Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
At least 8222 conjugacy classes of subgroups; only the 4048 normal subgroups are shown.
The subgroup lattice has 907 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. #72339081 | C2 | semidirect |
| 2. #72339080 | C2 | semidirect |
| 3. #72339078 | C2 | semidirect |
| 4. #72339075 | C2 | semidirect |
| 5. #72339073 | C2 | semidirect |
| 6. #72339070 | C2 | semidirect |
| 7. #72339068 | C2 | semidirect |
| 8. #72339033 | C2 | semidirect |
| 9. #72338954 | C2 | semidirect |
| 10. #72338740 | C2 | semidirect |
| 11. #72338736 | C2 | semidirect |
| 12. #72338475 | C2 | semidirect |
| 13. #72337659 | C2 | semidirect |
| 14. #72266070 | C2 | semidirect |
| 15. #72241017 | C2 | semidirect |
| 16. #72240645 | C2 | semidirect |
| 17. #72240627 | C2 | semidirect |
| 18. #72236108 | C2 | semidirect |
| 19. C2×#245233 | C2 | semidirect |
| 20. #72233156 | C2 | semidirect |
| 21. #72233042 | C2 | semidirect |
| 22. #72213228 | C2 | semidirect |
| 23. #72210439 | C2 | semidirect |
| 24. #10586066 | C22 | semidirect |
| 25. #8934620 | C22 | semidirect |
| 26. #8934366 | C22 | semidirect |
| 27. #8933771 | C22 | semidirect |
| 28. #8932883 | C22 | semidirect |
| 29. #8932553 | C22 | semidirect |
| 30. #8899001 | C22 | semidirect |
| 31. #8898948 | C22 | semidirect |
| 32. #7804411 | C22 | semidirect |
| 34. #7733149 | C22 | semidirect |
| 35. #7721792 | C22 | semidirect |
| 37. #7643002 | C22 | semidirect |
| 38. #7631286 | C22 | semidirect |
| 39. C2×#35527 | C22 | semidirect |
| 40. C2×#35527 | C22 | semidirect |
| 41. #6629399 | C22 | semidirect |
| 42. #6629267 | C22 | semidirect |
| 43. #6629267 | C22 | semidirect |
| 44. #6628901 | C22 | semidirect |
| 45. #6628901 | C22 | semidirect |
| 46. #6628901 | C22 | semidirect |
| 47. #6628896 | C22 | semidirect |
| 48. #6628892 | C22 | semidirect |
| 49. C2×#32898 | C22 | semidirect |
| 50. C2×#32898 | C22 | semidirect |
| 51. #6487657 | C22 | semidirect |
| 52. #6487657 | C22 | semidirect |
| 53. #6470244 | C22 | semidirect |
| 54. #6470244 | C22 | semidirect |
| 55. #6470244 | C22 | semidirect |
| 56. #6470231 | C22 | semidirect |
| 57. #6470231 | C22 | semidirect |
| 58. #6470225 | C22 | semidirect |
| 59. #6470225 | C22 | semidirect |
| 60. #6470225 | C22 | semidirect |
| 61. #6432958 | C22 | semidirect |
| 62. #6432958 | C22 | semidirect |
| 63. #6432958 | C22 | semidirect |
| 64. #6432958 | C22 | semidirect |
| 65. #6385975 | C22 | semidirect |
| 66. #6385975 | C22 | semidirect |
| 67. #6374211 | C22 | semidirect |
| 68. #6374211 | C22 | semidirect |
| 69. #6370693 | C22 | semidirect |
| 70. #251914 | C22 | semidirect |
| 71. #251913 | C22 | semidirect |
| 72. #251912 | C22 | semidirect |
| 73. #251911 | C22 | semidirect |
| 74. #251911 | C22 | semidirect |
| 75. #251909 | C22 | semidirect |
| 76. #251909 | C22 | semidirect |
| 77. #251908 | C22 | semidirect |
| 78. #251907 | C22 | semidirect |
| 79. #251907 | C22 | semidirect |
| 80. #251883 | C22 | semidirect |
| 81. #251864 | C22 | semidirect |
| 82. #251863 | C22 | semidirect |
| 83. #251862 | C22 | semidirect |
| 84. #251860 | C22 | semidirect |
| 85. #251860 | C22 | semidirect |
| 86. #251860 | C22 | semidirect |
| 87. #251860 | C22 | semidirect |
