The idea that Nazism was an extreme form of "capitalism" and Hitler primarily a tool serving the interests of "big business" is a longstanding myth that even now retains a measure of popularity in some quarters. This, despite the fact that the full name of the Nazi Party was the National Socialist German Workers' Party, and that Nazi political strategy was explicitly based on combining the appeal of socialism with that of nationalism (thus the choice of name). Once in power, the Nazis even went so far as to institute a Four Year Plan for running the German economy, modeled in large part on the Soviet Union's Five Year Plans.
I find this interesting, as I have long wondered why Nazism is usually classified as 'right-wing' when in fact it appears to hold more in common with the 'left-wing' philosophies such as Communism than it does with modern right-wing thought in the untied States. However, the answer is that the United States is in fact almost unique in its political divisions. In this country, the modern political Right is in fact closer to classical liberalism - standing strongly for individual rights, equality for all, small government and less regulation. On the other hand the modern political Left stands for big government, economic control by the State, identity politics and individual freedoms subject to regulation and dispersal by the elites. Therefore the correct classification -at least for American political schools of thought - would be to classify the divide as between statists and individualists.
The modern political Right cannot be said to have any real connection to statism, although some post-war Republican Presidents have shown fondness for Big Government - notably Richard Nixon and both Bush presidents. But the main philosophy on the political Right in the United States seems to be a consistent call for smaller government, more individual freedom and less regulation. Ronald Reagan is the most consistent practitioner of these principles, but they have been among the modern conservative planks for some time.
The American Left in contrast is and has been for some time a powerful supporter of statist totalitarianism. Leftist support for Josef Stalin, Mao Tse-tung, Pol Pot, Fidel Castro, Ho Chi Minh and other totalitarian leaders who are thought to have socialist or communist policies has been a marked aspect of the Left for over a century. Remember that until that fatal day in June of 1941, the Left in the West were fervent supporters of both Hitler's Germany and Stalin's USSR, since they were allied. Therefore, i think it is a fair statement to say that the American Left - including a wide swath of the Democratic Party - is in favor of statist approaches. And Nazism is definitely a statist philosophy.
In conclusion, the labels Left and Right are not really valid in determining where Nazism lies in the political spectrum. but if one divides political philosophies into those who are in favor of State control and those that are not, it is pretty clear that National Socialism is far closer to Marxism and Communism than it is to any definition of free-markets and individual rights. At its core Nazism is a statist doctrine and as such it is far closer to the modern American Left than is the American Right.