One of the most important social criticisms was of the separation of the classes. Dostoyevsky contended there were two classes--ordinary people and "supermen":
Ordinary people must obey the law, but "supermen" — of whom there are very few in any generation — are entitled to break existing laws and make their own laws. Raskolnikov cites the French emperor Napoleon as the epitome of the superman type. He argues that Napoleon rose to power by overstepping the laws that govern ordinary people. Napoleon made his own laws and achieved his goals by killing tens of thousands of people in wars. Because Napoleon was a genius, Raskolnikov reasons, he was not regarded as a criminal. On the contrary, he was hailed as a hero. (Enotes)
Dostoyevsky felt that those with power could make their own laws and rules; however, the ordinary people were forced to obey these laws and rules, which was unfair.
Another social criticism that some critics have brought up is Dostoyevsky's treatment of the "younger generation" in Russia. Some critics feel he was degrading the younger generation and that they were destined for failure due to "their liberal ideas and natural sciences" (Enotes).