| 88. #251859 | C22 | semidirect |
| 89. #251859 | C22 | semidirect |
| 90. #251858 | C22 | semidirect |
| 91. #251858 | C22 | semidirect |
| 92. #251857 | C22 | semidirect |
| 93. #251855 | C22 | semidirect |
| 94. #251855 | C22 | semidirect |
| 95. #251855 | C22 | semidirect |
| 96. #251855 | C22 | semidirect |
| 97. #251854 | C22 | semidirect |
| 98. #251854 | C22 | semidirect |
| 99. #251830 | C22 | semidirect |
| 100. #251828 | C22 | semidirect |
| 101. #251828 | C22 | semidirect |
| 102. #251828 | C22 | semidirect |
| 103. #251827 | C22 | semidirect |
| 104. #245255 | C22 | semidirect |
| 105. #245255 | C22 | semidirect |
| 106. #245255 | C22 | semidirect |
| 107. #245255 | C22 | semidirect |
| 108. #245255 | C22 | semidirect |
| 109. #245252 | C22 | semidirect |
| 110. #245252 | C22 | semidirect |
| 111. #245249 | C22 | semidirect |
| 112. #245249 | C22 | semidirect |
| 113. #245246 | C22 | semidirect |
| 114. #245246 | C22 | semidirect |
| 115. #245234 | C22 | semidirect |
| 116. #245234 | C22 | semidirect |
| 117. #245234 | C22 | semidirect |
| 118. #245233 | C22 | semidirect |
| 119. #245233 | C22 | semidirect |
| 120. #245233 | C22 | semidirect |
| 121. #245233 | C22 | semidirect |
| 122. #245233 | C22 | semidirect |
| 123. #245233 | C22 | semidirect |
| 124. #245233 | C22 | semidirect |
| 125. #245233 | C22 | semidirect |
| 126. #245233 | C22 | semidirect |
| 127. #245233 | C22 | semidirect |
| 128. #245233 | C22 | semidirect |
| 129. #245233 | C22 | semidirect |
| 130. #245233 | C22 | semidirect |
| 131. #245233 | C22 | semidirect |
| 132. #245231 | C22 | semidirect |
| 133. #245231 | C22 | semidirect |
| 134. #245228 | C22 | semidirect |
| 135. #245228 | C22 | semidirect |
| 136. #245225 | C22 | semidirect |
| 137. #245225 | C22 | semidirect |
| 138. #238090 | C22 | semidirect |
| 139. #238082 | C22 | semidirect |
| 140. #233541 | C22 | semidirect |
| 141. #233541 | C22 | semidirect |
| 142. C2×#10336 | C22 | semidirect |
| 143. C2×#10336 | C22 | semidirect |
| 144. #213884 | C22 | semidirect |
| 145. #213880 | C22 | semidirect |
| 146. #213880 | C22 | semidirect |
| 147. #213876 | C22 | semidirect |
| 148. #213869 | C22 | semidirect |
| 149. #213865 | C22 | semidirect |
| 150. #213861 | C22 | semidirect |
| 151. #213861 | C22 | semidirect |
| 152. #213860 | C22 | semidirect |
| 153. #213854 | C22 | semidirect |
| 154. #213849 | C22 | semidirect |
| 155. #213842 | C22 | semidirect |
| 156. #213838 | C22 | semidirect |
| 157. #213838 | C22 | semidirect |
| 158. #213829 | C22 | semidirect |
| 159. #201701 | C22 | semidirect |
| 160. #201690 | C22 | semidirect |
| 161. #201678 | C22 | semidirect |
| 162. #201678 | C22 | semidirect |
| 163. #201664 | C22 | semidirect |
| 164. #201664 | C22 | semidirect |
| 165. C2×#9497 | C22 | semidirect |
| 166. C2×#9497 | C22 | semidirect |
| 167. #190124 | C22 | semidirect |
| 168. #190107 | C22 | semidirect |
| 169. #188035 | C22 | semidirect |
| 170. C2×#8546 | C22 | semidirect |
| 171. C2×H(7,𝔽2) | C23 | semidirect |
| 173. C23×H(5,𝔽2) | C23 | semidirect |
| 174. #62842 | C23 | semidirect |
| 175. #62842 | C23 | semidirect |
| 176. #62842 | C23 | semidirect |
| 182. #62652 | C23 | semidirect |
| 184. #47563 | C23 | semidirect |
| 185. #46997 | C23 | semidirect |
