Finite Group Databasebeta

← C3×C3⋊(C11⋊#63118) #38788200

Subgroups — C3×C3⋊(C11⋊#63118) #38788200

Order 25740.

112 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C5×C11×D13C211yesmaximal, characteristic
2C3⋊(C11⋊#63118)C311yesmaximal, characteristic, direct product factor
3C3×C11⋊#63118—31nomaximal
4C32×C5×C11×C13C411yescharacteristic, complemented, Hall
5C3×C3⋊(C11⋊#261)—51nomaximal, Hall
6C3×C5×C11×D13—21no—
7C3×C5×C11×D13D311yescharacteristic
8C3×C5×C11×D13C2×C311yescharacteristic
9C11⋊#63118—31noHall
10C32×C11×D13D511yescharacteristic
11C3×C3⋊#63118—111nomaximal, Hall
12C3×C5×C11×C13—21no—
13C3×C5×C11×C13Dic311yescharacteristic, complemented
14C3×C5×C11×C13C3×C411yescharacteristic, complemented
15C3×Dic165—131nomaximal, Hall
16C3⋊(C11⋊#261)—51no—
17C3×C11⋊#261—151no—
18C5×C11×D13C3×D311yescharacteristic
19C32×C11×C13Dic511yescharacteristic, complemented, Hall
20C32×C5×D13D1111yescharacteristic
21C2×C32×C5×C11—131no—
22C3×C11×D13—21no—
23C3×C11×D13C3×D511yescharacteristic
24C3×C11×D13D1511yescharacteristic
25C3⋊#63118—111no—
26C3×#63118—331no—
27C5×C11×C13C3×Dic311yescharacteristic, complemented, Hall
28Dic165—131no—
29C3×Dic55—391no—
30C32×C5×C13Dic1111yescharacteristic, complemented, Hall
31C11⋊#261—151noHall
32C32×C5×C11#26111yescharacteristic, complemented, Hall
33C3×C3⋊#261—551noHall
34C3×C11×C13—21no—
35C3×C11×C13C3×Dic511yescharacteristic, complemented
36C3×C11×C13Dic1511yescharacteristic, complemented
37C3×Dic33—651noHall
38C3×C5×D13—21no—
39C3×C5×D13C3×D1111yescharacteristic
40C3×C5×D13D3311yescharacteristic
41C2×C3×C5×C11—131no—
42C2×C3×C5×C11—131no—
43C2×C3×C5×C11—261no—
44C11×D13C3×D1511yescharacteristic
45#63118—331noHall
46C32×D13D5511yescharacteristic
47Dic55—391noHall
48C2×C32×C11—131no—
49C3×C5×C13—21no—
50C3×C5×C13C3×Dic1111yescharacteristic, complemented
51C3×C5×C13Dic3311yescharacteristic, complemented
52C3×Dic15—1431noHall
53C3×C5×C11—21no—
54C3×C5×C11C3×#26111yescharacteristic, complemented
55C3×C5×C11C3⋊#26111yescharacteristic, complemented
56C3⋊#261—551no—
57C3×#261—1651no—
58C11×C13C3×Dic1511yescharacteristic, complemented, Hall
59Dic33—651no—
60C3×Dic11—1951no—
61C5×D13C3×D3311yescharacteristic
62C32×C13Dic5511yescharacteristic, complemented, Hall
63C2×C5×C11—131no—
64C32×C11#6311811yescharacteristic, complemented, Hall
65C2×C32×C5—131no—
66C3×D13—21no—
67C3×D13C3×D5511yescharacteristic
68C3×D13D16511yescharacteristic
69C2×C3×C11—131no—
70C2×C3×C11—131no—
71C2×C3×C11—261no—
72C5×C13C3×Dic3311yescharacteristic, complemented, Hall
73Dic15—1431no—
74C3×Dic5—4291no—
75C5×C11C3×C3⋊#26111yescharacteristic, complemented, Hall
76#261—1651noHall
77C32×C5C11⋊#26111yescharacteristic, complemented, Hall
78Dic11—1951noHall
79C3×C13—21no—
80C3×C13C3×Dic5511yescharacteristic, complemented
81C3×C13Dic16511yescharacteristic, complemented
82C3×Dic3—7151noHall
83C3×C11—21no—
84C3×C11C3×#6311811yescharacteristic, complemented
85C3×C11C3⋊#6311811yescharacteristic, complemented
86C2×C3×C5—131no—
87C2×C3×C5—131no—
88C2×C3×C5—261no—
89D13C3×D16511yescharacteristic
90C2×C11—131no—
91Dic5—4291noHall
92C2×C32—131no—
93C3×C5—21no—
94C3×C5C3×C11⋊#26111yescharacteristic, complemented
95C3×C5C3⋊(C11⋊#261)11yescharacteristic, complemented
96C13C3×Dic16511yescharacteristic, complemented, Sylow
97C3×C4—21451no—
98Dic3—7151no—
99C11C3×C3⋊#6311811yescharacteristic, complemented, Sylow
100C2×C5—131no—
101C32C11⋊#6311811yescharacteristic, complemented, Sylow
102C2×C3—131no—
103C2×C3—131no—
104C2×C3—261no—
105C5C3×C3⋊(C11⋊#261)11yescharacteristic, complemented, Sylow
106C4—21451noSylow
107C3—21no—
108C3C3×C11⋊#6311811yescharacteristic, complemented
109C3C3⋊(C11⋊#63118)11yescharacteristic, direct product factor
110C2—131no—
subgroupG/H
center, hypercenterC3C3⋊(C11⋊#63118)
commutator, hypocenterC3×C5×C11×C13C3×C4
FrattiniC1G
Fitting, socleC32×C5×C11×C13C4
prime radicalC32×C5×C11×D13C2
cosocleC3×C5×C11×D13C2×C3
LCSG ▷ C3×C5×C11×C13
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
2. C3⋊(C11⋊#63118)C3direct (N × H)
4. C32×C5×C11×C13C4semidirect
13. C3×C5×C11×C13Dic3semidirect
14. C3×C5×C11×C13C3×C4semidirect
19. C32×C11×C13Dic5semidirect
27. C5×C11×C13C3×Dic3semidirect
30. C32×C5×C13Dic11semidirect
32. C32×C5×C11#261semidirect
35. C3×C11×C13C3×Dic5semidirect
36. C3×C11×C13Dic15semidirect
50. C3×C5×C13C3×Dic11semidirect
51. C3×C5×C13Dic33semidirect
54. C3×C5×C11C3×#261semidirect
55. C3×C5×C11C3⋊#261semidirect
58. C11×C13C3×Dic15semidirect
62. C32×C13Dic55semidirect
64. C32×C11#63118semidirect
72. C5×C13C3×Dic33semidirect
75. C5×C11C3×C3⋊#261semidirect
77. C32×C5C11⋊#261semidirect
80. C3×C13C3×Dic55semidirect
81. C3×C13Dic165semidirect
84. C3×C11C3×#63118semidirect
85. C3×C11C3⋊#63118semidirect
94. C3×C5C3×C11⋊#261semidirect
95. C3×C5C3⋊(C11⋊#261)semidirect
96. C13C3×Dic165semidirect
99. C11C3×C3⋊#63118semidirect
101. C32C11⋊#63118semidirect
105. C5C3×C3⋊(C11⋊#261)semidirect
108. C3C3×C11⋊#63118semidirect
109. C3C3⋊(C11⋊#63118)direct (N × H)

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×C11⋊#631183
C3×C3⋊(C11⋊#261)5
C3×C3⋊#6311811
C3×Dic16513