Finite Group Databasebeta

← D3×C11×#63270 #31825060

Subgroups — D3×C11×#63270 #31825060

Order 18018.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C11×#63270C211yesmaximal, characteristic, complemented, Hall
2D3×C7×C11×C13C311yesmaximal, characteristic, complemented
3C2×C11×#63270—31nomaximal
4C11×#63270—21no—
5C11×#63270D311yescharacteristic, direct product factor
6C3×C7×C11×C13C2×C311yescharacteristic, complemented
7D3×C11×C13⋊C3—71nomaximal, Hall
8C2×C7×C11×C13—31noHall
9D3×#63270C1111yesmaximal, characteristic, direct product factor, Hall
10D3×C11×ΓL(1,𝔽8)—131nomaximal, Hall
11C3×C11×C13⋊C3—71noHall
12C7×C11×C13C3×D311yescharacteristic, complemented, Hall
13D3×C11×C13ΓL(1,𝔽8)11yescharacteristic, complemented
14C2×C11×C13⋊C3—211no—
15C3×#63270C2×C1111yescharacteristic, complemented, Hall
16C3×C11×ΓL(1,𝔽8)—131noHall
17D3×C7×C13C3×C1111yescharacteristic, complemented
18C2×#63270—31no—
19D3×C7×C11C13⋊C311yescharacteristic, complemented
20C2×C11×ΓL(1,𝔽8)—391no—
21C3×C11×C13C2×ΓL(1,𝔽8)11yescharacteristic, complemented
22C11×C13⋊C3—71no—
23C11×C13⋊C3—141no—
24C2×C11×C13—31noHall
25C3×C7×C13C2×C3×C1111yescharacteristic, complemented
26#63270—21no—
27#63270D3×C1111yescharacteristic, direct product factor
28D3×C13⋊C3—71noHall
29C3×C7×C11C2×C13⋊C311yescharacteristic, complemented
30C11×ΓL(1,𝔽8)—131no—
31C11×ΓL(1,𝔽8)—261no—
32C3×D3×C11—911noHall
33C2×C7×C13—31noHall
34C2×C7×C11—31noHall
35C11×C13D3×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
36D3×ΓL(1,𝔽8)—131noHall
37C3×C13⋊C3—71noHall
38C32×C11—911noHall
39C7×C13C3×D3×C1111yescharacteristic, complemented, Hall
40D3×C13C11×ΓL(1,𝔽8)11yescharacteristic, complemented
41C2×C13⋊C3—211no—
42C7×C11D3×C13⋊C311yescharacteristic, complemented, Hall
43C2×C3×C11—2731no—
44D3×C11#6327011yescharacteristic, direct product factor
45C3×ΓL(1,𝔽8)—131noHall
46D3×C7C11×C13⋊C311yescharacteristic, complemented
47C2×ΓL(1,𝔽8)—391no—
48C3×C13C2×C11×ΓL(1,𝔽8)11yescharacteristic, complemented
49C13⋊C3—71no—
50C13⋊C3—141no—
51C3×C11—911no—
52C3×C11—1821no—
53C3×C11C2×#6327011yescharacteristic, complemented
54C2×C13—31noHall
55C2×C11—31noHall
56C3×C7C2×C11×C13⋊C311yescharacteristic, complemented
57ΓL(1,𝔽8)—131no—
58ΓL(1,𝔽8)—261no—
59C3×D3—911noHall
60C2×C7—31noHall
61C13D3×C11×ΓL(1,𝔽8)11yescharacteristic, complemented, Sylow
62C11D3×#6327011yescharacteristic, direct product factor, Sylow
63C32—911noSylow
64C7D3×C11×C13⋊C311yescharacteristic, complemented, Sylow
65C2×C3—2731no—
66D3C11×#6327011yescharacteristic, direct product factor
67C3—911no—
68C3—1821no—
69C3C2×C11×#6327011yescharacteristic, complemented
70C2—31noSylow
subgroupG/H
center, hypercenterC11D3×#63270
commutator, cosocle, hypocenterC3×C7×C13C2×C3×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C13C2×C3
LCSG ▷ C3×C7×C13
UCSC1 ◁ C11

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×C11×#63270C2semidirect
2. D3×C7×C11×C13C3semidirect
5. C11×#63270D3direct (N × H)
6. C3×C7×C11×C13C2×C3semidirect
9. D3×#63270C11direct (N × H)
12. C7×C11×C13C3×D3semidirect
13. D3×C11×C13ΓL(1,𝔽8)semidirect
15. C3×#63270C2×C11semidirect
17. D3×C7×C13C3×C11semidirect
19. D3×C7×C11C13⋊C3semidirect
21. C3×C11×C13C2×ΓL(1,𝔽8)semidirect
25. C3×C7×C13C2×C3×C11semidirect
27. #63270D3×C11direct (N × H)
29. C3×C7×C11C2×C13⋊C3semidirect
35. C11×C13D3×ΓL(1,𝔽8)semidirect
39. C7×C13C3×D3×C11semidirect
40. D3×C13C11×ΓL(1,𝔽8)semidirect
42. C7×C11D3×C13⋊C3semidirect
44. D3×C11#63270direct (N × H)
46. D3×C7C11×C13⋊C3semidirect
48. C3×C13C2×C11×ΓL(1,𝔽8)semidirect
53. C3×C11C2×#63270semidirect
56. C3×C7C2×C11×C13⋊C3semidirect
61. C13D3×C11×ΓL(1,𝔽8)semidirect
62. C11D3×#63270direct (N × H)
64. C7D3×C11×C13⋊C3semidirect
66. D3C11×#63270direct (N × H)
69. C3C2×C11×#63270semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×C11×#632702
D3×C7×C11×C133
C2×C11×#632703
D3×C11×C13⋊C37
D3×#6327011
D3×C11×ΓL(1,𝔽8)13