If I select a subshape and move it the rest of the group doesn't move with it. How can I make all in group move?
You can change how the grouped shape works:
Select the shape
ribbon -> Developer -> Behavior -> Group Behavior -> Select Group Only or Select Group First
...adding a comment: when a subshape is selected, it has Visions focus. That is, all activity is set to that shape. The group must be selected so that Visio knows that it (and, thus, subshapes) are the focus.