Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
228 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #386 |
| commutator | C2×C4 | C22×C8 |
| Frattini, cosocle | C22×C8 | C23 |
| socle | C2 | #1869 |
| prime radical | C2×#135 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ C22×C8 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3407 | C2 | semidirect |
| 3. #2117 | C2 | semidirect |
| 4. #2117 | C2 | semidirect |
| 5. #2115 | C2 | semidirect |
| 6. #1377 | C2 | semidirect |
| 7. #1375 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3407 | 2 |
| C2×#444 | 2 |
| #2117 | 2 |
| #2115 | 2 |
| #1377 | 2 |
| #1375 | 2 |