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Extensions 1→N→G→Q→1 with N=C2×C4⋊C4 and Q=C4

Direct product G=N×Q with N=C2×C4⋊C4 and Q=C4
dρLabelID
C2×C4×C4⋊C4128C2xC4xC4:C4128,1001

Semidirect products G=N:Q with N=C2×C4⋊C4 and Q=C4
extensionφ:Q→Out NdρLabelID
(C2×C4⋊C4)⋊1C4 = C23.30D8φ: C4/C1 → C4 ⊆ Out C2×C4⋊C432(C2xC4:C4):1C4128,26
(C2×C4⋊C4)⋊2C4 = C23.4D8φ: C4/C1 → C4 ⊆ Out C2×C4⋊C432(C2xC4:C4):2C4128,76
(C2×C4⋊C4)⋊3C4 = C24.4D4φ: C4/C1 → C4 ⊆ Out C2×C4⋊C432(C2xC4:C4):3C4128,84
(C2×C4⋊C4)⋊4C4 = C24.6D4φ: C4/C1 → C4 ⊆ Out C2×C4⋊C432(C2xC4:C4):4C4128,125
(C2×C4⋊C4)⋊5C4 = C2×C22.SD16φ: C4/C1 → C4 ⊆ Out C2×C4⋊C432(C2xC4:C4):5C4128,230
(C2×C4⋊C4)⋊6C4 = C2×C23.31D4φ: C4/C1 → C4 ⊆ Out C2×C4⋊C432(C2xC4:C4):6C4128,231
(C2×C4⋊C4)⋊7C4 = C24.54D4φ: C4/C1 → C4 ⊆ Out C2×C4⋊C432(C2xC4:C4):7C4128,239
(C2×C4⋊C4)⋊8C4 = C24.55D4φ: C4/C1 → C4 ⊆ Out C2×C4⋊C432(C2xC4:C4):8C4128,240
(C2×C4⋊C4)⋊9C4 = C24.56D4φ: C4/C1 → C4 ⊆ Out C2×C4⋊C432(C2xC4:C4):9C4128,242
(C2×C4⋊C4)⋊10C4 = C24.57D4φ: C4/C1 → C4 ⊆ Out C2×C4⋊C432(C2xC4:C4):10C4128,243
(C2×C4⋊C4)⋊11C4 = C24.60D4φ: C4/C1 → C4 ⊆ Out C2×C4⋊C432(C2xC4:C4):11C4128,251
(C2×C4⋊C4)⋊12C4 = C24.61D4φ: C4/C1 → C4 ⊆ Out C2×C4⋊C432(C2xC4:C4):12C4128,252
(C2×C4⋊C4)⋊13C4 = C24.174C23φ: C4/C1 → C4 ⊆ Out C2×C4⋊C432(C2xC4:C4):13C4128,631
(C2×C4⋊C4)⋊14C4 = C24.175C23φ: C4/C1 → C4 ⊆ Out C2×C4⋊C432(C2xC4:C4):14C4128,696
(C2×C4⋊C4)⋊15C4 = C24.176C23φ: C4/C1 → C4 ⊆ Out C2×C4⋊C432(C2xC4:C4):15C4128,728
(C2×C4⋊C4)⋊16C4 = C24.625C23φ: C4/C2 → C2 ⊆ Out C2×C4⋊C4128(C2xC4:C4):16C4128,167
(C2×C4⋊C4)⋊17C4 = C24.626C23φ: C4/C2 → C2 ⊆ Out C2×C4⋊C4128(C2xC4:C4):17C4128,168
(C2×C4⋊C4)⋊18C4 = C24.631C23φ: C4/C2 → C2 ⊆ Out C2×C4⋊C4128(C2xC4:C4):18C4128,173
(C2×C4⋊C4)⋊19C4 = C24.635C23φ: C4/C2 → C2 ⊆ Out C2×C4⋊C4128(C2xC4:C4):19C4128,177
(C2×C4⋊C4)⋊20C4 = C2×C42⋊6C4φ: C4/C2 → C2 ⊆ Out C2×C4⋊C432(C2xC4:C4):20C4128,464
(C2×C4⋊C4)⋊21C4 = C24.63D4φ: C4/C2 → C2 ⊆ Out C2×C4⋊C432(C2xC4:C4):21C4128,465
(C2×C4⋊C4)⋊22C4 = C2×C22.4Q16φ: C4/C2 → C2 ⊆ Out C2×C4⋊C4128(C2xC4:C4):22C4128,466
(C2×C4⋊C4)⋊23C4 = C24.152D4φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4):23C4128,468
