Finite Group Databasebeta

← #49137498

Subgroups — #49137498

Order 36300.

200 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 40 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
1C11×C3⋊(C5⋊AGL(1,𝔽11))C211yesmaximal, characteristic, complemented
2C5×C3⋊((C11⋊C5)⋊D11)C211yesmaximal, characteristic, complemented
3C3×C11⋊C5×D55C211yesmaximal, characteristic, complemented
4(C5⋊AGL(1,𝔽11))⋊D11—31nomaximal, Hall
5C3×C5×C11×C11⋊C5C2211yescharacteristic, complemented, Hall
6D55⋊D33C511yesmaximal, characteristic, complemented
7D11×C3⋊AGL(1,𝔽11)—51nomaximal
8C11⋊C5×D55D311yescharacteristic, complemented
9C11×C5⋊AGL(1,𝔽11)—31no—
10C5×(C11⋊C5)⋊D11—31no—
11C11×D165C2×C511yescharacteristic, complemented
12C5×C3⋊(C11⋊D11)C2×C511yescharacteristic, complemented
13C3×C11×D55C2×C511yescharacteristic, complemented
14C3⋊((C11⋊C5)⋊D11)—21no—
15C3⋊((C11⋊C5)⋊D11)—21no—
16C3⋊((C11⋊C5)⋊D11)D511yescharacteristic, complemented
17C11×C3⋊AGL(1,𝔽11)—51no—
18C3×D11×C11⋊C5—51no—
19C5×D15⋊D11—111nomaximal
20D5×C3⋊AGL(1,𝔽11)—111nomaximal
21C5×C11×C11⋊C5C2×D311yescharacteristic, complemented, Hall
22D55⋊D11—31no—
23D11×AGL(1,𝔽11)—151no—
24C3×C5×C112C22×C511yescharacteristic, complemented
25C3×C11×C11⋊C5—21no—
26C3×C11×C11⋊C5—21no—
27C3×C11×C11⋊C5C2×D511yescharacteristic, complemented
28C5×C11×D15—111no—
29C52×D33—111no—
30C3×C5×D55—221no—
31C3⋊(C5⋊AGL(1,𝔽11))D1111yescharacteristic, complemented
32C5×C3⋊AGL(1,𝔽11)—111no—
33C3×D5×C11⋊C5—111no—
34D11×D33—51noHall
35C11×D55—31no—
36C11×D55C5×D311yescharacteristic, complemented
37C5×C11⋊D11—31no—
38D11×C11⋊C5—51no—
39(C11⋊C5)⋊D11—31no—
40(C11⋊C5)⋊D11—61no—
41(C11⋊C5)⋊D11—61no—
42C11×AGL(1,𝔽11)—151no—
43C5×D5×D11—331no—
44D5×AGL(1,𝔽11)—331no—
45C3×C52×C11—221no—
46C3×C5×C11⋊C5C2×D1111yescharacteristic, complemented
47C3⋊(C11⋊D11)C5×D511yescharacteristic, complemented
48C11×D33—51no—
49C3×C11×D11—51no—
50D15⋊D11—111no—
51D5×D33—111no—
52C5×D3×D11—551no—
53C2×C3⋊AGL(1,𝔽11)—551no—
54C5×C112C2×C5×D311yescharacteristic, complemented
55C11×C11⋊C5—21no—
56C11×C11⋊C5—21no—
57C11×C11⋊C5D3×D511yescharacteristic, complemented
58C5×D55—221no—
59C5×D5×C11—331no—
60C52×D11—331no—
61C5⋊AGL(1,𝔽11)—31no—
62D5×C11⋊C5—111no—
63C5×AGL(1,𝔽11)—331no—
64D112—151noHall
65C3×C112C2×C5×D511yescharacteristic, complemented, Hall
66D165C5×D1111yescharacteristic, complemented
67C11×D15—111no—
68C5×D33—111no—
69C5×D33—111no—
70C5×D33—111no—
71C5×D33—221no—
72C5×D33—221no—
73C5×D33—1101no—
74C5×D3×C11—551no—
75C3×D55AGL(1,𝔽11)11yescharacteristic, complemented
76C3×D5×C11—111no—
77C3×C5×D11—1101no—
78C2×C3×C11⋊C5—551no—
79C3⋊AGL(1,𝔽11)—51no—
80C3⋊AGL(1,𝔽11)—111no—
81C3⋊AGL(1,𝔽11)—221no—
82C3⋊AGL(1,𝔽11)—221no—
83C5×D3×D5—1211noHall
84C52×C11—221no—
85C5×C11⋊C5D3×D1111yescharacteristic, complemented
86C11⋊D11—31no—
87C11×D11—51no—
88C11×D11—151no—
89C2×C5×D11—1651no—
90D5×D11—331no—
91D5×D11—331no—
92C2×AGL(1,𝔽11)—1651no—
93C3×C5×C11—101no—
94C3×C5×C11—221no—
95C3×C5×C11—441no—
96C3×C5×C11—441no—
97C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
98C3×C5×C11C2×C5×D1111yescharacteristic, complemented
99C3×C11⋊C5—21no—
100C3×C11⋊C5—21no—
101C3×C11⋊C5D5×D1111yescharacteristic, complemented
102C5×D15—111no—
103C52×D3—1211no—
104C3×C5×D5—2421no—
105C2×D33—551no—
106D3×D11—551no—
107C112C5×D3×D511yescharacteristic, complemented, Sylow
108C2×C5×C11—1651no—
109D55—31no—
110D55C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
111C5×D11—331no—
112C5×D11—331no—
113C5×D11—331no—
114C5×D11—661no—
115C5×D11—661no—
116C5×D11—3301no—
117C5×D11—1101no—
118D5×C11—111no—
119D5×C11—331no—
120C2×C11⋊C5—551no—
121AGL(1,𝔽11)—151no—
122AGL(1,𝔽11)—331no—
123AGL(1,𝔽11)—661no—
124AGL(1,𝔽11)—661no—
125C2×C5×D5—3631noHall
126C3×C52—221noHall
127C2×C3×C11—551no—
128D33—51no—
129D33—111no—
130D33—111no—
131D33—1101no—
132C3×D11—51no—
133D3×C11—551no—
134C2×C5×D3—6051no—
135D3×D5—1211no—
136C5×C11—101no—
137C5×C11—221no—
138C5×C11—221no—
139C5×C11—441no—
140C5×C11C2×C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
141C5×C11C5×D3×D1111yescharacteristic, complemented
142C11⋊C5—21no—
143C11⋊C5—21no—
144C11⋊C5D15⋊D1111yescharacteristic, complemented
145C2×C52—3631no—
146C5×D5—331no—
147C5×D5—2421no—
148C2×D11—1651no—
149C2×D11—1651no—
150C3×C11—101no—
151C3×C11D5×AGL(1,𝔽11)11yescharacteristic, complemented
152C3×C11C5×D5×D1111yescharacteristic, complemented
153C2×C3×C5—12101no—
154D15—111no—
155C3×D5—111no—
156C5×D3—551no—
157C5×D3—1211no—
158C5×D3—1211no—
159C5×D3—2421no—
160C5×D3—2421no—
161C52—221noSylow
162C2×C11—551no—
163C2×C11—1651no—
164D11—51no—
165D11—151no—
166D11—331no—
167D11—331no—
168D11—3301no—
169C22×C5—18151no—
170C2×D5—3631no—
171C3×C5—221no—
172C3×C5—221no—
173C3×C5—441no—
174C3×C5D11×AGL(1,𝔽11)11yescharacteristic, complemented
175C2×D3—6051noHall
176C11—101no—
177C11D5×C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
178C11C5×D15⋊D1111yescharacteristic, complemented
179C2×C5—3631no—
180C2×C5—3631no—
181C2×C5—1651no—
182C2×C5—12101no—
183C2×C5—7261no—
184C2×C5—7261no—
185D5—111no—
186D5—331no—
187C2×C3—551no—
188D3—551no—
189D3—1211no—
190C5—221no—
191C5—441no—
192C5—441no—
193C5D11×C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
194C22—18151noSylow
195C3(C5⋊AGL(1,𝔽11))⋊D1111yescharacteristic, complemented, Sylow
196C2—551no—
197C2—3631no—
198C2—1651no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C112C22×C5
LCSG ▷ C3×C5×C112
UCSC1

