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Extensions 1→N→G→Q→1 with N=C4 and Q=C22≀C2

Direct product G=N×Q with N=C4 and Q=C22≀C2
dρLabelID
C4×C22≀C232C4xC2^2wrC2128,1031

Semidirect products G=N:Q with N=C4 and Q=C22≀C2
extensionφ:Q→Aut NdρLabelID
C4⋊1C22≀C2 = C23.333C24φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C432C4:1C2^2wrC2128,1165
C4⋊2C22≀C2 = C23.308C24φ: C22≀C2/C2×D4 → C2 ⊆ Aut C432C4:2C2^2wrC2128,1140
C4⋊3C22≀C2 = C24⋊13D4φ: C22≀C2/C24 → C2 ⊆ Aut C432C4:3C2^2wrC2128,1579

Non-split extensions G=N.Q with N=C4 and Q=C22≀C2
extensionφ:Q→Aut NdρLabelID
C4.1C22≀C2 = C42⋊9D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C416C4.1C2^2wrC2128,734
C4.2C22≀C2 = C42.129D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C432C4.2C2^2wrC2128,735
C4.3C22≀C2 = C42⋊10D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C432C4.3C2^2wrC2128,736
C4.4C22≀C2 = C42.130D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C432C4.4C2^2wrC2128,737
C4.5C22≀C2 = M4(2)⋊5D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C4168+C4.5C2^2wrC2128,740
C4.6C22≀C2 = M4(2).D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C4328-C4.6C2^2wrC2128,741
C4.7C22≀C2 = (C2×C4)⋊2D8φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C464C4.7C2^2wrC2128,743
C4.8C22≀C2 = (C22×D8).C2φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C464C4.8C2^2wrC2128,744
C4.9C22≀C2 = (C2×C4)⋊3SD16φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C464C4.9C2^2wrC2128,745
C4.10C22≀C2 = (C2×C8)⋊20D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C464C4.10C2^2wrC2128,746
C4.11C22≀C2 = (C2×C8).41D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C464C4.11C2^2wrC2128,747
C4.12C22≀C2 = (C2×C4)⋊2Q16φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C4128C4.12C2^2wrC2128,748
C4.13C22≀C2 = M4(2).4D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C432C4.13C2^2wrC2128,750
C4.14C22≀C2 = M4(2).5D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C432C4.14C2^2wrC2128,751
C4.15C22≀C2 = M4(2).6D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C464C4.15C2^2wrC2128,752
C4.16C22≀C2 = D8⋊7D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C432C4.16C2^2wrC2128,916
C4.17C22≀C2 = Q16⋊7D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C464C4.17C2^2wrC2128,917
C4.18C22≀C2 = D8⋊8D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C464C4.18C2^2wrC2128,918
C4.19C22≀C2 = D8.9D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C432C4.19C2^2wrC2128,919
C4.20C22≀C2 = Q16.8D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C464C4.20C2^2wrC2128,920
C4.21C22≀C2 = D8.10D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C464C4.21C2^2wrC2128,921
C4.22C22≀C2 = D8⋊D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C4168+C4.22C2^2wrC2128,922
C4.23C22≀C2 = D8.D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C4328-C4.23C2^2wrC2128,923
