Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
At least 9509 conjugacy classes of subgroups; only the 4144 normal subgroups are shown.
The subgroup lattice has 943 nodes (normal subgroups only) — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×#35346 |
| commutator, Frattini, cosocle | C25 | C26 |
| LCS | G ▷ C25 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C26 ◁ G | |
| LECS | G ▷ C25 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72265972 | C2 | semidirect |
| 2. #72265971 | C2 | semidirect |
| 3. #72265970 | C2 | semidirect |
| 4. #72265969 | C2 | semidirect |
| 5. #72265948 | C2 | semidirect |
| 6. #72265918 | C2 | semidirect |
| 7. #72252238 | C2 | semidirect |
| 8. #72252234 | C2 | semidirect |
| 9. #72241025 | C2 | semidirect |
| 10. #72241004 | C2 | semidirect |
| 11. C2×#251827 | C2 | semidirect |
| 12. #72240643 | C2 | semidirect |
| 13. #72240631 | C2 | semidirect |
| 14. #72240597 | C2 | semidirect |
| 15. #72237496 | C2 | semidirect |
| 16. #72236720 | C2 | semidirect |
| 17. #72235981 | C2 | semidirect |
| 18. #72234955 | C2 | semidirect |
| 19. #72233689 | C2 | semidirect |
| 20. #72233435 | C2 | semidirect |
| 21. #72233042 | C2 | semidirect |
| 22. #72216396 | C2 | semidirect |
| 23. C22×H(7,𝔽2) | C22 | semidirect |
| 24. #8932922 | C22 | semidirect |
| 25. #8932885 | C22 | semidirect |
| 26. #8932639 | C22 | semidirect |
| 27. #8926943 | C22 | semidirect |
| 28. #8926669 | C22 | semidirect |
| 29. #8926210 | C22 | semidirect |
| 30. #8899284 | C22 | semidirect |
| 31. #8898948 | C22 | semidirect |
| 32. #8898948 | C22 | semidirect |
| 33. #8898306 | C22 | semidirect |
| 34. #7806601 | C22 | semidirect |
| 35. #7733149 | C22 | semidirect |
| 36. #7721729 | C22 | semidirect |
| 37. #7721725 | C22 | semidirect |
| 38. #7712875 | C22 | semidirect |
| 39. C2×#46996 | C22 | semidirect |
| 40. #7644628 | C22 | semidirect |
| 42. #7631286 | C22 | semidirect |
| 44. #7630442 | C22 | semidirect |
| 45. #6628901 | C22 | semidirect |
| 46. #6628901 | C22 | semidirect |
| 47. #6628900 | C22 | semidirect |
| 48. #6628900 | C22 | semidirect |
| 49. #6628900 | C22 | semidirect |
| 50. #6628900 | C22 | semidirect |
| 51. #6628898 | C22 | semidirect |
| 52. #6628898 | C22 | semidirect |
| 53. #6628897 | C22 | semidirect |
| 54. #6628897 | C22 | semidirect |
| 55. #6628896 | C22 | semidirect |
| 56. #6628896 | C22 | semidirect |
| 57. #6628896 | C22 | semidirect |
| 58. #6628896 | C22 | semidirect |
| 59. #6628892 | C22 | semidirect |
| 60. #6628892 | C22 | semidirect |
| 61. #6628892 | C22 | semidirect |
| 62. #6628892 | C22 | semidirect |
| 63. C2×#32898 | C22 | semidirect |
| 64. C2×#32898 | C22 | semidirect |
| 65. #6470225 | C22 | semidirect |
| 66. #6370693 | C22 | semidirect |
| 67. #6370693 | C22 | semidirect |
| 68. C2×#20585 | C22 | semidirect |
