Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
Only the 5598 normal subgroups are shown; non-normal subgroups are omitted.
The subgroup lattice has 858 nodes (normal subgroups only) — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #1202 |
| commutator, Frattini, cosocle | C23×C4 | C26 |
| LCS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72341445 | C2 | semidirect |
| 2. #72341442 | C2 | semidirect |
| 3. #72341441 | C2 | semidirect |
| 4. #72341440 | C2 | semidirect |
| 5. #72341366 | C2 | semidirect |
| 6. #72341355 | C2 | semidirect |
| 7. #72341346 | C2 | semidirect |
| 8. #72341340 | C2 | semidirect |
| 9. #72341332 | C2 | semidirect |
| 10. #72312387 | C2 | semidirect |
| 11. #72311254 | C2 | semidirect |
| 12. #72310916 | C2 | semidirect |
| 13. #72241304 | C2 | semidirect |
| 14. #72241303 | C2 | semidirect |
| 15. #72241302 | C2 | semidirect |
| 16. #72241301 | C2 | semidirect |
| 17. #72241168 | C2 | semidirect |
| 18. #72241161 | C2 | semidirect |
| 19. #72238012 | C2 | semidirect |
| 20. #72227731 | C2 | semidirect |
| 22. #10586999 | C22 | semidirect |
| 23. #10586097 | C22 | semidirect |
| 24. #10576179 | C22 | semidirect |
| 25. #10576118 | C22 | semidirect |
| 27. #10574854 | C22 | semidirect |
| 28. #10574854 | C22 | semidirect |
| 30. #10574846 | C22 | semidirect |
| 31. #10574846 | C22 | semidirect |
| 33. #10574841 | C22 | semidirect |
| 34. #10574841 | C22 | semidirect |
| 35. C2×#60389 | C22 | semidirect |
| 37. C2×#60388 | C22 | semidirect |
| 38. C2×#60388 | C22 | semidirect |
| 39. #10574065 | C22 | semidirect |
| 40. #10574064 | C22 | semidirect |
| 41. #7674604 | C22 | semidirect |
| 42. #6629052 | C22 | semidirect |
| 43. #6628972 | C22 | semidirect |
| 44. #6628902 | C22 | semidirect |
| 45. #6628886 | C22 | semidirect |
| 46. #6628886 | C22 | semidirect |
| 47. #6628883 | C22 | semidirect |
| 48. #6628873 | C22 | semidirect |
| 49. #6628873 | C22 | semidirect |
| 50. #6628872 | C22 | semidirect |
| 51. #6443343 | C22 | semidirect |
| 52. #6443332 | C22 | semidirect |
| 53. C2×#25749 | C22 | semidirect |
| 54. #6443298 | C22 | semidirect |
| 55. #6442700 | C22 | semidirect |
| 56. #6442607 | C22 | semidirect |
| 57. #6442596 | C22 | semidirect |
| 58. #6442560 | C22 | semidirect |
| 59. #6437989 | C22 | semidirect |
| 60. #6437986 | C22 | semidirect |
| 61. #6437970 | C22 | semidirect |
| 62. #6437969 | C22 | semidirect |
| 63. #6437949 | C22 | semidirect |
| 64. C2×#24475 | C22 | semidirect |
| 65. #6437942 | C22 | semidirect |
| 66. #6437941 | C22 | semidirect |
| 67. #6437630 | C22 | semidirect |
| 68. #6437610 | C22 | semidirect |
| 69. #6437594 | C22 | semidirect |
| 70. #6437593 | C22 | semidirect |
| 71. #6437584 | C22 | semidirect |
| 72. C2×#23874 | C22 | semidirect |
| 73. #6437578 | C22 | semidirect |
| 74. #6437481 | C22 | semidirect |
| 75. #6437480 | C22 | semidirect |
| 76. #6437453 | C22 | semidirect |
