Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1435 conjugacy classes of subgroups; only the 239 normal subgroups are shown.
This group has 1435 conjugacy classes of subgroups — too many to draw. Only its 239 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D8 | C2 | semidirect |
| 2. C22×#121 | C2 | semidirect |
| 3. C22×#102 | C2 | semidirect |
| 4. C22×C22⋊C8 | C2 | semidirect |
| 5. #1999 | C2 | direct (N × H) |
| 6. C2×#340 | C2 | semidirect |
| 12. C22×D8 | C22 | semidirect |
| 18. C2×#121 | C22 | semidirect |
| 22. C2×#102 | C22 | semidirect |
| 24. C2×C22⋊C8 | C22 | semidirect |
| 25. #340 | C22 | semidirect |
| 38. C22×D4 | D4 | semidirect |
| 55. C22×C8 | D4 | semidirect |
| 63. C2×C4⋊C4 | D4 | semidirect |
| 81. C24 | D8 | semidirect |
| 100. C2×D4 | C2×D4 | semidirect |
| 129. C2×C8 | C2×D4 | semidirect |
| 132. C4⋊C4 | C2×D4 | semidirect |
| 160. C23 | C2×D8 | semidirect |
| 224. C2 | #1999 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D8 | 2 |
| C22×#121 | 2 |
| C22×#102 | 2 |
| C22×C22⋊C8 | 2 |
| #1999 | 2 |
| C2×#340 | 2 |