby. Hybrid maize seed, plant or plant part produced by crossing the variety PHEGW or a trait conversion of PHEGW with another maize variety. Inbred maize varieties derived from maize variety PHEGW, methods for producing other inbred maize varieties derived from maize variety PHEGW and the inbred maize varieties and their parts derived by the use of those methods.