Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
11505 conjugacy classes of subgroups.
The subgroup lattice has 2414 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C2×C42 | C2×C22⋊C4 |
| commutator | C2×C4 | C23×C42 |
| Frattini, cosocle | C2×C42 | C25 |
| socle | C23 | C22×#95 |
| prime radical | C26 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C42 ◁ C24×C42 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #181727 | C2 | direct (N × H) |
| 5. C2×#8094 | C2 | semidirect |
| 6. C2×#8093 | C2 | semidirect |
| 7. C2×#8092 | C2 | semidirect |
| 21. C2×#2920 | C4 | semidirect |
| 22. C2×#2920 | C4 | semidirect |
| 23. C2×#2920 | C4 | semidirect |
| 24. C2×#2920 | C4 | semidirect |
| 25. C2×#2920 | C4 | semidirect |
| 26. C2×#2920 | C4 | semidirect |
| 35. C22×#432 | C4 | semidirect |
| 36. C22×#432 | C4 | semidirect |
| 39. C22×#431 | C4 | semidirect |
| 41. C22×#423 | C4 | semidirect |
| 66. #8094 | C22 | semidirect |
| 67. #8093 | C22 | semidirect |
| 68. #8092 | C22 | semidirect |
| 69. C2×#1303 | C22 | semidirect |
| 146. #2920 | C2×C4 | semidirect |
| 147. #2920 | C2×C4 | semidirect |
| 148. #2920 | C2×C4 | semidirect |
| 149. #2920 | C2×C4 | semidirect |
| 176. C2×#432 | C2×C4 | semidirect |
| 177. C2×#432 | C2×C4 | semidirect |
| 201. C2×#431 | C2×C4 | semidirect |
| 215. C2×#423 | C2×C4 | semidirect |
| 322. #1303 | C23 | semidirect |
| 2409. C2 | #181727 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#2920 | 2 |
| C2×#34012 | 2 |
| #181727 | 2 |
| C2×#8094 | 2 |
| C2×#8093 | 2 |
| C2×#8092 | 2 |