Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
At least 6063 conjugacy classes of subgroups; only the 2914 normal subgroups are shown.
The subgroup lattice has 946 nodes (normal subgroups only) — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #8932885 |
| commutator, Frattini, cosocle | C25 | C26 |
| LCS | G ▷ C25 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C25 ◁ G | |
| LECS | G ▷ C25 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72338758 | C2 | semidirect |
| 2. #72338740 | C2 | semidirect |
| 3. #72338736 | C2 | semidirect |
| 4. #72338726 | C2 | semidirect |
| 5. #72338715 | C2 | semidirect |
| 6. #72337703 | C2 | semidirect |
| 7. #72337662 | C2 | semidirect |
| 8. #72337659 | C2 | semidirect |
| 9. #72337653 | C2 | semidirect |
| 10. #72310978 | C2 | semidirect |
| 11. #72310971 | C2 | semidirect |
| 12. #72310933 | C2 | semidirect |
| 13. #72285238 | C2 | semidirect |
| 14. #72284853 | C2 | semidirect |
| 15. #72284753 | C2 | semidirect |
| 16. #72284703 | C2 | semidirect |
| 17. #72284693 | C2 | semidirect |
| 18. #72283693 | C2 | semidirect |
| 19. #72241387 | C2 | semidirect |
| 20. #72241342 | C2 | semidirect |
| 21. #72240643 | C2 | semidirect |
| 22. #72240631 | C2 | semidirect |
| 23. #72240627 | C2 | semidirect |
| 24. #72213228 | C2 | semidirect |
| 25. #72213228 | C2 | semidirect |
| 26. #72210439 | C2 | semidirect |
| 27. #72210439 | C2 | semidirect |
| 28. #8934620 | C22 | semidirect |
| 30. #8933771 | C22 | semidirect |
| 31. #8898948 | C22 | semidirect |
| 32. #6628901 | C22 | semidirect |
| 33. #6628901 | C22 | semidirect |
| 34. #6628901 | C22 | semidirect |
| 35. #6628901 | C22 | semidirect |
| 36. #6628900 | C22 | semidirect |
| 37. #6628898 | C22 | semidirect |
| 38. #6628896 | C22 | semidirect |
| 39. #6628896 | C22 | semidirect |
| 40. #6487657 | C22 | semidirect |
| 41. #6470244 | C22 | semidirect |
| 42. #6470231 | C22 | semidirect |
| 43. #6432958 | C22 | semidirect |
| 44. #346293 | C22 | semidirect |
| 45. #346285 | C22 | semidirect |
| 46. #346284 | C22 | semidirect |
| 47. #346283 | C22 | semidirect |
| 48. #346282 | C22 | semidirect |
| 49. #346275 | C22 | semidirect |
| 50. #346275 | C22 | semidirect |
| 51. #346275 | C22 | semidirect |
| 52. #346274 | C22 | semidirect |
| 53. #346271 | C22 | semidirect |
| 54. #346270 | C22 | semidirect |
| 55. #346270 | C22 | semidirect |
| 56. #346269 | C22 | semidirect |
| 57. #346269 | C22 | semidirect |
| 58. #346269 | C22 | semidirect |
| 59. #346257 | C22 | semidirect |
| 60. #346243 | C22 | semidirect |
| 61. #346242 | C22 | semidirect |
| 62. #346242 | C22 | semidirect |
| 63. #346242 | C22 | semidirect |
| 64. #346242 | C22 | semidirect |
| 65. #346242 | C22 | semidirect |
| 66. #346242 | C22 | semidirect |
| 67. #346241 | C22 | semidirect |
| 68. #346237 | C22 | semidirect |
| 69. #346232 | C22 | semidirect |
| 70. #346232 | C22 | semidirect |
