Finite Group Databasebeta

← #13079662

Subgroups — #13079662

Order 1408.

420 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623336C211yesmaximal, characteristic, complemented
2#10623150C211yesmaximal, characteristic, complemented
3C11×#447C211yesmaximal, characteristic, complemented
4#10622830C211yesmaximal, characteristic, complemented
5#10622767C211yesmaximal, characteristic, complemented
6#10622766C211yesmaximal, characteristic, complemented
7#10622764C211yesmaximal, characteristic, complemented
8#10622763C211yesmaximal, characteristic, complemented
9#10622650C211yesmaximal, characteristic, complemented
10#10622400C211yesmaximal, characteristic, complemented
11#10622399C211yesmaximal, characteristic, complemented
12#10622381C211yesmaximal, characteristic, complemented
13#10622377C211yesmaximal, characteristic, complemented
14#10622347C211yesmaximal, characteristic, complemented
15#10622333C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C2×#4339C2211yescharacteristic
18C2×C11×D8C2211yescharacteristic
19C2×C11×D8C2211yescharacteristic
20C11×#121C2211yescharacteristic
21#67006—21no—
22#67006—21no—
23#66993C2211yescharacteristic
24#66993C2211yescharacteristic
25#66993C2211yescharacteristic, complemented
26#66992—21no—
27#66991—21no—
28#66991—21no—
29#66991—21no—
30#66989C2211yescharacteristic
31#66989C2211yescharacteristic
32D4×Dic11C2211yescharacteristic, complemented
33C2×#4324C2211yescharacteristic, complemented
34C2×#4323C2211yescharacteristic
35C2×#4323C2211yescharacteristic
36C2×#4323C2211yescharacteristic, complemented
37#66983C2211yescharacteristic
38#66979C2211yescharacteristic
39C2×D88C2211yescharacteristic, complemented
40C2×#4314C2211yescharacteristic, complemented
41#66946C2211yescharacteristic, complemented
42#66943C2211yescharacteristic, complemented
43#66939—21no—
44#66936—21no—
45C11×#102C2211yescharacteristic
46C11×#102C2211yescharacteristic
47C11×C22⋊C8C2211yescharacteristic
48#66896C2211yescharacteristic
49#66896C2211yescharacteristic
50C22⋊(C11⋊C8)C2211yescharacteristic
51#66885C2211yescharacteristic, complemented
52#66880C2211yescharacteristic, complemented
53#66879C2211yescharacteristic, complemented
54Dic11⋊C8C2211yescharacteristic, complemented
55Dic11⋊C8C2211yescharacteristic, complemented
56C8×Dic11C2211yescharacteristic, complemented
57#66874C2211yescharacteristic, complemented
58#66873C2211yescharacteristic, complemented
59C24×C11—21no—
60C2×D4×C11—21no—
61C2×D4×C11—21no—
62C2×D4×C11—41no—
63C2×D4×C11—41no—
64C2×D4×C11C2311yescharacteristic
65C2×D4×C11C2311yescharacteristic
66C2×D4×C11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70C2×C22⋊D11—21no—
71C2×C22⋊D11—21no—
72C2×C22⋊D11—21no—
73C2×C22⋊D11—21no—
74C2×C22⋊D11—21no—
75C2×C22⋊D11—21no—
76C22×Dic11—21no—
77#4339—41no—
78#4339—41no—
79C2×D44C2311yescharacteristic
80C2×D44C2311yescharacteristic
81C2×C4×D11—21no—
82C2×C4×D11—21no—
83C2×Dic22C2311yescharacteristic
84C11×D8—41no—
85C11×D8—41no—
86C2×C8×C11C2311yescharacteristic
87C2×C8×C11C2311yescharacteristic
88C11×C4⋊C4C2311yescharacteristic
89C11×C22⋊C4—21no—
90C22⋊Dic11—21no—
91C22⋊Dic11—21no—
92C22⋊Dic11—21no—
93C22⋊Dic11—21no—
94C22⋊Dic11—21no—
95C22⋊Dic11D411yescharacteristic
96C22⋊Dic11D411yescharacteristic
97#4324—41no—
98#4323—41no—
