Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1261 conjugacy classes of subgroups; only the 503 normal subgroups are shown.
This group has 1261 conjugacy classes of subgroups — too many to draw. Only its 503 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C23 | C25 |
| prime radical | C2×#550 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#557 | C2 | semidirect |
| 3. #2858 | C2 | semidirect |
| 4. #2548 | C2 | semidirect |
| 5. #2547 | C2 | semidirect |
| 6. #2490 | C2 | semidirect |
| 7. #2341 | C2 | semidirect |
| 8. C4×#124 | C2 | semidirect |
| 9. C42×Q8 | C2 | semidirect |
| 117. C42 | #41 | semidirect |
| 125. Q8 | #124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#557 | 2 |
| C2×#550 | 2 |
| #2858 | 2 |
| #2548 | 2 |
| #2547 | 2 |
| #2490 | 2 |
| #2341 | 2 |
| C4×#124 | 2 |
| C42×Q8 | 2 |