Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
At least 6895 conjugacy classes of subgroups; only the 2994 normal subgroups are shown.
The subgroup lattice has 1006 nodes (normal subgroups only) — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×#46996 |
| 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. #72338977 | C2 | semidirect |
| 2. #72338975 | C2 | semidirect |
| 3. #72338972 | C2 | semidirect |
| 4. #72338961 | C2 | semidirect |
| 5. #72338954 | C2 | semidirect |
| 6. C2×#213860 | C2 | semidirect |
| 7. #72338794 | C2 | semidirect |
| 8. #72338794 | C2 | semidirect |
| 9. #72338476 | C2 | semidirect |
| 10. #72337703 | C2 | semidirect |
| 11. #72337662 | C2 | semidirect |
| 12. #72337653 | C2 | semidirect |
| 13. #72310978 | C2 | semidirect |
| 14. #72285755 | C2 | semidirect |
| 15. #72285372 | C2 | semidirect |
| 16. #72284602 | C2 | semidirect |
| 17. #72284366 | C2 | semidirect |
| 18. #72283693 | C2 | semidirect |
| 19. #72251352 | C2 | semidirect |
| 20. #72241387 | C2 | semidirect |
| 21. #72241387 | C2 | semidirect |
| 22. #72241342 | C2 | semidirect |
| 23. #72240110 | C2 | semidirect |
| 24. #72236108 | C2 | semidirect |
| 25. #72236108 | C2 | semidirect |
| 26. C2×#245233 | C2 | semidirect |
| 27. #72234955 | C2 | semidirect |
| 32. #6628892 | C22 | semidirect |
| 33. #6628892 | C22 | semidirect |
| 34. C2×#32898 | C22 | semidirect |
| 35. C2×#32898 | C22 | semidirect |
| 36. #6470225 | C22 | semidirect |
| 37. #6470225 | C22 | semidirect |
| 38. #6385975 | C22 | semidirect |
| 39. #6370693 | C22 | semidirect |
| 40. C2×#20585 | C22 | semidirect |
| 41. #346293 | C22 | semidirect |
| 42. #346293 | C22 | semidirect |
| 43. #346293 | C22 | semidirect |
| 44. #346283 | C22 | semidirect |
| 45. #346283 | C22 | semidirect |
| 46. #346283 | C22 | semidirect |
| 47. #346282 | C22 | semidirect |
| 48. #346275 | C22 | semidirect |
| 49. #346274 | C22 | semidirect |
| 50. #346271 | C22 | semidirect |
| 51. #346270 | C22 | semidirect |
| 52. #346270 | C22 | semidirect |
| 53. #346269 | C22 | semidirect |
| 54. #346269 | C22 | semidirect |
| 55. #346269 | C22 | semidirect |
| 56. #346269 | C22 | semidirect |
| 57. #346266 | C22 | semidirect |
| 58. #346265 | C22 | semidirect |
| 59. #346258 | C22 | semidirect |
| 60. #346257 | C22 | semidirect |
| 61. #346257 | C22 | semidirect |
| 62. #346243 | C22 | semidirect |
| 63. #346243 | C22 | semidirect |
| 64. #346242 | C22 | semidirect |
| 65. #346242 | C22 | semidirect |
| 66. #346242 | C22 | semidirect |
| 67. #346242 | C22 | semidirect |
| 68. #346241 | C22 | semidirect |
| 69. #346241 | C22 | semidirect |
| 70. #346239 | C22 | semidirect |
| 71. #346239 | C22 | semidirect |
| 72. #346239 | C22 | semidirect |
| 73. #346237 | C22 | semidirect |
| 74. #346232 | C22 | semidirect |
| 75. #346232 | C22 | semidirect |
| 76. #346231 | C22 | semidirect |
| 77. #346231 | C22 | semidirect |
| 78. #346230 | C22 | semidirect |
| 79. #346228 | C22 | semidirect |
| 80. #346228 | C22 | semidirect |
