Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
At least 6725 conjugacy classes of subgroups; only the 3100 normal subgroups are shown.
The subgroup lattice has 995 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 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C26 ◁ G | |
| LECS | G ▷ C25 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72337181 | C2 | semidirect |
| 2. #72337178 | C2 | semidirect |
| 3. #72337176 | C2 | semidirect |
| 4. #72337173 | C2 | semidirect |
| 5. #72337171 | C2 | semidirect |
| 6. #72335102 | C2 | semidirect |
| 7. #72334904 | C2 | semidirect |
| 8. #72334903 | C2 | semidirect |
| 9. #72319334 | C2 | semidirect |
| 10. #72318802 | C2 | semidirect |
| 11. #72318453 | C2 | semidirect |
| 12. #72309339 | C2 | semidirect |
| 13. #72266816 | C2 | semidirect |
| 14. #72266798 | C2 | semidirect |
| 15. #72240433 | C2 | semidirect |
| 16. #72237912 | C2 | semidirect |
| 17. #72227421 | C2 | semidirect |
| 18. #72225733 | C2 | semidirect |
| 19. #72225716 | C2 | semidirect |
| 20. #72225715 | C2 | semidirect |
| 21. #72225695 | C2 | semidirect |
| 22. #72225672 | C2 | semidirect |
| 23. #72225658 | C2 | semidirect |
| 24. #72225632 | C2 | semidirect |
| 25. #72217643 | C2 | semidirect |
| 26. #72217617 | C2 | semidirect |
| 27. C2×#449475 | C2 | semidirect |
| 34. #6628892 | C22 | semidirect |
| 35. #6451874 | C22 | semidirect |
| 36. C2×#23984 | C22 | semidirect |
| 37. C2×#23984 | C22 | semidirect |
| 38. C2×#23984 | C22 | semidirect |
| 39. C2×#23996 | C22 | semidirect |
| 40. C2×#23996 | C22 | semidirect |
| 41. #6379246 | C22 | semidirect |
| 42. #6370693 | C22 | semidirect |
| 43. #6342371 | C22 | semidirect |
| 44. C2×#14679 | C22 | semidirect |
| 45. #479829 | C22 | semidirect |
| 46. #479829 | C22 | semidirect |
| 47. #479829 | C22 | semidirect |
| 48. #479756 | C22 | semidirect |
| 49. #479756 | C22 | semidirect |
| 50. #479756 | C22 | semidirect |
| 51. #479673 | C22 | semidirect |
| 52. #479673 | C22 | semidirect |
| 53. #479673 | C22 | semidirect |
| 54. #479578 | C22 | semidirect |
| 55. #478457 | C22 | semidirect |
| 56. #478457 | C22 | semidirect |
| 57. #478457 | C22 | semidirect |
| 58. #478457 | C22 | semidirect |
| 59. #478249 | C22 | semidirect |
| 60. #478249 | C22 | semidirect |
| 61. #478249 | C22 | semidirect |
| 62. #470999 | C22 | semidirect |
| 63. #470999 | C22 | semidirect |
| 64. #470999 | C22 | semidirect |
| 65. #470996 | C22 | semidirect |
| 66. #470996 | C22 | semidirect |
| 67. #470996 | C22 | semidirect |
| 68. #470591 | C22 | semidirect |
| 69. #470591 | C22 | semidirect |
| 70. #470584 | C22 | semidirect |
| 71. #470584 | C22 | semidirect |
| 72. #469683 | C22 | semidirect |
| 73. #469683 | C22 | semidirect |
| 74. #469683 | C22 | semidirect |
| 75. #469678 | C22 | semidirect |
| 76. #467129 | C22 | semidirect |
| 77. #461181 | C22 | semidirect |
| 78. #461181 | C22 | semidirect |
| 79. #461179 | C22 | semidirect |
| 80. #461179 | C22 | semidirect |
| 81. #460131 | C22 | semidirect |
| 82. #460131 | C22 | semidirect |
| 83. #460131 | C22 | semidirect |
| 84. #460096 | C22 | semidirect |
| 85. #454968 | C22 | semidirect |
| 86. #451035 | C22 | semidirect |
| 87. #451024 | C22 | semidirect |
| 88. #449883 | C22 | semidirect |