| 69. C2×#20585 | C22 | semidirect |
| 70. #251877 | C22 | semidirect |
| 71. #251877 | C22 | semidirect |
| 72. #251872 | C22 | semidirect |
| 73. #251872 | C22 | semidirect |
| 74. #251872 | C22 | semidirect |
| 75. #251871 | C22 | semidirect |
| 76. #251860 | C22 | semidirect |
| 77. #251859 | C22 | semidirect |
| 78. #251855 | C22 | semidirect |
| 79. #251854 | C22 | semidirect |
| 80. #251849 | C22 | semidirect |
| 81. #251849 | C22 | semidirect |
| 82. #251843 | C22 | semidirect |
| 83. #251838 | C22 | semidirect |
| 84. #251837 | C22 | semidirect |
| 85. #251837 | C22 | semidirect |
| 86. #251833 | C22 | semidirect |
| 87. #251832 | C22 | semidirect |
| 88. #251828 | C22 | semidirect |
| 89. #251827 | C22 | semidirect |
| 90. #251827 | C22 | semidirect |
| 91. #251827 | C22 | semidirect |
| 92. #251827 | C22 | semidirect |
| 93. #251827 | C22 | semidirect |
| 94. #251827 | C22 | semidirect |
| 95. #251827 | C22 | semidirect |
| 96. #251827 | C22 | semidirect |
| 97. #251827 | C22 | semidirect |
| 98. #245255 | C22 | semidirect |
| 99. #245255 | C22 | semidirect |
| 100. #245255 | C22 | semidirect |
| 101. #245254 | C22 | semidirect |
| 102. #245254 | C22 | semidirect |
| 103. #245254 | C22 | semidirect |
| 104. #245252 | C22 | semidirect |
| 105. #245252 | C22 | semidirect |
| 106. #245249 | C22 | semidirect |
| 107. #245247 | C22 | semidirect |
| 108. #245246 | C22 | semidirect |
| 109. #245246 | C22 | semidirect |
| 110. #245233 | C22 | semidirect |
| 111. #245231 | C22 | semidirect |
| 112. #245231 | C22 | semidirect |
| 113. #245230 | C22 | semidirect |
| 114. #245229 | C22 | semidirect |
| 115. #245229 | C22 | semidirect |
| 116. #245228 | C22 | semidirect |
| 117. #245227 | C22 | semidirect |
| 118. #245226 | C22 | semidirect |
| 119. #245225 | C22 | semidirect |
| 120. #245225 | C22 | semidirect |
| 121. #245225 | C22 | semidirect |
| 122. #238082 | C22 | semidirect |
| 123. C2×#10390 | C22 | semidirect |
| 124. #233549 | C22 | semidirect |
| 125. #233549 | C22 | semidirect |
| 126. #233541 | C22 | semidirect |
| 127. C2×#10336 | C22 | semidirect |
| 128. #213864 | C22 | semidirect |
| 129. #213864 | C22 | semidirect |
| 130. #213864 | C22 | semidirect |
| 131. #213860 | C22 | semidirect |
| 132. #213854 | C22 | semidirect |
| 133. #213852 | C22 | semidirect |
| 134. #213838 | C22 | semidirect |
| 135. #213836 | C22 | semidirect |
| 136. #213832 | C22 | semidirect |
| 137. #213831 | C22 | semidirect |
| 138. #213830 | C22 | semidirect |
| 139. #213829 | C22 | semidirect |
| 140. #213828 | C22 | semidirect |
| 141. #213828 | C22 | semidirect |
| 142. #201701 | C22 | semidirect |
| 143. #201701 | C22 | semidirect |
| 144. #201701 | C22 | semidirect |
| 145. #201687 | C22 | semidirect |
| 146. #201678 | C22 | semidirect |
| 147. #201678 | C22 | semidirect |