| 81. #346228 | C22 | semidirect |
| 82. #346228 | C22 | semidirect |
| 83. #346227 | C22 | semidirect |
| 84. #346226 | C22 | semidirect |
| 85. #346226 | C22 | semidirect |
| 86. #346226 | C22 | semidirect |
| 87. #346226 | C22 | semidirect |
| 88. #346226 | C22 | semidirect |
| 89. #346226 | C22 | semidirect |
| 90. #346225 | C22 | semidirect |
| 91. #346225 | C22 | semidirect |
| 92. #346225 | C22 | semidirect |
| 93. #346225 | C22 | semidirect |
| 94. #346225 | C22 | semidirect |
| 95. #346225 | C22 | semidirect |
| 96. #251914 | C22 | semidirect |
| 97. #251913 | C22 | semidirect |
| 98. #251912 | C22 | semidirect |
| 99. #251911 | C22 | semidirect |
| 100. #251885 | C22 | semidirect |
| 101. #251885 | C22 | semidirect |
| 102. #251884 | C22 | semidirect |
| 103. #251883 | C22 | semidirect |
| 104. #251877 | C22 | semidirect |
| 105. #251877 | C22 | semidirect |
| 106. #251872 | C22 | semidirect |
| 107. #251872 | C22 | semidirect |
| 108. #251871 | C22 | semidirect |
| 109. #251871 | C22 | semidirect |
| 110. #251871 | C22 | semidirect |
| 111. #251871 | C22 | semidirect |
| 112. #251864 | C22 | semidirect |
| 113. #251863 | C22 | semidirect |
| 114. #251860 | C22 | semidirect |
| 115. #251860 | C22 | semidirect |
| 116. #251860 | 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. #251859 | C22 | semidirect |
| 124. #251854 | C22 | semidirect |
| 125. #251854 | C22 | semidirect |
| 126. #251843 | C22 | semidirect |
| 127. #251843 | C22 | semidirect |
| 128. #251838 | C22 | semidirect |
| 129. #251838 | C22 | semidirect |
| 130. #251837 | C22 | semidirect |
| 131. #251837 | C22 | semidirect |
| 132. #251837 | C22 | semidirect |
| 133. #251837 | C22 | semidirect |
| 134. #251831 | C22 | semidirect |
| 135. #251831 | C22 | semidirect |
| 136. #251828 | C22 | semidirect |
| 137. #251828 | C22 | semidirect |
| 138. #251828 | C22 | semidirect |
| 139. #251827 | C22 | semidirect |
| 140. #251827 | C22 | semidirect |
| 141. #251827 | C22 | semidirect |
| 142. #251827 | C22 | semidirect |
| 143. #251827 | C22 | semidirect |
| 144. #245255 | C22 | semidirect |
| 145. #245255 | C22 | semidirect |
| 146. #245255 | C22 | semidirect |
| 147. #245255 | C22 | semidirect |
| 148. #245255 | C22 | semidirect |
| 149. #245255 | C22 | semidirect |
| 150. #245234 | C22 | semidirect |
| 151. #245234 | C22 | semidirect |
| 152. #245234 | C22 | semidirect |
| 153. #245234 | C22 | semidirect |
| 154. #245234 | C22 | semidirect |
| 155. #245234 | C22 | semidirect |
| 161. #245233 | C22 | semidirect |
| 162. #245233 | C22 | semidirect |
| 163. #245233 | C22 | semidirect |
| 164. #245233 | C22 | semidirect |
| 165. #245233 | C22 | semidirect |
| 166. #245233 | C22 | semidirect |
| 167. #245233 | C22 | semidirect |
| 168. #245233 | C22 | semidirect |
| 169. #245233 | C22 | semidirect |
| 170. #245233 | C22 | semidirect |
| 171. #10690⋊C2 | C22 | semidirect |
| 172. #10690⋊C2 | C22 | semidirect |
| 173. #238090 | C22 | semidirect |
