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

Direct product G=N×Q with N=C4 and Q=C4⋊Q8
dρLabelID
C4×C4⋊Q8128C4xC4:Q8128,1039

Semidirect products G=N:Q with N=C4 and Q=C4⋊Q8
extensionφ:Q→Aut NdρLabelID
C4⋊1(C4⋊Q8) = C42⋊19Q8φ: C4⋊Q8/C42 → C2 ⊆ Aut C4128C4:1(C4:Q8)128,1600
C4⋊2(C4⋊Q8) = C42⋊7Q8φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C4128C4:2(C4:Q8)128,1283
C4⋊3(C4⋊Q8) = C42.169D4φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C4128C4:3(C4:Q8)128,1278

Non-split extensions G=N.Q with N=C4 and Q=C4⋊Q8
extensionφ:Q→Aut NdρLabelID
C4.1(C4⋊Q8) = C42.58Q8φ: C4⋊Q8/C42 → C2 ⊆ Aut C4128C4.1(C4:Q8)128,576
C4.2(C4⋊Q8) = C42.59Q8φ: C4⋊Q8/C42 → C2 ⊆ Aut C4128C4.2(C4:Q8)128,577
C4.3(C4⋊Q8) = C42.60Q8φ: C4⋊Q8/C42 → C2 ⊆ Aut C4128C4.3(C4:Q8)128,578
C4.4(C4⋊Q8) = C42.26Q8φ: C4⋊Q8/C42 → C2 ⊆ Aut C4128C4.4(C4:Q8)128,579
C4.5(C4⋊Q8) = C16⋊2Q8φ: C4⋊Q8/C42 → C2 ⊆ Aut C4128C4.5(C4:Q8)128,984
C4.6(C4⋊Q8) = C16.5Q8φ: C4⋊Q8/C42 → C2 ⊆ Aut C4128C4.6(C4:Q8)128,985
C4.7(C4⋊Q8) = C16⋊3Q8φ: C4⋊Q8/C42 → C2 ⊆ Aut C4128C4.7(C4:Q8)128,986
C4.8(C4⋊Q8) = C16⋊Q8φ: C4⋊Q8/C42 → C2 ⊆ Aut C4128C4.8(C4:Q8)128,987
C4.9(C4⋊Q8) = C42⋊10Q8φ: C4⋊Q8/C42 → C2 ⊆ Aut C4128C4.9(C4:Q8)128,1392
C4.10(C4⋊Q8) = C43.15C2φ: C4⋊Q8/C42 → C2 ⊆ Aut C4128C4.10(C4:Q8)128,1591
C4.11(C4⋊Q8) = C42⋊18Q8φ: C4⋊Q8/C42 → C2 ⊆ Aut C4128C4.11(C4:Q8)128,1594
C4.12(C4⋊Q8) = C2×C8⋊3Q8φ: C4⋊Q8/C42 → C2 ⊆ Aut C4128C4.12(C4:Q8)128,1889
C4.13(C4⋊Q8) = C2×C8.5Q8φ: C4⋊Q8/C42 → C2 ⊆ Aut C4128C4.13(C4:Q8)128,1890
C4.14(C4⋊Q8) = C2×C8⋊2Q8φ: C4⋊Q8/C42 → C2 ⊆ Aut C4128C4.14(C4:Q8)128,1891
C4.15(C4⋊Q8) = C2×C8⋊Q8φ: C4⋊Q8/C42 → C2 ⊆ Aut C4128C4.15(C4:Q8)128,1893
C4.16(C4⋊Q8) = C42.29Q8φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C4128C4.16(C4:Q8)128,679
C4.17(C4⋊Q8) = C42.30Q8φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C4128C4.17(C4:Q8)128,680
C4.18(C4⋊Q8) = C42.31Q8φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C4128C4.18(C4:Q8)128,681
C4.19(C4⋊Q8) = M4(2).5Q8φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C464C4.19(C4:Q8)128,683
C4.20(C4⋊Q8) = M4(2).6Q8φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C464C4.20(C4:Q8)128,684
C4.21(C4⋊Q8) = C4⋊C4⋊Q8φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C4128C4.21(C4:Q8)128,789
C4.22(C4⋊Q8) = (C2×C8)⋊Q8φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C4128C4.22(C4:Q8)128,790
C4.23(C4⋊Q8) = C2.(C8⋊Q8)φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C4128C4.23(C4:Q8)128,791
C4.24(C4⋊Q8) = M4(2)⋊Q8φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C432C4.24(C4:Q8)128,792
C4.25(C4⋊Q8) = C42⋊3Q8φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C432C4.25(C4:Q8)128,793
C4.26(C4⋊Q8) = C42⋊6Q8φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C4128C4.26(C4:Q8)128,1282
