Finite Group Databasebeta

← #13079468

Subgroups — #13079468

Order 1408.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#535C211yesmaximal, characteristic, complemented
2#10623364C211yesmaximal, characteristic, complemented
3#10622847C211yesmaximal, characteristic, complemented
4#10622831C211yesmaximal, characteristic, complemented
5#10622830C211yesmaximal, characteristic, complemented
6#10622655C211yesmaximal, characteristic, complemented
7#10622654C211yesmaximal, characteristic, complemented
8#10622652C211yesmaximal, characteristic, complemented
9#10622651C211yesmaximal, characteristic, complemented
10#10622650C211yesmaximal, characteristic, complemented
11#10622650C211yesmaximal, characteristic, complemented
12#10622647C211yesmaximal, characteristic, complemented
13#10622646C211yesmaximal, characteristic, complemented
14#10622616C211yesmaximal, characteristic, complemented
15#10622609C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C2×#4339C2211yescharacteristic, complemented
19C11×#127—21no—
20C11×#124—21no—
21C11×#121C2211yescharacteristic
22C11×#121C2211yescharacteristic
23C11×#121C2211yescharacteristic
24C11×#121C2211yescharacteristic
25C11×#120—21no—
26C11×#120—21no—
27C11×#117C2211yescharacteristic
28#66999—21no—
29#66992—21no—
30#66992—21no—
31#66991—21no—
32C2×#4324C2211yescharacteristic
33C2×#4324C2211yescharacteristic
34C2×#4323C2211yescharacteristic
35C2×#4323C2211yescharacteristic
36#66983C2211yescharacteristic
37#66983C2211yescharacteristic, complemented
38C2×C4⋊Dic11C2211yescharacteristic, complemented
39#66977C2211yescharacteristic
40#66977C2211yescharacteristic, complemented
41C2×#4318C2211yescharacteristic, complemented
42C22×C11⋊C8C2211yescharacteristic, complemented
43#66896C2211yescharacteristic
44#66896C2211yescharacteristic
45#66896C2211yescharacteristic
46#66896C2211yescharacteristic
47C22⋊(C11⋊C8)C2211yescharacteristic
48C22⋊(C11⋊C8)C2211yescharacteristic
49C22⋊(C11⋊C8)C2211yescharacteristic, complemented
50C22⋊(C11⋊C8)C2211yescharacteristic, complemented
51#66874C2211yescharacteristic, complemented
52#66874C2211yescharacteristic, complemented
53#66873C2211yescharacteristic, complemented
54#66873C2211yescharacteristic, complemented
55#66872C2211yescharacteristic, complemented
56#66872C2211yescharacteristic, complemented
57#66871C2211yescharacteristic, complemented
58#66871C2211yescharacteristic, complemented
59C24×C11—21no—
60C11×#41—41no—
61C11×#41—41no—
62C2×Q8×C11D411yescharacteristic
63C2×D4×C11—21no—
64C2×D4×C11—21no—
65C2×D4×C11—21no—
66C2×D4×C11—21no—
67C2×D4×C11—21no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11D411yescharacteristic
71C2×D4×C11D411yescharacteristic
72C2×D4×C11D411yescharacteristic
73C2×D4×C11C2311yescharacteristic
74C2×D4×C11C2311yescharacteristic
75C22×C4×C11C2311yescharacteristic
76C22×C4×C11C2311yescharacteristic
77C22×C4×C11C2311yescharacteristic
78C2×C22⋊D11—21no—
79C2×C22⋊D11—21no—
80C2×C22⋊D11—21no—
81C22×Dic11—21no—
82#4339—41no—
83#4339—41no—
84C2×D44C2311yescharacteristic
85C2×C4×D11—21no—
86C2×Dic22C2311yescharacteristic
87C11×C4⋊C4C2311yescharacteristic
88C11×C4⋊C4C2311yescharacteristic
89C11×C22⋊C4—21no—
90C11×C22⋊C4—21no—
91C11×C22⋊C4—21no—
92C11×C22⋊C4—21no—
93C11×C22⋊C4—21no—
94C42×C11—21no—
95C22⋊Dic11—21no—
96C22⋊Dic11—21no—
97#4324—41no—
98#4324—41no—
99#4323—41no—
100#4323—41no—
101(C2×D11)⋊C4—21no—
102(C2×D11)⋊C4—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11C2311yescharacteristic
105C4⋊Dic11C2311yescharacteristic
106Dic11⋊C4—21no—
107Dic11⋊C4—21no—
108#4318—41no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8C2311yescharacteristic
111C2×C11⋊C8C2311yescharacteristic
112C2×C11⋊C8C2311yescharacteristic
113C2×C11⋊C8C2311yescharacteristic
114#3198—111nomaximal, Sylow
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—42no—
118C23×C11—81no—
119C23×C11—81no—
120C23×C11C2×D411yescharacteristic
121C23×C11C2×D411yescharacteristic
122C23×C11C2×D411yescharacteristic
123C22×D11—21no—
124Q8×C11—41no—
125D4×C11—21no—
126D4×C11—21no—
127D4×C11—21no—
128D4×C11—21no—
129D4×C11—41no—
130D4×C11—41no—
131D4×C11—41no—
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—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11C2×D411yescharacteristic
146C2×C4×C11C2×D411yescharacteristic
147C2×C4×C11C2×D411yescharacteristic
148C2×C4×C11C2411yescharacteristic
149C22⋊D11—42no—
150C22⋊D11—81no—
151C22⋊D11—81no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—81no—
