Finite Group Databasebeta

← D3×C11×D165 #36345331

Subgroups — D3×C11×D165 #36345331

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
1C3×C5×D3×C112C211yesmaximal, characteristic, complemented
2C3×C11×D165C211yesmaximal, characteristic, complemented
3C11×C3⋊D165C211yesmaximal, characteristic, complemented
4C2×C11×D165—31nomaximal
5D3×C11×D55—31nomaximal
6C32×C5×C112C2211yescharacteristic, complemented, Hall
7D3×C11×D33—51nomaximal, Hall
8C11×D165—31no—
9C11×D165—31no—
10C11×D165—61no—
11C11×D165D311yescharacteristic, direct product factor
12C5×D3×C112D311yescharacteristic, complemented
13C3×C11×D55—31no—
14C2×C3×C5×C112—31no—
15C2×C11×D55—91noHall
16C11×C3⋊D33—51no—
17C3×C11×D33—51no—
18C3×D3×C112D511yescharacteristic, complemented
19D3×D165C1111yesmaximal, characteristic, direct product factor
20D3×C11×D15—111nomaximal
21C3×C5×C112—21no—
22C3×C5×C112C2×D311yescharacteristic, complemented
23C3×C5×C112C2×D311yescharacteristic, complemented
24C2×C11×D33—151no—
25D3×C11×D11—151no—
26C2×C5×C112—31no—
27C11×D55—31no—
28C11×D55—91no—
29C32×C112C2×D511yescharacteristic, complemented, Hall
30C3⋊D165C2×C1111yescharacteristic, complemented
31C11×C3⋊D15—111no—
32C3×D165C2×C1111yescharacteristic, complemented
33C3×C11×D15—111no—
34C3×C5×D3×C11—25no—
35C3×C5×D3×C11D1111yescharacteristic, complemented
36C3×C5×D3×C11C2×C1111yescharacteristic, complemented
37C2×C3×C112—31no—
38C11×D33—51no—
39C11×D33—151no—
40C11×D33—151no—
41C11×D33—301no—
42D3×C112D1511yescharacteristic, complemented
43C3×C11×D11—151no—
44C2×D165—31no—
45C2×C11×D15—331no—
46D3×D55—31no—
47D3×D5×C11—331no—
48C5×C112D3211yescharacteristic, complemented, Hall
49C32×C5×C11—25no—
50C32×C5×C11C2×D1111yescharacteristic, complemented
51C32×C5×C11C22×C1111yescharacteristic, complemented
52C2×C11×D11—451noHall
53D3×D33—51no—
54D32×C11—551no—
55C3×C112—21no—
56C3×C112D3×D511yescharacteristic, complemented
57C3×C112C2×D1511yescharacteristic, complemented
58C2×C3×C5×C11—31no—
59C2×C3×C5×C11—31no—
60C2×C3×C5×C11—65no—
61D165—31no—
62D165—31no—
63D165—61no—
64D165D3×C1111yescharacteristic, direct product factor
65C11×D15—111no—
66C11×D15—331no—
67C11×D15—331no—
68C11×D15—661no—
69C5×D3×C11—25no—
70C5×D3×C11D3×C1111yescharacteristic, complemented
71C5×D3×C11D3311yescharacteristic, complemented
72C3×D55—31no—
73C3×D5×C11—331no—
74C2×C112—31no—
75C11×D11—151no—
76C11×D11—451no—
77C2×D55—91no—
78C2×D5×C11—991no—
79C3⋊D33—51no—
80C11×C3⋊D3—551no—
81C3×D33—51no—
82C3×D3×C11—25no—
83C3×D3×C11—551no—
84C3×D3×C11D5×C1111yescharacteristic, complemented
85C3×D3×C11D5511yescharacteristic, complemented
86D3×D15—111noHall
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×D3×C1111yescharacteristic, complemented
94C3×C5×C11C2×D3×C1111yescharacteristic, complemented
95C3×C5×C11C2×D3311yescharacteristic, complemented
96C2×D33—151no—
97C2×D3×C11—1651no—
98C2×D3×C11—1651no—
99D3×D11—151no—
100C112D3×D1511yescharacteristic, complemented, Sylow
101C2×C5×C11—31no—
102C2×C5×C11—31no—
103C2×C5×C11—65no—
104D55—31no—
105D55—91no—
106D5×C11—331no—
107D5×C11—991no—
108C32×C11—25no—
109C32×C11C2×D5×C1111yescharacteristic, complemented
110C32×C11C2×D5511yescharacteristic, complemented
111C3⋊D15—111no—
112C3×D15—111no—
113C3×C5×D3C11×D1111yescharacteristic, complemented
114C2×C3×C11—31no—
115C2×C3×C11—31no—
116C2×C3×C11—65no—
117C2×C3×C11—1651no—
118D33—51no—
119D33—151no—
120D33—151no—
121D33—301no—
122C3×D11—151no—
123D3×C11—25no—
124D3×C11—551no—
125D3×C11—3301no—
126D3×C11—1651no—
127D3×C11—1651no—
128D3×C11C11×D1511yescharacteristic, complemented
129D3×C11D16511yescharacteristic, direct product factor
