Clean File Structure - Adobe Illustrator

This is most probably a simple fix, I am hobbyist and not totally used to this stuff, but this issue is driving me mad.

When I construct my puppet in Adobe Illustrator I get lots of layers that confuses things. I have tried grouping the strokes and fills where ever possible, with limited success. When I compare my puppets to those that come with Character Animator, mine are so complicated compared to the to the simple and clean puppets provided as examples by Okay Samurai. That is what I am trying to get to. Therefore the question: How do I simplify the file structure. If you look below at my example I have four layers for the black surround of the eye pupil, this only needs to be one layer including the white centre of the pupil which is an additional four layer. If I review the puppet in Illustrator it tells me the four layers are  'grouped' but I 'ungroup it' to then 'group' the four layers I go back to where I started and Illustrator does not provide me with the option to 'group'.

Help me Obi-Wan Kenobi you my only hope. And thank you Okay Samurai for your monthly output and training videos they are really helpful even if they show up flaws in my own work like this.

https://www.youtube.com/user/okaysamurai