| 186. #46996 | C23 | semidirect |
| 187. #46389 | C23 | semidirect |
| 188. #46389 | C23 | semidirect |
| 190. #46387 | C23 | semidirect |
| 191. #46387 | C23 | semidirect |
| 192. #46387 | C23 | semidirect |
| 193. #46385 | C23 | semidirect |
| 195. #46384 | C23 | semidirect |
| 196. #46384 | C23 | semidirect |
| 197. #38020 | D4 | semidirect |
| 198. #37645 | D4 | semidirect |
| 199. #37475 | C23 | semidirect |
| 200. #37232 | D4 | semidirect |
| 209. #36626 | D4 | semidirect |
| 210. #36316 | D4 | semidirect |
| 211. D4×#120 | D4 | semidirect |
| 216. #35528 | D4 | semidirect |
| 217. #35528 | D4 | semidirect |
| 232. #35527 | C23 | semidirect |
| 233. #35527 | C23 | semidirect |
| 234. #35527 | C23 | semidirect |
| 235. #35527 | C23 | semidirect |
| 236. #35527 | C23 | semidirect |
| 237. #35512 | C23 | semidirect |
| 238. #35512 | C23 | semidirect |
| 241. #35347 | C23 | semidirect |
| 242. #35347 | C23 | semidirect |
| 245. #35346 | C23 | semidirect |
| 246. #35346 | C23 | semidirect |
| 247. #35222 | D4 | semidirect |
| 248. #34980 | D4 | semidirect |
| 256. C2×#2403 | C23 | semidirect |
| 257. C2×#2403 | C23 | semidirect |
| 262. #34171 | C23 | semidirect |
| 264. C2×#2309 | C23 | semidirect |
| 265. #33020 | C23 | semidirect |
| 266. #33020 | C23 | semidirect |
| 267. #33020 | C23 | semidirect |
| 268. #33020 | C23 | semidirect |
| 269. #33020 | C23 | semidirect |
| 270. #33020 | C23 | semidirect |
| 271. #32900 | C23 | semidirect |
| 272. #32900 | C23 | semidirect |
| 273. #32900 | C23 | semidirect |
| 274. #32898 | C23 | semidirect |
| 275. #32898 | C23 | semidirect |
| 276. #32898 | C23 | semidirect |
| 277. #32898 | C23 | semidirect |
| 278. #32898 | C23 | semidirect |
| 279. #32898 | C23 | semidirect |
| 280. #32898 | C23 | semidirect |
| 281. #32898 | C23 | semidirect |
| 282. #32898 | C23 | semidirect |
| 283. #32898 | C23 | semidirect |
| 284. #32898 | C23 | semidirect |
| 285. #32898 | C23 | semidirect |
| 286. #32898 | C23 | semidirect |
| 287. #32898 | C23 | semidirect |
| 288. #32898 | C23 | semidirect |
| 289. #32898 | C23 | semidirect |
| 290. #32898 | C23 | semidirect |
| 291. #32898 | C23 | semidirect |
| 292. #32898 | C23 | semidirect |
| 293. #32898 | C23 | semidirect |
| 294. #32898 | C23 | semidirect |
| 295. #29634 | C23 | semidirect |
| 296. #29634 | C23 | semidirect |
| 297. #29634 | C23 | semidirect |
| 298. #29634 | C23 | semidirect |
| 299. #29634 | C23 | semidirect |
| 300. #29634 | C23 | semidirect |
| 301. #29634 | C23 | semidirect |
| 302. #29634 | C23 | semidirect |
| 303. #29634 | C23 | semidirect |
| 304. #29634 | C23 | semidirect |
| 305. #21795 | C23 | semidirect |
| 306. #21795 | C23 | semidirect |
| 307. #21749 | C23 | semidirect |
| 308. #21749 | C23 | semidirect |
| 309. #21749 | C23 | semidirect |
| 310. #21749 | C23 | semidirect |
| 311. #21749 | C23 | semidirect |
| 316. #20724 | C23 | semidirect |
| 317. #20724 | C23 | semidirect |
| 318. #20690 | C23 | semidirect |
| 319. #20690 | C23 | semidirect |
| 320. #20690 | C23 | semidirect |
| 321. #20690 | C23 | semidirect |
| 322. #20586 | C23 | semidirect |
| 323. #20586 | C23 | semidirect |
| 324. #20586 | C23 | semidirect |
| 325. #20586 | C23 | semidirect |
| 326. #20586 | C23 | semidirect |
