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

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

Semidirect products G=N:Q with N=C2×C4 and Q=M4(2)
extensionφ:Q→Aut NdρLabelID
(C2×C4)⋊1M4(2) = C23⋊M4(2)φ: M4(2)/C4C4 ⊆ Aut C2×C432(C2xC4):1M4(2)128,197
(C2×C4)⋊2M4(2) = (C2×C8).195D4φ: M4(2)/C4C22 ⊆ Aut C2×C464(C2xC4):2M4(2)128,583
(C2×C4)⋊3M4(2) = C232M4(2)φ: M4(2)/C4C22 ⊆ Aut C2×C464(C2xC4):3M4(2)128,602
(C2×C4)⋊4M4(2) = C42.693C23φ: M4(2)/C4C22 ⊆ Aut C2×C432(C2xC4):4M4(2)128,1707
(C2×C4)⋊5M4(2) = C42.698C23φ: M4(2)/C4C22 ⊆ Aut C2×C464(C2xC4):5M4(2)128,1721
(C2×C4)⋊6M4(2) = (C2×C4)⋊M4(2)φ: M4(2)/C22C4 ⊆ Aut C2×C432(C2xC4):6M4(2)128,195
(C2×C4)⋊7M4(2) = C23.17C42φ: M4(2)/C8C2 ⊆ Aut C2×C464(C2xC4):7M4(2)128,485
(C2×C4)⋊8M4(2) = C2×C86D4φ: M4(2)/C8C2 ⊆ Aut C2×C464(C2xC4):8M4(2)128,1660
(C2×C4)⋊9M4(2) = C42.290C23φ: M4(2)/C8C2 ⊆ Aut C2×C464(C2xC4):9M4(2)128,1697
(C2×C4)⋊10M4(2) = C23.28C42φ: M4(2)/C2×C4C2 ⊆ Aut C2×C464(C2xC4):10M4(2)128,460
(C2×C4)⋊11M4(2) = C2×C4⋊M4(2)φ: M4(2)/C2×C4C2 ⊆ Aut C2×C464(C2xC4):11M4(2)128,1635
(C2×C4)⋊12M4(2) = C42.677C23φ: M4(2)/C2×C4C2 ⊆ Aut C2×C432(C2xC4):12M4(2)128,1652

Non-split extensions G=N.Q with N=C2×C4 and Q=M4(2)
extensionφ:Q→Aut NdρLabelID
(C2×C4).1M4(2) = (C2×D4)⋊C8φ: M4(2)/C4C4 ⊆ Aut C2×C432(C2xC4).1M4(2)128,50
(C2×C4).2M4(2) = (C2×C42).C4φ: M4(2)/C4C4 ⊆ Aut C2×C432(C2xC4).2M4(2)128,51
(C2×C4).3M4(2) = C22⋊C4.C8φ: M4(2)/C4C4 ⊆ Aut C2×C4324(C2xC4).3M4(2)128,60
(C2×C4).4M4(2) = C42.44D4φ: M4(2)/C4C4 ⊆ Aut C2×C464(C2xC4).4M4(2)128,199
(C2×C4).5M4(2) = C8.19M4(2)φ: M4(2)/C4C4 ⊆ Aut C2×C4324(C2xC4).5M4(2)128,898
(C2×C4).6M4(2) = (C2×C4).98D8φ: M4(2)/C4C22 ⊆ Aut C2×C464(C2xC4).6M4(2)128,2
(C2×C4).7M4(2) = C4⋊C4⋊C8φ: M4(2)/C4C22 ⊆ Aut C2×C4128(C2xC4).7M4(2)128,3
(C2×C4).8M4(2) = (C2×Q8)⋊C8φ: M4(2)/C4C22 ⊆ Aut C2×C4128(C2xC4).8M4(2)128,4
(C2×C4).9M4(2) = C42.3Q8φ: M4(2)/C4C22 ⊆ Aut C2×C464(C2xC4).9M4(2)128,15
(C2×C4).10M4(2) = C8.31D8φ: M4(2)/C4C22 ⊆ Aut C2×C464(C2xC4).10M4(2)128,62
(C2×C4).11M4(2) = C8.17Q16φ: M4(2)/C4C22 ⊆ Aut C2×C4128(C2xC4).11M4(2)128,70
(C2×C4).12M4(2) = M4(2).C8φ: M4(2)/C4C22 ⊆ Aut C2×C4324(C2xC4).12M4(2)128,110
