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

Direct product G=N×Q with N=C22 and Q=C4⋊Q8
dρLabelID
C22×C4⋊Q8128C2^2xC4:Q8128,2173

Semidirect products G=N:Q with N=C22 and Q=C4⋊Q8
extensionφ:Q→Aut NdρLabelID
C22⋊1(C4⋊Q8) = C42.440D4φ: C4⋊Q8/C42 → C2 ⊆ Aut C2264C2^2:1(C4:Q8)128,1589
C22⋊2(C4⋊Q8) = C24.568C23φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C2264C2^2:2(C4:Q8)128,1172
C22⋊3(C4⋊Q8) = C23.334C24φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C2264C2^2:3(C4:Q8)128,1166

Non-split extensions G=N.Q with N=C22 and Q=C4⋊Q8
extensionφ:Q→Aut NdρLabelID
C22.1(C4⋊Q8) = C42.324D4φ: C4⋊Q8/C42 → C2 ⊆ Aut C2264C2^2.1(C4:Q8)128,580
C22.2(C4⋊Q8) = C42.106D4φ: C4⋊Q8/C42 → C2 ⊆ Aut C2264C2^2.2(C4:Q8)128,581
C22.3(C4⋊Q8) = C23.559C24φ: C4⋊Q8/C42 → C2 ⊆ Aut C2264C2^2.3(C4:Q8)128,1391
C22.4(C4⋊Q8) = C42.364D4φ: C4⋊Q8/C42 → C2 ⊆ Aut C2264C2^2.4(C4:Q8)128,1892
C22.5(C4⋊Q8) = C42.252D4φ: C4⋊Q8/C42 → C2 ⊆ Aut C2264C2^2.5(C4:Q8)128,1894
C22.6(C4⋊Q8) = C42.430D4φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C2264C2^2.6(C4:Q8)128,682
C22.7(C4⋊Q8) = M4(2).27D4φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C22324C2^2.7(C4:Q8)128,685
C22.8(C4⋊Q8) = C23.449C24φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C2264C2^2.8(C4:Q8)128,1281
C22.9(C4⋊Q8) = M4(2)⋊3Q8φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C2264C2^2.9(C4:Q8)128,1895
C22.10(C4⋊Q8) = M4(2)⋊4Q8φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C2264C2^2.10(C4:Q8)128,1896
C22.11(C4⋊Q8) = M4(2)⋊7Q8φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C2232C2^2.11(C4:Q8)128,718
C22.12(C4⋊Q8) = C24.176C23φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C2232C2^2.12(C4:Q8)128,728
C22.13(C4⋊Q8) = M4(2)⋊Q8φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C2232C2^2.13(C4:Q8)128,792
C22.14(C4⋊Q8) = C42⋊3Q8φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C2232C2^2.14(C4:Q8)128,793
C22.15(C4⋊Q8) = C24.182C23φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C2232C2^2.15(C4:Q8)128,794
C22.16(C4⋊Q8) = C23.402C24φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C2264C2^2.16(C4:Q8)128,1234
C22.17(C4⋊Q8) = C23.483C24φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C2264C2^2.17(C4:Q8)128,1315
C22.18(C4⋊Q8) = M4(2)⋊5Q8φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C2264C2^2.18(C4:Q8)128,1897
C22.19(C4⋊Q8) = M4(2)⋊6Q8φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C2264C2^2.19(C4:Q8)128,1898
C22.20(C4⋊Q8) = C24.625C23central extension (φ=1)128C2^2.20(C4:Q8)128,167
