Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | D4×D7 |
| commutator, cosocle | C2×C4×C7 | C23 |
| Frattini | C2×C4 | C22×D7 |
| Fitting | C7×#103 | C2 |
| socle | C22×C7 | C2×D4 |
| hypercenter | #103 | D7 |
| hypocenter | C7 | #449 |
| LCS | G ▷ C2×C4×C7 ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ #103 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#1161 | C2 | semidirect |
| 2. C2×#1143 | C2 | semidirect |
| 3. C2×D56 | C2 | semidirect |
| 4. #6458 | C2 | semidirect |
| 5. C7×#103 | C2 | semidirect |
| 6. (C2×D7)⋊C8 | C2 | semidirect |
| 7. #6383 | C2 | semidirect |
| 28. C7×Q8 | D4 | semidirect |
| 38. D28 | D4 | semidirect |
| 48. #103 | D7 | semidirect |
| 91. Q8 | D28 | semidirect |
| 107. C7 | #449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1161 | 2 |
| C2×#1143 | 2 |
| C2×D56 | 2 |
| #6458 | 2 |
| C7×#103 | 2 |
| (C2×D7)⋊C8 | 2 |
| #6383 | 2 |
| #449 | 7 |