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Extensions 1→N→G→Q→1 with N=C4 and Q=C22⋊Q8

Direct product G=N×Q with N=C4 and Q=C22⋊Q8
dρLabelID
C4×C22⋊Q864C4xC2^2:Q8128,1034

Semidirect products G=N:Q with N=C4 and Q=C22⋊Q8
extensionφ:Q→Aut NdρLabelID
C4⋊1(C22⋊Q8) = C24.568C23φ: C22⋊Q8/C22⋊C4 → C2 ⊆ Aut C464C4:1(C2^2:Q8)128,1172
C4⋊2(C22⋊Q8) = C23.352C24φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C464C4:2(C2^2:Q8)128,1184
C4⋊3(C22⋊Q8) = C42.167D4φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C464C4:3(C2^2:Q8)128,1274
C4⋊4(C22⋊Q8) = C42.440D4φ: C22⋊Q8/C22×C4 → C2 ⊆ Aut C464C4:4(C2^2:Q8)128,1589
C4⋊5(C22⋊Q8) = C42.166D4φ: C22⋊Q8/C2×Q8 → C2 ⊆ Aut C464C4:5(C2^2:Q8)128,1270

Non-split extensions G=N.Q with N=C4 and Q=C22⋊Q8
extensionφ:Q→Aut NdρLabelID
C4.1(C22⋊Q8) = C23.37D8φ: C22⋊Q8/C22⋊C4 → C2 ⊆ Aut C464C4.1(C2^2:Q8)128,584
C4.2(C22⋊Q8) = C24.159D4φ: C22⋊Q8/C22⋊C4 → C2 ⊆ Aut C464C4.2(C2^2:Q8)128,585
C4.3(C22⋊Q8) = C24.71D4φ: C22⋊Q8/C22⋊C4 → C2 ⊆ Aut C464C4.3(C2^2:Q8)128,586
C4.4(C22⋊Q8) = C4≀C2⋊C4φ: C22⋊Q8/C22⋊C4 → C2 ⊆ Aut C432C4.4(C2^2:Q8)128,591
C4.5(C22⋊Q8) = C42⋊9(C2×C4)φ: C22⋊Q8/C22⋊C4 → C2 ⊆ Aut C432C4.5(C2^2:Q8)128,592
C4.6(C22⋊Q8) = C4⋊C4⋊Q8φ: C22⋊Q8/C22⋊C4 → C2 ⊆ Aut C4128C4.6(C2^2:Q8)128,789
C4.7(C22⋊Q8) = (C2×C8)⋊Q8φ: C22⋊Q8/C22⋊C4 → C2 ⊆ Aut C4128C4.7(C2^2:Q8)128,790
C4.8(C22⋊Q8) = C2.(C8⋊Q8)φ: C22⋊Q8/C22⋊C4 → C2 ⊆ Aut C4128C4.8(C2^2:Q8)128,791
C4.9(C22⋊Q8) = M4(2)⋊Q8φ: C22⋊Q8/C22⋊C4 → C2 ⊆ Aut C432C4.9(C2^2:Q8)128,792
C4.10(C22⋊Q8) = C42⋊3Q8φ: C22⋊Q8/C22⋊C4 → C2 ⊆ Aut C432C4.10(C2^2:Q8)128,793
C4.11(C22⋊Q8) = (C2×C8).1Q8φ: C22⋊Q8/C22⋊C4 → C2 ⊆ Aut C4128C4.11(C2^2:Q8)128,815
C4.12(C22⋊Q8) = C2.(C8⋊3Q8)φ: C22⋊Q8/C22⋊C4 → C2 ⊆ Aut C4128C4.12(C2^2:Q8)128,816
C4.13(C22⋊Q8) = (C2×C8).24Q8φ: C22⋊Q8/C22⋊C4 → C2 ⊆ Aut C4128C4.13(C2^2:Q8)128,817
C4.14(C22⋊Q8) = M4(2).Q8φ: C22⋊Q8/C22⋊C4 → C2 ⊆ Aut C464C4.14(C2^2:Q8)128,821
C4.15(C22⋊Q8) = M4(2).2Q8φ: C22⋊Q8/C22⋊C4 → C2 ⊆ Aut C464C4.15(C2^2:Q8)128,822
C4.16(C22⋊Q8) = C24.267C23φ: C22⋊Q8/C22⋊C4 → C2 ⊆ Aut C464C4.16(C2^2:Q8)128,1171
C4.17(C22⋊Q8) = C24.268C23φ: C22⋊Q8/C22⋊C4 → C2 ⊆ Aut C464C4.17(C2^2:Q8)128,1173
C4.18(C22⋊Q8) = C24.569C23φ: C22⋊Q8/C22⋊C4 → C2 ⊆ Aut C464C4.18(C2^2:Q8)128,1174
C4.19(C22⋊Q8) = C42.22C23φ: C22⋊Q8/C22⋊C4 → C2 ⊆ Aut C464C4.19(C2^2:Q8)128,1815
C4.20(C22⋊Q8) = C42.23C23φ: C22⋊Q8/C22⋊C4 → C2 ⊆ Aut C464C4.20(C2^2:Q8)128,1816
