Hugh has been with Willie since the early days, and is the Attorney General in his administration. Miller resigns when Willie fails to fire the corrupt State Auditor, Byram White. In the final pages of the novel we learn that Hugh and Jack become good friends (presumably after the novel ends). Whenever Hugh is mentioned in the novel, this description of him is never far away: "Harvard Law School, Lafayette Escadrille, Croix de Guerre, clean hands, pure heart" (3.241).
We all know what Harvard Law School is. Lafayette Escadrille is the team of American Volunteer Fighter Pilots in World War I. Croix de Guerre is a war medal. Hugh, Willie, and the Judge all served in World War I, though Jack did not, due to his "bad feet."