Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
601 conjugacy classes of subgroups; only the 223 normal subgroups are shown.
This group has 601 conjugacy classes of subgroups — too many to draw. Only its 223 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 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| prime radical | #3497 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C4×Q8 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2982 | C2 | semidirect |
| 3. #2351 | C2 | semidirect |
| 4. #1517 | C2 | semidirect |
| 5. #1502 | C2 | semidirect |
| 7. #550 | C4 | semidirect |
| 8. D4×Q8 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3497 | 2 |
| #2982 | 2 |
| #2351 | 2 |
| #1517 | 2 |
| #1502 | 2 |