| 71. #346232 | C22 | semidirect |
| 72. #346231 | C22 | semidirect |
| 73. #346231 | C22 | semidirect |
| 74. #346231 | C22 | semidirect |
| 75. #346228 | C22 | semidirect |
| 76. #346228 | C22 | semidirect |
| 77. #346226 | C22 | semidirect |
| 78. #346226 | C22 | semidirect |
| 79. #346226 | C22 | semidirect |
| 80. #346226 | C22 | semidirect |
| 81. #346226 | C22 | semidirect |
| 82. #346226 | C22 | semidirect |
| 83. #346226 | C22 | semidirect |
| 84. #346226 | C22 | semidirect |
| 85. #346225 | C22 | semidirect |
| 86. #346225 | C22 | semidirect |
| 87. #346225 | C22 | semidirect |
| 88. #346225 | C22 | semidirect |
| 89. #346224 | C22 | semidirect |
| 90. #346224 | C22 | semidirect |
| 91. #251914 | C22 | semidirect |
| 92. #251913 | C22 | semidirect |
| 93. #251913 | C22 | semidirect |
| 94. #251912 | C22 | semidirect |
| 95. #251911 | C22 | semidirect |
| 96. #251911 | C22 | semidirect |
| 97. #251911 | C22 | semidirect |
| 98. #251909 | C22 | semidirect |
| 99. #251908 | C22 | semidirect |
| 100. #251908 | C22 | semidirect |
| 101. #251908 | C22 | semidirect |
| 102. #251883 | C22 | semidirect |
| 103. #251878 | C22 | semidirect |
| 104. #251877 | C22 | semidirect |
| 105. #251877 | C22 | semidirect |
| 106. #251872 | C22 | semidirect |
| 107. #251872 | C22 | semidirect |
| 108. #251864 | C22 | semidirect |
| 109. #251863 | C22 | semidirect |
| 110. #251860 | C22 | semidirect |
| 111. #251860 | C22 | semidirect |
| 112. #251860 | C22 | semidirect |
| 113. #251860 | C22 | semidirect |
| 114. #251860 | C22 | semidirect |
| 115. #251860 | C22 | semidirect |
| 116. #251859 | C22 | semidirect |
| 117. #251859 | C22 | semidirect |
| 118. #251859 | C22 | semidirect |
| 119. #251859 | C22 | semidirect |
| 120. #251859 | C22 | semidirect |
| 121. #251859 | C22 | semidirect |
| 122. #251859 | C22 | semidirect |
| 123. #251857 | C22 | semidirect |
| 124. #251855 | C22 | semidirect |
| 125. #251855 | C22 | semidirect |
| 126. #251855 | C22 | semidirect |
| 127. #251855 | C22 | semidirect |
| 128. #251855 | C22 | semidirect |
| 129. #251855 | C22 | semidirect |
| 130. #251855 | C22 | semidirect |
| 131. #251855 | C22 | semidirect |
| 132. #251855 | C22 | semidirect |
| 133. #251855 | C22 | semidirect |
| 134. #251855 | C22 | semidirect |
| 135. #251855 | C22 | semidirect |
| 136. #251855 | C22 | semidirect |
| 137. #251855 | C22 | semidirect |
| 138. #251854 | C22 | semidirect |
| 139. #251854 | C22 | semidirect |
| 140. #251854 | C22 | semidirect |
| 141. #251844 | C22 | semidirect |
| 142. #251844 | C22 | semidirect |
| 143. #251843 | C22 | semidirect |
| 144. #251843 | C22 | semidirect |
| 145. #251843 | C22 | semidirect |
| 146. #251838 | C22 | semidirect |
| 147. #251838 | C22 | semidirect |
| 148. #251838 | C22 | semidirect |
| 149. #251838 | C22 | semidirect |
| 150. #251830 | C22 | semidirect |
| 151. #251828 | C22 | semidirect |
| 152. #251828 | C22 | semidirect |
