Finite Group Databasebeta

← #13080304

Subgroups — #13080304

Order 1408.

526 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 123 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
1C2×D8×D11C211yesmaximal, characteristic, complemented
2C2×#66957C211yesmaximal, characteristic, complemented
3#10623143C212yesmaximal, complemented
4C11×#466C211yesmaximal, characteristic, complemented
5#10622768C211yesmaximal, characteristic, complemented
6C8×C22⋊D11C211yesmaximal, characteristic, complemented
7#10622650C212yesmaximal, complemented
8#10622500C211yesmaximal, characteristic, complemented
9#10622485C211yesmaximal, characteristic, complemented
10#10622400C212yesmaximal, complemented
11#10622389C212yesmaximal, complemented
12C2×D4×D11C2212yes—
13C2×#4339C2212yescomplemented
14C2×C11×D8C2211yescharacteristic
15C22×C8×C11C2211yescharacteristic, complemented
16C11×#121C2212yescomplemented
17#66991—22no—
18#66990—22no—
19#66989C2212yescomplemented
20C2×#4324C2212yescomplemented
21C2×#4323C2212yes—
22C4×C22⋊D11C2211yescharacteristic
23D8×D11—24no—
24C2×Dic44C2211yescharacteristic, complemented
25#66957—24no—
26C2×D88C2211yescharacteristic
27C2×#4314C2212yescomplemented
28C2×C8×D11C2211yescharacteristic
29#66950C2212yes—
30#66946C2212yescomplemented
31#66936—22no—
32C22⋊C4×D11—22no—
33C11×#107C2211yescharacteristic, complemented
34C11×#102C2212yescomplemented
35C22⋊(C11⋊C8)C2211yescharacteristic, complemented
36(C2×D11)⋊C8C2211yescharacteristic
37Dic11⋊C8C2211yescharacteristic, complemented
38C8×Dic11C2211yescharacteristic, complemented
39#66874C2212yescomplemented
40#66873C2212yescomplemented
41C23×D11—22no—
42C2×D4×C11—22no—
43C2×D4×C11C2312yes—
44C22×C4×C11C2311yescharacteristic
45C2×C22⋊D11—22no—
46C2×C22⋊D11—22no—
47C2×C22⋊D11D411yescharacteristic
48D4×D11—24no—
49D4×D11—42no—
50#4339—24no—
51#4339—42no—
52C2×D44C2312yes—
53C2×C4×D11—22no—
54C2×C4×D11—22no—
55C2×C4×D11C2311yescharacteristic
56C2×Dic22C2312yes—
57C11×D8—22no—
58C2×C8×C11—22no—
59C2×C8×C11C2311yescharacteristic
60C2×C8×C11C2311yescharacteristic
61C11×C4⋊C4C2312yes—
62C11×C22⋊C4—22no—
63C22⋊Dic11—22no—
64C22⋊Dic11—22no—
65C22⋊Dic11D411yescharacteristic
66#4324—42no—
67#4323—24no—
68(C2×D11)⋊C4—22no—
69(C2×D11)⋊C4—22no—
70(C2×D11)⋊C4D411yescharacteristic
71C4⋊Dic11—22no—
72Dic11⋊C4D411yescharacteristic
73C4×Dic11C2311yescharacteristic
74C2×C11⋊C8C2311yescharacteristic
75C2×C11⋊C8C2311yescharacteristic
76Dic44—22no—
77D88D414yescomplemented
78#4314—24no—
79C8×D11—22no—
80#3280—111nomaximal, Sylow
81C23×C11—22no—
82C23×C11C2×D411yescharacteristic
83C22×D11—22no—
84C22×D11—44no—
85C22×D11—44no—
86C22×D11—82no—
87C22×D11C2×D411yescharacteristic
88D4×C11—22no—
89D4×C11—22no—
90D4×C11—82no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—22no—
94C2×C4×C11C2×D411yescharacteristic
95C2×C4×C11C2411yescharacteristic
96C22⋊D11—22no—
97C22⋊D11—44no—
98C22⋊D11—44no—
99C2×Dic11—22no—
100C2×Dic11C2×D411yescharacteristic
101C2×Dic11C2×D411yescharacteristic
102C2×Dic11C2×D411yescharacteristic
103D44—22no—
104D44C2×D414yes—
105C4×D11—21no—
106C4×D11—21no—
107C4×D11—44no—
108C4×D11—82no—
109Dic22—22no—
110Dic22—22no—
111C8×C11—21no—
112C8×C11C2×D412yes—
113C11⋊C8—21no—
114C11⋊C8—21no—
115C2×#135—111no—
116C22×D8—111no—
117#546—112no—
118#495—111no—
119#467—111no—
120#466D1111yescharacteristic, complemented
121#463—112no—
122#450—112no—
123#449—112no—
124C4×D8—111no—
125C8×D4—111no—
126C22×C11—21no—
127C22×C11—21no—
128C22×C11—21no—
129C22×C11—42no—
130C22×C11—42no—
131C22×C11—42no—
132C22×C11C22×D411yescharacteristic
133C2×D11—21no—
134C2×D11—21no—
135C2×D11—24no—
136C2×D11—42no—
137C2×D11—42no—
138C2×D11—88no—
139C2×D11#13512yescomplemented
140C4×C11—21no—
141C4×C11—42no—
142C4×C11C22×D411yescharacteristic
