Communism and capitalism are different in their ideologies. They never go together especially in terms of political and economic ideologies. Capitalism is a system of government that is democratic meanwhile communism is a system of government that is totalitarian which means a political system in which the government has total control over the public and private lives and actions of that state's citizens.
Based on capitalism ideology, people need freedom and they believe when people complete against one another, they achieve greater things. In contrary, communism believe that people need one another so when people work together as equals, they achieve greater things.
In terms of government control and economy based on capitalism ideology, government should not interfere with the rights of individuals to make their own living. They practice free enterprise meaning the freedom for private business to operate for a profit without interference from the government. When doing businesses, the resources or the means of production lies with a private owner, they self-regulated economic system. On the other hand, based on the communism, the community or society solely owns the resources and government should make sure that everyone's needs are being meet. The profit of any enterprise is equally shared by all the people in communism.
There is extension of both of the ideologies which is liberalism. Liberalism is an ideology that believes in individual freedom. It is a political ideology that thinks that an individual is free from all interferences and restrictions. However, liberalism is divided into classical and modern liberalism. Classical liberalism states that the government should take control of an institution in order to ensure that it continues to be of service to the people, free of charge. Classical liberalism does not see any need for the government to enforce law and order. On the other hand, modern liberalism asserts that it is also government's job to interfere with people's day-to-day affairs in order to maintain social security. Many modern politicians have been supporting modern liberalism because they believe that the government can solve all problems once it is granted total power.
Based on capitalism perspective on modern liberalism, it did not support the power that given to government because when government control the prices of goods and workers, privately-owned companies and institutions cannot flourish. It is because they believe that such ideologies limit a citizen's right to choose which products to buy, what jobs to take, what religious to belief and so on.
However in this era, most of countries in the world practice liberalism. It includes a belief in government as an institution whose primary functions is to define and enforce the laws. A Constitution must be developed as a rule and guidance to be followed. The practice of liberalism nowadays however did not clearly solely the capitalist and society.