Finite Group Databasebeta

← C11×D65⋊(C3⋊D3) #38788285

Subgroups — C11×D65⋊(C3⋊D3) #38788285

Order 25740.

240 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 70 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×C11×D65C211yesmaximal, characteristic, complemented
2C5×C11×C3⋊D39C211yesmaximal, characteristic, complemented
3C11×C13×C3⋊D15C211yesmaximal, characteristic, complemented
4C11×D15⋊D13—34nomaximal
5C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
6C11×C3⋊D3×D13—51nomaximal, Hall
7C11×C13×D15—34no—
8C5×C11×D39—34no—
9C3×C11×D65D314yescomplemented
10D5×C11×D13—91noHall
11C11×C3⋊D39D511yescharacteristic, complemented
12C11×C13×C3⋊D3—51no—
13C32×C11×D13—51no—
14D65⋊(C3⋊D3)C1111yesmaximal, characteristic, direct product factor, Hall
15C3×C5×C11×C13C2×D314yescomplemented
16D5×C11×C3⋊D3—131nomaximal, Hall
17D3×C11×D13—154no—
18C11×D65C3⋊D311yescharacteristic, complemented
19D5×C11×C13—91no—
20C5×C11×D13—91no—
21C32×C11×C13C2×D511yescharacteristic, complemented, Hall
22C13×C3⋊D15C2×C1111yescharacteristic, complemented
23C5×C3⋊D39C2×C1111yescharacteristic, complemented
24C32×D65C2×C1111yescharacteristic, complemented
25C11×C3⋊D15D1311yescharacteristic, complemented
26C5×C11×C3⋊D3—131no—
27C32×D5×C11—131no—
28C11×D39—34no—
29D3×C11×C13—154no—
30C3×C11×D13—54no—
31D15⋊D13—34no—
32C5×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
33D3×D5×C11—394no—
34C32×C5×C13C22×C1111yescharacteristic, complemented, Hall
35C2×C11×D13—451noHall
36C32×C5×C11C2×D1311yescharacteristic, complemented, Hall
37C3⋊D3×D13—51noHall
38C3×C11×C13D3×D514yescomplemented
39C2×C11×C3⋊D3—651noHall
40C13×D15—34no—
41C5×D39—34no—
42C3×D65D3×C1114yescomplemented
43C11×D15—34no—
44C5×D3×C11—394no—
45C3×D5×C11—134no—
46C2×C11×C13—451no—
47C11×D13—51no—
48C11×D13—91no—
49D5×D13—91noHall
50C3⋊D39D5×C1111yescharacteristic, complemented
51C13×C3⋊D3—51no—
52C32×D13—51no—
53C2×D5×C11—1171noHall
54C2×C32×C11—651no—
55C11×C3⋊D3—51no—
56C11×C3⋊D3—131no—
57C3×C5×C13C2×D3×C1114yescomplemented
58D5×C3⋊D3—131noHall
59C3×C5×C11D3×D1314yescomplemented
60D3×D13—154no—
61C11×C13D5×C3⋊D311yescharacteristic, complemented, Hall
62C2×D3×C11—1954no—
63D65C11×C3⋊D311yescharacteristic, complemented
64C5×D13—91no—
65D5×C13—91no—
66C32×C13C2×D5×C1111yescharacteristic, complemented, Hall
67C2×C5×C11—1171no—
68D5×C11—91no—
69D5×C11—131no—
70C32×C11D5×D1311yescharacteristic, complemented, Hall
71C3⋊D15C11×D1311yescharacteristic, complemented
72C5×C3⋊D3—131no—
73C32×D5—131no—
74D39—34no—
75C3×D13—54no—
76D3×C13—154no—
77C2×C3×C11—654no—
78D3×C11—154no—
