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

Direct product G=N×Q with N=C2×C4 and Q=C2×C4
dρLabelID
C22×C4264C2^2xC4^264,192

Semidirect products G=N:Q with N=C2×C4 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
(C2×C4)⋊1(C2×C4) = C2×C23⋊C4φ: C2×C4/C2 → C4 ⊆ Aut C2×C416(C2xC4):1(C2xC4)64,90
(C2×C4)⋊2(C2×C4) = C23.8Q8φ: C2×C4/C2 → C22 ⊆ Aut C2×C432(C2xC4):2(C2xC4)64,66
(C2×C4)⋊3(C2×C4) = C23.23D4φ: C2×C4/C2 → C22 ⊆ Aut C2×C432(C2xC4):3(C2xC4)64,67
(C2×C4)⋊4(C2×C4) = C22.11C24φ: C2×C4/C2 → C22 ⊆ Aut C2×C416(C2xC4):4(C2xC4)64,199
(C2×C4)⋊5(C2×C4) = C23.33C23φ: C2×C4/C2 → C22 ⊆ Aut C2×C432(C2xC4):5(C2xC4)64,201
(C2×C4)⋊6(C2×C4) = C4×C22⋊C4φ: C2×C4/C4 → C2 ⊆ Aut C2×C432(C2xC4):6(C2xC4)64,58
(C2×C4)⋊7(C2×C4) = C2×C4×D4φ: C2×C4/C4 → C2 ⊆ Aut C2×C432(C2xC4):7(C2xC4)64,196
(C2×C4)⋊8(C2×C4) = C4×C4○D4φ: C2×C4/C4 → C2 ⊆ Aut C2×C432(C2xC4):8(C2xC4)64,198
(C2×C4)⋊9(C2×C4) = C2×C2.C42φ: C2×C4/C22 → C2 ⊆ Aut C2×C464(C2xC4):9(C2xC4)64,56
(C2×C4)⋊10(C2×C4) = C22×C4⋊C4φ: C2×C4/C22 → C2 ⊆ Aut C2×C464(C2xC4):10(C2xC4)64,194
(C2×C4)⋊11(C2×C4) = C2×C42⋊C2φ: C2×C4/C22 → C2 ⊆ Aut C2×C432(C2xC4):11(C2xC4)64,195

Non-split extensions G=N.Q with N=C2×C4 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
(C2×C4).1(C2×C4) = C42⋊C4φ: C2×C4/C2 → C4 ⊆ Aut C2×C484+(C2xC4).1(C2xC4)64,34
(C2×C4).2(C2×C4) = C42⋊3C4φ: C2×C4/C2 → C4 ⊆ Aut C2×C4164(C2xC4).2(C2xC4)64,35
(C2×C4).3(C2×C4) = C42.C4φ: C2×C4/C2 → C4 ⊆ Aut C2×C4164(C2xC4).3(C2xC4)64,36
(C2×C4).4(C2×C4) = C42.3C4φ: C2×C4/C2 → C4 ⊆ Aut C2×C4164-(C2xC4).4(C2xC4)64,37
(C2×C4).5(C2×C4) = C23.C23φ: C2×C4/C2 → C4 ⊆ Aut C2×C4164(C2xC4).5(C2xC4)64,91
(C2×C4).6(C2×C4) = C2×C4.10D4φ: C2×C4/C2 → C4 ⊆ Aut C2×C432(C2xC4).6(C2xC4)64,93
(C2×C4).7(C2×C4) = M4(2).8C22φ: C2×C4/C2 → C4 ⊆ Aut C2×C4164(C2xC4).7(C2xC4)64,94
(C2×C4).8(C2×C4) = C22.SD16φ: C2×C4/C2 → C22 ⊆ Aut C2×C416(C2xC4).8(C2xC4)64,8
(C2×C4).9(C2×C4) = C23.31D4φ: C2×C4/C2 → C22 ⊆ Aut C2×C416(C2xC4).9(C2xC4)64,9
(C2×C4).10(C2×C4) = C42.C22φ: C2×C4/C2 → C22 ⊆ Aut C2×C432(C2xC4).10(C2xC4)64,10