C4.21(C22⋊Q8) = (C2×D4).24Q8φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C4324C4.21(C2^2:Q8)128,544
C4.22(C22⋊Q8) = C8○D4⋊C4φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C4324C4.22(C2^2:Q8)128,546
C4.23(C22⋊Q8) = C24.21D4φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C432C4.23(C2^2:Q8)128,588
C4.24(C22⋊Q8) = C4.10D4⋊2C4φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C432C4.24(C2^2:Q8)128,589
C4.25(C22⋊Q8) = C2.(C4×D8)φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C464C4.25(C2^2:Q8)128,594
C4.26(C22⋊Q8) = Q8⋊(C4⋊C4)φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C4128C4.26(C2^2:Q8)128,595
C4.27(C22⋊Q8) = D4⋊(C4⋊C4)φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C464C4.27(C2^2:Q8)128,596
C4.28(C22⋊Q8) = Q8⋊C4⋊C4φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C4128C4.28(C2^2:Q8)128,597
C4.29(C22⋊Q8) = (C2×D4)⋊Q8φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C464C4.29(C2^2:Q8)128,755
C4.30(C22⋊Q8) = (C2×Q8)⋊Q8φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C4128C4.30(C2^2:Q8)128,756
C4.31(C22⋊Q8) = C4⋊C4.84D4φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C464C4.31(C2^2:Q8)128,757
C4.32(C22⋊Q8) = C4⋊C4.85D4φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C4128C4.32(C2^2:Q8)128,758
C4.33(C22⋊Q8) = (C2×D4)⋊2Q8φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C432C4.33(C2^2:Q8)128,759
C4.34(C22⋊Q8) = (C2×Q8)⋊2Q8φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C432C4.34(C2^2:Q8)128,760
C4.35(C22⋊Q8) = C4⋊C4.106D4φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C464C4.35(C2^2:Q8)128,797
C4.36(C22⋊Q8) = (C2×Q8).8Q8φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C4128C4.36(C2^2:Q8)128,798
C4.37(C22⋊Q8) = (C2×C4).23D8φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C464C4.37(C2^2:Q8)128,799
C4.38(C22⋊Q8) = (C2×C8).52D4φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C4128C4.38(C2^2:Q8)128,800
C4.39(C22⋊Q8) = (C2×C8).168D4φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C464C4.39(C2^2:Q8)128,824
C4.40(C22⋊Q8) = (C2×C4).27D8φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C464C4.40(C2^2:Q8)128,825
C4.41(C22⋊Q8) = (C2×C8).169D4φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C464C4.41(C2^2:Q8)128,826
C4.42(C22⋊Q8) = (C2×C8).60D4φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C4128C4.42(C2^2:Q8)128,827
