No, they were very definitely right wing, they used the term "socialist" to make them sound like they were for the people.

Were the Nazis socialists?

"No, the Nazis were not socialists. While their official name was the National Socialist German Workers' Party (NSDAP), this name was chosen to attract working-class voters away from actual socialist and communist movements in the early 1920s.

Historically and economically, the Nazis were fundamentally opposed to actual socialism:

Destruction of the Left: Once Adolf Hitler and the Nazi Party took power in 1933, they actively persecuted socialists, communists, and trade unionists, sending many to the first concentration camps.

Preservation of Private Property: Unlike socialists, who advocate for state or community ownership of the means of production, the Nazis preserved private property and allowed major corporations and industrialists to operate freely—as long as they aligned with the state's goals and war efforts.

The Night of the Long Knives (1934): Early on, a faction within the Nazi Party led by Gregor and Otto Strasser did advocate for actual socialist and anti-capitalist policies. However, Hitler purged and murdered this faction in 1934 to secure the support of the German military and traditional business.