| 148. #201664 | C22 | semidirect |
| 149. C2×#9495 | C22 | semidirect |
| 150. C2×#9495 | C22 | semidirect |
| 151. #190107 | C22 | semidirect |
| 152. C2×#8746 | C22 | semidirect |
| 153. #188049 | C22 | semidirect |
| 154. #188035 | C22 | semidirect |
| 161. C2×#3484 | D4 | semidirect |
| 162. C2×#3484 | C23 | semidirect |
| 164. C22×#534 | D4 | semidirect |
| 166. #47563 | C23 | semidirect |
| 167. #46999 | C23 | semidirect |
| 168. #46998 | C23 | semidirect |
| 169. #46997 | C23 | semidirect |
| 170. #46997 | C23 | semidirect |
| 171. #46996 | C23 | semidirect |
| 172. #46996 | C23 | semidirect |
| 173. #46996 | C23 | semidirect |
| 174. #46996 | C23 | semidirect |
| 175. #46996 | C23 | semidirect |
| 176. #46996 | C23 | semidirect |
| 177. #46996 | C23 | semidirect |
| 178. #46996 | C23 | semidirect |
| 179. #46996 | C23 | semidirect |
| 180. #46837 | C23 | semidirect |
| 181. #46837 | C23 | semidirect |
| 182. #46387 | C23 | semidirect |
| 183. #46387 | C23 | semidirect |
| 184. #46386 | C23 | semidirect |
| 185. #46386 | C23 | semidirect |
| 186. #46386 | C23 | semidirect |
| 187. #46385 | C23 | semidirect |
| 188. #46385 | C23 | semidirect |
| 189. #46385 | C23 | semidirect |
| 190. #46385 | C23 | semidirect |
| 191. #46385 | C23 | semidirect |
| 192. #46384 | C23 | semidirect |
| 193. #46384 | C23 | semidirect |
| 194. #37475 | C23 | semidirect |
| 195. #37436 | C23 | semidirect |
| 196. #37436 | C23 | semidirect |
| 197. #37232 | C23 | semidirect |
| 198. #37232 | C23 | semidirect |
| 199. #37232 | C23 | semidirect |
| 200. #37117 | C23 | semidirect |
| 201. #37117 | C23 | semidirect |
| 202. #37117 | C23 | semidirect |
| 203. #36721 | C23 | semidirect |
| 204. #36717 | C23 | semidirect |
| 205. #36717 | C23 | semidirect |
| 206. #36717 | C23 | semidirect |
| 207. #36714 | C23 | semidirect |
| 208. #36714 | C23 | semidirect |
| 209. C2×#2840 | C23 | semidirect |
| 213. #35527 | C23 | semidirect |
| 217. #35512 | C23 | semidirect |
| 218. #35446 | D4 | semidirect |
| 222. #35355 | C23 | semidirect |
| 223. #35355 | C23 | semidirect |
| 224. #35355 | C23 | semidirect |
| 225. #35354 | C23 | semidirect |
| 226. #35351 | C23 | semidirect |
| 227. #35350 | C23 | semidirect |
| 228. #35347 | D4 | semidirect |
| 229. #35347 | D4 | semidirect |
| 236. #35347 | C23 | semidirect |
| 237. #35346 | D4 | semidirect |
| 238. #35346 | D4 | semidirect |
| 245. #35346 | C23 | semidirect |
| 246. #35346 | C23 | semidirect |
| 247. #35346 | C23 | semidirect |
| 248. #35250 | D4 | semidirect |
| 249. #35088 | D4 | semidirect |
| 250. #34980 | D4 | semidirect |
| 257. #34980 | C23 | semidirect |
| 258. #34736 | D4 | semidirect |
| 259. C2×#2403 | D4 | semidirect |
| 263. C2×#2403 | C23 | semidirect |
| 264. #34356 | C23 | semidirect |
| 265. #34356 | C23 | semidirect |
