Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
At least 8645 conjugacy classes of subgroups; only the 4048 normal subgroups are shown.
The subgroup lattice has 796 nodes (normal subgroups only) — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C23×B(4,𝔽2) |
| commutator, Frattini, cosocle | C22×D4 | C26 |
| LCS | G ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×#127 ◁ C2×#3498 ◁ G | |
| LECS | G ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72312280 | C2 | semidirect |
| 2. #72312204 | C2 | semidirect |
| 3. #72312194 | C2 | semidirect |
| 4. #72312193 | C2 | semidirect |
| 5. #72312148 | C2 | semidirect |
| 6. #72312146 | C2 | semidirect |
| 7. #72312141 | C2 | semidirect |
| 8. #72312140 | C2 | semidirect |
| 9. #72312087 | C2 | semidirect |
| 10. #72312074 | C2 | semidirect |
| 11. #72311970 | C2 | semidirect |
| 12. #72311256 | C2 | semidirect |
| 13. #72297638 | C2 | semidirect |
| 14. #72285985 | C2 | semidirect |
| 15. #72251992 | C2 | semidirect |
| 16. #72236702 | C2 | semidirect |
| 17. #72234498 | C2 | semidirect |
| 18. D4×#2196 | C2 | semidirect |
| 19. #72233119 | C2 | semidirect |
| 20. #10586097 | C22 | semidirect |
| 21. C2×#60399 | C22 | semidirect |
| 22. #8934377 | C22 | semidirect |
| 23. #8699271 | C22 | semidirect |
| 24. #8698843 | C22 | semidirect |
| 25. #8195238 | C22 | semidirect |
| 26. #7968183 | C22 | semidirect |
| 29. #7733149 | C22 | semidirect |
| 30. D43 | C22 | semidirect |
| 32. #7666097 | C22 | semidirect |
| 33. C22×#2196 | C22 | semidirect |
| 34. #6629390 | C22 | semidirect |
| 35. #6629364 | C22 | semidirect |
| 36. #6628984 | C22 | semidirect |
| 37. #6628901 | C22 | semidirect |
| 38. #6628896 | C22 | semidirect |
| 39. #6628872 | C22 | semidirect |
| 40. #6591514 | C22 | semidirect |
| 41. #6591488 | C22 | semidirect |
| 42. #6573726 | C22 | semidirect |
| 43. D4×B(4,𝔽2) | C22 | semidirect |
| 44. D4×B(4,𝔽2) | C22 | semidirect |
| 45. D4×#453 | C22 | semidirect |
| 46. #6487648 | C22 | semidirect |
| 47. #6487492 | C22 | semidirect |
| 48. #6470234 | C22 | semidirect |
| 49. #6470037 | C22 | semidirect |
| 50. #6443350 | C22 | semidirect |
| 51. #6442721 | C22 | semidirect |
| 52. #6438004 | C22 | semidirect |
| 53. #6437633 | C22 | semidirect |
| 54. #6385998 | C22 | semidirect |
| 55. #6385980 | C22 | semidirect |
| 56. #6379015 | C22 | semidirect |
| 57. C4×#3025 | C22 | semidirect |
| 58. #512151 | C22 | semidirect |
| 59. #511908 | C22 | semidirect |
| 60. #511771 | C22 | semidirect |
| 61. #508195 | C22 | semidirect |
| 62. #508091 | C22 | semidirect |
| 63. #508066 | C22 | semidirect |
| 64. #503567 | C22 | semidirect |
| 65. #503194 | C22 | semidirect |
| 66. #503182 | C22 | semidirect |
| 67. #503182 | C22 | semidirect |
| 68. #502792 | C22 | semidirect |
| 69. #502786 | C22 | semidirect |
