Finite Group Databasebeta

← #72247096

Subgroups — #72247096

Order 7920.

496 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 85 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
1#72247085C212yesmaximal, complemented
2C3×#63159⋊C5C212yesmaximal, complemented
3C2×(C3⋊D3)⋊AGL(1,𝔽11)C211yesmaximal, characteristic, complemented
4#72246894C211yesmaximal, characteristic, complemented
5C22×C3⋊D3×C11⋊C5C211yesmaximal, characteristic, complemented
6D3×C22⋊AGL(1,𝔽11)—32nomaximal
7C22×C32×C11⋊C5C2211yescharacteristic, complemented
8C2×C3⋊D3×C11⋊C5—22no—
9C2×C3⋊D3×C11⋊C5C2211yescharacteristic
10C2×C3⋊D3×C11⋊C5C2211yescharacteristic, complemented
11C2×C3×C3⋊AGL(1,𝔽11)C2212yescomplemented
12(C3⋊D3)⋊AGL(1,𝔽11)—22no—
13C3×C3⋊(Dic11⋊C5)C2212yescomplemented
14#13097430C511yesmaximal, characteristic, complemented, Hall
15C22×D3×C11⋊C5—32no—
16C22×D3×C11⋊C5—61no—
17C2×D3×AGL(1,𝔽11)—32no—
18#63159⋊C5D312yescomplemented
19C3×C22⋊AGL(1,𝔽11)—32no—
20#63142⋊C5—32no—
21#63140⋊C5—32no—
22D3×Dic11⋊C5—32no—
23C2×C32×C11⋊C5—21no—
24C2×C32×C11⋊C5C2311yescharacteristic
25C3⋊D3×C11⋊C5—21no—
26C3⋊D3×C11⋊C5D412yescomplemented
27C3×C3⋊AGL(1,𝔽11)—22no—
28C2×C22⋊AGL(1,𝔽11)—91noHall
29C22×C11×C3⋊D3C2×C511yescharacteristic, complemented
30C2×(C3⋊D3)⋊D11C2×C511yescharacteristic, complemented
31C3×#63159C2×C512yescomplemented
32#11716246C2×C512yescomplemented
33#11716245C2×C511yescharacteristic, complemented
34C5×#3811—111nomaximal, Hall
35C22×C3×C11⋊C5—21no—
36C22×C3×C11⋊C5C2×D312yescomplemented
37C2×C3⋊AGL(1,𝔽11)C2×D312yescomplemented
38C2×D3×C11⋊C5—32no—
39C2×D3×C11⋊C5—32no—
40C2×D3×C11⋊C5—64no—
41C2×D3×C11⋊C5—61no—
42C2×D3×C11⋊C5—62no—
43C2×D3×C11⋊C5—62no—
44C2×D3×C11⋊C5—61no—
45C2×C3×AGL(1,𝔽11)—32no—
46D3×AGL(1,𝔽11)—64no—
47C3⋊(Dic11⋊C5)C2×D312yescomplemented
48C3×Dic11⋊C5—32no—
49D3×C22⋊D11—32no—
50C32×C11⋊C5C2×D411yescharacteristic, complemented, Hall
51C23×C11⋊C5—91no—
52C22×AGL(1,𝔽11)—91no—
53C22⋊AGL(1,𝔽11)—32no—
54C22⋊AGL(1,𝔽11)—92no—
55C2×Dic11⋊C5—91no—
56C22×C32×C11C22×C511yescharacteristic, complemented
57C2×C11×C3⋊D3—22no—
58C2×C11×C3⋊D3C22×C511yescharacteristic
59C2×C11×C3⋊D3C22×C511yescharacteristic, complemented
60C2×C3×D33C22×C512yescomplemented
61(C3⋊D3)⋊D11—22no—
62C3×Dic33C22×C512yescomplemented
