Order 24576.
11036 conjugacy classes of subgroups.
The subgroup lattice has 1080 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4×C64 | C24×C3 |
| socle, prime radical | C24×C3 | C2×C4×C64 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C3×C4×C8×C128 | C2 | direct (N × H) |
| 5. C2×C4×C8×C128 | C3 | direct (N × H) |
| 17. C2×C3×C8×C128 | C4 | direct (N × H) |
| 22. C4×C8×C128 | C2×C3 | direct (N × H) |
| 45. C2×C3×C4×C128 | C8 | direct (N × H) |
| 51. C3×C8×C128 | C2×C4 | direct (N × H) |
| 61. C2×C8×C128 | C3×C4 | direct (N × H) |
| 116. C3×C4×C128 | C2×C8 | direct (N × H) |
| 141. C2×C4×C128 | C3×C8 | direct (N × H) |
| 146. C8×C128 | C2×C3×C4 | direct (N × H) |
| 206. C2×C3×C128 | C4×C8 | direct (N × H) |
| 272. C4×C128 | C2×C3×C8 | direct (N × H) |
| 369. C3×C128 | C2×C4×C8 | direct (N × H) |
| 429. C2×C128 | C3×C4×C8 | direct (N × H) |
| 471. C2×C3×C4×C8 | C128 | direct (N × H) |
| 632. C128 | C2×C3×C4×C8 | direct (N × H) |
| 690. C3×C4×C8 | C2×C128 | direct (N × H) |
| 734. C2×C4×C8 | C3×C128 | direct (N × H) |
| 818. C2×C3×C8 | C4×C128 | direct (N × H) |
| 913. C4×C8 | C2×C3×C128 | direct (N × H) |
| 937. C2×C3×C4 | C8×C128 | direct (N × H) |
| 954. C3×C8 | C2×C4×C128 | direct (N × H) |
| 976. C2×C8 | C3×C4×C128 | direct (N × H) |
| 1022. C3×C4 | C2×C8×C128 | direct (N × H) |
| 1032. C2×C4 | C3×C8×C128 | direct (N × H) |
| 1049. C8 | C2×C3×C4×C128 | direct (N × H) |
| 1057. C2×C3 | C4×C8×C128 | direct (N × H) |
| 1067. C4 | C2×C3×C8×C128 | direct (N × H) |
| 1074. C3 | C2×C4×C8×C128 | direct (N × H) |
| 1075. C2 | C3×C4×C8×C128 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×C8×C64 | 2 |
| C2×C3×C42×C128 | 2 |
| C22×C3×C8×C128 | 2 |
| C3×C4×C8×C128 | 2 |
| C2×C4×C8×C128 | 3 |