Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
604 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C43 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C43 |
| prime radical | C43×#2011 | C2 |
| LCS | G ▷ C2×C42 ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C43 ◁ C2×C42×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C43×#2732 | C2 | semidirect |
| 2. C43×#2041 | C2 | semidirect |
| 3. C43×#2014 | C2 | semidirect |
| 5. C43×#1272 | C2 | semidirect |
| 6. C43×#1271 | C2 | semidirect |
| 7. C43×#1270 | C2 | semidirect |
| 72. C2×Q8×C43 | D8 | semidirect |
| 94. C2×D4×C43 | SD16 | semidirect |
| 197. #7735 | C43 | direct (N × H) |
| 230. #2732 | C2×C43 | semidirect |
| 231. #2041 | C2×C43 | semidirect |
| 232. #2014 | C2×C43 | semidirect |
| 234. #1272 | C2×C43 | semidirect |
| 235. #1271 | C2×C43 | semidirect |
| 236. #1270 | C2×C43 | semidirect |
| 265. C43 | #7735 | direct (N × H) |
| 311. C2×Q8 | D8×C43 | semidirect |
| 333. C2×D4 | SD16×C43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#2732 | 2 |
| C43×#2041 | 2 |
| C43×#2014 | 2 |
| C43×#2011 | 2 |
| C43×#1272 | 2 |
| C43×#1271 | 2 |
| C43×#1270 | 2 |
| #7735 | 43 |