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Extensions 1→N→G→Q→1 with N=C2×C4×Q8 and Q=C2

Direct product G=N×Q with N=C2×C4×Q8 and Q=C2
dρLabelID
Q8×C22×C4128Q8xC2^2xC4128,2155

Semidirect products G=N:Q with N=C2×C4×Q8 and Q=C2
extensionφ:Q→Out NdρLabelID
(C2×C4×Q8)⋊1C2 = (C2×SD16)⋊15C4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):1C2128,612
(C2×C4×Q8)⋊2C2 = C4×C22⋊Q8φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):2C2128,1034
(C2×C4×Q8)⋊3C2 = C4×C4.4D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):3C2128,1035
(C2×C4×Q8)⋊4C2 = C42.159D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):4C2128,1055
(C2×C4×Q8)⋊5C2 = C42.160D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):5C2128,1058
(C2×C4×Q8)⋊6C2 = Q8×C22⋊C4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):6C2128,1072
(C2×C4×Q8)⋊7C2 = C23.223C24φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):7C2128,1073
(C2×C4×Q8)⋊8C2 = C24.558C23φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):8C2128,1092
(C2×C4×Q8)⋊9C2 = C23.244C24φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):9C2128,1094
(C2×C4×Q8)⋊10C2 = C24.220C23φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):10C2128,1099
(C2×C4×Q8)⋊11C2 = C42.162D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):11C2128,1128
(C2×C4×Q8)⋊12C2 = C42.163D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):12C2128,1130
(C2×C4×Q8)⋊13C2 = C23.321C24φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):13C2128,1153
(C2×C4×Q8)⋊14C2 = C23.323C24φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):14C2128,1155
(C2×C4×Q8)⋊15C2 = C24.259C23φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):15C2128,1158
(C2×C4×Q8)⋊16C2 = C23.329C24φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):16C2128,1161
(C2×C4×Q8)⋊17C2 = C23.348C24φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):17C2128,1180
(C2×C4×Q8)⋊18C2 = C24.279C23φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):18C2128,1190
(C2×C4×Q8)⋊19C2 = C24.285C23φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):19C2128,1197
(C2×C4×Q8)⋊20C2 = C23.369C24φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):20C2128,1201
(C2×C4×Q8)⋊21C2 = C42.165D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):21C2128,1268
(C2×C4×Q8)⋊22C2 = C42.166D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):22C2128,1270
(C2×C4×Q8)⋊23C2 = C42.168D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):23C2128,1277
(C2×C4×Q8)⋊24C2 = C42.171D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):24C2128,1280
(C2×C4×Q8)⋊25C2 = C42.178D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):25C2128,1312
(C2×C4×Q8)⋊26C2 = C42.182D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):26C2128,1324
(C2×C4×Q8)⋊27C2 = C42.183D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):27C2128,1331
(C2×C4×Q8)⋊28C2 = C42.184D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):28C2128,1336
(C2×C4×Q8)⋊29C2 = C42.189D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):29C2128,1364
(C2×C4×Q8)⋊30C2 = C42.192D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):30C2128,1369
(C2×C4×Q8)⋊31C2 = C2×C4×SD16φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):31C2128,1669
(C2×C4×Q8)⋊32C2 = C2×SD16⋊C4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):32C2128,1672
(C2×C4×Q8)⋊33C2 = C4×C8.C22φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):33C2128,1677
(C2×C4×Q8)⋊34C2 = C2×C4⋊SD16φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):34C2128,1764
(C2×C4×Q8)⋊35C2 = C2×Q8.D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):35C2128,1766
(C2×C4×Q8)⋊36C2 = C42.212D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):36C2128,1769
(C2×C4×Q8)⋊37C2 = C42.223D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):37C2128,1835
(C2×C4×Q8)⋊38C2 = C42.226D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):38C2128,1840
(C2×C4×Q8)⋊39C2 = C42.230D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):39C2128,1844