| 70. #502774 | C22 | semidirect |
| 71. #502768 | C22 | semidirect |
| 72. #502725 | C22 | semidirect |
| 73. #502685 | C22 | semidirect |
| 74. #501176 | C22 | semidirect |
| 75. #501156 | C22 | semidirect |
| 76. #501156 | C22 | semidirect |
| 77. #501084 | C22 | semidirect |
| 78. #500943 | C22 | semidirect |
| 79. #500769 | C22 | semidirect |
| 80. #500757 | C22 | semidirect |
| 81. #500757 | C22 | semidirect |
| 82. #500501 | C22 | semidirect |
| 83. #500495 | C22 | semidirect |
| 84. #500483 | C22 | semidirect |
| 85. #500477 | C22 | semidirect |
| 86. #500398 | C22 | semidirect |
| 87. #500227 | C22 | semidirect |
| 88. #500221 | C22 | semidirect |
| 89. #500073 | C22 | semidirect |
| 90. #500050 | C22 | semidirect |
| 91. #500050 | C22 | semidirect |
| 92. #500033 | C22 | semidirect |
| 93. #499843 | C22 | semidirect |
| 94. #499804 | C22 | semidirect |
| 95. #499803 | C22 | semidirect |
| 96. #499803 | C22 | semidirect |
| 97. #499803 | C22 | semidirect |
| 98. #499788 | C22 | semidirect |
| 99. #499788 | C22 | semidirect |
| 100. #499787 | C22 | semidirect |
| 101. #499787 | C22 | semidirect |
| 102. #499284 | C22 | semidirect |
| 103. #498923 | C22 | semidirect |
| 104. #498886 | C22 | semidirect |
| 105. #497496 | C22 | semidirect |
| 106. #497484 | C22 | semidirect |
| 107. D4×#353 | C22 | semidirect |
| 108. #497295 | C22 | semidirect |
| 109. D4×AΣL(1,𝔽16) | C22 | semidirect |
| 110. D4×AΣL(1,𝔽16) | C22 | semidirect |
| 111. #496532 | C22 | semidirect |
| 112. #496520 | C22 | semidirect |
| 113. #496336 | C22 | semidirect |
| 114. #496244 | C22 | semidirect |
| 115. #496237 | C22 | semidirect |
| 116. #496198 | C22 | semidirect |
| 117. C4×#2196 | C22 | semidirect |
| 118. #495603 | C22 | semidirect |
| 119. #495592 | C22 | semidirect |
| 120. #494717 | C22 | semidirect |
| 121. #494700 | C22 | semidirect |
| 122. #494575 | C22 | semidirect |
| 123. #493997 | C22 | semidirect |
| 124. #493424 | C22 | semidirect |
| 125. C2×H(7,𝔽2) | C23 | semidirect |
| 126. D4×H(5,𝔽2) | C23 | semidirect |
| 127. #62852 | C23 | semidirect |
| 128. #62812 | C23 | semidirect |
| 131. C2×#3549 | D4 | semidirect |
| 132. C22×D42 | D4 | semidirect |
| 133. C22×D42 | C23 | semidirect |
| 134. C23×#127 | D4 | semidirect |
| 135. C4×#585 | C23 | semidirect |
| 136. C2×#3027 | C23 | semidirect |
| 137. C2×#3027 | C23 | semidirect |
| 138. C2×#3027 | C23 | semidirect |
| 139. C2×#3026 | C23 | semidirect |
| 143. C22×B(4,𝔽2) | C23 | semidirect |
| 144. C22×#453 | C23 | semidirect |
| 145. C2×#2883 | C23 | semidirect |
| 147. #59816 | C23 | semidirect |
| 148. #59632 | C23 | semidirect |
| 149. #59378 | C23 | semidirect |
| 150. #59199 | C23 | semidirect |
| 151. #59126 | C23 | semidirect |
| 153. #58997 | C23 | semidirect |
| 154. #58997 | C23 | semidirect |
| 155. #58990 | C23 | semidirect |
