# Extensions 1→N→G→Q→1 with N=C4 and Q=C2×C8

Direct product G=N×Q with N=C4 and Q=C2×C8
dρLabelID
C2×C4×C864C2xC4xC864,83

Semidirect products G=N:Q with N=C4 and Q=C2×C8
extensionφ:Q→Aut NdρLabelID
C41(C2×C8) = C8×D4φ: C2×C8/C8C2 ⊆ Aut C432C4:1(C2xC8)64,115
C42(C2×C8) = C2×C4⋊C8φ: C2×C8/C2×C4C2 ⊆ Aut C464C4:2(C2xC8)64,103

Non-split extensions G=N.Q with N=C4 and Q=C2×C8
extensionφ:Q→Aut NdρLabelID
C4.1(C2×C8) = D4⋊C8φ: C2×C8/C8C2 ⊆ Aut C432C4.1(C2xC8)64,6
C4.2(C2×C8) = Q8⋊C8φ: C2×C8/C8C2 ⊆ Aut C464C4.2(C2xC8)64,7
C4.3(C2×C8) = D4.C8φ: C2×C8/C8C2 ⊆ Aut C4322C4.3(C2xC8)64,31
C4.4(C2×C8) = C8×Q8φ: C2×C8/C8C2 ⊆ Aut C464C4.4(C2xC8)64,126
C4.5(C2×C8) = D4○C16φ: C2×C8/C8C2 ⊆ Aut C4322C4.5(C2xC8)64,185
C4.6(C2×C8) = C82C8φ: C2×C8/C2×C4C2 ⊆ Aut C464C4.6(C2xC8)64,15
C4.7(C2×C8) = C81C8φ: C2×C8/C2×C4C2 ⊆ Aut C464C4.7(C2xC8)64,16
C4.8(C2×C8) = C8.C8φ: C2×C8/C2×C4C2 ⊆ Aut C4162C4.8(C2xC8)64,45
C4.9(C2×C8) = C42.12C4φ: C2×C8/C2×C4C2 ⊆ Aut C432C4.9(C2xC8)64,112
C4.10(C2×C8) = C2×M5(2)φ: C2×C8/C2×C4C2 ⊆ Aut C432C4.10(C2xC8)64,184
C4.11(C2×C8) = C8⋊C8central extension (φ=1)64C4.11(C2xC8)64,3
C4.12(C2×C8) = C165C4central extension (φ=1)64C4.12(C2xC8)64,27
C4.13(C2×C8) = M6(2)central extension (φ=1)322C4.13(C2xC8)64,51

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