no, to be a normal subgroup the right and left cosets have to be equal. obviously subgroups that lie in the center of D_{4}xZ_{2}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.