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Extensions 1→N→G→Q→1 with N=C4 and Q=C4.4D4

Direct product G=N×Q with N=C4 and Q=C4.4D4
dρLabelID
C4×C4.4D464C4xC4.4D4128,1035

Semidirect products G=N:Q with N=C4 and Q=C4.4D4
extensionφ:Q→Aut NdρLabelID
C4⋊1(C4.4D4) = C43⋊12C2φ: C4.4D4/C42 → C2 ⊆ Aut C464C4:1(C4.4D4)128,1590
C4⋊2(C4.4D4) = C23.391C24φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C464C4:2(C4.4D4)128,1223
C4⋊3(C4.4D4) = C42.170D4φ: C4.4D4/C2×D4 → C2 ⊆ Aut C464C4:3(C4.4D4)128,1279
C4⋊4(C4.4D4) = C42.171D4φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C464C4:4(C4.4D4)128,1280

Non-split extensions G=N.Q with N=C4 and Q=C4.4D4
extensionφ:Q→Aut NdρLabelID
C4.1(C4.4D4) = (C2×C4)⋊9SD16φ: C4.4D4/C42 → C2 ⊆ Aut C464C4.1(C4.4D4)128,700
C4.2(C4.4D4) = (C2×C4)⋊6Q16φ: C4.4D4/C42 → C2 ⊆ Aut C4128C4.2(C4.4D4)128,701
C4.3(C4.4D4) = (C2×C4)⋊6D8φ: C4.4D4/C42 → C2 ⊆ Aut C464C4.3(C4.4D4)128,702
C4.4(C4.4D4) = (C2×Q16)⋊10C4φ: C4.4D4/C42 → C2 ⊆ Aut C4128C4.4(C4.4D4)128,703
C4.5(C4.4D4) = (C2×D8)⋊10C4φ: C4.4D4/C42 → C2 ⊆ Aut C464C4.5(C4.4D4)128,704
C4.6(C4.4D4) = C8⋊(C22⋊C4)φ: C4.4D4/C42 → C2 ⊆ Aut C464C4.6(C4.4D4)128,705
C4.7(C4.4D4) = C4.4D16φ: C4.4D4/C42 → C2 ⊆ Aut C464C4.7(C4.4D4)128,972
C4.8(C4.4D4) = C4.SD32φ: C4.4D4/C42 → C2 ⊆ Aut C4128C4.8(C4.4D4)128,973
C4.9(C4.4D4) = C8.22SD16φ: C4.4D4/C42 → C2 ⊆ Aut C464C4.9(C4.4D4)128,974
C4.10(C4.4D4) = C8.12SD16φ: C4.4D4/C42 → C2 ⊆ Aut C464C4.10(C4.4D4)128,975
C4.11(C4.4D4) = C8.13SD16φ: C4.4D4/C42 → C2 ⊆ Aut C464C4.11(C4.4D4)128,976
C4.12(C4.4D4) = C8.14SD16φ: C4.4D4/C42 → C2 ⊆ Aut C4128C4.12(C4.4D4)128,977
C4.13(C4.4D4) = C42.193D4φ: C4.4D4/C42 → C2 ⊆ Aut C464C4.13(C4.4D4)128,1372
C4.14(C4.4D4) = C42.194D4φ: C4.4D4/C42 → C2 ⊆ Aut C464C4.14(C4.4D4)128,1373
C4.15(C4.4D4) = C42.195D4φ: C4.4D4/C42 → C2 ⊆ Aut C4128C4.15(C4.4D4)128,1374
C4.16(C4.4D4) = C43⋊14C2φ: C4.4D4/C42 → C2 ⊆ Aut C464C4.16(C4.4D4)128,1593
C4.17(C4.4D4) = C42⋊18Q8φ: C4.4D4/C42 → C2 ⊆ Aut C4128C4.17(C4.4D4)128,1594
C4.18(C4.4D4) = C2×C4.4D8φ: C4.4D4/C42 → C2 ⊆ Aut C464C4.18(C4.4D4)128,1860
C4.19(C4.4D4) = C2×C4.SD16φ: C4.4D4/C42 → C2 ⊆ Aut C4128C4.19(C4.4D4)128,1861
C4.20(C4.4D4) = C2×C42.78C22φ: C4.4D4/C42 → C2 ⊆ Aut C464C4.20(C4.4D4)128,1862
C4.21(C4.4D4) = C2×C42.28C22φ: C4.4D4/C42 → C2 ⊆ Aut C464C4.21(C4.4D4)128,1864
C4.22(C4.4D4) = C2×C42.29C22φ: C4.4D4/C42 → C2 ⊆ Aut C464C4.22(C4.4D4)128,1865
C4.23(C4.4D4) = C2×C42.30C22φ: C4.4D4/C42 → C2 ⊆ Aut C4128C4.23(C4.4D4)128,1866
C4.24(C4.4D4) = D4⋊C4⋊C4φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C464C4.24(C4.4D4)128,657
C4.25(C4.4D4) = C4.67(C4×D4)φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C464C4.25(C4.4D4)128,658
C4.26(C4.4D4) = C4.68(C4×D4)φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C4128C4.26(C4.4D4)128,659
C4.27(C4.4D4) = C2.(C4×Q16)φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C4128C4.27(C4.4D4)128,660
C4.28(C4.4D4) = C4.10D4⋊3C4φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C464C4.28(C4.4D4)128,662
C4.29(C4.4D4) = C4.D4⋊3C4φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C432C4.29(C4.4D4)128,663
C4.30(C4.4D4) = (C2×D4)⋊Q8φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C464C4.30(C4.4D4)128,755
C4.31(C4.4D4) = (C2×Q8)⋊Q8φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C4128C4.31(C4.4D4)128,756
