Finite Group Databasebeta

← #13078751

Subgroups — #13078751

Order 1408.

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

normal subgroups only

This group has 450 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#10623131C211yesmaximal, characteristic, complemented
2C2×#66946C211yesmaximal, characteristic, complemented
3C11×#480C211yesmaximal, characteristic, complemented
4#10622649C211yesmaximal, characteristic
5#10622584C211yesmaximal, characteristic, complemented
6#10622504C212yesmaximal, complemented
7#10622502C212yesmaximal, complemented
8#10622400C212yesmaximal, complemented
9#10622398C212yesmaximal, complemented
10#10622344C211yesmaximal, characteristic, complemented
11#10622332C211yesmaximal, characteristic, complemented
12C22×D44C2211yescharacteristic
13C22×C4×D11—21no—
14C11×#121C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16#66989C2211yescharacteristic, complemented
17#66988—21no—
18D4×Dic11—21no—
19D4×Dic11C2211yescharacteristic, complemented
20C2×#4323C2212yes—
21C2×(C2×D11)⋊C4—21no—
22#66977C2211yescharacteristic
23C2×C4×Dic11C2211yescharacteristic
24C2×#4314C2212yes—
25#66946—21no—
26#66946—21no—
27#66946C2212yes—
28#66946C2212yes—
29#66943C2211yescharacteristic, complemented
30#66940C2211yescharacteristic, complemented
31#66932—21no—
32#66930—21no—
33C11×#107C2212yescomplemented
34C11×#102C2212yescomplemented
35C11×C22⋊C8C2211yescharacteristic
36C22⋊(C11⋊C8)C2211yescharacteristic
37#66885C2212yes—
38#66879C2212yescomplemented
39Dic11⋊C8C2212yescomplemented
40#66874C2212yescomplemented
41#66873C2212yes—
42#66872C2212yescomplemented
43C23×D11—21no—
44C2×D4×C11—21no—
45C2×D4×C11C2311yescharacteristic
46C22×C4×C11—21no—
47C22×C4×C11C2311yescharacteristic
48C22×Dic11—21no—
49C22×Dic11D411yescharacteristic
50C22×Dic11D411yescharacteristic
51C2×D44—24no—
52C2×D44—21no—
53C2×D44C2312yes—
54C2×C4×D11—22no—
55C2×C4×D11—22no—
56C2×C4×D11—44no—
57C2×Dic22C2311yescharacteristic
58C2×C8×C11C2312yes—
59C11×C4⋊C4—21no—
60C11×C4⋊C4C2312yes—
61C11×C4⋊C4C2311yescharacteristic
62C11×C22⋊C4—21no—
63C22⋊Dic11—21no—
64C22⋊Dic11—21no—
65C22⋊Dic11—21no—
66C22⋊Dic11—21no—
67#4323—24no—
68(C2×D11)⋊C4—22no—
69(C2×D11)⋊C4—22no—
70C4⋊Dic11—21no—
71C4⋊Dic11C2311yescharacteristic
72Dic11⋊C4—21no—
73Dic11⋊C4—21no—
74Dic11⋊C4—21no—
75C4×Dic11—21no—
76C4×Dic11D411yescharacteristic
77C4×Dic11D411yescharacteristic
78C4×Dic11C2311yescharacteristic
79C4×Dic11C2311yescharacteristic
80C2×C11⋊C8C2312yes—
81#4314—24no—
82#3114—111nomaximal, Sylow
83C23×C11—21no—
84C23×C11C2×D411yescharacteristic
85C22×D11—24no—
86C22×D11—22no—
87C22×D11—42no—
88C22×D11—42no—
89D4×C11—22no—
90D4×C11—42no—
91C2×C4×C11—22no—
92C2×C4×C11—21no—
93C2×C4×C11—22no—
94C2×C4×C11—42no—
95C2×C4×C11C2×D411yescharacteristic
96C2×C4×C11C2411yescharacteristic
97C2×Dic11—22no—
98C2×Dic11—21no—
99C2×Dic11—21no—
100C2×Dic11—41no—
101C2×Dic11—42no—
102C2×Dic11C2×D411yescharacteristic
103C2×Dic11C2×D411yescharacteristic
104C2×Dic11C2×D411yescharacteristic
105C2×Dic11C2×D411yescharacteristic
106D44—24no—
107D44—22no—
108D44#4114yes—
109C4×D11—44no—
110C4×D11—44no—
111Dic22—22no—
112C8×C11—22no—
113C11⋊C8—22no—
114#529—111no—
115C2×C4×D4—111no—
116#483—111no—
117#480D1111yescharacteristic, complemented
118#478—112no—
119#463—112no—
120#450—111no—
121#447—111no—
122#442—112no—
123#440—112no—
124#432—111no—
125C22×C11—21no—
126C22×C11—21no—
127C22×C11—41no—
128C22×C11—41no—
129C22×C11—41no—
130C22×C11AGL(1,ℤ/8)12yes—
131C22×C11C22×D411yescharacteristic
132C2×D11—24no—
133C2×D11—48no—
134C2×D11—42no—
135C2×D11—42no—
136C4×C11—21no—
