Pop culture is an important aspect of communication. On social media people often post pop culture reference images that connect an event, product or other entity to a pop culture domain. Creating these images is a creative challenge that requires finding a conceptual connection between the users' topic and a pop culture domain. In cognitive theory, this task is called conceptual blending. We present a system called PopBlends that automatically suggests conceptual blends. The system explores three approaches that involve both traditional knowledge extraction methods and large language models. Our annotation study shows that all three methods provide connections with similar accuracy, but with very different characteristics. Our user study shows that people found twice as many blend suggestions as they did without the system, and with half the mental demand. We discuss the advantages of combining large language models with knowledge bases for supporting divergent and convergent thinking.