| 174. #238082 | C22 | semidirect |
| 175. #238082 | C22 | semidirect |
| 176. #238082 | C22 | semidirect |
| 177. #238082 | C22 | semidirect |
| 178. #238082 | C22 | semidirect |
| 183. #213880 | C22 | semidirect |
| 184. #213880 | C22 | semidirect |
| 185. #213865 | C22 | semidirect |
| 186. #213865 | C22 | semidirect |
| 187. #213861 | C22 | semidirect |
| 188. #213861 | C22 | semidirect |
| 189. #213861 | C22 | semidirect |
| 190. #213861 | C22 | semidirect |
| 191. #213860 | C22 | semidirect |
| 192. #213860 | C22 | semidirect |
| 193. #213860 | C22 | semidirect |
| 194. #213860 | C22 | semidirect |
| 195. #213860 | C22 | semidirect |
| 196. #213860 | C22 | semidirect |
| 197. #213860 | C22 | semidirect |
| 198. #213860 | C22 | semidirect |
| 199. #213860 | C22 | semidirect |
| 200. #213860 | C22 | semidirect |
| 201. #213860 | C22 | semidirect |
| 202. #213860 | C22 | semidirect |
| 203. #213842 | C22 | semidirect |
| 204. #213838 | C22 | semidirect |
| 205. #213838 | C22 | semidirect |
| 206. #213838 | C22 | semidirect |
| 207. #201701 | C22 | semidirect |
| 208. #201690 | C22 | semidirect |
| 209. #201690 | C22 | semidirect |
| 210. #201687 | C22 | semidirect |
| 211. #201678 | C22 | semidirect |
| 212. #201678 | C22 | semidirect |
| 213. #201678 | C22 | semidirect |
| 214. #201678 | C22 | semidirect |
| 215. #201664 | C22 | semidirect |
| 216. #201664 | C22 | semidirect |
| 217. #201664 | C22 | semidirect |
| 218. #201664 | C22 | semidirect |
| 219. #201664 | C22 | semidirect |
| 220. C2×#9497 | C22 | semidirect |
| 221. C2×#9497 | C22 | semidirect |
| 222. C2×#9495 | C22 | semidirect |
| 223. C2×#9495 | C22 | semidirect |
| 224. C2×#9495 | C22 | semidirect |
| 225. #190124 | C22 | semidirect |
| 226. #190117 | C22 | semidirect |
| 227. #190116 | C22 | semidirect |
| 228. #190107 | C22 | semidirect |
| 229. #190107 | C22 | semidirect |
| 230. C2×#8748 | C22 | semidirect |
| 281. #33020 | C23 | semidirect |
| 282. #33020 | C23 | semidirect |
| 283. #33020 | C23 | semidirect |
| 284. #33020 | C23 | semidirect |
| 285. #32900 | C23 | semidirect |
| 286. #32900 | C23 | semidirect |
| 287. #32900 | C23 | semidirect |
| 288. #32900 | C23 | semidirect |
| 289. #32900 | C23 | semidirect |
| 290. #32900 | C23 | semidirect |
| 303. #32898 | C23 | semidirect |
| 304. #32898 | C23 | semidirect |
| 305. #32898 | C23 | semidirect |
| 306. #32898 | C23 | semidirect |
| 307. #32898 | C23 | semidirect |
| 308. #32898 | C23 | semidirect |
| 309. #32898 | C23 | semidirect |
| 310. #32898 | C23 | semidirect |
| 311. #32898 | C23 | semidirect |
| 312. #32898 | C23 | semidirect |
| 313. #29634 | C23 | semidirect |
| 314. #29634 | C23 | semidirect |
| 315. #29634 | C23 | semidirect |
| 316. #29634 | C23 | semidirect |
| 317. #21795 | C23 | semidirect |
| 318. #21749 | C23 | semidirect |
| 322. #20724 | C23 | semidirect |
| 323. #20724 | C23 | semidirect |
| 324. #20586 | C23 | semidirect |
| 325. #20586 | C23 | semidirect |
| 326. #20586 | C23 | semidirect |
