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

Direct product G=N×Q with N=C4 and Q=Q8⋊C4
dρLabelID
C4×Q8⋊C4128C4xQ8:C4128,493

Semidirect products G=N:Q with N=C4 and Q=Q8⋊C4
extensionφ:Q→Aut NdρLabelID
C4⋊1(Q8⋊C4) = C42.117D4φ: Q8⋊C4/C4⋊C4 → C2 ⊆ Aut C4128C4:1(Q8:C4)128,713
C4⋊2(Q8⋊C4) = C42.431D4φ: Q8⋊C4/C2×C8 → C2 ⊆ Aut C4128C4:2(Q8:C4)128,688
C4⋊3(Q8⋊C4) = C42.99D4φ: Q8⋊C4/C2×Q8 → C2 ⊆ Aut C4128C4:3(Q8:C4)128,535

Non-split extensions G=N.Q with N=C4 and Q=Q8⋊C4
extensionφ:Q→Aut NdρLabelID
C4.1(Q8⋊C4) = C8.16Q16φ: Q8⋊C4/C4⋊C4 → C2 ⊆ Aut C4128C4.1(Q8:C4)128,95
C4.2(Q8⋊C4) = C4.10D16φ: Q8⋊C4/C4⋊C4 → C2 ⊆ Aut C4128C4.2(Q8:C4)128,96
C4.3(Q8⋊C4) = C4.6Q32φ: Q8⋊C4/C4⋊C4 → C2 ⊆ Aut C4128C4.3(Q8:C4)128,97
C4.4(Q8⋊C4) = C8.1Q16φ: Q8⋊C4/C4⋊C4 → C2 ⊆ Aut C4324C4.4(Q8:C4)128,98
C4.5(Q8⋊C4) = C8.11C42φ: Q8⋊C4/C4⋊C4 → C2 ⊆ Aut C432C4.5(Q8:C4)128,115
C4.6(Q8⋊C4) = C23.9D8φ: Q8⋊C4/C4⋊C4 → C2 ⊆ Aut C4324C4.6(Q8:C4)128,116
C4.7(Q8⋊C4) = C8.C42φ: Q8⋊C4/C4⋊C4 → C2 ⊆ Aut C432C4.7(Q8:C4)128,118
C4.8(Q8⋊C4) = C8.4C42φ: Q8⋊C4/C4⋊C4 → C2 ⊆ Aut C4324C4.8(Q8:C4)128,121
C4.9(Q8⋊C4) = C42.46D4φ: Q8⋊C4/C4⋊C4 → C2 ⊆ Aut C464C4.9(Q8:C4)128,213
C4.10(Q8⋊C4) = C2×C4.10D8φ: Q8⋊C4/C4⋊C4 → C2 ⊆ Aut C4128C4.10(Q8:C4)128,271
C4.11(Q8⋊C4) = C2×C4.6Q16φ: Q8⋊C4/C4⋊C4 → C2 ⊆ Aut C4128C4.11(Q8:C4)128,273
C4.12(Q8⋊C4) = C42.121D4φ: Q8⋊C4/C4⋊C4 → C2 ⊆ Aut C4128C4.12(Q8:C4)128,719
C4.13(Q8⋊C4) = C8.7C42φ: Q8⋊C4/C2×C8 → C2 ⊆ Aut C4128C4.13(Q8:C4)128,112
C4.14(Q8⋊C4) = C8.9C42φ: Q8⋊C4/C2×C8 → C2 ⊆ Aut C464C4.14(Q8:C4)128,114
C4.15(Q8⋊C4) = C8.2C42φ: Q8⋊C4/C2×C8 → C2 ⊆ Aut C464C4.15(Q8:C4)128,119
C4.16(Q8⋊C4) = C42.316D4φ: Q8⋊C4/C2×C8 → C2 ⊆ Aut C464C4.16(Q8:C4)128,225
C4.17(Q8⋊C4) = C42.415D4φ: Q8⋊C4/C2×C8 → C2 ⊆ Aut C464C4.17(Q8:C4)128,280
C4.18(Q8⋊C4) = C42.416D4φ: Q8⋊C4/C2×C8 → C2 ⊆ Aut C464C4.18(Q8:C4)128,281
C4.19(Q8⋊C4) = C42.436D4φ: Q8⋊C4/C2×C8 → C2 ⊆ Aut C4128C4.19(Q8:C4)128,722
C4.20(Q8⋊C4) = C42.5Q8φ: Q8⋊C4/C2×Q8 → C2 ⊆ Aut C432C4.20(Q8:C4)128,18
C4.21(Q8⋊C4) = C42.27D4φ: Q8⋊C4/C2×Q8 → C2 ⊆ Aut C464C4.21(Q8:C4)128,24
C4.22(Q8⋊C4) = C42.8Q8φ: Q8⋊C4/C2×Q8 → C2 ⊆ Aut C4128C4.22(Q8:C4)128,28
C4.23(Q8⋊C4) = C42.389D4φ: Q8⋊C4/C2×Q8 → C2 ⊆ Aut C464C4.23(Q8:C4)128,33
C4.24(Q8⋊C4) = Q8⋊M4(2)φ: Q8⋊C4/C2×Q8 → C2 ⊆ Aut C464C4.24(Q8:C4)128,219
C4.25(Q8⋊C4) = C42.62D4φ: Q8⋊C4/C2×Q8 → C2 ⊆ Aut C432C4.25(Q8:C4)128,250
C4.26(Q8⋊C4) = C42.79D4φ: Q8⋊C4/C2×Q8 → C2 ⊆ Aut C464C4.26(Q8:C4)128,282
C4.27(Q8⋊C4) = C42.385D4central extension (φ=1)128C4.27(Q8:C4)128,9
C4.28(Q8⋊C4) = C42.46Q8central extension (φ=1)128C4.28(Q8:C4)128,11
C4.29(Q8⋊C4) = C42.10Q8central extension (φ=1)32C4.29(Q8:C4)128,35
C4.30(Q8⋊C4) = Q8⋊C16central extension (φ=1)128C4.30(Q8:C4)128,69
C4.31(Q8⋊C4) = C8.17Q16central extension (φ=1)128C4.31(Q8:C4)128,70
C4.32(Q8⋊C4) = C2×Q8⋊C8central extension (φ=1)128C4.32(Q8:C4)128,207
C4.33(Q8⋊C4) = C42.404D4central extension (φ=1)32C4.33(Q8:C4)128,235
C4.34(Q8⋊C4) = C42.410D4central extension (φ=1)64C4.34(Q8:C4)128,274

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