Finite Group DatabasebetaFinite Group DatabasebetaOrder 128.
84 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #500 | C2 | 1 | 2 | yes | maximal |
| 2 | #487 | C2 | 1 | 4 | yes | maximal |
| 3 | C82 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C4⋊Q8 | C22 | 1 | 4 | yes | — |
| 5 | #107 | — | 2 | 4 | no | — |
| 6 | #103 | — | 2 | 8 | no | — |
| 7 | C4×C8 | C22 | 1 | 2 | yes | — |
| 8 | C4×C8 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×Q8 | — | 2 | 4 | no | — |
| 10 | C2×C8 | D4 | 1 | 4 | yes | — |
| 11 | C2×C8 | D4 | 1 | 2 | yes | — |
| 12 | C4⋊C4 | — | 2 | 4 | no | — |
| 13 | C4⋊C4 | — | 2 | 4 | no | — |
| 14 | C42 | C23 | 1 | 1 | yes | characteristic |
| 15 | Q8 | — | 4 | 8 | no | — |
| 16 | C2×C4 | — | 4 | 4 | no | — |
| 17 | C2×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 18 | C2×C4 | C2×D4 | 1 | 2 | yes | — |
| 19 | C8 | — | 2 | 4 | no | — |
| 20 | C8 | Q16 | 1 | 4 | yes | — |
| 21 | C22 | #127 | 1 | 1 | yes | characteristic |
| 22 | C4 | — | 8 | 4 | no | — |
| 23 | C4 | C2×Q16 | 1 | 2 | yes | — |
| 24 | C4 | #135 | 1 | 4 | yes | — |
| 25 | C2 | #494 | 1 | 1 | yes | characteristic |
| 26 | C2 | #495 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22 | #127 |
| commutator, Frattini, cosocle | C42 | C23 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #500 | 2 |
| #487 | 2 |
| C82 | 2 |