| 153. #251828 | C22 | semidirect |
| 154. #251828 | C22 | semidirect |
| 155. #251828 | C22 | semidirect |
| 156. #251828 | C22 | semidirect |
| 157. #251828 | C22 | semidirect |
| 158. #251827 | C22 | semidirect |
| 159. #251827 | C22 | semidirect |
| 160. #251827 | C22 | semidirect |
| 161. #251827 | C22 | semidirect |
| 162. #251827 | C22 | semidirect |
| 163. #245255 | C22 | semidirect |
| 164. #245255 | C22 | semidirect |
| 165. #245255 | C22 | semidirect |
| 166. #245255 | C22 | semidirect |
| 167. #245252 | C22 | semidirect |
| 168. #245252 | C22 | semidirect |
| 169. #245249 | C22 | semidirect |
| 170. #245249 | C22 | semidirect |
| 171. #245246 | C22 | semidirect |
| 172. #245246 | C22 | semidirect |
| 173. #245246 | C22 | semidirect |
| 174. #245246 | C22 | semidirect |
| 175. #245234 | C22 | semidirect |
| 176. #245234 | C22 | semidirect |
| 177. #245234 | C22 | semidirect |
| 178. #245234 | C22 | semidirect |
| 183. #245233 | C22 | semidirect |
| 184. #245233 | C22 | semidirect |
| 185. #245233 | C22 | semidirect |
| 186. #245233 | C22 | semidirect |
| 187. #245233 | C22 | semidirect |
| 188. #245233 | C22 | semidirect |
| 189. #245233 | C22 | semidirect |
| 190. #245233 | C22 | semidirect |
| 191. #245233 | C22 | semidirect |
| 192. #245233 | C22 | semidirect |
| 193. #245233 | C22 | semidirect |
| 194. #245233 | C22 | semidirect |
| 195. #245233 | C22 | semidirect |
| 196. #245233 | C22 | semidirect |
| 197. #245233 | C22 | semidirect |
| 198. #245231 | C22 | semidirect |
| 199. #245229 | C22 | semidirect |
| 200. #245229 | C22 | semidirect |
| 201. #245229 | C22 | semidirect |
| 202. #245228 | C22 | semidirect |
| 203. #245225 | C22 | semidirect |
| 204. #245225 | C22 | semidirect |
| 205. #245225 | C22 | semidirect |
| 206. #245225 | C22 | semidirect |
| 207. #245225 | C22 | semidirect |
| 208. #213884 | C22 | semidirect |
| 209. #213880 | C22 | semidirect |
| 210. #213876 | C22 | semidirect |
| 211. #213865 | C22 | semidirect |
| 212. #213864 | C22 | semidirect |
| 213. #213864 | C22 | semidirect |
| 214. #213861 | C22 | semidirect |
| 215. #213861 | C22 | semidirect |
| 216. #213861 | C22 | semidirect |
| 217. #213861 | C22 | semidirect |
| 218. #213861 | C22 | semidirect |
| 219. #213861 | C22 | semidirect |
| 220. #213860 | C22 | semidirect |
| 221. #213860 | C22 | semidirect |
| 222. #213860 | C22 | semidirect |
| 223. #213860 | C22 | semidirect |
| 224. #213860 | C22 | semidirect |
| 225. #213854 | C22 | semidirect |
| 226. #213854 | C22 | semidirect |
| 227. #213854 | C22 | semidirect |
| 228. #213853 | C22 | semidirect |
| 229. #213849 | C22 | semidirect |
| 230. #213838 | C22 | semidirect |
| 231. #213838 | C22 | semidirect |
| 232. #213832 | C22 | semidirect |
| 233. #213829 | C22 | semidirect |
| 234. #213829 | C22 | semidirect |
| 235. C2×H(7,𝔽2) | C23 | semidirect |
| 236. C2×H(7,𝔽2) | C23 | semidirect |
| 237. #62842 | C23 | semidirect |
