In Germany - as well as in several other European countries - all leading political parties are in reality social democratic, even those which call themselves conservative. It has for years now been evident that e.g. Angela Merkel is no real conservative - her policies with regard to the euro, the environment, climate change and energy are basically socialist, seasoned with some fashionable "green" ingredients.
Merkel's close party and government colleague, environment minister Peter Altmaier, is another de facto socialist, disguised as a conservative.
A true conservative would e.g. never express this opinion:
"For now I cannot see that fracking is acceptable anywhere in Europe. This also applies to Germany".
(Peter Altmaier, interviewed by the Frankfurter Allgemeine Zeitung this week)
There are some real conservatives in the CDU's Bavarian sister party, the CSU, but they have mostly been relegated to second rank positions, without much influence.