Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
107417 conjugacy classes of subgroups.
The subgroup lattice has 396 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C23×D4 |
| commutator | C4 | C26×C4 |
| Frattini, cosocle | C2×C4 | C27 |
| socle | C23 | C23×C4⋊C4 |
| prime radical | C24×#41 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C24×#41 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#60113 | C2 | direct (N × H) |
| 4. C22×#2916 | C2 | semidirect |
| 5. C23×#430 | C2 | semidirect |
| 18. #60113 | C22 | direct (N × H) |
| 19. C2×#2916 | C22 | semidirect |
| 21. C22×#430 | C22 | semidirect |
| 22. C22×#430 | C22 | semidirect |
| 23. C23×#108 | C22 | semidirect |
| 61. #2916 | C23 | semidirect |
| 63. C2×#430 | C23 | semidirect |
| 64. C2×#430 | C23 | semidirect |
| 66. C22×#108 | C23 | semidirect |
| 141. #430 | C24 | semidirect |
| 143. C2×#108 | C24 | semidirect |
| 377. C22 | #60113 | direct (N × H) |
| 393. C2 | C2×#60113 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#568 | 2 |
| C2×#60113 | 2 |
| C22×#2916 | 2 |
| C23×#430 | 2 |