# Extensions 1→N→G→Q→1 with N=C2×M4(2) and Q=C4

Direct product G=N×Q with N=C2×M4(2) and Q=C4
dρLabelID
C2×C4×M4(2)64C2xC4xM4(2)128,1603

Semidirect products G=N:Q with N=C2×M4(2) and Q=C4
extensionφ:Q→Out NdρLabelID
(C2×M4(2))⋊1C4 = C24.48D4φ: C4/C1C4 ⊆ Out C2×M4(2)32(C2xM4(2)):1C4128,29
(C2×M4(2))⋊2C4 = C23.C42φ: C4/C1C4 ⊆ Out C2×M4(2)32(C2xM4(2)):2C4128,37
(C2×M4(2))⋊3C4 = C23.2C42φ: C4/C1C4 ⊆ Out C2×M4(2)324(C2xM4(2)):3C4128,123
(C2×M4(2))⋊4C4 = (C22×C8)⋊C4φ: C4/C1C4 ⊆ Out C2×M4(2)324(C2xM4(2)):4C4128,127
(C2×M4(2))⋊5C4 = C24.67D4φ: C4/C2C2 ⊆ Out C2×M4(2)64(C2xM4(2)):5C4128,541
(C2×M4(2))⋊6C4 = (C2×D4).24Q8φ: C4/C2C2 ⊆ Out C2×M4(2)324(C2xM4(2)):6C4128,544
(C2×M4(2))⋊7C4 = C2×M4(2)⋊C4φ: C4/C2C2 ⊆ Out C2×M4(2)64(C2xM4(2)):7C4128,1642
(C2×M4(2))⋊8C4 = C24.100D4φ: C4/C2C2 ⊆ Out C2×M4(2)32(C2xM4(2)):8C4128,1643
(C2×M4(2))⋊9C4 = C23.28C42φ: C4/C2C2 ⊆ Out C2×M4(2)64(C2xM4(2)):9C4128,460
(C2×M4(2))⋊10C4 = C23.29C42φ: C4/C2C2 ⊆ Out C2×M4(2)64(C2xM4(2)):10C4128,461
(C2×M4(2))⋊11C4 = C2×C4.9C42φ: C4/C2C2 ⊆ Out C2×M4(2)32(C2xM4(2)):11C4128,462
(C2×M4(2))⋊12C4 = C2×C426C4φ: C4/C2C2 ⊆ Out C2×M4(2)32(C2xM4(2)):12C4128,464
(C2×M4(2))⋊13C4 = C24.63D4φ: C4/C2C2 ⊆ Out C2×M4(2)32(C2xM4(2)):13C4128,465
(C2×M4(2))⋊14C4 = C24.152D4φ: C4/C2C2 ⊆ Out C2×M4(2)64(C2xM4(2)):14C4128,468
(C2×M4(2))⋊15C4 = C2×C22.C42φ: C4/C2C2 ⊆ Out C2×M4(2)64(C2xM4(2)):15C4128,473
(C2×M4(2))⋊16C4 = C23.15C42φ: C4/C2C2 ⊆ Out C2×M4(2)32(C2xM4(2)):16C4128,474
(C2×M4(2))⋊17C4 = C2×M4(2)⋊4C4φ: C4/C2C2 ⊆ Out C2×M4(2)32(C2xM4(2)):17C4128,475
(C2×M4(2))⋊18C4 = C23.17C42φ: C4/C2C2 ⊆ Out C2×M4(2)64(C2xM4(2)):18C4128,485
(C2×M4(2))⋊19C4 = C23.5C42φ: C4/C2C2 ⊆ Out C2×M4(2)324(C2xM4(2)):19C4128,489
(C2×M4(2))⋊20C4 = M4(2)○2M4(2)φ: C4/C2C2 ⊆ Out C2×M4(2)32(C2xM4(2)):20C4128,1605
(C2×M4(2))⋊21C4 = C2×C82M4(2)φ: trivial image64(C2xM4(2)):21C4128,1604

