# Extensions 1→N→G→Q→1 with N=D4 and Q=C2×Q8

Direct product G=N×Q with N=D4 and Q=C2×Q8
dρLabelID
C2×D4×Q864C2xD4xQ8128,2198

Semidirect products G=N:Q with N=D4 and Q=C2×Q8
extensionφ:Q→Out NdρLabelID
D41(C2×Q8) = C2×D4⋊Q8φ: C2×Q8/C2×C4C2 ⊆ Out D464D4:1(C2xQ8)128,1802
D42(C2×Q8) = C2×D42Q8φ: C2×Q8/C2×C4C2 ⊆ Out D464D4:2(C2xQ8)128,1803
D43(C2×Q8) = C42.448D4φ: C2×Q8/C2×C4C2 ⊆ Out D464D4:3(C2xQ8)128,1811
D44(C2×Q8) = Q8×D8φ: C2×Q8/Q8C2 ⊆ Out D464D4:4(C2xQ8)128,2110
D45(C2×Q8) = D84Q8φ: C2×Q8/Q8C2 ⊆ Out D464D4:5(C2xQ8)128,2116
D46(C2×Q8) = C2×D43Q8φ: trivial image64D4:6(C2xQ8)128,2204
D47(C2×Q8) = Q8×C4○D4φ: trivial image64D4:7(C2xQ8)128,2210
D48(C2×Q8) = C22.90C25φ: trivial image32D4:8(C2xQ8)128,2233
D49(C2×Q8) = C22.92C25φ: trivial image64D4:9(C2xQ8)128,2235

Non-split extensions G=N.Q with N=D4 and Q=C2×Q8
extensionφ:Q→Out NdρLabelID
D4.1(C2×Q8) = C2×D4.Q8φ: C2×Q8/C2×C4C2 ⊆ Out D464D4.1(C2xQ8)128,1804
D4.2(C2×Q8) = C42.447D4φ: C2×Q8/C2×C4C2 ⊆ Out D464D4.2(C2xQ8)128,1808
D4.3(C2×Q8) = C42.219D4φ: C2×Q8/C2×C4C2 ⊆ Out D432D4.3(C2xQ8)128,1809
D4.4(C2×Q8) = C42.449D4φ: C2×Q8/C2×C4C2 ⊆ Out D464D4.4(C2xQ8)128,1812
D4.5(C2×Q8) = C42.20C23φ: C2×Q8/C2×C4C2 ⊆ Out D432D4.5(C2xQ8)128,1813
D4.6(C2×Q8) = C42.22C23φ: C2×Q8/C2×C4C2 ⊆ Out D464D4.6(C2xQ8)128,1815
D4.7(C2×Q8) = C42.23C23φ: C2×Q8/C2×C4C2 ⊆ Out D464D4.7(C2xQ8)128,1816
D4.8(C2×Q8) = Q8×SD16φ: C2×Q8/Q8C2 ⊆ Out D464D4.8(C2xQ8)128,2111
D4.9(C2×Q8) = D86Q8φ: C2×Q8/Q8C2 ⊆ Out D464D4.9(C2xQ8)128,2112
D4.10(C2×Q8) = SD164Q8φ: C2×Q8/Q8C2 ⊆ Out D464D4.10(C2xQ8)128,2113
D4.11(C2×Q8) = SD16⋊Q8φ: C2×Q8/Q8C2 ⊆ Out D464D4.11(C2xQ8)128,2117
D4.12(C2×Q8) = SD162Q8φ: C2×Q8/Q8C2 ⊆ Out D464D4.12(C2xQ8)128,2118
D4.13(C2×Q8) = SD163Q8φ: C2×Q8/Q8C2 ⊆ Out D464D4.13(C2xQ8)128,2120
D4.14(C2×Q8) = D85Q8φ: C2×Q8/Q8C2 ⊆ Out D464D4.14(C2xQ8)128,2121
D4.15(C2×Q8) = C22.93C25φ: trivial image64D4.15(C2xQ8)128,2236

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