| 266. #34256 | D4 | semidirect |
| 269. C2×#2308 | D4 | semidirect |
| 272. C2×#2308 | C23 | semidirect |
| 273. #33020 | C23 | semidirect |
| 298. #32898 | C23 | semidirect |
| 299. #29634 | C23 | semidirect |
| 300. #29634 | C23 | semidirect |
| 301. #21746 | C23 | semidirect |
| 302. #21746 | C23 | semidirect |
| 325. C2×#1781 | C23 | semidirect |
| 326. #10392 | C23 | semidirect |
| 327. #10392 | C23 | semidirect |
| 328. #10390 | C23 | semidirect |
| 329. #10390 | C23 | semidirect |
| 330. #10390 | C23 | semidirect |
| 331. #10390 | C23 | semidirect |
| 332. #10338 | C23 | semidirect |
| 333. #10338 | C23 | semidirect |
| 334. #10337 | C23 | semidirect |
| 335. #10337 | C23 | semidirect |
| 336. #10337 | C23 | semidirect |
| 337. #10337 | C23 | semidirect |
| 338. #10337 | C23 | semidirect |
| 339. #10336 | C23 | semidirect |
| 340. #10336 | C23 | semidirect |
| 341. #10336 | C23 | semidirect |
| 342. #10336 | C23 | semidirect |
| 343. #10336 | C23 | semidirect |
| 344. #10336 | C23 | semidirect |
| 345. #10336 | C23 | semidirect |
| 346. #9501 | C23 | semidirect |
| 347. #9501 | C23 | semidirect |
| 348. #9501 | C23 | semidirect |
| 349. #9499 | C23 | semidirect |
| 350. #9499 | C23 | semidirect |
| 351. #9499 | C23 | semidirect |
| 352. #9499 | C23 | semidirect |
| 353. #9499 | C23 | semidirect |
| 354. #9498 | C23 | semidirect |
| 355. #9498 | C23 | semidirect |
| 356. #9497 | C23 | semidirect |
| 357. #9497 | C23 | semidirect |
| 358. #9497 | C23 | semidirect |
| 359. #9497 | C23 | semidirect |
| 360. #9497 | C23 | semidirect |
| 361. #9497 | C23 | semidirect |
| 362. #9497 | C23 | semidirect |
| 363. #9496 | C23 | semidirect |
| 364. #9496 | C23 | semidirect |
| 365. #9495 | C23 | semidirect |
| 366. #9495 | C23 | semidirect |
| 367. #9495 | C23 | semidirect |
| 368. #9495 | C23 | semidirect |
| 369. #9495 | C23 | semidirect |
| 370. #9495 | C23 | semidirect |
| 371. #9495 | C23 | semidirect |
| 372. #9495 | C23 | semidirect |
| 373. #9495 | C23 | semidirect |
| 374. #9495 | C23 | semidirect |
| 375. #9495 | C23 | semidirect |
| 376. #9495 | C23 | semidirect |
| 377. #9495 | C23 | semidirect |
| 378. #9495 | C23 | semidirect |
| 379. #9495 | C23 | semidirect |
| 380. #9495 | C23 | semidirect |
| 381. #9495 | C23 | semidirect |
| 382. #8749 | C23 | semidirect |
| 383. #8748 | C23 | semidirect |
| 384. #8747 | C23 | semidirect |
| 385. #8746 | C23 | semidirect |
| 386. #8746 | C23 | semidirect |
| 387. #8746 | C23 | semidirect |
| 388. #8746 | C23 | semidirect |
| 389. #8746 | C23 | semidirect |
| 390. #8546 | C23 | semidirect |
| 391. #8543 | C23 | semidirect |
| 392. #8542 | C23 | semidirect |
| 393. #8542 | C23 | semidirect |
| 394. #8542 | C23 | semidirect |
| 395. #8541 | C23 | semidirect |
| 396. #8541 | C23 | semidirect |
| 397. #8101 | C23 | semidirect |