| 89. #449578 | C22 | semidirect |
| 90. #449578 | C22 | semidirect |
| 91. #449521 | C22 | semidirect |
| 92. #449521 | C22 | semidirect |
| 102. #440784 | C22 | semidirect |
| 103. #440777 | C22 | semidirect |
| 104. #437718 | C22 | semidirect |
| 105. #437718 | C22 | semidirect |
| 106. #437714 | C22 | semidirect |
| 107. #437714 | C22 | semidirect |
| 108. #434716 | C22 | semidirect |
| 109. #432900 | C22 | semidirect |
| 110. #432900 | C22 | semidirect |
| 111. #432891 | C22 | semidirect |
| 112. #432891 | C22 | semidirect |
| 113. #427387 | C22 | semidirect |
| 114. #427387 | C22 | semidirect |
| 115. #427379 | C22 | semidirect |
| 116. #427374 | C22 | semidirect |
| 117. #427260 | C22 | semidirect |
| 118. #427239 | C22 | semidirect |
| 119. #419823 | C22 | semidirect |
| 120. #419812 | C22 | semidirect |
| 121. #417969 | C22 | semidirect |
| 122. #417969 | C22 | semidirect |
| 123. #417896 | C22 | semidirect |
| 124. #417896 | C22 | semidirect |
| 125. #417896 | C22 | semidirect |
| 126. #417890 | C22 | semidirect |
| 127. #417890 | C22 | semidirect |
| 128. #417890 | C22 | semidirect |
| 129. #417890 | C22 | semidirect |
| 130. #417890 | C22 | semidirect |
| 131. #417824 | C22 | semidirect |
| 132. #417824 | C22 | semidirect |
| 133. #417824 | C22 | semidirect |
| 134. #417744 | C22 | semidirect |
| 135. #417744 | C22 | semidirect |
| 136. #417744 | C22 | semidirect |
| 137. #417542 | C22 | semidirect |
| 138. #417542 | C22 | semidirect |
| 139. #417538 | C22 | semidirect |
| 140. #417538 | C22 | semidirect |
| 141. #417532 | C22 | semidirect |
| 142. #417532 | C22 | semidirect |
| 143. #417532 | C22 | semidirect |
| 144. #417493 | C22 | semidirect |
| 145. #417493 | C22 | semidirect |
| 146. #417493 | C22 | semidirect |
| 147. #417493 | C22 | semidirect |
| 148. #417493 | C22 | semidirect |
| 149. #417493 | C22 | semidirect |
| 150. #417493 | C22 | semidirect |
| 151. #406727 | C22 | semidirect |
| 152. #405606 | C22 | semidirect |
| 153. #405481 | C22 | semidirect |
| 154. #405274 | C22 | semidirect |
| 155. #405274 | C22 | semidirect |
| 156. #405156 | C22 | semidirect |
| 157. #405156 | C22 | semidirect |
| 158. #404015 | C22 | semidirect |
| 159. #403032 | C22 | semidirect |
| 160. C22⋊#2104 | C22 | semidirect |
| 161. C22⋊#2104 | C22 | semidirect |
| 162. #398102 | C22 | semidirect |
| 163. #394470 | C22 | semidirect |
| 164. #394470 | C22 | semidirect |
| 165. #394412 | C22 | semidirect |
| 166. #394412 | C22 | semidirect |
| 167. #394273 | C22 | semidirect |
| 168. #394273 | C22 | semidirect |
| 169. #394167 | C22 | semidirect |
| 170. #394167 | C22 | semidirect |
| 174. #391798 | C22 | semidirect |
| 175. #391709 | C22 | semidirect |
| 176. #391709 | C22 | semidirect |
| 177. #391692 | C22 | semidirect |
| 178. #391692 | C22 | semidirect |
| 179. #387715 | C22 | semidirect |
| 180. #387715 | C22 | semidirect |
| 181. #386017 | C22 | semidirect |
| 182. #386017 | C22 | semidirect |
| 183. #384256 | C22 | semidirect |
| 184. #384249 | C22 | semidirect |
| 185. #382707 | C22 | semidirect |
| 186. #382686 | C22 | semidirect |
| 190. #381249 | C22 | semidirect |
| 191. #380554 | C22 | semidirect |
| 192. #379806 | C22 | semidirect |
| 193. #379806 | C22 | semidirect |
