Finite Group Databasebeta

← D3×C5⋊((C11⋊C5)⋊D11) #49137492

Subgroups — D3×C5⋊((C11⋊C5)⋊D11) #49137492

Order 36300.

232 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 44 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×D3×C11×C11⋊C5C211yesmaximal, characteristic, complemented
3C3×C5⋊((C11⋊C5)⋊D11)C211yesmaximal, characteristic, complemented
4C2×C5⋊((C11⋊C5)⋊D11)—31nomaximal, Hall
5C3×C5×C11×C11⋊C5C2211yescharacteristic, complemented, Hall
6D3×C5⋊(C11⋊D11)C511yesmaximal, characteristic, complemented
7D3×(C11⋊C5)⋊D11—51nomaximal
8C2×C5×C11×C11⋊C5—31no—
9C5⋊((C11⋊C5)⋊D11)—31no—
10C5⋊((C11⋊C5)⋊D11)D311yescharacteristic, direct product factor
11C3⋊(C5⋊(C11⋊D11))C2×C511yescharacteristic, complemented
12C5×D3×C112C2×C511yescharacteristic, complemented
13C3×C5⋊(C11⋊D11)C2×C511yescharacteristic, complemented
14C3⋊((C11⋊C5)⋊D11)—51no—
15D3×C11×C11⋊C5—22no—
16D3×C11×C11⋊C5D511yescharacteristic, complemented
17C3×(C11⋊C5)⋊D11—51no—
18C5×D3×D55—111nomaximal
19D3×C5⋊AGL(1,𝔽11)—111nomaximal
20C5×C11×C11⋊C5C2×D311yescharacteristic, complemented, Hall
21C2×C5⋊(C11⋊D11)—31no—
22C2×(C11⋊C5)⋊D11—151no—
23C3×C5×C112C22×C511yescharacteristic, complemented
24C3×C11×C11⋊C5—22no—
25C3×C11×C11⋊C5C2×D511yescharacteristic, complemented
26C5×D165—111no—
27C52×D3×C11—221no—
28C3×C5×D55—111no—
29C3⋊(C5⋊AGL(1,𝔽11))—111no—
30C5×D3×C11⋊C5D1111yescharacteristic, complemented
31C3×C5⋊AGL(1,𝔽11)—111no—
32D3×C11⋊D11—51noHall
33C2×C5×C112—31no—
34C5⋊(C11⋊D11)—31no—
35C5⋊(C11⋊D11)C5×D311yescharacteristic, complemented
36C2×C11×C11⋊C5—31no—
37C2×C11×C11⋊C5—62no—
38(C11⋊C5)⋊D11—51no—
39(C11⋊C5)⋊D11—151no—
40C2×C5×D55—331no—
41C2×C5⋊AGL(1,𝔽11)—331no—
42C3×C52×C11—221no—
43C3×C5×C11⋊C5C2×D1111yescharacteristic, complemented
44C3⋊(C11⋊D11)—51no—
45D3×C112C5×D511yescharacteristic, complemented
46C3×C11⋊D11—51no—
47D3×D55—111no—
48D3×D55—111no—
49D3×D55—552no—
50C5×D3×D11—551no—
51D3×AGL(1,𝔽11)—551no—
52C5×C112C2×C5×D311yescharacteristic, complemented
53C11×C11⋊C5—22no—
54C11×C11⋊C5D3×D511yescharacteristic, complemented
55C2×C52×C11—661no—
56C5×D55—111no—
57C5×D55—331no—
58C2×C5×C11⋊C5—31no—
59C5⋊AGL(1,𝔽11)—111no—
60C5⋊AGL(1,𝔽11)—331no—
61C2×C11⋊D11—151noHall
62C3×C112C2×C5×D511yescharacteristic, complemented, Hall
63D165—111no—
64D165—111no—
65D165—552no—
66C5×D33—551no—
67C5×D3×C11—52no—
68C5×D3×C11—111no—
69C5×D3×C11—222no—
70C5×D3×C11AGL(1,𝔽11)11yescharacteristic, complemented
71C5×D3×C11C5×D1111yescharacteristic, complemented
72C3×D55—111no—
73C3×D55—111no—
74C3×D55—552no—
75C3×C5×D11—551no—
76C3⋊AGL(1,𝔽11)—551no—
77D3×C11⋊C5—22no—
78D3×C11⋊C5D5511yescharacteristic, complemented
79C3×AGL(1,𝔽11)—551no—
80C5×D3×D5—1211noHall
81C52×C11—221no—
82C5×C11⋊C5D3×D1111yescharacteristic, complemented
83C2×C112—31no—
84C11⋊D11—51no—
85C11⋊D11—151no—
86C2×D55—331no—
87C2×D55—331no—
88C2×D55—1652no—
89C2×C5×D11—1651no—
90C2×AGL(1,𝔽11)—1651no—
91C3×C5×C11—52no—
92C3×C5×C11—111no—
93C3×C5×C11—222no—
94C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
95C3×C5×C11C2×C5×D1111yescharacteristic, complemented
96C3×C11⋊C5—22no—
97C3×C11⋊C5C2×D5511yescharacteristic, complemented
98C5×D15—1211no—
99C52×D3—221no—
100C3×C5×D5—1211no—
101D3×D11—2752no—
102D3×D11—551no—
103D3×D11—551no—
104C112C5×D3×D511yescharacteristic, complemented, Sylow
105C2×C5×C11—31no—
106C2×C5×C11—31no—
107C2×C5×C11—152no—
108C2×C5×C11—661no—
109C2×C5×C11—662no—
110D55—111no—
111D55—111no—
112D55—331no—
113D55—331no—
114D55—552no—
