# Extensions 1→N→G→Q→1 with N=C22 and Q=C2×M4(2)

Direct product G=N×Q with N=C22 and Q=C2×M4(2)
dρLabelID
C23×M4(2)64C2^3xM4(2)128,2302

Semidirect products G=N:Q with N=C22 and Q=C2×M4(2)
extensionφ:Q→Aut NdρLabelID
C221(C2×M4(2)) = C2×C89D4φ: C2×M4(2)/C2×C8C2 ⊆ Aut C2264C2^2:1(C2xM4(2))128,1659
C222(C2×M4(2)) = D4×M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C2232C2^2:2(C2xM4(2))128,1666
C223(C2×M4(2)) = C2×C24.4C4φ: C2×M4(2)/C22×C4C2 ⊆ Aut C2232C2^2:3(C2xM4(2))128,1609

Non-split extensions G=N.Q with N=C22 and Q=C2×M4(2)
extensionφ:Q→Aut NdρLabelID
C22.1(C2×M4(2)) = C2×D4.C8φ: C2×M4(2)/C2×C8C2 ⊆ Aut C2264C2^2.1(C2xM4(2))128,848
C22.2(C2×M4(2)) = M5(2)⋊12C22φ: C2×M4(2)/C2×C8C2 ⊆ Aut C22324C2^2.2(C2xM4(2))128,849
C22.3(C2×M4(2)) = C42.290C23φ: C2×M4(2)/C2×C8C2 ⊆ Aut C2264C2^2.3(C2xM4(2))128,1697
C22.4(C2×M4(2)) = C233M4(2)φ: C2×M4(2)/C2×C8C2 ⊆ Aut C2232C2^2.4(C2xM4(2))128,1705
C22.5(C2×M4(2)) = C42.698C23φ: C2×M4(2)/C2×C8C2 ⊆ Aut C2264C2^2.5(C2xM4(2))128,1721
C22.6(C2×M4(2)) = D46M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C2264C2^2.6(C2xM4(2))128,1702
C22.7(C2×M4(2)) = D47M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C2232C2^2.7(C2xM4(2))128,1706
C22.8(C2×M4(2)) = D48M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C2264C2^2.8(C2xM4(2))128,1722
C22.9(C2×M4(2)) = C2×C23⋊C8φ: C2×M4(2)/C22×C4C2 ⊆ Aut C2232C2^2.9(C2xM4(2))128,188
C22.10(C2×M4(2)) = C2×C22.M4(2)φ: C2×M4(2)/C22×C4C2 ⊆ Aut C2264C2^2.10(C2xM4(2))128,189
C22.11(C2×M4(2)) = C42.371D4φ: C2×M4(2)/C22×C4C2 ⊆ Aut C2232C2^2.11(C2xM4(2))128,190
C22.12(C2×M4(2)) = C23.8M4(2)φ: C2×M4(2)/C22×C4C2 ⊆ Aut C2232C2^2.12(C2xM4(2))128,191
C22.13(C2×M4(2)) = C42.393D4φ: C2×M4(2)/C22×C4C2 ⊆ Aut C2232C2^2.13(C2xM4(2))128,192
C22.14(C2×M4(2)) = C42.394D4φ: C2×M4(2)/C22×C4C2 ⊆ Aut C2264C2^2.14(C2xM4(2))128,193
C22.15(C2×M4(2)) = C25.3C4φ: C2×M4(2)/C22×C4C2 ⊆ Aut C2216C2^2.15(C2xM4(2))128,194
C22.16(C2×M4(2)) = (C2×C4)⋊M4(2)φ: C2×M4(2)/C22×C4C2 ⊆ Aut C2232C2^2.16(C2xM4(2))128,195
C22.17(C2×M4(2)) = C42.42D4φ: C2×M4(2)/C22×C4C2 ⊆ Aut C2232C2^2.17(C2xM4(2))128,196
C22.18(C2×M4(2)) = C23⋊M4(2)φ: C2×M4(2)/C22×C4C2 ⊆ Aut C2232C2^2.18(C2xM4(2))128,197
