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Extensions 1→N→G→Q→1 with N=C4 and Q=C22.D4

Direct product G=N×Q with N=C4 and Q=C22.D4
dρLabelID
C4×C22.D464C4xC2^2.D4128,1033

Semidirect products G=N:Q with N=C4 and Q=C22.D4
extensionφ:Q→Aut NdρLabelID
C4⋊1(C22.D4) = C23.322C24φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4:1(C2^2.D4)128,1154
C4⋊2(C22.D4) = C23.401C24φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4:2(C2^2.D4)128,1233
C4⋊3(C22.D4) = C23.345C24φ: C22.D4/C4⋊C4 → C2 ⊆ Aut C464C4:3(C2^2.D4)128,1177
C4⋊4(C22.D4) = C24.598C23φ: C22.D4/C22×C4 → C2 ⊆ Aut C464C4:4(C2^2.D4)128,1586
C4⋊5(C22.D4) = C24.299C23φ: C22.D4/C2×D4 → C2 ⊆ Aut C464C4:5(C2^2.D4)128,1218

Non-split extensions G=N.Q with N=C4 and Q=C22.D4
extensionφ:Q→Aut NdρLabelID
C4.1(C22.D4) = (C2×C42)⋊C4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C4164C4.1(C2^2.D4)128,559
C4.2(C22.D4) = C24.6(C2×C4)φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C4168+C4.2(C2^2.D4)128,561
C4.3(C22.D4) = (C2×Q8).211D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C4328-C4.3(C2^2.D4)128,562
C4.4(C22.D4) = C4≀C2⋊C4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C432C4.4(C2^2.D4)128,591
C4.5(C22.D4) = C42⋊9(C2×C4)φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C432C4.5(C2^2.D4)128,592
C4.6(C22.D4) = C2.(C4×D8)φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.6(C2^2.D4)128,594
C4.7(C22.D4) = Q8⋊(C4⋊C4)φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C4128C4.7(C2^2.D4)128,595
C4.8(C22.D4) = D4⋊(C4⋊C4)φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.8(C2^2.D4)128,596
C4.9(C22.D4) = Q8⋊C4⋊C4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C4128C4.9(C2^2.D4)128,597
C4.10(C22.D4) = C42.5D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C4168+C4.10(C2^2.D4)128,636
C4.11(C22.D4) = C42.6D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C4328-C4.11(C2^2.D4)128,637
C4.12(C22.D4) = C42.426D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C4164C4.12(C2^2.D4)128,638
C4.13(C22.D4) = C4.(C4×D4)φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C4328-C4.13(C2^2.D4)128,641
C4.14(C22.D4) = (C2×C8)⋊4D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C4168+C4.14(C2^2.D4)128,642
C4.15(C22.D4) = M4(2)⋊21D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C4168+C4.15(C2^2.D4)128,646
C4.16(C22.D4) = M4(2).50D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C4328-C4.16(C2^2.D4)128,647
C4.17(C22.D4) = C24.83D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.17(C2^2.D4)128,765
C4.18(C22.D4) = C24.84D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.18(C2^2.D4)128,766
C4.19(C22.D4) = C24.85D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.19(C2^2.D4)128,767
