Finite Group Databasebeta

← #13079710

Subgroups — #13079710

Order 1408.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#535C211yesmaximal, characteristic, complemented
2#10623065C211yesmaximal, characteristic, complemented
3#10622852C211yesmaximal, characteristic, complemented
4#10622851C211yesmaximal, characteristic, complemented
5#10622831C211yesmaximal, characteristic, complemented
6#10622830C211yesmaximal, characteristic, complemented
7#10622688C211yesmaximal, characteristic, complemented
8#10622687C211yesmaximal, characteristic, complemented
9#10622685C211yesmaximal, characteristic, complemented
10#10622683C211yesmaximal, characteristic, complemented
11#10622672C211yesmaximal, characteristic, complemented
12#10622670C211yesmaximal, characteristic, complemented
13#10622668C211yesmaximal, characteristic, complemented
14#10622667C211yesmaximal, characteristic, complemented
15#10622613C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C11×#127C2211yescharacteristic
19C11×#127C2211yescharacteristic
20C11×#124C2211yescharacteristic
21C11×#124C2211yescharacteristic
22C11×#121—21no—
23C11×#121—21no—
24C11×#120—21no—
25C11×#120—21no—
26C11×#117C2211yescharacteristic
27C2×#4326C2211yescharacteristic, complemented
28C2×#4325C2211yescharacteristic, complemented
29C2×#4324C2211yescharacteristic
30C2×#4324C2211yescharacteristic
31C2×#4324C2211yescharacteristic, complemented
32C2×#4323C2211yescharacteristic
33C2×#4323C2211yescharacteristic
34C2×#4323C2211yescharacteristic, complemented
35#66983C2211yescharacteristic
36#66977C2211yescharacteristic
37#66951—21no—
38#66949—21no—
39#66938—21no—
40#66936—21no—
41#66928C2211yescharacteristic, complemented
42C4×D44C2211yescharacteristic, complemented
43#66922C2211yescharacteristic, complemented
44C4×Dic22C2211yescharacteristic, complemented
45#66899C2211yescharacteristic, complemented
46#66899C2211yescharacteristic, complemented
47#66896C2211yescharacteristic
48#66896C2211yescharacteristic
49#66896C2211yescharacteristic
50#66896C2211yescharacteristic
51#66896C2211yescharacteristic, complemented
52#66896C2211yescharacteristic, complemented
53C22⋊(C11⋊C8)C2211yescharacteristic
54C22⋊(C11⋊C8)C2211yescharacteristic
55C4⋊(C11⋊C8)C2211yescharacteristic, complemented
56C4⋊(C11⋊C8)C2211yescharacteristic, complemented
57#66867C2211yescharacteristic, complemented
58C4×C11⋊C8C2211yescharacteristic, complemented
59C24×C11—21no—
60C11×#41—41no—
61C11×#41—41no—
62C2×Q8×C11C2311yescharacteristic
63C2×D4×C11—21no—
64C2×D4×C11—21no—
65C2×D4×C11—21no—
66C2×D4×C11—21no—
67C2×D4×C11—21no—
68C2×D4×C11—21no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C2×D4×C11C2311yescharacteristic
72C2×D4×C11C2311yescharacteristic
73C2×D4×C11C2311yescharacteristic
74C22×C4×C11—21no—
75C22×C4×C11C2311yescharacteristic
76C2×C22⋊D11—21no—
77C2×D44C2311yescharacteristic
78C2×C4×D11—21no—
79C2×Dic22—21no—
80C2×Dic22C2311yescharacteristic
81C11×C4⋊C4D411yescharacteristic
82C11×C4⋊C4D411yescharacteristic
83C11×C22⋊C4—21no—
84C11×C22⋊C4—21no—
85C11×C22⋊C4—21no—
86C11×C22⋊C4—21no—
87C11×C22⋊C4D411yescharacteristic
88C11×C22⋊C4D411yescharacteristic
89C42×C11C2311yescharacteristic
