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

Direct product G=N×Q with N=Q8 and Q=C22×C4
dρLabelID
Q8×C22×C4128Q8xC2^2xC4128,2155

Semidirect products G=N:Q with N=Q8 and Q=C22×C4
extensionφ:Q→Out NdρLabelID
Q81(C22×C4) = C2×C4×SD16φ: C22×C4/C2×C4C2 ⊆ Out Q864Q8:1(C2^2xC4)128,1669
Q82(C22×C4) = C2×SD16⋊C4φ: C22×C4/C2×C4C2 ⊆ Out Q864Q8:2(C2^2xC4)128,1672
Q83(C22×C4) = C4×C8⋊C22φ: C22×C4/C2×C4C2 ⊆ Out Q832Q8:3(C2^2xC4)128,1676
Q84(C22×C4) = C22×Q8⋊C4φ: C22×C4/C23C2 ⊆ Out Q8128Q8:4(C2^2xC4)128,1623
Q85(C22×C4) = C2×C23.36D4φ: C22×C4/C23C2 ⊆ Out Q864Q8:5(C2^2xC4)128,1627
Q86(C22×C4) = C22×C4≀C2φ: C22×C4/C23C2 ⊆ Out Q832Q8:6(C2^2xC4)128,1631
Q87(C22×C4) = C2×C4×C4○D4φ: trivial image64Q8:7(C2^2xC4)128,2156
Q88(C22×C4) = C2×C23.33C23φ: trivial image64Q8:8(C2^2xC4)128,2159
Q89(C22×C4) = C4×2+ 1+4φ: trivial image32Q8:9(C2^2xC4)128,2161

Non-split extensions G=N.Q with N=Q8 and Q=C22×C4
extensionφ:Q→Out NdρLabelID
Q8.1(C22×C4) = C2×C4×Q16φ: C22×C4/C2×C4C2 ⊆ Out Q8128Q8.1(C2^2xC4)128,1670
Q8.2(C22×C4) = C4×C4○D8φ: C22×C4/C2×C4C2 ⊆ Out Q864Q8.2(C2^2xC4)128,1671
Q8.3(C22×C4) = C2×Q16⋊C4φ: C22×C4/C2×C4C2 ⊆ Out Q8128Q8.3(C2^2xC4)128,1673
Q8.4(C22×C4) = C42.383D4φ: C22×C4/C2×C4C2 ⊆ Out Q864Q8.4(C2^2xC4)128,1675
Q8.5(C22×C4) = C4×C8.C22φ: C22×C4/C2×C4C2 ⊆ Out Q864Q8.5(C2^2xC4)128,1677
Q8.6(C22×C4) = C42.275C23φ: C22×C4/C2×C4C2 ⊆ Out Q832Q8.6(C2^2xC4)128,1678
Q8.7(C22×C4) = C42.276C23φ: C22×C4/C2×C4C2 ⊆ Out Q864Q8.7(C2^2xC4)128,1679
Q8.8(C22×C4) = C42.278C23φ: C22×C4/C2×C4C2 ⊆ Out Q832Q8.8(C2^2xC4)128,1681
Q8.9(C22×C4) = C42.279C23φ: C22×C4/C2×C4C2 ⊆ Out Q864Q8.9(C2^2xC4)128,1682
Q8.10(C22×C4) = C42.280C23φ: C22×C4/C2×C4C2 ⊆ Out Q864Q8.10(C2^2xC4)128,1683
Q8.11(C22×C4) = C42.281C23φ: C22×C4/C2×C4C2 ⊆ Out Q864Q8.11(C2^2xC4)128,1684
Q8.12(C22×C4) = C2×C8○D8φ: C22×C4/C2×C4C2 ⊆ Out Q832Q8.12(C2^2xC4)128,1685
Q8.13(C22×C4) = C2×C8.26D4φ: C22×C4/C2×C4C2 ⊆ Out Q832Q8.13(C2^2xC4)128,1686
Q8.14(C22×C4) = C42.283C23φ: C22×C4/C2×C4C2 ⊆ Out Q8324Q8.14(C2^2xC4)128,1687
Q8.15(C22×C4) = M4(2).51D4φ: C22×C4/C2×C4C2 ⊆ Out Q8164Q8.15(C2^2xC4)128,1688
Q8.16(C22×C4) = M4(2)○D8φ: C22×C4/C2×C4C2 ⊆ Out Q8324Q8.16(C2^2xC4)128,1689
Q8.17(C22×C4) = C2×C23.24D4φ: C22×C4/C23C2 ⊆ Out Q864Q8.17(C2^2xC4)128,1624
Q8.18(C22×C4) = C2×C23.38D4φ: C22×C4/C23C2 ⊆ Out Q864Q8.18(C2^2xC4)128,1626
Q8.19(C22×C4) = C24.98D4φ: C22×C4/C23C2 ⊆ Out Q832Q8.19(C2^2xC4)128,1628
Q8.20(C22×C4) = 2+ 1+45C4φ: C22×C4/C23C2 ⊆ Out Q832Q8.20(C2^2xC4)128,1629
Q8.21(C22×C4) = 2- 1+44C4φ: C22×C4/C23C2 ⊆ Out Q864Q8.21(C2^2xC4)128,1630
Q8.22(C22×C4) = C2×C42⋊C22φ: C22×C4/C23C2 ⊆ Out Q832Q8.22(C2^2xC4)128,1632
Q8.23(C22×C4) = 2- 1+45C4φ: C22×C4/C23C2 ⊆ Out Q8164Q8.23(C2^2xC4)128,1633
Q8.24(C22×C4) = C2×C23.32C23φ: trivial image64Q8.24(C2^2xC4)128,2158
Q8.25(C22×C4) = C22.14C25φ: trivial image32Q8.25(C2^2xC4)128,2160
Q8.26(C22×C4) = C4×2- 1+4φ: trivial image64Q8.26(C2^2xC4)128,2162
Q8.27(C22×C4) = C22×C8○D4φ: trivial image64Q8.27(C2^2xC4)128,2303
Q8.28(C22×C4) = C2×Q8○M4(2)φ: trivial image32Q8.28(C2^2xC4)128,2304
Q8.29(C22×C4) = C4.22C25φ: trivial image324Q8.29(C2^2xC4)128,2305

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