| 327. #20586 | C23 | semidirect |
| 328. #20585 | C23 | semidirect |
| 329. #20585 | C23 | semidirect |
| 330. #20585 | C23 | semidirect |
| 331. #20585 | C23 | semidirect |
| 332. #20585 | C23 | semidirect |
| 333. #20585 | C23 | semidirect |
| 334. #20585 | C23 | semidirect |
| 335. #20585 | C23 | semidirect |
| 336. #20585 | C23 | semidirect |
| 337. #20585 | C23 | semidirect |
| 356. #10691 | C23 | semidirect |
| 357. #10691 | C23 | semidirect |
| 358. #10690 | C23 | semidirect |
| 359. #10690 | C23 | semidirect |
| 360. #10690 | C23 | semidirect |
| 361. #10690 | C23 | semidirect |
| 362. #10690 | C23 | semidirect |
| 363. #10690 | C23 | semidirect |
| 364. #10690 | C23 | semidirect |
| 365. #10690 | C23 | semidirect |
| 366. #10690 | C23 | semidirect |
| 367. #10690 | C23 | semidirect |
| 368. #10690 | C23 | semidirect |
| 369. #10690 | C23 | semidirect |
| 370. #10690 | C23 | semidirect |
| 371. #10690 | C23 | semidirect |
| 372. #10393 | C23 | semidirect |
| 373. #10393 | C23 | semidirect |
| 374. #10393 | C23 | semidirect |
| 375. #10392 | C23 | semidirect |
| 376. #10392 | C23 | semidirect |
| 377. #10392 | C23 | semidirect |
| 378. #10392 | C23 | semidirect |
| 379. #10392 | C23 | semidirect |
| 380. #10392 | 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. #10392 | C23 | semidirect |
| 404. #10392 | C23 | semidirect |
| 405. #10392 | C23 | semidirect |
| 406. #10392 | C23 | semidirect |
| 407. #10392 | C23 | semidirect |
| 408. #10391 | 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 |
| 452. #9501 | C23 | semidirect |
| 453. #9501 | C23 | semidirect |
| 454. #9501 | C23 | semidirect |
| 455. #9501 | C23 | semidirect |
| 456. #9501 | C23 | semidirect |
| 457. #9501 | C23 | semidirect |
| 458. #9501 | C23 | semidirect |
| 459. #9501 | C23 | semidirect |
| 460. #9499 | C23 | semidirect |
| 461. #9499 | C23 | semidirect |
| 462. #9499 | C23 | semidirect |
| 463. #9499 | C23 | semidirect |
| 464. #9499 | C23 | semidirect |
| 465. #9499 | C23 | semidirect |
| 466. #9498 | C23 | semidirect |
| 467. #9498 | C23 | semidirect |
| 468. #9498 | C23 | semidirect |
| 469. #9498 | C23 | semidirect |
| 470. #9498 | C23 | semidirect |
| 471. #9498 | C23 | semidirect |
| 472. #9498 | C23 | semidirect |
| 473. #9498 | C23 | semidirect |
| 494. #9497 | C23 | semidirect |
| 495. #9497 | C23 | semidirect |
| 496. #9497 | C23 | semidirect |
| 497. #9497 | C23 | semidirect |
| 498. #9497 | C23 | semidirect |
| 499. #9497 | C23 | semidirect |
| 500. #9497 | C23 | semidirect |
| 501. #9497 | C23 | semidirect |
| 502. #9497 | C23 | semidirect |
| 503. #9497 | C23 | semidirect |
| 504. #9497 | C23 | semidirect |
| 505. #9497 | C23 | semidirect |
| 506. #9497 | C23 | semidirect |
| 507. #9497 | C23 | semidirect |
| 508. #9497 | C23 | semidirect |
| 509. #9497 | C23 | semidirect |
| 510. #9497 | C23 | semidirect |
| 511. #9497 | C23 | semidirect |
| 512. #9497 | 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. #9496 | C23 | semidirect |
