What Linux kernel modules are required for docker.io 1.10 to work?

Question

Docker

docker.io installs without problems when the 4.4.0-22-generic kernel is loaded, but gives errors when the rebuilt 4.5.5 kernel is loaded.
docker.io explicitly throws an error about the aufs module not found, but after installing this module, docker.io still throws errors.
Apparently there are not enough modules in the kernel.
Q: What Linux kernel modules are required for docker.io 1.10 to work?