Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
491 conjugacy classes of subgroups; only the 247 normal subgroups are shown.
This group has 491 conjugacy classes of subgroups — too many to draw. Only its 247 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C22×D4 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| prime radical | C24 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C2×#117 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #1944 | C2 | semidirect |
| 6. #1942 | C2 | semidirect |
| 13. #427 | C4 | semidirect |
| 56. #107 | C2×C4 | semidirect |
| 57. #106 | C2×C4 | semidirect |
| 79. C2×C8 | C4⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#427 | 2 |
| C22×#107 | 2 |
| C2×#405 | 2 |
| #2317 | 2 |
| #1944 | 2 |
| #1942 | 2 |
| #1736 | 2 |