According to Socialists, what parts of the economy should the government control?

Most of it.

Explanation:

A socialist economy is a system of production where goods and services are produced directly for use, in contrast to a capitalist economic system, where goods and services are produced to generate profit (and therefore indirectly for use). "Production under socialism would be directly and solely for use.

In a capitalist economy, the government acts as a regulatory and complementary body. On the other hand, in a socialist economy, the government plays a comprehensive role in almost all economic activities, such as production, distribution, and consumption, of a nation.