Finite Group Databasebeta

← C11×C3⋊D3×D65 #38788284

Subgroups — C11×C3⋊D3×D65 #38788284

Order 25740.

240 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 72 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×C13×C3⋊D3C211yesmaximal, characteristic, complemented
3C11×C3⋊D195C211yesmaximal, characteristic, complemented
4D3×C11×D65—34nomaximal
5C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
6C11×C3⋊D3×D13—51nomaximal, Hall
7C11×D195—34no—
8C5×D3×C11×C13—34no—
9C3×C11×D65D314yescomplemented
10C2×C11×D65—91noHall
11C11×C3⋊D39—51no—
12C11×C13×C3⋊D3D511yescharacteristic, complemented
13C32×C11×D13—51no—
14C3⋊D3×D65C1111yesmaximal, characteristic, direct product factor, Hall
15C3×C5×C11×C13C2×D314yescomplemented
16D5×C11×C3⋊D3—131nomaximal, Hall
17D3×C11×D13—154no—
18C2×C5×C11×C13—91no—
19C11×D65—91no—
20C11×D65C3⋊D311yescharacteristic, direct product factor
21C32×C11×C13C2×D511yescharacteristic, complemented, Hall
22C3⋊D195C2×C1111yescharacteristic, complemented
23C5×C13×C3⋊D3C2×C1111yescharacteristic, complemented
24C32×D65C2×C1111yescharacteristic, complemented
25C11×C3⋊D15—131no—
26C5×C11×C3⋊D3D1311yescharacteristic, complemented
27C32×D5×C11—131no—
28C11×D39—154no—
29D3×C11×C13—34no—
30C3×C11×D13—54no—
31D3×D65—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
40D195—34no—
41C5×D3×C13—34no—
42C3×D65D3×C1114yescomplemented
43C11×D15—394no—
44C5×D3×C11—34no—
45C3×D5×C11—134no—
46C2×C11×C13—91no—
47C11×D13—51no—
48C11×D13—451no—
49C2×D65—91noHall
50C3⋊D39—51no—
51C13×C3⋊D3D5×C1111yescharacteristic, complemented
52C32×D13—51no—
53C2×D5×C11—1171noHall
54C2×C32×C11—651no—
55C11×C3⋊D3—651no—
56C11×C3⋊D3D6511yescharacteristic, direct product factor
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—
63C2×C5×C13—91no—
64D65—91no—
65D65C11×C3⋊D311yescharacteristic, direct product factor
66C32×C13C2×D5×C1111yescharacteristic, complemented, Hall
67C2×C5×C11—91no—
68D5×C11—131no—
69D5×C11—1171no—
70C32×C11C2×D6511yescharacteristic, complemented, Hall
71C3⋊D15—131no—
72C5×C3⋊D3C11×D1311yescharacteristic, complemented
73C32×D5—131no—
74D39—154no—
75C3×D13—54no—
76D3×C13—34no—
77C2×C3×C11—654no—
78D3×C11—34no—
79D3×C11—1954no—
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×C11D3×D6514yescomplemented
89D15—394no—
90C3×D5—134no—
91C5×D3—34no—
92C2×C13—91no—
93D13—51no—
94D13—451no—
95C2×C11—91no—
96C2×C11—651no—
97C2×C11—5851no—
98C2×D5—1171noHall
99C2×C32—651no—
100C3⋊D3—651no—
101C3⋊D3C11×D6511yescharacteristic, direct product factor
102C3×C5D3×C11×D1314yescomplemented
103C13D5×C11×C3⋊D311yescharacteristic, complemented, Sylow
104C2×D3—1954no—
105C11C3⋊D3×D6511yescharacteristic, direct product factor, Sylow
106C2×C5—91no—
107D5—131no—
108D5—1171no—
109C32C2×C11×D6511yescharacteristic, complemented, Sylow
110C2×C3—654no—
111D3—34no—
112D3—1954no—
113C5C11×C3⋊D3×D1311yescharacteristic, complemented, Sylow
114C22—5851noSylow
115C3D3×C11×D6514yescomplemented
116C2—91no—
117C2—651no—
118C2—5851no—
subgroupG/H
center, hypercenterC11C3⋊D3×D65
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×C13×C3⋊D3C2semidirect
3. C11×C3⋊D195C2semidirect
5. C32×C5×C11×C13C22semidirect
9. C3×C11×D65D3semidirect
12. C11×C13×C3⋊D3D5semidirect
14. C3⋊D3×D65C11direct (N × H)
15. C3×C5×C11×C13C2×D3semidirect
20. C11×D65C3⋊D3direct (N × H)
21. C32×C11×C13C2×D5semidirect
22. C3⋊D195C2×C11semidirect
23. C5×C13×C3⋊D3C2×C11semidirect
24. C32×D65C2×C11semidirect
26. C5×C11×C3⋊D3D13semidirect
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
51. C13×C3⋊D3D5×C11semidirect
56. C11×C3⋊D3D65direct (N × H)
57. C3×C5×C13C2×D3×C11semidirect
59. C3×C5×C11D3×D13semidirect
61. C11×C13D5×C3⋊D3semidirect
65. D65C11×C3⋊D3direct (N × H)
66. C32×C13C2×D5×C11semidirect
70. C32×C11C2×D65semidirect
72. C5×C3⋊D3C11×D13semidirect
80. C5×C13C2×C11×C3⋊D3semidirect
82. C5×C11C3⋊D3×D13semidirect
84. C32×C5C2×C11×D13semidirect
86. C3×C13D3×D5×C11semidirect
88. C3×C11D3×D65semidirect
101. C3⋊D3C11×D65direct (N × H)
102. C3×C5D3×C11×D13semidirect
103. C13D5×C11×C3⋊D3semidirect
105. C11C3⋊D3×D65direct (N × H)
109. C32C2×C11×D65semidirect
113. C5C11×C3⋊D3×D13semidirect
115. C3D3×C11×D65semidirect

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×C13×C3⋊D32
C11×C3⋊D1952
D3×C11×D653
C11×C3⋊D3×D135
C3⋊D3×D6511
D5×C11×C3⋊D313