C22.21(C4⋊Q8) = C24.626C23central extension (φ=1)128C2^2.21(C4:Q8)128,168
C22.22(C4⋊Q8) = C24.631C23central extension (φ=1)128C2^2.22(C4:Q8)128,173
C22.23(C4⋊Q8) = C24.632C23central extension (φ=1)128C2^2.23(C4:Q8)128,174
C22.24(C4⋊Q8) = C24.634C23central extension (φ=1)128C2^2.24(C4:Q8)128,176
C22.25(C4⋊Q8) = C24.635C23central extension (φ=1)128C2^2.25(C4:Q8)128,177
C22.26(C4⋊Q8) = C24.636C23central extension (φ=1)128C2^2.26(C4:Q8)128,178
C22.27(C4⋊Q8) = C42.58Q8central extension (φ=1)128C2^2.27(C4:Q8)128,576
C22.28(C4⋊Q8) = C42.59Q8central extension (φ=1)128C2^2.28(C4:Q8)128,577
C22.29(C4⋊Q8) = C42.60Q8central extension (φ=1)128C2^2.29(C4:Q8)128,578
C22.30(C4⋊Q8) = C42.26Q8central extension (φ=1)128C2^2.30(C4:Q8)128,579
C22.31(C4⋊Q8) = C8⋊7(C4⋊C4)central extension (φ=1)128C2^2.31(C4:Q8)128,673
C22.32(C4⋊Q8) = C8⋊5(C4⋊C4)central extension (φ=1)128C2^2.32(C4:Q8)128,674
C22.33(C4⋊Q8) = C4.(C4×Q8)central extension (φ=1)128C2^2.33(C4:Q8)128,675
C22.34(C4⋊Q8) = C8⋊(C4⋊C4)central extension (φ=1)128C2^2.34(C4:Q8)128,676
C22.35(C4⋊Q8) = C42.436D4central extension (φ=1)128C2^2.35(C4:Q8)128,722
C22.36(C4⋊Q8) = C42.437D4central extension (φ=1)128C2^2.36(C4:Q8)128,723
C22.37(C4⋊Q8) = C42.124D4central extension (φ=1)128C2^2.37(C4:Q8)128,724
C22.38(C4⋊Q8) = C42.125D4central extension (φ=1)128C2^2.38(C4:Q8)128,725
C22.39(C4⋊Q8) = C2×C42⋊9C4central extension (φ=1)128C2^2.39(C4:Q8)128,1016
C22.40(C4⋊Q8) = C2×C23.65C23central extension (φ=1)128C2^2.40(C4:Q8)128,1023
C22.41(C4⋊Q8) = C2×C23.67C23central extension (φ=1)128C2^2.41(C4:Q8)128,1026
C22.42(C4⋊Q8) = C2×C23.78C23central extension (φ=1)128C2^2.42(C4:Q8)128,1119
C22.43(C4⋊Q8) = C2×C23.81C23central extension (φ=1)128C2^2.43(C4:Q8)128,1123
C22.44(C4⋊Q8) = C2×C8⋊3Q8central extension (φ=1)128C2^2.44(C4:Q8)128,1889
C22.45(C4⋊Q8) = C2×C8.5Q8central extension (φ=1)128C2^2.45(C4:Q8)128,1890
C22.46(C4⋊Q8) = C2×C8⋊2Q8central extension (φ=1)128C2^2.46(C4:Q8)128,1891
C22.47(C4⋊Q8) = C2×C8⋊Q8central extension (φ=1)128C2^2.47(C4:Q8)128,1893
C22.48(C4⋊Q8) = C4⋊C4⋊Q8central stem extension (φ=1)128C2^2.48(C4:Q8)128,789
C22.49(C4⋊Q8) = (C2×C8)⋊Q8central stem extension (φ=1)128C2^2.49(C4:Q8)128,790
C22.50(C4⋊Q8) = C2.(C8⋊Q8)central stem extension (φ=1)128C2^2.50(C4:Q8)128,791
C22.51(C4⋊Q8) = (C2×C8).1Q8central stem extension (φ=1)128C2^2.51(C4:Q8)128,815
C22.52(C4⋊Q8) = C2.(C8⋊3Q8)central stem extension (φ=1)128C2^2.52(C4:Q8)128,816
C22.53(C4⋊Q8) = (C2×C8).24Q8central stem extension (φ=1)128C2^2.53(C4:Q8)128,817

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