# Extensions 1→N→G→Q→1 with N=C4 and Q=C2×M4(2)

Direct product G=N×Q with N=C4 and Q=C2×M4(2)
dρLabelID
C2×C4×M4(2)64C2xC4xM4(2)128,1603

Semidirect products G=N:Q with N=C4 and Q=C2×M4(2)
extensionφ:Q→Aut NdρLabelID
C41(C2×M4(2)) = C2×C86D4φ: C2×M4(2)/C2×C8C2 ⊆ Aut C464C4:1(C2xM4(2))128,1660
C42(C2×M4(2)) = D4×M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C432C4:2(C2xM4(2))128,1666
C43(C2×M4(2)) = C2×C4⋊M4(2)φ: C2×M4(2)/C22×C4C2 ⊆ Aut C464C4:3(C2xM4(2))128,1635

Non-split extensions G=N.Q with N=C4 and Q=C2×M4(2)
extensionφ:Q→Aut NdρLabelID
C4.1(C2×M4(2)) = C2×D4⋊C8φ: C2×M4(2)/C2×C8C2 ⊆ Aut C464C4.1(C2xM4(2))128,206
C4.2(C2×M4(2)) = C2×Q8⋊C8φ: C2×M4(2)/C2×C8C2 ⊆ Aut C4128C4.2(C2xM4(2))128,207
C4.3(C2×M4(2)) = C42.455D4φ: C2×M4(2)/C2×C8C2 ⊆ Aut C464C4.3(C2xM4(2))128,208
C4.4(C2×M4(2)) = C42.397D4φ: C2×M4(2)/C2×C8C2 ⊆ Aut C464C4.4(C2xM4(2))128,209
C4.5(C2×M4(2)) = C42.398D4φ: C2×M4(2)/C2×C8C2 ⊆ Aut C432C4.5(C2xM4(2))128,210
C4.6(C2×M4(2)) = C42.399D4φ: C2×M4(2)/C2×C8C2 ⊆ Aut C464C4.6(C2xM4(2))128,211
C4.7(C2×M4(2)) = C86D8φ: C2×M4(2)/C2×C8C2 ⊆ Aut C464C4.7(C2xM4(2))128,321
C4.8(C2×M4(2)) = C89SD16φ: C2×M4(2)/C2×C8C2 ⊆ Aut C464C4.8(C2xM4(2))128,322
C4.9(C2×M4(2)) = C86Q16φ: C2×M4(2)/C2×C8C2 ⊆ Aut C4128C4.9(C2xM4(2))128,323
C4.10(C2×M4(2)) = C8⋊M4(2)φ: C2×M4(2)/C2×C8C2 ⊆ Aut C464C4.10(C2xM4(2))128,324
C4.11(C2×M4(2)) = C8.M4(2)φ: C2×M4(2)/C2×C8C2 ⊆ Aut C4128C4.11(C2xM4(2))128,325
C4.12(C2×M4(2)) = C83M4(2)φ: C2×M4(2)/C2×C8C2 ⊆ Aut C464C4.12(C2xM4(2))128,326
C4.13(C2×M4(2)) = C2×C84Q8φ: C2×M4(2)/C2×C8C2 ⊆ Aut C4128C4.13(C2xM4(2))128,1691
C4.14(C2×M4(2)) = C42.290C23φ: C2×M4(2)/C2×C8C2 ⊆ Aut C464C4.14(C2xM4(2))128,1697
C4.15(C2×M4(2)) = C42.693C23φ: C2×M4(2)/C2×C8C2 ⊆ Aut C432C4.15(C2xM4(2))128,1707
C4.16(C2×M4(2)) = C42.302C23φ: C2×M4(2)/C2×C8C2 ⊆ Aut C464C4.16(C2xM4(2))128,1715
C4.17(C2×M4(2)) = C42.698C23φ: C2×M4(2)/C2×C8C2 ⊆ Aut C464C4.17(C2xM4(2))128,1721
C4.18(C2×M4(2)) = D4⋊M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C432C4.18(C2xM4(2))128,218
C4.19(C2×M4(2)) = Q8⋊M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C464C4.19(C2xM4(2))128,219
C4.20(C2×M4(2)) = C42.374D4φ: C2×M4(2)/M4(2)C2 ⊆ Aut C464C4.20(C2xM4(2))128,220
C4.21(C2×M4(2)) = D44M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C464C4.21(C2xM4(2))128,221
C4.22(C2×M4(2)) = D45M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C432C4.22(C2xM4(2))128,222
C4.23(C2×M4(2)) = Q85M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C464C4.23(C2xM4(2))128,223
C4.24(C2×M4(2)) = C89D8φ: C2×M4(2)/M4(2)C2 ⊆ Aut C464C4.24(C2xM4(2))128,313
C4.25(C2×M4(2)) = C812SD16φ: C2×M4(2)/M4(2)C2 ⊆ Aut C464C4.25(C2xM4(2))128,314
C4.26(C2×M4(2)) = C815SD16φ: C2×M4(2)/M4(2)C2 ⊆ Aut C464C4.26(C2xM4(2))128,315
C4.27(C2×M4(2)) = C89Q16φ: C2×M4(2)/M4(2)C2 ⊆ Aut C4128C4.27(C2xM4(2))128,316
C4.28(C2×M4(2)) = D4.M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C464C4.28(C2xM4(2))128,317
C4.29(C2×M4(2)) = D42M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C464C4.29(C2xM4(2))128,318
C4.30(C2×M4(2)) = Q8.M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C4128C4.30(C2xM4(2))128,319
C4.31(C2×M4(2)) = Q82M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C464C4.31(C2xM4(2))128,320