63C22×C5×C3⋊D3—221no—
64C2×C5×D32—111no—
65C3×C5×#67—112no—
66C5×#626—112no—
67C5×#624—111no—
68C2×C3×C11⋊C5—21no—
69C2×C3×C11⋊C5—21no—
70C2×C3×C11⋊C5—22no—
71C2×C3×C11⋊C5—21no—
72C2×C3×C11⋊C5C22×D312yes—
73C3⋊AGL(1,𝔽11)—22no—
74D3×C11⋊C5—34no—
75D3×C11⋊C5—62no—
76D3×C11⋊C5—61no—
77D3×C11⋊C5—61no—
78D3×C11⋊C5—62no—
79C3×AGL(1,𝔽11)—62no—
80C22×D3×C11—32no—
81C22×D3×C11—61no—
82C2×D3×D11—32no—
83#63159C5×D312yescomplemented
84C3×C22⋊D11—32no—
85#63142—32no—
86#63140—32no—
87D3×Dic11—32no—
88C5×D3×D4—332no—
89C22×C11⋊C5—91no—
90C22×C11⋊C5—91no—
91C22×C11⋊C5—182no—
92C22×C11⋊C5D3211yescharacteristic, complemented
93C2×AGL(1,𝔽11)—32no—
94C2×AGL(1,𝔽11)—182no—
95Dic11⋊C5—32no—
96C2×C32×C11—21no—
97C2×C32×C11C23×C511yescharacteristic
98C11×C3⋊D3—21no—
99C11×C3⋊D3C5×D412yescomplemented
100C3×D33—22no—
101C22×C32×C5—221no—
102C2×C5×C3⋊D3—221no—
103C2×C5×C3⋊D3—222no—
104C2×C5×C3⋊D3—221no—
105C2×C3×C5×D3—112no—
106C5×D32—222no—
107C3×C5×Dic3—112no—
108C2×C22⋊D11—91noHall
109C3×C11⋊C5—21no—
110C3×C11⋊C5D3×D412yescomplemented
111#3811—111noHall
112C22×C3×C11—21no—
113C22×C3×C11C2×C5×D312yescomplemented
114C2×D33C2×C5×D312yescomplemented
115C2×D3×C11—32no—
116C2×D3×C11—32no—
117C2×D3×C11—64no—
118C2×D3×C11—61no—
119C2×D3×C11—62no—
120C2×D3×C11—62no—
121C2×D3×C11—61no—
122C2×C3×D11—32no—
123D3×D11—64no—
124Dic33C2×C5×D312yescomplemented
125C3×Dic11—32no—
126C22×C5×D3—332no—
127C22×C5×D3—332no—
128C22×C5×D3—661no—
129C3×C5×D4—332no—
130C5×#67—112no—
131C5×#67—332no—
132C5×D12—332no—
133C4×C5×D3—332no—
134C2×C11⋊C5—21no—
135C2×C11⋊C5—92no—
136C2×C11⋊C5—181no—
137C2×C11⋊C5C2×D3211yescharacteristic
138AGL(1,𝔽11)—62no—
139C32×C11C2×C5×D411yescharacteristic, complemented, Hall
140C2×C32×C5—221no—
141C2×C32×C5—221no—
142C5×C3⋊D3—221no—
143C5×C3⋊D3—222no—
144C3×C5×D3—222no—
145C23×C11—91no—
146C22×D11—91no—
147C22⋊D11—32no—
148C22⋊D11—92no—
149C2×Dic11—91no—
150C2×C5×D4—991noHall
151C22×C3⋊D3AGL(1,𝔽11)11yescharacteristic, complemented
152C2×D32—111no—
153C3×#67—112no—
154#626—112no—
155#624—111no—
156C2×C3×C11—21no—
157C2×C3×C11—21no—
158C2×C3×C11—22no—
159C2×C3×C11—21no—
160C2×C3×C11C22×C5×D312yes—
161D33—22no—
162C3×D11—62no—
163D3×C11—34no—
164D3×C11—62no—
165D3×C11—61no—
166D3×C11—61no—
167D3×C11—62no—
168C22×C3×C5—112no—
