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Extensions 1→N→G→Q→1 with N=C4 and Q=C42⋊2C2

Direct product G=N×Q with N=C4 and Q=C42⋊2C2
dρLabelID
C4×C42⋊2C264C4xC4^2:2C2128,1036

Semidirect products G=N:Q with N=C4 and Q=C42⋊2C2
extensionφ:Q→Aut NdρLabelID
C4⋊1(C42⋊2C2) = C43⋊13C2φ: C42⋊2C2/C42 → C2 ⊆ Aut C464C4:1(C4^2:2C2)128,1592
C4⋊2(C42⋊2C2) = C23.396C24φ: C42⋊2C2/C22⋊C4 → C2 ⊆ Aut C464C4:2(C4^2:2C2)128,1228
C4⋊3(C42⋊2C2) = C23.412C24φ: C42⋊2C2/C4⋊C4 → C2 ⊆ Aut C464C4:3(C4^2:2C2)128,1244

Non-split extensions G=N.Q with N=C4 and Q=C42⋊2C2
extensionφ:Q→Aut NdρLabelID
C4.1(C42⋊2C2) = C2.(C8⋊8D4)φ: C42⋊2C2/C42 → C2 ⊆ Aut C4128C4.1(C4^2:2C2)128,665
C4.2(C42⋊2C2) = C2.(C8⋊7D4)φ: C42⋊2C2/C42 → C2 ⊆ Aut C464C4.2(C4^2:2C2)128,666
C4.3(C42⋊2C2) = C2.(C8⋊D4)φ: C42⋊2C2/C42 → C2 ⊆ Aut C4128C4.3(C4^2:2C2)128,667
C4.4(C42⋊2C2) = C2.(C8⋊2D4)φ: C42⋊2C2/C42 → C2 ⊆ Aut C464C4.4(C4^2:2C2)128,668
C4.5(C42⋊2C2) = C24.Q8φ: C42⋊2C2/C42 → C2 ⊆ Aut C4168+C4.5(C4^2:2C2)128,801
C4.6(C42⋊2C2) = M4(2).15D4φ: C42⋊2C2/C42 → C2 ⊆ Aut C4328-C4.6(C4^2:2C2)128,802
C4.7(C42⋊2C2) = (C2×C8).D4φ: C42⋊2C2/C42 → C2 ⊆ Aut C4168+C4.7(C4^2:2C2)128,813
C4.8(C42⋊2C2) = (C2×C8).6D4φ: C42⋊2C2/C42 → C2 ⊆ Aut C4328-C4.8(C4^2:2C2)128,814
C4.9(C42⋊2C2) = C23.544C24φ: C42⋊2C2/C42 → C2 ⊆ Aut C464C4.9(C4^2:2C2)128,1376
C4.10(C42⋊2C2) = C23.545C24φ: C42⋊2C2/C42 → C2 ⊆ Aut C4128C4.10(C4^2:2C2)128,1377
C4.11(C42⋊2C2) = C42⋊15Q8φ: C42⋊2C2/C42 → C2 ⊆ Aut C4128C4.11(C4^2:2C2)128,1595
C4.12(C42⋊2C2) = C8⋊C4⋊17C4φ: C42⋊2C2/C22⋊C4 → C2 ⊆ Aut C4164C4.12(C4^2:2C2)128,573
C4.13(C42⋊2C2) = C2.D8⋊4C4φ: C42⋊2C2/C22⋊C4 → C2 ⊆ Aut C4128C4.13(C4^2:2C2)128,650
C4.14(C42⋊2C2) = C4.Q8⋊9C4φ: C42⋊2C2/C22⋊C4 → C2 ⊆ Aut C4128C4.14(C4^2:2C2)128,651
C4.15(C42⋊2C2) = C4.Q8⋊10C4φ: C42⋊2C2/C22⋊C4 → C2 ⊆ Aut C4128C4.15(C4^2:2C2)128,652
C4.16(C42⋊2C2) = C2.D8⋊5C4φ: C42⋊2C2/C22⋊C4 → C2 ⊆ Aut C4128C4.16(C4^2:2C2)128,653
C4.17(C42⋊2C2) = C42.427D4φ: C42⋊2C2/C22⋊C4 → C2 ⊆ Aut C4164C4.17(C4^2:2C2)128,664
C4.18(C42⋊2C2) = C23.12D8φ: C42⋊2C2/C22⋊C4 → C2 ⊆ Aut C464C4.18(C4^2:2C2)128,807
C4.19(C42⋊2C2) = C24.88D4φ: C42⋊2C2/C22⋊C4 → C2 ⊆ Aut C464C4.19(C4^2:2C2)128,808
C4.20(C42⋊2C2) = C24.89D4φ: C42⋊2C2/C22⋊C4 → C2 ⊆ Aut C464C4.20(C4^2:2C2)128,809
C4.21(C42⋊2C2) = C42.9D4φ: C42⋊2C2/C22⋊C4 → C2 ⊆ Aut C4324C4.21(C4^2:2C2)128,812
C4.22(C42⋊2C2) = (C2×C4).28D8φ: C42⋊2C2/C22⋊C4 → C2 ⊆ Aut C4128C4.22(C4^2:2C2)128,831
