Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
463 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #1443 | C2 | 1 | 5 | yes | maximal |
| 2 | #1442 | C2 | 1 | 5 | yes | maximal |
| 3 | #1441 | C2 | 1 | 5 | yes | maximal |
| 4 | C22×C4⋊C4 | C22 | 1 | 5 | yes | — |
| 5 | C2×#95 | C22 | 1 | 5 | yes | — |
| 6 | C2×#95 | C22 | 1 | 5 | yes | — |
| 7 | C2×#95 | C22 | 1 | 5 | yes | — |
| 8 | C2×#95 | C22 | 1 | 5 | yes | — |
| 9 | C2×#95 | C22 | 1 | 5 | yes | — |
| 10 | C2×#95 | C22 | 1 | 5 | yes | — |
| 11 | C23×C4 | C23 | 1 | 5 | yes | — |
| 12 | C23×C4 | C23 | 1 | 5 | yes | — |
| 13 | C23×C4 | C23 | 1 | 5 | yes | — |
| 14 | C2×C4⋊C4 | — | 2 | 10 | no | — |
| 15 | C2×C4⋊C4 | — | 4 | 5 | no | — |
| 16 | C2×C4⋊C4 | — | 4 | 5 | no | — |
| 17 | #95 | — | 2 | 10 | no | — |
| 18 | #95 | — | 2 | 10 | no | — |
| 19 | #95 | — | 4 | 5 | no | — |
| 20 | #95 | — | 4 | 5 | no | — |
| 21 | #95 | — | 4 | 5 | no | — |
| 22 | #95 | — | 4 | 5 | no | — |
| 23 | C24 | C24 | 1 | 1 | yes | characteristic |
| 24 | C22×C4 | — | 2 | 5 | no | — |
| 25 | C22×C4 | — | 2 | 5 | no | — |
| 26 | C22×C4 | — | 2 | 5 | no | — |
| 27 | C22×C4 | — | 2 | 5 | no | — |
| 28 | C22×C4 | — | 2 | 5 | no | — |
| 29 | C22×C4 | — | 2 | 5 | no | — |
| 30 | C22×C4 | — | 2 | 5 | no | — |
| 31 | C22×C4 | — | 2 | 5 | no | — |
| 32 | C22×C4 | — | 2 | 5 | no | — |
| 33 | C22×C4 | — | 2 | 5 | no | — |
| 34 | C22×C4 | — | 2 | 5 | no | — |
| 35 | C22×C4 | — | 2 | 5 | no | — |
| 36 | C22×C4 | — | 2 | 5 | no | — |
| 37 | C22×C4 | — | 2 | 5 | no | — |
| 38 | C22×C4 | — | 2 | 5 | no | — |
| 39 | C22×C4 | — | 2 | 5 | no | — |
| 40 | C22×C4 | — | 2 | 5 | no | — |
| 41 | C22×C4 | — | 2 | 5 | no | — |
| 42 | C22×C4 | — | 2 | 5 | no | — |
| 43 | C22×C4 | — | 2 | 5 | no | — |
| 44 | C22×C4 | #41 | 1 | 10 | yes | — |
| 45 | C4⋊C4 | — | 4 | 20 | no | — |
| 46 | C23 | C2×#41 | 1 | 5 | yes | — |
| 47 | C23 | H(5,𝔽2) | 1 | 5 | yes | — |
| 48 | C23 | 2−1+4 | 1 | 5 | yes | — |
| 49 | C2×C4 | — | 2 | 10 | no | — |
| 50 | C2×C4 | — | 2 | 10 | no | — |
| 51 | C2×C4 | — | 2 | 10 | no | — |
| 52 | C2×C4 | — | 4 | 5 | no | — |
| 53 | C2×C4 | — | 4 | 5 | no | — |
| 54 | C2×C4 | — | 4 | 5 | no | — |
| 55 | C2×C4 | — | 4 | 5 | no | — |
| 56 | C2×C4 | — | 4 | 5 | no | — |
| 57 | C2×C4 | — | 4 | 5 | no | — |
| 58 | C2×C4 | — | 4 | 5 | no | — |
| 59 | C2×C4 | — | 4 | 5 | no | — |
| 60 | C2×C4 | — | 4 | 5 | no | — |
| 61 | C2×C4 | — | 4 | 5 | no | — |
| 62 | C2×C4 | — | 4 | 5 | no | — |
| 63 | C2×C4 | — | 4 | 5 | no | — |
| 64 | C2×C4 | — | 4 | 5 | no | — |
| 65 | C2×C4 | — | 4 | 5 | no | — |
| 66 | C2×C4 | — | 4 | 5 | no | — |
| 67 | C2×C4 | — | 4 | 5 | no | — |
| 68 | C2×C4 | — | 4 | 5 | no | — |
| 69 | C2×C4 | — | 4 | 5 | no | — |
| 70 | C22 | #538 | 1 | 5 | yes | — |
| 71 | C22 | #541 | 1 | 5 | yes | — |
| 72 | C22 | #542 | 1 | 5 | yes | — |
| 73 | C22 | #552 | 1 | 5 | yes | — |
| 74 | C22 | #553 | 1 | 5 | yes | — |
| 75 | C22 | #562 | 1 | 5 | yes | — |
| 76 | C22 | #563 | 1 | 5 | yes | — |
| 77 | C4 | — | 4 | 10 | no | — |
| 78 | C4 | — | 8 | 5 | no | — |
| 79 | C4 | — | 8 | 5 | no | — |
| 80 | C2 | #2766 | 1 | 5 | yes | — |
| 81 | C2 | #2779 | 1 | 5 | yes | — |
| 82 | C2 | #2831 | 1 | 5 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, prime radical, cosocle | C24 | C24 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ G | |
| LECS | G ▷ C24 ▷ C1 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #1443 | 2 |
| #1442 | 2 |
| #1441 | 2 |