Finite Group Databasebeta

← C3×D11×D165 #36345310

Subgroups — C3×D11×D165 #36345310

Order 21780.

266 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 56 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×D11C211yesmaximal, characteristic, complemented
2C3×C11×D165C211yesmaximal, characteristic, complemented
3C3×C3⋊(C5⋊(C11⋊D11))C211yesmaximal, characteristic, complemented
4D11×D165C311yesmaximal, characteristic, direct product factor
5C3×D11×D55—31nomaximal
6C32×C5×C112C2211yescharacteristic, complemented, Hall
7C3×D11×D33—51nomaximal, Hall
8C3⋊(C5⋊(C11⋊D11))C2×C311yescharacteristic, complemented
9C11×D165C2×C311yescharacteristic, complemented
10C3×C5⋊(C11⋊D11)—31no—
11C3×C11×D55—31no—
12C3×C5×C11×D11—21no—
13C3×C5×C11×D11D311yescharacteristic, complemented
14C3×C5×C11×D11C2×C311yescharacteristic, complemented
15D11×D55—31noHall
16C3×C3⋊(C11⋊D11)—51no—
17C3×C11×D33—51no—
18C32×C11×D11D511yescharacteristic, complemented
19C2×C3×D165—111nomaximal
20C3×D11×D15—111nomaximal
21C3×C5×C112—21no—
22C3×C5×C112C2×D311yescharacteristic, complemented
23C3×C5×C112C22×C311yescharacteristic, complemented
24D11×D33—51no—
25C3×D112—151no—
26C5⋊(C11⋊D11)—31no—
27C11×D55—31no—
28C5×C11×D11C3×D311yescharacteristic, complemented
29C32×C112C2×D511yescharacteristic, complemented, Hall
30C2×C32×C5×C11—111no—
31C3×D165—111no—
32C3×D165—111no—
33C3×D165—225no—
34C3×D165D1111yescharacteristic, direct product factor
35C3×C11×D15—111no—
36C32×C5×D11D1111yescharacteristic, complemented
37C3⋊(C11⋊D11)—51no—
38C11×D33—51no—
39C3×C11⋊D11—151no—
40C3×C11×D11—21no—
41C3×C11×D11—151no—
42C3×C11×D11C3×D511yescharacteristic, complemented
43C3×C11×D11D1511yescharacteristic, complemented
44C2×D165—111no—
45C2×C3×D55—331no—
46D11×D15—111no—
47C3×D5×D11—331no—
48C5×C112C2×C3×D311yescharacteristic, complemented, Hall
49C32×C5×C11—25no—
50C32×C5×C11C2×D1111yescharacteristic, complemented
51C32×C5×C11C2×D1111yescharacteristic, complemented
52D112—151noHall
53C2×C3×D33—551no—
54C3×D3×D11—551no—
55C3×C112—21no—
56C3×C112C2×C3×D511yescharacteristic, complemented
57C3×C112C2×D1511yescharacteristic, complemented
58C2×C3×C5×C11—111no—
59C2×C3×C5×C11—111no—
60C2×C3×C5×C11—221no—
61D165—111no—
62D165—111no—
63D165—225no—
64D165C3×D1111yescharacteristic, direct product factor
65C11×D15—111no—
66C3×D55—31no—
67C3×D55—331no—
68C3×D55—331no—
69C3×D55—665no—
70C3×D5×C11—331no—
71C3×C5×D11—21no—
72C3×C5×D11C3×D1111yescharacteristic, complemented
73C3×C5×D11D3311yescharacteristic, complemented
74C11⋊D11—151no—
75C11×D11—151no—
76C11×D11C3×D1511yescharacteristic, complemented
77C2×D55—331no—
78D5×D11—331no—
79C2×C32×C11—111no—
80C3×D33—51no—
81C3×D33—551no—
82C3×D33—551no—
83C3×D33—1105no—
84C3×D3×C11—551no—
85C32×D11D5511yescharacteristic, complemented
86C2×C3×D15—1211noHall
87C3×C5×C11—25no—
88C3×C5×C11—25no—
89C3×C5×C11—21no—
90C3×C5×C11—21no—
91C3×C5×C11—45no—
92C3×C5×C11D3×D1111yescharacteristic, complemented
93C3×C5×C11C2×C3×D1111yescharacteristic, complemented
94C3×C5×C11C2×C3×D1111yescharacteristic, complemented
95C3×C5×C11C2×D3311yescharacteristic, complemented
96C2×D33—551no—
97C2×C3×D11—1651no—
98C2×C3×D11—1651no—
99D3×D11—551no—
100C112C2×C3×D1511yescharacteristic, complemented, Sylow
101C2×C5×C11—111no—
102D55—31no—
103D55—331no—
104D55—331no—
105D55—665no—
106C5×D11C3×D3311yescharacteristic, complemented
107D5×C11—331no—
108C32×C11—25no—
109C32×C11D5×D1111yescharacteristic, complemented
110C32×C11C2×D5511yescharacteristic, complemented
111C2×C32×C5—111no—
112C3×D15—111no—
113C3×D15—1211no—
114C2×C3×C11—111no—
115C2×C3×C11—111no—
116C2×C3×C11—221no—
117C2×C3×C11—1651no—
118D33—51no—
119D33—551no—
120D33—551no—
121D33—1105no—
122C3×D11—21no—
123C3×D11—151no—