(C2×C4⋊C4)⋊24C4 = C24.162C23φ: C4/C2 → C2 ⊆ Out C2×C4⋊C432(C2xC4:C4):24C4128,472
(C2×C4⋊C4)⋊25C4 = C4×C23⋊C4φ: C4/C2 → C2 ⊆ Out C2×C4⋊C432(C2xC4:C4):25C4128,486
(C2×C4⋊C4)⋊26C4 = C24.167C23φ: C4/C2 → C2 ⊆ Out C2×C4⋊C432(C2xC4:C4):26C4128,531
(C2×C4⋊C4)⋊27C4 = C24.169C23φ: C4/C2 → C2 ⊆ Out C2×C4⋊C432(C2xC4:C4):27C4128,552
(C2×C4⋊C4)⋊28C4 = C23.36D8φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4):28C4128,555
(C2×C4⋊C4)⋊29C4 = C24.157D4φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4):29C4128,556
(C2×C4⋊C4)⋊30C4 = C24.70D4φ: C4/C2 → C2 ⊆ Out C2×C4⋊C432(C2xC4:C4):30C4128,558
(C2×C4⋊C4)⋊31C4 = C24.524C23φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4):31C4128,1006
(C2×C4⋊C4)⋊32C4 = C2×C23.63C23φ: C4/C2 → C2 ⊆ Out C2×C4⋊C4128(C2xC4:C4):32C4128,1020
(C2×C4⋊C4)⋊33C4 = C2×C23.65C23φ: C4/C2 → C2 ⊆ Out C2×C4⋊C4128(C2xC4:C4):33C4128,1023
(C2×C4⋊C4)⋊34C4 = C23.195C24φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4):34C4128,1045
(C2×C4⋊C4)⋊35C4 = C24.545C23φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4):35C4128,1048
(C2×C4⋊C4)⋊36C4 = C23.226C24φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4):36C4128,1076
(C2×C4⋊C4)⋊37C4 = C23.227C24φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4):37C4128,1077

Non-split extensions G=N.Q with N=C2×C4⋊C4 and Q=C4
extensionφ:Q→Out NdρLabelID
(C2×C4⋊C4).1C4 = (C2×C4).98D8φ: C4/C1 → C4 ⊆ Out C2×C4⋊C464(C2xC4:C4).1C4128,2
(C2×C4⋊C4).2C4 = C4⋊C4⋊C8φ: C4/C1 → C4 ⊆ Out C2×C4⋊C4128(C2xC4:C4).2C4128,3
(C2×C4⋊C4).3C4 = (C2×Q8)⋊C8φ: C4/C1 → C4 ⊆ Out C2×C4⋊C4128(C2xC4:C4).3C4128,4
(C2×C4⋊C4).4C4 = C42.7Q8φ: C4/C1 → C4 ⊆ Out C2×C4⋊C4128(C2xC4:C4).4C4128,27
(C2×C4⋊C4).5C4 = C42.8Q8φ: C4/C1 → C4 ⊆ Out C2×C4⋊C4128(C2xC4:C4).5C4128,28
(C2×C4⋊C4).6C4 = C42⋊C8φ: C4/C1 → C4 ⊆ Out C2×C4⋊C432(C2xC4:C4).6C4128,56
(C2×C4⋊C4).7C4 = C42⋊3C8φ: C4/C1 → C4 ⊆ Out C2×C4⋊C432(C2xC4:C4).7C4128,57
(C2×C4⋊C4).8C4 = (C2×C4).D8φ: C4/C1 → C4 ⊆ Out C2×C4⋊C432(C2xC4:C4).8C4128,78
(C2×C4⋊C4).9C4 = (C2×C4).Q16φ: C4/C1 → C4 ⊆ Out C2×C4⋊C432(C2xC4:C4).9C4128,85
(C2×C4⋊C4).10C4 = (C2×Q8).Q8φ: C4/C1 → C4 ⊆ Out C2×C4⋊C432(C2xC4:C4).10C4128,126
(C2×C4⋊C4).11C4 = C23⋊C8⋊C2φ: C4/C1 → C4 ⊆ Out C2×C4⋊C432(C2xC4:C4).11C4128,200
