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Extensions 1→N→G→Q→1 with N=C4 and Q=C2×C22⋊C4

Direct product G=N×Q with N=C4 and Q=C2×C22⋊C4
dρLabelID
C2×C4×C22⋊C464C2xC4xC2^2:C4128,1000

Semidirect products G=N:Q with N=C4 and Q=C2×C22⋊C4
extensionφ:Q→Aut NdρLabelID
C4⋊1(C2×C22⋊C4) = D4×C22⋊C4φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C432C4:1(C2xC2^2:C4)128,1070
C4⋊2(C2×C22⋊C4) = C2×C24.3C22φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C464C4:2(C2xC2^2:C4)128,1024
C4⋊3(C2×C22⋊C4) = C2×C23.7Q8φ: C2×C22⋊C4/C24 → C2 ⊆ Aut C464C4:3(C2xC2^2:C4)128,1010

Non-split extensions G=N.Q with N=C4 and Q=C2×C22⋊C4
extensionφ:Q→Aut NdρLabelID
C4.1(C2×C22⋊C4) = C23.35D8φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C432C4.1(C2xC2^2:C4)128,518
C4.2(C2×C22⋊C4) = C24.155D4φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C464C4.2(C2xC2^2:C4)128,519
C4.3(C2×C22⋊C4) = C24.65D4φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C464C4.3(C2xC2^2:C4)128,520
C4.4(C2×C22⋊C4) = C24.66D4φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C432C4.4(C2xC2^2:C4)128,521
C4.5(C2×C22⋊C4) = 2+ 1+4⋊3C4φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C432C4.5(C2xC2^2:C4)128,524
C4.6(C2×C22⋊C4) = 2- 1+4⋊2C4φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C432C4.6(C2xC2^2:C4)128,525
C4.7(C2×C22⋊C4) = 2+ 1+4⋊4C4φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C4324C4.7(C2xC2^2:C4)128,526
C4.8(C2×C22⋊C4) = C4○D4.D4φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C4168+C4.8(C2xC2^2:C4)128,527
C4.9(C2×C22⋊C4) = (C22×Q8)⋊C4φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C4328-C4.9(C2xC2^2:C4)128,528
C4.10(C2×C22⋊C4) = M4(2).43D4φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C432C4.10(C2xC2^2:C4)128,608
C4.11(C2×C22⋊C4) = (C2×SD16)⋊14C4φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C464C4.11(C2xC2^2:C4)128,609
C4.12(C2×C22⋊C4) = (C2×C4)⋊9Q16φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C4128C4.12(C2xC2^2:C4)128,610
C4.13(C2×C22⋊C4) = (C2×C4)⋊9D8φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C464C4.13(C2xC2^2:C4)128,611
C4.14(C2×C22⋊C4) = (C2×SD16)⋊15C4φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C464C4.14(C2xC2^2:C4)128,612
C4.15(C2×C22⋊C4) = M4(2).44D4φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C4324C4.15(C2xC2^2:C4)128,613
C4.16(C2×C22⋊C4) = C8.C22⋊C4φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C432C4.16(C2xC2^2:C4)128,614
C4.17(C2×C22⋊C4) = C8⋊C22⋊C4φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C432C4.17(C2xC2^2:C4)128,615
C4.18(C2×C22⋊C4) = M4(2).46D4φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C4328-C4.18(C2xC2^2:C4)128,634
C4.19(C2×C22⋊C4) = M4(2).47D4φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C4168+C4.19(C2xC2^2:C4)128,635
C4.20(C2×C22⋊C4) = C42.5D4φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C4168+C4.20(C2xC2^2:C4)128,636
C4.21(C2×C22⋊C4) = C42.6D4φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C4328-C4.21(C2xC2^2:C4)128,637
C4.22(C2×C22⋊C4) = C42.426D4φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C4164C4.22(C2xC2^2:C4)128,638
C4.23(C2×C22⋊C4) = M4(2).48D4φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C432C4.23(C2xC2^2:C4)128,639
