In the past decade, the public discourse on immigration in Germany has been strongly affected by right-wing populist, racist, and Islamophobic positions. This becomes evident especially in the comment sections of news websites and social media platforms, where user discussions often escalate and trigger hate comments against refugees and immigrants and also against journalists, politicians, and other groups. In view of the threatening consequences such sentiments can have for groups who are targeted by right-wing extremist violence, we take a closer look into such user discussions to gain detailed insights into the various forms of hate speech and offensive language against these groups. Using a modularized framework that goes beyond the common "hate/no-hate" dichotomy in the field, we conducted a structured text annotation of 5,031 user comments posted on German news websites and social media in March 2019. Most of the hate speech we found was directed against refugees and immigrants, while other groups were mostly exposed to various forms of offensive language. In comments containing hate speech, refugees and Muslims were frequently stereotyped as criminals, whereas extreme forms of hate speech, such as calls for violence, were rare in our data. These findings are discussed with a focus on their potential consequences for public discourse on immigration in Germany.