Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
166 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #1842 | C2 | 1 | 3 | yes | maximal |
| 2 | C2×C4⋊C8 | — | 2 | 6 | no | — |
| 3 | C2×C4⋊C8 | C4 | 1 | 6 | yes | — |
| 4 | C43 | C22 | 1 | 1 | yes | characteristic |
| 5 | C22×C8 | — | 2 | 6 | no | — |
| 6 | C2×C42 | C2×C4 | 1 | 3 | yes | — |
| 7 | C2×C42 | D4 | 1 | 3 | yes | — |
| 8 | C2×C42 | Q8 | 1 | 1 | yes | characteristic |
| 9 | C4⋊C8 | — | 4 | 6 | no | — |
| 10 | C4⋊C8 | — | 4 | 6 | no | — |
| 11 | C4⋊C8 | — | 4 | 6 | no | — |
| 12 | C22×C4 | C42 | 1 | 1 | yes | characteristic |
| 13 | C22×C4 | C22⋊C4 | 1 | 3 | yes | — |
| 14 | C22×C4 | C4⋊C4 | 1 | 3 | yes | — |
| 15 | C2×C8 | — | 4 | 6 | no | — |
| 16 | C2×C8 | — | 4 | 12 | no | — |
| 17 | C42 | — | 2 | 3 | no | — |
| 18 | C42 | — | 2 | 3 | no | — |
| 19 | C42 | — | 4 | 1 | no | — |
| 20 | C42 | D8 | 1 | 3 | yes | — |
| 21 | C42 | SD16 | 1 | 6 | yes | — |
| 22 | C42 | Q16 | 1 | 3 | yes | — |
| 23 | C23 | #95 | 1 | 1 | yes | characteristic |
| 24 | C2×C4 | — | 2 | 3 | no | — |
| 25 | C2×C4 | — | 2 | 3 | no | — |
| 26 | C2×C4 | — | 2 | 3 | no | — |
| 27 | C2×C4 | #100 | 1 | 3 | yes | — |
| 28 | C2×C4 | #101 | 1 | 3 | yes | — |
| 29 | C2×C4 | #102 | 1 | 6 | yes | — |
| 30 | C2×C4 | #103 | 1 | 6 | yes | — |
| 31 | C2×C4 | #106 | 1 | 3 | yes | — |
| 32 | C2×C4 | #107 | 1 | 3 | yes | — |
| 33 | C8 | — | 8 | 6 | no | — |
| 34 | C22 | #338 | 1 | 1 | yes | characteristic |
| 35 | C22 | #340 | 1 | 3 | yes | — |
| 36 | C22 | #343 | 1 | 3 | yes | — |
| 37 | C4 | — | 2 | 3 | no | — |
| 38 | C4 | — | 2 | 3 | no | — |
| 39 | C4 | — | 4 | 1 | no | — |
| 40 | C4 | #331 | 1 | 3 | yes | — |
| 41 | C4 | #332 | 1 | 6 | yes | — |
| 42 | C4 | #333 | 1 | 3 | yes | — |
| 43 | C2 | #1292 | 1 | 3 | yes | — |
| 44 | C2 | #1296 | 1 | 3 | yes | — |
| 45 | C2 | #1309 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23 | #95 |
| commutator | C22×C4 | C42 |
| Frattini, cosocle | C43 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C43 ◁ G | |
| LECS | G ▷ C43 ▷ C23 ▷ C1 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #1842 | 2 |