Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×C22⋊D7 |
| commutator, cosocle | C4×C7 | C24 |
| Frattini | C4 | C23×D7 |
| Fitting | C2×C7×#41 | C2 |
| socle | C2×C7 | C22×D4 |
| hypercenter | C2×#41 | D7 |
| hypocenter | C7 | #575 |
| LCS | G ▷ C4×C7 ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C7×#41 | C2 | semidirect |
| 2. C2×#1157 | C2 | semidirect |
| 3. #6514 | C2 | semidirect |
| 4. #6513 | C2 | semidirect |
| 5. #6512 | C2 | semidirect |
| 6. #6505 | C2 | semidirect |
| 7. #6495 | C2 | semidirect |
| 8. C2×#1136 | C2 | semidirect |
| 12. C7×#41 | C22 | semidirect |
| 13. C2×C7×Q8 | C22 | semidirect |
| 15. C2×C7×D4 | C22 | semidirect |
| 22. #1157 | C22 | semidirect |
| 23. C2×D28 | C22 | semidirect |
| 25. C2×Dic14 | C22 | semidirect |
| 26. #1144 | C22 | semidirect |
| 27. #1143 | C22 | semidirect |
| 28. #1142 | C22 | semidirect |
| 29. #1141 | C22 | semidirect |
| 30. #1136 | C22 | semidirect |
| 31. #1136 | C22 | semidirect |
| 32. C2×C7⋊C8 | C22 | semidirect |
| 63. C2×#41 | D7 | semidirect |
| 91. #41 | C2×D7 | semidirect |
| 93. C2×Q8 | C2×D7 | semidirect |
| 97. C2×D4 | C2×D7 | semidirect |
| 142. C7 | #575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#41 | 2 |
| C2×#1157 | 2 |
| #6514 | 2 |
| #6513 | 2 |
| #6512 | 2 |
| #6505 | 2 |
| #6495 | 2 |
| C2×#1136 | 2 |
| #575 | 7 |