Finite Group Databasebeta

← C52×D11×D33 #49137743

Subgroups — C52×D11×D33 #49137743

Order 36300.

480 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 128 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
1C3×C52×C11×D11C211yesmaximal, characteristic, complemented
2C52×C11×D33C211yesmaximal, characteristic, complemented
3C52×C3⋊(C11⋊D11)C211yesmaximal, characteristic, complemented
4C52×D112—31nomaximal, Hall
5C3×C52×C112C2211yescharacteristic, complemented, Hall
6C5×D11×D33C516yesmaximal, direct product factor
7C52×C11⋊D11—31no—
8C52×C11×D11—31no—
9C52×C11×D11D311yescharacteristic, complemented
10C5×C3⋊(C11⋊D11)C2×C516yescomplemented
11C5×C11×D33C2×C516yescomplemented
12C3×C5×C11×D11C2×C516yescomplemented
13C2×C52×D33—111nomaximal
14C52×D3×D11—111nomaximal
15C52×C112C2×D311yescharacteristic, complemented, Hall
16C5×D112—36no—
17C3×C5×C112C22×C516yescomplemented
18C2×C3×C52×C11—111no—
19C52×D33—111no—
20C52×D33—111no—
21C52×D33—225no—
22C52×D33D1111yescharacteristic, direct product factor
23C52×D3×C11—111no—
24C3×C52×D11D1111yescharacteristic, complemented
25D11×D33C5211yescharacteristic, direct product factor, Hall
26C5×C11⋊D11—36no—
27C5×C11×D11—36no—
28C5×C11×D11C5×D316yescomplemented
29C2×C52×D11—331no—
30C2×C52×D11—331no—
31C3×C52×C11—25no—
32C3×C52×C11C2×D1111yescharacteristic, complemented
33C3×C52×C11C2×D1111yescharacteristic, complemented
34C3⋊(C11⋊D11)C2×C5211yescharacteristic, complemented
35C11×D33C2×C5211yescharacteristic, complemented
36C3×C11×D11C2×C5211yescharacteristic, complemented
37C2×C5×D33—116no—
38C5×D3×D11—116no—
39C5×C112C2×C5×D316yescomplemented
40C2×C52×C11—111no—
41C2×C52×C11—331no—
42C52×D11—31no—
43C52×D11—331no—
44C52×D11—331no—
45C52×D11—665no—
46C52×D11D3311yescharacteristic, direct product factor
47D112—31noHall
48C3×C112C22×C5211yescharacteristic, complemented, Hall
49C2×C3×C5×C11—116no—
50C5×D33—116no—
51C5×D33—116no—
52C5×D33—2230no—
53C5×D33C5×D1116yesdirect product factor
54C5×D3×C11—116no—
55C3×C5×D11C5×D1116yescomplemented
56C2×C52×D3—1211noHall
57C52×C11—25no—
58C52×C11D3×D1111yescharacteristic, complemented
59C52×C11C2×D3311yescharacteristic, complemented
60C11⋊D11—31no—
61C11×D11—31no—
62C11×D11C52×D311yescharacteristic, complemented
63C2×C5×D11—336no—
64C2×C5×D11—336no—
65C3×C5×C11—230no—
66C3×C5×C11C2×C5×D1116yescomplemented
67C3×C5×C11C2×C5×D1116yescomplemented
68C2×C3×C52—111no—
69C52×D3—111no—
70C52×D3—1211no—
71C2×D33—111no—
72D3×D11—111no—
73C112C2×C52×D311yescharacteristic, complemented, Sylow
74C2×C5×C11—116no—
75C2×C5×C11—336no—
76C5×D11—36no—
77C5×D11—336no—
78C5×D11—336no—
79C5×D11—6630no—
80C5×D11C5×D3316yesdirect product factor
81C22×C52—3631noHall
82C3×C52D11211yescharacteristic, complemented, Hall
83C2×C3×C11—111no—
84D33—111no—
85D33—111no—
86D33—225no—
87D33C52×D1111yescharacteristic, direct product factor
88C3×D11C52×D1111yescharacteristic, complemented
89D3×C11—111no—
90C2×C5×D3—1216no—
91C5×C11—230no—
92C5×C11C5×D3×D1116yescomplemented
93C5×C11C2×C5×D3316yescomplemented
94C2×C52—111no—
95C2×C52—331no—
96C2×C52—3631no—
97C2×D11—331no—
98C2×D11—331no—
99C3×C11—25no—
100C3×C11C2×C52×D1111yescharacteristic, complemented
101C3×C11C2×C52×D1111yescharacteristic, complemented
102C2×C3×C5—116no—
103C5×D3—116no—
104C5×D3—1216no—
105C52D11×D3311yescharacteristic, direct product factor, Sylow
106C2×C11—111no—
107C2×C11—331no—
108D11—31no—
109D11—331no—
110D11—331no—
111D11—665no—
112D11C52×D3311yescharacteristic, direct product factor
113C22×C5—3636no—
114C3×C5C5×D11216yescomplemented
115C2×D3—1211noHall
116C11—25no—
117C11C52×D3×D1111yescharacteristic, complemented
118C11C2×C52×D3311yescharacteristic, complemented
119C2×C5—116no—
120C2×C5—336no—
121C2×C5—3636no—
122C2×C3—111no—
123D3—111no—
124D3—1211no—
125C5C5×D11×D3316yesdirect product factor
126C22—3631noSylow
127C3C52×D11211yescharacteristic, complemented, Sylow
128C2—111no—
129C2—331no—
130C2—3631no—
subgroupG/H
center, hypercenterC52D11×D33
commutator, cosocle, hypocenterC3×C112C22×C52
FrattiniC1G
Fitting, socleC3×C52×C112C22
LCSG ▷ C3×C112
UCSC1 ◁ C52