C4.32(C4.4D4) = C4⋊C4.84D4φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C464C4.32(C4.4D4)128,757
C4.33(C4.4D4) = C4⋊C4.85D4φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C4128C4.33(C4.4D4)128,758
C4.34(C4.4D4) = (C2×D4)⋊2Q8φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C432C4.34(C4.4D4)128,759
C4.35(C4.4D4) = (C2×Q8)⋊2Q8φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C432C4.35(C4.4D4)128,760
C4.36(C4.4D4) = C24.83D4φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C464C4.36(C4.4D4)128,765
C4.37(C4.4D4) = C24.84D4φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C464C4.37(C4.4D4)128,766
C4.38(C4.4D4) = C24.85D4φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C464C4.38(C4.4D4)128,767
C4.39(C4.4D4) = C24.86D4φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C464C4.39(C4.4D4)128,768
C4.40(C4.4D4) = M4(2)⋊6D4φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C432C4.40(C4.4D4)128,769
C4.41(C4.4D4) = M4(2).7D4φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C432C4.41(C4.4D4)128,770
C4.42(C4.4D4) = C24.301C23φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C464C4.42(C4.4D4)128,1221
C4.43(C4.4D4) = C23.390C24φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C464C4.43(C4.4D4)128,1222
C4.44(C4.4D4) = C23.392C24φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C464C4.44(C4.4D4)128,1224
C4.45(C4.4D4) = C42.366C23φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C432C4.45(C4.4D4)128,1868
C4.46(C4.4D4) = C42.367C23φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C464C4.46(C4.4D4)128,1869
C4.47(C4.4D4) = C8.(C4⋊C4)φ: C4.4D4/C2×D4 → C2 ⊆ Aut C4324C4.47(C4.4D4)128,565
C4.48(C4.4D4) = M4(2).30D4φ: C4.4D4/C2×D4 → C2 ⊆ Aut C4324C4.48(C4.4D4)128,708
C4.49(C4.4D4) = C42.121D4φ: C4.4D4/C2×D4 → C2 ⊆ Aut C4128C4.49(C4.4D4)128,719
C4.50(C4.4D4) = C42.122D4φ: C4.4D4/C2×D4 → C2 ⊆ Aut C4128C4.50(C4.4D4)128,720
C4.51(C4.4D4) = C42.123D4φ: C4.4D4/C2×D4 → C2 ⊆ Aut C4128C4.51(C4.4D4)128,721
C4.52(C4.4D4) = M4(2)⋊8Q8φ: C4.4D4/C2×D4 → C2 ⊆ Aut C464C4.52(C4.4D4)128,729
C4.53(C4.4D4) = C42.128D4φ: C4.4D4/C2×D4 → C2 ⊆ Aut C464C4.53(C4.4D4)128,730
C4.54(C4.4D4) = C23.12D8φ: C4.4D4/C2×D4 → C2 ⊆ Aut C464C4.54(C4.4D4)128,807
C4.55(C4.4D4) = C24.88D4φ: C4.4D4/C2×D4 → C2 ⊆ Aut C464C4.55(C4.4D4)128,808
C4.56(C4.4D4) = C24.89D4φ: C4.4D4/C2×D4 → C2 ⊆ Aut C464C4.56(C4.4D4)128,809
C4.57(C4.4D4) = (C2×C8).55D4φ: C4.4D4/C2×D4 → C2 ⊆ Aut C464C4.57(C4.4D4)128,810
C4.58(C4.4D4) = (C2×C8).165D4φ: C4.4D4/C2×D4 → C2 ⊆ Aut C464C4.58(C4.4D4)128,811
C4.59(C4.4D4) = C42.172D4φ: C4.4D4/C2×D4 → C2 ⊆ Aut C464C4.59(C4.4D4)128,1294
C4.60(C4.4D4) = C42.173D4φ: C4.4D4/C2×D4 → C2 ⊆ Aut C464C4.60(C4.4D4)128,1295
C4.61(C4.4D4) = C42.243D4φ: C4.4D4/C2×D4 → C2 ⊆ Aut C464C4.61(C4.4D4)128,1873
C4.62(C4.4D4) = C42.244D4φ: C4.4D4/C2×D4 → C2 ⊆ Aut C464C4.62(C4.4D4)128,1874
C4.63(C4.4D4) = M4(2)⋊12D4φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C432C4.63(C4.4D4)128,697
C4.64(C4.4D4) = C42.114D4φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C464C4.64(C4.4D4)128,698
C4.65(C4.4D4) = C42.115D4φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C432C4.65(C4.4D4)128,699
C4.66(C4.4D4) = C42.117D4φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C4128C4.66(C4.4D4)128,713