Complements

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

NH ≅ G/Ntype
1. C11×C3⋊(C5⋊AGL(1,𝔽11))C2semidirect
2. C5×C3⋊((C11⋊C5)⋊D11)C2semidirect
3. C3×C11⋊C5×D55C2semidirect
5. C3×C5×C11×C11⋊C5C22semidirect
6. D55⋊D33C5semidirect
8. C11⋊C5×D55D3semidirect
11. C11×D165C2×C5semidirect
12. C5×C3⋊(C11⋊D11)C2×C5semidirect
13. C3×C11×D55C2×C5semidirect
16. C3⋊((C11⋊C5)⋊D11)D5semidirect
21. C5×C11×C11⋊C5C2×D3semidirect
24. C3×C5×C112C22×C5semidirect
27. C3×C11×C11⋊C5C2×D5semidirect
31. C3⋊(C5⋊AGL(1,𝔽11))D11semidirect
36. C11×D55C5×D3semidirect
46. C3×C5×C11⋊C5C2×D11semidirect
47. C3⋊(C11⋊D11)C5×D5semidirect
54. C5×C112C2×C5×D3semidirect
57. C11×C11⋊C5D3×D5semidirect
65. C3×C112C2×C5×D5semidirect
66. D165C5×D11semidirect
75. C3×D55AGL(1,𝔽11)semidirect
85. C5×C11⋊C5D3×D11semidirect
97. C3×C5×C11C2×AGL(1,𝔽11)semidirect
98. C3×C5×C11C2×C5×D11semidirect
101. C3×C11⋊C5D5×D11semidirect
107. C112C5×D3×D5semidirect
110. D55C3⋊AGL(1,𝔽11)semidirect
140. C5×C11C2×C3⋊AGL(1,𝔽11)semidirect
141. C5×C11C5×D3×D11semidirect
144. C11⋊C5D15⋊D11semidirect
151. C3×C11D5×AGL(1,𝔽11)semidirect
152. C3×C11C5×D5×D11semidirect
174. C3×C5D11×AGL(1,𝔽11)semidirect
177. C11D5×C3⋊AGL(1,𝔽11)semidirect
178. C11C5×D15⋊D11semidirect
193. C5D11×C3⋊AGL(1,𝔽11)semidirect
195. C3(C5⋊AGL(1,𝔽11))⋊D11semidirect

Maximal subgroups

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

subgroupindex
C11×C3⋊(C5⋊AGL(1,𝔽11))2
C5×C3⋊((C11⋊C5)⋊D11)2
C3×C11⋊C5×D552
(C5⋊AGL(1,𝔽11))⋊D113
D55⋊D335
D11×C3⋊AGL(1,𝔽11)5
C5×D15⋊D1111
D5×C3⋊AGL(1,𝔽11)11