(C2×C4).11(C2×C4) = C42.2C22φ: C2×C4/C2 → C22 ⊆ Aut C2×C464(C2xC4).11(C2xC4)64,11
(C2×C4).12(C2×C4) = C4.D8φ: C2×C4/C2 → C22 ⊆ Aut C2×C432(C2xC4).12(C2xC4)64,12
(C2×C4).13(C2×C4) = C4.10D8φ: C2×C4/C2 → C22 ⊆ Aut C2×C464(C2xC4).13(C2xC4)64,13
(C2×C4).14(C2×C4) = C4.6Q16φ: C2×C4/C2 → C22 ⊆ Aut C2×C464(C2xC4).14(C2xC4)64,14
(C2×C4).15(C2×C4) = C22.C42φ: C2×C4/C2 → C22 ⊆ Aut C2×C432(C2xC4).15(C2xC4)64,24
(C2×C4).16(C2×C4) = C23.63C23φ: C2×C4/C2 → C22 ⊆ Aut C2×C464(C2xC4).16(C2xC4)64,68
(C2×C4).17(C2×C4) = C24.C22φ: C2×C4/C2 → C22 ⊆ Aut C2×C432(C2xC4).17(C2xC4)64,69
(C2×C4).18(C2×C4) = C23.65C23φ: C2×C4/C2 → C22 ⊆ Aut C2×C464(C2xC4).18(C2xC4)64,70
(C2×C4).19(C2×C4) = C23.67C23φ: C2×C4/C2 → C22 ⊆ Aut C2×C464(C2xC4).19(C2xC4)64,72
(C2×C4).20(C2×C4) = C2×C4.D4φ: C2×C4/C2 → C22 ⊆ Aut C2×C416(C2xC4).20(C2xC4)64,92
(C2×C4).21(C2×C4) = C23.36D4φ: C2×C4/C2 → C22 ⊆ Aut C2×C432(C2xC4).21(C2xC4)64,98
(C2×C4).22(C2×C4) = C23.37D4φ: C2×C4/C2 → C22 ⊆ Aut C2×C416(C2xC4).22(C2xC4)64,99
(C2×C4).23(C2×C4) = C23.38D4φ: C2×C4/C2 → C22 ⊆ Aut C2×C432(C2xC4).23(C2xC4)64,100
(C2×C4).24(C2×C4) = C42⋊C22φ: C2×C4/C2 → C22 ⊆ Aut C2×C4164(C2xC4).24(C2xC4)64,102
(C2×C4).25(C2×C4) = C42.6C22φ: C2×C4/C2 → C22 ⊆ Aut C2×C432(C2xC4).25(C2xC4)64,105
(C2×C4).26(C2×C4) = M4(2)⋊C4φ: C2×C4/C2 → C22 ⊆ Aut C2×C432(C2xC4).26(C2xC4)64,109
(C2×C4).27(C2×C4) = M4(2).C4φ: C2×C4/C2 → C22 ⊆ Aut C2×C4164(C2xC4).27(C2xC4)64,111
(C2×C4).28(C2×C4) = C42.7C22φ: C2×C4/C2 → C22 ⊆ Aut C2×C432(C2xC4).28(C2xC4)64,114
(C2×C4).29(C2×C4) = C8⋊6D4φ: C2×C4/C2 → C22 ⊆ Aut C2×C432(C2xC4).29(C2xC4)64,117
(C2×C4).30(C2×C4) = C8⋊4Q8φ: C2×C4/C2 → C22 ⊆ Aut C2×C464(C2xC4).30(C2xC4)64,127
(C2×C4).31(C2×C4) = C23.32C23φ: C2×C4/C2 → C22 ⊆ Aut C2×C432(C2xC4).31(C2xC4)64,200
(C2×C4).32(C2×C4) = Q8○M4(2)φ: C2×C4/C2 → C22 ⊆ Aut C2×C4164(C2xC4).32(C2xC4)64,249
(C2×C4).33(C2×C4) = C4×C4⋊C4φ: C2×C4/C4 → C2 ⊆ Aut C2×C464(C2xC4).33(C2xC4)64,59
(C2×C4).34(C2×C4) = C8○2M4(2)φ: C2×C4/C4 → C2 ⊆ Aut C2×C432(C2xC4).34(C2xC4)64,86
(C2×C4).35(C2×C4) = C8×D4φ: C2×C4/C4 → C2 ⊆ Aut C2×C432(C2xC4).35(C2xC4)64,115