(C2×C4×Q8)⋊40C2 = C42.235D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):40C2128,1849
(C2×C4×Q8)⋊41C2 = C2×C23.32C23φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):41C2128,2158
(C2×C4×Q8)⋊42C2 = C2×C23.33C23φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):42C2128,2159
(C2×C4×Q8)⋊43C2 = C4×2- 1+4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):43C2128,2162
(C2×C4×Q8)⋊44C2 = C2×C23.36C23φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):44C2128,2171
(C2×C4×Q8)⋊45C2 = C2×C23.37C23φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):45C2128,2175
(C2×C4×Q8)⋊46C2 = C2×C22.35C24φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):46C2128,2185
(C2×C4×Q8)⋊47C2 = C2×C22.36C24φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):47C2128,2186
(C2×C4×Q8)⋊48C2 = C22.50C25φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):48C2128,2193
(C2×C4×Q8)⋊49C2 = C2×Q8⋊5D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):49C2128,2197
(C2×C4×Q8)⋊50C2 = C2×D4×Q8φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):50C2128,2198
(C2×C4×Q8)⋊51C2 = C2×Q8⋊6D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):51C2128,2199
(C2×C4×Q8)⋊52C2 = C2×C22.46C24φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):52C2128,2202
(C2×C4×Q8)⋊53C2 = C2×D4⋊3Q8φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):53C2128,2204
(C2×C4×Q8)⋊54C2 = C2×C22.50C24φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):54C2128,2206
(C2×C4×Q8)⋊55C2 = Q8×C4○D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):55C2128,2210
(C2×C4×Q8)⋊56C2 = C2×C22.53C24φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):56C2128,2211
(C2×C4×Q8)⋊57C2 = C22.69C25φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):57C2128,2212
(C2×C4×Q8)⋊58C2 = C22.71C25φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):58C2128,2214
(C2×C4×Q8)⋊59C2 = C4⋊2- 1+4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):59C2128,2229
(C2×C4×Q8)⋊60C2 = C22.96C25φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):60C2128,2239
(C2×C4×Q8)⋊61C2 = C22.105C25φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):61C2128,2248
(C2×C4×Q8)⋊62C2 = C22.111C25φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):62C2128,2254
(C2×C4×Q8)⋊63C2 = C23.146C24φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8):63C2128,2255
(C2×C4×Q8)⋊64C2 = C2×C4×C4○D4φ: trivial image64(C2xC4xQ8):64C2128,2156

Non-split extensions G=N.Q with N=C2×C4×Q8 and Q=C2
extensionφ:Q→Out NdρLabelID
(C2×C4×Q8).1C2 = C42.394D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8).1C2128,193
(C2×C4×Q8).2C2 = C42.44D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8).2C2128,199
(C2×C4×Q8).3C2 = C2×Q8⋊C8φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).3C2128,207
(C2×C4×Q8).4C2 = C42.399D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8).4C2128,211
(C2×C4×Q8).5C2 = Q8⋊M4(2)φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8).5C2128,219
(C2×C4×Q8).6C2 = Q8⋊5M4(2)φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8).6C2128,223
(C2×C4×Q8).7C2 = C4×C4.10D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8).7C2128,488
(C2×C4×Q8).8C2 = C4×Q8⋊C4φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).8C2128,493
(C2×C4×Q8).9C2 = Q8⋊C42φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).9C2128,495
(C2×C4×Q8).10C2 = C42.97D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8).10C2128,533
(C2×C4×Q8).11C2 = C42.99D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).11C2128,535
(C2×C4×Q8).12C2 = C42.101D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).12C2128,537
(C2×C4×Q8).13C2 = Q8⋊(C4⋊C4)φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).13C2128,595
(C2×C4×Q8).14C2 = Q8⋊C4⋊C4φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).14C2128,597
(C2×C4×Q8).15C2 = (C2×C4)⋊9Q16φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).15C2128,610
(C2×C4×Q8).16C2 = C42.327D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).16C2128,716
(C2×C4×Q8).17C2 = C42.120D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).17C2128,717