| 77. #6437452 | C22 | semidirect |
| 78. #6379196 | C22 | semidirect |
| 79. #6379191 | C22 | semidirect |
| 80. #6379114 | C22 | semidirect |
| 81. #6379033 | C22 | semidirect |
| 82. #6372723 | C22 | semidirect |
| 83. #6372704 | C22 | semidirect |
| 84. #449493 | C22 | semidirect |
| 85. #449490 | C22 | semidirect |
| 86. #419045 | C22 | semidirect |
| 87. #419041 | C22 | semidirect |
| 88. #419010 | C22 | semidirect |
| 89. #418910 | C22 | semidirect |
| 90. #418906 | C22 | semidirect |
| 91. #418884 | C22 | semidirect |
| 92. #417817 | C22 | semidirect |
| 93. #417806 | C22 | semidirect |
| 94. #417802 | C22 | semidirect |
| 95. #417800 | C22 | semidirect |
| 96. #417712 | C22 | semidirect |
| 97. #417702 | C22 | semidirect |
| 98. #417669 | C22 | semidirect |
| 99. #417626 | C22 | semidirect |
| 100. #417566 | C22 | semidirect |
| 101. #395638 | C22 | semidirect |
| 102. #395628 | C22 | semidirect |
| 103. #395616 | C22 | semidirect |
| 104. #395587 | C22 | semidirect |
| 105. #395560 | C22 | semidirect |
| 106. #395528 | C22 | semidirect |
| 107. #394382 | C22 | semidirect |
| 108. #394366 | C22 | semidirect |
| 109. #394356 | C22 | semidirect |
| 110. #394343 | C22 | semidirect |
| 111. #394287 | C22 | semidirect |
| 112. #394265 | C22 | semidirect |
| 113. #394133 | C22 | semidirect |
| 114. #394131 | C22 | semidirect |
| 115. #394127 | C22 | semidirect |
| 116. #394106 | C22 | semidirect |
| 117. #394098 | C22 | semidirect |
| 118. #394054 | C22 | semidirect |
| 119. #394043 | C22 | semidirect |
| 120. #394032 | C22 | semidirect |
| 121. #394022 | C22 | semidirect |
| 122. #393998 | C22 | semidirect |
| 123. #393986 | C22 | semidirect |
| 124. #393907 | C22 | semidirect |
| 125. #392714 | C22 | semidirect |
| 126. #392711 | C22 | semidirect |
| 127. #392703 | C22 | semidirect |
| 128. #392140 | C22 | semidirect |
| 129. #392140 | C22 | semidirect |
| 130. #392138 | C22 | semidirect |
| 131. #392138 | C22 | semidirect |
| 132. #392136 | C22 | semidirect |
| 133. #374127 | C22 | semidirect |
| 134. #374021 | C22 | semidirect |
| 135. #374010 | C22 | semidirect |
| 136. #366736 | C22 | semidirect |
| 137. #366729 | C22 | semidirect |
| 138. #366702 | C22 | semidirect |
| 139. #366640 | C22 | semidirect |
| 140. #366636 | C22 | semidirect |
| 141. #366624 | C22 | semidirect |
| 142. #364608 | C22 | semidirect |
| 143. #364606 | C22 | semidirect |
| 144. #364599 | C22 | semidirect |
| 145. #364542 | C22 | semidirect |
| 146. #364512 | C22 | semidirect |
| 147. #364504 | C22 | semidirect |
| 148. #360593 | C22 | semidirect |
| 149. #360585 | C22 | semidirect |
| 150. #360561 | C22 | semidirect |
| 151. #360531 | C22 | semidirect |
| 152. #359685 | C22 | semidirect |
| 153. #359681 | C22 | semidirect |
| 154. #359673 | C22 | semidirect |
| 155. #359652 | C22 | semidirect |
| 156. #359619 | C22 | semidirect |
| 157. #359605 | C22 | semidirect |
| 158. #359548 | C22 | semidirect |
