Finite Group Databasebeta

← #13079489

Subgroups — #13079489

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
1#10623361C211yesmaximal, characteristic
2#10623356C211yesmaximal, characteristic, complemented
3C11×#408C211yesmaximal, characteristic, complemented
4#10622747C212yesmaximal, complemented
5#10622727C212yesmaximal, complemented
6#10622351C212yesmaximal, complemented
7#10622350C212yesmaximal, complemented
8#10622344C212yesmaximal, complemented
9#10622336C212yesmaximal, complemented
10C2×C11×#41C2211yescharacteristic
11C22×D44C2211yescharacteristic
12C22×Dic22C2211yescharacteristic, complemented
13C2×C11×M16C2211yescharacteristic, complemented
14C22×C8×C11C2211yescharacteristic, complemented
15#67000—21no—
16#66997—21no—
17#66993—21no—
18#66990—21no—
19#66990—21no—
20#66989—21no—
21#66988—21no—
22#66988—21no—
23#66983C2212yes—
24#66983C2212yes—
25#66979C2211yescharacteristic
26#66979C2211yescharacteristic, complemented
27#66977C2212yes—
28#66977C2212yescomplemented
29C2×#4314C2212yes—
30C2×#4314C2212yes—
31C11×C22⋊C8C2212yes—
32C11×C22⋊C8C2212yescomplemented
33#66885C2212yes—
34#66885C2212yes—
35#66882C2212yescomplemented
36#66881C2212yescomplemented
37#66880C2212yescomplemented
38#66880C2212yescomplemented
39C23×D11—21no—
40C11×#41—41no—
41C11×#41—41no—
42C2×Q8×C11D411yescharacteristic
43C2×D4×C11D411yescharacteristic
44C2×D4×C11D411yescharacteristic
45C2×D4×C11D411yescharacteristic
46C22×C4×C11C2311yescharacteristic
47C22×C4×C11C2311yescharacteristic
48C22×C4×C11C2311yescharacteristic
49C2×C22⋊D11—22no—
50C2×C22⋊D11—22no—
51C22×Dic11—21no—
52C2×D44—21no—
53C2×D44—41no—
54C2×D44—41no—
55C2×D44C2312yes—
56C2×Dic22—21no—
57C2×Dic22—41no—
58C2×Dic22—41no—
59C2×Dic22C2312yes—
60C11×M16—41no—
61C2×C8×C11—41no—
62C2×C8×C11C2312yes—
63C2×C8×C11C2312yes—
64C22⋊Dic11—22no—
65C22⋊Dic11—22no—
66C22⋊Dic11—21no—
67C22⋊Dic11—21no—
68(C2×D11)⋊C4—22no—
69(C2×D11)⋊C4—22no—
70C4⋊Dic11C2312yes—
71C4⋊Dic11C2312yes—
72Dic11⋊C4—22no—
73Dic11⋊C4—22no—
74C4×Dic11—21no—
75C4×Dic11—21no—
76#4314—42no—
77#4314—42no—
78#3200—111nomaximal, Sylow
79C23×C11C2×D411yescharacteristic
80C23×C11C2×D411yescharacteristic
81C23×C11C2×D411yescharacteristic
82C22×D11—22no—
83C22×D11—42no—
84C22×D11—82no—
85Q8×C11—41no—
86D4×C11—41no—
87D4×C11—41no—
88D4×C11—41no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11C2×D411yescharacteristic
96C2×C4×C11C2×D411yescharacteristic
97C2×C4×C11C2×D411yescharacteristic
98C2×C4×C11C2411yescharacteristic
99C22⋊D11—82no—
100C22⋊D11—82no—
101C2×Dic11—22no—
102C2×Dic11—22no—
103C2×Dic11—22no—
104C2×Dic11—42no—
105D44—22no—
106D44—22no—
107D44—42no—
108Dic22—22no—
109Dic22—22no—
110Dic22—42no—
111C8×C11—22no—
112C8×C11—22no—
113#536—111no—
114#535—111no—
115#485—112no—
116#482—112no—
117#468—112no—
118#465—112no—
119#450—112no—
120#448—112no—
121#408D1111yescharacteristic, complemented
122C22×C11—21no—
123C22×C11—21no—
124C22×C11—21no—
125C22×C11—22no—
126C22×C11—22no—
127C22×C11—22no—
128C22×C11C22×D411yescharacteristic
129C2×D11—42no—
130C2×D11—42no—
131C2×D11—42no—
132C2×D11—84no—
133C4×C11—21no—
134C4×C11—21no—
135C4×C11—21no—
136C4×C11H(5,𝔽2)11yescharacteristic
137C4×C11H(5,𝔽2)11yescharacteristic
138Dic11—42no—
139Dic11—42no—
140Dic11—42no—
141C2×#41C2×D1111yescharacteristic
142C22×Q8—111no—
143C22×D4—111no—
144C2×SD16—112no—
145C2×SD16—112no—
