Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
447 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 447 conjugacy classes of subgroups — too many to draw. Only its 175 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 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #1928 | C2 | semidirect |
| 4. #1921 | C2 | semidirect |
| 6. #1878 | C2 | semidirect |
| 7. #1863 | C2 | semidirect |
| 16. #467 | C4 | semidirect |
| 42. C2×Q16 | C2×C4 | semidirect |
| 72. #107 | C2×C4 | semidirect |
| 75. #103 | C2×C4 | semidirect |
| 101. C22×C4 | Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#467 | 2 |
| C4×C22⋊Q8 | 2 |
| #1928 | 2 |
| #1921 | 2 |
| #1892 | 2 |
| #1878 | 2 |
| #1863 | 2 |
| #1808 | 2 |
| C2×#336 | 2 |