Subparhelia (sub-sundogs) are the reflected version of parhelia (sundogs) as seen from the air. In other words, they are the sundogs on the sides of the subsun instead of the real sun. Because ice crystals in clouds are often not perfectly horizontal, subparhelia may look 'taller' than normal sundogs. Note the occurance of subparhelia does not depend on parhelia: the former can appear without the latter.

Subparhelion. 2003/2/13.

2003/2/13 17:52 EST. Close up of the subparhelion. It was particularly bright at that time.