99#4323—41no—
100#4323—41no—
101(C2×D11)⋊C4—21no—
102(C2×D11)⋊C4—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11D411yescharacteristic
105C4⋊Dic11D411yescharacteristic
106C4⋊Dic11C2311yescharacteristic
107Dic11⋊C4—21no—
108C4×Dic11C2311yescharacteristic
109C4×Dic11C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111C2×C11⋊C8C2311yescharacteristic
112D88—41no—
113#4314—41no—
114#3220—111nomaximal, Sylow
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—42no—
119C23×C11—81no—
120C23×C11—81no—
121C23×C11C2×D411yescharacteristic
122C22×D11—21no—
123C22×D11—21no—
124D4×C11—21no—
125D4×C11—21no—
126D4×C11—21no—
127D4×C11—21no—
128D4×C11—21no—
129D4×C11—21no—
130D4×C11—42no—
131D4×C11—81no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11C2×D411yescharacteristic
136C2×C4×C11C2411yescharacteristic
137C22⋊D11—42no—
138C22⋊D11—81no—
139C22⋊D11—81no—
140C22⋊D11—81no—
141C22⋊D11—81no—
142C22⋊D11—81no—
143C22⋊D11—81no—
144C22⋊D11—81no—
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—81no—
148C2×Dic11C2×D411yescharacteristic
149C2×Dic11C2×D411yescharacteristic
150C2×Dic11C2×D411yescharacteristic
151C2×Dic11C2×D411yescharacteristic
152D44—21no—
153D44—21no—
154D44—21no—
155D44—21no—
156C4×D11—42no—
157C4×D11—81no—
158Dic22—21no—
159Dic22—21no—
160C8×C11—21no—
161C8×C11—21no—
162C11⋊C8—21no—
163C11⋊C8—21no—
164#540—111no—
165#535—111no—
166#496—111no—
167#493—111no—
168#490—111no—
169#488—111no—
170#463—111no—
171#463—111no—
172#459—111no—
173#459—111no—
174#449—111no—
175#449—111no—
176#447—111no—
177#447D1111yescharacteristic, complemented
178#433—111no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11—41no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—84no—
192C22×C11C22×D411yescharacteristic
193C2×D11—41no—
194C2×D11—41no—
195C2×D11—41no—
196C2×D11—41no—
197C2×D11—41no—
198C2×D11—41no—
199C4×C11—21no—
200C4×C11—41no—
201C4×C11H(5,𝔽2)11yescharacteristic
202C4×C11H(5,𝔽2)11yescharacteristic
203Dic11—21no—
204Dic11—21no—
205Dic11—21no—
206Dic11—21no—
207Dic11—41no—
208Dic11—41no—
209C2×#41—111no—
210C22×D4C2×D1111yescharacteristic
211C2×SD16—111no—
212C2×SD16—111no—
213C2×D8—111no—
214C2×D8—111no—
215C2×D8—111no—
216C2×D8—111no—
217C2×D8C2×D1111yescharacteristic
218C2×D8C2×D1111yescharacteristic
219#127—111no—
220#127—111no—
221#127—111no—
222#125—111no—
223#124—111no—
224#124—111no—
225#123—221no—
226#123—221no—
227#121—111no—
228#121—221no—
229#121—221no—
230#121—221no—
231#121—221no—
232#121C2×D1111yescharacteristic
233#120—221no—
234#120—221no—
235C4×D4—111no—
236C4×D4—111no—
237#117—111no—
238C4⋊C8—111no—
239C4⋊C8—111no—
240#103—111no—
241#103—111no—
242#102—111no—
243#102—111no—
244#102—111no—
245#102—111no—
246#102C2×D1111yescharacteristic
247#102C2×D1111yescharacteristic
248C22⋊C8—111no—
249C22⋊C8C2×D1111yescharacteristic
250#97—111no—
251C4×C8—111no—
252C2×C11—41no—
253C2×C11—81no—
254C2×C11—81no—
255C2×C11—81no—
256C2×C11#53511yescharacteristic
257C2×C11#57611yescharacteristic
258C2×C11#57611yescharacteristic
259D11—81no—
260D11—81no—
261C24—21no—
262#41—441no—
263#41—441no—
264C2×Q8—111no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—111no—
270C2×D4—111no—
271C2×D4—221no—
272C2×D4—221no—
273C2×D4—221no—
274C2×D4—221no—
275C2×D4—221no—
276C2×D4—221no—
277C2×D4—221no—