Non-split extensions G=N.Q with N=C2×M4(2) and Q=C4
extensionφ:Q→Out NdρLabelID
(C2×M4(2)).1C4 = C24.3Q8φ: C4/C1C4 ⊆ Out C2×M4(2)32(C2xM4(2)).1C4128,30
(C2×M4(2)).2C4 = C42.388D4φ: C4/C1C4 ⊆ Out C2×M4(2)64(C2xM4(2)).2C4128,31
(C2×M4(2)).3C4 = C42.30D4φ: C4/C1C4 ⊆ Out C2×M4(2)64(C2xM4(2)).3C4128,39
(C2×M4(2)).4C4 = C42.32D4φ: C4/C1C4 ⊆ Out C2×M4(2)64(C2xM4(2)).4C4128,41
(C2×M4(2)).5C4 = C23.M4(2)φ: C4/C1C4 ⊆ Out C2×M4(2)64(C2xM4(2)).5C4128,47
(C2×M4(2)).6C4 = C24.C8φ: C4/C1C4 ⊆ Out C2×M4(2)164(C2xM4(2)).6C4128,52
(C2×M4(2)).7C4 = C23.7M4(2)φ: C4/C1C4 ⊆ Out C2×M4(2)64(C2xM4(2)).7C4128,55
(C2×M4(2)).8C4 = C42.C8φ: C4/C1C4 ⊆ Out C2×M4(2)164(C2xM4(2)).8C4128,59
(C2×M4(2)).9C4 = C23.3C42φ: C4/C1C4 ⊆ Out C2×M4(2)324(C2xM4(2)).9C4128,124
(C2×M4(2)).10C4 = M4(2)⋊1C8φ: C4/C2C2 ⊆ Out C2×M4(2)64(C2xM4(2)).10C4128,297
(C2×M4(2)).11C4 = C81M4(2)φ: C4/C2C2 ⊆ Out C2×M4(2)64(C2xM4(2)).11C4128,301
(C2×M4(2)).12C4 = C24.9Q8φ: C4/C2C2 ⊆ Out C2×M4(2)32(C2xM4(2)).12C4128,543
(C2×M4(2)).13C4 = (C2×C8).103D4φ: C4/C2C2 ⊆ Out C2×M4(2)324(C2xM4(2)).13C4128,545
(C2×M4(2)).14C4 = M4(2).1C8φ: C4/C2C2 ⊆ Out C2×M4(2)324(C2xM4(2)).14C4128,885
(C2×M4(2)).15C4 = C8.5M4(2)φ: C4/C2C2 ⊆ Out C2×M4(2)164(C2xM4(2)).15C4128,897
(C2×M4(2)).16C4 = C2×M4(2).C4φ: C4/C2C2 ⊆ Out C2×M4(2)32(C2xM4(2)).16C4128,1647
(C2×M4(2)).17C4 = M4(2)⋊C8φ: C4/C2C2 ⊆ Out C2×M4(2)64(C2xM4(2)).17C4128,10
(C2×M4(2)).18C4 = C42.3Q8φ: C4/C2C2 ⊆ Out C2×M4(2)64(C2xM4(2)).18C4128,15
(C2×M4(2)).19C4 = M4(2).C8φ: C4/C2C2 ⊆ Out C2×M4(2)324(C2xM4(2)).19C4128,110
(C2×M4(2)).20C4 = M5(2)⋊7C4φ: C4/C2C2 ⊆ Out C2×M4(2)64(C2xM4(2)).20C4128,111
(C2×M4(2)).21C4 = C89M4(2)φ: C4/C2C2 ⊆ Out C2×M4(2)64(C2xM4(2)).21C4128,183
(C2×M4(2)).22C4 = C8215C2φ: C4/C2C2 ⊆ Out C2×M4(2)64(C2xM4(2)).22C4128,185
(C2×M4(2)).23C4 = C86M4(2)φ: C4/C2C2 ⊆ Out C2×M4(2)64(C2xM4(2)).23C4128,187
(C2×M4(2)).24C4 = C2×C4.10C42φ: C4/C2C2 ⊆ Out C2×M4(2)32(C2xM4(2)).24C4128,463
(C2×M4(2)).25C4 = C2×C4.C42φ: C4/C2C2 ⊆ Out C2×M4(2)64(C2xM4(2)).25C4128,469
(C2×M4(2)).26C4 = C24.7Q8φ: C4/C2C2 ⊆ Out C2×M4(2)32(C2xM4(2)).26C4128,470
(C2×M4(2)).27C4 = C8.23C42φ: C4/C2C2 ⊆ Out C2×M4(2)324(C2xM4(2)).27C4128,842
(C2×M4(2)).28C4 = (C2×D4).5C8φ: C4/C2C2 ⊆ Out C2×M4(2)64(C2xM4(2)).28C4128,845
(C2×M4(2)).29C4 = C2×C23.C8φ: C4/C2C2 ⊆ Out C2×M4(2)32(C2xM4(2)).29C4128,846
(C2×M4(2)).30C4 = M5(2).19C22φ: C4/C2C2 ⊆ Out C2×M4(2)324(C2xM4(2)).30C4128,847
(C2×M4(2)).31C4 = C2×D4.C8φ: C4/C2C2 ⊆ Out C2×M4(2)64(C2xM4(2)).31C4128,848
(C2×M4(2)).32C4 = M5(2)⋊12C22φ: C4/C2C2 ⊆ Out C2×M4(2)324(C2xM4(2)).32C4128,849
(C2×M4(2)).33C4 = C4⋊C4.7C8φ: C4/C2C2 ⊆ Out C2×M4(2)64(C2xM4(2)).33C4128,883
(C2×M4(2)).34C4 = C8.12M4(2)φ: C4/C2C2 ⊆ Out C2×M4(2)64(C2xM4(2)).34C4128,896
(C2×M4(2)).35C4 = Q8○M5(2)φ: C4/C2C2 ⊆ Out C2×M4(2)324(C2xM4(2)).35C4128,2139
(C2×M4(2)).36C4 = C8×M4(2)φ: trivial image64(C2xM4(2)).36C4128,181
(C2×M4(2)).37C4 = C162M5(2)φ: trivial image64(C2xM4(2)).37C4128,840
(C2×M4(2)).38C4 = C2×D4○C16φ: trivial image64(C2xM4(2)).38C4128,2138

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