Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1257 conjugacy classes of subgroups; only the 263 normal subgroups are shown.
This group has 1257 conjugacy classes of subgroups — too many to draw. Only its 263 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D4 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| socle | C23 | C2×C22⋊C4 |
| prime radical | C2×#525 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×C42 | C2 | semidirect |
| 3. C22×#104 | C2 | semidirect |
| 4. C2×#407 | C2 | semidirect |
| 5. #1896 | C2 | direct (N × H) |
| 6. C2×#339 | C2 | semidirect |
| 13. #525 | C4 | semidirect |
| 16. C2×C22⋊Q8 | C4 | semidirect |
| 17. C2×#121 | C4 | semidirect |
| 25. C22×C42 | C22 | semidirect |
| 27. C2×#104 | C22 | semidirect |
| 29. #407 | C22 | semidirect |
| 31. #339 | C22 | semidirect |
| 37. C2×#41 | C2×C4 | semidirect |
| 39. C22×Q8 | C2×C4 | semidirect |
| 42. C22×D4 | C2×C4 | semidirect |
| 66. C22⋊Q8 | C2×C4 | semidirect |
| 68. #121 | C2×C4 | semidirect |
| 75. #117 | C2×C4 | semidirect |
| 78. C2×C4⋊C4 | C2×C4 | semidirect |
| 89. C2×C42 | D4 | semidirect |
| 109. C2×Q8 | C22×C4 | semidirect |
| 118. C2×D4 | C22×C4 | semidirect |
| 162. C4⋊C4 | C22×C4 | semidirect |
| 172. C42 | C2×D4 | semidirect |
| 186. C23 | #104 | semidirect |
| 249. C22 | C2×#104 | semidirect |
| 266. C2 | #1896 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#525 | 2 |
| C23×C42 | 2 |
| C22×#104 | 2 |
| C2×#407 | 2 |
| #1896 | 2 |
| C2×#339 | 2 |