| 156. #58990 | C23 | semidirect |
| 157. #52293 | C23 | semidirect |
| 158. #51940 | C23 | semidirect |
| 160. #48143 | C23 | semidirect |
| 161. #47827 | C23 | semidirect |
| 162. #46338 | C23 | semidirect |
| 163. #45645 | C23 | semidirect |
| 164. #39361 | D4 | semidirect |
| 165. #39336 | D4 | semidirect |
| 168. #38904 | D4 | semidirect |
| 170. #37297 | D4 | semidirect |
| 171. #37232 | C23 | semidirect |
| 172. #36714 | C23 | semidirect |
| 173. #36702 | D4 | semidirect |
| 174. #36624 | D4 | semidirect |
| 175. #36412 | D4 | semidirect |
| 177. D4×#120 | D4 | semidirect |
| 178. D4×#120 | D4 | semidirect |
| 181. #35528 | D4 | semidirect |
| 185. #35274 | D4 | semidirect |
| 186. #35274 | D4 | semidirect |
| 188. #35237 | D4 | semidirect |
| 189. #35222 | D4 | semidirect |
| 192. #34364 | D4 | semidirect |
| 193. #34356 | C23 | semidirect |
| 194. #34210 | D4 | semidirect |
| 195. C4×D42 | C23 | semidirect |
| 196. #34155 | D4 | semidirect |
| 199. C2×#2196 | C23 | semidirect |
| 200. C2×#2196 | C23 | semidirect |
| 201. C2×#2196 | C23 | semidirect |
| 202. C2×#2196 | C23 | semidirect |
| 203. C22×#353 | C23 | semidirect |
| 204. C2×#2121 | C23 | semidirect |
| 205. C22×AΣL(1,𝔽16) | C23 | semidirect |
| 206. C22×AΣL(1,𝔽16) | C23 | semidirect |
| 207. #33021 | C23 | semidirect |
| 208. #32992 | C23 | semidirect |
| 209. #32976 | C23 | semidirect |
| 210. #32971 | C23 | semidirect |
| 212. #32926 | C23 | semidirect |
| 214. #32899 | C23 | semidirect |
| 215. #32899 | C23 | semidirect |
| 216. #32898 | C23 | semidirect |
| 217. #32898 | C23 | semidirect |
| 218. #32890 | C23 | semidirect |
| 219. #32890 | C23 | semidirect |
| 220. #32888 | C23 | semidirect |
| 221. #25900 | C23 | semidirect |
| 222. #25869 | C23 | semidirect |
| 224. #25771 | C23 | semidirect |
| 226. #24412 | C23 | semidirect |
| 227. #24404 | C23 | semidirect |
| 228. #24404 | C23 | semidirect |
| 229. #24261 | C23 | semidirect |
| 231. #24260 | C23 | semidirect |
| 232. #24222 | C23 | semidirect |
| 233. #24058 | C23 | semidirect |
| 234. #24022 | C23 | semidirect |
| 235. #23906 | C23 | semidirect |
| 236. #23903 | C23 | semidirect |
| 238. #23900 | C23 | semidirect |
| 239. D4×#100 | C23 | semidirect |
| 240. D4×#99 | C23 | semidirect |
| 241. D4×#99 | C23 | semidirect |
| 242. C4×#458 | C23 | semidirect |
| 244. C4×B(4,𝔽2) | C23 | semidirect |
| 245. C4×#453 | C23 | semidirect |
| 246. #20961 | C23 | semidirect |
| 248. #20888 | C23 | semidirect |
| 249. #20728 | C23 | semidirect |
| 250. #20723 | C23 | semidirect |
| 251. #20632 | C23 | semidirect |
| 252. #20616 | C23 | semidirect |
| 253. #20609 | C23 | semidirect |
| 254. #20608 | C23 | semidirect |
| 255. #20608 | C23 | semidirect |
| 256. #20592 | C23 | semidirect |
| 257. #20586 | C23 | semidirect |
| 258. #20585 | C23 | semidirect |