C4.43(C22⋊Q8) = (C2×C8).170D4φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C4128C4.43(C2^2:Q8)128,828
C4.44(C22⋊Q8) = (C2×C8).171D4φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C4128C4.44(C2^2:Q8)128,829
C4.45(C22⋊Q8) = D8⋊1Q8φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C464C4.45(C2^2:Q8)128,956
C4.46(C22⋊Q8) = Q16⋊Q8φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C4128C4.46(C2^2:Q8)128,957
C4.47(C22⋊Q8) = D8⋊Q8φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C464C4.47(C2^2:Q8)128,958
C4.48(C22⋊Q8) = C4.Q32φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C4128C4.48(C2^2:Q8)128,959
C4.49(C22⋊Q8) = D8.Q8φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C464C4.49(C2^2:Q8)128,960
C4.50(C22⋊Q8) = Q16.Q8φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C4128C4.50(C2^2:Q8)128,961
C4.51(C22⋊Q8) = D8⋊3Q8φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C4164C4.51(C2^2:Q8)128,962
C4.52(C22⋊Q8) = D8.2Q8φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C4324C4.52(C2^2:Q8)128,963
C4.53(C22⋊Q8) = C23.351C24φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C4128C4.53(C2^2:Q8)128,1183
C4.54(C22⋊Q8) = C23.353C24φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C4128C4.54(C2^2:Q8)128,1185
C4.55(C22⋊Q8) = C23.354C24φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C464C4.55(C2^2:Q8)128,1186
C4.56(C22⋊Q8) = C42.173D4φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C464C4.56(C2^2:Q8)128,1295
C4.57(C22⋊Q8) = C42.174D4φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C4128C4.57(C2^2:Q8)128,1297
C4.58(C22⋊Q8) = C42.175D4φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C464C4.58(C2^2:Q8)128,1298
C4.59(C22⋊Q8) = C42.176D4φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C4128C4.59(C2^2:Q8)128,1299
C4.60(C22⋊Q8) = C42.177D4φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C4128C4.60(C2^2:Q8)128,1300
C4.61(C22⋊Q8) = C2×D4⋊Q8φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C464C4.61(C2^2:Q8)128,1802
C4.62(C22⋊Q8) = C2×D4⋊2Q8φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C464C4.62(C2^2:Q8)128,1803
C4.63(C22⋊Q8) = C2×D4.Q8φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C464C4.63(C2^2:Q8)128,1804
C4.64(C22⋊Q8) = C2×Q8⋊Q8φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C4128C4.64(C2^2:Q8)128,1805
C4.65(C22⋊Q8) = C2×C4.Q16φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C4128C4.65(C2^2:Q8)128,1806
