We classify all Hopf algebras which factor through $H_8$ and $H_4$. The set of all matched pair $(H_8,H_4,\triangleright,\triangleleft)$ is explicitly described, and then the associated bicrossed products is given by generators and relations.

中文翻译：

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$H_4$和$H_8$的双杂交产物

我们通过$H_8$和$H_4$对所有Hopf代数进行分类。所有匹配对的集合 $(H_8,H_4,\triangleright,\triangleleft)$ 被明确描述，然后相关的双交叉产品由生成器和关系给出。