C4.27(C4⋊Q8) = C42.35Q8φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C4128C4.27(C4:Q8)128,1284
C4.28(C4⋊Q8) = M4(2)⋊3Q8φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C464C4.28(C4:Q8)128,1895
C4.29(C4⋊Q8) = M4(2)⋊4Q8φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C464C4.29(C4:Q8)128,1896
C4.30(C4⋊Q8) = C42.121D4φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C4128C4.30(C4:Q8)128,719
C4.31(C4⋊Q8) = C42.122D4φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C4128C4.31(C4:Q8)128,720
C4.32(C4⋊Q8) = C42.123D4φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C4128C4.32(C4:Q8)128,721
C4.33(C4⋊Q8) = M4(2)⋊8Q8φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C464C4.33(C4:Q8)128,729
C4.34(C4⋊Q8) = C42.128D4φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C464C4.34(C4:Q8)128,730
C4.35(C4⋊Q8) = (C2×C4).26D8φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C4128C4.35(C4:Q8)128,818
C4.36(C4⋊Q8) = (C2×C4).21Q16φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C4128C4.36(C4:Q8)128,819
C4.37(C4⋊Q8) = C4.(C4⋊Q8)φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C4128C4.37(C4:Q8)128,820
C4.38(C4⋊Q8) = M4(2).Q8φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C464C4.38(C4:Q8)128,821
C4.39(C4⋊Q8) = M4(2).2Q8φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C464C4.39(C4:Q8)128,822
C4.40(C4⋊Q8) = C42.176D4φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C4128C4.40(C4:Q8)128,1299
C4.41(C4⋊Q8) = C42.181D4φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C4128C4.41(C4:Q8)128,1316
C4.42(C4⋊Q8) = M4(2)⋊5Q8φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C464C4.42(C4:Q8)128,1897
C4.43(C4⋊Q8) = M4(2)⋊6Q8φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C464C4.43(C4:Q8)128,1898
C4.44(C4⋊Q8) = C42⋊9C8central extension (φ=1)128C4.44(C4:Q8)128,574
C4.45(C4⋊Q8) = C42.25Q8central extension (φ=1)128C4.45(C4:Q8)128,575
C4.46(C4⋊Q8) = C42.324D4central extension (φ=1)64C4.46(C4:Q8)128,580
C4.47(C4⋊Q8) = C42.106D4central extension (φ=1)64C4.47(C4:Q8)128,581
C4.48(C4⋊Q8) = C42.61Q8central extension (φ=1)128C4.48(C4:Q8)128,671
C4.49(C4⋊Q8) = C42.27Q8central extension (φ=1)128C4.49(C4:Q8)128,672
C4.50(C4⋊Q8) = C42.62Q8central extension (φ=1)32C4.50(C4:Q8)128,677
C4.51(C4⋊Q8) = C42.28Q8central extension (φ=1)32C4.51(C4:Q8)128,678
C4.52(C4⋊Q8) = C42.327D4central extension (φ=1)128C4.52(C4:Q8)128,716
C4.53(C4⋊Q8) = C42.120D4central extension (φ=1)128C4.53(C4:Q8)128,717
C4.54(C4⋊Q8) = C42⋊16Q8central extension (φ=1)32C4.54(C4:Q8)128,726
C4.55(C4⋊Q8) = C42⋊Q8central extension (φ=1)32C4.55(C4:Q8)128,727
C4.56(C4⋊Q8) = C42⋊5Q8central extension (φ=1)128C4.56(C4:Q8)128,1131
C4.57(C4⋊Q8) = C42.364D4central extension (φ=1)64C4.57(C4:Q8)128,1892
C4.58(C4⋊Q8) = C42.252D4central extension (φ=1)64C4.58(C4:Q8)128,1894

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