Extensions 1→N→G→Q→1 with N=C2×C4⋊D4 and Q=C2

Direct product G=N×Q with N=C2×C4⋊D4 and Q=C2
dρLabelID
C22×C4⋊D464C2^2xC4:D4128,2164

Semidirect products G=N:Q with N=C2×C4⋊D4 and Q=C2
extensionφ:Q→Out NdρLabelID
(C2×C4⋊D4)⋊1C2 = C232D8φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):1C2128,731
(C2×C4⋊D4)⋊2C2 = C24.244C23φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):2C2128,1139
(C2×C4⋊D4)⋊3C2 = C23.308C24φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):3C2128,1140
(C2×C4⋊D4)⋊4C2 = C248D4φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):4C2128,1142
(C2×C4⋊D4)⋊5C2 = C24.249C23φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):5C2128,1146
(C2×C4⋊D4)⋊6C2 = C23.316C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):6C2128,1148
(C2×C4⋊D4)⋊7C2 = C23.324C24φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):7C2128,1156
(C2×C4⋊D4)⋊8C2 = C23.328C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):8C2128,1160
(C2×C4⋊D4)⋊9C2 = C24.262C23φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):9C2128,1162
(C2×C4⋊D4)⋊10C2 = C24.263C23φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):10C2128,1163
(C2×C4⋊D4)⋊11C2 = C23.333C24φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):11C2128,1165
(C2×C4⋊D4)⋊12C2 = C23.356C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):12C2128,1188
(C2×C4⋊D4)⋊13C2 = C23.364C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):13C2128,1196
(C2×C4⋊D4)⋊14C2 = C4217D4φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):14C2128,1267
(C2×C4⋊D4)⋊15C2 = C4218D4φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):15C2128,1269
(C2×C4⋊D4)⋊16C2 = C23.439C24φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):16C2128,1271
(C2×C4⋊D4)⋊17C2 = C4219D4φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):17C2128,1272
(C2×C4⋊D4)⋊18C2 = C4220D4φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):18C2128,1273
(C2×C4⋊D4)⋊19C2 = C23.443C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):19C2128,1275
(C2×C4⋊D4)⋊20C2 = C23.455C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):20C2128,1287
(C2×C4⋊D4)⋊21C2 = C24.360C23φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):21C2128,1347
(C2×C4⋊D4)⋊22C2 = C2410D4φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):22C2128,1349
(C2×C4⋊D4)⋊23C2 = C4227D4φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):23C2128,1351
(C2×C4⋊D4)⋊24C2 = C23.535C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):24C2128,1367
(C2×C4⋊D4)⋊25C2 = C23.556C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):25C2128,1388
(C2×C4⋊D4)⋊26C2 = C24.377C23φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):26C2128,1393
(C2×C4⋊D4)⋊27C2 = C23.568C24φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):27C2128,1400
(C2×C4⋊D4)⋊28C2 = C23.569C24φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):28C2128,1401
(C2×C4⋊D4)⋊29C2 = C23.571C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):29C2128,1403
(C2×C4⋊D4)⋊30C2 = C23.573C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):30C2128,1405
(C2×C4⋊D4)⋊31C2 = C24.384C23φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):31C2128,1407
(C2×C4⋊D4)⋊32C2 = C23.576C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):32C2128,1408
(C2×C4⋊D4)⋊33C2 = C23.578C24φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):33C2128,1410
(C2×C4⋊D4)⋊34C2 = C24.389C23φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):34C2128,1414
(C2×C4⋊D4)⋊35C2 = C24.395C23φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):35C2128,1420
(C2×C4⋊D4)⋊36C2 = C24.406C23φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):36C2128,1431
(C2×C4⋊D4)⋊37C2 = C23.603C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):37C2128,1435
(C2×C4⋊D4)⋊38C2 = C24.413C23φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):38C2128,1446
(C2×C4⋊D4)⋊39C2 = C24.459C23φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):39C2128,1545
(C2×C4⋊D4)⋊40C2 = C23.715C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):40C2128,1547
(C2×C4⋊D4)⋊41C2 = C2413D4φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):41C2128,1579
(C2×C4⋊D4)⋊42C2 = C4247D4φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):42C2128,1588
(C2×C4⋊D4)⋊43C2 = C2×C22⋊D8φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):43C2128,1728
(C2×C4⋊D4)⋊44C2 = C2×D4⋊D4φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):44C2128,1732
(C2×C4⋊D4)⋊45C2 = C24.105D4φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):45C2128,1738
(C2×C4⋊D4)⋊46C2 = C2×C87D4φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):46C2128,1780
