Those two players, along with senior linebacker Brandin Hawthorne, will not travel to Tampa, Fla. for the New Year's Day game against the Gamecocks (No. 10 BCS, No. 11 AP) because of the suspension.
"It is an honor to play football for the University of Michigan and we have high standards and expectations for everyone that represents our program," Michigan coach Brady Hoke said in a statement. "These young men used poor judgment in each circumstance, and these suspensions are teaching moments for our team."
For Floyd and Hawthorne, it also means the end of their Michigan careers. Floyd was a two-year starter at cornerback for Michigan (No. 18 BCS, No. 19 AP), making 179 tackles, 18 pass breakups and three interceptions.
Floyd apologized Monday in a lengthy statement.
"I have given my heart and soul to this program, and it truly disappointments me that I will not be with my teammates in Florida," Floyd said. "This is a deep pain that I am dealing with to the best of my ability."
Hawthorne played mostly on special teams, although he saw some time as a linebacker last season. In his career, he made 63 tackles and had one interception.
Hagerup, a junior who was named the Big Ten's punter of the year this season, averaged 45 yards a punt this year with a long of 62 yards. This is the third time in his career Hagerup has been suspended. He was suspended for the 2010 Ohio State game and the first four games of the 2011 season.