C4.24C22≀C2 = Q16.10D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C4324+C4.24C2^2wrC2128,924
C4.25C22≀C2 = Q16.D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C4324C4.25C2^2wrC2128,925
C4.26C22≀C2 = D8.3D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C4324C4.26C2^2wrC2128,926
C4.27C22≀C2 = D8.12D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C4644-C4.27C2^2wrC2128,927
C4.28C22≀C2 = C24.263C23φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C464C4.28C2^2wrC2128,1163
C4.29C22≀C2 = C24.264C23φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C464C4.29C2^2wrC2128,1164
C4.30C22≀C2 = C23.334C24φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C464C4.30C2^2wrC2128,1166
C4.31C22≀C2 = C23.335C24φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C432C4.31C2^2wrC2128,1167
C4.32C22≀C2 = C24.565C23φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C464C4.32C2^2wrC2128,1168
C4.33C22≀C2 = C2×C22⋊D8φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C432C4.33C2^2wrC2128,1728
C4.34C22≀C2 = C2×C22⋊SD16φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C432C4.34C2^2wrC2128,1729
C4.35C22≀C2 = C2×Q8⋊D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C464C4.35C2^2wrC2128,1730
C4.36C22≀C2 = C2×C22⋊Q16φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C464C4.36C2^2wrC2128,1731
C4.37C22≀C2 = C2×D4⋊D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C464C4.37C2^2wrC2128,1732
C4.38C22≀C2 = C2×D4.7D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C464C4.38C2^2wrC2128,1733
C4.39C22≀C2 = C4○D4⋊D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C432C4.39C2^2wrC2128,1740
C4.40C22≀C2 = D4.(C2×D4)φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C432C4.40C2^2wrC2128,1741
C4.41C22≀C2 = (C2×Q8)⋊16D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C432C4.41C2^2wrC2128,1742
C4.42C22≀C2 = Q8.(C2×D4)φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C464C4.42C2^2wrC2128,1743
C4.43C22≀C2 = C2×D4⋊4D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C416C4.43C2^2wrC2128,1746
C4.44C22≀C2 = C2×D4.9D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C432C4.44C2^2wrC2128,1747
C4.45C22≀C2 = C2×D4.8D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C432C4.45C2^2wrC2128,1748
C4.46C22≀C2 = C2×D4.10D4φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C432C4.46C2^2wrC2128,1749
C4.47C22≀C2 = C23.9C24φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C4168+C4.47C2^2wrC2128,1759
C4.48C22≀C2 = C23.10C24φ: C22≀C2/C22⋊C4 → C2 ⊆ Aut C4328-C4.48C2^2wrC2128,1760
C4.49C22≀C2 = C25.C4φ: C22≀C2/C2×D4 → C2 ⊆ Aut C416C4.49C2^2wrC2128,515
C4.50C22≀C2 = C4.C22≀C2φ: C22≀C2/C2×D4 → C2 ⊆ Aut C432C4.50C2^2wrC2128,516
C4.51C22≀C2 = (C23×C4).C4φ: C22≀C2/C2×D4 → C2 ⊆ Aut C432C4.51C2^2wrC2128,517
C4.52C22≀C2 = C23.35D8φ: C22≀C2/C2×D4 → C2 ⊆ Aut C432C4.52C2^2wrC2128,518
C4.53C22≀C2 = C24.155D4φ: C22≀C2/C2×D4 → C2 ⊆ Aut C464C4.53C2^2wrC2128,519
