Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
2079 conjugacy classes of subgroups; only the 903 normal subgroups are shown.
This group has 2079 conjugacy classes of subgroups — too many to draw. Only its 903 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C25 | C23 |
| commutator, Frattini, cosocle | C23 | C25 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C25 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2×#398 | C2 | direct (N × H) |
| 18. #398 | C22 | direct (N × H) |
| 109. C22 | #398 | direct (N × H) |
| 125. C2 | C2×#398 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4⋊C4 | 2 |
| C2×#398 | 2 |
| C22×#95 | 2 |