137C4×C11—42no—
138C4×C11—41no—
139C4×C11C2×#4112yes—
140Dic11—21no—
141Dic11—21no—
142Dic11—21no—
143Dic11—21no—
144Dic11—41no—
145Dic11—41no—
146C22×D4—111no—
147C23×C4—221no—
148C2×SD16—112no—
149C2×D8—112no—
150#126—221no—
151#125—111no—
152#124—111no—
153#123—221no—
154C22⋊Q8—111no—
155#121C2×D1111yescharacteristic
156C4×Q8—111no—
157C4×D4—111no—
158C4×D4—112no—
159C4×D4—112no—
160C4×D4—221no—
161C4×D4—221no—
162C4×D4—221no—
163#117—221no—
164C2×C4⋊C4C2×D1111yescharacteristic
165C2×C22⋊C4—221no—
166C2×C42—111no—
167#107C2×D1112yescomplemented
168#106—112no—
169C4⋊C8—112no—
170#103—112no—
171#102—112no—
172#102—112no—
173#102C2×D1112yescomplemented
174C22⋊C8—111no—
175C22⋊C8C2×D1111yescharacteristic
176#97—112no—
177C2×C11—22no—
178C2×C11—81no—
179C2×C11#52511yescharacteristic
180C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
181C2×C11#57511yescharacteristic
182D11—44no—
183C24—221no—
184C2×Q8—111no—
185C2×D4—21no—
186C2×D4—112no—
187C2×D4—224no—
188C2×D4—221no—
189C2×D4C22×D1111yescharacteristic
190C22×C4—21no—
191C22×C4—111no—
192C22×C4—111no—
193C22×C4—222no—
194C22×C4—222no—
195C22×C4—221no—
196C22×C4—444no—
197C22×C4C22×D1111yescharacteristic
198SD16—224no—
199D8—224no—
200C2×C8—112no—
201C2×C8C22×D1112yes—
202C4⋊C4—21no—
203C4⋊C4—111no—
204C4⋊C4—221no—
205C4⋊C4—221no—
206C4⋊C4—221no—
207C4⋊C4—221no—
208C4⋊C4C22×D1111yescharacteristic
209C4⋊C4C22×D1112yes—
210C22⋊C4—21no—
211C22⋊C4—222no—
212C22⋊C4—222no—
213C22⋊C4—221no—
214C22⋊C4—221no—
215C22⋊C4—221no—
216C22⋊C4—221no—
217C42—111no—
218C42—111no—
219C42—111no—
220C42—111no—
221C42—221no—
222C11#311411yescharacteristic, complemented, Sylow
223C23—21no—
224C23—224no—
225C23—222no—
226C23—442no—
227C23—442no—
228C23D4×D1111yescharacteristic
229Q8—222no—
230D4—22no—
231D4—42no—
232D4—114no—
233D4—224no—
234D4—222no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—111no—
240C2×C4—111no—
241C2×C4—111no—
242C2×C4—111no—
243C2×C4—222no—
244C2×C4—221no—
245C2×C4—221no—
246C2×C4—444no—
247C2×C4—444no—
248C2×C4—441no—
249C2×C4—442no—
250C2×C4D4×D1111yescharacteristic
251C2×C4C23×D1111yescharacteristic
252C8—22no—
253C8—222no—
254C22—21no—
255C22—21no—
256C22—41no—
257C22—41no—
258C22—41no—
259C22—224no—
260C22—448no—
261C22—442no—
262C22—442no—
263C22#6696412yes—
264C22C2×D4×D1111yescharacteristic
265C4—21no—
266C4—42no—
267C4—41no—
268C4—221no—
269C4—221no—
270C4—221no—
271C4—221no—
272C4—441no—
273C4—441no—
274C4#41×D1112yes—
275C2—22no—
276C2—81no—
277C2—444no—
278C2#1062318711yescharacteristic
279C2C2×#6696411yescharacteristic
280C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#480C2
socleC22×C11C22×D4
prime radical#10622649C2
hypercenter#480D11
hypocenterC11#3114
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #10623131C2semidirect
2. C2×#66946C2semidirect
3. C11×#480C2semidirect
5. #10622584C2semidirect
6. #10622504C2semidirect
7. #10622502C2semidirect
8. #10622400C2semidirect
9. #10622398C2semidirect
10. #10622344C2semidirect
11. #10622332C2semidirect
16. #66989C22semidirect
19. D4×Dic11C22semidirect
29. #66943C22semidirect
30. #66940C22semidirect
33. C11×#107C22semidirect
34. C11×#102C22semidirect
38. #66879C22semidirect
39. Dic11⋊C8C22semidirect
40. #66874C22semidirect
42. #66872C22semidirect
117. #480D11semidirect
167. #107C2×D11semidirect
173. #102C2×D11semidirect
222. C11#3114semidirect

Maximal subgroups

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

subgroupindex
#106231312
C2×#669462
C11×#4802
#106226492
#106225842
#106225042
#106225022
#106224002
#106223982
#106223442
#106223322
#311411