Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
284 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24 |
| prime radical | #3280 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ G | |
| LECS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3336 | C2 | semidirect |
| 3. #2242 | C2 | semidirect |
| 4. #2235 | C2 | semidirect |
| 5. #2234 | C2 | semidirect |
| 6. #2228 | C2 | semidirect |
| 7. #2217 | C2 | semidirect |
| 8. #2216 | C2 | semidirect |
| 9. #2211 | C2 | semidirect |
| 10. #2189 | C2 | semidirect |
| 11. #2187 | C2 | semidirect |
| 12. C4×SD32 | C2 | semidirect |
| 13. D4×C16 | C2 | semidirect |
| 14. #2138 | C2 | semidirect |
| 15. C2×#357 | C2 | semidirect |
| 20. C2×Q32 | C22 | semidirect |
| 24. C22×C16 | C22 | semidirect |
| 25. #499 | C22 | semidirect |
| 32. #467 | C22 | semidirect |
| 37. C4×Q16 | C22 | semidirect |
| 40. #427 | C22 | semidirect |
| 42. #367 | C22 | semidirect |
| 43. #367 | C22 | semidirect |
| 44. #366 | C22 | semidirect |
| 45. C4⋊C16 | C22 | semidirect |
| 46. #358 | C22 | semidirect |
| 47. #358 | C22 | semidirect |
| 48. #358 | C22 | semidirect |
| 49. #358 | C22 | semidirect |
| 57. C22⋊C16 | C22 | semidirect |
| 58. C4×C16 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3336 | 2 |
| #3280 | 2 |
| #2242 | 2 |
| #2235 | 2 |
| #2234 | 2 |
| #2228 | 2 |
| #2217 | 2 |
| #2216 | 2 |
| #2211 | 2 |
| #2189 | 2 |
| #2187 | 2 |
| C4×SD32 | 2 |
| D4×C16 | 2 |
| #2138 | 2 |
| C2×#357 | 2 |