C22.19(C2×M4(2)) = C42.43D4φ: C2×M4(2)/C22×C4C2 ⊆ Aut C2232C2^2.19(C2xM4(2))128,198
C22.20(C2×M4(2)) = C42.44D4φ: C2×M4(2)/C22×C4C2 ⊆ Aut C2264C2^2.20(C2xM4(2))128,199
C22.21(C2×M4(2)) = C2×C16⋊C4φ: C2×M4(2)/C22×C4C2 ⊆ Aut C2232C2^2.21(C2xM4(2))128,841
C22.22(C2×M4(2)) = C8.23C42φ: C2×M4(2)/C22×C4C2 ⊆ Aut C22324C2^2.22(C2xM4(2))128,842
C22.23(C2×M4(2)) = C2×C8.C8φ: C2×M4(2)/C22×C4C2 ⊆ Aut C2232C2^2.23(C2xM4(2))128,884
C22.24(C2×M4(2)) = M4(2).1C8φ: C2×M4(2)/C22×C4C2 ⊆ Aut C22324C2^2.24(C2xM4(2))128,885
C22.25(C2×M4(2)) = C8.5M4(2)φ: C2×M4(2)/C22×C4C2 ⊆ Aut C22164C2^2.25(C2xM4(2))128,897
C22.26(C2×M4(2)) = C8.19M4(2)φ: C2×M4(2)/C22×C4C2 ⊆ Aut C22324C2^2.26(C2xM4(2))128,898
C22.27(C2×M4(2)) = C2×C42.6C4φ: C2×M4(2)/C22×C4C2 ⊆ Aut C2264C2^2.27(C2xM4(2))128,1650
C22.28(C2×M4(2)) = C42.677C23φ: C2×M4(2)/C22×C4C2 ⊆ Aut C2232C2^2.28(C2xM4(2))128,1652
C22.29(C2×M4(2)) = C42.693C23φ: C2×M4(2)/C22×C4C2 ⊆ Aut C2232C2^2.29(C2xM4(2))128,1707
C22.30(C2×M4(2)) = C42.302C23φ: C2×M4(2)/C22×C4C2 ⊆ Aut C2264C2^2.30(C2xM4(2))128,1715
C22.31(C2×M4(2)) = C4×C8⋊C4central extension (φ=1)128C2^2.31(C2xM4(2))128,457
C22.32(C2×M4(2)) = C2×C22.7C42central extension (φ=1)128C2^2.32(C2xM4(2))128,459
C22.33(C2×M4(2)) = C23.28C42central extension (φ=1)64C2^2.33(C2xM4(2))128,460
C22.34(C2×M4(2)) = C424C8central extension (φ=1)128C2^2.34(C2xM4(2))128,476
C22.35(C2×M4(2)) = C43.C2central extension (φ=1)128C2^2.35(C2xM4(2))128,477
C22.36(C2×M4(2)) = C4×C22⋊C8central extension (φ=1)64C2^2.36(C2xM4(2))128,480
C22.37(C2×M4(2)) = C42.378D4central extension (φ=1)64C2^2.37(C2xM4(2))128,481
C22.38(C2×M4(2)) = C23.36C42central extension (φ=1)64C2^2.38(C2xM4(2))128,484
C22.39(C2×M4(2)) = C23.17C42central extension (φ=1)64C2^2.39(C2xM4(2))128,485
C22.40(C2×M4(2)) = C4×C4⋊C8central extension (φ=1)128C2^2.40(C2xM4(2))128,498
C22.41(C2×M4(2)) = C43.7C2central extension (φ=1)128C2^2.41(C2xM4(2))128,499
C22.42(C2×M4(2)) = C4⋊C813C4central extension (φ=1)128C2^2.42(C2xM4(2))128,502
C22.43(C2×M4(2)) = C4⋊C814C4central extension (φ=1)128C2^2.43(C2xM4(2))128,503
C22.44(C2×M4(2)) = C243C8central extension (φ=1)32C2^2.44(C2xM4(2))128,511
C22.45(C2×M4(2)) = C42.425D4central extension (φ=1)64C2^2.45(C2xM4(2))128,529
