  In \cite{SCH1} Schuster proved that $mod$ 2 Morava $K$-theory $K(s)^*(BG)$ is
evenly generated for all groups $G$ of order 32. There exist 51 non-isomorphic
groups of order 32. In \cite{H}, these groups are numbered by $1, \cdots ,51$.
For the groups $G_{38},\cdots, G_{41}$, that fit in the title, the explicit
ring structure is determined in \cite{BJ}. In particular, $K(s)^*(BG)$ is the
quotient of a polynomial ring in 6 variables over $K(s)^*(pt)$ by an ideal
generated by explicit polynomials. In this article we present some calculations
using the same arguments in combination with a theorem of \cite{B0} on good
groups in the sense of Hopkins-Kuhn-Ravenel. In particular, we consider the
groups $G_{36},G_{37}$, each isomorphic to a semidirect product $(C_4\times
C_2\times C_2)\rtimes C_2$, the group $G_{34}\cong (C_4\times C_4)\rtimes C_2$
and its non-split version $G_{35}$. For these groups the action of $C_2$ is
diagonal, i.e., simpler than for the groups $G_{38},\cdots, G_{41}$, however
the rings $K(s)^*(BG)$ have the same complexity.