(C2×C4⋊C4).12C4 = C42.396D4φ: C4/C1 → C4 ⊆ Out C2×C4⋊C464(C2xC4:C4).12C4128,202
(C2×C4⋊C4).13C4 = C24.(C2×C4)φ: C4/C1 → C4 ⊆ Out C2×C4⋊C432(C2xC4:C4).13C4128,203
(C2×C4⋊C4).14C4 = C24.45(C2×C4)φ: C4/C1 → C4 ⊆ Out C2×C4⋊C432(C2xC4:C4).14C4128,204
(C2×C4⋊C4).15C4 = C42.372D4φ: C4/C1 → C4 ⊆ Out C2×C4⋊C432(C2xC4:C4).15C4128,205
(C2×C4⋊C4).16C4 = C2×C42.2C22φ: C4/C1 → C4 ⊆ Out C2×C4⋊C4128(C2xC4:C4).16C4128,255
(C2×C4⋊C4).17C4 = C42.408D4φ: C4/C1 → C4 ⊆ Out C2×C4⋊C464(C2xC4:C4).17C4128,260
(C2×C4⋊C4).18C4 = C42.71D4φ: C4/C1 → C4 ⊆ Out C2×C4⋊C464(C2xC4:C4).18C4128,266
(C2×C4⋊C4).19C4 = C2×C4.10D8φ: C4/C1 → C4 ⊆ Out C2×C4⋊C4128(C2xC4:C4).19C4128,271
(C2×C4⋊C4).20C4 = C42.414D4φ: C4/C1 → C4 ⊆ Out C2×C4⋊C464(C2xC4:C4).20C4128,278
(C2×C4⋊C4).21C4 = C42.416D4φ: C4/C1 → C4 ⊆ Out C2×C4⋊C464(C2xC4:C4).21C4128,281
(C2×C4⋊C4).22C4 = C42.83D4φ: C4/C1 → C4 ⊆ Out C2×C4⋊C464(C2xC4:C4).22C4128,288
(C2×C4⋊C4).23C4 = M4(2).45D4φ: C4/C1 → C4 ⊆ Out C2×C4⋊C432(C2xC4:C4).23C4128,633
(C2×C4⋊C4).24C4 = C42.114D4φ: C4/C1 → C4 ⊆ Out C2×C4⋊C464(C2xC4:C4).24C4128,698
(C2×C4⋊C4).25C4 = M4(2)⋊8Q8φ: C4/C1 → C4 ⊆ Out C2×C4⋊C464(C2xC4:C4).25C4128,729
(C2×C4⋊C4).26C4 = C42.128D4φ: C4/C1 → C4 ⊆ Out C2×C4⋊C464(C2xC4:C4).26C4128,730
(C2×C4⋊C4).27C4 = C42.46Q8φ: C4/C2 → C2 ⊆ Out C2×C4⋊C4128(C2xC4:C4).27C4128,11
(C2×C4⋊C4).28C4 = C2×C22.M4(2)φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4).28C4128,189
(C2×C4⋊C4).29C4 = C42.371D4φ: C4/C2 → C2 ⊆ Out C2×C4⋊C432(C2xC4:C4).29C4128,190
(C2×C4⋊C4).30C4 = C42.393D4φ: C4/C2 → C2 ⊆ Out C2×C4⋊C432(C2xC4:C4).30C4128,192
(C2×C4⋊C4).31C4 = C42.394D4φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4).31C4128,193
(C2×C4⋊C4).32C4 = (C2×C4)⋊M4(2)φ: C4/C2 → C2 ⊆ Out C2×C4⋊C432(C2xC4:C4).32C4128,195
(C2×C4⋊C4).33C4 = C42.42D4φ: C4/C2 → C2 ⊆ Out C2×C4⋊C432(C2xC4:C4).33C4128,196
(C2×C4⋊C4).34C4 = C42.43D4φ: C4/C2 → C2 ⊆ Out C2×C4⋊C432(C2xC4:C4).34C4128,198
(C2×C4⋊C4).35C4 = C42.44D4φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4).35C4128,199
(C2×C4⋊C4).36C4 = C2×D4⋊C8φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4).36C4128,206
(C2×C4⋊C4).37C4 = C2×Q8⋊C8φ: C4/C2 → C2 ⊆ Out C2×C4⋊C4128(C2xC4:C4).37C4128,207