C4.20(C22.D4) = C24.86D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.20(C2^2.D4)128,768
C4.21(C22.D4) = C42⋊11D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C432C4.21(C2^2.D4)128,771
C4.22(C22.D4) = C42⋊12D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C432C4.22(C2^2.D4)128,772
C4.23(C22.D4) = M4(2).8D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C4168+C4.23(C2^2.D4)128,780
C4.24(C22.D4) = M4(2).9D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C4328-C4.24(C2^2.D4)128,781
C4.25(C22.D4) = C22⋊C4.7D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C4324C4.25(C2^2.D4)128,785
C4.26(C22.D4) = (C2×C4).24D8φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.26(C2^2.D4)128,803
C4.27(C22.D4) = (C2×C4).19Q16φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C4128C4.27(C2^2.D4)128,804
C4.28(C22.D4) = C42⋊8C4⋊C2φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.28(C2^2.D4)128,805
C4.29(C22.D4) = (C2×Q8).109D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C4128C4.29(C2^2.D4)128,806
C4.30(C22.D4) = C42.9D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C4324C4.30(C2^2.D4)128,812
C4.31(C22.D4) = (C2×C8).D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C4168+C4.31(C2^2.D4)128,813
C4.32(C22.D4) = (C2×C8).6D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C4328-C4.32(C2^2.D4)128,814
C4.33(C22.D4) = (C2×C8).168D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.33(C2^2.D4)128,824
C4.34(C22.D4) = (C2×C4).27D8φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.34(C2^2.D4)128,825
C4.35(C22.D4) = (C2×C8).169D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.35(C2^2.D4)128,826
C4.36(C22.D4) = (C2×C8).60D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C4128C4.36(C2^2.D4)128,827
C4.37(C22.D4) = (C2×C8).170D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C4128C4.37(C2^2.D4)128,828
C4.38(C22.D4) = (C2×C8).171D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C4128C4.38(C2^2.D4)128,829
C4.39(C22.D4) = C22.D16φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.39(C2^2.D4)128,964
C4.40(C22.D4) = C23.49D8φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.40(C2^2.D4)128,965
C4.41(C22.D4) = C23.19D8φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.41(C2^2.D4)128,966
C4.42(C22.D4) = C23.50D8φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.42(C2^2.D4)128,967
C4.43(C22.D4) = C23.51D8φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.43(C2^2.D4)128,968
C4.44(C22.D4) = C23.20D8φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.44(C2^2.D4)128,969
C4.45(C22.D4) = M5(2).C22φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C4168+C4.45(C2^2.D4)128,970
C4.46(C22.D4) = C23.10SD16φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C4328-C4.46(C2^2.D4)128,971
