Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
294 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D7 |
| commutator | C2×C7 | C23×C4 |
| Fitting | C4×C7×D4 | C2 |
| socle, cosocle | C22×C7 | C24 |
| prime radical | C2×#1159 | C2 |
| hypercenter | C4×D4 | D7 |
| hypocenter | C7 | #520 |
| LCS | G ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×C7×D4 | C2 | semidirect |
| 3. D4×Dic7 | C2 | semidirect |
| 4. C4×C22⋊D7 | C2 | semidirect |
| 5. C2×Dic7⋊C4 | C2 | semidirect |
| 6. D7×C4⋊C4 | C2 | semidirect |
| 7. #6450 | C2 | semidirect |
| 8. (C22⋊D7)⋊C4 | C2 | semidirect |
| 9. #6440 | C2 | semidirect |
| 10. #6435 | C2 | semidirect |
| 11. C4×Dic14 | C2 | semidirect |
| 17. #1159 | C4 | semidirect |
| 39. C7×D4 | C2×C4 | semidirect |
| 45. C22⋊D7 | C2×C4 | semidirect |
| 47. C2×Dic7 | C2×C4 | semidirect |
| 54. C4×D7 | C2×C4 | semidirect |
| 55. Dic14 | C2×C4 | semidirect |
| 62. C4×D4 | D7 | semidirect |
| 116. D4 | C4×D7 | semidirect |
| 131. C7 | #520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1159 | 2 |
| C4×C7×D4 | 2 |
| D4×Dic7 | 2 |
| C4×C22⋊D7 | 2 |
| C2×Dic7⋊C4 | 2 |
| D7×C4⋊C4 | 2 |
| #6450 | 2 |
| (C22⋊D7)⋊C4 | 2 |
| #6440 | 2 |
| #6435 | 2 |
| C4×Dic14 | 2 |
| #520 | 7 |