C4.24(C2×C22⋊C4) = M4(2).49D4φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C464C4.24(C2xC2^2:C4)128,640
C4.25(C2×C22⋊C4) = C24.549C23φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C464C4.25(C2xC2^2:C4)128,1071
C4.26(C2×C22⋊C4) = Q8×C22⋊C4φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C464C4.26(C2xC2^2:C4)128,1072
C4.27(C2×C22⋊C4) = C23.223C24φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C464C4.27(C2xC2^2:C4)128,1073
C4.28(C2×C22⋊C4) = D4○(C22⋊C8)φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C432C4.28(C2xC2^2:C4)128,1612
C4.29(C2×C22⋊C4) = C23.C24φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C4168+C4.29(C2xC2^2:C4)128,1615
C4.30(C2×C22⋊C4) = C23.4C24φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C4328-C4.30(C2xC2^2:C4)128,1616
C4.31(C2×C22⋊C4) = M4(2).24C23φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C4168+C4.31(C2xC2^2:C4)128,1620
C4.32(C2×C22⋊C4) = M4(2).25C23φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C4328-C4.32(C2xC2^2:C4)128,1621
C4.33(C2×C22⋊C4) = 2+ 1+4⋊5C4φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C432C4.33(C2xC2^2:C4)128,1629
C4.34(C2×C22⋊C4) = 2- 1+4⋊4C4φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C464C4.34(C2xC2^2:C4)128,1630
C4.35(C2×C22⋊C4) = 2- 1+4⋊5C4φ: C2×C22⋊C4/C22⋊C4 → C2 ⊆ Aut C4164C4.35(C2xC2^2:C4)128,1633
C4.36(C2×C22⋊C4) = (C2×C4)⋊9SD16φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C464C4.36(C2xC2^2:C4)128,700
C4.37(C2×C22⋊C4) = (C2×C4)⋊6Q16φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C4128C4.37(C2xC2^2:C4)128,701
C4.38(C2×C22⋊C4) = (C2×C4)⋊6D8φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C464C4.38(C2xC2^2:C4)128,702
C4.39(C2×C22⋊C4) = (C2×Q16)⋊10C4φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C4128C4.39(C2xC2^2:C4)128,703
C4.40(C2×C22⋊C4) = (C2×D8)⋊10C4φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C464C4.40(C2xC2^2:C4)128,704
C4.41(C2×C22⋊C4) = C8⋊(C22⋊C4)φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C464C4.41(C2xC2^2:C4)128,705
C4.42(C2×C22⋊C4) = C42.326D4φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C432C4.42(C2xC2^2:C4)128,706
C4.43(C2×C22⋊C4) = C42.116D4φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C432C4.43(C2xC2^2:C4)128,707
C4.44(C2×C22⋊C4) = M4(2).30D4φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C4324C4.44(C2xC2^2:C4)128,708
C4.45(C2×C22⋊C4) = M4(2).31D4φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C432C4.45(C2xC2^2:C4)128,709
C4.46(C2×C22⋊C4) = M4(2).32D4φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C432C4.46(C2xC2^2:C4)128,710
C4.47(C2×C22⋊C4) = M4(2).33D4φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C464C4.47(C2xC2^2:C4)128,711
C4.48(C2×C22⋊C4) = C2×C2.D16φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C464C4.48(C2xC2^2:C4)128,868
C4.49(C2×C22⋊C4) = C2×C2.Q32φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C4128C4.49(C2xC2^2:C4)128,869
C4.50(C2×C22⋊C4) = C23.24D8φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C464C4.50(C2xC2^2:C4)128,870
C4.51(C2×C22⋊C4) = C23.39D8φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C464C4.51(C2xC2^2:C4)128,871
C4.52(C2×C22⋊C4) = C23.40D8φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C432C4.52(C2xC2^2:C4)128,872
