To get you started,
God's number is 28. Also see @Ben Whitmore website page on it.
As Ben said, there are 274337280000 total configurations (on the regular 6 colored 4x4x4). There are 10 wing edges, 10 X centers, and 4 corners in reach of <U,r>. 10!*10!*4. But there are four X center color...