no, to be a normal subgroup the right and left cosets have to be equal. obviously subgroups that lie in the center of D4xZ2 are normal, but there may be others.
some things that may help you:
any subgroup of order 8 will be normal.
any subgroup that is in the center will be normal.
the real trouble is going to be finding the subgroups of order 4 and 2. determining if a subgroup of order 2 is normal will be easy: <a> where a is an element of order 2 is normal if and only if <a> is in the center.