Finite Group Databasebeta

← #13079488

Subgroups — #13079488

Order 1408.

410 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 117 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×#535C211yesmaximal, characteristic
2#10623356C211yesmaximal, characteristic, complemented
3#10622847C211yesmaximal, characteristic, complemented
4#10622831C212yesmaximal, complemented
5#10622655C212yesmaximal, complemented
6#10622654C212yesmaximal, complemented
7#10622653C212yesmaximal, complemented
8#10622648C212yesmaximal, complemented
9#10622609C212yesmaximal, complemented
10C2×C11×#41C2211yescharacteristic
11C22×D4×C11C2211yescharacteristic
12C22×Dic22C2211yescharacteristic, complemented
13C11×#127—21no—
14C11×#124—21no—
15C11×#121C2212yes—
16C11×#121C2212yes—
17C11×#120—21no—
18C11×#120—21no—
19C11×#117C2211yescharacteristic
20#66997—21no—
21#66989—21no—
22#66988—21no—
23#66988—21no—
24C2×#4324C2212yes—
25C2×#4324C2212yes—
26#66979C2211yescharacteristic, complemented
27#66977C2212yes—
28#66977C2212yescomplemented
29C2×#4318C2211yescharacteristic, complemented
30C22×C11⋊C8C2211yescharacteristic, complemented
31#66896C2212yes—
32#66896C2212yes—
33C22⋊(C11⋊C8)C2212yes—
34C22⋊(C11⋊C8)C2212yescomplemented
35#66874C2212yescomplemented
36#66874C2212yescomplemented
37#66872C2212yescomplemented
38#66871C2212yescomplemented
39C24×C11—21no—
40C11×#41—41no—
41C11×#41—41no—
42C2×Q8×C11D411yescharacteristic
43C2×D4×C11—22no—
44C2×D4×C11—22no—
45C2×D4×C11—21no—
46C2×D4×C11—41no—
47C2×D4×C11—41no—
48C2×D4×C11D411yescharacteristic
49C2×D4×C11D411yescharacteristic
50C2×D4×C11D411yescharacteristic
51C2×D4×C11C2312yes—
52C22×C4×C11C2311yescharacteristic
53C22×C4×C11C2311yescharacteristic
54C22×C4×C11C2311yescharacteristic
55C22×Dic11—21no—
56C2×Dic22—21no—
57C2×Dic22—41no—
58C2×Dic22—41no—
59C2×Dic22C2312yes—
60C11×C4⋊C4C2312yes—
61C11×C22⋊C4—21no—
62C11×C22⋊C4—22no—
63C11×C22⋊C4—22no—
64C42×C11—21no—
65C22⋊Dic11—22no—
66C22⋊Dic11—22no—
67C22⋊Dic11—21no—
68#4324—42no—
69#4324—42no—
70C4⋊Dic11C2312yes—
71Dic11⋊C4—22no—
72Dic11⋊C4—22no—
73C4×Dic11—21no—
74#4318—41no—
75C2×C11⋊C8—41no—
76C2×C11⋊C8C2312yes—
77C2×C11⋊C8C2312yes—
78#3200—111nomaximal, Sylow
79C23×C11—22no—
80C23×C11—42no—
81C23×C11—82no—
82C23×C11C2×D411yescharacteristic
83C23×C11C2×D411yescharacteristic
84C23×C11C2×D411yescharacteristic
85Q8×C11—41no—
86D4×C11—22no—
87D4×C11—22no—
88D4×C11—41no—
89D4×C11—41no—
90D4×C11—41no—
91D4×C11—42no—
92D4×C11—82no—
93D4×C11—82no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—22no—
101C2×C4×C11C2×D411yescharacteristic
102C2×C4×C11C2×D411yescharacteristic
103C2×C4×C11C2×D411yescharacteristic
104C2×C4×C11C2411yescharacteristic
105C2×Dic11—22no—
106C2×Dic11—22no—
107C2×Dic11—42no—
108Dic22—22no—
109Dic22—22no—
110Dic22—42no—
111C11⋊C8—22no—
112C11⋊C8—22no—
113#536—111no—
114#535D1111yescharacteristic
115#485—112no—
116#482—112no—
117#468—112no—
118#465—112no—
119#450—112no—
120#448—112no—
121#408—111no—
122C22×C11—21no—
123C22×C11—21no—
124C22×C11—21no—
125C22×C11—22no—
126C22×C11—22no—
127C22×C11—22no—
128C22×C11—42no—
129C22×C11—42no—
130C22×C11—42no—
131C22×C11—84no—
132C22×C11C22×D411yescharacteristic
133C4×C11—21no—
134C4×C11—21no—
135C4×C11—21no—
136C4×C11—42no—
137C4×C11H(5,𝔽2)11yescharacteristic
138C4×C11H(5,𝔽2)11yescharacteristic
