subgroups of Q8 by order: [1, 2, 4, 4, 4, 8]
4 linear characters verified
K of order 4 = [(-1, '1'), (-1, 'i'), (1, '1'), (1, 'i')]: contains -1: True; rank of restriction H' -> C^K = 2
K of order 4 = [(-1, '1'), (-1, 'k'), (1, '1'), (1, 'k')]: contains -1: True; rank of restriction H' -> C^K = 2
K of order 4 = [(-1, '1'), (-1, 'j'), (1, '1'), (1, 'j')]: contains -1: True; rank of restriction H' -> C^K = 2
some Hopf ideal I_K with H = H' (+) I_K exists: False
