Supergroups of groups of order 8

By Lagrange's theorem, any group that contains a group of order 8 must be a group of order a multiple of 8. Conversely, because Sylow subgroups exist and prime power order implies subgroups of all orders dividing the group order, any group whose order is a multiple of 8 must contain at least one subgroup of order 8.

Direct products
We list here some of the direct products of groups of order 8 with other groups:

Groups whose order has 8 as the largest prime divisor
Because Sylow subgroups exist and Sylow implies order-conjugate, any group whose order is of the form $$8m$$ with $$m$$ odd must have a unique isomorphism class of subgroup of order 8. Below is given some information about groups of such orders.