| 259. C4×#410 | C23 | semidirect |
| 260. #13462 | C23 | semidirect |
| 261. #13423 | C23 | semidirect |
| 262. #13422 | C23 | semidirect |
| 263. #13422 | C23 | semidirect |
| 264. #13420 | C23 | semidirect |
| 265. #13419 | C23 | semidirect |
| 266. #13376 | C23 | semidirect |
| 267. #13376 | C23 | semidirect |
| 268. #13347 | C23 | semidirect |
| 269. #13347 | C23 | semidirect |
| 271. #13346 | C23 | semidirect |
| 272. #13346 | C23 | semidirect |
| 273. #13346 | C23 | semidirect |
| 274. #13346 | C23 | semidirect |
| 275. #13344 | C23 | semidirect |
| 276. #13344 | C23 | semidirect |
| 277. #13343 | C23 | semidirect |
| 278. #13343 | C23 | semidirect |
| 279. #13343 | C23 | semidirect |
| 280. #13299 | C23 | semidirect |
| 281. #13299 | C23 | semidirect |
| 282. #13295 | C23 | semidirect |
| 283. #13292 | C23 | semidirect |
| 284. #13223 | C23 | semidirect |
| 285. #13223 | C23 | semidirect |
| 286. #13221 | C23 | semidirect |
| 287. #13221 | C23 | semidirect |
| 288. #13218 | C23 | semidirect |
| 289. #13218 | C23 | semidirect |
| 290. #13089 | C23 | semidirect |
| 291. #13089 | C23 | semidirect |
| 292. #13089 | C23 | semidirect |
| 293. #13088 | C23 | semidirect |
| 294. #13088 | C23 | semidirect |
| 295. #13087 | C23 | semidirect |
| 296. #13087 | C23 | semidirect |
| 297. #13087 | C23 | semidirect |
| 298. #13086 | C23 | semidirect |
| 299. #13086 | C23 | semidirect |
| 300. #13082 | C23 | semidirect |
| 301. #13082 | C23 | semidirect |
| 302. #13047 | C23 | semidirect |
| 303. #13047 | C23 | semidirect |
| 304. #13043 | C23 | semidirect |
| 305. #13043 | C23 | semidirect |
| 306. #13043 | C23 | semidirect |
| 308. #13041 | C23 | semidirect |
| 309. #13041 | C23 | semidirect |
| 310. #13041 | C23 | semidirect |
| 311. #12964 | C23 | semidirect |
| 312. #12960 | C23 | semidirect |
| 313. #12958 | C23 | semidirect |
| 314. #12958 | C23 | semidirect |
| 315. #12858 | C23 | semidirect |
| 316. #12854 | C23 | semidirect |
| 317. #12853 | C23 | semidirect |
| 318. #12797 | C23 | semidirect |
| 319. #12794 | C23 | semidirect |
| 320. #12793 | C23 | semidirect |
| 321. #12793 | C23 | semidirect |
| 322. #12759 | C23 | semidirect |
| 323. #12759 | C23 | semidirect |
| 324. #12693 | C23 | semidirect |
| 325. #12691 | C23 | semidirect |
| 326. #12690 | C23 | semidirect |
| 328. #12687 | C23 | semidirect |
| 329. #12687 | C23 | semidirect |
| 330. C4×#353 | C23 | semidirect |
| 331. C4×#352 | C23 | semidirect |
| 332. C4×AΣL(1,𝔽16) | C23 | semidirect |
| 333. C4×AΣL(1,𝔽16) | C23 | semidirect |
| 334. #12582 | C23 | semidirect |
| 335. #12574 | C23 | semidirect |
| 340. C24×D4 | C2×D4 | semidirect |
| 341. C24×D4 | C2×D4 | semidirect |
| 342. C24×D4 | C2×D4 | semidirect |
| 345. C2×#555 | C2×D4 | semidirect |
| 349. C2×D42 | C2×D4 | semidirect |
| 356. C2×#535 | C2×D4 | semidirect |