| 280. #33020 | C23 | semidirect |
| 281. #33020 | C23 | semidirect |
| 282. #33020 | C23 | semidirect |
| 283. #33020 | C23 | semidirect |
| 284. #32900 | C23 | semidirect |
| 285. #32900 | C23 | semidirect |
| 286. #32900 | C23 | semidirect |
| 287. #32900 | C23 | semidirect |
| 288. #32900 | C23 | semidirect |
| 289. #32900 | C23 | semidirect |
| 310. #32898 | C23 | semidirect |
| 311. #32898 | C23 | semidirect |
| 312. #32898 | C23 | semidirect |
| 313. #32898 | C23 | semidirect |
| 314. #32898 | C23 | semidirect |
| 315. #32898 | C23 | semidirect |
| 316. #32898 | C23 | semidirect |
| 317. #32898 | C23 | semidirect |
| 318. #32898 | C23 | semidirect |
| 319. #32898 | C23 | semidirect |
| 320. #32898 | C23 | semidirect |
| 321. #32898 | C23 | semidirect |
| 322. #32898 | C23 | semidirect |
| 323. #32898 | C23 | semidirect |
| 324. #32898 | C23 | semidirect |
| 325. #32898 | C23 | semidirect |
| 326. #32898 | C23 | semidirect |
| 327. #32898 | C23 | semidirect |
| 328. #32898 | C23 | semidirect |
| 329. #32898 | C23 | semidirect |
| 330. #32898 | C23 | semidirect |
| 331. #32898 | C23 | semidirect |
| 332. #29634 | C23 | semidirect |
| 333. #29634 | C23 | semidirect |
| 334. #29634 | C23 | semidirect |
| 335. #29634 | C23 | semidirect |
| 336. #29634 | C23 | semidirect |
| 337. #29634 | C23 | semidirect |
| 338. #29634 | C23 | semidirect |
| 339. #29634 | C23 | semidirect |
| 340. #21795 | C23 | semidirect |
| 341. #21749 | C23 | semidirect |
| 342. #21749 | C23 | semidirect |
| 343. #20724 | C23 | semidirect |
| 344. #20690 | C23 | semidirect |
| 345. #20586 | C23 | semidirect |
| 346. #20586 | C23 | semidirect |
| 347. #20586 | C23 | semidirect |
| 348. #20586 | C23 | semidirect |
| 349. #20586 | C23 | semidirect |
| 350. #20586 | C23 | semidirect |
| 351. #20586 | C23 | semidirect |
| 352. #20586 | C23 | semidirect |
| 353. #20586 | C23 | semidirect |
| 354. #20586 | C23 | semidirect |
| 355. #20586 | C23 | semidirect |
| 356. #20586 | C23 | semidirect |
| 357. #20586 | C23 | semidirect |
| 358. #20586 | C23 | semidirect |
| 359. #20586 | C23 | semidirect |
| 360. #20585 | C23 | semidirect |
| 361. #20585 | C23 | semidirect |
| 362. #20585 | C23 | semidirect |
| 363. #20585 | C23 | semidirect |
| 364. #20585 | C23 | semidirect |
| 365. #20585 | C23 | semidirect |
| 366. #20585 | C23 | semidirect |
| 367. #10691 | C23 | semidirect |
| 368. #10691 | C23 | semidirect |
| 369. #10690 | C23 | semidirect |
| 370. #10690 | C23 | semidirect |
| 371. #10690 | C23 | semidirect |
| 372. #10690 | C23 | semidirect |
| 373. #10690 | C23 | semidirect |
| 374. #10690 | C23 | semidirect |
| 375. #10690 | C23 | semidirect |
| 376. #10690 | C23 | semidirect |
| 377. #10690 | C23 | semidirect |
| 378. #10690 | C23 | semidirect |
| 379. #10393 | C23 | semidirect |
| 380. #10393 | C23 | semidirect |
| 381. #10392 | C23 | semidirect |
| 382. #10392 | C23 | semidirect |
| 383. #10392 | C23 | semidirect |