C4.67(C4.4D4) = C42.118D4φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C464C4.67(C4.4D4)128,714
C4.68(C4.4D4) = C42.119D4φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C464C4.68(C4.4D4)128,715
C4.69(C4.4D4) = C4⋊C4.96D4φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C432C4.69(C4.4D4)128,777
C4.70(C4.4D4) = C4⋊C4.97D4φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C432C4.70(C4.4D4)128,778
C4.71(C4.4D4) = C4⋊C4.98D4φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C464C4.71(C4.4D4)128,779
C4.72(C4.4D4) = (C2×C4)⋊3D8φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C464C4.72(C4.4D4)128,786
C4.73(C4.4D4) = (C2×C4)⋊5SD16φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C464C4.73(C4.4D4)128,787
C4.74(C4.4D4) = (C2×C4)⋊3Q16φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C4128C4.74(C4.4D4)128,788
C4.75(C4.4D4) = C42.177D4φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C4128C4.75(C4.4D4)128,1300
C4.76(C4.4D4) = C42.182D4φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C464C4.76(C4.4D4)128,1324
C4.77(C4.4D4) = C42.240D4φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C432C4.77(C4.4D4)128,1870
C4.78(C4.4D4) = C42.241D4φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C464C4.78(C4.4D4)128,1871
C4.79(C4.4D4) = C42.242D4φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C432C4.79(C4.4D4)128,1872
C4.80(C4.4D4) = C42⋊8C8central extension (φ=1)128C4.80(C4.4D4)128,563
C4.81(C4.4D4) = C42.23Q8central extension (φ=1)128C4.81(C4.4D4)128,564
C4.82(C4.4D4) = C42.322D4central extension (φ=1)64C4.82(C4.4D4)128,569
C4.83(C4.4D4) = C42.104D4central extension (φ=1)64C4.83(C4.4D4)128,570
C4.84(C4.4D4) = C22⋊C4⋊4C8central extension (φ=1)64C4.84(C4.4D4)128,655
C4.85(C4.4D4) = C23.9M4(2)central extension (φ=1)64C4.85(C4.4D4)128,656
C4.86(C4.4D4) = C42.428D4central extension (φ=1)32C4.86(C4.4D4)128,669
C4.87(C4.4D4) = C42.107D4central extension (φ=1)32C4.87(C4.4D4)128,670
C4.88(C4.4D4) = C42.325D4central extension (φ=1)64C4.88(C4.4D4)128,686
C4.89(C4.4D4) = C42.109D4central extension (φ=1)64C4.89(C4.4D4)128,687
C4.90(C4.4D4) = C43⋊C2central extension (φ=1)32C4.90(C4.4D4)128,694
C4.91(C4.4D4) = C42⋊8D4central extension (φ=1)32C4.91(C4.4D4)128,695
C4.92(C4.4D4) = C42.327D4central extension (φ=1)128C4.92(C4.4D4)128,716
C4.93(C4.4D4) = C42.120D4central extension (φ=1)128C4.93(C4.4D4)128,717
C4.94(C4.4D4) = C42⋊16Q8central extension (φ=1)32C4.94(C4.4D4)128,726
C4.95(C4.4D4) = C42⋊Q8central extension (φ=1)32C4.95(C4.4D4)128,727
C4.96(C4.4D4) = C42.163D4central extension (φ=1)64C4.96(C4.4D4)128,1130
C4.97(C4.4D4) = C42.355D4central extension (φ=1)64C4.97(C4.4D4)128,1863
C4.98(C4.4D4) = C42.239D4central extension (φ=1)64C4.98(C4.4D4)128,1867
C4.99(C4.4D4) = C42.8D4central stem extension (φ=1)164C4.99(C4.4D4)128,763
C4.100(C4.4D4) = C42.131D4central stem extension (φ=1)164C4.100(C4.4D4)128,782
C4.101(C4.4D4) = C22⋊C4.7D4central stem extension (φ=1)324C4.101(C4.4D4)128,785
C4.102(C4.4D4) = C42.9D4central stem extension (φ=1)324C4.102(C4.4D4)128,812
C4.103(C4.4D4) = C42.32Q8central stem extension (φ=1)164C4.103(C4.4D4)128,834
C4.104(C4.4D4) = C22⋊C4.Q8central stem extension (φ=1)324C4.104(C4.4D4)128,835

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