(C2×C4).13M4(2) = C42.393D4φ: M4(2)/C4C22 ⊆ Aut C2×C432(C2xC4).13M4(2)128,192
(C2×C4).14M4(2) = C42.394D4φ: M4(2)/C4C22 ⊆ Aut C2×C464(C2xC4).14M4(2)128,193
(C2×C4).15M4(2) = C42.397D4φ: M4(2)/C4C22 ⊆ Aut C2×C464(C2xC4).15M4(2)128,209
(C2×C4).16M4(2) = C42.398D4φ: M4(2)/C4C22 ⊆ Aut C2×C432(C2xC4).16M4(2)128,210
(C2×C4).17M4(2) = C42.399D4φ: M4(2)/C4C22 ⊆ Aut C2×C464(C2xC4).17M4(2)128,211
(C2×C4).18M4(2) = M4(2)⋊1C8φ: M4(2)/C4C22 ⊆ Aut C2×C464(C2xC4).18M4(2)128,297
(C2×C4).19M4(2) = (C2×C8).Q8φ: M4(2)/C4C22 ⊆ Aut C2×C4128(C2xC4).19M4(2)128,649
(C2×C4).20M4(2) = C23.9M4(2)φ: M4(2)/C4C22 ⊆ Aut C2×C464(C2xC4).20M4(2)128,656
(C2×C4).21M4(2) = C42.27Q8φ: M4(2)/C4C22 ⊆ Aut C2×C4128(C2xC4).21M4(2)128,672
(C2×C4).22M4(2) = C42.120D4φ: M4(2)/C4C22 ⊆ Aut C2×C4128(C2xC4).22M4(2)128,717
(C2×C4).23M4(2) = C8.23C42φ: M4(2)/C4C22 ⊆ Aut C2×C4324(C2xC4).23M4(2)128,842
(C2×C4).24M4(2) = M5(2).19C22φ: M4(2)/C4C22 ⊆ Aut C2×C4324(C2xC4).24M4(2)128,847
(C2×C4).25M4(2) = M5(2)⋊12C22φ: M4(2)/C4C22 ⊆ Aut C2×C4324(C2xC4).25M4(2)128,849
(C2×C4).26M4(2) = M4(2).1C8φ: M4(2)/C4C22 ⊆ Aut C2×C4324(C2xC4).26M4(2)128,885
(C2×C4).27M4(2) = C42.302C23φ: M4(2)/C4C22 ⊆ Aut C2×C464(C2xC4).27M4(2)128,1715
(C2×C4).28M4(2) = C24.C8φ: M4(2)/C22C4 ⊆ Aut C2×C4164(C2xC4).28M4(2)128,52
(C2×C4).29M4(2) = C42⋊C8φ: M4(2)/C22C4 ⊆ Aut C2×C432(C2xC4).29M4(2)128,56
(C2×C4).30M4(2) = C423C8φ: M4(2)/C22C4 ⊆ Aut C2×C432(C2xC4).30M4(2)128,57
(C2×C4).31M4(2) = C42.42D4φ: M4(2)/C22C4 ⊆ Aut C2×C432(C2xC4).31M4(2)128,196
(C2×C4).32M4(2) = C8.5M4(2)φ: M4(2)/C22C4 ⊆ Aut C2×C4164(C2xC4).32M4(2)128,897
(C2×C4).33M4(2) = D4⋊C16φ: M4(2)/C8C2 ⊆ Aut C2×C464(C2xC4).33M4(2)128,61
(C2×C4).34M4(2) = Q8⋊C16φ: M4(2)/C8C2 ⊆ Aut C2×C4128(C2xC4).34M4(2)128,69
(C2×C4).35M4(2) = C4⋊C814C4φ: M4(2)/C8C2 ⊆ Aut C2×C4128(C2xC4).35M4(2)128,503
(C2×C4).36M4(2) = C4⋊C43C8φ: M4(2)/C8C2 ⊆ Aut C2×C4128(C2xC4).36M4(2)128,648
(C2×C4).37M4(2) = C22⋊C44C8φ: M4(2)/C8C2 ⊆ Aut C2×C464(C2xC4).37M4(2)128,655
(C2×C4).38M4(2) = M4(2)⋊C8φ: M4(2)/C8C2 ⊆ Aut C2×C464(C2xC4).38M4(2)128,10
(C2×C4).39M4(2) = C42.46Q8φ: M4(2)/C8C2 ⊆ Aut C2×C4128(C2xC4).39M4(2)128,11
(C2×C4).40M4(2) = M5(2)⋊7C4φ: M4(2)/C8C2 ⊆ Aut C2×C464(C2xC4).40M4(2)128,111
