There is CDU and CSU. Together they form the Union. CSU is only active in Bavaria, but they are even more conservative than the CDU. Both would cooperate with the far right tho so we can sink most of Germany
Bavaria voted CSU, which is Bavaria's own, even more "conservative" splinter group of the CDU that has run Bavaria as a de facto one party state for the most part of its post WW2 history. One of the reasons why the AfD doesn't score that high in Bavaria is that the domestic Bavarian parties are so far right that there is virtually no demand for a dedicated Nazi party.