C4.53(C2×C22⋊C4) = C23.41D8φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C464C4.53(C2xC2^2:C4)128,873
C4.54(C2×C22⋊C4) = C2×D8.C4φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C464C4.54(C2xC2^2:C4)128,874
C4.55(C2×C22⋊C4) = C23.20SD16φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C4324C4.55(C2xC2^2:C4)128,875
C4.56(C2×C22⋊C4) = C2×D8⋊2C4φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C432C4.56(C2xC2^2:C4)128,876
C4.57(C2×C22⋊C4) = C23.13D8φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C4324C4.57(C2xC2^2:C4)128,877
C4.58(C2×C22⋊C4) = C2×M5(2)⋊C2φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C432C4.58(C2xC2^2:C4)128,878
C4.59(C2×C22⋊C4) = C2×C8.17D4φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C464C4.59(C2xC2^2:C4)128,879
C4.60(C2×C22⋊C4) = C23.21SD16φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C4324C4.60(C2xC2^2:C4)128,880
C4.61(C2×C22⋊C4) = C2×C23.67C23φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C4128C4.61(C2xC2^2:C4)128,1026
C4.62(C2×C22⋊C4) = C23.179C24φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C464C4.62(C2xC2^2:C4)128,1029
C4.63(C2×C22⋊C4) = C23.191C24φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C432C4.63(C2xC2^2:C4)128,1041
C4.64(C2×C22⋊C4) = C23.192C24φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C464C4.64(C2xC2^2:C4)128,1042
C4.65(C2×C22⋊C4) = C24.542C23φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C464C4.65(C2xC2^2:C4)128,1043
C4.66(C2×C22⋊C4) = C2×(C22×C8)⋊C2φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C464C4.66(C2xC2^2:C4)128,1610
C4.67(C2×C22⋊C4) = C24.73(C2×C4)φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C432C4.67(C2xC2^2:C4)128,1611
C4.68(C2×C22⋊C4) = C2×C23.C23φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C432C4.68(C2xC2^2:C4)128,1614
C4.69(C2×C22⋊C4) = C22×C4.D4φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C432C4.69(C2xC2^2:C4)128,1617
C4.70(C2×C22⋊C4) = C22×C4.10D4φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C464C4.70(C2xC2^2:C4)128,1618
C4.71(C2×C22⋊C4) = C22×D4⋊C4φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C464C4.71(C2xC2^2:C4)128,1622
C4.72(C2×C22⋊C4) = C22×Q8⋊C4φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C4128C4.72(C2xC2^2:C4)128,1623
C4.73(C2×C22⋊C4) = C2×C23.37D4φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C432C4.73(C2xC2^2:C4)128,1625
C4.74(C2×C22⋊C4) = C2×C23.38D4φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C464C4.74(C2xC2^2:C4)128,1626
C4.75(C2×C22⋊C4) = C24.98D4φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C432C4.75(C2xC2^2:C4)128,1628
C4.76(C2×C22⋊C4) = C22×C4≀C2φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C432C4.76(C2xC2^2:C4)128,1631
C4.77(C2×C22⋊C4) = C2×C42⋊C22φ: C2×C22⋊C4/C22×C4 → C2 ⊆ Aut C432C4.77(C2xC2^2:C4)128,1632
C4.78(C2×C22⋊C4) = C2×C4.9C42φ: C2×C22⋊C4/C24 → C2 ⊆ Aut C432C4.78(C2xC2^2:C4)128,462
C4.79(C2×C22⋊C4) = C2×C4.10C42φ: C2×C22⋊C4/C24 → C2 ⊆ Aut C432C4.79(C2xC2^2:C4)128,463
C4.80(C2×C22⋊C4) = C2×C22.4Q16φ: C2×C22⋊C4/C24 → C2 ⊆ Aut C4128C4.80(C2xC2^2:C4)128,466
C4.81(C2×C22⋊C4) = C24.132D4φ: C2×C22⋊C4/C24 → C2 ⊆ Aut C464C4.81(C2xC2^2:C4)128,467
C4.82(C2×C22⋊C4) = C24.152D4φ: C2×C22⋊C4/C24 → C2 ⊆ Aut C464C4.82(C2xC2^2:C4)128,468
