Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
760 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 153 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, Frattini, cosocle | C22×C4 | C24 |
| socle | C23 | C22×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#532 | C2 | semidirect |
| 2. C2×C4×D8 | C2 | semidirect |
| 3. C4×#121 | C2 | semidirect |
| 4. #2057 | C2 | semidirect |
| 5. #2041 | C2 | semidirect |
| 6. #2033 | C2 | semidirect |
| 7. #2023 | C2 | semidirect |
| 8. #2011 | C2 | semidirect |
| 9. #1999 | C2 | semidirect |
| 10. C4×#102 | C2 | semidirect |
| 11. C4×C22⋊C8 | C2 | semidirect |
| 77. C4×D4 | D4 | semidirect |
| 135. C2×D4 | #41 | semidirect |
| 155. C22×C4 | D8 | semidirect |
| 168. C2×C8 | #41 | semidirect |
| 176. C4⋊C4 | #41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#532 | 2 |
| C2×C4×D8 | 2 |
| C4×#121 | 2 |
| #2057 | 2 |
| #2041 | 2 |
| #2033 | 2 |
| #2023 | 2 |
| #2011 | 2 |
| #1999 | 2 |
| C4×#102 | 2 |
| C4×C22⋊C8 | 2 |