| 159. #359529 | C22 | semidirect |
| 160. #356106 | C22 | semidirect |
| 161. #356068 | C22 | semidirect |
| 162. #356056 | C22 | semidirect |
| 168. C2×H(7,𝔽2) | C23 | semidirect |
| 171. #63090 | C23 | semidirect |
| 172. #63090 | C23 | semidirect |
| 173. C2×#3586 | C23 | semidirect |
| 176. C2×#3585 | C23 | semidirect |
| 177. C2×#3585 | C23 | semidirect |
| 178. #63076 | C23 | semidirect |
| 181. #62852 | C23 | semidirect |
| 182. #62852 | C23 | semidirect |
| 184. #62812 | C23 | semidirect |
| 185. C2×#3500 | C23 | semidirect |
| 187. C2×#3498 | C23 | semidirect |
| 188. C4×#585 | C23 | semidirect |
| 189. #60645 | C23 | semidirect |
| 190. C2×#3153 | C23 | semidirect |
| 191. #60469 | C23 | semidirect |
| 192. C2×#3069 | C23 | semidirect |
| 193. #60455 | C23 | semidirect |
| 194. #60454 | C23 | semidirect |
| 195. #60415 | C23 | semidirect |
| 196. C2×#3040 | C23 | semidirect |
| 197. #60398 | C23 | semidirect |
| 198. C2×#3028 | C23 | semidirect |
| 199. #60391 | D4 | semidirect |
| 200. #60390 | D4 | semidirect |
| 201. #60389 | D4 | semidirect |
| 202. #60388 | D4 | semidirect |
| 209. #60387 | C23 | semidirect |
| 210. #60387 | C23 | semidirect |
| 211. #60387 | C23 | semidirect |
| 213. C2×#3022 | C23 | semidirect |
| 214. C2×#3022 | C23 | semidirect |
| 215. C2×#3022 | C23 | semidirect |
| 216. C2×#3022 | C23 | semidirect |
| 217. C2×#3021 | D4 | semidirect |
| 222. C2×#3021 | C23 | semidirect |
| 223. C2×#3021 | C23 | semidirect |
| 224. C2×#3020 | C23 | semidirect |
| 225. C2×#3019 | D4 | semidirect |
| 228. C2×#3019 | C23 | semidirect |
| 229. C2×#3019 | C23 | semidirect |
| 230. C2×#3019 | C23 | semidirect |
| 231. C2×#3018 | D4 | semidirect |
| 236. C2×#3018 | C23 | semidirect |
| 237. C2×#3018 | C23 | semidirect |
| 238. C22×#455 | C23 | semidirect |
| 239. C22×#455 | C23 | semidirect |
| 240. C22×#453 | D4 | semidirect |
| 242. C22×#453 | C23 | semidirect |
| 243. C22×#453 | C23 | semidirect |
| 245. #60370 | C23 | semidirect |
| 246. #60369 | C23 | semidirect |
| 247. #60368 | C23 | semidirect |
| 248. #60367 | C23 | semidirect |
| 249. #60367 | C23 | semidirect |
| 250. #60182 | C23 | semidirect |
| 251. C4×#575 | C23 | semidirect |
| 252. #60144 | C23 | semidirect |
| 255. #60093 | C23 | semidirect |
| 256. #60093 | C23 | semidirect |
| 259. C2×#2901 | C23 | semidirect |
| 260. C2×#2901 | C23 | semidirect |
| 261. C2×#2901 | C23 | semidirect |
| 264. #60076 | C23 | semidirect |
| 267. C2×#2888 | C23 | semidirect |
| 268. C2×#2888 | C23 | semidirect |
| 269. #35676 | C23 | semidirect |
| 271. #35616 | C23 | semidirect |
| 272. #35527 | C23 | semidirect |
| 273. #35327 | C23 | semidirect |
| 274. #35272 | C23 | semidirect |
| 275. C2×#2657 | C23 | semidirect |
| 276. #34070 | C23 | semidirect |
| 277. C2×#2050 | C23 | semidirect |
| 278. #23525 | C23 | semidirect |
| 279. C2×#2048 | C23 | semidirect |
| 280. #23498 | C23 | semidirect |
