The men sentenced on Monday had initially been charged with third-degree murder, but they pleaded guilty in May to reduced charges of voluntary manslaughter and hindering apprehension.

They were among 37 people, as well as the fraternity, who faced various charges. Most of the others have been sentenced, facing penalties that, the authorities said, ranged from six months to five years of probation. The fraternity was acquitted of the murder charge in November.

“Mike is my only son and only child, and the truth that he is gone can’t be erased or wiped away no matter how hard I try,” Mr. Deng’s mother, Mary Deng, said in a statement submitted to the court. “I feel like I have no big words to explain this. How can somebody treat another person’s life like this? Like it’s a joke? My husband and I spent 18 years raising Michael to be a good person, a good son. And in a single night, all those years are suddenly gone.”

Mr. Deng, an 18-year-old from Queens, collapsed while taking part in a ritual known as the “glass ceiling,” a gantlet meant to represent the plight of Asian-Americans, where pledges wore the backpack and blindfold as they were confronted by fraternity members. He was the most defiant of the pledges, riling other members by resisting and not following their orders, according to a grand jury report released in 2015. The others reacted forcefully, knocking him to the ground, and one of them ran toward him from 15 feet away with his head lowered, the report said.

The members carried him inside; Mr. Deng’s body was stiff and his breathing became labored. They changed his clothes and tried unsuccessfully to revive him. Some of them used their phones to search phrases like “concussion can’t wake up,” the report said.

One of the fraternity members later told investigators, according to the report, they had resisted calling for an ambulance because they had looked up the cost and thought it was expensive. A national fraternity official told members over the phone to hide anything bearing the fraternity’s logo, the report said. About an hour later, Mr. Deng was driven to a hospital, where doctors found that he had sustained severe head trauma and his body was badly bruised.