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Extensions 1→N→G→Q→1 with N=C2×C4×C8 and Q=C2

Direct product G=N×Q with N=C2×C4×C8 and Q=C2
dρLabelID
C22×C4×C8128C2^2xC4xC8128,1601

Semidirect products G=N:Q with N=C2×C4×C8 and Q=C2
extensionφ:Q→Aut NdρLabelID
(C2×C4×C8)⋊1C2 = C2×D4⋊C8φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):1C2128,206
(C2×C4×C8)⋊2C2 = C42.455D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):2C2128,208
(C2×C4×C8)⋊3C2 = C42.315D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):3C2128,224
(C2×C4×C8)⋊4C2 = C42.305D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):4C2128,226
(C2×C4×C8)⋊5C2 = C4×C22⋊C8φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):5C2128,480
(C2×C4×C8)⋊6C2 = C42.379D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):6C2128,482
(C2×C4×C8)⋊7C2 = C8×C22⋊C4φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):7C2128,483
(C2×C4×C8)⋊8C2 = C4×D4⋊C4φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):8C2128,492
(C2×C4×C8)⋊9C2 = C22⋊C4⋊4C8φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):9C2128,655
(C2×C4×C8)⋊10C2 = C2.(C8⋊7D4)φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):10C2128,666
(C2×C4×C8)⋊11C2 = C42.428D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C832(C2xC4xC8):11C2128,669
(C2×C4×C8)⋊12C2 = C42.325D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):12C2128,686
(C2×C4×C8)⋊13C2 = C42.432D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):13C2128,689
(C2×C4×C8)⋊14C2 = C42.433D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):14C2128,690
(C2×C4×C8)⋊15C2 = C2×C42.12C4φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):15C2128,1649
(C2×C4×C8)⋊16C2 = C2×C42.7C22φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):16C2128,1651
(C2×C4×C8)⋊17C2 = C42.260C23φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):17C2128,1654
(C2×C4×C8)⋊18C2 = D4×C2×C8φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):18C2128,1658
(C2×C4×C8)⋊19C2 = C8×C4○D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):19C2128,1696
(C2×C4×C8)⋊20C2 = C2×C4.4D8φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):20C2128,1860
(C2×C4×C8)⋊21C2 = C2×C42.78C22φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):21C2128,1862
(C2×C4×C8)⋊22C2 = C42.355D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):22C2128,1863
(C2×C4×C8)⋊23C2 = (C2×C4)⋊6D8φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):23C2128,702
(C2×C4×C8)⋊24C2 = C2×C4×D8φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):24C2128,1668
(C2×C4×C8)⋊25C2 = C2×C8⋊4D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):25C2128,1876
(C2×C4×C8)⋊26C2 = C42.366D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):26C2128,1901
(C2×C4×C8)⋊27C2 = C42.326D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C832(C2xC4xC8):27C2128,706
(C2×C4×C8)⋊28C2 = C4×C4○D8φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):28C2128,1671
(C2×C4×C8)⋊29C2 = C2×C8.12D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):29C2128,1878
(C2×C4×C8)⋊30C2 = C42.360D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):30C2128,1879
(C2×C4×C8)⋊31C2 = C42.308D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):31C2128,1900
(C2×C4×C8)⋊32C2 = C2×C8○D8φ: C2/C1 → C2 ⊆ Aut C2×C4×C832(C2xC4xC8):32C2128,1685
(C2×C4×C8)⋊33C2 = (C2×C4)⋊9SD16φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):33C2128,700
(C2×C4×C8)⋊34C2 = C2×C4×SD16φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):34C2128,1669
(C2×C4×C8)⋊35C2 = C2×C8⋊5D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):35C2128,1875
(C2×C4×C8)⋊36C2 = C42.365D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):36C2128,1899
(C2×C4×C8)⋊37C2 = C23.17C42φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):37C2128,485
(C2×C4×C8)⋊38C2 = Q8.C42φ: C2/C1 → C2 ⊆ Aut C2×C4×C832(C2xC4xC8):38C2128,496
(C2×C4×C8)⋊39C2 = C2×C4×M4(2)φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):39C2128,1603
(C2×C4×C8)⋊40C2 = C2×C8○2M4(2)φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):40C2128,1604
(C2×C4×C8)⋊41C2 = C4×C8○D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):41C2128,1606
(C2×C4×C8)⋊42C2 = C2×C8⋊6D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):42C2128,1660
(C2×C4×C8)⋊43C2 = C42.681C23φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):43C2128,1663
(C2×C4×C8)⋊44C2 = C42.290C23φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):44C2128,1697
(C2×C4×C8)⋊45C2 = C42.291C23φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8):45C2128,1698

