Finite Group Databasebeta

← #13079398

Subgroups — #13079398

Order 1408.

420 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623158C211yesmaximal, characteristic
2D11×C22⋊Q8C211yesmaximal, characteristic, complemented
3C11×#467C211yesmaximal, characteristic, complemented
4#10622800C211yesmaximal, characteristic, complemented
5#10622799C211yesmaximal, characteristic, complemented
6#10622727C211yesmaximal, characteristic, complemented
7C2×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
8#10622664C211yesmaximal, characteristic, complemented
9#10622661C211yesmaximal, characteristic, complemented
10#10622501C211yesmaximal, characteristic, complemented
11#10622495C211yesmaximal, characteristic, complemented
12#10622428C211yesmaximal, characteristic, complemented
13#10622423C211yesmaximal, characteristic, complemented
14#10622419C211yesmaximal, characteristic, complemented
15#10622418C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×Q8×D11C2211yescharacteristic
18C22×C4×D11C2211yescharacteristic
19C2×C11×Q16C2211yescharacteristic, complemented
20C22×C8×C11C2211yescharacteristic
21C11×C22⋊Q8C2211yescharacteristic
22C11×C22⋊Q8C2211yescharacteristic
23#66999C2211yescharacteristic
24#66999C2211yescharacteristic
25C2×#4326C2211yescharacteristic, complemented
26C2×#4325C2211yescharacteristic, complemented
27#66983C2211yescharacteristic
28#66977C2211yescharacteristic
29C22×C11⋊C8C2211yescharacteristic
30C2×#4314C2211yescharacteristic, complemented
31#66950C2211yescharacteristic
32#66949—21no—
33#66948C2211yescharacteristic
34#66947—21no—
35#66946—21no—
36#66945C2211yescharacteristic
37C4⋊C4×D11—21no—
38C4⋊C4×D11C2211yescharacteristic
39#66935—21no—
40(C22⋊D11)⋊C4—21no—
41C22⋊C4×D11—21no—
42#66931—21no—
43C11×#107C2211yescharacteristic, complemented
44C11×#103C2211yescharacteristic, complemented
45C11×#103C2211yescharacteristic, complemented
46#66899C2211yescharacteristic, complemented
47#66899C2211yescharacteristic, complemented
48#66885C2211yescharacteristic, complemented
49(C2×D11)⋊C8C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51(C2×D11)⋊C8C2211yescharacteristic
52(C2×D11)⋊C8C2211yescharacteristic
53#66881C2211yescharacteristic, complemented
54#66880C2211yescharacteristic, complemented
55#66874C2211yescharacteristic, complemented
56#66873C2211yescharacteristic, complemented
57#66872C2211yescharacteristic, complemented
58#66871C2211yescharacteristic, complemented
59C23×D11D411yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C2×Q8×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C2×C22⋊D11—21no—
64C22×Dic11D411yescharacteristic
65#4343—41no—
66#4343—41no—
67Q8×D11—41no—
68Q8×D11—41no—
69C2×D44—21no—
70C2×D44—21no—
71C2×D44C2311yescharacteristic
72C2×C4×D11—21no—
73C2×C4×D11—21no—
74C2×C4×D11—21no—
75C2×C4×D11—41no—
76C2×C4×D11—41no—
77C2×C4×D11D411yescharacteristic
78C2×C4×D11D411yescharacteristic
79C2×C4×D11C2311yescharacteristic
80C2×C4×D11C2311yescharacteristic
81C2×Dic22—21no—
82C2×Dic22C2311yescharacteristic
83C11×Q16—41no—
84C2×C8×C11—41no—
85C2×C8×C11C2311yescharacteristic
86C2×C8×C11C2311yescharacteristic
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4C2311yescharacteristic
90C11×C4⋊C4C2311yescharacteristic
91C11×C22⋊C4—21no—
92C11×C22⋊C4—21no—
93C22⋊Dic11—21no—
94#4326—41no—
95#4325—41no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4—21no—
