In this three years old thread
viewtopic.php?f=14&t=15541
I presented a series of subgroups of the 3x3x3 made up by visible pieces.

The same principle can be applied to a 4x4x4 as well.
With the edgeless 4x4x4 I lately purchased from Chino I could finish this series and want to present it here:
Here we have:
CEF - The traditional 4x4x4
CF - The edgeless 4x4x4 by Chino
EF - Faceless octahedral 4x4x4 by Andreas Nortmann
CE - The faceless 4x4x4 aka Brilicube Revenge by Chino
E - The true edges only 4x4x4 by Sanne Marx
C - The traditional 2x2x2
F - Rhombiminx invented by Laurent Blanc; this sample comes from Claus Wenicker
{} - The 1x1x1

I want to thank again all those fellow puzzles who helped me completing this series.
Enjoy