C4.47(C22.D4) = C24.254C23φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.47(C2^2.D4)128,1152
C4.48(C22.D4) = C23.321C24φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.48(C2^2.D4)128,1153
C4.49(C22.D4) = C23.323C24φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.49(C2^2.D4)128,1155
C4.50(C22.D4) = C24.308C23φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.50(C2^2.D4)128,1231
C4.51(C22.D4) = C23.400C24φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.51(C2^2.D4)128,1232
C4.52(C22.D4) = C23.402C24φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.52(C2^2.D4)128,1234
C4.53(C22.D4) = C24.579C23φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.53(C2^2.D4)128,1235
C4.54(C22.D4) = C23.404C24φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.54(C2^2.D4)128,1236
C4.55(C22.D4) = C2×C22.D8φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.55(C2^2.D4)128,1817
C4.56(C22.D4) = C2×C23.47D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.56(C2^2.D4)128,1818
C4.57(C22.D4) = C2×C23.19D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.57(C2^2.D4)128,1819
C4.58(C22.D4) = C2×C23.20D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.58(C2^2.D4)128,1820
C4.59(C22.D4) = C2×C23.46D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.59(C2^2.D4)128,1821
C4.60(C22.D4) = C2×C23.48D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.60(C2^2.D4)128,1822
C4.61(C22.D4) = (C2×D4).303D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.61(C2^2.D4)128,1830
C4.62(C22.D4) = (C2×D4).304D4φ: C22.D4/C22⋊C4 → C2 ⊆ Aut C464C4.62(C2^2.D4)128,1831
C4.63(C22.D4) = (C2×SD16)⋊14C4φ: C22.D4/C4⋊C4 → C2 ⊆ Aut C464C4.63(C2^2.D4)128,609
C4.64(C22.D4) = (C2×C4)⋊9Q16φ: C22.D4/C4⋊C4 → C2 ⊆ Aut C4128C4.64(C2^2.D4)128,610
C4.65(C22.D4) = (C2×C4)⋊9D8φ: C22.D4/C4⋊C4 → C2 ⊆ Aut C464C4.65(C2^2.D4)128,611
C4.66(C22.D4) = (C2×SD16)⋊15C4φ: C22.D4/C4⋊C4 → C2 ⊆ Aut C464C4.66(C2^2.D4)128,612
C4.67(C22.D4) = C8.C22⋊C4φ: C22.D4/C4⋊C4 → C2 ⊆ Aut C432C4.67(C2^2.D4)128,614
C4.68(C22.D4) = C8⋊C22⋊C4φ: C22.D4/C4⋊C4 → C2 ⊆ Aut C432C4.68(C2^2.D4)128,615
C4.69(C22.D4) = M4(2)⋊6D4φ: C22.D4/C4⋊C4 → C2 ⊆ Aut C432C4.69(C2^2.D4)128,769
C4.70(C22.D4) = M4(2).7D4φ: C22.D4/C4⋊C4 → C2 ⊆ Aut C432C4.70(C2^2.D4)128,770
C4.71(C22.D4) = C4⋊C4⋊7D4φ: C22.D4/C4⋊C4 → C2 ⊆ Aut C464C4.71(C2^2.D4)128,773
C4.72(C22.D4) = C4⋊C4.94D4φ: C22.D4/C4⋊C4 → C2 ⊆ Aut C464C4.72(C2^2.D4)128,774
C4.73(C22.D4) = C4⋊C4.95D4φ: C22.D4/C4⋊C4 → C2 ⊆ Aut C4128C4.73(C2^2.D4)128,775
C4.74(C22.D4) = M4(2).10D4φ: C22.D4/C4⋊C4 → C2 ⊆ Aut C432C4.74(C2^2.D4)128,783
C4.75(C22.D4) = M4(2).11D4φ: C22.D4/C4⋊C4 → C2 ⊆ Aut C464C4.75(C2^2.D4)128,784
C4.76(C22.D4) = (C2×C4)⋊3D8φ: C22.D4/C4⋊C4 → C2 ⊆ Aut C464C4.76(C2^2.D4)128,786