115D55—1652no—
116C5×D11—551no—
117C5×D11—1651no—
118C2×C11⋊C5—31no—
119C2×C11⋊C5—62no—
120AGL(1,𝔽11)—551no—
121AGL(1,𝔽11)—1651no—
122C2×C5×D5—3631noHall
123C3×C52—221noHall
124D33—2752no—
125D33—551no—
126D33—551no—
127C3×D11—2752no—
128C3×D11—551no—
129C3×D11—551no—
130D3×C11—52no—
131D3×C11C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
132D3×C11C5×D5511yescharacteristic, complemented
133C2×C5×D3—6051no—
134D3×D5—1211no—
135C5×C11—52no—
136C5×C11—221no—
137C5×C11—222no—
138C5×C11D3×AGL(1,𝔽11)11yescharacteristic, complemented
139C5×C11C5×D3×D1111yescharacteristic, complemented
140C11⋊C5—22no—
141C11⋊C5D3×D5511yescharacteristic, complemented
142C2×C52—661no—
143C5×D5—3631no—
144C5×D5—1211no—
145C2×D11—8252no—
146C2×D11—1651no—
147C2×D11—1651no—
148C3×C11—52no—
149C3×C11C2×C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
150C3×C11C2×C5×D5511yescharacteristic, complemented
151C2×C3×C5—6051no—
152D15—1211no—
153C3×D5—1211no—
154C5×D3—221no—
155C5×D3—222no—
156C5×D3—6051no—
157C5×D3(C11⋊C5)⋊D1111yescharacteristic, complemented
158C52—221noSylow
159C2×C11—31no—
160C2×C11—31no—
161C2×C11—152no—
162D11—2752no—
163D11—551no—
164D11—551no—
165D11—8252no—
166D11—1651no—
167D11—1651no—
168C22×C5—18151no—
169C2×D5—3631no—
170C3×C5—221no—
171C3×C5—222no—
172C3×C5C2×(C11⋊C5)⋊D1111yescharacteristic, complemented
173C2×D3—6051noHall
174C11—52no—
175C11D3×C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
176C11C5×D3×D5511yescharacteristic, complemented
177C2×C5—31no—
178C2×C5—18151no—
179C2×C5—661no—
180C2×C5—662no—
181C2×C5—6051no—
182D5—3631no—
183D5—1211no—
184C2×C3—6051no—
185D3—6051no—
186D3C5⋊((C11⋊C5)⋊D11)11yescharacteristic, direct product factor
187C5—221no—
188C5—222no—
189C5D3×(C11⋊C5)⋊D1111yescharacteristic, complemented
190C22—18151noSylow
191C3C2×C5⋊((C11⋊C5)⋊D11)11yescharacteristic, complemented, Sylow
192C2—31no—
193C2—18151no—
194C2—6051no—
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×D3×C11×C11⋊C5C2semidirect
3. C3×C5⋊((C11⋊C5)⋊D11)C2semidirect
5. C3×C5×C11×C11⋊C5C22semidirect
6. D3×C5⋊(C11⋊D11)C5semidirect
10. C5⋊((C11⋊C5)⋊D11)D3direct (N × H)
11. C3⋊(C5⋊(C11⋊D11))C2×C5semidirect
12. C5×D3×C112C2×C5semidirect
13. C3×C5⋊(C11⋊D11)C2×C5semidirect
16. D3×C11×C11⋊C5D5semidirect
20. C5×C11×C11⋊C5C2×D3semidirect
23. C3×C5×C112C22×C5semidirect
25. C3×C11×C11⋊C5C2×D5semidirect
30. C5×D3×C11⋊C5D11semidirect
35. C5⋊(C11⋊D11)C5×D3semidirect
43. C3×C5×C11⋊C5C2×D11semidirect
45. D3×C112C5×D5semidirect
52. C5×C112C2×C5×D3semidirect
54. C11×C11⋊C5D3×D5semidirect
62. C3×C112C2×C5×D5semidirect
70. C5×D3×C11AGL(1,𝔽11)semidirect
71. C5×D3×C11C5×D11semidirect
78. D3×C11⋊C5D55semidirect
82. C5×C11⋊C5D3×D11semidirect
94. C3×C5×C11C2×AGL(1,𝔽11)semidirect
95. C3×C5×C11C2×C5×D11semidirect
97. C3×C11⋊C5C2×D55semidirect
104. C112C5×D3×D5semidirect
131. D3×C11C5⋊AGL(1,𝔽11)semidirect
132. D3×C11C5×D55semidirect
138. C5×C11D3×AGL(1,𝔽11)semidirect
139. C5×C11C5×D3×D11semidirect
141. C11⋊C5D3×D55semidirect
149. C3×C11C2×C5⋊AGL(1,𝔽11)semidirect
150. C3×C11C2×C5×D55semidirect
157. C5×D3(C11⋊C5)⋊D11semidirect
172. C3×C5C2×(C11⋊C5)⋊D11semidirect
175. C11D3×C5⋊AGL(1,𝔽11)semidirect
176. C11C5×D3×D55semidirect
186. D3C5⋊((C11⋊C5)⋊D11)direct (N × H)
189. C5D3×(C11⋊C5)⋊D11semidirect
191. C3C2×C5⋊((C11⋊C5)⋊D11)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×D3×C11×C11⋊C52
C3×C5⋊((C11⋊C5)⋊D11)2
C2×C5⋊((C11⋊C5)⋊D11)3
D3×C5⋊(C11⋊D11)5
D3×(C11⋊C5)⋊D115
C5×D3×D5511
D3×C5⋊AGL(1,𝔽11)11