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Extensions 1→N→G→Q→1 with N=C4 and Q=C23×C4

Direct product G=N×Q with N=C4 and Q=C23×C4
dρLabelID
C23×C42128C2^3xC4^2128,2150

Semidirect products G=N:Q with N=C4 and Q=C23×C4
extensionφ:Q→Aut NdρLabelID
C4⋊1(C23×C4) = D4×C22×C4φ: C23×C4/C22×C4 → C2 ⊆ Aut C464C4:1(C2^3xC4)128,2154
C4⋊2(C23×C4) = C23×C4⋊C4φ: C23×C4/C24 → C2 ⊆ Aut C4128C4:2(C2^3xC4)128,2152

Non-split extensions G=N.Q with N=C4 and Q=C23×C4
extensionφ:Q→Aut NdρLabelID
C4.1(C23×C4) = C22×D4⋊C4φ: C23×C4/C22×C4 → C2 ⊆ Aut C464C4.1(C2^3xC4)128,1622
C4.2(C23×C4) = C22×Q8⋊C4φ: C23×C4/C22×C4 → C2 ⊆ Aut C4128C4.2(C2^3xC4)128,1623
C4.3(C23×C4) = C2×C23.24D4φ: C23×C4/C22×C4 → C2 ⊆ Aut C464C4.3(C2^3xC4)128,1624
C4.4(C23×C4) = C2×C23.37D4φ: C23×C4/C22×C4 → C2 ⊆ Aut C432C4.4(C2^3xC4)128,1625
C4.5(C23×C4) = C2×C23.38D4φ: C23×C4/C22×C4 → C2 ⊆ Aut C464C4.5(C2^3xC4)128,1626
C4.6(C23×C4) = C2×C23.36D4φ: C23×C4/C22×C4 → C2 ⊆ Aut C464C4.6(C2^3xC4)128,1627
C4.7(C23×C4) = C24.98D4φ: C23×C4/C22×C4 → C2 ⊆ Aut C432C4.7(C2^3xC4)128,1628
C4.8(C23×C4) = 2+ 1+4⋊5C4φ: C23×C4/C22×C4 → C2 ⊆ Aut C432C4.8(C2^3xC4)128,1629
C4.9(C23×C4) = 2- 1+4⋊4C4φ: C23×C4/C22×C4 → C2 ⊆ Aut C464C4.9(C2^3xC4)128,1630
C4.10(C23×C4) = C22×C4≀C2φ: C23×C4/C22×C4 → C2 ⊆ Aut C432C4.10(C2^3xC4)128,1631
C4.11(C23×C4) = C2×C42⋊C22φ: C23×C4/C22×C4 → C2 ⊆ Aut C432C4.11(C2^3xC4)128,1632
C4.12(C23×C4) = 2- 1+4⋊5C4φ: C23×C4/C22×C4 → C2 ⊆ Aut C4164C4.12(C2^3xC4)128,1633
C4.13(C23×C4) = C2×C4×D8φ: C23×C4/C22×C4 → C2 ⊆ Aut C464C4.13(C2^3xC4)128,1668
C4.14(C23×C4) = C2×C4×SD16φ: C23×C4/C22×C4 → C2 ⊆ Aut C464C4.14(C2^3xC4)128,1669
C4.15(C23×C4) = C2×C4×Q16φ: C23×C4/C22×C4 → C2 ⊆ Aut C4128C4.15(C2^3xC4)128,1670
C4.16(C23×C4) = C4×C4○D8φ: C23×C4/C22×C4 → C2 ⊆ Aut C464C4.16(C2^3xC4)128,1671
C4.17(C23×C4) = C2×SD16⋊C4φ: C23×C4/C22×C4 → C2 ⊆ Aut C464C4.17(C2^3xC4)128,1672
C4.18(C23×C4) = C2×Q16⋊C4φ: C23×C4/C22×C4 → C2 ⊆ Aut C4128C4.18(C2^3xC4)128,1673
C4.19(C23×C4) = C2×D8⋊C4φ: C23×C4/C22×C4 → C2 ⊆ Aut C464C4.19(C2^3xC4)128,1674
C4.20(C23×C4) = C42.383D4φ: C23×C4/C22×C4 → C2 ⊆ Aut C464C4.20(C2^3xC4)128,1675
C4.21(C23×C4) = C4×C8⋊C22φ: C23×C4/C22×C4 → C2 ⊆ Aut C432C4.21(C2^3xC4)128,1676
C4.22(C23×C4) = C4×C8.C22φ: C23×C4/C22×C4 → C2 ⊆ Aut C464C4.22(C2^3xC4)128,1677
C4.23(C23×C4) = C42.275C23φ: C23×C4/C22×C4 → C2 ⊆ Aut C432C4.23(C2^3xC4)128,1678
C4.24(C23×C4) = C42.276C23φ: C23×C4/C22×C4 → C2 ⊆ Aut C464C4.24(C2^3xC4)128,1679
C4.25(C23×C4) = C42.277C23φ: C23×C4/C22×C4 → C2 ⊆ Aut C432C4.25(C2^3xC4)128,1680
C4.26(C23×C4) = C42.278C23φ: C23×C4/C22×C4 → C2 ⊆ Aut C432C4.26(C2^3xC4)128,1681
C4.27(C23×C4) = C42.279C23φ: C23×C4/C22×C4 → C2 ⊆ Aut C464C4.27(C2^3xC4)128,1682
C4.28(C23×C4) = C42.280C23φ: C23×C4/C22×C4 → C2 ⊆ Aut C464C4.28(C2^3xC4)128,1683
C4.29(C23×C4) = C42.281C23φ: C23×C4/C22×C4 → C2 ⊆ Aut C464C4.29(C2^3xC4)128,1684
C4.30(C23×C4) = C2×C8○D8φ: C23×C4/C22×C4 → C2 ⊆ Aut C432C4.30(C2^3xC4)128,1685
