Knowledge distillation often involves how to define and transfer knowledge from teacher to student effectively. Although recent self-supervised contrastive knowledge achieves the best performance, forcing the network to learn such knowledge may damage the representation learning of the original class recognition task. We therefore adopt an alternative self-supervised augmented task to guide the network to learn the joint distribution of the original recognition task and self-supervised auxiliary task. It is demonstrated as a richer knowledge to improve the representation power without losing the normal classification capability. Moreover, it is incomplete that previous methods only transfer the probabilistic knowledge between the final layers. We propose to append several auxiliary classifiers to hierarchical intermediate feature maps to generate diverse self-supervised knowledge and perform the one-to-one transfer to teach the student network thoroughly. Our method significantly surpasses the previous SOTA SSKD with an average improvement of 2.56\% on CIFAR-100 and an improvement of 0.77\% on ImageNet across widely used network pairs. Codes are available at https://github.com/winycg/HSAKD.