Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
639 conjugacy classes of subgroups; only the 263 normal subgroups are shown.
This group has 639 conjugacy classes of subgroups — too many to draw. Only its 263 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 | C22 | C23×C8 |
| Frattini, cosocle | C22×C4 | C24 |
| prime radical | C22×#41 | C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C4×D4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2972 | C2 | semidirect |
| 3. #1461 | C2 | semidirect |
| 4. #1459 | C2 | semidirect |
| 5. #1458 | C2 | semidirect |
| 6. C2×#324 | C2 | semidirect |
| 27. C2×#41 | C8 | semidirect |
| 71. C2×Q8 | C2×C8 | semidirect |
| 76. C2×D4 | C2×C8 | semidirect |
| 87. C22×C4 | C2×C8 | semidirect |
| 88. C22×C4 | C2×C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#520 | 2 |
| #2972 | 2 |
| #1461 | 2 |
| #1459 | 2 |
| #1458 | 2 |
| C2×#324 | 2 |