Finite Group Databasebeta

← #13079372

Subgroups — #13079372

Order 1408.

468 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 121 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
1D11×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#66948C211yesmaximal, characteristic
3C11×#483C211yesmaximal, characteristic, complemented
4#10622659C211yesmaximal, characteristic, complemented
5#10622584C211yesmaximal, characteristic, complemented
6#10622477C212yesmaximal, complemented
7#10622476C212yesmaximal, complemented
8#10622420C212yesmaximal, complemented
9#10622419C212yesmaximal, complemented
10#10622344C211yesmaximal, characteristic, complemented
11D11×C22⋊C8C211yesmaximal, characteristic, complemented
12C2×Q8×D11C2211yescharacteristic, complemented
13C22×D44—21no—
14C22×D44C2211yescharacteristic
15C22×C4×D11C2211yescharacteristic
16C11×C22⋊Q8C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18#66999C2211yescharacteristic, complemented
19C2×#4325C2212yescomplemented
20C2×(C2×D11)⋊C4—21no—
21#66977C2211yescharacteristic
22C2×#4314C2212yescomplemented
23C2×C8×D11C2212yescomplemented
24#66950C2211yescharacteristic, complemented
25#66949—21no—
26#66948—21no—
27#66948—21no—
28#66948C2212yes—
29#66948C2212yes—
30C4⋊C4×D11—21no—
31C4⋊C4×D11C2211yescharacteristic, complemented
32C22⋊C4×D11—21no—
33#66931—21no—
34C11×#106C2212yescomplemented
35C11×#103C2212yescomplemented
36C11×C22⋊C8C2211yescharacteristic
37C22⋊(C11⋊C8)C2211yescharacteristic
38#66885C2212yescomplemented
39(C2×D11)⋊C8C2212yescomplemented
40#66874C2212yescomplemented
41#66873C2212yescomplemented
42#66872C2212yescomplemented
43C23×D11—21no—
44C23×D11D411yescharacteristic
45C2×Q8×C11C2311yescharacteristic
46C22×C4×C11—21no—
47C22×C4×C11C2311yescharacteristic
48C22×Dic11D411yescharacteristic
49Q8×D11—42no—
50C2×D44—22no—
51C2×D44—22no—
52C2×D44—21no—
53C2×D44—42no—
54C2×D44—44no—
55C2×D44C2312yes—
56C2×C4×D11—21no—
57C2×C4×D11—21no—
58C2×C4×D11—42no—
59C2×C4×D11D411yescharacteristic
60C2×C4×D11D411yescharacteristic
61C2×C4×D11C2311yescharacteristic
62C2×C4×D11C2311yescharacteristic
63C2×Dic22—21no—
64C2×Dic22C2311yescharacteristic
65C2×C8×C11C2312yes—
66C11×C4⋊C4—21no—
67C11×C4⋊C4—21no—
68C11×C4⋊C4C2312yes—
69C11×C4⋊C4C2311yescharacteristic
70C11×C22⋊C4—21no—
71C22⋊Dic11—21no—
72#4325—42no—
73(C2×D11)⋊C4—22no—
74(C2×D11)⋊C4—22no—
75(C2×D11)⋊C4—21no—
76(C2×D11)⋊C4—21no—
77C4⋊Dic11—21no—
78C4⋊Dic11C2311yescharacteristic
79Dic11⋊C4—21no—
80Dic11⋊C4—21no—
81Dic11⋊C4—21no—
82C2×C11⋊C8C2312yes—
83#4314—42no—
84C8×D11—42no—
85#3187—111nomaximal, Sylow
86C23×C11C2×D411yescharacteristic
87C22×D11—22no—
88C22×D11—41no—
89C22×D11—41no—
90C22×D11—42no—
91C22×D11—42no—
92C22×D11—42no—
93C22×D11SD1614yescomplemented
94C22×D11C2×D411yescharacteristic
95C22×D11C2×D411yescharacteristic
96Q8×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—22no—
101C2×C4×C11—42no—
102C2×C4×C11C2×D411yescharacteristic
103C2×C4×C11C2411yescharacteristic
104C2×Dic11—21no—
105C2×Dic11—21no—
106C2×Dic11—41no—
107C2×Dic11C2×D411yescharacteristic
108C2×Dic11C2×D411yescharacteristic
109D44—22no—
110D44—22no—
111D44—42no—
112D44—44no—
113D44—44no—
114C4×D11—22no—
115C4×D11—22no—
116C4×D11—41no—
117C4×D11—41no—
118C4×D11—42no—
119C4×D11—42no—
120Dic22—22no—
121Dic22—42no—
122C8×C11—22no—
123C11⋊C8—22no—
124C2×C22⋊Q8—111no—
125C2×#121—111no—
126#483—111no—
127#483D1111yescharacteristic, complemented
128#481—112no—
129#465—112no—
130#465—112no—
131#450—111no—
132#450—111no—
133#448—112no—
134C2×C22⋊C8—111no—
135C22×C11—21no—
136C22×C11—21no—
137C22×C11C2×SD1612yes—
138C22×C11C22×D411yescharacteristic
139C2×D11—21no—
140C2×D11—21no—
141C2×D11—21no—
142C2×D11—21no—
143C2×D11—44no—
144C2×D11—42no—
145C2×D11—42no—
146C2×D11—42no—
147C2×D11—84no—
148C2×D11C2×SD1612yes—
149C2×D11C2×SD1612yes—
150C4×C11—21no—
151C4×C11—41no—
152C4×C11—42no—
153C4×C11—41no—
