Finite Group Databasebeta

← C3⋊(C3⋊(C11⋊#63118)) #38788276

Subgroups — C3⋊(C3⋊(C11⋊#63118)) #38788276

Order 25740.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C5×C11×D13C211yesmaximal, characteristic
2C3⋊(C11⋊#63118)—34nomaximal
3C32×C5×C11×C13C411yescharacteristic, complemented, Hall
4C3⋊(C3⋊(C11⋊#261))—51nomaximal, Hall
5C3×C5×C11×D13D314yes—
6C11⋊#63118—91noHall
7C32×C11×D13D511yescharacteristic
8C3⋊(C3⋊#63118)—111nomaximal, Hall
9C3×C5×C11×C13Dic314yescomplemented
10C3⋊Dic165—131nomaximal, Hall
11C3⋊(C11⋊#261)—154no—
12C5×C11×D13C3⋊D311yescharacteristic
13C32×C11×C13Dic511yescharacteristic, complemented, Hall
14C32×C5×D13D1111yescharacteristic
15C2×C32×C5×C11—131no—
16C3×C11×D13D1514yes—
17C3⋊#63118—334no—
18C5×C11×C13C3⋊Dic311yescharacteristic, complemented, Hall
19Dic165—394no—
20C32×C5×C13Dic1111yescharacteristic, complemented, Hall
21C11⋊#261—451noHall
22C32×C5×C11#26111yescharacteristic, complemented, Hall
23C3⋊(C3⋊#261)—551noHall
24C3×C11×C13Dic1514yescomplemented
25C3⋊Dic33—651noHall
26C3×C5×D13D3314yes—
27C2×C3×C5×C11—134no—
28C11×D13C3⋊D1511yescharacteristic
29#63118—991noHall
30C32×D13D5511yescharacteristic
31Dic55—1171noHall
32C2×C32×C11—131no—
33C3×C5×C13Dic3314yescomplemented
34C3⋊Dic15—1431noHall
35C3×C5×C11C3⋊#26114yescomplemented
36C3⋊#261—1654no—
37C11×C13C3⋊Dic1511yescharacteristic, complemented, Hall
38Dic33—1954no—
39C5×D13C3⋊D3311yescharacteristic
40C32×C13Dic5511yescharacteristic, complemented, Hall
41C2×C5×C11—131no—
42C32×C11#6311811yescharacteristic, complemented, Hall
43C2×C32×C5—131no—
44C3×D13D16514yes—
45C2×C3×C11—134no—
46C5×C13C3⋊Dic3311yescharacteristic, complemented, Hall
47Dic15—4294no—
48C5×C11C3⋊(C3⋊#261)11yescharacteristic, complemented, Hall
49#261—4951noHall
50C32×C5C11⋊#26111yescharacteristic, complemented, Hall
51Dic11—5851noHall
52C3×C13Dic16514yescomplemented
53C3⋊Dic3—7151noHall
54C3×C11C3⋊#6311814yescomplemented
55C2×C3×C5—134no—
56D13C3⋊D16511yescharacteristic
57C2×C11—131no—
58Dic5—12871noHall
59C2×C32—131no—
60C3×C5C3⋊(C11⋊#261)14yescomplemented
61C13C3⋊Dic16511yescharacteristic, complemented, Sylow
62Dic3—21454no—
63C11C3⋊(C3⋊#63118)11yescharacteristic, complemented, Sylow
64C2×C5—131no—
65C32C11⋊#6311811yescharacteristic, complemented, Sylow
66C2×C3—134no—
67C5C3⋊(C3⋊(C11⋊#261))11yescharacteristic, complemented, Sylow
68C4—64351noSylow
69C3C3⋊(C11⋊#63118)14yescomplemented
70C2—131no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC32×C5×C11×C13C4
prime radical, cosocleC32×C5×C11×D13C2
LCSG ▷ C32×C5×C11×C13
UCSC1

Complements

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

NH ≅ G/Ntype
3. C32×C5×C11×C13C4semidirect
9. C3×C5×C11×C13Dic3semidirect
13. C32×C11×C13Dic5semidirect
18. C5×C11×C13C3⋊Dic3semidirect
20. C32×C5×C13Dic11semidirect
22. C32×C5×C11#261semidirect
24. C3×C11×C13Dic15semidirect
33. C3×C5×C13Dic33semidirect
35. C3×C5×C11C3⋊#261semidirect
37. C11×C13C3⋊Dic15semidirect
40. C32×C13Dic55semidirect
42. C32×C11#63118semidirect
46. C5×C13C3⋊Dic33semidirect
48. C5×C11C3⋊(C3⋊#261)semidirect
50. C32×C5C11⋊#261semidirect
52. C3×C13Dic165semidirect
54. C3×C11C3⋊#63118semidirect
60. C3×C5C3⋊(C11⋊#261)semidirect
61. C13C3⋊Dic165semidirect
63. C11C3⋊(C3⋊#63118)semidirect
65. C32C11⋊#63118semidirect
67. C5C3⋊(C3⋊(C11⋊#261))semidirect
69. C3C3⋊(C11⋊#63118)semidirect

Maximal subgroups

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

subgroupindex
C32×C5×C11×D132
C3⋊(C11⋊#63118)3
C3⋊(C3⋊(C11⋊#261))5
C3⋊(C3⋊#63118)11
C3⋊Dic16513