100(C2×D11)⋊C4—21no—
101(C2×D11)⋊C4—21no—
102C4⋊Dic11—21no—
103C4⋊Dic11C2311yescharacteristic
104C4⋊Dic11C2311yescharacteristic
105Dic11⋊C4—21no—
106Dic11⋊C4—21no—
107Dic11⋊C4—21no—
108Dic11⋊C4—21no—
109C4×Dic11—21no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8C2311yescharacteristic
112C2×C11⋊C8C2311yescharacteristic
113#4314—41no—
114#3190—111nomaximal, Sylow
115C23×C11C2×D411yescharacteristic
116C22×D11—22no—
117C22×D11—22no—
118C22×D11—21no—
119C22×D11—41no—
120C22×D11C2×D411yescharacteristic
121C22×D11C2×D411yescharacteristic
122Q8×C11—21no—
123Q8×C11—21no—
124Q8×C11—21no—
125Q8×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11C2×D411yescharacteristic
133C2×C4×C11C2411yescharacteristic
134C22⋊D11—42no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—41no—
139C2×Dic11C2×D411yescharacteristic
140C2×Dic11C2×D411yescharacteristic
141D44—21no—
142D44—21no—
143D44—42no—
144D44—42no—
145C4×D11—21no—
146C4×D11—21no—
147C4×D11—21no—
148C4×D11—21no—
149C4×D11—41no—
150C4×D11—41no—
151C4×D11—42no—
152C4×D11—42no—
153C4×D11—42no—
154Dic22—21no—
155Dic22—21no—
156Dic22—42no—
157C8×C11—21no—
158C8×C11—21no—
159C11⋊C8—21no—
160C11⋊C8—21no—
161#525—111no—
162C2×C22⋊Q8—111no—
163#485—111no—
164#485—111no—
165#483—111no—
166#480—111no—
167#467—111no—
168#467D1111yescharacteristic, complemented
169#465—111no—
170#465—111no—
171#452—111no—
172#452—111no—
173#451—111no—
174#448—111no—
175C2×C22⋊C8—111no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11#13712yes—
179C22×C11C22×D411yescharacteristic
180C2×D11—21no—
181C2×D11—21no—
182C2×D11—21no—
183C2×D11—21no—
184C2×D11—21no—
185C2×D11—44no—
186C2×D11—41no—
187C2×D11—41no—
188C2×D11—41no—
189C2×D11#13512yes—
190C4×C11—21no—
191C4×C11—41no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11—41no—
195C4×C11H(5,𝔽2)11yescharacteristic
196C4×C11H(5,𝔽2)11yescharacteristic
197Dic11—21no—
198Dic11—21no—
199Dic11—41no—
200Dic11—41no—
201Dic11—41no—
202C2×#41—111no—
203C22×Q8—111no—
204C23×C4—111no—
205C2×Q16—111no—
206C2×Q16C2×D1111yescharacteristic, complemented
207C2×SD16—111no—
208C2×SD16—111no—
209C22×C8—111no—
210C22×C8C2×D1111yescharacteristic
211#123—221no—
212C22⋊Q8—111no—
213C22⋊Q8—111no—
214C22⋊Q8—111no—
215C22⋊Q8—111no—
216C22⋊Q8—221no—
217C22⋊Q8—221no—
218C22⋊Q8C2×D1111yescharacteristic
219C22⋊Q8C2×D1111yescharacteristic
220#121—111no—
221#121—111no—
222#120—221no—
223C4×D4—221no—
224C4×D4—221no—
225#117—111no—
226C2×C4⋊C4—111no—
227C2×C4⋊C4—221no—
228C2×C22⋊C4—221no—
229#107—111no—
230#107C2×D1111yescharacteristic, complemented
231#106—111no—
232#106—111no—
233#103—111no—
234#103—111no—
235#103—111no—
236#103—111no—
237#103C2×D1111yescharacteristic, complemented
238#103C2×D1111yescharacteristic, complemented
239#102—111no—
240#102—111no—
241C22⋊C8—111no—
242C22⋊C8—111no—
243C22⋊C8—111no—
244C22⋊C8—111no—
245C2×C11—22no—
246C2×C11#53411yescharacteristic
247C2×C11C2×#13511yescharacteristic
248C2×C11C2×#13711yescharacteristic
249D11—22no—
250D11—41no—
251D11—81no—
252C24—111no—
253#41—441no—
254#41—441no—
255C2×Q8—111no—
256C2×Q8—221no—
257C2×Q8—441no—
258C2×Q8—441no—
259C2×Q8C22×D1111yescharacteristic
260C2×Q8C22×D1111yescharacteristic
261C2×D4—111no—
262C2×D4—221no—
263C2×D4—221no—
264C2×D4—221no—
265C22×C4—111no—
266C22×C4—111no—
267C22×C4—111no—
268C22×C4—111no—
269C22×C4—111no—