| 281. #23493 | C23 | semidirect |
| 282. #23493 | C23 | semidirect |
| 283. #23445 | C23 | semidirect |
| 284. #23440 | C23 | semidirect |
| 285. #23439 | C23 | semidirect |
| 286. #23439 | C23 | semidirect |
| 287. #23434 | C23 | semidirect |
| 288. #23430 | C23 | semidirect |
| 289. #23414 | C23 | semidirect |
| 290. #23412 | C23 | semidirect |
| 291. #23412 | C23 | semidirect |
| 292. C2×#2009 | C23 | semidirect |
| 293. C2×#2008 | C23 | semidirect |
| 294. C2×#2008 | C23 | semidirect |
| 295. #23408 | C23 | semidirect |
| 296. #23407 | C23 | semidirect |
| 297. #23406 | C23 | semidirect |
| 298. #23406 | C23 | semidirect |
| 299. #23402 | C23 | semidirect |
| 300. #23402 | C23 | semidirect |
| 301. #23399 | C23 | semidirect |
| 302. C2×#2003 | C23 | semidirect |
| 303. C2×#2004 | C23 | semidirect |
| 304. C2×#2004 | C23 | semidirect |
| 305. C2×#2002 | C23 | semidirect |
| 306. C2×#2002 | C23 | semidirect |
| 307. #21252 | C23 | semidirect |
| 308. #21249 | C23 | semidirect |
| 309. #21244 | C23 | semidirect |
| 310. #21241 | C23 | semidirect |
| 311. C2×#1965 | C23 | semidirect |
| 312. C2×#1963 | C23 | semidirect |
| 313. #21017 | C23 | semidirect |
| 314. C2×#1915 | C23 | semidirect |
| 315. #21014 | C23 | semidirect |
| 316. C2×#1910 | C23 | semidirect |
| 317. #21005 | C23 | semidirect |
| 318. C2×#1906 | C23 | semidirect |
| 319. C2×#1906 | C23 | semidirect |
| 320. #20998 | C23 | semidirect |
| 321. #20995 | C23 | semidirect |
| 322. #20995 | C23 | semidirect |
| 323. C2×#1903 | C23 | semidirect |
| 324. C2×#1902 | C23 | semidirect |
| 325. #20990 | C23 | semidirect |
| 326. #20990 | C23 | semidirect |
| 327. #20980 | C23 | semidirect |
| 328. #20980 | C23 | semidirect |
| 329. #20964 | C23 | semidirect |
| 330. #20956 | C23 | semidirect |
| 331. #20955 | C23 | semidirect |
| 332. #20952 | C23 | semidirect |
| 333. C2×#1884 | C23 | semidirect |
| 334. #20945 | C23 | semidirect |
| 335. #20944 | C23 | semidirect |
| 336. #20942 | C23 | semidirect |
| 337. #20939 | C23 | semidirect |
| 338. #20939 | C23 | semidirect |
| 339. #20939 | C23 | semidirect |
| 340. #20918 | C23 | semidirect |
| 341. #20903 | C23 | semidirect |
| 342. #20903 | C23 | semidirect |
| 343. C2×#1861 | C23 | semidirect |
| 344. #20863 | C23 | semidirect |
| 345. #20860 | C23 | semidirect |
| 346. #20855 | C23 | semidirect |
| 347. #20675 | C23 | semidirect |
| 348. #20673 | C23 | semidirect |
| 349. #20654 | C23 | semidirect |
| 350. #20637 | C23 | semidirect |
| 353. #20623 | C23 | semidirect |
| 354. #20623 | C23 | semidirect |
| 355. C2×#1795 | C23 | semidirect |
| 356. C2×#1795 | C23 | semidirect |
| 358. #20620 | C23 | semidirect |
| 359. #20620 | C23 | semidirect |
| 360. #20620 | C23 | semidirect |
| 361. #20620 | C23 | semidirect |
| 362. #20616 | C23 | semidirect |
| 363. #20616 | C23 | semidirect |
| 364. #20616 | C23 | semidirect |
| 366. #20615 | C23 | semidirect |
| 367. #20615 | C23 | semidirect |