(C2×C4×Q8).18C2 = Q8⋊4C42φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).18C2128,1008
(C2×C4×Q8).19C2 = C42⋊14Q8φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).19C2128,1027
(C2×C4×Q8).20C2 = C4×C4⋊Q8φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).20C2128,1039
(C2×C4×Q8).21C2 = C23.202C24φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).21C2128,1052
(C2×C4×Q8).22C2 = C42.161D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).22C2128,1059
(C2×C4×Q8).23C2 = Q8×C4⋊C4φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).23C2128,1082
(C2×C4×Q8).24C2 = C23.233C24φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).24C2128,1083
(C2×C4×Q8).25C2 = C23.237C24φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).25C2128,1087
(C2×C4×Q8).26C2 = C23.238C24φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).26C2128,1088
(C2×C4×Q8).27C2 = C23.247C24φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).27C2128,1097
(C2×C4×Q8).28C2 = C42⋊5Q8φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).28C2128,1131
(C2×C4×Q8).29C2 = C23.346C24φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).29C2128,1178
(C2×C4×Q8).30C2 = C23.351C24φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).30C2128,1183
(C2×C4×Q8).31C2 = C23.353C24φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).31C2128,1185
(C2×C4×Q8).32C2 = C23.362C24φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).32C2128,1194
(C2×C4×Q8).33C2 = C42.169D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).33C2128,1278
(C2×C4×Q8).34C2 = C42.174D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).34C2128,1297
(C2×C4×Q8).35C2 = C42.176D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).35C2128,1299
(C2×C4×Q8).36C2 = C42.177D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).36C2128,1300
(C2×C4×Q8).37C2 = C42.179D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).37C2128,1313
(C2×C4×Q8).38C2 = C42.180D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).38C2128,1314
(C2×C4×Q8).39C2 = C42.181D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).39C2128,1316
(C2×C4×Q8).40C2 = C42.191D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).40C2128,1366
(C2×C4×Q8).41C2 = C2×C4×Q16φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).41C2128,1670
(C2×C4×Q8).42C2 = C2×Q16⋊C4φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).42C2128,1673
(C2×C4×Q8).43C2 = C2×C8⋊4Q8φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).43C2128,1691
(C2×C4×Q8).44C2 = Q8×M4(2)φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8).44C2128,1695
(C2×C4×Q8).45C2 = C42.695C23φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8).45C2128,1714
(C2×C4×Q8).46C2 = C42.302C23φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8).46C2128,1715
(C2×C4×Q8).47C2 = Q8.4M4(2)φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8).47C2128,1716
(C2×C4×Q8).48C2 = C2×C4⋊2Q16φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).48C2128,1765
(C2×C4×Q8).49C2 = C2×Q8⋊Q8φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).49C2128,1805
(C2×C4×Q8).50C2 = C2×C4.Q16φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).50C2128,1806
(C2×C4×Q8).51C2 = C2×Q8.Q8φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).51C2128,1807
(C2×C4×Q8).52C2 = C42.220D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8).52C2128,1810
(C2×C4×Q8).53C2 = C42.224D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8).53C2128,1836
(C2×C4×Q8).54C2 = C42.231D4φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8).54C2128,1845
(C2×C4×Q8).55C2 = C2×Q8⋊3Q8φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).55C2128,2208
(C2×C4×Q8).56C2 = C2×Q82φ: C2/C1 → C2 ⊆ Out C2×C4×Q8128(C2xC4xQ8).56C2128,2209
(C2×C4×Q8).57C2 = C22.91C25φ: C2/C1 → C2 ⊆ Out C2×C4×Q864(C2xC4xQ8).57C2128,2234
(C2×C4×Q8).58C2 = Q8×C42φ: trivial image128(C2xC4xQ8).58C2128,1004
(C2×C4×Q8).59C2 = Q8×C2×C8φ: trivial image128(C2xC4xQ8).59C2128,1690

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