270C22×C4—221no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4—441no—
274C22×C4—441no—
275C22×C4C22×D1111yescharacteristic
276Q16—41no—
277Q16—441no—
278SD16—441no—
279SD16—441no—
280C2×C8—41no—
281C2×C8—111no—
282C2×C8—111no—
283C2×C8—441no—
284C2×C8C22×D1111yescharacteristic
285C2×C8C22×D1111yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—111no—
289C4⋊C4—111no—
290C4⋊C4—221no—
291C4⋊C4—221no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C4⋊C4—221no—
295C4⋊C4C22×D1111yescharacteristic
296C4⋊C4C22×D1111yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—221no—
300C22⋊C4—221no—
301C22⋊C4—221no—
302C22⋊C4—221no—
303C22⋊C4—221no—
304C22⋊C4—221no—
305C22⋊C4—221no—
306C42—221no—
307C11#319011yescharacteristic, complemented, Sylow
308C23—111no—
309C23—111no—
310C23—222no—
311C23—222no—
312C23—221no—
313C23—441no—
314C23D4×D1111yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—21no—
318Q8—21no—
319Q8—221no—
320Q8—221no—
321Q8—442no—
322D4—221no—
323D4—221no—
324D4—442no—
325D4—442no—
326D4—442no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—111no—
334C2×C4—111no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—221no—
339C2×C4—221no—
340C2×C4—221no—
341C2×C4—221no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—442no—
345C2×C4—442no—
346C2×C4—442no—
347C2×C4—441no—
348C2×C4D4×D1111yescharacteristic
349C2×C4C23×D1111yescharacteristic
350C8—21no—
351C8—21no—
352C8—221no—
353C8—221no—
354C22—21no—
355C22—21no—
356C22—112no—
357C22—221no—
358C22—221no—
359C22—221no—
360C22—221no—
361C22—221no—
362C22—444no—
363C22—441no—
364C22—441no—
365C22—441no—
366C22#6697112yes—
367C22C2×D4×D1111yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—221no—
374C4—221no—
375C4—441no—
376C4—441no—
377C4—441no—
378C4#6703711yescharacteristic
379C4#6704211yescharacteristic
380C2—22no—
381C2—222no—
382C2—441no—
383C2—881no—
384C2#1062313611yescharacteristic
385C2C2×#6697111yescharacteristic
386C2D11×#13511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#467C2
socleC22×C11C22×D4
prime radical#10623158C2
hypercenter#467D11
hypocenterC11#3190
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
2. D11×C22⋊Q8C2semidirect
3. C11×#467C2semidirect
4. #10622800C2semidirect
5. #10622799C2semidirect
6. #10622727C2semidirect
7. C2×(C2×D11)⋊C8C2semidirect
8. #10622664C2semidirect
9. #10622661C2semidirect
10. #10622501C2semidirect
11. #10622495C2semidirect
12. #10622428C2semidirect
13. #10622423C2semidirect
14. #10622419C2semidirect
15. #10622418C2semidirect
19. C2×C11×Q16C22semidirect
25. C2×#4326C22semidirect
26. C2×#4325C22semidirect
30. C2×#4314C22semidirect
43. C11×#107C22semidirect
44. C11×#103C22semidirect
45. C11×#103C22semidirect
46. #66899C22semidirect
47. #66899C22semidirect
48. #66885C22semidirect
53. #66881C22semidirect
54. #66880C22semidirect
55. #66874C22semidirect
56. #66873C22semidirect
57. #66872C22semidirect
58. #66871C22semidirect
168. #467D11semidirect
206. C2×Q16C2×D11semidirect
230. #107C2×D11semidirect
237. #103C2×D11semidirect
238. #103C2×D11semidirect
307. C11#3190semidirect

Maximal subgroups

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

subgroupindex
#106231582
D11×C22⋊Q82
C11×#4672
#106228002
#106227992
#106227272
C2×(C2×D11)⋊C82
#106226642
#106226612
#106225012
#106224952
#106224282
#106224232
#106224192
#106224182
#319011