Finite Group DatabasebetaFinite Group DatabasebetaOrder 24576.
75921180 conjugacy classes of subgroups.
The subgroup lattice has 480 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C23×C4 | C28×C3 |
| socle, prime radical | C28×C3 | C23×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×C3×C43×C8 | C2 | direct (N × H) |
| 4. C24×C43×C8 | C3 | direct (N × H) |
| 10. C24×C3×C42×C8 | C4 | direct (N × H) |
| 12. C22×C3×C43×C8 | C22 | direct (N × H) |
| 15. C23×C43×C8 | C2×C3 | direct (N × H) |
| 16. C24×C3×C43 | C8 | direct (N × H) |
| 26. C23×C3×C42×C8 | C2×C4 | direct (N × H) |
| 30. C2×C3×C43×C8 | C23 | direct (N × H) |
| 36. C24×C42×C8 | C3×C4 | direct (N × H) |
| 38. C22×C43×C8 | C22×C3 | direct (N × H) |
| 48. C23×C3×C43 | C2×C8 | direct (N × H) |
| 57. C24×C3×C4×C8 | C42 | direct (N × H) |
| 60. C22×C3×C42×C8 | C22×C4 | direct (N × H) |
| 62. C3×C43×C8 | C24 | direct (N × H) |
| 65. C24×C43 | C3×C8 | direct (N × H) |
| 75. C23×C42×C8 | C2×C3×C4 | direct (N × H) |
| 77. C2×C43×C8 | C23×C3 | direct (N × H) |
| 88. C24×C3×C42 | C4×C8 | direct (N × H) |
| 97. C23×C3×C4×C8 | C2×C42 | direct (N × H) |
| 101. C22×C3×C43 | C22×C8 | direct (N × H) |
| 106. C2×C3×C42×C8 | C23×C4 | direct (N × H) |
| 120. C24×C4×C8 | C3×C42 | direct (N × H) |
| 124. C23×C43 | C2×C3×C8 | direct (N × H) |
| 129. C22×C42×C8 | C22×C3×C4 | direct (N × H) |
| 133. C43×C8 | C24×C3 | direct (N × H) |
| 147. C24×C3×C8 | C43 | direct (N × H) |
| 152. C23×C3×C42 | C2×C4×C8 | direct (N × H) |
| 161. C22×C3×C4×C8 | C22×C42 | direct (N × H) |
| 165. C2×C3×C43 | C23×C8 | direct (N × H) |
| 170. C3×C42×C8 | C24×C4 | direct (N × H) |
| 181. C24×C42 | C3×C4×C8 | direct (N × H) |
| 190. C23×C4×C8 | C2×C3×C42 | direct (N × H) |
| 194. C22×C43 | C22×C3×C8 | direct (N × H) |
| 199. C2×C42×C8 | C23×C3×C4 | direct (N × H) |
| 208. C24×C3×C4 | C42×C8 | direct (N × H) |
| 221. C23×C3×C8 | C2×C43 | direct (N × H) |
| 226. C22×C3×C42 | C22×C4×C8 | direct (N × H) |
| 235. C2×C3×C4×C8 | C23×C42 | direct (N × H) |
| 238. C3×C43 | C24×C8 | direct (N × H) |
| 253. C24×C8 | C3×C43 | direct (N × H) |
| 258. C23×C42 | C2×C3×C4×C8 | direct (N × H) |
| 267. C22×C4×C8 | C22×C3×C42 | direct (N × H) |
| 271. C2×C43 | C23×C3×C8 | direct (N × H) |
| 276. C42×C8 | C24×C3×C4 | direct (N × H) |
| 285. C23×C3×C4 | C2×C42×C8 | direct (N × H) |
| 298. C22×C3×C8 | C22×C43 | direct (N × H) |
| 302. C2×C3×C42 | C23×C4×C8 | direct (N × H) |
| 308. C3×C4×C8 | C24×C42 | direct (N × H) |
| 314. C24×C4 | C3×C42×C8 | direct (N × H) |
| 327. C23×C8 | C2×C3×C43 | direct (N × H) |
| 332. C22×C42 | C22×C3×C4×C8 | direct (N × H) |
| 341. C2×C4×C8 | C23×C3×C42 | direct (N × H) |
| 344. C43 | C24×C3×C8 | direct (N × H) |
| 346. C24×C3 | C43×C8 | direct (N × H) |
| 355. C22×C3×C4 | C22×C42×C8 | direct (N × H) |
| 365. C2×C3×C8 | C23×C43 | direct (N × H) |
| 368. C3×C42 | C24×C4×C8 | direct (N × H) |
| 378. C23×C4 | C2×C3×C42×C8 | direct (N × H) |
| 391. C22×C8 | C22×C3×C43 | direct (N × H) |
| 395. C2×C42 | C23×C3×C4×C8 | direct (N × H) |
| 401. C4×C8 | C24×C3×C42 | direct (N × H) |
| 402. C23×C3 | C2×C43×C8 | direct (N × H) |
| 409. C2×C3×C4 | C23×C42×C8 | direct (N × H) |
| 416. C3×C8 | C24×C43 | direct (N × H) |
| 417. C24 | C3×C43×C8 | direct (N × H) |
| 425. C22×C4 | C22×C3×C42×C8 | direct (N × H) |
| 436. C2×C8 | C23×C3×C43 | direct (N × H) |
| 438. C42 | C24×C3×C4×C8 | direct (N × H) |
| 441. C22×C3 | C22×C43×C8 | direct (N × H) |
| 446. C3×C4 | C24×C42×C8 | direct (N × H) |
| 449. C23 | C2×C3×C43×C8 | direct (N × H) |
| 457. C2×C4 | C23×C3×C42×C8 | direct (N × H) |
| 463. C8 | C24×C3×C43 | direct (N × H) |
| 464. C2×C3 | C23×C43×C8 | direct (N × H) |
| 467. C22 | C22×C3×C43×C8 | direct (N × H) |
| 472. C4 | C24×C3×C42×C8 | direct (N × H) |
| 475. C3 | C24×C43×C8 | direct (N × H) |
| 477. C2 | C23×C3×C43×C8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C3×C44 | 2 |
| C23×C3×C43×C8 | 2 |
| C25×C3×C42×C8 | 2 |
| C24×C43×C8 | 3 |