The old pawnbroker is an evil person who is actually harming the poor people who come to her for pawning. According to Hegel, any harmful segment of society should be removed. Therefore, Raskolnikov reasons that by murdering the old pawnbroker, he will be removing a harmful "louse" from society.
If the ends are noble, the means can be justified. The old pawnbroker has a lot of money that will be "wasted" upon useless requiem services for her soul after her death. With that money, Raskolnikov will be able to complete his education and devote himself to the service of humanity, or he could distribute the money among needy and starving families, thus saving hundreds of people from ruin and destitution.
Dostoevsky had also apparently encountered other views of the Superman or Ubermensch — views that were not yet formulated in any coherent whole but were heard wherever intellectuals gathered. Svidrigailov was born from these ideas of self-gratification. Svidrigailov would reason: Since there is no will (or power) beyond that of my own, I must completely assert my own will until it is totally free of all restraint against it. Since there is no power beyond me that functions to punish, I am free to assert completely my own will.
Therefore, the Svidrigailov type of Ubermensch is one who possesses the strongest will and is able to make his desires and his power dominant over others. Svidrigailov can rape a 15-year-old girl and cause the death of a servant without any fear of punishment. He asserts his own will in order to gratify his own desires.
The test of this type of Ubermensch is that he must stand completely alone and must not allow his will to be influenced by the wishes of others. Thus, this assertion of the will isolates man from society. When Raskolnikov attempts to assert his will, he finds himself cut off from the rest of humanity. It is this dreadful solitude that Raskolnikov cannot stand and that makes him confess to become part of humanity again.