278C2×D4—221no—
279C2×D4C22×D1111yescharacteristic
280C2×D4C22×D1111yescharacteristic
281C2×D4C22×D1111yescharacteristic
282C22×C4—221no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4C22×D1111yescharacteristic
286SD16—441no—
287SD16—441no—
288D8—41no—
289D8—41no—
290D8—441no—
291D8—441no—
292D8—441no—
293D8—441no—
294C2×C8—111no—
295C2×C8—111no—
296C2×C8C22×D1111yescharacteristic
297C2×C8C22×D1111yescharacteristic
298C4⋊C4—111no—
299C4⋊C4—111no—
300C4⋊C4—111no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C4⋊C4C22×D1111yescharacteristic
304C22⋊C4—21no—
305C22⋊C4—111no—
306C22⋊C4—111no—
307C22⋊C4—221no—
308C22⋊C4—221no—
309C22⋊C4—221no—
310C22⋊C4—221no—
311C22⋊C4—221no—
312C22⋊C4—221no—
313C22⋊C4—221no—
314C42—111no—
315C42—111no—
316C11#322011yescharacteristic, complemented, Sylow
317C23—21no—
318C23—21no—
319C23—21no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—221no—
324C23—221no—
325C23D4×D1111yescharacteristic
326Q8—221no—
327Q8—221no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—42no—
335D4—81no—
336D4—221no—
337D4—221no—
338D4—221no—
339D4—221no—
340D4—442no—
341D4—881no—
342D4—881no—
343D4—881no—
344D4—881no—
345D4—881no—
346D4—881no—
347D4—881no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—111no—
352C2×C4—111no—
353C2×C4—111no—
354C2×C4—111no—
355C2×C4—221no—
356C2×C4—221no—
357C2×C4—442no—
358C2×C4—881no—
359C2×C4—881no—
360C2×C4D4×D1111yescharacteristic
361C2×C4C23×D1111yescharacteristic
362C8—21no—
363C8—21no—
364C8—221no—
365C8—221no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—84no—
379C22—441no—
380C22—441no—
381C22—441no—
382C22—441no—
383C22—441no—
384C22—441no—
385C22C2×D4×D1111yescharacteristic
386C4—21no—
387C4—41no—
388C4—221no—
389C4—221no—
390C4—221no—
391C4—221no—
392C4—441no—
393C4—441no—
394C4#6703711yescharacteristic
395C4#6703711yescharacteristic
396C2—41no—
397C2—81no—
398C2—81no—
399C2—81no—
400C2—881no—
401C2—881no—
402C2#1062312311yescharacteristic
403C2#1062328811yescharacteristic
404C2#1062330511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#447C2
socleC22×C11C22×D4
hypercenter#447D11
hypocenterC11#3220
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #10623336C2semidirect
2. #10623150C2semidirect
3. C11×#447C2semidirect
4. #10622830C2semidirect
5. #10622767C2semidirect
6. #10622766C2semidirect
7. #10622764C2semidirect
8. #10622763C2semidirect
9. #10622650C2semidirect
10. #10622400C2semidirect
11. #10622399C2semidirect
12. #10622381C2semidirect
13. #10622377C2semidirect
14. #10622347C2semidirect
15. #10622333C2semidirect
25. #66993C22semidirect
32. D4×Dic11C22semidirect
33. C2×#4324C22semidirect
36. C2×#4323C22semidirect
39. C2×D88C22semidirect
40. C2×#4314C22semidirect
41. #66946C22semidirect
42. #66943C22semidirect
51. #66885C22semidirect
52. #66880C22semidirect
53. #66879C22semidirect
54. Dic11⋊C8C22semidirect
55. Dic11⋊C8C22semidirect
56. C8×Dic11C22semidirect
57. #66874C22semidirect
58. #66873C22semidirect
177. #447D11semidirect
316. C11#3220semidirect

Maximal subgroups

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

subgroupindex
#106233362
#106231502
C11×#4472
#106228302
#106227672
#106227662
#106227642
#106227632
#106226502
#106224002
#106223992
#106223812
#106223772
#106223472
#106223332
#322011