(C2×C4⋊C4).38C4 = C42.398D4φ: C4/C2 → C2 ⊆ Out C2×C4⋊C432(C2xC4:C4).38C4128,210
(C2×C4⋊C4).39C4 = C42.399D4φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4).39C4128,211
(C2×C4⋊C4).40C4 = D4⋊M4(2)φ: C4/C2 → C2 ⊆ Out C2×C4⋊C432(C2xC4:C4).40C4128,218
(C2×C4⋊C4).41C4 = Q8⋊M4(2)φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4).41C4128,219
(C2×C4⋊C4).42C4 = D4⋊5M4(2)φ: C4/C2 → C2 ⊆ Out C2×C4⋊C432(C2xC4:C4).42C4128,222
(C2×C4⋊C4).43C4 = Q8⋊5M4(2)φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4).43C4128,223
(C2×C4⋊C4).44C4 = C23.29C42φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4).44C4128,461
(C2×C4⋊C4).45C4 = C2×C22.C42φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4).45C4128,473
(C2×C4⋊C4).46C4 = C42.379D4φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4).46C4128,482
(C2×C4⋊C4).47C4 = C4×C4.10D4φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4).47C4128,488
(C2×C4⋊C4).48C4 = C4⋊C8⋊13C4φ: C4/C2 → C2 ⊆ Out C2×C4⋊C4128(C2xC4:C4).48C4128,502
(C2×C4⋊C4).49C4 = C4⋊C8⋊14C4φ: C4/C2 → C2 ⊆ Out C2×C4⋊C4128(C2xC4:C4).49C4128,503
(C2×C4⋊C4).50C4 = C42.95D4φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4).50C4128,530
(C2×C4⋊C4).51C4 = C42.97D4φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4).51C4128,533
(C2×C4⋊C4).52C4 = C24.53(C2×C4)φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4).52C4128,550
(C2×C4⋊C4).53C4 = (C22×C4).275D4φ: C4/C2 → C2 ⊆ Out C2×C4⋊C432(C2xC4:C4).53C4128,553
(C2×C4⋊C4).54C4 = C23.22M4(2)φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4).54C4128,601
(C2×C4⋊C4).55C4 = C23⋊2M4(2)φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4).55C4128,602
(C2×C4⋊C4).56C4 = C4⋊C4⋊3C8φ: C4/C2 → C2 ⊆ Out C2×C4⋊C4128(C2xC4:C4).56C4128,648
(C2×C4⋊C4).57C4 = (C2×C8).Q8φ: C4/C2 → C2 ⊆ Out C2×C4⋊C4128(C2xC4:C4).57C4128,649
(C2×C4⋊C4).58C4 = C42.61Q8φ: C4/C2 → C2 ⊆ Out C2×C4⋊C4128(C2xC4:C4).58C4128,671
(C2×C4⋊C4).59C4 = C42.27Q8φ: C4/C2 → C2 ⊆ Out C2×C4⋊C4128(C2xC4:C4).59C4128,672
(C2×C4⋊C4).60C4 = C42.325D4φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4).60C4128,686