| 194. #379806 | C22 | semidirect |
| 195. #379806 | C22 | semidirect |
| 196. #379733 | C22 | semidirect |
| 197. #379723 | C22 | semidirect |
| 198. #379723 | C22 | semidirect |
| 199. #379723 | C22 | semidirect |
| 200. #379723 | C22 | semidirect |
| 201. #379723 | C22 | semidirect |
| 202. #376180 | C22 | semidirect |
| 203. #375194 | C22 | semidirect |
| 204. #374058 | C22 | semidirect |
| 205. #374022 | C22 | semidirect |
| 206. #374022 | C22 | semidirect |
| 207. #374022 | C22 | semidirect |
| 208. #374004 | C22 | semidirect |
| 209. #374004 | C22 | semidirect |
| 210. #364532 | C22 | semidirect |
| 211. #364532 | C22 | semidirect |
| 212. #364440 | C22 | semidirect |
| 213. #364440 | C22 | semidirect |
| 214. #364410 | C22 | semidirect |
| 215. #364410 | C22 | semidirect |
| 216. #364410 | C22 | semidirect |
| 217. #364410 | C22 | semidirect |
| 218. #364054 | C22 | semidirect |
| 219. #363953 | C22 | semidirect |
| 220. #361312 | C22 | semidirect |
| 221. #359892 | C22 | semidirect |
| 222. #359811 | C22 | semidirect |
| 223. #359799 | C22 | semidirect |
| 224. #359799 | C22 | semidirect |
| 225. #359756 | C22 | semidirect |
| 226. #359705 | C22 | semidirect |
| 243. C2×#3026 | C23 | semidirect |
| 244. C2×#3026 | C23 | semidirect |
| 245. C2×#3026 | C23 | semidirect |
| 252. C2×#2883 | C23 | semidirect |
| 253. C2×#2883 | C23 | semidirect |
| 254. C2×#2883 | C23 | semidirect |
| 271. C2×#2846 | C23 | semidirect |
| 272. C2×#2846 | C23 | semidirect |
| 273. C2×#2846 | C23 | semidirect |
| 306. C22×#379 | C23 | semidirect |
| 307. C22×#379 | C23 | semidirect |
| 308. C22×#379 | C23 | semidirect |
| 309. C2×#2104 | C23 | semidirect |
| 310. C2×#2104 | C23 | semidirect |
| 311. C2×#2032 | C23 | semidirect |
| 312. C2×#2032 | C23 | semidirect |
| 313. C2×#2032 | C23 | semidirect |
| 314. C2×#2032 | C23 | semidirect |
| 315. C2×#2032 | C23 | semidirect |
| 316. #23468 | C23 | semidirect |
| 317. #23468 | C23 | semidirect |
| 318. C2×#2029 | C23 | semidirect |
| 319. C2×#2029 | C23 | semidirect |
| 320. C2×#2029 | C23 | semidirect |
| 321. C2×#2029 | C23 | semidirect |
| 322. C2×#2029 | C23 | semidirect |
| 323. C2×#2029 | C23 | semidirect |
| 324. #23444 | C23 | semidirect |
| 325. #23444 | C23 | semidirect |
| 338. C2×#2021 | C23 | semidirect |
| 339. C2×#2021 | C23 | semidirect |
| 340. #21333 | C23 | semidirect |
| 341. C2×#1913 | C23 | semidirect |
| 342. C2×#1913 | C23 | semidirect |
| 343. C2×#1913 | C23 | semidirect |
| 344. C2×#1913 | C23 | semidirect |
| 345. C2×#1913 | C23 | semidirect |
| 346. C2×#1913 | C23 | semidirect |
| 347. #20984 | C23 | semidirect |
| 359. C2×#1898 | C23 | semidirect |
| 360. C2×#1898 | C23 | semidirect |
| 361. #20960 | C23 | semidirect |
| 362. #20960 | C23 | semidirect |
| 371. C2×#1889 | C23 | semidirect |
| 372. C2×#1889 | C23 | semidirect |
| 373. C2×#1889 | C23 | semidirect |
| 374. C2×#1889 | C23 | semidirect |
| 375. C2×#1889 | C23 | semidirect |
| 376. C2×#1889 | C23 | semidirect |
| 377. C2×#1828 | C23 | semidirect |
| 378. C2×#1828 | C23 | semidirect |
| 379. C2×#1828 | C23 | semidirect |
| 380. #20689 | C23 | semidirect |
| 384. C2×#1819 | C23 | semidirect |
| 385. C2×#1819 | C23 | semidirect |
| 386. #20633 | C23 | semidirect |