| 384. #10392 | C23 | semidirect |
| 385. #10392 | C23 | semidirect |
| 386. #10392 | C23 | semidirect |
| 387. #10392 | C23 | semidirect |
| 388. #10392 | C23 | semidirect |
| 389. #10392 | C23 | semidirect |
| 390. #10392 | C23 | semidirect |
| 391. #10392 | C23 | semidirect |
| 392. #10392 | C23 | semidirect |
| 393. #10392 | C23 | semidirect |
| 394. #10392 | C23 | semidirect |
| 395. #10392 | C23 | semidirect |
| 396. #10392 | C23 | semidirect |
| 397. #10392 | C23 | semidirect |
| 398. #10392 | C23 | semidirect |
| 399. #10392 | C23 | semidirect |
| 400. #10392 | C23 | semidirect |
| 401. #10392 | C23 | semidirect |
| 402. #10392 | C23 | semidirect |
| 403. #10391 | C23 | semidirect |
| 404. #10391 | C23 | semidirect |
| 405. #10390 | C23 | semidirect |
| 406. #10390 | C23 | semidirect |
| 407. #10390 | C23 | semidirect |
| 408. #10390 | C23 | semidirect |
| 409. #10390 | C23 | semidirect |
| 410. #10390 | C23 | semidirect |
| 411. #10390 | C23 | semidirect |
| 412. #10390 | C23 | semidirect |
| 413. #10390 | C23 | semidirect |
| 414. #10390 | C23 | semidirect |
| 415. #10390 | C23 | semidirect |
| 416. #10390 | C23 | semidirect |
| 417. #10390 | C23 | semidirect |
| 418. #10390 | C23 | semidirect |
| 419. #10390 | C23 | semidirect |
| 420. #10390 | C23 | semidirect |
| 463. #9501 | C23 | semidirect |
| 464. #9501 | C23 | semidirect |
| 465. #9501 | C23 | semidirect |
| 466. #9501 | C23 | semidirect |
| 467. #9501 | C23 | semidirect |
| 468. #9501 | C23 | semidirect |
| 469. #9501 | C23 | semidirect |
| 470. #9501 | C23 | semidirect |
| 471. #9501 | C23 | semidirect |
| 472. #9499 | C23 | semidirect |
| 473. #9499 | C23 | semidirect |
| 474. #9499 | C23 | semidirect |
| 475. #9499 | C23 | semidirect |
| 476. #9499 | C23 | semidirect |
| 477. #9498 | C23 | semidirect |
| 478. #9498 | C23 | semidirect |
| 479. #9498 | C23 | semidirect |
| 480. #9498 | C23 | semidirect |
| 481. #9498 | C23 | semidirect |
| 482. #9498 | C23 | semidirect |
| 513. #9497 | C23 | semidirect |
| 514. #9497 | C23 | semidirect |
| 515. #9497 | C23 | semidirect |
| 516. #9497 | C23 | semidirect |
| 517. #9497 | C23 | semidirect |
| 518. #9497 | C23 | semidirect |
| 519. #9497 | C23 | semidirect |
| 520. #9497 | C23 | semidirect |
| 521. #9497 | C23 | semidirect |
| 522. #9497 | C23 | semidirect |
| 523. #9497 | C23 | semidirect |
| 524. #9497 | C23 | semidirect |
| 525. #9497 | C23 | semidirect |
| 526. #9497 | C23 | semidirect |
| 527. #9497 | C23 | semidirect |
| 528. #9497 | C23 | semidirect |
| 529. #9497 | C23 | semidirect |
| 530. #9497 | C23 | semidirect |
| 531. #9497 | C23 | semidirect |
| 532. #9497 | C23 | semidirect |
| 533. #9497 | C23 | semidirect |
| 534. #9497 | C23 | semidirect |
| 535. #9497 | C23 | semidirect |
| 536. #9497 | C23 | semidirect |
| 537. #9497 | C23 | semidirect |
| 538. #9497 | C23 | semidirect |
| 539. #9497 | C23 | semidirect |