| 327. #20586 | C23 | semidirect |
| 328. #20586 | C23 | semidirect |
| 329. #20586 | C23 | semidirect |
| 330. #20586 | C23 | semidirect |
| 331. #20586 | C23 | semidirect |
| 332. #20585 | C23 | semidirect |
| 333. #20585 | C23 | semidirect |
| 334. #20585 | C23 | semidirect |
| 338. C2×#1781 | C23 | semidirect |
| 339. C2×#1781 | C23 | semidirect |
| 340. C2×#1781 | C23 | semidirect |
| 341. C2×#1781 | C23 | semidirect |
| 342. #10393 | C23 | semidirect |
| 343. #10393 | C23 | semidirect |
| 344. #10392 | C23 | semidirect |
| 345. #10392 | C23 | semidirect |
| 346. #10392 | C23 | semidirect |
| 347. #10392 | C23 | semidirect |
| 348. #10392 | C23 | semidirect |
| 349. #10392 | C23 | semidirect |
| 350. #10391 | C23 | semidirect |
| 351. #10390 | C23 | semidirect |
| 352. #10390 | C23 | semidirect |
| 353. #10390 | C23 | semidirect |
| 354. #10337 | C23 | semidirect |
| 355. #10337 | C23 | semidirect |
| 356. #10337 | C23 | semidirect |
| 357. #10337 | C23 | semidirect |
| 358. #10337 | C23 | semidirect |
| 359. #10337 | C23 | semidirect |
| 360. #10337 | C23 | semidirect |
| 368. #10336 | C23 | semidirect |
| 369. #10336 | C23 | semidirect |
| 370. #10336 | C23 | semidirect |
| 371. #10336 | C23 | semidirect |
| 372. #10336 | C23 | semidirect |
| 373. #10336 | C23 | semidirect |
| 374. #10336 | C23 | semidirect |
| 375. #10336 | C23 | semidirect |
| 376. #10336 | C23 | semidirect |
| 377. #10336 | C23 | semidirect |
| 378. #10336 | C23 | semidirect |
| 379. #10336 | C23 | semidirect |
| 380. #10336 | C23 | semidirect |
| 381. #10336 | C23 | semidirect |
| 382. #9501 | C23 | semidirect |
| 383. #9501 | C23 | semidirect |
| 384. #9501 | C23 | semidirect |
| 385. #9501 | C23 | semidirect |
| 386. #9501 | C23 | semidirect |
| 387. #9499 | C23 | semidirect |
| 388. #9499 | C23 | semidirect |
| 389. #9498 | C23 | semidirect |
| 390. #9498 | C23 | semidirect |
| 391. #9498 | C23 | semidirect |
| 392. #9498 | C23 | semidirect |
| 393. #9497 | C23 | semidirect |
| 394. #9497 | C23 | semidirect |
| 395. #9497 | C23 | semidirect |
| 396. #9497 | C23 | semidirect |
| 397. #9497 | C23 | semidirect |
| 398. #9497 | C23 | semidirect |
| 399. #9497 | C23 | semidirect |
| 400. #9497 | C23 | semidirect |
| 401. #9497 | C23 | semidirect |
| 402. #9497 | C23 | semidirect |
| 403. #9497 | C23 | semidirect |
| 404. #9497 | C23 | semidirect |
| 405. #9497 | C23 | semidirect |
| 406. #9497 | C23 | semidirect |
| 407. #9497 | C23 | semidirect |
| 408. #9497 | C23 | semidirect |
| 409. #9497 | C23 | semidirect |
| 410. #9497 | C23 | semidirect |
| 411. #9497 | C23 | semidirect |
| 412. #9497 | C23 | semidirect |
| 413. #9497 | C23 | semidirect |
| 414. #9497 | C23 | semidirect |
| 415. #9497 | C23 | semidirect |
| 416. #9497 | C23 | semidirect |
| 417. #9497 | C23 | semidirect |
| 418. #9497 | C23 | semidirect |
| 419. #9497 | C23 | semidirect |
| 420. #9497 | C23 | semidirect |
| 421. #9497 | C23 | semidirect |
| 422. #9496 | C23 | semidirect |
| 423. #9496 | C23 | semidirect |
| 424. #9496 | C23 | semidirect |
| 425. #9496 | C23 | semidirect |
| 426. #9495 | C23 | semidirect |
| 427. #9495 | C23 | semidirect |
| 428. #9495 | C23 | semidirect |
| 429. #9495 | C23 | semidirect |
| 430. #9495 | C23 | semidirect |
