I would refine it a bit. Capitalism is the theory that humanity is best served by private ownership of the means of production and distribution. This of course leads to monopolies and market rigging, so some amount of regulation is required, although (as is being seen with Google, Amazon, et al.) the market eventually has enough and will find ways to circumvent the monompoly.

Socialism states that the State should own the means of production and distribution, and must regulate everything down to the last iota. This naturally leads to widespread systemic corruption - as seen in the US and USSR - with collapse as the result.

Fascism says that corporations are the ultimate power and should own both production and the powers of the State. This is where diversity comes into the equation, as corporations are artificial persons (single entity) created out of many parts. This concept was created by the Roman Catholic Church in the Middle Ages as a concept for the Body of the Church - a prime reason the Church supported the Nazis and Ustase.

The racial purity aspect of Nazism grew out of both the occult elements of the Party, as well as the need to justify ridding the nation of Jews and other immigrants. Some 'entity' is attempting to resurrect these forces now in the EU and US with uncontrolled immigration. It is not a fundamental aspect of Fascism, but was over-laid on it due to socio-economic conditions of the time.

Marxism and Communism has never been tried on a mass scale, but would likely fail miserably, as they require small, tight-knit communities bound by a single focus, such as religion or other ideal. This could never exist in groups larger than a few hundred to a thousand. Marxism was an attempt to create an economic system based on Communism using classism and economic goals as the cohesive element.