C4.54C22≀C2 = C24.65D4φ: C22≀C2/C2×D4 → C2 ⊆ Aut C464C4.54C2^2wrC2128,520
C4.55C22≀C2 = 2+ 1+4.2C4φ: C22≀C2/C2×D4 → C2 ⊆ Aut C4324C4.55C2^2wrC2128,523
C4.56C22≀C2 = 2+ 1+4⋊3C4φ: C22≀C2/C2×D4 → C2 ⊆ Aut C432C4.56C2^2wrC2128,524
C4.57C22≀C2 = 2- 1+4⋊2C4φ: C22≀C2/C2×D4 → C2 ⊆ Aut C432C4.57C2^2wrC2128,525
C4.58C22≀C2 = C4○D4.D4φ: C22≀C2/C2×D4 → C2 ⊆ Aut C4168+C4.58C2^2wrC2128,527
C4.59C22≀C2 = (C22×Q8)⋊C4φ: C22≀C2/C2×D4 → C2 ⊆ Aut C4328-C4.59C2^2wrC2128,528
C4.60C22≀C2 = C23⋊2D8φ: C22≀C2/C2×D4 → C2 ⊆ Aut C464C4.60C2^2wrC2128,731
C4.61C22≀C2 = C23⋊3SD16φ: C22≀C2/C2×D4 → C2 ⊆ Aut C464C4.61C2^2wrC2128,732
C4.62C22≀C2 = C23⋊2Q16φ: C22≀C2/C2×D4 → C2 ⊆ Aut C464C4.62C2^2wrC2128,733
C4.63C22≀C2 = M4(2)⋊D4φ: C22≀C2/C2×D4 → C2 ⊆ Aut C432C4.63C2^2wrC2128,738
C4.64C22≀C2 = M4(2)⋊4D4φ: C22≀C2/C2×D4 → C2 ⊆ Aut C432C4.64C2^2wrC2128,739
C4.65C22≀C2 = C42⋊2D4φ: C22≀C2/C2×D4 → C2 ⊆ Aut C4164C4.65C2^2wrC2128,742
C4.66C22≀C2 = (C2×C8).2D4φ: C22≀C2/C2×D4 → C2 ⊆ Aut C4324C4.66C2^2wrC2128,749
C4.67C22≀C2 = C4⋊C4.96D4φ: C22≀C2/C2×D4 → C2 ⊆ Aut C432C4.67C2^2wrC2128,777
C4.68C22≀C2 = C4⋊C4.97D4φ: C22≀C2/C2×D4 → C2 ⊆ Aut C432C4.68C2^2wrC2128,778
C4.69C22≀C2 = C4⋊C4.98D4φ: C22≀C2/C2×D4 → C2 ⊆ Aut C464C4.69C2^2wrC2128,779
C4.70C22≀C2 = M4(2).8D4φ: C22≀C2/C2×D4 → C2 ⊆ Aut C4168+C4.70C2^2wrC2128,780
C4.71C22≀C2 = M4(2).9D4φ: C22≀C2/C2×D4 → C2 ⊆ Aut C4328-C4.71C2^2wrC2128,781
C4.72C22≀C2 = C42.131D4φ: C22≀C2/C2×D4 → C2 ⊆ Aut C4164C4.72C2^2wrC2128,782
C4.73C22≀C2 = M4(2).10D4φ: C22≀C2/C2×D4 → C2 ⊆ Aut C432C4.73C2^2wrC2128,783
C4.74C22≀C2 = M4(2).11D4φ: C22≀C2/C2×D4 → C2 ⊆ Aut C464C4.74C2^2wrC2128,784
C4.75C22≀C2 = C22⋊C4.7D4φ: C22≀C2/C2×D4 → C2 ⊆ Aut C4324C4.75C2^2wrC2128,785
C4.76C22≀C2 = (C2×C4)⋊3D8φ: C22≀C2/C2×D4 → C2 ⊆ Aut C464C4.76C2^2wrC2128,786
C4.77C22≀C2 = (C2×C4)⋊5SD16φ: C22≀C2/C2×D4 → C2 ⊆ Aut C464C4.77C2^2wrC2128,787
C4.78C22≀C2 = (C2×C4)⋊3Q16φ: C22≀C2/C2×D4 → C2 ⊆ Aut C4128C4.78C2^2wrC2128,788
C4.79C22≀C2 = C24.244C23φ: C22≀C2/C2×D4 → C2 ⊆ Aut C464C4.79C2^2wrC2128,1139
C4.80C22≀C2 = C23.309C24φ: C22≀C2/C2×D4 → C2 ⊆ Aut C464C4.80C2^2wrC2128,1141
C4.81C22≀C2 = C24.177D4φ: C22≀C2/C2×D4 → C2 ⊆ Aut C416C4.81C2^2wrC2128,1735
C4.82C22≀C2 = C24.178D4φ: C22≀C2/C2×D4 → C2 ⊆ Aut C432C4.82C2^2wrC2128,1736
C4.83C22≀C2 = C24.104D4φ: C22≀C2/C2×D4 → C2 ⊆ Aut C432C4.83C2^2wrC2128,1737
C4.84C22≀C2 = (C2×D4)⋊21D4φ: C22≀C2/C2×D4 → C2 ⊆ Aut C432C4.84C2^2wrC2128,1744
C4.85C22≀C2 = (C2×Q8)⋊17D4φ: C22≀C2/C2×D4 → C2 ⊆ Aut C464C4.85C2^2wrC2128,1745
C4.86C22≀C2 = M4(2)⋊C23φ: C22≀C2/C2×D4 → C2 ⊆ Aut C4168+C4.86C2^2wrC2128,1751
C4.87C22≀C2 = M4(2).C23φ: C22≀C2/C2×D4 → C2 ⊆ Aut C4328-C4.87C2^2wrC2128,1752
C4.88C22≀C2 = C23.7C24φ: C22≀C2/C2×D4 → C2 ⊆ Aut C4164C4.88C2^2wrC2128,1757
C4.89C22≀C2 = C24.135D4φ: C22≀C2/C24 → C2 ⊆ Aut C464C4.89C2^2wrC2128,624
C4.90C22≀C2 = C23.23D8φ: C22≀C2/C24 → C2 ⊆ Aut C464C4.90C2^2wrC2128,625
C4.91C22≀C2 = C24.75D4φ: C22≀C2/C24 → C2 ⊆ Aut C464C4.91C2^2wrC2128,626
C4.92C22≀C2 = C24.76D4φ: C22≀C2/C24 → C2 ⊆ Aut C464C4.92C2^2wrC2128,627
