Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
411 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 411 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #152892 |
| commutator | C2×C32 | C22×C4 |
| Frattini, cosocle | C22×C32 | C23 |
| prime radical | #513054 | C2 |
| LCS | G ▷ C2×C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #405 ◁ #2108 ◁ #13549 ◁ G | |
| LECS | G ▷ C22×C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#7541 | C2 | semidirect |
| 3. #153562 | C2 | semidirect |
| 4. #153560 | C2 | semidirect |
| 5. #153557 | C2 | semidirect |
| 6. #153425 | C2 | semidirect |
| 7. #152409 | C2 | semidirect |
| 15. #13728 | C4 | semidirect |
| 16. #13725 | C4 | semidirect |
| 61. M128 | D4 | semidirect |
| 63. C2×C64 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #513054 | 2 |
| C2×#7541 | 2 |
| #153562 | 2 |
| #153560 | 2 |
| #153557 | 2 |
| #153425 | 2 |
| #152409 | 2 |