79D3×C11—394no—
80C5×C13C2×C11×C3⋊D311yescharacteristic, complemented, Hall
81D3×D5—394no—
82C5×C11C3⋊D3×D1311yescharacteristic, complemented, Hall
83C2×D13—451noHall
84C32×C5C2×C11×D1311yescharacteristic, complemented, Hall
85C22×C11—5851noHall
86C3×C13D3×D5×C1114yescomplemented
87C2×C3⋊D3—651noHall
88C3×C11D15⋊D1314yescomplemented
89D15—34no—
90C3×D5—134no—
91C5×D3—394no—
92C2×C13—451no—
93D13—51no—
94D13—91no—
95C2×C11—451no—
96C2×C11—651no—
97C2×C11—1171no—
98C2×D5—1171noHall
99C2×C32—651no—
100C3⋊D3—51no—
101C3⋊D3—131no—
102C3×C5D3×C11×D1314yescomplemented
103C13D5×C11×C3⋊D311yescharacteristic, complemented, Sylow
104C2×D3—1954no—
105C11D65⋊(C3⋊D3)11yescharacteristic, direct product factor, Sylow
106C2×C5—1171no—
107D5—91no—
108D5—131no—
109C32D5×C11×D1311yescharacteristic, complemented, Sylow
110C2×C3—654no—
111D3—154no—
112D3—394no—
113C5C11×C3⋊D3×D1311yescharacteristic, complemented, Sylow
114C22—5851noSylow
115C3C11×D15⋊D1314yescomplemented
116C2—451no—
117C2—651no—
118C2—1171no—
subgroupG/H
center, hypercenterC11D65⋊(C3⋊D3)
commutator, cosocle, hypocenterC32×C5×C13C22×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C13C22
LCSG ▷ C32×C5×C13
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C32×C11×D65C2semidirect
2. C5×C11×C3⋊D39C2semidirect
3. C11×C13×C3⋊D15C2semidirect
5. C32×C5×C11×C13C22semidirect
9. C3×C11×D65D3semidirect
11. C11×C3⋊D39D5semidirect
14. D65⋊(C3⋊D3)C11direct (N × H)
15. C3×C5×C11×C13C2×D3semidirect
18. C11×D65C3⋊D3semidirect
21. C32×C11×C13C2×D5semidirect
22. C13×C3⋊D15C2×C11semidirect
23. C5×C3⋊D39C2×C11semidirect
24. C32×D65C2×C11semidirect
25. C11×C3⋊D15D13semidirect
32. C5×C11×C13C2×C3⋊D3semidirect
34. C32×C5×C13C22×C11semidirect
36. C32×C5×C11C2×D13semidirect
38. C3×C11×C13D3×D5semidirect
42. C3×D65D3×C11semidirect
50. C3⋊D39D5×C11semidirect
57. C3×C5×C13C2×D3×C11semidirect
59. C3×C5×C11D3×D13semidirect
61. C11×C13D5×C3⋊D3semidirect
63. D65C11×C3⋊D3semidirect
66. C32×C13C2×D5×C11semidirect
70. C32×C11D5×D13semidirect
71. C3⋊D15C11×D13semidirect
80. C5×C13C2×C11×C3⋊D3semidirect
82. C5×C11C3⋊D3×D13semidirect
84. C32×C5C2×C11×D13semidirect
86. C3×C13D3×D5×C11semidirect
88. C3×C11D15⋊D13semidirect
102. C3×C5D3×C11×D13semidirect
103. C13D5×C11×C3⋊D3semidirect
105. C11D65⋊(C3⋊D3)direct (N × H)
109. C32D5×C11×D13semidirect
113. C5C11×C3⋊D3×D13semidirect
115. C3C11×D15⋊D13semidirect

Maximal subgroups

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

subgroupindex
C32×C11×D652
C5×C11×C3⋊D392
C11×C13×C3⋊D152
C11×D15⋊D133
C11×C3⋊D3×D135
D65⋊(C3⋊D3)11
D5×C11×C3⋊D313