Finite Group Databasebeta

← D33×C5⋊AGL(1,𝔽11) #49137494

Subgroups — D33×C5⋊AGL(1,𝔽11) #49137494

Order 36300.

200 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 42 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⋊((C11⋊C5)⋊D11))C211yesmaximal, characteristic, complemented
2C5×C11⋊C5×D33C211yesmaximal, characteristic, complemented
3C3×C11×C5⋊AGL(1,𝔽11)C211yesmaximal, characteristic, complemented
4D11×C5⋊AGL(1,𝔽11)—31nomaximal, Hall
5C3×C5×C11×C11⋊C5C2211yescharacteristic, complemented, Hall
6D33×D55C511yesmaximal, characteristic, complemented
7D33×AGL(1,𝔽11)—51nomaximal
8C5⋊((C11⋊C5)⋊D11)—31no—
9C11×C5⋊AGL(1,𝔽11)D311yescharacteristic, complemented
10C5×D11×C11⋊C5—31no—
11C3⋊(C5⋊(C11⋊D11))C2×C511yescharacteristic, complemented
12C5×C11×D33C2×C511yescharacteristic, complemented
13C3×C11×D55C2×C511yescharacteristic, complemented
14C11⋊C5×D33—22no—
15C11⋊C5×D33D511yescharacteristic, complemented
16C3⋊((C11⋊C5)⋊D11)—51no—
17C3×C11×AGL(1,𝔽11)—51no—
18C5×D5×D33—111nomaximal
19D3×C5⋊AGL(1,𝔽11)—111nomaximal
20C5×C11×C11⋊C5C2×D311yescharacteristic, complemented, Hall
21D11×D55—31no—
22D11×AGL(1,𝔽11)—151no—
23C3×C5×C112C22×C511yescharacteristic, complemented
24C3×C11×C11⋊C5—22no—
25C3×C11×C11⋊C5C2×D511yescharacteristic, complemented
26C5×D165—111no—
27C52×D33—221no—
28C3×C5×D5×C11—111no—
29C3⋊(C5⋊AGL(1,𝔽11))—111no—
30C5×D3×C11⋊C5—111no—
31C3×C5⋊AGL(1,𝔽11)D1111yescharacteristic, complemented
32D11×D33—51noHall
33C5⋊(C11⋊D11)—31no—
34C11×D55C5×D311yescharacteristic, complemented
35C5×C11×D11—31no—
36D11×C11⋊C5—31no—
37D11×C11⋊C5—62no—
38(C11⋊C5)⋊D11—151no—
39C11×AGL(1,𝔽11)—51no—
40C5×D5×D11—331no—
41C2×C5⋊AGL(1,𝔽11)—331no—
42C3×C52×C11—221no—
43C3×C5×C11⋊C5C2×D1111yescharacteristic, complemented
44C3⋊(C11⋊D11)—51no—
45C11×D33C5×D511yescharacteristic, complemented
46C3×C11×D11—51no—
47C2×C5×D33—551no—
48D3×D55—111no—
49D5×D33—111no—
50D3×AGL(1,𝔽11)—551no—
51C5×C112C2×C5×D311yescharacteristic, complemented
52C11×C11⋊C5—22no—
53C11×C11⋊C5D3×D511yescharacteristic, complemented
54C5×D55—331no—
55C5×D5×C11—111no—
56C52×D11—331no—
57C2×C5×C11⋊C5—331no—
58C5⋊AGL(1,𝔽11)—331no—
59C5⋊AGL(1,𝔽11)D3311yescharacteristic, direct product factor
60D112—151noHall
61C3×C112C2×C5×D511yescharacteristic, complemented, Hall
62C2×C3×C5×C11—551no—
63D165—111no—
64D165—111no—
65D165—1101no—
66C5×D33—221no—
67C5×D33—222no—
68C5×D33—551no—
69C5×D33AGL(1,𝔽11)11yescharacteristic, complemented
70C5×D3×C11—111no—
71C3×D55C5×D1111yescharacteristic, complemented
72C3×D5×C11—111no—
73C3⋊AGL(1,𝔽11)—551no—
74D3×C11⋊C5—111no—
75D3×C11⋊C5—222no—
76C3×AGL(1,𝔽11)—51no—
77C5×D3×D5—1211noHall
78C52×C11—111no—
79C5×C11⋊C5C2×D3311yescharacteristic, complemented
80C11⋊D11—151no—
81C11×D11—31no—
82C11×D11—51no—
83C2×D55—331no—
84C2×C5×D11—1651no—
85D5×D11—331no—
86C2×AGL(1,𝔽11)—1651no—
87C3×C5×C11—101no—
88C3×C5×C11—222no—
89C3×C5×C11—221no—
90C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
91C3×C5×C11C2×C5×D1111yescharacteristic, complemented
92C3×C11⋊C5—22no—
93C3×C11⋊C5D5×D1111yescharacteristic, complemented
94C5×D15—1211no—
95C52×D3—2421no—
96C3×C5×D5—111no—
97C2×D33—551no—
98D3×D11—551no—
99C112C5×D3×D511yescharacteristic, complemented, Sylow
100C2×C5×C11—331no—
101C2×C5×C11—551no—
102D55—331no—
103D55—331no—
104D55—3301no—