C4.32(C2×M4(2)) = Q8×M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C464C4.32(C2xM4(2))128,1695
C4.33(C2×M4(2)) = D46M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C464C4.33(C2xM4(2))128,1702
C4.34(C2×M4(2)) = Q86M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C464C4.34(C2xM4(2))128,1703
C4.35(C2×M4(2)) = D47M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C432C4.35(C2xM4(2))128,1706
C4.36(C2×M4(2)) = Q8.4M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C464C4.36(C2xM4(2))128,1716
C4.37(C2×M4(2)) = D48M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C464C4.37(C2xM4(2))128,1722
C4.38(C2×M4(2)) = Q87M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C464C4.38(C2xM4(2))128,1723
C4.39(C2×M4(2)) = C2×C82C8φ: C2×M4(2)/C22×C4C2 ⊆ Aut C4128C4.39(C2xM4(2))128,294
C4.40(C2×M4(2)) = C2×C81C8φ: C2×M4(2)/C22×C4C2 ⊆ Aut C4128C4.40(C2xM4(2))128,295
C4.41(C2×M4(2)) = C42.42Q8φ: C2×M4(2)/C22×C4C2 ⊆ Aut C464C4.41(C2xM4(2))128,296
C4.42(C2×M4(2)) = M4(2)⋊1C8φ: C2×M4(2)/C22×C4C2 ⊆ Aut C464C4.42(C2xM4(2))128,297
C4.43(C2×M4(2)) = C88M4(2)φ: C2×M4(2)/C22×C4C2 ⊆ Aut C464C4.43(C2xM4(2))128,298
C4.44(C2×M4(2)) = C87M4(2)φ: C2×M4(2)/C22×C4C2 ⊆ Aut C464C4.44(C2xM4(2))128,299
C4.45(C2×M4(2)) = C42.43Q8φ: C2×M4(2)/C22×C4C2 ⊆ Aut C464C4.45(C2xM4(2))128,300
C4.46(C2×M4(2)) = C81M4(2)φ: C2×M4(2)/C22×C4C2 ⊆ Aut C464C4.46(C2xM4(2))128,301
C4.47(C2×M4(2)) = C2×C16⋊C4φ: C2×M4(2)/C22×C4C2 ⊆ Aut C432C4.47(C2xM4(2))128,841
C4.48(C2×M4(2)) = C8.23C42φ: C2×M4(2)/C22×C4C2 ⊆ Aut C4324C4.48(C2xM4(2))128,842
C4.49(C2×M4(2)) = C2×C23.C8φ: C2×M4(2)/C22×C4C2 ⊆ Aut C432C4.49(C2xM4(2))128,846
C4.50(C2×M4(2)) = M5(2).19C22φ: C2×M4(2)/C22×C4C2 ⊆ Aut C4324C4.50(C2xM4(2))128,847
C4.51(C2×M4(2)) = C8.5M4(2)φ: C2×M4(2)/C22×C4C2 ⊆ Aut C4164C4.51(C2xM4(2))128,897
C4.52(C2×M4(2)) = C8.19M4(2)φ: C2×M4(2)/C22×C4C2 ⊆ Aut C4324C4.52(C2xM4(2))128,898
C4.53(C2×M4(2)) = C2×C42.6C4φ: C2×M4(2)/C22×C4C2 ⊆ Aut C464C4.53(C2xM4(2))128,1650
C4.54(C2×M4(2)) = C42.677C23φ: C2×M4(2)/C22×C4C2 ⊆ Aut C432C4.54(C2xM4(2))128,1652
C4.55(C2×M4(2)) = C2×C8⋊C8central extension (φ=1)128C4.55(C2xM4(2))128,180
C4.56(C2×M4(2)) = C8×M4(2)central extension (φ=1)64C4.56(C2xM4(2))128,181
C4.57(C2×M4(2)) = C89M4(2)central extension (φ=1)64C4.57(C2xM4(2))128,183
C4.58(C2×M4(2)) = C23.27C42central extension (φ=1)64C4.58(C2xM4(2))128,184
C4.59(C2×M4(2)) = C8215C2central extension (φ=1)64C4.59(C2xM4(2))128,185
C4.60(C2×M4(2)) = C86M4(2)central extension (φ=1)64C4.60(C2xM4(2))128,187
C4.61(C2×M4(2)) = C2×C22⋊C16central extension (φ=1)64C4.61(C2xM4(2))128,843
C4.62(C2×M4(2)) = C24.5C8central extension (φ=1)32C4.62(C2xM4(2))128,844
C4.63(C2×M4(2)) = (C2×D4).5C8central extension (φ=1)64C4.63(C2xM4(2))128,845
C4.64(C2×M4(2)) = C2×C4⋊C16central extension (φ=1)128C4.64(C2xM4(2))128,881
C4.65(C2×M4(2)) = C4⋊M5(2)central extension (φ=1)64C4.65(C2xM4(2))128,882
C4.66(C2×M4(2)) = C4⋊C4.7C8central extension (φ=1)64C4.66(C2xM4(2))128,883
C4.67(C2×M4(2)) = C42.13C8central extension (φ=1)64C4.67(C2xM4(2))128,894
C4.68(C2×M4(2)) = C42.6C8central extension (φ=1)64C4.68(C2xM4(2))128,895
C4.69(C2×M4(2)) = C8.12M4(2)central extension (φ=1)64C4.69(C2xM4(2))128,896
C4.70(C2×M4(2)) = C2×C42.12C4central extension (φ=1)64C4.70(C2xM4(2))128,1649

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