146C2×M16C2×D1111yescharacteristic, complemented
147C22×C8C2×D1111yescharacteristic, complemented
148C4⋊Q8—221no—
149#127—221no—
150#124—221no—
151#124—221no—
152#123—221no—
153#123—221no—
154C22⋊Q8—112no—
155C22⋊Q8—112no—
156#121—112no—
157#121—112no—
158#120—221no—
159#120—221no—
160#117—111no—
161#117—111no—
162#107—112no—
163#106—112no—
164#103—112no—
165#103—112no—
166#102—112no—
167#102—112no—
168C22⋊C8C2×D1112yes—
169C22⋊C8C2×D1112yescomplemented
170C2×C11—41no—
171C2×C11—41no—
172C2×C11—41no—
173C2×C11#53411yescharacteristic
174C2×C11#57712yes—
175D11—82no—
176C24—221no—
177#41—41no—
178#41—41no—
179C2×Q8—112no—
180C2×Q8—221no—
181C2×Q8—441no—
182C2×Q8—441no—
183C2×Q8D4411yescharacteristic
184C2×D4—112no—
185C2×D4—222no—
186C2×D4—222no—
187C2×D4—221no—
188C2×D4—441no—
189C2×D4—441no—
190C2×D4D4411yescharacteristic
191C2×D4D4411yescharacteristic
192C2×D4D4411yescharacteristic
193C22×C4—221no—
194C22×C4C22×D1111yescharacteristic
195C22×C4C22×D1111yescharacteristic
196C22×C4C22×D1111yescharacteristic
197SD16—442no—
198SD16—442no—
199M16—41no—
200C2×C8—41no—
201C2×C8C22×D1112yes—
202C2×C8C22×D1112yes—
203C4⋊C4—112no—
204C4⋊C4—112no—
205C4⋊C4—222no—
206C4⋊C4—222no—
207C22⋊C4—221no—
208C22⋊C4—221no—
209C22⋊C4—222no—
210C22⋊C4—222no—
211C22⋊C4—222no—
212C22⋊C4—222no—
213C42—221no—
214C42—221no—
215C11#320011yescharacteristic, complemented, Sylow
216C23—222no—
217C23—442no—
218C23—882no—
219C23C2×D4411yescharacteristic
220C23C2×D4411yescharacteristic
221C23C2×D4411yescharacteristic
222Q8—41no—
223Q8—222no—
224Q8—222no—
225Q8—442no—
226D4—41no—
227D4—41no—
228D4—41no—
229D4—222no—
230D4—222no—
231D4—442no—
232D4—882no—
233D4—882no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—222no—
241C2×C4—222no—
242C2×C4—222no—
243C2×C4—442no—
244C2×C4C2×D4411yescharacteristic
245C2×C4C2×D4411yescharacteristic
246C2×C4C2×D4411yescharacteristic
247C2×C4C23×D1111yescharacteristic
248C8—22no—
249C8—22no—
250C22—21no—
251C22—21no—
252C22—21no—
253C22—22no—
254C22—22no—
255C22—22no—
256C22—442no—
257C22—442no—
258C22—442no—
259C22—884no—
260C22C22×D4411yescharacteristic
261C4—21no—
262C4—21no—
263C4—21no—
264C4—442no—
265C4—442no—
266C4—442no—
267C4#6703711yescharacteristic
268C4#6703711yescharacteristic
269C2—41no—
270C2—41no—
271C2—41no—
272C2—882no—
273C2#1062302411yescharacteristic
274C2#1062328212yes—
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#408C2
socleC22×C11C22×D4
prime radical#10623361C2
hypercenter#408D11
hypocenterC11#3200
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #10623356C2semidirect
3. C11×#408C2semidirect
4. #10622747C2semidirect
5. #10622727C2semidirect
6. #10622351C2semidirect
7. #10622350C2semidirect
8. #10622344C2semidirect
9. #10622336C2semidirect
12. C22×Dic22C22semidirect
13. C2×C11×M16C22semidirect
14. C22×C8×C11C22semidirect
26. #66979C22semidirect
28. #66977C22semidirect
32. C11×C22⋊C8C22semidirect
35. #66882C22semidirect
36. #66881C22semidirect
37. #66880C22semidirect
38. #66880C22semidirect
121. #408D11semidirect
146. C2×M16C2×D11semidirect
147. C22×C8C2×D11semidirect
169. C22⋊C8C2×D11semidirect
215. C11#3200semidirect

Maximal subgroups

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

subgroupindex
#106233612
#106233562
C11×#4082
#106227472
#106227272
#106223512
#106223502
#106223442
#106223362
#320011