Non-split extensions G=N.Q with N=C2×C4×C8 and Q=C2
extensionφ:Q→Aut NdρLabelID
(C2×C4×C8).1C2 = C2.C82φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).1C2128,5
(C2×C4×C8).2C2 = C42.385D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).2C2128,9
(C2×C4×C8).3C2 = M4(2)⋊C8φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8).3C2128,10
(C2×C4×C8).4C2 = C42.46Q8φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).4C2128,11
(C2×C4×C8).5C2 = C22.7M5(2)φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).5C2128,106
(C2×C4×C8).6C2 = C2×C8⋊C8φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).6C2128,180
(C2×C4×C8).7C2 = C8×M4(2)φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8).7C2128,181
(C2×C4×C8).8C2 = C23.27C42φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8).8C2128,184
(C2×C4×C8).9C2 = C2×Q8⋊C8φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).9C2128,207
(C2×C4×C8).10C2 = C42.316D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8).10C2128,225
(C2×C4×C8).11C2 = C42⋊4C8φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).11C2128,476
(C2×C4×C8).12C2 = (C4×C8)⋊12C4φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).12C2128,478
(C2×C4×C8).13C2 = C4×Q8⋊C4φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).13C2128,493
(C2×C4×C8).14C2 = C4×C4⋊C8φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).14C2128,498
(C2×C4×C8).15C2 = C42.45Q8φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).15C2128,500
(C2×C4×C8).16C2 = C8×C4⋊C4φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).16C2128,501
(C2×C4×C8).17C2 = C42.55Q8φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).17C2128,566
(C2×C4×C8).18C2 = C42.56Q8φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).18C2128,567
(C2×C4×C8).19C2 = C42.322D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8).19C2128,569
(C2×C4×C8).20C2 = C4⋊C4⋊3C8φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).20C2128,648
(C2×C4×C8).21C2 = C2.(C8⋊8D4)φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).21C2128,665
(C2×C4×C8).22C2 = C42.61Q8φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).22C2128,671
(C2×C4×C8).23C2 = C42.431D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).23C2128,688
(C2×C4×C8).24C2 = C42.327D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).24C2128,716
(C2×C4×C8).25C2 = C42.436D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).25C2128,722
(C2×C4×C8).26C2 = C42.437D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).26C2128,723
(C2×C4×C8).27C2 = C2×C4⋊C16φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).27C2128,881
(C2×C4×C8).28C2 = C42.13C8φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8).28C2128,894
(C2×C4×C8).29C2 = Q8×C2×C8φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).29C2128,1690
(C2×C4×C8).30C2 = C2×C4.SD16φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).30C2128,1861
(C2×C4×C8).31C2 = C2×C8⋊1C8φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).31C2128,295
(C2×C4×C8).32C2 = C8⋊7M4(2)φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8).32C2128,299
(C2×C4×C8).33C2 = C4×C2.D8φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).33C2128,507
(C2×C4×C8).34C2 = C42.59Q8φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).34C2128,577
(C2×C4×C8).35C2 = C8⋊5(C4⋊C4)φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).35C2128,674
(C2×C4×C8).36C2 = (C2×C4)⋊6Q16φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).36C2128,701
(C2×C4×C8).37C2 = C2×C4×Q16φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).37C2128,1670
(C2×C4×C8).38C2 = C2×C4⋊Q16φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).38C2128,1877
(C2×C4×C8).39C2 = C2×C8⋊2Q8φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).39C2128,1891
(C2×C4×C8).40C2 = C42.367D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8).40C2128,1902
(C2×C4×C8).41C2 = C42.42Q8φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8).41C2128,296
(C2×C4×C8).42C2 = C42.43Q8φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8).42C2128,300
(C2×C4×C8).43C2 = C4×C8.C4φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8).43C2128,509
(C2×C4×C8).44C2 = C42.60Q8φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).44C2128,578
(C2×C4×C8).45C2 = C42.324D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8).45C2128,580
(C2×C4×C8).46C2 = C42.62Q8φ: C2/C1 → C2 ⊆ Aut C2×C4×C832(C2xC4xC8).46C2128,677
(C2×C4×C8).47C2 = C2×C8.5Q8φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).47C2128,1890
(C2×C4×C8).48C2 = C42.364D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8).48C2128,1892
(C2×C4×C8).49C2 = C8.14C42φ: C2/C1 → C2 ⊆ Aut C2×C4×C832(C2xC4xC8).49C2128,504
(C2×C4×C8).50C2 = C2×C8.C8φ: C2/C1 → C2 ⊆ Aut C2×C4×C832(C2xC4xC8).50C2128,884
(C2×C4×C8).51C2 = C2×C8⋊2C8φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).51C2128,294
(C2×C4×C8).52C2 = C8⋊8M4(2)φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8).52C2128,298
(C2×C4×C8).53C2 = C4×C4.Q8φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).53C2128,506
(C2×C4×C8).54C2 = C42.58Q8φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).54C2128,576
(C2×C4×C8).55C2 = C8⋊7(C4⋊C4)φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).55C2128,673
(C2×C4×C8).56C2 = C2×C8⋊3Q8φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).56C2128,1889
(C2×C4×C8).57C2 = C42.7C8φ: C2/C1 → C2 ⊆ Aut C2×C4×C832(C2xC4xC8).57C2128,108
(C2×C4×C8).58C2 = C82⋊C2φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8).58C2128,182
(C2×C4×C8).59C2 = C8⋊9M4(2)φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8).59C2128,183
(C2×C4×C8).60C2 = C4×C8⋊C4φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).60C2128,457
(C2×C4×C8).61C2 = C2.C43φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).61C2128,458
(C2×C4×C8).62C2 = C4⋊C8⋊13C4φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).62C2128,502
(C2×C4×C8).63C2 = C4⋊C8⋊14C4φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).63C2128,503
(C2×C4×C8).64C2 = C2×C16⋊5C4φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).64C2128,838
(C2×C4×C8).65C2 = C4×M5(2)φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8).65C2128,839
(C2×C4×C8).66C2 = C4⋊M5(2)φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8).66C2128,882
(C2×C4×C8).67C2 = C42.6C8φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8).67C2128,895
(C2×C4×C8).68C2 = C2×C8⋊4Q8φ: C2/C1 → C2 ⊆ Aut C2×C4×C8128(C2xC4xC8).68C2128,1691
(C2×C4×C8).69C2 = C42.286C23φ: C2/C1 → C2 ⊆ Aut C2×C4×C864(C2xC4xC8).69C2128,1692

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