105D55C5×D3311yescharacteristic, complemented
106C5×D11—31no—
107C5×D11—661no—
108C5×D11—662no—
109C5×D11—1651no—
110D5×C11—111no—
111C2×C11⋊C5—331no—
112C2×C11⋊C5—662no—
113AGL(1,𝔽11)—51no—
114AGL(1,𝔽11)—1651no—
115C2×C5×D5—3631noHall
116C3×C52—221noHall
117C2×C3×C11—551no—
118D33—5501no—
119D33—551no—
120D33—551no—
121D33C5⋊AGL(1,𝔽11)11yescharacteristic, direct product factor
122C3×D11—51no—
123D3×C11—111no—
124C2×C5×D3—6051no—
125D3×D5—1211no—
126C5×C11—101no—
127C5×C11—221no—
128C5×C11—222no—
129C5×C11D3×AGL(1,𝔽11)11yescharacteristic, complemented
130C5×C11C2×C5×D3311yescharacteristic, complemented
131C11⋊C5—22no—
132C11⋊C5D5×D3311yescharacteristic, complemented
133C2×C52—7261no—
134C5×D5—111no—
135C5×D5—3631no—
136C2×D11—1651no—
137C2×D11—1651no—
138C3×C11—101no—
139C3×C11C2×C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
140C3×C11C5×D5×D1111yescharacteristic, complemented
141C2×C3×C5—551no—
142D15—1211no—
143C3×D5—111no—
144C5×D3—111no—
145C5×D3—6051no—
146C5×D3—2421no—
147C5×D3—2422no—
148C52—221noSylow
149C2×C11—331no—
150C2×C11—551no—
151D11—31no—
152D11—51no—
153D11—16501no—
154D11—1651no—
155D11—1651no—
156C22×C5—18151no—
157C2×D5—3631no—
158C3×C5—221no—
159C3×C5—222no—
160C3×C5D11×AGL(1,𝔽11)11yescharacteristic, complemented
161C2×D3—6051noHall
162C11—101no—
163C11D3×C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
164C11C5×D5×D3311yescharacteristic, complemented
165C2×C5—18151no—
166C2×C5—331no—
167C2×C5—551no—
168C2×C5—7261no—
169C2×C5—7262no—
170D5—111no—
171D5—3631no—
172C2×C3—551no—
173D3—111no—
174D3—6051no—
175C5—221no—
176C5—222no—
177C5D33×AGL(1,𝔽11)11yescharacteristic, complemented
178C22—18151noSylow
179C3D11×C5⋊AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
180C2—18151no—
181C2—331no—
182C2—551no—
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. C3⋊(C5⋊((C11⋊C5)⋊D11))C2semidirect
2. C5×C11⋊C5×D33C2semidirect
3. C3×C11×C5⋊AGL(1,𝔽11)C2semidirect
5. C3×C5×C11×C11⋊C5C22semidirect
6. D33×D55C5semidirect
9. C11×C5⋊AGL(1,𝔽11)D3semidirect
11. C3⋊(C5⋊(C11⋊D11))C2×C5semidirect
12. C5×C11×D33C2×C5semidirect
13. C3×C11×D55C2×C5semidirect
15. C11⋊C5×D33D5semidirect
20. C5×C11×C11⋊C5C2×D3semidirect
23. C3×C5×C112C22×C5semidirect
25. C3×C11×C11⋊C5C2×D5semidirect
31. C3×C5⋊AGL(1,𝔽11)D11semidirect
34. C11×D55C5×D3semidirect
43. C3×C5×C11⋊C5C2×D11semidirect
45. C11×D33C5×D5semidirect
51. C5×C112C2×C5×D3semidirect
53. C11×C11⋊C5D3×D5semidirect
59. C5⋊AGL(1,𝔽11)D33direct (N × H)
61. C3×C112C2×C5×D5semidirect
69. C5×D33AGL(1,𝔽11)semidirect
71. C3×D55C5×D11semidirect
79. C5×C11⋊C5C2×D33semidirect
90. C3×C5×C11C2×AGL(1,𝔽11)semidirect
91. C3×C5×C11C2×C5×D11semidirect
93. C3×C11⋊C5D5×D11semidirect
99. C112C5×D3×D5semidirect
105. D55C5×D33semidirect
121. D33C5⋊AGL(1,𝔽11)direct (N × H)
129. C5×C11D3×AGL(1,𝔽11)semidirect
130. C5×C11C2×C5×D33semidirect
132. C11⋊C5D5×D33semidirect
139. C3×C11C2×C5⋊AGL(1,𝔽11)semidirect
140. C3×C11C5×D5×D11semidirect
160. C3×C5D11×AGL(1,𝔽11)semidirect
163. C11D3×C5⋊AGL(1,𝔽11)semidirect
164. C11C5×D5×D33semidirect
177. C5D33×AGL(1,𝔽11)semidirect
179. C3D11×C5⋊AGL(1,𝔽11)semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C5⋊((C11⋊C5)⋊D11))2
C5×C11⋊C5×D332
C3×C11×C5⋊AGL(1,𝔽11)2
D11×C5⋊AGL(1,𝔽11)3
D33×D555
D33×AGL(1,𝔽11)5
C5×D5×D3311
D3×C5⋊AGL(1,𝔽11)11