In the past decade, social media platforms have been used for information dissemination and consumption. While a major portion of the content is posted to promote citizen journalism and public awareness, some content is posted to mislead users. Among different content types such as text, images, and videos, memes (text overlaid on images) are particularly prevalent and can serve as powerful vehicles for propaganda, hate, and humor. In the current literature, there have been efforts to individually detect such content in memes. However, the study of their intersection is very limited. In this study, we explore the intersection between propaganda and hate in memes using a multi-agent LLM-based approach. We extend the propagandistic meme dataset with coarse and fine-grained hate labels. Our finding suggests that there is an association between propaganda and hate in memes. We provide detailed experimental results that can serve as a baseline for future studies. We will make the experimental resources publicly available to the community (https://github.com/firojalam/propaganda-and-hateful-memes).