154C4×C11H(5,𝔽2)12yes—
155Dic11—21no—
156Dic11—21no—
157Dic11—41no—
158Dic11—41no—
159C22×Q8—111no—
160C22×D4—111no—
161C22×D4—221no—
162C23×C4—111no—
163C2×SD16—112no—
164C2×SD16—112no—
165C22×C8—112no—
166C22⋊Q8—111no—
167C22⋊Q8—111no—
168C22⋊Q8—111no—
169C22⋊Q8—221no—
170C22⋊Q8—221no—
171C22⋊Q8C2×D1111yescharacteristic
172#121—112no—
173#121—112no—
174#121—221no—
175#121—221no—
176C2×C4⋊C4—111no—
177C2×C4⋊C4—221no—
178C2×C4⋊C4C2×D1111yescharacteristic
179C2×C22⋊C4—221no—
180C2×C22⋊C4—221no—
181#106—112no—
182#106C2×D1112yescomplemented
183#103—112no—
184#103C2×D1112yescomplemented
185#102—112no—
186#102—112no—
187C22⋊C8—111no—
188C22⋊C8—112no—
189C22⋊C8C2×D1111yescharacteristic
190C2×C11—22no—
191C2×C11#53411yescharacteristic
192C2×C11C22×SD1611yescharacteristic
193C2×C11#57511yescharacteristic
194D11—22no—
195D11—22no—
196D11—82no—
197C24—111no—
198C24—221no—
199C2×Q8—111no—
200C2×Q8—221no—
201C2×Q8—442no—
202C2×Q8C22×D1111yescharacteristic
203C2×D4—112no—
204C2×D4—222no—
205C2×D4—222no—
206C2×D4—221no—
207C2×D4—442no—
208C2×D4—444no—
209C22×C4—21no—
210C22×C4—111no—
211C22×C4—111no—
212C22×C4—111no—
213C22×C4—111no—
214C22×C4—111no—
215C22×C4—221no—
216C22×C4—221no—
217C22×C4—442no—
218C22×C4C22×D1111yescharacteristic
219SD16—442no—
220SD16—442no—
221C2×C8—112no—
222C2×C8—442no—
223C2×C8C22×D1112yes—
224C4⋊C4—21no—
225C4⋊C4—21no—
226C4⋊C4—111no—
227C4⋊C4—221no—
228C4⋊C4—221no—
229C4⋊C4—221no—
230C4⋊C4—221no—
231C4⋊C4C22×D1111yescharacteristic
232C4⋊C4C22×D1112yes—
233C22⋊C4—21no—
234C22⋊C4—222no—
235C22⋊C4—222no—
236C22⋊C4—221no—
237C22⋊C4—221no—
238C22⋊C4—221no—
239C11#318711yescharacteristic, complemented, Sylow
240C23—111no—
241C23—111no—
242C23—114no—
243C23—222no—
244C23—441no—
245C23—441no—
246C23—442no—
247C23—442no—
248C23—442no—
249C23D4×D1111yescharacteristic
250Q8—22no—
251Q8—222no—
252Q8—442no—
253D4—222no—
254D4—222no—
255D4—442no—
256D4—444no—
257D4—444no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—42no—
263C2×C4—111no—
264C2×C4—111no—
265C2×C4—222no—
266C2×C4—222no—
267C2×C4—221no—
268C2×C4—221no—
269C2×C4—441no—
270C2×C4—441no—
271C2×C4—442no—
272C2×C4—442no—
273C2×C4—441no—
274C2×C4D4×D1111yescharacteristic
275C2×C4C23×D1111yescharacteristic
276C8—22no—
277C8—222no—
278C22—21no—
279C22—21no—
280C22—112no—
281C22—112no—
282C22—221no—
283C22—221no—
284C22—221no—
285C22—221no—
286C22—444no—
287C22—442no—
288C22—442no—
289C22—442no—
290C22—884no—
291C22SD16×D1112yes—
292C22C2×D4×D1111yescharacteristic
293C4—21no—
294C4—42no—
295C4—41no—
296C4—41no—
297C4—221no—
298C4—221no—
299C4—441no—
300C4—441no—
301C4#6704212yes—
302C2—22no—
303C2—222no—
304C2—222no—
305C2—882no—
306C2#1062318411yescharacteristic
307C2C2×SD16×D1111yescharacteristic
308C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#483C2
socleC22×C11C22×D4
prime radicalC2×#66948C2
hypercenter#483D11
hypocenterC11#3187
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. D11×C22⋊Q8C2semidirect
3. C11×#483C2semidirect
4. #10622659C2semidirect
5. #10622584C2semidirect
6. #10622477C2semidirect
7. #10622476C2semidirect
8. #10622420C2semidirect
9. #10622419C2semidirect
10. #10622344C2semidirect
11. D11×C22⋊C8C2semidirect
12. C2×Q8×D11C22semidirect
18. #66999C22semidirect
19. C2×#4325C22semidirect
22. C2×#4314C22semidirect
23. C2×C8×D11C22semidirect
24. #66950C22semidirect
31. C4⋊C4×D11C22semidirect
34. C11×#106C22semidirect
35. C11×#103C22semidirect
38. #66885C22semidirect
39. (C2×D11)⋊C8C22semidirect
40. #66874C22semidirect
41. #66873C22semidirect
42. #66872C22semidirect
93. C22×D11SD16semidirect
127. #483D11semidirect
182. #106C2×D11semidirect
184. #103C2×D11semidirect
239. C11#3187semidirect

Maximal subgroups

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

subgroupindex
D11×C22⋊Q82
C2×#669482
C11×#4832
#106226592
#106225842
#106224772
#106224762
#106224202
#106224192
#106223442
D11×C22⋊C82
#318711