143C4×C11H(5,𝔽2)11yescharacteristic
144Dic11—21no—
145Dic11—21no—
146Dic11—21no—
147Dic11—42no—
148C2×#41—112no—
149C22×D4—112no—
150#135—224no—
151C2×Q16—111no—
152C2×SD16—112no—
153C2×SD16—112no—
154C2×D8—112no—
155C2×D8—111no—
156C2×D8—224no—
157C2×D8C2×D1111yescharacteristic
158C22×C8—111no—
159C22×C8C2×D1111yescharacteristic, complemented
160#124—112no—
161#123—222no—
162C22⋊Q8—112no—
163#121—222no—
164#121C2×D1112yescomplemented
165#120—222no—
166C4×D4—111no—
167C4×D4—112no—
168C2×C22⋊C4—222no—
169#107C2×D1111yescharacteristic, complemented
170C4⋊C8—111no—
171#103—112no—
172#102—112no—
173#102C2×D1112yescomplemented
174C22⋊C8—111no—
175C22⋊C8—111no—
176C4×C8—111no—
177C2×C11—41no—
178C2×C11—82no—
179C2×C11D4211yescharacteristic
180C2×C11C2×#13511yescharacteristic
181C2×C11#57611yescharacteristic
182D11—22no—
183D11—44no—
184C24—222no—
185#41—224no—
186#41—442no—
187C2×Q8—112no—
188C2×D4—22no—
189C2×D4—111no—
190C2×D4—112no—
191C2×D4—222no—
192C2×D4—224no—
193C2×D4—222no—
194C2×D4—442no—
195C2×D4C22×D1112yes—
196C22×C4—111no—
197C22×C4—222no—
198C22×C4—222no—
199C22×C4C22×D1111yescharacteristic
200Q16—222no—
201SD16—224no—
202SD16—442no—
203D8—22no—
204D8—114no—
205D8—224no—
206C2×C8—22no—
207C2×C8—111no—
208C2×C8—111no—
209C2×C8—222no—
210C2×C8C22×D1111yescharacteristic
211C2×C8C22×D1111yescharacteristic
212C4⋊C4—111no—
213C4⋊C4—222no—
214C4⋊C4C22×D1112yes—
215C22⋊C4—22no—
216C22⋊C4—111no—
217C22⋊C4—111no—
218C22⋊C4—222no—
219C22⋊C4—222no—
220C22⋊C4—222no—
221C22⋊C4—222no—
222C42—111no—
223C11#328011yescharacteristic, complemented, Sylow
224C23—22no—
225C23—111no—
226C23—222no—
227C23—444no—
228C23—444no—
229C23—882no—
230C23D4×D1111yescharacteristic
231Q8—222no—
232Q8—222no—
233D4—22no—
234D4—22no—
235D4—82no—
236D4—114no—
237D4—222no—
238D4—222no—
239D4—444no—
240D4—444no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—111no—
245C2×C4—111no—
246C2×C4—111no—
247C2×C4—221no—
248C2×C4—221no—
249C2×C4—222no—
250C2×C4—444no—
251C2×C4—882no—
252C2×C4D4×D1111yescharacteristic
253C2×C4C23×D1111yescharacteristic
254C8—21no—
255C8—221no—
256C8—221no—
257C8D4×D1112yes—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—112no—
265C22—221no—
266C22—221no—
267C22—224no—
268C22—442no—
269C22—442no—
270C22—888no—
271C22C2×D4×D1111yescharacteristic
272C4—21no—
273C4—42no—
274C4—221no—
275C4—221no—
276C4—221no—
277C4—442no—
278C4C2×D4×D1111yescharacteristic
279C4#6704211yescharacteristic
280C2—41no—
281C2—82no—
282C2—222no—
283C2—444no—
284C2#1062314011yescharacteristic
285C2#1062328811yescharacteristic
286C2D11×#13511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#466C2
socleC22×C11C22×D4
hypercenter#466D11
hypocenterC11#3280
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C2×D8×D11C2semidirect
2. C2×#66957C2semidirect
3. #10623143C2semidirect
4. C11×#466C2semidirect
5. #10622768C2semidirect
6. C8×C22⋊D11C2semidirect
7. #10622650C2semidirect
8. #10622500C2semidirect
9. #10622485C2semidirect
10. #10622400C2semidirect
11. #10622389C2semidirect
13. C2×#4339C22semidirect
15. C22×C8×C11C22semidirect
16. C11×#121C22semidirect
19. #66989C22semidirect
20. C2×#4324C22semidirect
24. C2×Dic44C22semidirect
27. C2×#4314C22semidirect
30. #66946C22semidirect
33. C11×#107C22semidirect
34. C11×#102C22semidirect
35. C22⋊(C11⋊C8)C22semidirect
37. Dic11⋊C8C22semidirect
38. C8×Dic11C22semidirect
39. #66874C22semidirect
40. #66873C22semidirect
77. D88D4semidirect
120. #466D11semidirect
139. C2×D11#135semidirect
159. C22×C8C2×D11semidirect
164. #121C2×D11semidirect
169. #107C2×D11semidirect
173. #102C2×D11semidirect
223. C11#3280semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D112
C2×#669572
#106231432
C11×#4662
#106227682
C8×C22⋊D112
#106226502
#106225002
#106224852
#106224002
#106223892
#328011