130C2×D15—331no—
131D3×D5—331no—
132C5×C11—25no—
133C5×C11D32×C1111yescharacteristic, complemented
134C5×C11D3×D3311yescharacteristic, complemented
135C32×C5C2×C11×D1111yescharacteristic, complemented, Hall
136C22×C11—4951no—
137C2×D11—451no—
138D32—551noHall
139C3×C11—21no—
140C3×C11—21no—
141C3×C11—25no—
142C3×C11—25no—
143C3×C11—45no—
144C3×C11D3×D5×C1111yescharacteristic, complemented
145C3×C11D3×D5511yescharacteristic, complemented
146C3×C11C2×C11×D1511yescharacteristic, complemented
147C3×C11C2×D16511yescharacteristic, complemented
148C2×C3×C5—31no—
149D15—111no—
150D15—331no—
151D15—331no—
152D15—661no—
153C3×D5—331no—
154C5×D3C11×D3311yescharacteristic, complemented
155C2×C11—31no—
156C2×C11—31no—
157C2×C11—65no—
158C2×C11—1651no—
159C2×C11—4951no—
160D11—151no—
161D11—451no—
162C2×D5—991noHall
163C3⋊D3—551no—
164C3×D3—551no—
165C3×D3C11×D5511yescharacteristic, complemented
166C3×C5—21no—
167C3×C5D3×C11×D1111yescharacteristic, complemented
168C3×C5C2×C11×D3311yescharacteristic, complemented
169C2×D3—1651no—
170C2×D3—1651no—
171C11—25no—
172C11D3×C11×D1511yescharacteristic, complemented
173C11D3×D16511yescharacteristic, direct product factor
174C2×C5—31no—
175D5—331no—
176D5—991no—
177C32C2×C11×D5511yescharacteristic, complemented, Sylow
178C2×C3—31no—
179C2×C3—1651no—
180D3—551no—
181D3—3301no—
182D3—1651no—
183D3—1651no—
184D3C11×D16511yescharacteristic, direct product factor
185C5D3×C11×D3311yescharacteristic, complemented, Sylow
186C22—4951noSylow
187C3—21no—
188C3D3×C11×D5511yescharacteristic, complemented
189C3C2×C11×D16511yescharacteristic, complemented
190C2—31no—
191C2—1651no—
192C2—4951no—
subgroupG/H
center, hypercenterC11D3×D165
commutator, cosocle, hypocenterC32×C5×C11C22×C11
FrattiniC1G
Fitting, socleC32×C5×C112C22
LCSG ▷ C32×C5×C11
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C3×C5×D3×C112C2semidirect
2. C3×C11×D165C2semidirect
3. C11×C3⋊D165C2semidirect
6. C32×C5×C112C22semidirect
11. C11×D165D3direct (N × H)
12. C5×D3×C112D3semidirect
18. C3×D3×C112D5semidirect
19. D3×D165C11direct (N × H)
22. C3×C5×C112C2×D3semidirect
23. C3×C5×C112C2×D3semidirect
29. C32×C112C2×D5semidirect
30. C3⋊D165C2×C11semidirect
32. C3×D165C2×C11semidirect
35. C3×C5×D3×C11D11semidirect
36. C3×C5×D3×C11C2×C11semidirect
42. D3×C112D15semidirect
48. C5×C112D32semidirect
50. C32×C5×C11C2×D11semidirect
51. C32×C5×C11C22×C11semidirect
56. C3×C112D3×D5semidirect
57. C3×C112C2×D15semidirect
64. D165D3×C11direct (N × H)
70. C5×D3×C11D3×C11semidirect
71. C5×D3×C11D33semidirect
84. C3×D3×C11D5×C11semidirect
85. C3×D3×C11D55semidirect
92. C3×C5×C11D3×D11semidirect
93. C3×C5×C11C2×D3×C11semidirect
94. C3×C5×C11C2×D3×C11semidirect
95. C3×C5×C11C2×D33semidirect
100. C112D3×D15semidirect
109. C32×C11C2×D5×C11semidirect
110. C32×C11C2×D55semidirect
113. C3×C5×D3C11×D11semidirect
128. D3×C11C11×D15semidirect
129. D3×C11D165direct (N × H)
133. C5×C11D32×C11semidirect
134. C5×C11D3×D33semidirect
135. C32×C5C2×C11×D11semidirect
144. C3×C11D3×D5×C11semidirect
145. C3×C11D3×D55semidirect
146. C3×C11C2×C11×D15semidirect
147. C3×C11C2×D165semidirect
154. C5×D3C11×D33semidirect
165. C3×D3C11×D55semidirect
167. C3×C5D3×C11×D11semidirect
168. C3×C5C2×C11×D33semidirect
172. C11D3×C11×D15semidirect
173. C11D3×D165direct (N × H)
177. C32C2×C11×D55semidirect
184. D3C11×D165direct (N × H)
185. C5D3×C11×D33semidirect
188. C3D3×C11×D55semidirect
189. C3C2×C11×D165semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D3×C1122
C3×C11×D1652
C11×C3⋊D1652
C2×C11×D1653
D3×C11×D553
D3×C11×D335
D3×D16511
D3×C11×D1511