A historc reference to the righ&left topic:
The left in the weimarer republik were the communists (Kommunistische Partei Deutschlands (KPD)) and to a lesser degree the social democrats (Sozialdemokratische Partei Deutschlands (SPD) and Unabhängige Sozialdemokratische Partei Deutschlands (USPD)). They were mainly representing the international working class and soldiers.
The parties on the right were the Deutsch-Nationale Volkspartei (DNVP), Deutsche Demokratische Partei (DDP) or the Deutsche Volkspartei (DVP). They were mainly representing nationalists, monarchists, industrialists and other conservative groups.
There also were center-parties like "Die Zentrumspartei".
While (in the early 30s) the NSDAP and the KPD were both trying to prevent a stable w.-republic to push their agenda, but they never worked together!
The NSDAP did see itself as a omni-topic-party superior to any other group, but used the support of other right parties (e.g. the DNVP forming the „Harzburger Front“) and especially the conservative, monarchist, industrial circles who feared the leftist revolutionarys and believed they could use the Nazi movement for their goals. That's why Hindenburg made Hitler the Reichskanzler... him and the rest of the conservatives were wrong when they thaught they could contain and steer him.
When in power ("Ermächtigungsgesetz", 1933) Hitler first took all opposition powers from the other parties in the Reichstag, terrorised their members and then removed ALL other political parties (later also all kinds of clubs, unions, societys = "Gleichschaltung") starting from the opposing left.
Based on that history, the Nazis were for sure a right wing party - supported by and speaking for - the conservative circles of that time. They very much prefered a strong leader to revolutionary communists! Hitler never tried to change the economy into something socialist - he generally abused all assets of the country for his goals.
So it's also not very surprising where former nazis did resurface in the Bundesrepublik Deutschland past 1945... within the ranks of the - right of the center - conservative parties cdu/csu (e.g. Otto Graf Lambsdorff, Josef Ertel, KG Kiesinger, Carl Carstens, HM Schleyer, Martin Heidegger, Gottfried Benn)!