The Collaborative International Dictionary of English v.0.48:

submarine sandwich \sub`ma*rine" sand"wich\, n.
   A large sandwich on an elongated roll, usually incompletely
   cut into two halves, filed with various cold cuts, meatballs,
   lettuce, cheese, tomatoes, olives, etc., and spiced
   variously, and often having oil or other dressing applied;
   called also hoagie, hero, hero sandwich, grinder,
   sub, submarine, poor boy, and Italian sandwich. A
   single such sandwich may consitute a substantial meal. Very
   large variants are sometimes prepared for social gatherings
   and cut into pieces for individual consumption.
   [PJC]

The Collaborative International Dictionary of English v.0.48:

Sub \Sub\, n.
   1. A subordinate; a subaltern. [Colloq.]
      [1913 Webster]

   2. a shortened form of submarine, the boat.
      [PJC]

   3. a shortened form of submarine sandwich; also called
      hero, hero sandwich, and grinder.
      [PJC]

WordNet (r) 3.0 (2006):

hero sandwich
    n 1: a large sandwich made of a long crusty roll split
         lengthwise and filled with meats and cheese (and tomato and
         onion and lettuce and condiments); different names are used
         in different sections of the United States [syn: bomber,
         grinder, hero, hero sandwich, hoagie, hoagy,
         Cuban sandwich, Italian sandwich, poor boy, sub,
         submarine, submarine sandwich, torpedo, wedge,
         zep]