C22.46(C2×M4(2)) = C23.32M4(2)central extension (φ=1)64C2^2.46(C2xM4(2))128,549
C22.47(C2×M4(2)) = C428C8central extension (φ=1)128C2^2.47(C2xM4(2))128,563
C22.48(C2×M4(2)) = C425C8central extension (φ=1)128C2^2.48(C2xM4(2))128,571
C22.49(C2×M4(2)) = C429C8central extension (φ=1)128C2^2.49(C2xM4(2))128,574
C22.50(C2×M4(2)) = C23.21M4(2)central extension (φ=1)64C2^2.50(C2xM4(2))128,582
C22.51(C2×M4(2)) = C23.22M4(2)central extension (φ=1)64C2^2.51(C2xM4(2))128,601
C22.52(C2×M4(2)) = C4⋊C43C8central extension (φ=1)128C2^2.52(C2xM4(2))128,648
C22.53(C2×M4(2)) = C22⋊C44C8central extension (φ=1)64C2^2.53(C2xM4(2))128,655
C22.54(C2×M4(2)) = C42.61Q8central extension (φ=1)128C2^2.54(C2xM4(2))128,671
C22.55(C2×M4(2)) = C42.325D4central extension (φ=1)64C2^2.55(C2xM4(2))128,686
C22.56(C2×M4(2)) = C42.327D4central extension (φ=1)128C2^2.56(C2xM4(2))128,716
C22.57(C2×M4(2)) = C22×C8⋊C4central extension (φ=1)128C2^2.57(C2xM4(2))128,1602
C22.58(C2×M4(2)) = C2×C4×M4(2)central extension (φ=1)64C2^2.58(C2xM4(2))128,1603
C22.59(C2×M4(2)) = C22×C22⋊C8central extension (φ=1)64C2^2.59(C2xM4(2))128,1608
C22.60(C2×M4(2)) = C22×C4⋊C8central extension (φ=1)128C2^2.60(C2xM4(2))128,1634
C22.61(C2×M4(2)) = C2×C4⋊M4(2)central extension (φ=1)64C2^2.61(C2xM4(2))128,1635
C22.62(C2×M4(2)) = C2×C42.12C4central extension (φ=1)64C2^2.62(C2xM4(2))128,1649
C22.63(C2×M4(2)) = C2×C86D4central extension (φ=1)64C2^2.63(C2xM4(2))128,1660
C22.64(C2×M4(2)) = C2×C84Q8central extension (φ=1)128C2^2.64(C2xM4(2))128,1691
C22.65(C2×M4(2)) = (C2×C8).195D4central stem extension (φ=1)64C2^2.65(C2xM4(2))128,583
C22.66(C2×M4(2)) = C232M4(2)central stem extension (φ=1)64C2^2.66(C2xM4(2))128,602
C22.67(C2×M4(2)) = (C2×C8).Q8central stem extension (φ=1)128C2^2.67(C2xM4(2))128,649
C22.68(C2×M4(2)) = C23.9M4(2)central stem extension (φ=1)64C2^2.68(C2xM4(2))128,656
C22.69(C2×M4(2)) = C42.27Q8central stem extension (φ=1)128C2^2.69(C2xM4(2))128,672
C22.70(C2×M4(2)) = C42.109D4central stem extension (φ=1)64C2^2.70(C2xM4(2))128,687
C22.71(C2×M4(2)) = C42.120D4central stem extension (φ=1)128C2^2.71(C2xM4(2))128,717

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