Assignment is submitted by a group member and it only shows as submitted for grading for that group member.

Set up an assignment with separate groups and allow for 'Students submit in groups' to be Yes.
Log in as a student and upload a document for your group.
Log in as a teacher and notice that in the assignment status column it only shows as 'submitted for grading' for the student that submitted on behalf of his group members.
Improvement would be to have the assignment show as submitted for grading for all members in that group.