C4.83(C2×C22⋊C4) = C24.7Q8φ: C2×C22⋊C4/C24 → C2 ⊆ Aut C432C4.83(C2xC2^2:C4)128,470
C4.84(C2×C22⋊C4) = C2×C22.C42φ: C2×C22⋊C4/C24 → C2 ⊆ Aut C464C4.84(C2xC2^2:C4)128,473
C4.85(C2×C22⋊C4) = C23.15C42φ: C2×C22⋊C4/C24 → C2 ⊆ Aut C432C4.85(C2xC2^2:C4)128,474
C4.86(C2×C22⋊C4) = C24.133D4φ: C2×C22⋊C4/C24 → C2 ⊆ Aut C464C4.86(C2xC2^2:C4)128,539
C4.87(C2×C22⋊C4) = C23.22D8φ: C2×C22⋊C4/C24 → C2 ⊆ Aut C464C4.87(C2xC2^2:C4)128,540
C4.88(C2×C22⋊C4) = C24.67D4φ: C2×C22⋊C4/C24 → C2 ⊆ Aut C464C4.88(C2xC2^2:C4)128,541
C4.89(C2×C22⋊C4) = C24.19Q8φ: C2×C22⋊C4/C24 → C2 ⊆ Aut C432C4.89(C2xC2^2:C4)128,542
C4.90(C2×C22⋊C4) = C24.9Q8φ: C2×C22⋊C4/C24 → C2 ⊆ Aut C432C4.90(C2xC2^2:C4)128,543
C4.91(C2×C22⋊C4) = (C2×D4).24Q8φ: C2×C22⋊C4/C24 → C2 ⊆ Aut C4324C4.91(C2xC2^2:C4)128,544
C4.92(C2×C22⋊C4) = (C2×C8).103D4φ: C2×C22⋊C4/C24 → C2 ⊆ Aut C4324C4.92(C2xC2^2:C4)128,545
C4.93(C2×C22⋊C4) = C8○D4⋊C4φ: C2×C22⋊C4/C24 → C2 ⊆ Aut C4324C4.93(C2xC2^2:C4)128,546
C4.94(C2×C22⋊C4) = C4○D4.4Q8φ: C2×C22⋊C4/C24 → C2 ⊆ Aut C464C4.94(C2xC2^2:C4)128,547
C4.95(C2×C22⋊C4) = C4○D4.5Q8φ: C2×C22⋊C4/C24 → C2 ⊆ Aut C464C4.95(C2xC2^2:C4)128,548
C4.96(C2×C22⋊C4) = C25.85C22φ: C2×C22⋊C4/C24 → C2 ⊆ Aut C432C4.96(C2xC2^2:C4)128,1012
C4.97(C2×C22⋊C4) = C2×C24.4C4φ: C2×C22⋊C4/C24 → C2 ⊆ Aut C432C4.97(C2xC2^2:C4)128,1609
C4.98(C2×C22⋊C4) = C2×C23.36D4φ: C2×C22⋊C4/C24 → C2 ⊆ Aut C464C4.98(C2xC2^2:C4)128,1627
C4.99(C2×C22⋊C4) = C2×C22.7C42central extension (φ=1)128C4.99(C2xC2^2:C4)128,459
C4.100(C2×C22⋊C4) = C23.28C42central extension (φ=1)64C4.100(C2xC2^2:C4)128,460
C4.101(C2×C22⋊C4) = C23.29C42central extension (φ=1)64C4.101(C2xC2^2:C4)128,461
C4.102(C2×C22⋊C4) = C2×C42⋊6C4central extension (φ=1)32C4.102(C2xC2^2:C4)128,464
C4.103(C2×C22⋊C4) = C24.63D4central extension (φ=1)32C4.103(C2xC2^2:C4)128,465
C4.104(C2×C22⋊C4) = C2×C4.C42central extension (φ=1)64C4.104(C2xC2^2:C4)128,469
C4.105(C2×C22⋊C4) = C2×M4(2)⋊4C4central extension (φ=1)32C4.105(C2xC2^2:C4)128,475
C4.106(C2×C22⋊C4) = C8×C22⋊C4central extension (φ=1)64C4.106(C2xC2^2:C4)128,483
C4.107(C2×C22⋊C4) = C23.36C42central extension (φ=1)64C4.107(C2xC2^2:C4)128,484
C4.108(C2×C22⋊C4) = C23.17C42central extension (φ=1)64C4.108(C2xC2^2:C4)128,485
C4.109(C2×C22⋊C4) = C23.5C42central extension (φ=1)324C4.109(C2xC2^2:C4)128,489
C4.110(C2×C22⋊C4) = Q8.C42central extension (φ=1)32C4.110(C2xC2^2:C4)128,496
C4.111(C2×C22⋊C4) = D4.3C42central extension (φ=1)32C4.111(C2xC2^2:C4)128,497
C4.112(C2×C22⋊C4) = C2×C22⋊C16central extension (φ=1)64C4.112(C2xC2^2:C4)128,843
C4.113(C2×C22⋊C4) = C24.5C8central extension (φ=1)32C4.113(C2xC2^2:C4)128,844
C4.114(C2×C22⋊C4) = (C2×D4).5C8central extension (φ=1)64C4.114(C2xC2^2:C4)128,845
C4.115(C2×C22⋊C4) = C2×C23.C8central extension (φ=1)32C4.115(C2xC2^2:C4)128,846
C4.116(C2×C22⋊C4) = M5(2).19C22central extension (φ=1)324C4.116(C2xC2^2:C4)128,847
C4.117(C2×C22⋊C4) = C2×D4.C8central extension (φ=1)64C4.117(C2xC2^2:C4)128,848
C4.118(C2×C22⋊C4) = M5(2)⋊12C22central extension (φ=1)324C4.118(C2xC2^2:C4)128,849
C4.119(C2×C22⋊C4) = C22×C22⋊C8central extension (φ=1)64C4.119(C2xC2^2:C4)128,1608
C4.120(C2×C22⋊C4) = C2×M4(2).8C22central extension (φ=1)32C4.120(C2xC2^2:C4)128,1619
C4.121(C2×C22⋊C4) = C2×C23.24D4central extension (φ=1)64C4.121(C2xC2^2:C4)128,1624

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