(C2×C4⋊D4)⋊47C2 = C2×C82D4φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):47C2128,1784
(C2×C4⋊D4)⋊48C2 = M4(2)⋊14D4φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):48C2128,1787
(C2×C4⋊D4)⋊49C2 = C233D8φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):49C2128,1918
(C2×C4⋊D4)⋊50C2 = C24.121D4φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):50C2128,1920
(C2×C4⋊D4)⋊51C2 = C24.125D4φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):51C2128,1924
(C2×C4⋊D4)⋊52C2 = C24.127D4φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):52C2128,1926
(C2×C4⋊D4)⋊53C2 = C2×C233D4φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):53C2128,2177
(C2×C4⋊D4)⋊54C2 = C2×C22.29C24φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):54C2128,2178
(C2×C4⋊D4)⋊55C2 = C2×C22.31C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):55C2128,2180
(C2×C4⋊D4)⋊56C2 = C2×C22.32C24φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):56C2128,2182
(C2×C4⋊D4)⋊57C2 = C2×C22.34C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):57C2128,2184
(C2×C4⋊D4)⋊58C2 = C2×D42φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):58C2128,2194
(C2×C4⋊D4)⋊59C2 = C2×D45D4φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):59C2128,2195
(C2×C4⋊D4)⋊60C2 = C2×D46D4φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):60C2128,2196
(C2×C4⋊D4)⋊61C2 = C2×Q85D4φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):61C2128,2197
(C2×C4⋊D4)⋊62C2 = C2×Q86D4φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):62C2128,2199
(C2×C4⋊D4)⋊63C2 = C2×C22.47C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):63C2128,2203
(C2×C4⋊D4)⋊64C2 = C2×C22.49C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):64C2128,2205
(C2×C4⋊D4)⋊65C2 = C22.77C25φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):65C2128,2220
(C2×C4⋊D4)⋊66C2 = C22.83C25φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):66C2128,2226
(C2×C4⋊D4)⋊67C2 = C4⋊2+ 1+4φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):67C2128,2228
(C2×C4⋊D4)⋊68C2 = C22.94C25φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):68C2128,2237
(C2×C4⋊D4)⋊69C2 = C22.108C25φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):69C2128,2251
(C2×C4⋊D4)⋊70C2 = C2×C22.54C24φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):70C2128,2257
(C2×C4⋊D4)⋊71C2 = C2×C22.56C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4):71C2128,2259
(C2×C4⋊D4)⋊72C2 = C22.123C25φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):72C2128,2266
(C2×C4⋊D4)⋊73C2 = C22.125C25φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):73C2128,2268
(C2×C4⋊D4)⋊74C2 = C22.126C25φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):74C2128,2269
(C2×C4⋊D4)⋊75C2 = C22.131C25φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4):75C2128,2274
(C2×C4⋊D4)⋊76C2 = C2×C22.19C24φ: trivial image32(C2xC4:D4):76C2128,2167
(C2×C4⋊D4)⋊77C2 = C2×C22.26C24φ: trivial image64(C2xC4:D4):77C2128,2174

Non-split extensions G=N.Q with N=C2×C4⋊D4 and Q=C2
extensionφ:Q→Out NdρLabelID
(C2×C4⋊D4).1C2 = C24.(C2×C4)φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4).1C2128,203
(C2×C4⋊D4).2C2 = C2×C22.SD16φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4).2C2128,230
(C2×C4⋊D4).3C2 = C24.54D4φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4).3C2128,239
(C2×C4⋊D4).4C2 = C24.56D4φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4).4C2128,242
(C2×C4⋊D4).5C2 = C24.60D4φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4).5C2128,251
(C2×C4⋊D4).6C2 = C23.38D8φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).6C2128,606
(C2×C4⋊D4).7C2 = C24.74D4φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).7C2128,607
(C2×C4⋊D4).8C2 = C23.23D8φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).8C2128,625
(C2×C4⋊D4).9C2 = C24.76D4φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).9C2128,627
(C2×C4⋊D4).10C2 = M4(2)⋊20D4φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4).10C2128,632
(C2×C4⋊D4).11C2 = C24.175C23φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4).11C2128,696
(C2×C4⋊D4).12C2 = C233SD16φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).12C2128,732
(C2×C4⋊D4).13C2 = C24.83D4φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).13C2128,765
(C2×C4⋊D4).14C2 = C24.84D4φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).14C2128,766
(C2×C4⋊D4).15C2 = C4213D4φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).15C2128,1056
(C2×C4⋊D4).16C2 = C24.198C23φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).16C2128,1057
