Because (Z/55Z)* has no subgroups of order 8. Am I wrong ?
In[89]:= FiniteGroupData[{"CyclicGroupUnits", 55}, "Subgroups"]
Out[89]= {"Trivial", {"CyclicGroup",
2}, {"AbelianGroup", {2, 2}}, {"CyclicGroup",
4}, **{"AbelianGroup", {4, 2}}**, {"CyclicGroup",
5}, {"AbelianGroup", {5, 2}}, {"AbelianGroup", {5, 2,
2}}, {"AbelianGroup", {5, 4}}, {"AbelianGroup", {5, 4, 2}}}