| 368. #20615 | C23 | semidirect |
| 369. #20615 | C23 | semidirect |
| 370. #20612 | C23 | semidirect |
| 371. #20612 | C23 | semidirect |
| 372. #20612 | C23 | semidirect |
| 373. #20608 | C23 | semidirect |
| 375. #20606 | C23 | semidirect |
| 376. #20606 | C23 | semidirect |
| 378. #20592 | C23 | semidirect |
| 379. #20592 | C23 | semidirect |
| 381. #20586 | C23 | semidirect |
| 382. #20421 | C23 | semidirect |
| 383. C2×#1759 | C23 | semidirect |
| 384. #20401 | C23 | semidirect |
| 385. C4×#413 | C23 | semidirect |
| 386. #11179 | C23 | semidirect |
| 387. #11167 | C23 | semidirect |
| 388. #11159 | C23 | semidirect |
| 389. #11146 | C23 | semidirect |
| 390. #11141 | C23 | semidirect |
| 391. #11139 | C23 | semidirect |
| 392. #11119 | C23 | semidirect |
| 393. #11118 | C23 | semidirect |
| 394. #11116 | C23 | semidirect |
| 395. #11082 | C23 | semidirect |
| 396. #11081 | C23 | semidirect |
| 397. #11080 | C23 | semidirect |
| 398. #11041 | C23 | semidirect |
| 399. #11039 | C23 | semidirect |
| 400. #11037 | C23 | semidirect |
| 401. #11037 | C23 | semidirect |
| 402. #11035 | C23 | semidirect |
| 403. #11034 | C23 | semidirect |
| 404. #11033 | C23 | semidirect |
| 405. #11032 | C23 | semidirect |
| 406. #11032 | C23 | semidirect |
| 407. #11032 | C23 | semidirect |
| 408. #11019 | C23 | semidirect |
| 409. #11014 | C23 | semidirect |
| 410. #11012 | C23 | semidirect |
| 411. #11007 | C23 | semidirect |
| 412. #11004 | C23 | semidirect |
| 413. #11003 | C23 | semidirect |
| 414. #11000 | C23 | semidirect |
| 415. #10990 | C23 | semidirect |
| 416. #10989 | C23 | semidirect |
| 417. #10982 | C23 | semidirect |
| 418. #10979 | C23 | semidirect |
| 419. #10975 | C23 | semidirect |
| 420. #10973 | C23 | semidirect |
| 421. #10959 | C23 | semidirect |
| 422. #10955 | C23 | semidirect |
| 423. #10946 | C23 | semidirect |
| 424. #10946 | C23 | semidirect |
| 425. #10939 | C23 | semidirect |
| 426. #10924 | C23 | semidirect |
| 427. #10794 | C23 | semidirect |
| 428. #10787 | C23 | semidirect |
| 429. #10783 | C23 | semidirect |
| 430. #10780 | C23 | semidirect |
| 431. #10778 | C23 | semidirect |
| 432. #10772 | C23 | semidirect |
| 433. #10771 | C23 | semidirect |
| 434. #10767 | C23 | semidirect |
| 435. #10758 | C23 | semidirect |
| 436. #10756 | C23 | semidirect |
| 437. #10746 | C23 | semidirect |
| 438. #10744 | C23 | semidirect |
| 451. C22×2−1+4 | C24 | semidirect |
| 458. #3586 | C2×D4 | semidirect |
| 459. #3585 | C2×D4 | semidirect |
| 468. C2×#575 | C24 | semidirect |
| 471. C22×#137 | C24 | semidirect |
| 476. C22×AGL(1,ℤ/8) | C24 | semidirect |
| 481. C2×#568 | C24 | semidirect |
| 482. #3500 | C2×D4 | semidirect |
| 483. #3500 | C2×D4 | semidirect |
| 484. #3499 | C2×D4 | semidirect |
| 485. #3498 | C2×D4 | semidirect |
| 489. #3449 | C24 | semidirect |
| 498. C2×#535 | C24 | semidirect |
| 504. C22×#127 | C24 | semidirect |
| 506. C22×#124 | C24 | semidirect |