(C2×C4⋊D4).17C2 = C23.215C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).17C2128,1065
(C2×C4⋊D4).18C2 = C24.215C23φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).18C2128,1093
(C2×C4⋊D4).19C2 = C24.217C23φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).19C2128,1095
(C2×C4⋊D4).20C2 = C24.218C23φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).20C2128,1096
(C2×C4⋊D4).21C2 = C23.259C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).21C2128,1109
(C2×C4⋊D4).22C2 = C24.254C23φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).22C2128,1152
(C2×C4⋊D4).23C2 = C23.322C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).23C2128,1154
(C2×C4⋊D4).24C2 = C24.258C23φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).24C2128,1157
(C2×C4⋊D4).25C2 = C24.259C23φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).25C2128,1158
(C2×C4⋊D4).26C2 = C23.327C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).26C2128,1159
(C2×C4⋊D4).27C2 = C24.565C23φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).27C2128,1168
(C2×C4⋊D4).28C2 = C24.269C23φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).28C2128,1175
(C2×C4⋊D4).29C2 = C23.344C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).29C2128,1176
(C2×C4⋊D4).30C2 = C24.293C23φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).30C2128,1208
(C2×C4⋊D4).31C2 = C23.390C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).31C2128,1222
(C2×C4⋊D4).32C2 = C23.391C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).32C2128,1223
(C2×C4⋊D4).33C2 = C23.400C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).33C2128,1232
(C2×C4⋊D4).34C2 = C23.401C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).34C2128,1233
(C2×C4⋊D4).35C2 = C23.404C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).35C2128,1236
(C2×C4⋊D4).36C2 = C24.331C23φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).36C2128,1291
(C2×C4⋊D4).37C2 = C23.491C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).37C2128,1323
(C2×C4⋊D4).38C2 = C24.587C23φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).38C2128,1350
(C2×C4⋊D4).39C2 = C4228D4φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).39C2128,1352
(C2×C4⋊D4).40C2 = C23.524C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).40C2128,1356
(C2×C4⋊D4).41C2 = C24.592C23φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).41C2128,1371
(C2×C4⋊D4).42C2 = C23.572C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).42C2128,1404
(C2×C4⋊D4).43C2 = C23.581C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).43C2128,1413
(C2×C4⋊D4).44C2 = C24.393C23φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).44C2128,1418
(C2×C4⋊D4).45C2 = C23.591C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).45C2128,1423
(C2×C4⋊D4).46C2 = C24.407C23φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).46C2128,1433
(C2×C4⋊D4).47C2 = C23.608C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).47C2128,1440
(C2×C4⋊D4).48C2 = C23.611C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).48C2128,1443
(C2×C4⋊D4).49C2 = C23.716C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).49C2128,1548
(C2×C4⋊D4).50C2 = C4246D4φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).50C2128,1582
(C2×C4⋊D4).51C2 = C24.598C23φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).51C2128,1586
(C2×C4⋊D4).52C2 = C2×Q8⋊D4φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).52C2128,1730
(C2×C4⋊D4).53C2 = C2×C88D4φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).53C2128,1779
(C2×C4⋊D4).54C2 = C2×C8⋊D4φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).54C2128,1783
(C2×C4⋊D4).55C2 = C2×C22.D8φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).55C2128,1817
(C2×C4⋊D4).56C2 = C2×C23.19D4φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).56C2128,1819
(C2×C4⋊D4).57C2 = C2×C23.46D4φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).57C2128,1821
(C2×C4⋊D4).58C2 = C24.117D4φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4).58C2128,1826
(C2×C4⋊D4).59C2 = C234SD16φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4).59C2128,1919
(C2×C4⋊D4).60C2 = C24.126D4φ: C2/C1C2 ⊆ Out C2×C4⋊D432(C2xC4:D4).60C2128,1925
(C2×C4⋊D4).61C2 = C2×C22.33C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).61C2128,2183
(C2×C4⋊D4).62C2 = C2×C22.36C24φ: C2/C1C2 ⊆ Out C2×C4⋊D464(C2xC4:D4).62C2128,2186
(C2×C4⋊D4).63C2 = C4×C4⋊D4φ: trivial image64(C2xC4:D4).63C2128,1032
(C2×C4⋊D4).64C2 = C2×C23.36C23φ: trivial image64(C2xC4:D4).64C2128,2171

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