| 387. #20609 | C23 | semidirect |
| 388. #20609 | C23 | semidirect |
| 389. #20609 | C23 | semidirect |
| 390. #20585 | C23 | semidirect |
| 391. #20585 | C23 | semidirect |
| 392. #20585 | C23 | semidirect |
| 398. #20392 | C23 | semidirect |
| 399. #20354 | C23 | semidirect |
| 407. #14679 | C23 | semidirect |
| 408. #14679 | C23 | semidirect |
| 409. #14679 | C23 | semidirect |
| 410. #14679 | C23 | semidirect |
| 411. #14679 | C23 | semidirect |
| 412. #14679 | C23 | semidirect |
| 413. #11394 | C23 | semidirect |
| 414. #11394 | C23 | semidirect |
| 415. #11394 | C23 | semidirect |
| 416. #11351 | C23 | semidirect |
| 417. #11351 | C23 | semidirect |
| 418. #11351 | C23 | semidirect |
| 419. #11351 | C23 | semidirect |
| 420. #11351 | C23 | semidirect |
| 421. #11351 | C23 | semidirect |
| 422. #11318 | C23 | semidirect |
| 423. #11318 | C23 | semidirect |
| 424. #11318 | C23 | semidirect |
| 425. #11318 | C23 | semidirect |
| 426. #11318 | C23 | semidirect |
| 427. #11318 | C23 | semidirect |
| 428. #11318 | C23 | semidirect |
| 429. #11318 | C23 | semidirect |
| 430. #11318 | C23 | semidirect |
| 431. #11318 | C23 | semidirect |
| 432. #11318 | C23 | semidirect |
| 433. #11318 | C23 | semidirect |
| 434. #11318 | C23 | semidirect |
| 435. #11318 | C23 | semidirect |
| 436. #11279 | C23 | semidirect |
| 437. #11279 | C23 | semidirect |
| 438. #11279 | C23 | semidirect |
| 439. #11279 | C23 | semidirect |
| 440. #11279 | C23 | semidirect |
| 441. #11279 | C23 | semidirect |
| 442. #11279 | C23 | semidirect |
| 443. #11279 | C23 | semidirect |
| 444. #11279 | C23 | semidirect |
| 445. #11196 | C23 | semidirect |
| 446. #11196 | C23 | semidirect |
| 447. #11196 | C23 | semidirect |
| 448. #11196 | C23 | semidirect |
| 449. #11196 | C23 | semidirect |
| 450. #11196 | C23 | semidirect |
| 451. #11196 | C23 | semidirect |
| 452. #11196 | C23 | semidirect |
| 453. #11196 | C23 | semidirect |
| 454. #11196 | C23 | semidirect |
| 455. #11196 | C23 | semidirect |
| 456. #11196 | C23 | semidirect |
| 457. #11196 | C23 | semidirect |
| 458. #11196 | C23 | semidirect |
| 459. #11196 | C23 | semidirect |
| 460. #11196 | C23 | semidirect |
| 461. #11196 | C23 | semidirect |
| 462. #11196 | C23 | semidirect |
| 463. #11196 | C23 | semidirect |
| 464. #11172 | C23 | semidirect |
| 465. #11172 | C23 | semidirect |
| 466. #11172 | C23 | semidirect |
| 467. #11172 | C23 | semidirect |
| 468. #11172 | C23 | semidirect |
| 469. #11172 | C23 | semidirect |
| 470. #11172 | C23 | semidirect |
| 471. #11172 | C23 | semidirect |
| 472. #11172 | C23 | semidirect |
| 473. #11169 | C23 | semidirect |
| 474. #11169 | C23 | semidirect |
| 475. #11169 | C23 | semidirect |
| 476. #11169 | C23 | semidirect |
| 477. #11169 | C23 | semidirect |
| 478. #11166 | C23 | semidirect |
| 479. #11166 | C23 | semidirect |
| 480. #11166 | C23 | semidirect |
| 481. #11166 | C23 | semidirect |
| 482. #11166 | C23 | semidirect |
| 483. #11166 | C23 | semidirect |
| 484. #11166 | C23 | semidirect |
| 485. #11089 | C23 | semidirect |
| 486. #11089 | C23 | semidirect |
| 487. #11089 | C23 | semidirect |
| 488. #11089 | C23 | semidirect |
| 489. #11089 | C23 | semidirect |
| 490. #11089 | C23 | semidirect |
| 491. #11089 | C23 | semidirect |
