Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
40 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C7×C16 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #6393 | C2 | 1 | 2 | yes | maximal |
| 3 | C2×C7×C8 | C22 | 1 | 1 | yes | characteristic |
| 4 | #1136 | — | 2 | 2 | no | — |
| 5 | C7×C16 | C4 | 1 | 2 | yes | — |
| 6 | #368 | — | 7 | 1 | no | maximal, Sylow |
| 7 | C2×C4×C7 | D4 | 1 | 1 | yes | characteristic |
| 8 | C7×C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 9 | C7×C8 | Q8 | 1 | 1 | yes | characteristic |
| 10 | C7⋊C8 | — | 4 | 2 | no | — |
| 11 | C2×C16 | D7 | 1 | 1 | yes | characteristic |
| 12 | #108 | — | 7 | 2 | no | — |
| 13 | C22×C7 | Q16 | 1 | 1 | yes | characteristic |
| 14 | C4×C7 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 15 | C4×C7 | D8 | 1 | 1 | yes | characteristic |
| 16 | M16 | — | 14 | 2 | no | — |
| 17 | C2×C8 | C2×D7 | 1 | 1 | yes | characteristic |
| 18 | C16 | Dic7 | 1 | 2 | yes | — |
| 19 | C2×C7 | — | 2 | 1 | no | — |
| 20 | C2×C7 | #107 | 1 | 1 | yes | characteristic |
| 21 | C2×C4 | D28 | 1 | 1 | yes | characteristic |
| 22 | C8 | — | 28 | 2 | no | — |
| 23 | C8 | Dic14 | 1 | 1 | yes | characteristic |
| 24 | C8 | C2×Dic7 | 1 | 1 | yes | characteristic |
| 25 | C7 | #368 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 26 | C22 | Dic28 | 1 | 1 | yes | characteristic |
| 27 | C4 | D56 | 1 | 1 | yes | characteristic |
| 28 | C4 | C4⋊Dic7 | 1 | 1 | yes | characteristic |
| 29 | C2 | — | 2 | 1 | no | — |
| 30 | C2 | #6392 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 25. C7 | #368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×C16 | 2 |
| #6393 | 2 |
| #368 | 7 |