Dragonflies, like most insects, have multifaceted compound eyes. They don't have eyelids or pupils. The part that looks like a pupil is just the way that light reflects off the eye.

http://en.wikipedia.org/wiki/File:Dragon...

A lot of pictures of dragonfly eyes appear as though they have pupils, which is a black dot at the center of the eye. Other dragonflies appear not to have pupils at all. Without thinking about this I was drawing a dragonfly and gave its eyes pupils, but now I am wondering if perhaps this is a mistake and it shouldn't have them? Here is the picture: http://th07.deviantart.net/fs71/PRE/i/2014/107/6/7/meganeurabrongniarti_by_lil_cheetah-d7eva9b.png