Finite Group Databasebeta

← C3⋊(C11⋊#10587716) #31825064

Subgroups — C3⋊(C11⋊#10587716) #31825064

Order 18018.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C11×#63270C211yesmaximal, characteristic, complemented, Hall
2C11⋊#10587716—31nomaximal
3C7×D429C311yesmaximal, characteristic, complemented
4C11×#63270—21no—
5C11×#63270D311yescharacteristic, complemented
6C3×C7×C11×C13C2×C311yescharacteristic, complemented
7C3⋊(C11⋊(D13⋊C3))—71nomaximal, Hall
8C7×D143—31noHall
9C3⋊#10587716—111nomaximal, Hall
10ΓL(1,𝔽8)×D33—131nomaximal, Hall
11C3×C11×C13⋊C3—71noHall
12C7×C11×C13C3×D311yescharacteristic, complemented, Hall
13D429ΓL(1,𝔽8)11yescharacteristic, complemented
14C11⋊(D13⋊C3)—211no—
15C3×#63270D1111yescharacteristic, complemented, Hall
16C3×C11×ΓL(1,𝔽8)—261noHall
17C7×D39—111no—
18#10587716—331no—
19C7×D33—131no—
20ΓL(1,𝔽8)×D11—391no—
21C3×C11×C13C2×ΓL(1,𝔽8)11yescharacteristic, complemented
22C11×C13⋊C3—71no—
23C11×C13⋊C3—141no—
24D143—31noHall
25C3×C7×C13C3×D1111yescharacteristic, complemented
26#63270—21no—
27#63270D3311yescharacteristic, complemented
28C3⋊(D13⋊C3)—771noHall
29C3×C7×C11D13⋊C311yescharacteristic, complemented
30C11×ΓL(1,𝔽8)—261no—
31C11×ΓL(1,𝔽8)—261no—
32C3×D33—911noHall
33C7×D13—331noHall
34C7×D11—391noHall
35C11×C13D3×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
36D3×ΓL(1,𝔽8)—1431noHall
37C3×C13⋊C3—71noHall
38C32×C11—1821noHall
39C7×C13C3×D3311yescharacteristic, complemented, Hall
40D39—111no—
41D13⋊C3—2311no—
42C7×C11C3⋊(D13⋊C3)11yescharacteristic, complemented, Hall
43D33—131no—
44C3×D11—2731no—
45C3×ΓL(1,𝔽8)—261noHall
46D3×C7—1431no—
47C2×ΓL(1,𝔽8)—4291no—
48C3×C13ΓL(1,𝔽8)×D1111yescharacteristic, complemented
49C13⋊C3—71no—
50C13⋊C3—141no—
51C3×C11—1821no—
52C3×C11—1821no—
53C3×C11#1058771611yescharacteristic, complemented
54D13—331noHall
55D11—391noHall
56C3×C7C11⋊(D13⋊C3)11yescharacteristic, complemented
57ΓL(1,𝔽8)—261no—
58ΓL(1,𝔽8)—261no—
59C3×D3—10011noHall
60C2×C7—4291noHall
61C13ΓL(1,𝔽8)×D3311yescharacteristic, complemented, Sylow
62C11C3⋊#1058771611yescharacteristic, complemented, Sylow
63C32—911noSylow
64C7C3⋊(C11⋊(D13⋊C3))11yescharacteristic, complemented, Sylow
65C2×C3—30031no—
66D3—1431no—
67C3—911no—
68C3—1821no—
69C3C11⋊#1058771611yescharacteristic, complemented
70C2—4291noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C11×C13C2×C3
LCSG ▷ C3×C7×C11×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C11×#63270C2semidirect
3. C7×D429C3semidirect
5. C11×#63270D3semidirect
6. C3×C7×C11×C13C2×C3semidirect
12. C7×C11×C13C3×D3semidirect
13. D429ΓL(1,𝔽8)semidirect
15. C3×#63270D11semidirect
21. C3×C11×C13C2×ΓL(1,𝔽8)semidirect
25. C3×C7×C13C3×D11semidirect
27. #63270D33semidirect
29. C3×C7×C11D13⋊C3semidirect
35. C11×C13D3×ΓL(1,𝔽8)semidirect
39. C7×C13C3×D33semidirect
42. C7×C11C3⋊(D13⋊C3)semidirect
48. C3×C13ΓL(1,𝔽8)×D11semidirect
53. C3×C11#10587716semidirect
56. C3×C7C11⋊(D13⋊C3)semidirect
61. C13ΓL(1,𝔽8)×D33semidirect
62. C11C3⋊#10587716semidirect
64. C7C3⋊(C11⋊(D13⋊C3))semidirect
69. C3C11⋊#10587716semidirect

Maximal subgroups

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

subgroupindex
C3×C11×#632702
C11⋊#105877163
C7×D4293
C3⋊(C11⋊(D13⋊C3))7
C3⋊#1058771611
ΓL(1,𝔽8)×D3313