C4.23(C42⋊2C2) = (C2×C4).23Q16φ: C42⋊2C2/C22⋊C4 → C2 ⊆ Aut C4128C4.23(C4^2:2C2)128,832
C4.24(C42⋊2C2) = C4⋊C4.Q8φ: C42⋊2C2/C22⋊C4 → C2 ⊆ Aut C4128C4.24(C4^2:2C2)128,833
C4.25(C42⋊2C2) = C22⋊C4.Q8φ: C42⋊2C2/C22⋊C4 → C2 ⊆ Aut C4324C4.25(C4^2:2C2)128,835
C4.26(C42⋊2C2) = C24.304C23φ: C42⋊2C2/C22⋊C4 → C2 ⊆ Aut C464C4.26(C4^2:2C2)128,1226
C4.27(C42⋊2C2) = C23.395C24φ: C42⋊2C2/C22⋊C4 → C2 ⊆ Aut C464C4.27(C4^2:2C2)128,1227
C4.28(C42⋊2C2) = C23.397C24φ: C42⋊2C2/C22⋊C4 → C2 ⊆ Aut C464C4.28(C4^2:2C2)128,1229
C4.29(C42⋊2C2) = D4⋊C4⋊C4φ: C42⋊2C2/C4⋊C4 → C2 ⊆ Aut C464C4.29(C4^2:2C2)128,657
C4.30(C42⋊2C2) = C4.67(C4×D4)φ: C42⋊2C2/C4⋊C4 → C2 ⊆ Aut C464C4.30(C4^2:2C2)128,658
C4.31(C42⋊2C2) = C4.68(C4×D4)φ: C42⋊2C2/C4⋊C4 → C2 ⊆ Aut C4128C4.31(C4^2:2C2)128,659
C4.32(C42⋊2C2) = C2.(C4×Q16)φ: C42⋊2C2/C4⋊C4 → C2 ⊆ Aut C4128C4.32(C4^2:2C2)128,660
C4.33(C42⋊2C2) = C4⋊C4.106D4φ: C42⋊2C2/C4⋊C4 → C2 ⊆ Aut C464C4.33(C4^2:2C2)128,797
C4.34(C42⋊2C2) = (C2×Q8).8Q8φ: C42⋊2C2/C4⋊C4 → C2 ⊆ Aut C4128C4.34(C4^2:2C2)128,798
C4.35(C42⋊2C2) = (C2×C4).23D8φ: C42⋊2C2/C4⋊C4 → C2 ⊆ Aut C464C4.35(C4^2:2C2)128,799
C4.36(C42⋊2C2) = (C2×C8).52D4φ: C42⋊2C2/C4⋊C4 → C2 ⊆ Aut C4128C4.36(C4^2:2C2)128,800
C4.37(C42⋊2C2) = (C2×C4).24D8φ: C42⋊2C2/C4⋊C4 → C2 ⊆ Aut C464C4.37(C4^2:2C2)128,803
C4.38(C42⋊2C2) = (C2×C4).19Q16φ: C42⋊2C2/C4⋊C4 → C2 ⊆ Aut C4128C4.38(C4^2:2C2)128,804
C4.39(C42⋊2C2) = C42⋊8C4⋊C2φ: C42⋊2C2/C4⋊C4 → C2 ⊆ Aut C464C4.39(C4^2:2C2)128,805
C4.40(C42⋊2C2) = (C2×Q8).109D4φ: C42⋊2C2/C4⋊C4 → C2 ⊆ Aut C4128C4.40(C4^2:2C2)128,806
C4.41(C42⋊2C2) = C23.411C24φ: C42⋊2C2/C4⋊C4 → C2 ⊆ Aut C4128C4.41(C4^2:2C2)128,1243
C4.42(C42⋊2C2) = C23.413C24φ: C42⋊2C2/C4⋊C4 → C2 ⊆ Aut C464C4.42(C4^2:2C2)128,1245
C4.43(C42⋊2C2) = C23.414C24φ: C42⋊2C2/C4⋊C4 → C2 ⊆ Aut C4128C4.43(C4^2:2C2)128,1246
C4.44(C42⋊2C2) = C42⋊5C8central extension (φ=1)128C4.44(C4^2:2C2)128,571
C4.45(C42⋊2C2) = C42⋊4C4.C2central extension (φ=1)128C4.45(C4^2:2C2)128,572
C4.46(C42⋊2C2) = C4⋊C4⋊3C8central extension (φ=1)128C4.46(C4^2:2C2)128,648
C4.47(C42⋊2C2) = (C2×C8).Q8central extension (φ=1)128C4.47(C4^2:2C2)128,649
C4.48(C42⋊2C2) = C22⋊C4⋊4C8central extension (φ=1)64C4.48(C4^2:2C2)128,655
C4.49(C42⋊2C2) = C23.9M4(2)central extension (φ=1)64C4.49(C4^2:2C2)128,656
C4.50(C42⋊2C2) = C23.301C24central extension (φ=1)64C4.50(C4^2:2C2)128,1133

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