(C2×C4⋊C4).61C4 = C42.109D4φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4).61C4128,687
(C2×C4⋊C4).62C4 = C42.327D4φ: C4/C2 → C2 ⊆ Out C2×C4⋊C4128(C2xC4:C4).62C4128,716
(C2×C4⋊C4).63C4 = C42.120D4φ: C4/C2 → C2 ⊆ Out C2×C4⋊C4128(C2xC4:C4).63C4128,717
(C2×C4⋊C4).64C4 = M4(2)○2M4(2)φ: C4/C2 → C2 ⊆ Out C2×C4⋊C432(C2xC4:C4).64C4128,1605
(C2×C4⋊C4).65C4 = C2×C42.6C22φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4).65C4128,1636
(C2×C4⋊C4).66C4 = C42.257C23φ: C4/C2 → C2 ⊆ Out C2×C4⋊C432(C2xC4:C4).66C4128,1637
(C2×C4⋊C4).67C4 = C2×C42.7C22φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4).67C4128,1651
(C2×C4⋊C4).68C4 = C42.259C23φ: C4/C2 → C2 ⊆ Out C2×C4⋊C432(C2xC4:C4).68C4128,1653
(C2×C4⋊C4).69C4 = C42.262C23φ: C4/C2 → C2 ⊆ Out C2×C4⋊C432(C2xC4:C4).69C4128,1656
(C2×C4⋊C4).70C4 = C2×C8⋊9D4φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4).70C4128,1659
(C2×C4⋊C4).71C4 = C2×C8⋊6D4φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4).71C4128,1660
(C2×C4⋊C4).72C4 = D4×M4(2)φ: C4/C2 → C2 ⊆ Out C2×C4⋊C432(C2xC4:C4).72C4128,1666
(C2×C4⋊C4).73C4 = C2×C8⋊4Q8φ: C4/C2 → C2 ⊆ Out C2×C4⋊C4128(C2xC4:C4).73C4128,1691
(C2×C4⋊C4).74C4 = Q8×M4(2)φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4).74C4128,1695
(C2×C4⋊C4).75C4 = C42.691C23φ: C4/C2 → C2 ⊆ Out C2×C4⋊C432(C2xC4:C4).75C4128,1704
(C2×C4⋊C4).76C4 = C23⋊3M4(2)φ: C4/C2 → C2 ⊆ Out C2×C4⋊C432(C2xC4:C4).76C4128,1705
(C2×C4⋊C4).77C4 = D4⋊7M4(2)φ: C4/C2 → C2 ⊆ Out C2×C4⋊C432(C2xC4:C4).77C4128,1706
(C2×C4⋊C4).78C4 = C42.693C23φ: C4/C2 → C2 ⊆ Out C2×C4⋊C432(C2xC4:C4).78C4128,1707
(C2×C4⋊C4).79C4 = C42.695C23φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4).79C4128,1714
(C2×C4⋊C4).80C4 = C42.302C23φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4).80C4128,1715
(C2×C4⋊C4).81C4 = Q8.4M4(2)φ: C4/C2 → C2 ⊆ Out C2×C4⋊C464(C2xC4:C4).81C4128,1716
(C2×C4⋊C4).82C4 = C8×C4⋊C4φ: trivial image128(C2xC4:C4).82C4128,501
(C2×C4⋊C4).83C4 = C2×C8○2M4(2)φ: trivial image64(C2xC4:C4).83C4128,1604
(C2×C4⋊C4).84C4 = D4×C2×C8φ: trivial image64(C2xC4:C4).84C4128,1658
(C2×C4⋊C4).85C4 = Q8×C2×C8φ: trivial image128(C2xC4:C4).85C4128,1690

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