Complements

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

NH ≅ G/Ntype
1. C3×C52×C11×D11C2semidirect
2. C52×C11×D33C2semidirect
3. C52×C3⋊(C11⋊D11)C2semidirect
5. C3×C52×C112C22semidirect
6. C5×D11×D33C5direct (N × H)
9. C52×C11×D11D3semidirect
10. C5×C3⋊(C11⋊D11)C2×C5semidirect
11. C5×C11×D33C2×C5semidirect
12. C3×C5×C11×D11C2×C5semidirect
15. C52×C112C2×D3semidirect
17. C3×C5×C112C22×C5semidirect
22. C52×D33D11direct (N × H)
24. C3×C52×D11D11semidirect
25. D11×D33C52direct (N × H)
28. C5×C11×D11C5×D3semidirect
32. C3×C52×C11C2×D11semidirect
33. C3×C52×C11C2×D11semidirect
34. C3⋊(C11⋊D11)C2×C52semidirect
35. C11×D33C2×C52semidirect
36. C3×C11×D11C2×C52semidirect
39. C5×C112C2×C5×D3semidirect
46. C52×D11D33direct (N × H)
48. C3×C112C22×C52semidirect
53. C5×D33C5×D11direct (N × H)
55. C3×C5×D11C5×D11semidirect
58. C52×C11D3×D11semidirect
59. C52×C11C2×D33semidirect
62. C11×D11C52×D3semidirect
66. C3×C5×C11C2×C5×D11semidirect
67. C3×C5×C11C2×C5×D11semidirect
73. C112C2×C52×D3semidirect
80. C5×D11C5×D33direct (N × H)
82. C3×C52D112semidirect
87. D33C52×D11direct (N × H)
88. C3×D11C52×D11semidirect
92. C5×C11C5×D3×D11semidirect
93. C5×C11C2×C5×D33semidirect
100. C3×C11C2×C52×D11semidirect
101. C3×C11C2×C52×D11semidirect
105. C52D11×D33direct (N × H)
112. D11C52×D33direct (N × H)
114. C3×C5C5×D112semidirect
117. C11C52×D3×D11semidirect
118. C11C2×C52×D33semidirect
125. C5C5×D11×D33direct (N × H)
127. C3C52×D112semidirect

Maximal subgroups

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

subgroupindex
C3×C52×C11×D112
C52×C11×D332
C52×C3⋊(C11⋊D11)2
C52×D1123
C5×D11×D335
C2×C52×D3311
C52×D3×D1111