Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
186 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #1304 | C2 | 1 | 7 | yes | maximal |
| 2 | #379 | C22 | 1 | 7 | yes | — |
| 3 | C25 | C23 | 1 | 1 | yes | characteristic |
| 4 | C2×C22⋊C4 | — | 2 | 21 | no | — |
| 5 | C24 | — | 8 | 3 | no | — |
| 6 | C24 | #41 | 1 | 7 | yes | — |
| 7 | C22×C4 | — | 4 | 7 | no | — |
| 8 | C22⋊C4 | — | 8 | 21 | no | — |
| 9 | C23 | — | 4 | 21 | no | — |
| 10 | C23 | — | 8 | 8 | no | — |
| 11 | C23 | #126 | 1 | 7 | yes | — |
| 12 | C2×C4 | — | 8 | 21 | no | — |
| 13 | C22 | — | 2 | 21 | no | — |
| 14 | C22 | — | 8 | 14 | no | — |
| 15 | C22 | #401 | 1 | 1 | yes | characteristic |
| 16 | C4 | — | 16 | 7 | no | — |
| 17 | C2 | — | 4 | 7 | no | — |
| 18 | C2 | #2104 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #401 |
| commutator, Frattini, prime radical, cosocle | C25 | C23 |
| LCS | G ▷ C25 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C25 ◁ G | |
| LECS | G ▷ C25 ▷ C22 ▷ C1 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #1304 | 2 |