Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
423 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 423 conjugacy classes of subgroups — too many to draw. Only its 199 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 | D42 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| prime radical | C2×#135 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #2912 | C2 | semidirect |
| 4. #1952 | C2 | semidirect |
| 5. #1860 | C2 | semidirect |
| 6. #1846 | C2 | semidirect |
| 7. #1815 | C2 | semidirect |
| 8. #1772 | C2 | semidirect |
| 12. #443 | C4 | semidirect |
| 39. #131 | C2×C4 | semidirect |
| 55. #108 | C2×C4 | semidirect |
| 65. #104 | C2×C4 | semidirect |
| 70. C4×C8 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#443 | 2 |
| #2951 | 2 |
| #2912 | 2 |
| #1952 | 2 |
| #1860 | 2 |
| #1846 | 2 |
| #1815 | 2 |
| #1772 | 2 |