C4.66(C22⋊Q8) = C2×Q8.Q8φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C4128C4.66(C2^2:Q8)128,1807
C4.67(C22⋊Q8) = C42.20C23φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C432C4.67(C2^2:Q8)128,1813
C4.68(C22⋊Q8) = C42.21C23φ: C22⋊Q8/C4⋊C4 → C2 ⊆ Aut C464C4.68(C2^2:Q8)128,1814
C4.69(C22⋊Q8) = C24.133D4φ: C22⋊Q8/C22×C4 → C2 ⊆ Aut C464C4.69(C2^2:Q8)128,539
C4.70(C22⋊Q8) = C23.22D8φ: C22⋊Q8/C22×C4 → C2 ⊆ Aut C464C4.70(C2^2:Q8)128,540
C4.71(C22⋊Q8) = C24.67D4φ: C22⋊Q8/C22×C4 → C2 ⊆ Aut C464C4.71(C2^2:Q8)128,541
C4.72(C22⋊Q8) = C4○D4.4Q8φ: C22⋊Q8/C22×C4 → C2 ⊆ Aut C464C4.72(C2^2:Q8)128,547
C4.73(C22⋊Q8) = C4○D4.5Q8φ: C22⋊Q8/C22×C4 → C2 ⊆ Aut C464C4.73(C2^2:Q8)128,548
C4.74(C22⋊Q8) = C8⋊7(C4⋊C4)φ: C22⋊Q8/C22×C4 → C2 ⊆ Aut C4128C4.74(C2^2:Q8)128,673
C4.75(C22⋊Q8) = C8⋊5(C4⋊C4)φ: C22⋊Q8/C22×C4 → C2 ⊆ Aut C4128C4.75(C2^2:Q8)128,674
C4.76(C22⋊Q8) = C4.(C4×Q8)φ: C22⋊Q8/C22×C4 → C2 ⊆ Aut C4128C4.76(C2^2:Q8)128,675
C4.77(C22⋊Q8) = C8⋊(C4⋊C4)φ: C22⋊Q8/C22×C4 → C2 ⊆ Aut C4128C4.77(C2^2:Q8)128,676
C4.78(C22⋊Q8) = M4(2).5Q8φ: C22⋊Q8/C22×C4 → C2 ⊆ Aut C464C4.78(C2^2:Q8)128,683
C4.79(C22⋊Q8) = M4(2).6Q8φ: C22⋊Q8/C22×C4 → C2 ⊆ Aut C464C4.79(C2^2:Q8)128,684
C4.80(C22⋊Q8) = C42.436D4φ: C22⋊Q8/C22×C4 → C2 ⊆ Aut C4128C4.80(C2^2:Q8)128,722
C4.81(C22⋊Q8) = C42.437D4φ: C22⋊Q8/C22×C4 → C2 ⊆ Aut C4128C4.81(C2^2:Q8)128,723
C4.82(C22⋊Q8) = C42.124D4φ: C22⋊Q8/C22×C4 → C2 ⊆ Aut C4128C4.82(C2^2:Q8)128,724
C4.83(C22⋊Q8) = C42.125D4φ: C22⋊Q8/C22×C4 → C2 ⊆ Aut C4128C4.83(C2^2:Q8)128,725
C4.84(C22⋊Q8) = M4(2)⋊8Q8φ: C22⋊Q8/C22×C4 → C2 ⊆ Aut C464C4.84(C2^2:Q8)128,729
C4.85(C22⋊Q8) = C42.128D4φ: C22⋊Q8/C22×C4 → C2 ⊆ Aut C464C4.85(C2^2:Q8)128,730
C4.86(C22⋊Q8) = C42.187D4φ: C22⋊Q8/C22×C4 → C2 ⊆ Aut C464C4.86(C2^2:Q8)128,1360
C4.87(C22⋊Q8) = C42.188D4φ: C22⋊Q8/C22×C4 → C2 ⊆ Aut C464C4.87(C2^2:Q8)128,1361
C4.88(C22⋊Q8) = C42.439D4φ: C22⋊Q8/C22×C4 → C2 ⊆ Aut C464C4.88(C2^2:Q8)128,1583
C4.89(C22⋊Q8) = C42.448D4φ: C22⋊Q8/C22×C4 → C2 ⊆ Aut C464C4.89(C2^2:Q8)128,1811
C4.90(C22⋊Q8) = C42.449D4φ: C22⋊Q8/C22×C4 → C2 ⊆ Aut C464C4.90(C2^2:Q8)128,1812
C4.91(C22⋊Q8) = C42.96D4φ: C22⋊Q8/C2×Q8 → C2 ⊆ Aut C432C4.91(C2^2:Q8)128,532
C4.92(C22⋊Q8) = C42.97D4φ: C22⋊Q8/C2×Q8 → C2 ⊆ Aut C464C4.92(C2^2:Q8)128,533
C4.93(C22⋊Q8) = C42.98D4φ: C22⋊Q8/C2×Q8 → C2 ⊆ Aut C464C4.93(C2^2:Q8)128,534
C4.94(C22⋊Q8) = C42.99D4φ: C22⋊Q8/C2×Q8 → C2 ⊆ Aut C4128C4.94(C2^2:Q8)128,535