(C2×C4).36(C2×C4) = C8⋊9D4φ: C2×C4/C4 → C2 ⊆ Aut C2×C432(C2xC4).36(C2xC4)64,116
(C2×C4).37(C2×C4) = D4⋊C8φ: C2×C4/C4 → C2 ⊆ Aut C2×C432(C2xC4).37(C2xC4)64,6
(C2×C4).38(C2×C4) = Q8⋊C8φ: C2×C4/C4 → C2 ⊆ Aut C2×C464(C2xC4).38(C2xC4)64,7
(C2×C4).39(C2×C4) = C22.4Q16φ: C2×C4/C4 → C2 ⊆ Aut C2×C464(C2xC4).39(C2xC4)64,21
(C2×C4).40(C2×C4) = D4.C8φ: C2×C4/C4 → C2 ⊆ Aut C2×C4322(C2xC4).40(C2xC4)64,31
(C2×C4).41(C2×C4) = C24.3C22φ: C2×C4/C4 → C2 ⊆ Aut C2×C432(C2xC4).41(C2xC4)64,71
(C2×C4).42(C2×C4) = (C22×C8)⋊C2φ: C2×C4/C4 → C2 ⊆ Aut C2×C432(C2xC4).42(C2xC4)64,89
(C2×C4).43(C2×C4) = C2×D4⋊C4φ: C2×C4/C4 → C2 ⊆ Aut C2×C432(C2xC4).43(C2xC4)64,95
(C2×C4).44(C2×C4) = C2×Q8⋊C4φ: C2×C4/C4 → C2 ⊆ Aut C2×C464(C2xC4).44(C2xC4)64,96
(C2×C4).45(C2×C4) = C23.24D4φ: C2×C4/C4 → C2 ⊆ Aut C2×C432(C2xC4).45(C2xC4)64,97
(C2×C4).46(C2×C4) = C2×C4≀C2φ: C2×C4/C4 → C2 ⊆ Aut C2×C416(C2xC4).46(C2xC4)64,101
(C2×C4).47(C2×C4) = C8×Q8φ: C2×C4/C4 → C2 ⊆ Aut C2×C464(C2xC4).47(C2xC4)64,126
(C2×C4).48(C2×C4) = D4○C16φ: C2×C4/C4 → C2 ⊆ Aut C2×C4322(C2xC4).48(C2xC4)64,185
(C2×C4).49(C2×C4) = C2×C4×Q8φ: C2×C4/C4 → C2 ⊆ Aut C2×C464(C2xC4).49(C2xC4)64,197
(C2×C4).50(C2×C4) = C2×C8○D4φ: C2×C4/C4 → C2 ⊆ Aut C2×C432(C2xC4).50(C2xC4)64,248
(C2×C4).51(C2×C4) = C42⋊4C4φ: C2×C4/C22 → C2 ⊆ Aut C2×C464(C2xC4).51(C2xC4)64,57
(C2×C4).52(C2×C4) = C23.34D4φ: C2×C4/C22 → C2 ⊆ Aut C2×C432(C2xC4).52(C2xC4)64,62
(C2×C4).53(C2×C4) = C42⋊8C4φ: C2×C4/C22 → C2 ⊆ Aut C2×C464(C2xC4).53(C2xC4)64,63
(C2×C4).54(C2×C4) = C42⋊5C4φ: C2×C4/C22 → C2 ⊆ Aut C2×C464(C2xC4).54(C2xC4)64,64
(C2×C4).55(C2×C4) = C2×C22⋊C8φ: C2×C4/C22 → C2 ⊆ Aut C2×C432(C2xC4).55(C2xC4)64,87
(C2×C4).56(C2×C4) = C4⋊M4(2)φ: C2×C4/C22 → C2 ⊆ Aut C2×C432(C2xC4).56(C2xC4)64,104
(C2×C4).57(C2×C4) = C42.12C4φ: C2×C4/C22 → C2 ⊆ Aut C2×C432(C2xC4).57(C2xC4)64,112
(C2×C4).58(C2×C4) = C42.6C4φ: C2×C4/C22 → C2 ⊆ Aut C2×C432(C2xC4).58(C2xC4)64,113
(C2×C4).59(C2×C4) = C8⋊2C8φ: C2×C4/C22 → C2 ⊆ Aut C2×C464(C2xC4).59(C2xC4)64,15
(C2×C4).60(C2×C4) = C8⋊1C8φ: C2×C4/C22 → C2 ⊆ Aut C2×C464(C2xC4).60(C2xC4)64,16