| 492. #11089 | C23 | semidirect |
| 493. #11089 | C23 | semidirect |
| 494. #11089 | C23 | semidirect |
| 495. #11089 | C23 | semidirect |
| 496. #11089 | C23 | semidirect |
| 497. #11089 | C23 | semidirect |
| 498. #11089 | C23 | semidirect |
| 499. #11089 | C23 | semidirect |
| 500. #11069 | C23 | semidirect |
| 501. #11069 | C23 | semidirect |
| 502. #11069 | C23 | semidirect |
| 503. #11069 | C23 | semidirect |
| 504. #11069 | C23 | semidirect |
| 505. #11069 | C23 | semidirect |
| 506. #11069 | C23 | semidirect |
| 507. #11069 | C23 | semidirect |
| 508. #11069 | C23 | semidirect |
| 509. #11069 | C23 | semidirect |
| 510. #11069 | C23 | semidirect |
| 511. #11069 | C23 | semidirect |
| 512. #11069 | C23 | semidirect |
| 513. #11069 | C23 | semidirect |
| 514. #11069 | C23 | semidirect |
| 515. #11069 | C23 | semidirect |
| 516. #11069 | C23 | semidirect |
| 517. #11069 | C23 | semidirect |
| 518. #11046 | C23 | semidirect |
| 519. #11046 | C23 | semidirect |
| 520. #11046 | C23 | semidirect |
| 521. #11046 | C23 | semidirect |
| 522. #11046 | C23 | semidirect |
| 523. #11046 | C23 | semidirect |
| 558. #10991 | C23 | semidirect |
| 559. #10991 | C23 | semidirect |
| 560. #10991 | C23 | semidirect |
| 561. #10991 | C23 | semidirect |
| 562. #10972 | C23 | semidirect |
| 563. #10972 | C23 | semidirect |
| 564. #10972 | C23 | semidirect |
| 565. #10972 | C23 | semidirect |
| 566. #10972 | C23 | semidirect |
| 567. #10972 | C23 | semidirect |
| 568. #10972 | C23 | semidirect |
| 569. #10972 | C23 | semidirect |
| 570. #10972 | C23 | semidirect |
| 605. #10965 | C23 | semidirect |
| 606. #10965 | C23 | semidirect |
| 607. #10965 | C23 | semidirect |
| 608. #10965 | C23 | semidirect |
| 609. #10965 | C23 | semidirect |
| 610. #10938 | C23 | semidirect |
| 611. #10938 | C23 | semidirect |
| 612. #10938 | C23 | semidirect |
| 613. #10938 | C23 | semidirect |
| 614. #10938 | C23 | semidirect |
| 615. #10938 | C23 | semidirect |
| 616. #10938 | C23 | semidirect |
| 617. #10938 | C23 | semidirect |
| 618. #10935 | C23 | semidirect |
| 619. #10935 | C23 | semidirect |
| 620. #10935 | C23 | semidirect |
| 621. #10935 | C23 | semidirect |
| 622. #10935 | C23 | semidirect |
| 623. #10935 | C23 | semidirect |
| 624. #10935 | C23 | semidirect |
| 625. #10935 | C23 | semidirect |
| 626. #10829 | C23 | semidirect |
| 627. #10829 | C23 | semidirect |
| 628. #10829 | C23 | semidirect |
| 629. #10829 | C23 | semidirect |
| 630. #10768 | C23 | semidirect |
| 631. #10768 | C23 | semidirect |
| 632. #10768 | C23 | semidirect |
| 633. #10754 | C23 | semidirect |
| 634. #10754 | C23 | semidirect |
| 635. #10754 | C23 | semidirect |
| 636. #10754 | C23 | semidirect |
| 637. #10754 | C23 | semidirect |
| 638. #10754 | C23 | semidirect |
| 646. #10735 | C23 | semidirect |
| 647. #10735 | C23 | semidirect |
| 648. #10735 | C23 | semidirect |
| 649. #10735 | C23 | semidirect |
| 650. #10735 | C23 | semidirect |
| 651. #10735 | C23 | semidirect |
| 656. #10725 | C23 | semidirect |
| 657. #10725 | C23 | semidirect |
| 666. C24×D4 | #41 | semidirect |
| 676. C22×#120 | #41 | semidirect |
| 677. C22×#120 | #41 | semidirect |
| 703. C23×C22⋊C4 | #41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.