C4.95(C22⋊Q8) = C42.100D4φ: C22⋊Q8/C2×Q8 → C2 ⊆ Aut C464C4.95(C2^2:Q8)128,536
C4.96(C22⋊Q8) = C42.101D4φ: C22⋊Q8/C2×Q8 → C2 ⊆ Aut C4128C4.96(C2^2:Q8)128,537
C4.97(C22⋊Q8) = M4(2).41D4φ: C22⋊Q8/C2×Q8 → C2 ⊆ Aut C4164C4.97(C2^2:Q8)128,593
C4.98(C22⋊Q8) = (C2×D4).Q8φ: C22⋊Q8/C2×Q8 → C2 ⊆ Aut C4324C4.98(C2^2:Q8)128,600
C4.99(C22⋊Q8) = C42.8D4φ: C22⋊Q8/C2×Q8 → C2 ⊆ Aut C4164C4.99(C2^2:Q8)128,763
C4.100(C22⋊Q8) = M4(2).12D4φ: C22⋊Q8/C2×Q8 → C2 ⊆ Aut C432C4.100(C2^2:Q8)128,795
C4.101(C22⋊Q8) = M4(2).13D4φ: C22⋊Q8/C2×Q8 → C2 ⊆ Aut C464C4.101(C2^2:Q8)128,796
C4.102(C22⋊Q8) = C42.10D4φ: C22⋊Q8/C2×Q8 → C2 ⊆ Aut C4324C4.102(C2^2:Q8)128,830
C4.103(C22⋊Q8) = C42.178D4φ: C22⋊Q8/C2×Q8 → C2 ⊆ Aut C464C4.103(C2^2:Q8)128,1312
C4.104(C22⋊Q8) = C42.179D4φ: C22⋊Q8/C2×Q8 → C2 ⊆ Aut C4128C4.104(C2^2:Q8)128,1313
C4.105(C22⋊Q8) = C42.180D4φ: C22⋊Q8/C2×Q8 → C2 ⊆ Aut C4128C4.105(C2^2:Q8)128,1314
C4.106(C22⋊Q8) = C42.219D4φ: C22⋊Q8/C2×Q8 → C2 ⊆ Aut C432C4.106(C2^2:Q8)128,1809
C4.107(C22⋊Q8) = C42.220D4φ: C22⋊Q8/C2×Q8 → C2 ⊆ Aut C464C4.107(C2^2:Q8)128,1810
C4.108(C22⋊Q8) = C42.425D4central extension (φ=1)64C4.108(C2^2:Q8)128,529
C4.109(C22⋊Q8) = C42.95D4central extension (φ=1)64C4.109(C2^2:Q8)128,530
C4.110(C22⋊Q8) = C42.102D4central extension (φ=1)32C4.110(C2^2:Q8)128,538
C4.111(C22⋊Q8) = C23.21M4(2)central extension (φ=1)64C4.111(C2^2:Q8)128,582
C4.112(C22⋊Q8) = (C2×C8).195D4central extension (φ=1)64C4.112(C2^2:Q8)128,583
C4.113(C22⋊Q8) = M4(2).42D4central extension (φ=1)32C4.113(C2^2:Q8)128,598
C4.114(C22⋊Q8) = C4⋊C4⋊3C8central extension (φ=1)128C4.114(C2^2:Q8)128,648
C4.115(C22⋊Q8) = (C2×C8).Q8central extension (φ=1)128C4.115(C2^2:Q8)128,649
C4.116(C22⋊Q8) = M4(2).3Q8central extension (φ=1)32C4.116(C2^2:Q8)128,654
C4.117(C22⋊Q8) = C42.61Q8central extension (φ=1)128C4.117(C2^2:Q8)128,671
C4.118(C22⋊Q8) = C42.27Q8central extension (φ=1)128C4.118(C2^2:Q8)128,672
C4.119(C22⋊Q8) = C42.430D4central extension (φ=1)64C4.119(C2^2:Q8)128,682
C4.120(C22⋊Q8) = C42.327D4central extension (φ=1)128C4.120(C2^2:Q8)128,716
C4.121(C22⋊Q8) = C42.120D4central extension (φ=1)128C4.121(C2^2:Q8)128,717
C4.122(C22⋊Q8) = M4(2)⋊7Q8central extension (φ=1)32C4.122(C2^2:Q8)128,718
C4.123(C22⋊Q8) = C42.162D4central extension (φ=1)64C4.123(C2^2:Q8)128,1128
C4.124(C22⋊Q8) = C42.447D4central extension (φ=1)64C4.124(C2^2:Q8)128,1808

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