| 398. C2×#1304 | C23 | semidirect |
| 399. C2×#1304 | C23 | semidirect |
| 400. C2×#1304 | C23 | semidirect |
| 412. C22×H(5,𝔽2) | C24 | semidirect |
| 417. C24×D4 | C2×D4 | semidirect |
| 418. C24×D4 | C2×D4 | semidirect |
| 419. C24×D4 | C2×D4 | semidirect |
| 424. C2×#535 | C2×D4 | semidirect |
| 425. C2×#535 | C2×D4 | semidirect |
| 426. C2×#534 | C2×D4 | semidirect |
| 427. C2×#534 | C2×D4 | semidirect |
| 428. C2×#534 | C2×D4 | semidirect |
| 429. C2×#534 | C2×D4 | semidirect |
| 430. C2×#534 | C2×D4 | semidirect |
| 431. C2×#534 | C2×D4 | semidirect |
| 432. C2×#534 | C2×D4 | semidirect |
| 433. C2×#534 | C2×D4 | semidirect |
| 434. C2×#534 | C24 | semidirect |
| 435. C2×#534 | C24 | semidirect |
| 437. C2×#525 | C2×D4 | semidirect |
| 438. C2×#525 | C2×D4 | semidirect |
| 439. C22×#123 | C2×D4 | semidirect |
| 440. C22×#123 | C2×D4 | semidirect |
| 441. C22×#123 | C2×D4 | semidirect |
| 442. C22×#123 | C2×D4 | semidirect |
| 444. C22×#121 | C2×D4 | semidirect |
| 445. C22×#121 | C2×D4 | semidirect |
| 446. C22×#121 | C2×D4 | semidirect |
| 450. C22×#120 | C2×D4 | semidirect |
| 451. C22×#120 | C2×D4 | semidirect |
| 452. C22×#120 | C2×D4 | semidirect |
| 453. C22×#120 | C2×D4 | semidirect |
| 454. C22×#120 | C2×D4 | semidirect |
| 455. C22×#120 | C2×D4 | semidirect |
| 456. C22×#120 | C2×D4 | semidirect |
| 457. C22×#120 | C2×D4 | semidirect |
| 458. C22×#120 | C2×D4 | semidirect |
| 463. C2×#518 | C2×D4 | semidirect |
| 464. C2×#518 | C24 | semidirect |
| 465. C22×C4×D4 | C2×D4 | semidirect |
| 466. C22×C4×D4 | C2×D4 | semidirect |
| 467. C23×C22⋊C4 | C2×D4 | semidirect |
| 468. C23×C22⋊C4 | C2×D4 | semidirect |
| 469. #2842 | C24 | semidirect |
| 470. #2842 | C24 | semidirect |
| 471. #2840 | C24 | semidirect |
| 472. #2840 | C24 | semidirect |
| 473. #2840 | C24 | semidirect |
| 474. #2840 | C24 | semidirect |
| 475. #2483 | C24 | semidirect |
| 476. #2483 | C24 | semidirect |
| 477. #2406 | C2×D4 | semidirect |
| 478. #2406 | C2×D4 | semidirect |
| 479. #2406 | C2×D4 | semidirect |
| 480. #2406 | C2×D4 | semidirect |
| 481. #2406 | C2×D4 | semidirect |
| 482. #2406 | C2×D4 | semidirect |
| 483. #2405 | C2×D4 | semidirect |
| 484. #2405 | C2×D4 | semidirect |
| 485. #2405 | C2×D4 | semidirect |
| 486. #2405 | C2×D4 | semidirect |
| 487. #2405 | C2×D4 | semidirect |
| 488. #2405 | C2×D4 | semidirect |
| 499. #2405 | C24 | semidirect |
| 500. #2405 | C24 | semidirect |
| 501. #2405 | C24 | semidirect |
| 502. #2405 | C24 | semidirect |
| 503. #2405 | C24 | semidirect |
| 504. #2404 | C2×D4 | semidirect |
| 505. #2404 | C2×D4 | semidirect |
| 506. #2404 | C2×D4 | semidirect |
| 507. #2404 | C2×D4 | semidirect |
| 508. #2404 | C2×D4 | semidirect |
| 509. #2404 | C2×D4 | semidirect |
| 510. #2404 | C2×D4 | semidirect |
| 511. #2404 | C2×D4 | semidirect |
| 512. #2404 | C2×D4 | semidirect |