C4.93C22≀C2 = M4(2)⋊20D4φ: C22≀C2/C24 → C2 ⊆ Aut C432C4.93C2^2wrC2128,632
C4.94C22≀C2 = M4(2).45D4φ: C22≀C2/C24 → C2 ⊆ Aut C432C4.94C2^2wrC2128,633
C4.95C22≀C2 = M4(2).46D4φ: C22≀C2/C24 → C2 ⊆ Aut C4328-C4.95C2^2wrC2128,634
C4.96C22≀C2 = M4(2).47D4φ: C22≀C2/C24 → C2 ⊆ Aut C4168+C4.96C2^2wrC2128,635
C4.97C22≀C2 = M4(2).48D4φ: C22≀C2/C24 → C2 ⊆ Aut C432C4.97C2^2wrC2128,639
C4.98C22≀C2 = M4(2).49D4φ: C22≀C2/C24 → C2 ⊆ Aut C464C4.98C2^2wrC2128,640
C4.99C22≀C2 = C4.(C4×D4)φ: C22≀C2/C24 → C2 ⊆ Aut C4328-C4.99C2^2wrC2128,641
C4.100C22≀C2 = (C2×C8)⋊4D4φ: C22≀C2/C24 → C2 ⊆ Aut C4168+C4.100C2^2wrC2128,642
C4.101C22≀C2 = M4(2)⋊21D4φ: C22≀C2/C24 → C2 ⊆ Aut C4168+C4.101C2^2wrC2128,646
C4.102C22≀C2 = M4(2).50D4φ: C22≀C2/C24 → C2 ⊆ Aut C4328-C4.102C2^2wrC2128,647
C4.103C22≀C2 = C24.360C23φ: C22≀C2/C24 → C2 ⊆ Aut C464C4.103C2^2wrC2128,1347
C4.104C22≀C2 = C24.361C23φ: C22≀C2/C24 → C2 ⊆ Aut C464C4.104C2^2wrC2128,1348
C4.105C22≀C2 = C24⋊8Q8φ: C22≀C2/C24 → C2 ⊆ Aut C432C4.105C2^2wrC2128,1580
C4.106C22≀C2 = C24.105D4φ: C22≀C2/C24 → C2 ⊆ Aut C432C4.106C2^2wrC2128,1738
C4.107C22≀C2 = C24.106D4φ: C22≀C2/C24 → C2 ⊆ Aut C432C4.107C2^2wrC2128,1739
C4.108C22≀C2 = C42.12C23φ: C22≀C2/C24 → C2 ⊆ Aut C4168+C4.108C2^2wrC2128,1753
C4.109C22≀C2 = C42.13C23φ: C22≀C2/C24 → C2 ⊆ Aut C4328-C4.109C2^2wrC2128,1754
C4.110C22≀C2 = C24⋊3C8central extension (φ=1)32C4.110C2^2wrC2128,511
C4.111C22≀C2 = C24.51(C2×C4)central extension (φ=1)64C4.111C2^2wrC2128,512
C4.112C22≀C2 = C24.66D4central extension (φ=1)32C4.112C2^2wrC2128,521
C4.113C22≀C2 = 2+ 1+4⋊4C4central extension (φ=1)324C4.113C2^2wrC2128,526
C4.114C22≀C2 = C23.21M4(2)central extension (φ=1)64C4.114C2^2wrC2128,582
C4.115C22≀C2 = (C2×C8).195D4central extension (φ=1)64C4.115C2^2wrC2128,583
C4.116C22≀C2 = C24.10Q8central extension (φ=1)32C4.116C2^2wrC2128,587
C4.117C22≀C2 = M4(2).40D4central extension (φ=1)324C4.117C2^2wrC2128,590
C4.118C22≀C2 = M4(2).41D4central extension (φ=1)164C4.118C2^2wrC2128,593
C4.119C22≀C2 = M4(2).42D4central extension (φ=1)32C4.119C2^2wrC2128,598
C4.120C22≀C2 = (C2×D4).Q8central extension (φ=1)324C4.120C2^2wrC2128,600
C4.121C22≀C2 = C23.22M4(2)central extension (φ=1)64C4.121C2^2wrC2128,601
C4.122C22≀C2 = C23⋊2M4(2)central extension (φ=1)64C4.122C2^2wrC2128,602
C4.123C22≀C2 = C24.72D4central extension (φ=1)32C4.123C2^2wrC2128,603
C4.124C22≀C2 = M4(2).43D4central extension (φ=1)32C4.124C2^2wrC2128,608
C4.125C22≀C2 = M4(2).44D4central extension (φ=1)324C4.125C2^2wrC2128,613
C4.126C22≀C2 = M4(2)⋊19D4central extension (φ=1)164C4.126C2^2wrC2128,616
C4.127C22≀C2 = (C2×C8)⋊D4central extension (φ=1)164C4.127C2^2wrC2128,623
C4.128C22≀C2 = C23.288C24central extension (φ=1)64C4.128C2^2wrC2128,1120
C4.129C22≀C2 = C24.103D4central extension (φ=1)32C4.129C2^2wrC2128,1734
C4.130C22≀C2 = C42.313C23central extension (φ=1)164C4.130C2^2wrC2128,1750

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