| 357. C2×#535 | C2×D4 | semidirect |
| 358. C2×#535 | C2×D4 | semidirect |
| 359. C2×#535 | C2×D4 | semidirect |
| 361. C2×#534 | C2×D4 | semidirect |
| 366. C2×#532 | C2×D4 | semidirect |
| 370. C22×#127 | C2×D4 | semidirect |
| 371. C22×#127 | C2×D4 | semidirect |
| 372. C22×#127 | C2×D4 | semidirect |
| 374. C2×#525 | C2×D4 | semidirect |
| 376. C22×#121 | C2×D4 | semidirect |
| 377. C22×#120 | C2×D4 | semidirect |
| 378. C22×#120 | C2×D4 | semidirect |
| 379. C22×#120 | C2×D4 | semidirect |
| 384. C2×#518 | C2×D4 | semidirect |
| 386. C22×C4×D4 | C2×D4 | semidirect |
| 387. C23×C42 | C2×D4 | semidirect |
| 405. #2867 | C2×D4 | semidirect |
| 406. #2858 | C2×D4 | semidirect |
| 407. #2856 | C2×D4 | semidirect |
| 408. #2854 | C2×D4 | semidirect |
| 409. #2847 | C2×D4 | semidirect |
| 410. #2847 | C2×D4 | semidirect |
| 411. #2847 | C2×D4 | semidirect |
| 412. #2846 | C2×D4 | semidirect |
| 413. #2846 | C2×D4 | semidirect |
| 420. #2622 | C2×D4 | semidirect |
| 421. #2619 | C2×D4 | semidirect |
| 422. #2613 | C2×D4 | semidirect |
| 423. #2567 | C2×D4 | semidirect |
| 425. #2548 | C2×D4 | semidirect |
| 426. #2541 | C2×D4 | semidirect |
| 427. #2541 | C2×D4 | semidirect |
| 429. #2504 | C2×D4 | semidirect |
| 430. #2500 | C2×D4 | semidirect |
| 431. #2500 | C2×D4 | semidirect |
| 432. #2487 | C2×D4 | semidirect |
| 434. #2482 | C2×D4 | semidirect |
| 435. #2433 | C2×D4 | semidirect |
| 436. #2433 | C2×D4 | semidirect |
| 437. #2433 | C2×D4 | semidirect |
| 438. #2433 | C2×D4 | semidirect |
| 439. #2433 | C2×D4 | semidirect |
| 441. #2431 | C2×D4 | semidirect |
| 443. #2410 | C2×D4 | semidirect |
| 444. #2410 | C2×D4 | semidirect |
| 445. #2410 | C2×D4 | semidirect |
| 446. #2410 | C2×D4 | semidirect |
| 447. #2408 | C2×D4 | semidirect |
| 448. #2408 | C2×D4 | semidirect |
| 451. #2404 | C2×D4 | semidirect |
| 453. #2403 | C2×D4 | semidirect |
| 454. #2403 | C2×D4 | semidirect |
| 461. D4×C22⋊C4 | C2×D4 | semidirect |
| 462. D4×C22⋊C4 | C2×D4 | semidirect |
| 463. D4×C22⋊C4 | C2×D4 | semidirect |
| 464. D4×C22⋊C4 | C2×D4 | semidirect |
| 465. #2309 | C2×D4 | semidirect |
| 466. #2309 | C2×D4 | semidirect |
| 468. #2308 | C2×D4 | semidirect |
| 469. #2308 | C2×D4 | semidirect |
| 472. C4×#124 | C2×D4 | semidirect |
| 473. C4×#123 | C2×D4 | semidirect |
| 475. C4×#120 | C2×D4 | semidirect |
| 476. C4×#120 | C2×D4 | semidirect |
| 479. #2297 | C2×D4 | semidirect |
| 480. #2297 | C2×D4 | semidirect |
| 481. #2297 | C2×D4 | semidirect |
| 483. #2296 | C2×D4 | semidirect |
| 484. #2293 | C2×D4 | semidirect |
| 485. #2285 | C2×D4 | semidirect |
| 486. #2283 | C2×D4 | semidirect |
| 487. #2280 | C2×D4 | semidirect |
| 488. C42×D4 | C2×D4 | semidirect |
| 489. C4×#117 | C2×D4 | semidirect |
| 490. C4×#117 | C2×D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.