C4.77(C22.D4) = (C2×C4)⋊5SD16φ: C22.D4/C4⋊C4 → C2 ⊆ Aut C464C4.77(C2^2.D4)128,787
C4.78(C22.D4) = (C2×C4)⋊3Q16φ: C22.D4/C4⋊C4 → C2 ⊆ Aut C4128C4.78(C2^2.D4)128,788
C4.79(C22.D4) = C23.346C24φ: C22.D4/C4⋊C4 → C2 ⊆ Aut C4128C4.79(C2^2.D4)128,1178
C4.80(C22.D4) = C24.271C23φ: C22.D4/C4⋊C4 → C2 ⊆ Aut C464C4.80(C2^2.D4)128,1179
C4.81(C22.D4) = C23.348C24φ: C22.D4/C4⋊C4 → C2 ⊆ Aut C464C4.81(C2^2.D4)128,1180
C4.82(C22.D4) = (C2×D4).301D4φ: C22.D4/C4⋊C4 → C2 ⊆ Aut C432C4.82(C2^2.D4)128,1828
C4.83(C22.D4) = (C2×D4).302D4φ: C22.D4/C4⋊C4 → C2 ⊆ Aut C464C4.83(C2^2.D4)128,1829
C4.84(C22.D4) = C24.135D4φ: C22.D4/C22×C4 → C2 ⊆ Aut C464C4.84(C2^2.D4)128,624
C4.85(C22.D4) = C23.23D8φ: C22.D4/C22×C4 → C2 ⊆ Aut C464C4.85(C2^2.D4)128,625
C4.86(C22.D4) = C24.75D4φ: C22.D4/C22×C4 → C2 ⊆ Aut C464C4.86(C2^2.D4)128,626
C4.87(C22.D4) = C24.76D4φ: C22.D4/C22×C4 → C2 ⊆ Aut C464C4.87(C2^2.D4)128,627
C4.88(C22.D4) = M4(2)⋊20D4φ: C22.D4/C22×C4 → C2 ⊆ Aut C432C4.88(C2^2.D4)128,632
C4.89(C22.D4) = M4(2).45D4φ: C22.D4/C22×C4 → C2 ⊆ Aut C432C4.89(C2^2.D4)128,633
C4.90(C22.D4) = C4.10D4⋊3C4φ: C22.D4/C22×C4 → C2 ⊆ Aut C464C4.90(C2^2.D4)128,662
C4.91(C22.D4) = C4.D4⋊3C4φ: C22.D4/C22×C4 → C2 ⊆ Aut C432C4.91(C2^2.D4)128,663
C4.92(C22.D4) = C2.(C8⋊8D4)φ: C22.D4/C22×C4 → C2 ⊆ Aut C4128C4.92(C2^2.D4)128,665
C4.93(C22.D4) = C2.(C8⋊7D4)φ: C22.D4/C22×C4 → C2 ⊆ Aut C464C4.93(C2^2.D4)128,666
C4.94(C22.D4) = C2.(C8⋊D4)φ: C22.D4/C22×C4 → C2 ⊆ Aut C4128C4.94(C2^2.D4)128,667
C4.95(C22.D4) = C2.(C8⋊2D4)φ: C22.D4/C22×C4 → C2 ⊆ Aut C464C4.95(C2^2.D4)128,668
C4.96(C22.D4) = C23.524C24φ: C22.D4/C22×C4 → C2 ⊆ Aut C464C4.96(C2^2.D4)128,1356
C4.97(C22.D4) = C23.525C24φ: C22.D4/C22×C4 → C2 ⊆ Aut C464C4.97(C2^2.D4)128,1357
C4.98(C22.D4) = C24.599C23φ: C22.D4/C22×C4 → C2 ⊆ Aut C464C4.98(C2^2.D4)128,1587
C4.99(C22.D4) = C24.117D4φ: C22.D4/C22×C4 → C2 ⊆ Aut C432C4.99(C2^2.D4)128,1826
C4.100(C22.D4) = C24.118D4φ: C22.D4/C22×C4 → C2 ⊆ Aut C432C4.100(C2^2.D4)128,1827
C4.101(C22.D4) = (C22×C4).275D4φ: C22.D4/C2×D4 → C2 ⊆ Aut C432C4.101(C2^2.D4)128,553
C4.102(C22.D4) = (C22×C4).276D4φ: C22.D4/C2×D4 → C2 ⊆ Aut C432C4.102(C2^2.D4)128,554
C4.103(C22.D4) = C23.36D8φ: C22.D4/C2×D4 → C2 ⊆ Aut C464C4.103(C2^2.D4)128,555
C4.104(C22.D4) = C24.157D4φ: C22.D4/C2×D4 → C2 ⊆ Aut C464C4.104(C2^2.D4)128,556
C4.105(C22.D4) = C24.69D4φ: C22.D4/C2×D4 → C2 ⊆ Aut C464C4.105(C2^2.D4)128,557
C4.106(C22.D4) = M4(2).40D4φ: C22.D4/C2×D4 → C2 ⊆ Aut C4324C4.106(C2^2.D4)128,590
C4.107(C22.D4) = (C2×D4).Q8φ: C22.D4/C2×D4 → C2 ⊆ Aut C4324C4.107(C2^2.D4)128,600
C4.108(C22.D4) = M4(2)⋊19D4φ: C22.D4/C2×D4 → C2 ⊆ Aut C4164C4.108(C2^2.D4)128,616
C4.109(C22.D4) = (C2×C8)⋊D4φ: C22.D4/C2×D4 → C2 ⊆ Aut C4164C4.109(C2^2.D4)128,623
C4.110(C22.D4) = C23.12D8φ: C22.D4/C2×D4 → C2 ⊆ Aut C464C4.110(C2^2.D4)128,807