169C22×C3×C5—221no—
170C22×C3×C5—332no—
171C2×C5×D3—112no—
172C2×C5×D3—332no—
173C2×C5×D3—332no—
174C2×C5×D3—664no—
175C2×C5×D3—662no—
176C2×C5×D3—661no—
177C2×C5×D3—662no—
178C2×C5×D3—661no—
179C2×C5×D3—664no—
180C3×C4×C5—332no—
181C5×Dic3—112no—
182C11⋊C5#381111yescharacteristic, complemented, Hall
183D3×D4—332no—
184C32×C5—221noHall
185C22×C11—91no—
186C22×C11—91no—
187C22×C11—182no—
188C22×C11C5×D3211yescharacteristic, complemented
189C2×D11—32no—
190C2×D11—182no—
191Dic11—32no—
192C23×C5—991no—
193C23×C5—1981no—
194C5×D4—332no—
195C5×D4—992no—
196C2×C4×C5—991no—
197C22×C32C2×AGL(1,𝔽11)11yescharacteristic, complemented
198C2×C3⋊D3—22no—
199C2×C3⋊D3C2×AGL(1,𝔽11)11yescharacteristic
200C2×C3⋊D3C2×AGL(1,𝔽11)11yescharacteristic, complemented
201C2×C3×D3—112no—
202D32—222no—
203C3×Dic3—112no—
204C3×C11—21no—
205C3×C11C5×D3×D412yescomplemented
206C2×C3×C5—112no—
207C2×C3×C5—222no—
208C2×C3×C5—221no—
209C2×C3×C5—221no—
210C2×C3×C5—221no—
211C2×C3×C5—662no—
212C5×D3—222no—
213C5×D3—334no—
214C5×D3—662no—
215C5×D3—662no—
216C5×D3—661no—
217C5×D3—661no—
218C22×D3—32no—
219C22×D3—61no—
220C22×D3—332no—
221C3×D4—332no—
222#67—112no—
223#67—332no—
224D12—332no—
225C4×D3—332no—
226C2×C11—21no—
227C2×C11—92no—
228C2×C11—181no—
229C2×C11C2×C5×D3211yescharacteristic
230D11—62no—
231C22×C5—221no—
232C22×C5—332no—
233C22×C5—1981no—
234C22×C5—1981no—
235C22×C5—1982no—
236C22×C5—1982no—
237C4×C5—332no—
238C2×C32—21no—
239C2×C32C22×AGL(1,𝔽11)11yescharacteristic
240C3⋊D3—21no—
241C3⋊D3C22⋊AGL(1,𝔽11)12yescomplemented
242C3×D3—222no—
243C2×D4—991noSylow
244C3×C5—112no—
245C3×C5—221no—
246C22×C3—21no—
247C22×C3—332no—
248C22×C3D3×AGL(1,𝔽11)12yescomplemented
249C2×D3—32no—
250C2×D3—32no—
251C2×D3—61no—
252C2×D3—61no—
253C2×D3—64no—
254C2×D3—62no—
255C2×D3—62no—
256C2×D3—112no—
257C2×D3—664no—
258C3×C4—332no—
259Dic3—112no—
260C11C5×#381111yescharacteristic, complemented, Sylow
261C2×C5—221no—
262C2×C5—221no—
263C2×C5—662no—
264C2×C5—1982no—
265C2×C5—1981no—
266C32C2×C22⋊AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
267C23—91no—
268C23—991no—
269D4—332no—
270D4—992no—
271C2×C4—991no—
272C2×C3—21no—
273C2×C3—21no—
274C2×C3—22no—
275C2×C3—21no—
276C2×C3—662no—
277C2×C3C2×D3×AGL(1,𝔽11)12yes—
278D3—34no—
279D3—62no—