| 513. #2404 | C2×D4 | semidirect |
| 514. #2403 | C2×D4 | semidirect |
| 515. #2403 | C2×D4 | semidirect |
| 516. #2403 | C2×D4 | semidirect |
| 517. #2403 | C2×D4 | semidirect |
| 518. #2403 | C2×D4 | semidirect |
| 519. #2403 | C2×D4 | semidirect |
| 520. #2403 | C2×D4 | semidirect |
| 521. #2403 | C2×D4 | semidirect |
| 522. #2403 | C2×D4 | semidirect |
| 523. #2403 | C2×D4 | semidirect |
| 524. #2403 | C2×D4 | semidirect |
| 525. #2403 | C2×D4 | semidirect |
| 526. #2403 | C2×D4 | semidirect |
| 527. #2403 | C2×D4 | semidirect |
| 548. #2403 | C24 | semidirect |
| 549. #2403 | C24 | semidirect |
| 550. #2403 | C24 | semidirect |
| 551. #2403 | C24 | semidirect |
| 552. #2403 | C24 | semidirect |
| 553. #2403 | C24 | semidirect |
| 554. #2403 | C24 | semidirect |
| 555. #2312 | C24 | semidirect |
| 556. #2312 | C24 | semidirect |
| 557. #2312 | C24 | semidirect |
| 558. #2312 | C24 | semidirect |
| 559. #2311 | C2×D4 | semidirect |
| 560. #2311 | C2×D4 | semidirect |
| 564. #2309 | C24 | semidirect |
| 565. #2309 | C24 | semidirect |
| 566. #2308 | C2×D4 | semidirect |
| 567. #2308 | C2×D4 | semidirect |
| 568. #2308 | C2×D4 | semidirect |
| 569. #2308 | C2×D4 | semidirect |
| 570. #2308 | C2×D4 | semidirect |
| 571. #2308 | C2×D4 | semidirect |
| 572. #2308 | C2×D4 | semidirect |
| 573. #2308 | C2×D4 | semidirect |
| 574. #2308 | C2×D4 | semidirect |
| 575. #2308 | C2×D4 | semidirect |
| 576. #2308 | C2×D4 | semidirect |
| 577. #2308 | C2×D4 | semidirect |
| 578. #2308 | C2×D4 | semidirect |
| 588. #2308 | C24 | semidirect |
| 589. #2308 | C24 | semidirect |
| 590. #2308 | C24 | semidirect |
| 591. #2308 | C24 | semidirect |
| 592. #2308 | C24 | semidirect |
| 593. #2308 | C24 | semidirect |
| 594. #2297 | C2×D4 | semidirect |
| 595. #2297 | C2×D4 | semidirect |
| 596. C2×#386 | C2×D4 | semidirect |
| 597. C2×#386 | C2×D4 | semidirect |
| 598. C2×#386 | C2×D4 | semidirect |
| 599. C2×#386 | C2×D4 | semidirect |
| 600. C2×#386 | C2×D4 | semidirect |
| 601. C2×#386 | C2×D4 | semidirect |
| 602. #2280 | C2×D4 | semidirect |
| 603. C2×#381 | C2×D4 | semidirect |
| 604. C2×#379 | C2×D4 | semidirect |
| 611. #1819 | C24 | semidirect |
| 612. #1819 | C24 | semidirect |
| 627. #1781 | C24 | semidirect |
| 628. #1781 | C24 | semidirect |
| 629. #1781 | C24 | semidirect |
| 630. #1781 | C24 | semidirect |
| 631. #1304 | C24 | semidirect |
| 632. #1304 | C24 | semidirect |
| 633. #1304 | C24 | semidirect |
| 634. #1304 | C24 | semidirect |
| 635. #1304 | C24 | semidirect |
| 636. #1304 | C24 | semidirect |
| 637. #1304 | C24 | semidirect |
| 638. #1304 | C24 | semidirect |
| 645. C26 | H(5,𝔽2) | semidirect |
| 700. C23×D4 | H(5,𝔽2) | semidirect |
| 719. C24×C4 | H(5,𝔽2) | semidirect |
| 848. C22×D4 | B(4,𝔽2) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.