C4.111(C22.D4) = C24.88D4φ: C22.D4/C2×D4 → C2 ⊆ Aut C464C4.111(C2^2.D4)128,808
C4.112(C22.D4) = C24.89D4φ: C22.D4/C2×D4 → C2 ⊆ Aut C464C4.112(C2^2.D4)128,809
C4.113(C22.D4) = (C2×C8).55D4φ: C22.D4/C2×D4 → C2 ⊆ Aut C464C4.113(C2^2.D4)128,810
C4.114(C22.D4) = (C2×C8).165D4φ: C22.D4/C2×D4 → C2 ⊆ Aut C464C4.114(C2^2.D4)128,811
C4.115(C22.D4) = (C2×C4).26D8φ: C22.D4/C2×D4 → C2 ⊆ Aut C4128C4.115(C2^2.D4)128,818
C4.116(C22.D4) = (C2×C4).21Q16φ: C22.D4/C2×D4 → C2 ⊆ Aut C4128C4.116(C2^2.D4)128,819
C4.117(C22.D4) = C4.(C4⋊Q8)φ: C22.D4/C2×D4 → C2 ⊆ Aut C4128C4.117(C2^2.D4)128,820
C4.118(C22.D4) = M4(2).Q8φ: C22.D4/C2×D4 → C2 ⊆ Aut C464C4.118(C2^2.D4)128,821
C4.119(C22.D4) = M4(2).2Q8φ: C22.D4/C2×D4 → C2 ⊆ Aut C464C4.119(C2^2.D4)128,822
C4.120(C22.D4) = C24.11Q8φ: C22.D4/C2×D4 → C2 ⊆ Aut C4164C4.120(C2^2.D4)128,823
C4.121(C22.D4) = C42.10D4φ: C22.D4/C2×D4 → C2 ⊆ Aut C4324C4.121(C2^2.D4)128,830
C4.122(C22.D4) = C42.32Q8φ: C22.D4/C2×D4 → C2 ⊆ Aut C4164C4.122(C2^2.D4)128,834
C4.123(C22.D4) = C22⋊C4.Q8φ: C22.D4/C2×D4 → C2 ⊆ Aut C4324C4.123(C2^2.D4)128,835
C4.124(C22.D4) = C23.385C24φ: C22.D4/C2×D4 → C2 ⊆ Aut C464C4.124(C2^2.D4)128,1217
C4.125(C22.D4) = C24.300C23φ: C22.D4/C2×D4 → C2 ⊆ Aut C464C4.125(C2^2.D4)128,1219
C4.126(C22.D4) = C24.183D4φ: C22.D4/C2×D4 → C2 ⊆ Aut C432C4.126(C2^2.D4)128,1824
C4.127(C22.D4) = C24.116D4φ: C22.D4/C2×D4 → C2 ⊆ Aut C432C4.127(C2^2.D4)128,1825
C4.128(C22.D4) = C23.32M4(2)central extension (φ=1)64C4.128(C2^2.D4)128,549
C4.129(C22.D4) = C24.53(C2×C4)central extension (φ=1)64C4.129(C2^2.D4)128,550
C4.130(C22.D4) = C24.70D4central extension (φ=1)32C4.130(C2^2.D4)128,558
C4.131(C22.D4) = C23.21M4(2)central extension (φ=1)64C4.131(C2^2.D4)128,582
C4.132(C22.D4) = (C2×C8).195D4central extension (φ=1)64C4.132(C2^2.D4)128,583
C4.133(C22.D4) = C24.10Q8central extension (φ=1)32C4.133(C2^2.D4)128,587
C4.134(C22.D4) = C23.22M4(2)central extension (φ=1)64C4.134(C2^2.D4)128,601
C4.135(C22.D4) = C23⋊2M4(2)central extension (φ=1)64C4.135(C2^2.D4)128,602
C4.136(C22.D4) = C24.72D4central extension (φ=1)32C4.136(C2^2.D4)128,603
C4.137(C22.D4) = C4⋊C4⋊3C8central extension (φ=1)128C4.137(C2^2.D4)128,648
C4.138(C22.D4) = (C2×C8).Q8central extension (φ=1)128C4.138(C2^2.D4)128,649
C4.139(C22.D4) = M4(2).3Q8central extension (φ=1)32C4.139(C2^2.D4)128,654
C4.140(C22.D4) = C22⋊C4⋊4C8central extension (φ=1)64C4.140(C2^2.D4)128,655
C4.141(C22.D4) = C23.9M4(2)central extension (φ=1)64C4.141(C2^2.D4)128,656
C4.142(C22.D4) = M4(2).24D4central extension (φ=1)32C4.142(C2^2.D4)128,661
C4.143(C22.D4) = C23.295C24central extension (φ=1)64C4.143(C2^2.D4)128,1127
C4.144(C22.D4) = C24.115D4central extension (φ=1)32C4.144(C2^2.D4)128,1823

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