(C2×C4).41M4(2) = C89M4(2)φ: M4(2)/C8C2 ⊆ Aut C2×C464(C2xC4).41M4(2)128,183
(C2×C4).42M4(2) = C2×D4⋊C8φ: M4(2)/C8C2 ⊆ Aut C2×C464(C2xC4).42M4(2)128,206
(C2×C4).43M4(2) = C2×Q8⋊C8φ: M4(2)/C8C2 ⊆ Aut C2×C4128(C2xC4).43M4(2)128,207
(C2×C4).44M4(2) = C42.455D4φ: M4(2)/C8C2 ⊆ Aut C2×C464(C2xC4).44M4(2)128,208
(C2×C4).45M4(2) = C4⋊C813C4φ: M4(2)/C8C2 ⊆ Aut C2×C4128(C2xC4).45M4(2)128,502
(C2×C4).46M4(2) = C42.61Q8φ: M4(2)/C8C2 ⊆ Aut C2×C4128(C2xC4).46M4(2)128,671
(C2×C4).47M4(2) = C42.325D4φ: M4(2)/C8C2 ⊆ Aut C2×C464(C2xC4).47M4(2)128,686
(C2×C4).48M4(2) = C42.327D4φ: M4(2)/C8C2 ⊆ Aut C2×C4128(C2xC4).48M4(2)128,716
(C2×C4).49M4(2) = (C2×D4).5C8φ: M4(2)/C8C2 ⊆ Aut C2×C464(C2xC4).49M4(2)128,845
(C2×C4).50M4(2) = C2×D4.C8φ: M4(2)/C8C2 ⊆ Aut C2×C464(C2xC4).50M4(2)128,848
(C2×C4).51M4(2) = C4⋊C4.7C8φ: M4(2)/C8C2 ⊆ Aut C2×C464(C2xC4).51M4(2)128,883
(C2×C4).52M4(2) = C2×C84Q8φ: M4(2)/C8C2 ⊆ Aut C2×C4128(C2xC4).52M4(2)128,1691
(C2×C4).53M4(2) = C16⋊C8φ: M4(2)/C2×C4C2 ⊆ Aut C2×C4128(C2xC4).53M4(2)128,45
(C2×C4).54M4(2) = C23⋊C16φ: M4(2)/C2×C4C2 ⊆ Aut C2×C432(C2xC4).54M4(2)128,46
(C2×C4).55M4(2) = C22.M5(2)φ: M4(2)/C2×C4C2 ⊆ Aut C2×C464(C2xC4).55M4(2)128,54
(C2×C4).56M4(2) = C82C16φ: M4(2)/C2×C4C2 ⊆ Aut C2×C4128(C2xC4).56M4(2)128,99
(C2×C4).57M4(2) = C8.36D8φ: M4(2)/C2×C4C2 ⊆ Aut C2×C4128(C2xC4).57M4(2)128,102
(C2×C4).58M4(2) = C43.C2φ: M4(2)/C2×C4C2 ⊆ Aut C2×C4128(C2xC4).58M4(2)128,477
(C2×C4).59M4(2) = C42.378D4φ: M4(2)/C2×C4C2 ⊆ Aut C2×C464(C2xC4).59M4(2)128,481
(C2×C4).60M4(2) = C42.425D4φ: M4(2)/C2×C4C2 ⊆ Aut C2×C464(C2xC4).60M4(2)128,529
(C2×C4).61M4(2) = C23.32M4(2)φ: M4(2)/C2×C4C2 ⊆ Aut C2×C464(C2xC4).61M4(2)128,549
(C2×C4).62M4(2) = C425C8φ: M4(2)/C2×C4C2 ⊆ Aut C2×C4128(C2xC4).62M4(2)128,571
(C2×C4).63M4(2) = C421C8φ: M4(2)/C2×C4C2 ⊆ Aut C2×C432(C2xC4).63M4(2)128,6
(C2×C4).64M4(2) = C42.20D4φ: M4(2)/C2×C4C2 ⊆ Aut C2×C464(C2xC4).64M4(2)128,7
(C2×C4).65M4(2) = C426C8φ: M4(2)/C2×C4C2 ⊆ Aut C2×C432(C2xC4).65M4(2)128,8
(C2×C4).66M4(2) = C42.385D4φ: M4(2)/C2×C4C2 ⊆ Aut C2×C4128(C2xC4).66M4(2)128,9
(C2×C4).67M4(2) = C42.2Q8φ: M4(2)/C2×C4C2 ⊆ Aut C2×C464(C2xC4).67M4(2)128,13