C4.31(C23×C4) = C2×C8.26D4φ: C23×C4/C22×C4 → C2 ⊆ Aut C432C4.31(C2^3xC4)128,1686
C4.32(C23×C4) = C42.283C23φ: C23×C4/C22×C4 → C2 ⊆ Aut C4324C4.32(C2^3xC4)128,1687
C4.33(C23×C4) = M4(2).51D4φ: C23×C4/C22×C4 → C2 ⊆ Aut C4164C4.33(C2^3xC4)128,1688
C4.34(C23×C4) = M4(2)○D8φ: C23×C4/C22×C4 → C2 ⊆ Aut C4324C4.34(C2^3xC4)128,1689
C4.35(C23×C4) = Q8×C22×C4φ: C23×C4/C22×C4 → C2 ⊆ Aut C4128C4.35(C2^3xC4)128,2155
C4.36(C23×C4) = C2×C4×C4○D4φ: C23×C4/C22×C4 → C2 ⊆ Aut C464C4.36(C2^3xC4)128,2156
C4.37(C23×C4) = C2×C22.11C24φ: C23×C4/C22×C4 → C2 ⊆ Aut C432C4.37(C2^3xC4)128,2157
C4.38(C23×C4) = C2×C23.32C23φ: C23×C4/C22×C4 → C2 ⊆ Aut C464C4.38(C2^3xC4)128,2158
C4.39(C23×C4) = C2×C23.33C23φ: C23×C4/C22×C4 → C2 ⊆ Aut C464C4.39(C2^3xC4)128,2159
C4.40(C23×C4) = C22.14C25φ: C23×C4/C22×C4 → C2 ⊆ Aut C432C4.40(C2^3xC4)128,2160
C4.41(C23×C4) = C4×2+ 1+4φ: C23×C4/C22×C4 → C2 ⊆ Aut C432C4.41(C2^3xC4)128,2161
C4.42(C23×C4) = C4×2- 1+4φ: C23×C4/C22×C4 → C2 ⊆ Aut C464C4.42(C2^3xC4)128,2162
C4.43(C23×C4) = C2×Q8○M4(2)φ: C23×C4/C22×C4 → C2 ⊆ Aut C432C4.43(C2^3xC4)128,2304
C4.44(C23×C4) = C4.22C25φ: C23×C4/C22×C4 → C2 ⊆ Aut C4324C4.44(C2^3xC4)128,2305
C4.45(C23×C4) = C22×C4.Q8φ: C23×C4/C24 → C2 ⊆ Aut C4128C4.45(C2^3xC4)128,1639
C4.46(C23×C4) = C22×C2.D8φ: C23×C4/C24 → C2 ⊆ Aut C4128C4.46(C2^3xC4)128,1640
C4.47(C23×C4) = C2×C23.25D4φ: C23×C4/C24 → C2 ⊆ Aut C464C4.47(C2^3xC4)128,1641
C4.48(C23×C4) = C2×M4(2)⋊C4φ: C23×C4/C24 → C2 ⊆ Aut C464C4.48(C2^3xC4)128,1642
C4.49(C23×C4) = C24.100D4φ: C23×C4/C24 → C2 ⊆ Aut C432C4.49(C2^3xC4)128,1643
C4.50(C23×C4) = C4○D4.7Q8φ: C23×C4/C24 → C2 ⊆ Aut C464C4.50(C2^3xC4)128,1644
C4.51(C23×C4) = C4○D4.8Q8φ: C23×C4/C24 → C2 ⊆ Aut C464C4.51(C2^3xC4)128,1645
C4.52(C23×C4) = C22×C8.C4φ: C23×C4/C24 → C2 ⊆ Aut C464C4.52(C2^3xC4)128,1646
C4.53(C23×C4) = C2×M4(2).C4φ: C23×C4/C24 → C2 ⊆ Aut C432C4.53(C2^3xC4)128,1647
C4.54(C23×C4) = M4(2).29C23φ: C23×C4/C24 → C2 ⊆ Aut C4324C4.54(C2^3xC4)128,1648
C4.55(C23×C4) = C23×M4(2)φ: C23×C4/C24 → C2 ⊆ Aut C464C4.55(C2^3xC4)128,2302
C4.56(C23×C4) = C22×C8⋊C4central extension (φ=1)128C4.56(C2^3xC4)128,1602
C4.57(C23×C4) = C2×C4×M4(2)central extension (φ=1)64C4.57(C2^3xC4)128,1603
C4.58(C23×C4) = C2×C8○2M4(2)central extension (φ=1)64C4.58(C2^3xC4)128,1604
C4.59(C23×C4) = M4(2)○2M4(2)central extension (φ=1)32C4.59(C2^3xC4)128,1605
C4.60(C23×C4) = C4×C8○D4central extension (φ=1)64C4.60(C2^3xC4)128,1606
C4.61(C23×C4) = D4.5C42central extension (φ=1)64C4.61(C2^3xC4)128,1607
C4.62(C23×C4) = C22×M5(2)central extension (φ=1)64C4.62(C2^3xC4)128,2137
C4.63(C23×C4) = C2×D4○C16central extension (φ=1)64C4.63(C2^3xC4)128,2138
C4.64(C23×C4) = Q8○M5(2)central extension (φ=1)324C4.64(C2^3xC4)128,2139
C4.65(C23×C4) = C22×C42⋊C2central extension (φ=1)64C4.65(C2^3xC4)128,2153
C4.66(C23×C4) = C22×C8○D4central extension (φ=1)64C4.66(C2^3xC4)128,2303

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