90C42×C11C2311yescharacteristic
91C22⋊Dic11—21no—
92#4326—41no—
93#4325—41no—
94#4324—41no—
95#4324—41no—
96#4324—41no—
97#4323—41no—
98#4323—41no—
99#4323—41no—
100(C2×D11)⋊C4—21no—
101(C2×D11)⋊C4—21no—
102(C2×D11)⋊C4—21no—
103(C2×D11)⋊C4—21no—
104C4⋊Dic11—21no—
105C4⋊Dic11C2311yescharacteristic
106C4⋊Dic11C2311yescharacteristic
107Dic11⋊C4—21no—
108Dic11⋊C4—21no—
109C4×Dic11—21no—
110C2×C11⋊C8C2311yescharacteristic
111C2×C11⋊C8C2311yescharacteristic
112C2×C11⋊C8C2311yescharacteristic
113C2×C11⋊C8C2311yescharacteristic
114#3224—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—
123Q8×C11—21no—
124Q8×C11—21no—
125D4×C11—21no—
126D4×C11—21no—
127D4×C11—21no—
128D4×C11—21no—
129D4×C11—21no—
130D4×C11—21no—
131D4×C11—42no—
132D4×C11—42no—
133D4×C11—81no—
134D4×C11—81no—
135D4×C11—81no—
136D4×C11—81no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—42no—
141C2×C4×C11C2×D411yescharacteristic
142C2×C4×C11C2×D411yescharacteristic
143C2×C4×C11C2×D411yescharacteristic
144C2×C4×C11C2×D411yescharacteristic
145C2×C4×C11C2×D411yescharacteristic
146C2×C4×C11C2411yescharacteristic
147C22⋊D11—81no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151D44—21no—
152D44—21no—
153C4×D11—81no—
154Dic22—21no—
155Dic22—21no—
156Dic22—81no—
157C11⋊C8—21no—
158C11⋊C8—21no—
159C11⋊C8—21no—
160C11⋊C8—21no—
161#542—111no—
162#535D1111yescharacteristic, complemented
163#496—111no—
164#495—111no—
165#489—111no—
166#486—111no—
167#464—111no—
168#463—111no—
169#460—111no—
170#459—111no—
171#452—111no—
172#450—111no—
173#449—111no—
174#447—111no—
175#433—111no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11—41no—
187C22×C11—41no—
188C22×C11—84no—
189C22×C11C22×D411yescharacteristic
190C2×D11—41no—
191C2×D11—41no—
192C2×D11—41no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—41no—
199C4×C11H(5,𝔽2)11yescharacteristic
200C4×C11H(5,𝔽2)11yescharacteristic
201Dic11—41no—
202Dic11—41no—
203Dic11—41no—
204C2×#41C2×D1111yescharacteristic
205C22×D4C2×D1111yescharacteristic
206C2×Q16—111no—
207C2×SD16—111no—
208C2×SD16—111no—
209C2×SD16—111no—
210C2×SD16—111no—
211C2×D8—111no—
212C2×D8—111no—
213C2×D8—111no—
214C4⋊Q8—111no—
215#127C2×D1111yescharacteristic
216#127C2×D1111yescharacteristic
217#126—221no—
218#124—111no—
219#124—221no—
220#124C2×D1111yescharacteristic
221#124C2×D1111yescharacteristic
222#123—221no—
223C22⋊Q8—111no—
224C22⋊Q8—221no—
225#121—21no—
226#121—21no—
227#121—111no—
228#120—21no—
229#120—21no—
230C4×Q8—111no—
231C4×D4—111no—
232#117C2×D1111yescharacteristic
233C4⋊C8—111no—
234C4⋊C8—111no—
235#103—111no—
236#103—111no—
237#102—111no—
238#102—111no—
239#102—111no—
240#102—111no—
241#102—111no—
242#102—111no—
243C22⋊C8—111no—
244C22⋊C8—111no—
245#97—111no—
246C4×C8—111no—
247C2×C11—41no—
248C2×C11—81no—
249C2×C11—81no—
250C2×C11—81no—
251C2×C11#53511yescharacteristic
252C2×C11#57611yescharacteristic
253C2×C11#57711yescharacteristic
254D11—81no—
255C24—21no—
256#41—41no—
257#41—41no—
258C2×Q8—111no—
259C2×Q8—221no—
260C2×Q8C22×D1111yescharacteristic
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—111no—
270C2×D4—221no—
271C2×D4C22×D1111yescharacteristic
272C2×D4C22×D1111yescharacteristic