| 540. #9497 | C23 | semidirect |
| 541. #9497 | C23 | semidirect |
| 542. #9497 | C23 | semidirect |
| 543. #9497 | C23 | semidirect |
| 544. #9497 | C23 | semidirect |
| 545. #9497 | C23 | semidirect |
| 546. #9497 | C23 | semidirect |
| 547. #9497 | C23 | semidirect |
| 548. #9497 | C23 | semidirect |
| 549. #9497 | C23 | semidirect |
| 550. #9497 | C23 | semidirect |
| 551. #9497 | C23 | semidirect |
| 552. #9497 | C23 | semidirect |
| 553. #9497 | C23 | semidirect |
| 554. #9497 | C23 | semidirect |
| 555. #9497 | C23 | semidirect |
| 556. #9497 | C23 | semidirect |
| 557. #9497 | C23 | semidirect |
| 558. #9496 | C23 | semidirect |
| 559. #9496 | C23 | semidirect |
| 560. #9496 | C23 | semidirect |
| 561. #9496 | C23 | semidirect |
| 562. #9496 | C23 | semidirect |
| 563. #9496 | C23 | semidirect |
| 582. #9495 | C23 | semidirect |
| 583. #9495 | C23 | semidirect |
| 584. #9495 | C23 | semidirect |
| 585. #9495 | C23 | semidirect |
| 586. #9495 | C23 | semidirect |
| 587. #9495 | C23 | semidirect |
| 588. #9495 | C23 | semidirect |
| 589. #9495 | C23 | semidirect |
| 590. #9495 | C23 | semidirect |
| 591. #9495 | C23 | semidirect |
| 592. #9495 | C23 | semidirect |
| 593. #9495 | C23 | semidirect |
| 594. #9495 | C23 | semidirect |
| 595. #9495 | C23 | semidirect |
| 596. #9495 | C23 | semidirect |
| 597. #9495 | C23 | semidirect |
| 598. #9495 | C23 | semidirect |
| 599. #9495 | C23 | semidirect |
| 600. #9495 | C23 | semidirect |
| 601. #9495 | C23 | semidirect |
| 602. #9495 | C23 | semidirect |
| 603. #9495 | C23 | semidirect |
| 604. #9495 | C23 | semidirect |
| 605. #9495 | C23 | semidirect |
| 606. #9495 | C23 | semidirect |
| 607. #8750 | C23 | semidirect |
| 608. #8750 | C23 | semidirect |
| 609. #8750 | C23 | semidirect |
| 610. #8749 | C23 | semidirect |
| 611. #8749 | C23 | semidirect |
| 612. #8749 | C23 | semidirect |
| 613. #8749 | C23 | semidirect |
| 614. #8749 | C23 | semidirect |
| 615. #8749 | C23 | semidirect |
| 616. #8748 | C23 | semidirect |
| 617. #8748 | C23 | semidirect |
| 618. #8748 | C23 | semidirect |
| 619. #8748 | C23 | semidirect |
| 620. #8748 | C23 | semidirect |
| 621. #8748 | C23 | semidirect |
| 622. #8748 | C23 | semidirect |
| 623. #8748 | C23 | semidirect |
| 624. #8748 | C23 | semidirect |
| 625. #8748 | C23 | semidirect |
| 626. #8748 | C23 | semidirect |
| 627. #8748 | C23 | semidirect |
| 628. #8748 | C23 | semidirect |
| 629. #8748 | C23 | semidirect |
| 630. #8748 | C23 | semidirect |
| 631. #8747 | C23 | semidirect |
| 632. #8747 | C23 | semidirect |
| 633. #8747 | C23 | semidirect |
| 634. #8747 | C23 | semidirect |
| 635. #8747 | C23 | semidirect |
| 636. #8746 | C23 | semidirect |
| 637. #8746 | C23 | semidirect |
| 638. #8746 | C23 | semidirect |
| 639. #8746 | C23 | semidirect |
| 640. #8746 | C23 | semidirect |
| 641. #8746 | C23 | semidirect |
| 642. #8746 | C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.