| 523. #9496 | C23 | semidirect |
| 524. #9496 | C23 | semidirect |
| 525. #9496 | C23 | semidirect |
| 526. #9496 | C23 | semidirect |
| 527. #9496 | C23 | semidirect |
| 528. #9496 | C23 | semidirect |
| 529. #9496 | C23 | semidirect |
| 554. #9495 | C23 | semidirect |
| 555. #9495 | C23 | semidirect |
| 556. #9495 | C23 | semidirect |
| 557. #9495 | C23 | semidirect |
| 558. #9495 | C23 | semidirect |
| 559. #9495 | C23 | semidirect |
| 560. #9495 | C23 | semidirect |
| 561. #9495 | C23 | semidirect |
| 562. #9495 | C23 | semidirect |
| 563. #9495 | C23 | semidirect |
| 564. #9495 | C23 | semidirect |
| 565. #9495 | C23 | semidirect |
| 566. #9495 | C23 | semidirect |
| 567. #9495 | C23 | semidirect |
| 568. #9495 | C23 | semidirect |
| 569. #9495 | C23 | semidirect |
| 570. #9495 | C23 | semidirect |
| 571. #9495 | C23 | semidirect |
| 572. #9495 | C23 | semidirect |
| 573. #9495 | C23 | semidirect |
| 574. #9495 | C23 | semidirect |
| 575. #9495 | C23 | semidirect |
| 576. #9495 | C23 | semidirect |
| 577. #9495 | C23 | semidirect |
| 578. #9495 | C23 | semidirect |
| 579. #9495 | C23 | semidirect |
| 580. #9495 | C23 | semidirect |
| 581. #9495 | C23 | semidirect |
| 582. #9495 | C23 | semidirect |
| 583. #9495 | C23 | semidirect |
| 584. #8750 | C23 | semidirect |
| 585. #8750 | C23 | semidirect |
| 586. #8750 | C23 | semidirect |
| 587. #8750 | C23 | semidirect |
| 588. #8749 | C23 | semidirect |
| 589. #8749 | C23 | semidirect |
| 590. #8749 | C23 | semidirect |
| 591. #8749 | C23 | semidirect |
| 592. #8749 | C23 | semidirect |
| 593. #8749 | C23 | semidirect |
| 594. #8749 | C23 | semidirect |
| 595. #8748 | C23 | semidirect |
| 596. #8748 | C23 | semidirect |
| 597. #8748 | C23 | semidirect |
| 598. #8748 | C23 | semidirect |
| 599. #8748 | C23 | semidirect |
| 600. #8748 | C23 | semidirect |
| 601. #8748 | C23 | semidirect |
| 602. #8748 | C23 | semidirect |
| 603. #8748 | C23 | semidirect |
| 604. #8748 | C23 | semidirect |
| 605. #8748 | C23 | semidirect |
| 606. #8748 | C23 | semidirect |
| 607. #8748 | C23 | semidirect |
| 608. #8748 | C23 | semidirect |
| 609. #8748 | C23 | semidirect |
| 610. #8747 | C23 | semidirect |
| 611. #8747 | C23 | semidirect |
| 612. #8747 | C23 | semidirect |
| 613. #8747 | C23 | semidirect |
| 614. #8747 | C23 | semidirect |
| 615. #8747 | C23 | semidirect |
| 616. #8747 | C23 | semidirect |
| 617. #8747 | C23 | semidirect |
| 618. #8746 | C23 | semidirect |
| 619. #8746 | C23 | semidirect |
| 620. #8746 | C23 | semidirect |
| 621. #8746 | C23 | semidirect |
| 622. #8746 | C23 | semidirect |
| 623. #8746 | C23 | semidirect |
| 624. #8746 | C23 | semidirect |
| 625. #8746 | C23 | semidirect |
| 665. C24×D4 | #41 | semidirect |
| 666. C24×D4 | #41 | semidirect |
| 667. C24×D4 | #41 | semidirect |
| 674. C22×#127 | #41 | semidirect |
| 675. C22×#127 | #41 | semidirect |
| 676. C22×#127 | #41 | semidirect |
| 677. C22×#127 | #41 | semidirect |
| 684. C23×C42 | #41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.