(C2×C4).68M4(2) = C42.2C8φ: M4(2)/C2×C4C2 ⊆ Aut C2×C432(C2xC4).68M4(2)128,107
(C2×C4).69M4(2) = C42.7C8φ: M4(2)/C2×C4C2 ⊆ Aut C2×C432(C2xC4).69M4(2)128,108
(C2×C4).70M4(2) = M5(2)⋊C4φ: M4(2)/C2×C4C2 ⊆ Aut C2×C464(C2xC4).70M4(2)128,109
(C2×C4).71M4(2) = C23.27C42φ: M4(2)/C2×C4C2 ⊆ Aut C2×C464(C2xC4).71M4(2)128,184
(C2×C4).72M4(2) = C42.371D4φ: M4(2)/C2×C4C2 ⊆ Aut C2×C432(C2xC4).72M4(2)128,190
(C2×C4).73M4(2) = C2×C82C8φ: M4(2)/C2×C4C2 ⊆ Aut C2×C4128(C2xC4).73M4(2)128,294
(C2×C4).74M4(2) = C2×C81C8φ: M4(2)/C2×C4C2 ⊆ Aut C2×C4128(C2xC4).74M4(2)128,295
(C2×C4).75M4(2) = C42.42Q8φ: M4(2)/C2×C4C2 ⊆ Aut C2×C464(C2xC4).75M4(2)128,296
(C2×C4).76M4(2) = C43.7C2φ: M4(2)/C2×C4C2 ⊆ Aut C2×C4128(C2xC4).76M4(2)128,499
(C2×C4).77M4(2) = C428C8φ: M4(2)/C2×C4C2 ⊆ Aut C2×C4128(C2xC4).77M4(2)128,563
(C2×C4).78M4(2) = C429C8φ: M4(2)/C2×C4C2 ⊆ Aut C2×C4128(C2xC4).78M4(2)128,574
(C2×C4).79M4(2) = C2×C16⋊C4φ: M4(2)/C2×C4C2 ⊆ Aut C2×C432(C2xC4).79M4(2)128,841
(C2×C4).80M4(2) = C24.5C8φ: M4(2)/C2×C4C2 ⊆ Aut C2×C432(C2xC4).80M4(2)128,844
(C2×C4).81M4(2) = C2×C23.C8φ: M4(2)/C2×C4C2 ⊆ Aut C2×C432(C2xC4).81M4(2)128,846
(C2×C4).82M4(2) = C4⋊M5(2)φ: M4(2)/C2×C4C2 ⊆ Aut C2×C464(C2xC4).82M4(2)128,882
(C2×C4).83M4(2) = C2×C8.C8φ: M4(2)/C2×C4C2 ⊆ Aut C2×C432(C2xC4).83M4(2)128,884
(C2×C4).84M4(2) = C2×C42.6C4φ: M4(2)/C2×C4C2 ⊆ Aut C2×C464(C2xC4).84M4(2)128,1650
(C2×C4).85M4(2) = C2.C82central extension (φ=1)128(C2xC4).85M4(2)128,5
(C2×C4).86M4(2) = C22.7M5(2)central extension (φ=1)128(C2xC4).86M4(2)128,106
(C2×C4).87M4(2) = C2×C8⋊C8central extension (φ=1)128(C2xC4).87M4(2)128,180
(C2×C4).88M4(2) = C4×C8⋊C4central extension (φ=1)128(C2xC4).88M4(2)128,457
(C2×C4).89M4(2) = C424C8central extension (φ=1)128(C2xC4).89M4(2)128,476
(C2×C4).90M4(2) = C4×C22⋊C8central extension (φ=1)64(C2xC4).90M4(2)128,480
(C2×C4).91M4(2) = C4×C4⋊C8central extension (φ=1)128(C2xC4).91M4(2)128,498
(C2×C4).92M4(2) = C2×C22⋊C16central extension (φ=1)64(C2xC4).92M4(2)128,843
(C2×C4).93M4(2) = C2×C4⋊C16central extension (φ=1)128(C2xC4).93M4(2)128,881
(C2×C4).94M4(2) = C2×C42.12C4central extension (φ=1)64(C2xC4).94M4(2)128,1649

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