| 511. C2×C4×#41 | C24 | semidirect |
| 513. #3022 | C2×D4 | semidirect |
| 515. #3021 | C2×D4 | semidirect |
| 516. #3020 | C2×D4 | semidirect |
| 517. #3019 | C2×D4 | semidirect |
| 520. #3018 | C2×D4 | semidirect |
| 521. #3018 | C2×D4 | semidirect |
| 524. C2×#456 | C2×D4 | semidirect |
| 529. C2×#454 | C2×D4 | semidirect |
| 533. C2×#455 | C2×D4 | semidirect |
| 541. C2×#453 | C2×D4 | semidirect |
| 542. C2×#430 | C24 | semidirect |
| 543. #2911 | C24 | semidirect |
| 544. C2×#423 | C24 | semidirect |
| 545. #2901 | C2×D4 | semidirect |
| 546. #2901 | C2×D4 | semidirect |
| 559. C2×#421 | C24 | semidirect |
| 560. C2×#421 | C24 | semidirect |
| 561. C2×#421 | C24 | semidirect |
| 568. C22×#104 | C24 | semidirect |
| 569. C22×#104 | C24 | semidirect |
| 574. #2896 | C24 | semidirect |
| 575. #2896 | C24 | semidirect |
| 576. C2×#419 | C24 | semidirect |
| 577. C2×#418 | C24 | semidirect |
| 578. C2×#418 | C24 | semidirect |
| 579. #2889 | C2×D4 | semidirect |
| 580. #2888 | C2×D4 | semidirect |
| 591. C2×#413 | C24 | semidirect |
| 592. C22×#101 | C24 | semidirect |
| 597. C22×#100 | C24 | semidirect |
| 598. C22×#100 | C24 | semidirect |
| 601. C2×#410 | C24 | semidirect |
| 604. #2879 | C24 | semidirect |
| 605. #2879 | C24 | semidirect |
| 606. #2873 | C24 | semidirect |
| 607. C2×C4×M16 | C24 | semidirect |
| 608. #2310 | C24 | semidirect |
| 611. #2309 | C24 | semidirect |
| 614. #2297 | C24 | semidirect |
| 615. #2285 | C24 | semidirect |
| 616. C2×#376 | C24 | semidirect |
| 617. C2×#344 | C24 | semidirect |
| 618. C2×#344 | C24 | semidirect |
| 619. C2×#344 | C24 | semidirect |
| 620. C2×#344 | C24 | semidirect |
| 621. #1742 | C24 | semidirect |
| 622. #1742 | C24 | semidirect |
| 623. #1742 | C24 | semidirect |
| 624. #1740 | C24 | semidirect |
| 625. #1738 | C24 | semidirect |
| 626. #1738 | C24 | semidirect |
| 627. #1733 | C24 | semidirect |
| 628. #1733 | C24 | semidirect |
| 629. C2×#339 | C24 | semidirect |
| 630. C2×#339 | C24 | semidirect |
| 631. C2×#339 | C24 | semidirect |
| 632. C2×#338 | C24 | semidirect |
| 633. C2×H(3,ℤ/4) | C24 | semidirect |
| 634. #1728 | C24 | semidirect |
| 642. C2×2−1+4 | C22×D4 | semidirect |
| 650. C2×H(5,𝔽2) | C22×D4 | semidirect |
| 669. #575 | C22×D4 | semidirect |
| 673. C2×#137 | C22×D4 | semidirect |
| 679. C2×AGL(1,ℤ/8) | C22×D4 | semidirect |
| 680. #568 | C22×D4 | semidirect |
| 688. #536 | C22×D4 | semidirect |
| 690. #535 | C22×D4 | semidirect |
| 694. C2×C4⋊Q8 | C22×D4 | semidirect |
| 700. C2×#127 | C22×D4 | semidirect |
| 705. C2×#124 | C22×D4 | semidirect |
| 706. C2×#124 | C22×D4 | semidirect |
| 707. C4×#41 | C22×D4 | semidirect |
| 708. C4×#41 | C22×D4 | semidirect |
| 724. #421 | C22×D4 | semidirect |
| 733. C2×#104 | C22×D4 | semidirect |
| 734. C2×#104 | C22×D4 | semidirect |
| 739. C2×#101 | C22×D4 | semidirect |
| 743. C2×#100 | C22×D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.