124C3×D11—3305no—
125C3×D11—1651no—
126C3×D11—1651no—
127C3×D11C3×D5511yescharacteristic, complemented
128C3×D11D16511yescharacteristic, direct product factor
129D3×C11—551no—
130C2×D15—1211no—
131C2×C3×D5—3631no—
132C5×C11—25no—
133C5×C11C3×D3×D1111yescharacteristic, complemented
134C5×C11C2×C3×D3311yescharacteristic, complemented
135C32×C5D11211yescharacteristic, complemented, Hall
136C2×D11—1651no—
137C2×D11—1651no—
138C2×C3×D3—6051noHall
139C3×C11—21no—
140C3×C11—21no—
141C3×C11—25no—
142C3×C11—25no—
143C3×C11—45no—
144C3×C11C3×D5×D1111yescharacteristic, complemented
145C3×C11D11×D1511yescharacteristic, complemented
146C3×C11C2×C3×D5511yescharacteristic, complemented
147C3×C11C2×D16511yescharacteristic, complemented
148C2×C3×C5—111no—
149C2×C3×C5—111no—
150C2×C3×C5—221no—
151D15—111no—
152D15—1211no—
153C3×D5—331no—
154C3×D5—3631no—
155C2×C11—111no—
156C2×C11—1651no—
157D11—151no—
158D11—3305no—
159D11—1651no—
160D11—1651no—
161D11C3×D16511yescharacteristic, direct product factor
162C2×D5—3631noHall
163C2×C32—111no—
164C3×D3—551no—
165C3×D3—6051no—
166C3×C5—21no—
167C3×C5C3×D11211yescharacteristic, complemented
168C3×C5D11×D3311yescharacteristic, complemented
169C22×C3—18151no—
170C2×D3—6051no—
171C11—25no—
172C11C3×D11×D1511yescharacteristic, complemented
173C11C2×C3×D16511yescharacteristic, complemented
174C2×C5—111no—
175D5—331no—
176D5—3631no—
177C32D11×D5511yescharacteristic, complemented, Sylow
178C2×C3—111no—
179C2×C3—111no—
180C2×C3—221no—
181C2×C3—18151no—
182C2×C3—1651no—
183D3—551no—
184D3—6051no—
185C5C3×D11×D3311yescharacteristic, complemented, Sylow
186C22—18151noSylow
187C3—21no—
188C3C3×D11×D5511yescharacteristic, complemented
189C3D11×D16511yescharacteristic, direct product factor
190C2—111no—
191C2—18151no—
192C2—1651no—
subgroupG/H
center, hypercenterC3D11×D165
commutator, cosocle, hypocenterC3×C5×C112C22×C3
FrattiniC1G
Fitting, socleC32×C5×C112C22
LCSG ▷ C3×C5×C112
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C5×C11×D11C2semidirect
2. C3×C11×D165C2semidirect
3. C3×C3⋊(C5⋊(C11⋊D11))C2semidirect
4. D11×D165C3direct (N × H)
6. C32×C5×C112C22semidirect
8. C3⋊(C5⋊(C11⋊D11))C2×C3semidirect
9. C11×D165C2×C3semidirect
13. C3×C5×C11×D11D3semidirect
14. C3×C5×C11×D11C2×C3semidirect
18. C32×C11×D11D5semidirect
22. C3×C5×C112C2×D3semidirect
23. C3×C5×C112C22×C3semidirect
28. C5×C11×D11C3×D3semidirect
29. C32×C112C2×D5semidirect
34. C3×D165D11direct (N × H)
36. C32×C5×D11D11semidirect
42. C3×C11×D11C3×D5semidirect
43. C3×C11×D11D15semidirect
48. C5×C112C2×C3×D3semidirect
50. C32×C5×C11C2×D11semidirect
51. C32×C5×C11C2×D11semidirect
56. C3×C112C2×C3×D5semidirect
57. C3×C112C2×D15semidirect
64. D165C3×D11direct (N × H)
72. C3×C5×D11C3×D11semidirect
73. C3×C5×D11D33semidirect
76. C11×D11C3×D15semidirect
85. C32×D11D55semidirect
92. C3×C5×C11D3×D11semidirect
93. C3×C5×C11C2×C3×D11semidirect
94. C3×C5×C11C2×C3×D11semidirect
95. C3×C5×C11C2×D33semidirect
100. C112C2×C3×D15semidirect
106. C5×D11C3×D33semidirect
109. C32×C11D5×D11semidirect
110. C32×C11C2×D55semidirect
127. C3×D11C3×D55semidirect
128. C3×D11D165direct (N × H)
133. C5×C11C3×D3×D11semidirect
134. C5×C11C2×C3×D33semidirect
135. C32×C5D112semidirect
144. C3×C11C3×D5×D11semidirect
145. C3×C11D11×D15semidirect
146. C3×C11C2×C3×D55semidirect
147. C3×C11C2×D165semidirect
161. D11C3×D165direct (N × H)
167. C3×C5C3×D112semidirect
168. C3×C5D11×D33semidirect
172. C11C3×D11×D15semidirect
173. C11C2×C3×D165semidirect
177. C32D11×D55semidirect
185. C5C3×D11×D33semidirect
188. C3C3×D11×D55semidirect
189. C3D11×D165direct (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×D112
C3×C11×D1652
C3×C3⋊(C5⋊(C11⋊D11))2
D11×D1653
C3×D11×D553
C3×D11×D335
C2×C3×D16511
C3×D11×D1511