(C2×C4).61(C2×C4) = C4.9C42φ: C2×C4/C22 → C2 ⊆ Aut C2×C4164(C2xC4).61(C2xC4)64,18
(C2×C4).62(C2×C4) = C4.10C42φ: C2×C4/C22 → C2 ⊆ Aut C2×C4164(C2xC4).62(C2xC4)64,19
(C2×C4).63(C2×C4) = C42⋊6C4φ: C2×C4/C22 → C2 ⊆ Aut C2×C416(C2xC4).63(C2xC4)64,20
(C2×C4).64(C2×C4) = C4.C42φ: C2×C4/C22 → C2 ⊆ Aut C2×C432(C2xC4).64(C2xC4)64,22
(C2×C4).65(C2×C4) = M4(2)⋊4C4φ: C2×C4/C22 → C2 ⊆ Aut C2×C4164(C2xC4).65(C2xC4)64,25
(C2×C4).66(C2×C4) = C16⋊C4φ: C2×C4/C22 → C2 ⊆ Aut C2×C4164(C2xC4).66(C2xC4)64,28
(C2×C4).67(C2×C4) = C23.C8φ: C2×C4/C22 → C2 ⊆ Aut C2×C4164(C2xC4).67(C2xC4)64,30
(C2×C4).68(C2×C4) = C8.C8φ: C2×C4/C22 → C2 ⊆ Aut C2×C4162(C2xC4).68(C2xC4)64,45
(C2×C4).69(C2×C4) = C23.7Q8φ: C2×C4/C22 → C2 ⊆ Aut C2×C432(C2xC4).69(C2xC4)64,61
(C2×C4).70(C2×C4) = C42⋊9C4φ: C2×C4/C22 → C2 ⊆ Aut C2×C464(C2xC4).70(C2xC4)64,65
(C2×C4).71(C2×C4) = C24.4C4φ: C2×C4/C22 → C2 ⊆ Aut C2×C416(C2xC4).71(C2xC4)64,88
(C2×C4).72(C2×C4) = C2×C4.Q8φ: C2×C4/C22 → C2 ⊆ Aut C2×C464(C2xC4).72(C2xC4)64,106
(C2×C4).73(C2×C4) = C2×C2.D8φ: C2×C4/C22 → C2 ⊆ Aut C2×C464(C2xC4).73(C2xC4)64,107
(C2×C4).74(C2×C4) = C23.25D4φ: C2×C4/C22 → C2 ⊆ Aut C2×C432(C2xC4).74(C2xC4)64,108
(C2×C4).75(C2×C4) = C2×C8.C4φ: C2×C4/C22 → C2 ⊆ Aut C2×C432(C2xC4).75(C2xC4)64,110
(C2×C4).76(C2×C4) = C2×M5(2)φ: C2×C4/C22 → C2 ⊆ Aut C2×C432(C2xC4).76(C2xC4)64,184
(C2×C4).77(C2×C4) = C22×M4(2)φ: C2×C4/C22 → C2 ⊆ Aut C2×C432(C2xC4).77(C2xC4)64,247
(C2×C4).78(C2×C4) = C8⋊C8central extension (φ=1)64(C2xC4).78(C2xC4)64,3
(C2×C4).79(C2×C4) = C22.7C42central extension (φ=1)64(C2xC4).79(C2xC4)64,17
(C2×C4).80(C2×C4) = C16⋊5C4central extension (φ=1)64(C2xC4).80(C2xC4)64,27
(C2×C4).81(C2×C4) = C22⋊C16central extension (φ=1)32(C2xC4).81(C2xC4)64,29
(C2×C4).82(C2×C4) = C4⋊C16central extension (φ=1)64(C2xC4).82(C2xC4)64,44
(C2×C4).83(C2×C4) = C2×C8⋊C4central extension (φ=1)64(C2xC4).83(C2xC4)64,84
(C2×C4).84(C2×C4) = C4×M4(2)central extension (φ=1)32(C2xC4).84(C2xC4)64,85
(C2×C4).85(C2×C4) = C2×C4⋊C8central extension (φ=1)64(C2xC4).85(C2xC4)64,103

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