139Dic11—42no—
140Dic11—42no—
141C2×#41C2×D1111yescharacteristic
142C22×Q8—111no—
143C22×D4C2×D1111yescharacteristic
144C2×SD16—112no—
145C2×SD16—112no—
146C2×M16—111no—
147C22×C8—111no—
148C4⋊Q8—221no—
149#127—21no—
150#124—21no—
151#124—221no—
152#123—221no—
153#123—221no—
154C22⋊Q8—112no—
155C22⋊Q8—112no—
156#121C2×D1112yes—
157#121C2×D1112yes—
158#120—21no—
159#120—21no—
160#117—111no—
161#117C2×D1111yescharacteristic
162#107—112no—
163#106—112no—
164#103—112no—
165#103—112no—
166#102—112no—
167#102—112no—
168C22⋊C8—112no—
169C22⋊C8—112no—
170C2×C11—41no—
171C2×C11—41no—
172C2×C11—41no—
173C2×C11—82no—
174C2×C11#53411yescharacteristic
175C2×C11#57712yes—
176C24—21no—
177#41—41no—
178#41—41no—
179C2×Q8—112no—
180C2×Q8—221no—
181C2×Q8—441no—
182C2×Q8—441no—
183C2×Q8C22⋊D1111yescharacteristic
184C2×D4—22no—
185C2×D4—22no—
186C2×D4—21no—
187C2×D4—41no—
188C2×D4—41no—
189C2×D4C22⋊D1111yescharacteristic
190C2×D4C22⋊D1111yescharacteristic
191C2×D4C22⋊D1111yescharacteristic
192C2×D4C22×D1112yes—
193C22×C4—221no—
194C22×C4C22×D1111yescharacteristic
195C22×C4C22×D1111yescharacteristic
196C22×C4C22×D1111yescharacteristic
197SD16—442no—
198SD16—442no—
199M16—441no—
200C2×C8—112no—
201C2×C8—112no—
202C2×C8—441no—
203C4⋊C4—112no—
204C4⋊C4—222no—
205C4⋊C4—222no—
206C4⋊C4C22×D1112yes—
207C22⋊C4—21no—
208C22⋊C4—22no—
209C22⋊C4—22no—
210C22⋊C4—221no—
211C22⋊C4—222no—
212C22⋊C4—222no—
213C42—21no—
214C42—221no—
215C11#320011yescharacteristic, complemented, Sylow
216C23—22no—
217C23—42no—
218C23—82no—
219C23C2×C22⋊D1111yescharacteristic
220C23C2×C22⋊D1111yescharacteristic
221C23C2×C22⋊D1111yescharacteristic
222Q8—41no—
223Q8—222no—
224Q8—222no—
225Q8—442no—
226D4—22no—
227D4—22no—
228D4—41no—
229D4—41no—
230D4—41no—
231D4—42no—
232D4—82no—
233D4—82no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—222no—
242C2×C4—222no—
243C2×C4—442no—
244C2×C4C2×C22⋊D1111yescharacteristic
245C2×C4C2×C22⋊D1111yescharacteristic
246C2×C4C2×C22⋊D1111yescharacteristic
247C2×C4C23×D1111yescharacteristic
248C8—222no—
249C8—222no—
250C22—21no—
251C22—21no—
252C22—21no—
253C22—22no—
254C22—22no—
255C22—22no—
256C22—42no—
257C22—42no—
258C22—42no—
259C22—84no—
260C22C22×C22⋊D1111yescharacteristic
261C4—21no—
262C4—21no—
263C4—21no—
264C4—42no—
265C4—442no—
266C4—442no—
267C4#6703711yescharacteristic
268C4#6703711yescharacteristic
269C2—41no—
270C2—41no—
271C2—41no—
272C2—82no—
273C2#1062333511yescharacteristic
274C2#1062336712yes—
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC11×#535C2
socleC22×C11C22×D4
hypercenter#535D11
hypocenterC11#3200
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
2. #10623356C2semidirect
3. #10622847C2semidirect
4. #10622831C2semidirect
5. #10622655C2semidirect
6. #10622654C2semidirect
7. #10622653C2semidirect
8. #10622648C2semidirect
9. #10622609C2semidirect
12. C22×Dic22C22semidirect
26. #66979C22semidirect
28. #66977C22semidirect
29. C2×#4318C22semidirect
30. C22×C11⋊C8C22semidirect
34. C22⋊(C11⋊C8)C22semidirect
35. #66874C22semidirect
36. #66874C22semidirect
37. #66872C22semidirect
38. #66871C22semidirect
215. C11#3200semidirect

Maximal subgroups

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

subgroupindex
C11×#5352
#106233562
#106228472
#106228312
#106226552
#106226542
#106226532
#106226482
#106226092
#320011