280D3—61no—
281D3—61no—
282D3—62no—
283D3—222no—
284C5—221noSylow
285C22—91no—
286C22—91no—
287C22—182no—
288C22—332no—
289C22—1982no—
290C22(C3⋊D3)⋊AGL(1,𝔽11)11yescharacteristic, complemented
291C4—332no—
292C3—21no—
293C3D3×C22⋊AGL(1,𝔽11)12yescomplemented
294C2—21no—
295C2—92no—
296C2—181no—
297C2—662no—
298C2C2×(C3⋊D3)⋊AGL(1,𝔽11)11yescharacteristic
subgroupG/H
center, FrattiniC2C2×(C3⋊D3)⋊AGL(1,𝔽11)
commutator, socle, cosocleC2×C32×C11C23×C5
FittingC22×C32×C11C22×C5
hypercenterC22(C3⋊D3)⋊AGL(1,𝔽11)
hypocenterC32×C11C2×C5×D4
LCSG ▷ C2×C32×C11 ▷ C32×C11
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. #72247085C2semidirect
2. C3×#63159⋊C5C2semidirect
3. C2×(C3⋊D3)⋊AGL(1,𝔽11)C2semidirect
4. #72246894C2semidirect
5. C22×C3⋊D3×C11⋊C5C2semidirect
7. C22×C32×C11⋊C5C22semidirect
10. C2×C3⋊D3×C11⋊C5C22semidirect
11. C2×C3×C3⋊AGL(1,𝔽11)C22semidirect
13. C3×C3⋊(Dic11⋊C5)C22semidirect
14. #13097430C5semidirect
18. #63159⋊C5D3semidirect
26. C3⋊D3×C11⋊C5D4semidirect
29. C22×C11×C3⋊D3C2×C5semidirect
30. C2×(C3⋊D3)⋊D11C2×C5semidirect
31. C3×#63159C2×C5semidirect
32. #11716246C2×C5semidirect
33. #11716245C2×C5semidirect
36. C22×C3×C11⋊C5C2×D3semidirect
37. C2×C3⋊AGL(1,𝔽11)C2×D3semidirect
47. C3⋊(Dic11⋊C5)C2×D3semidirect
50. C32×C11⋊C5C2×D4semidirect
56. C22×C32×C11C22×C5semidirect
59. C2×C11×C3⋊D3C22×C5semidirect
60. C2×C3×D33C22×C5semidirect
62. C3×Dic33C22×C5semidirect
83. #63159C5×D3semidirect
92. C22×C11⋊C5D32semidirect
99. C11×C3⋊D3C5×D4semidirect
110. C3×C11⋊C5D3×D4semidirect
113. C22×C3×C11C2×C5×D3semidirect
114. C2×D33C2×C5×D3semidirect
124. Dic33C2×C5×D3semidirect
139. C32×C11C2×C5×D4semidirect
151. C22×C3⋊D3AGL(1,𝔽11)semidirect
182. C11⋊C5#3811semidirect
188. C22×C11C5×D32semidirect
197. C22×C32C2×AGL(1,𝔽11)semidirect
200. C2×C3⋊D3C2×AGL(1,𝔽11)semidirect
205. C3×C11C5×D3×D4semidirect
241. C3⋊D3C22⋊AGL(1,𝔽11)semidirect
248. C22×C3D3×AGL(1,𝔽11)semidirect
260. C11C5×#3811semidirect
266. C32C2×C22⋊AGL(1,𝔽11)semidirect
290. C22(C3⋊D3)⋊AGL(1,𝔽11)semidirect
293. C3D3×C22⋊AGL(1,𝔽11)semidirect

Maximal subgroups

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

subgroupindex
#722470852
C3×#63159⋊C52
C2×(C3⋊D3)⋊AGL(1,𝔽11)2
#722468942
C22×C3⋊D3×C11⋊C52
D3×C22⋊AGL(1,𝔽11)3
#130974305
C5×#381111