Government sues BP?

Among other companies, BP was sued by the Justice Department in an effort to recover losses and hold them fully liable for the spill. Since when can the government sue a private business? I'm pretty sure that's not in the Constitution. If someone's livelihood was ruined or they got hurt, then they have the right to sue the company responsible. HOWEVER, the government does not also maintain that right. This is between those companies (BP, et. al.) and those individuals they harmed.