| 431. #9495 | C23 | semidirect |
| 432. #9495 | C23 | semidirect |
| 433. #9495 | C23 | semidirect |
| 434. #9495 | C23 | semidirect |
| 435. #9495 | C23 | semidirect |
| 436. #9495 | C23 | semidirect |
| 437. #9495 | C23 | semidirect |
| 438. #8750 | C23 | semidirect |
| 439. #8750 | C23 | semidirect |
| 440. #8749 | C23 | semidirect |
| 441. #8749 | C23 | semidirect |
| 442. #8748 | C23 | semidirect |
| 443. #8748 | C23 | semidirect |
| 444. #8748 | C23 | semidirect |
| 445. #8747 | C23 | semidirect |
| 446. #8747 | C23 | semidirect |
| 447. #8746 | C23 | semidirect |
| 448. #8746 | C23 | semidirect |
| 452. #8546 | C23 | semidirect |
| 453. #8546 | C23 | semidirect |
| 454. #8546 | C23 | semidirect |
| 455. #8546 | C23 | semidirect |
| 456. #8542 | C23 | semidirect |
| 457. #8542 | C23 | semidirect |
| 458. #8541 | C23 | semidirect |
| 459. #8541 | C23 | semidirect |
| 460. #8101 | C23 | semidirect |
| 461. #8101 | C23 | semidirect |
| 462. C2×#1304 | C23 | semidirect |
| 463. C2×#1304 | C23 | semidirect |
| 473. C24×D4 | C2×D4 | semidirect |
| 474. C24×D4 | C2×D4 | semidirect |
| 475. C24×D4 | C2×D4 | semidirect |
| 483. C2×#535 | C2×D4 | semidirect |
| 484. C2×#535 | C2×D4 | semidirect |
| 485. C2×#535 | C2×D4 | semidirect |
| 491. C22×#127 | C2×D4 | semidirect |
| 492. C22×#127 | C2×D4 | semidirect |
| 493. C22×#127 | C2×D4 | semidirect |
| 499. C22×#121 | C2×D4 | semidirect |
| 502. C22×#120 | C2×D4 | semidirect |
| 503. C22×#120 | C2×D4 | semidirect |
| 504. C22×#120 | C2×D4 | semidirect |
| 508. C2×#518 | C2×D4 | semidirect |
| 512. C22×C4×D4 | C2×D4 | semidirect |
| 513. C23×C42 | C2×D4 | semidirect |
| 514. #2853 | C2×D4 | semidirect |
| 515. #2853 | C2×D4 | semidirect |
| 517. #2849 | C2×D4 | semidirect |
| 518. #2847 | C2×D4 | semidirect |
| 520. #2846 | C2×D4 | semidirect |
| 521. #2846 | C2×D4 | semidirect |
| 525. #2622 | C2×D4 | semidirect |
| 526. #2617 | C2×D4 | semidirect |
| 527. #2613 | C2×D4 | semidirect |
| 528. #2613 | C2×D4 | semidirect |
| 529. #2591 | C2×D4 | semidirect |
| 530. #2579 | C2×D4 | semidirect |
| 531. #2433 | C2×D4 | semidirect |
| 532. #2411 | C2×D4 | semidirect |
| 535. #2410 | C2×D4 | semidirect |
| 536. #2410 | C2×D4 | semidirect |
| 537. #2410 | C2×D4 | semidirect |
| 538. #2410 | C2×D4 | semidirect |
| 539. #2410 | C2×D4 | semidirect |
| 540. #2408 | C2×D4 | semidirect |
| 541. #2405 | C2×D4 | semidirect |
| 542. #2405 | C2×D4 | semidirect |
| 551. #2404 | C2×D4 | semidirect |
| 552. #2403 | C2×D4 | semidirect |
| 553. #2403 | C2×D4 | semidirect |
| 554. #2403 | C2×D4 | semidirect |
| 555. #2403 | C2×D4 | semidirect |
| 556. #2403 | C2×D4 | semidirect |
| 584. #2342 | C2×D4 | semidirect |
| 585. D4×C22⋊C4 | C2×D4 | semidirect |
| 586. #2321 | C2×D4 | semidirect |
| 589. #2309 | C2×D4 | semidirect |
| 590. #2309 | C2×D4 | semidirect |
| 605. #2308 | C2×D4 | semidirect |
| 606. #2308 | C2×D4 | semidirect |
| 613. C4×#120 | C2×D4 | semidirect |
| 614. #2297 | C2×D4 | semidirect |
| 615. #2297 | C2×D4 | semidirect |
| 616. #2297 | C2×D4 | semidirect |
| 617. #2296 | C2×D4 | semidirect |
| 618. #2296 | C2×D4 | semidirect |
| 619. C2×#386 | C2×D4 | semidirect |
| 620. #2280 | C2×D4 | semidirect |
| 621. C2×#379 | C2×D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.