Finite Group DatabasebetaFinite Group DatabasebetaOrder 24576.
37512988 conjugacy classes of subgroups.
The subgroup lattice has 504 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C42 | C28×C3 |
| socle, prime radical | C28×C3 | C2×C42 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C24×C3×C4×C82 | C2 | direct (N × H) |
| 4. C25×C4×C82 | C3 | direct (N × H) |
| 10. C25×C3×C82 | C4 | direct (N × H) |
| 12. C23×C3×C4×C82 | C22 | direct (N × H) |
| 15. C24×C4×C82 | C2×C3 | direct (N × H) |
| 23. C25×C3×C4×C8 | C8 | direct (N × H) |
| 28. C24×C3×C82 | C2×C4 | direct (N × H) |
| 30. C22×C3×C4×C82 | C23 | direct (N × H) |
| 36. C25×C82 | C3×C4 | direct (N × H) |
| 38. C23×C4×C82 | C22×C3 | direct (N × H) |
| 54. C24×C3×C4×C8 | C2×C8 | direct (N × H) |
| 61. C23×C3×C82 | C22×C4 | direct (N × H) |
| 63. C2×C3×C4×C82 | C24 | direct (N × H) |
| 68. C25×C4×C8 | C3×C8 | direct (N × H) |
| 76. C22×C4×C82 | C23×C3 | direct (N × H) |
| 77. C24×C82 | C2×C3×C4 | direct (N × H) |
| 86. C25×C3×C8 | C4×C8 | direct (N × H) |
| 100. C23×C3×C4×C8 | C22×C8 | direct (N × H) |
| 110. C22×C3×C82 | C23×C4 | direct (N × H) |
| 112. C3×C4×C82 | C25 | direct (N × H) |
| 125. C24×C4×C8 | C2×C3×C8 | direct (N × H) |
| 135. C23×C82 | C22×C3×C4 | direct (N × H) |
| 137. C2×C4×C82 | C24×C3 | direct (N × H) |
| 141. C25×C3×C4 | C82 | direct (N × H) |
| 151. C24×C3×C8 | C2×C4×C8 | direct (N × H) |
| 166. C22×C3×C4×C8 | C23×C8 | direct (N × H) |
| 176. C2×C3×C82 | C24×C4 | direct (N × H) |
| 185. C25×C8 | C3×C4×C8 | direct (N × H) |
| 199. C23×C4×C8 | C22×C3×C8 | direct (N × H) |
| 209. C22×C82 | C23×C3×C4 | direct (N × H) |
| 211. C4×C82 | C25×C3 | direct (N × H) |
| 217. C24×C3×C4 | C2×C82 | direct (N × H) |
| 228. C23×C3×C8 | C22×C4×C8 | direct (N × H) |
| 243. C2×C3×C4×C8 | C24×C8 | direct (N × H) |
| 251. C3×C82 | C25×C4 | direct (N × H) |
| 255. C25×C4 | C3×C82 | direct (N × H) |
| 265. C24×C8 | C2×C3×C4×C8 | direct (N × H) |
| 280. C22×C4×C8 | C23×C3×C8 | direct (N × H) |
| 290. C2×C82 | C24×C3×C4 | direct (N × H) |
| 292. C25×C3 | C4×C82 | direct (N × H) |
| 298. C23×C3×C4 | C22×C82 | direct (N × H) |
| 309. C22×C3×C8 | C23×C4×C8 | direct (N × H) |
| 324. C3×C4×C8 | C25×C8 | direct (N × H) |
| 331. C24×C4 | C2×C3×C82 | direct (N × H) |
| 342. C23×C8 | C22×C3×C4×C8 | direct (N × H) |
| 357. C2×C4×C8 | C24×C3×C8 | direct (N × H) |
| 365. C82 | C25×C3×C4 | direct (N × H) |
| 366. C24×C3 | C2×C4×C82 | direct (N × H) |
| 372. C22×C3×C4 | C23×C82 | direct (N × H) |
| 383. C2×C3×C8 | C24×C4×C8 | direct (N × H) |
| 391. C25 | C3×C4×C82 | direct (N × H) |
| 397. C23×C4 | C22×C3×C82 | direct (N × H) |
| 408. C22×C8 | C23×C3×C4×C8 | direct (N × H) |
| 423. C4×C8 | C25×C3×C8 | direct (N × H) |
| 426. C23×C3 | C22×C4×C82 | direct (N × H) |
| 431. C2×C3×C4 | C24×C82 | direct (N × H) |
| 439. C3×C8 | C25×C4×C8 | direct (N × H) |
| 440. C24 | C2×C3×C4×C82 | direct (N × H) |
| 446. C22×C4 | C23×C3×C82 | direct (N × H) |
| 457. C2×C8 | C24×C3×C4×C8 | direct (N × H) |
| 465. C22×C3 | C23×C4×C82 | direct (N × H) |
| 470. C3×C4 | C25×C82 | direct (N × H) |
| 473. C23 | C22×C3×C4×C82 | direct (N × H) |
| 479. C2×C4 | C24×C3×C82 | direct (N × H) |
| 487. C8 | C25×C3×C4×C8 | direct (N × H) |
| 488. C2×C3 | C24×C4×C82 | direct (N × H) |
| 491. C22 | C23×C3×C4×C82 | direct (N × H) |
| 496. C4 | C25×C3×C82 | direct (N × H) |
| 499. C3 | C25×C4×C82 | direct (N × H) |
| 500. C2 | C24×C3×C4×C82 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×C3×C42×C8 | 2 |
| C26×C3×C82 | 2 |
| C24×C3×C4×C82 | 2 |
| C25×C4×C82 | 3 |