Finite Group Databasebeta

← C11×C3⋊#10587717 #31825059

Subgroups — C11×C3⋊#10587717 #31825059

Order 18018.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C11×#63271C211yesmaximal, characteristic, complemented, Hall
2C11×#10587717—31nomaximal
3C7×C11×D39C311yesmaximal, characteristic, complemented
4C11×#63271—21no—
5C11×#63271D311yescharacteristic, complemented
6C3×C7×C11×C13C2×C311yescharacteristic, complemented
7C11×C3⋊(D13⋊C3)—71nomaximal, Hall
8C7×C11×D13—31noHall
9C3⋊#10587717C1111yesmaximal, characteristic, direct product factor, Hall
10D3×C11×ΓL(1,𝔽8)—131nomaximal, Hall
11C3×C11×C13⋊C3—71noHall
12C7×C11×C13C3×D311yescharacteristic, complemented, Hall
13C11×D39ΓL(1,𝔽8)11yescharacteristic, complemented
14C11×D13⋊C3—211no—
15C3×#63271C2×C1111yescharacteristic, complemented, Hall
16C3×C11×ΓL(1,𝔽8)—131noHall
17C7×D39C3×C1111yescharacteristic, complemented
18#10587717—31no—
19D3×C7×C11—131no—
20C2×C11×ΓL(1,𝔽8)—391no—
21C3×C11×C13C2×ΓL(1,𝔽8)11yescharacteristic, complemented
22C11×C13⋊C3—71no—
23C11×C13⋊C3—141no—
24C11×D13—31noHall
25C3×C7×C13C2×C3×C1111yescharacteristic, complemented
26#63271—21no—
27#63271D3×C1111yescharacteristic, complemented
28C3⋊(D13⋊C3)—71noHall
29C3×C7×C11D13⋊C311yescharacteristic, complemented
30C11×ΓL(1,𝔽8)—131no—
31C11×ΓL(1,𝔽8)—261no—
32C3×D3×C11—911noHall
33C7×D13—31noHall
34C2×C7×C11—391noHall
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
40D39C11×ΓL(1,𝔽8)11yescharacteristic, complemented
41D13⋊C3—211no—
42C7×C11C3⋊(D13⋊C3)11yescharacteristic, complemented, Hall
43C2×C3×C11—2731no—
44D3×C11—131no—
45C3×ΓL(1,𝔽8)—131noHall
46D3×C7—131no—
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×C11#1058771711yescharacteristic, complemented
54D13—31noHall
55C2×C11—391noHall
56C3×C7C11×D13⋊C311yescharacteristic, complemented
57ΓL(1,𝔽8)—131no—
58ΓL(1,𝔽8)—261no—
59C3×D3—911noHall
60C2×C7—391noHall
61C13D3×C11×ΓL(1,𝔽8)11yescharacteristic, complemented, Sylow
62C11C3⋊#1058771711yescharacteristic, direct product factor, Sylow
63C32—911noSylow
64C7C11×C3⋊(D13⋊C3)11yescharacteristic, complemented, Sylow
65C2×C3—2731no—
66D3—131no—
67C3—911no—
68C3—1821no—
69C3C11×#1058771711yescharacteristic, complemented
70C2—391noSylow
subgroupG/H
center, hypercenterC11C3⋊#10587717
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×#63271C2semidirect
3. C7×C11×D39C3semidirect
5. C11×#63271D3semidirect
6. C3×C7×C11×C13C2×C3semidirect
9. C3⋊#10587717C11direct (N × H)
12. C7×C11×C13C3×D3semidirect
13. C11×D39ΓL(1,𝔽8)semidirect
15. C3×#63271C2×C11semidirect
17. C7×D39C3×C11semidirect
21. C3×C11×C13C2×ΓL(1,𝔽8)semidirect
25. C3×C7×C13C2×C3×C11semidirect
27. #63271D3×C11semidirect
29. C3×C7×C11D13⋊C3semidirect
35. C11×C13D3×ΓL(1,𝔽8)semidirect
39. C7×C13C3×D3×C11semidirect
40. D39C11×ΓL(1,𝔽8)semidirect
42. C7×C11C3⋊(D13⋊C3)semidirect
48. C3×C13C2×C11×ΓL(1,𝔽8)semidirect
53. C3×C11#10587717semidirect
56. C3×C7C11×D13⋊C3semidirect
61. C13D3×C11×ΓL(1,𝔽8)semidirect
62. C11C3⋊#10587717direct (N × H)
64. C7C11×C3⋊(D13⋊C3)semidirect
69. C3C11×#10587717semidirect

Maximal subgroups

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

subgroupindex
C3×C11×#632712
C11×#105877173
C7×C11×D393
C11×C3⋊(D13⋊C3)7
C3⋊#1058771711
D3×C11×ΓL(1,𝔽8)13