Gopchik is a bit like Shukhov's mini-me. The youngest member of Gang 104, only sixteen, he's is clever and crafty, much like Shukhov himself. We don't see Gopchik that often, but when we do he's usually up to something sneaky:
Sure enough, Gopchik, the little scamp, was lugging another [tray] over.
"They took their eyes off it, so I nicked it," he said with a laugh.
Gopchik has the makings of a really good camp dweller. Give him another three years [...] and fate had something good in store for him - a bread cutter's job at least. (998-1000)
Shukhov clearly approves of Gopchik and his cleverness. Gopchik definitely has it in him to be a survivor, much like Shukhov himself. In fact, Shukhov even references Gopchik as a son at one point, which ties into the theme of the gang functioning as a family.
Ivan Denisovich was fond of Gopchik, the rascal (his own son had died when he was little [...]). (330)
But even as Shukhov approves of Gopchik and his intelligence, he raises a rather disturbing point. He notes that Gopchik has it in him to rise through the ranks in the camp and to maybe become something privileged, like a "bread cutter." Camp standards are really pathetic. The problem with this is that most of the people we see in positions of some sort of power, like the cooks or the orderlies, are total jerks. Granted, a bread cutter job isn't as high ranking, and therefore not as corrupt.
But it does raise an interesting question: in order to really survive and succeed in the camps, is it necessary to be at least a little corrupt? It really throws some doubt on Gopchik's future and whether or not he'll be able to remain a decent person for long if he wants to survive, and especially if he really wants to get ahead in the camps.