273C2×D4C22×D1111yescharacteristic
274C22×C4—21no—
275C22×C4—221no—
276C22×C4C22×D1111yescharacteristic
277Q16—441no—
278SD16—441no—
279SD16—441no—
280SD16—441no—
281SD16—441no—
282D8—441no—
283D8—441no—
284D8—441no—
285C2×C8—111no—
286C2×C8—111no—
287C2×C8—111no—
288C2×C8—111no—
289C4⋊C4—111no—
290C4⋊C4—111no—
291C4⋊C4—221no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C4⋊C4C22⋊D1111yescharacteristic
295C4⋊C4C22⋊D1111yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—221no—
301C22⋊C4—221no—
302C22⋊C4—221no—
303C22⋊C4—221no—
304C22⋊C4—221no—
305C22⋊C4C22⋊D1111yescharacteristic
306C22⋊C4C22⋊D1111yescharacteristic
307C42—221no—
308C42C22×D1111yescharacteristic
309C42C22×D1111yescharacteristic
310C11#322411yescharacteristic, complemented, Sylow
311C23—21no—
312C23—21no—
313C23—21no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—221no—
318C23C2×C22⋊D1111yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—221no—
322Q8—221no—
323Q8—881no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—42no—
332D4—81no—
333D4—81no—
334D4—81no—
335D4—81no—
336D4—221no—
337D4—221no—
338D4—881no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—221no—
344C2×C4—221no—
345C2×C4—221no—
346C2×C4—881no—
347C2×C4C2×C22⋊D1111yescharacteristic
348C2×C4C2×C22⋊D1111yescharacteristic
349C2×C4C2×C22⋊D1111yescharacteristic
350C2×C4C2×C22⋊D1111yescharacteristic
351C2×C4C2×C22⋊D1111yescharacteristic
352C2×C4C23×D1111yescharacteristic
353C8—221no—
354C8—221no—
355C8—221no—
356C8—221no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—84no—
370C22—441no—
371C22—441no—
372C22—441no—
373C22C22×C22⋊D1111yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—441no—
381C4—441no—
382C4—441no—
383C4#6703711yescharacteristic
384C4#6703711yescharacteristic
385C2—41no—
386C2—81no—
387C2—81no—
388C2—81no—
389C2—881no—
390C2#1062333611yescharacteristic
391C2#1062336611yescharacteristic
392C2#1062336711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#535C2
socleC22×C11C22×D4
hypercenter#535D11
hypocenterC11#3224
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C11×#535C2semidirect
2. #10623065C2semidirect
3. #10622852C2semidirect
4. #10622851C2semidirect
5. #10622831C2semidirect
6. #10622830C2semidirect
7. #10622688C2semidirect
8. #10622687C2semidirect
9. #10622685C2semidirect
10. #10622683C2semidirect
11. #10622672C2semidirect
12. #10622670C2semidirect
13. #10622668C2semidirect
14. #10622667C2semidirect
15. #10622613C2semidirect
27. C2×#4326C22semidirect
28. C2×#4325C22semidirect
31. C2×#4324C22semidirect
34. C2×#4323C22semidirect
41. #66928C22semidirect
42. C4×D44C22semidirect
43. #66922C22semidirect
44. C4×Dic22C22semidirect
45. #66899C22semidirect
46. #66899C22semidirect
51. #66896C22semidirect
52. #66896C22semidirect
55. C4⋊(C11⋊C8)C22semidirect
56. C4⋊(C11⋊C8)C22semidirect
57. #66867C22semidirect
58. C4×C11⋊C8C22semidirect
162. #535D11semidirect
310. C11#3224semidirect

Maximal subgroups

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

subgroupindex
C11×#5352
#106230652
#106228522
#106228512
#106228312
#106228302
#106226882
#106226872
#106226852
#106226832
#106226722
#106226702
#106226682
#106226672
#106226132
#322411