156D44—21no—
157D44—21no—
158C4×D11—42no—
159Dic22—21no—
160Dic22—21no—
161C11⋊C8—21no—
162C11⋊C8—21no—
163C11⋊C8—21no—
164C11⋊C8—21no—
165#537—111no—
166#535D1111yescharacteristic, complemented
167#485—111no—
168#482—111no—
169#481—111no—
170#480—111no—
171#469—111no—
172#468—111no—
173#466—111no—
174#465—111no—
175#450—111no—
176#449—111no—
177#449—111no—
178#447—111no—
179#408—111no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11—41no—
195C22×C11—84no—
196C22×C11C22×D411yescharacteristic
197C2×D11—41no—
198C2×D11—41no—
199C2×D11—41no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—41no—
204C4×C11—41no—
205C4×C11H(5,𝔽2)11yescharacteristic
206C4×C11H(5,𝔽2)11yescharacteristic
207Dic11—41no—
208Dic11—41no—
209Dic11—41no—
210C2×#41—111no—
211C2×#41C2×D1111yescharacteristic
212C22×D4C2×D1111yescharacteristic
213C2×SD16—111no—
214C2×SD16—111no—
215C2×D8—111no—
216C2×D8—111no—
217C2×M16—111no—
218C22×C8—111no—
219#127—21no—
220#124—21no—
221C22⋊Q8—111no—
222C22⋊Q8—111no—
223C22⋊Q8—221no—
224#121—111no—
225#121—111no—
226#121—221no—
227#121—221no—
228#121—221no—
229#121C2×D1111yescharacteristic
230#121C2×D1111yescharacteristic
231#121C2×D1111yescharacteristic
232#121C2×D1111yescharacteristic
233#120—21no—
234#120—21no—
235#117C2×D1111yescharacteristic
236C2×C4⋊C4—111no—
237#107—111no—
238#107—111no—
239#106—111no—
240#106—111no—
241#103—111no—
242#103—111no—
243#102—111no—
244#102—111no—
245#102—111no—
246#102—111no—
247#102—111no—
248#102—111no—
249C22⋊C8—111no—
250C22⋊C8—111no—
251C22⋊C8—111no—
252C22⋊C8—111no—
253C2×C11—41no—
254C2×C11—41no—
255C2×C11—41no—
256C2×C11—81no—
257C2×C11—81no—
258C2×C11#53411yescharacteristic
259C2×C11#57611yescharacteristic
260C2×C11#57711yescharacteristic
261D11—81no—
262C24—21no—
263#41—41no—
264#41—41no—
265#41—441no—
266#41—441no—
267C2×Q8—111no—
268C2×Q8C22⋊D1111yescharacteristic
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—111no—
277C2×D4—221no—
278C2×D4—221no—
279C2×D4—221no—
280C2×D4C22⋊D1111yescharacteristic
281C2×D4C22⋊D1111yescharacteristic
282C2×D4C22⋊D1111yescharacteristic
283C2×D4C22×D1111yescharacteristic
284C2×D4C22×D1111yescharacteristic
285C22×C4—221no—
286C22×C4—221no—
287C22×C4C22×D1111yescharacteristic
288C22×C4C22×D1111yescharacteristic
289C22×C4C22×D1111yescharacteristic
290SD16—441no—
291SD16—441no—
292D8—441no—
293D8—441no—
294M16—441no—
295C2×C8—111no—
296C2×C8—111no—
297C2×C8—111no—
298C2×C8—111no—
299C2×C8—441no—
300C4⋊C4—111no—
301C4⋊C4—111no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C4⋊C4—221no—
305C4⋊C4C22×D1111yescharacteristic
306C4⋊C4C22×D1111yescharacteristic
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—221no—
313C22⋊C4—221no—
314C22⋊C4—221no—
315C22⋊C4—221no—
316C42—21no—
317C11#319811yescharacteristic, complemented, Sylow
318C23—21no—
319C23—21no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—221no—
324C23C2×C22⋊D1111yescharacteristic
325C23C2×C22⋊D1111yescharacteristic
326C23C2×C22⋊D1111yescharacteristic
327Q8—41no—
328Q8—221no—
329Q8—221no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—41no—
335D4—41no—
336D4—41no—
337D4—42no—
338D4—81no—
339D4—81no—
340D4—81no—
341D4—81no—
342D4—221no—
343D4—221no—
344D4—442no—
345D4—881no—
346D4—881no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—221no—
356C2×C4—221no—
357C2×C4—221no—
358C2×C4—442no—
359C2×C4—881no—
360C2×C4C2×C22⋊D1111yescharacteristic
361C2×C4C2×C22⋊D1111yescharacteristic
362C2×C4C2×C22⋊D1111yescharacteristic
363C2×C4C23×D1111yescharacteristic
364C8—221no—
365C8—221no—
366C8—221no—
367C8—221no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—84no—
384C22—441no—
385C22—441no—
386C22—441no—
387C22C22×C22⋊D1111yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—41no—
392C4—41no—
393C4—441no—
394C4—441no—
395C4—441no—
396C4#6703711yescharacteristic
397C4#6703711yescharacteristic
398C2—41no—
399C2—41no—
400C2—41no—
401C2—81no—
402C2—81no—
403C2—881no—
404C2#1062333511yescharacteristic
405C2#1062336611yescharacteristic
406C2#1062336711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#535C2
socleC22×C11C22×D4
hypercenter#535D11
hypocenterC11#3198
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C11×#535C2semidirect
2. #10623364C2semidirect
3. #10622847C2semidirect
4. #10622831C2semidirect
5. #10622830C2semidirect
6. #10622655C2semidirect
7. #10622654C2semidirect
8. #10622652C2semidirect
9. #10622651C2semidirect
10. #10622650C2semidirect
11. #10622650C2semidirect
12. #10622647C2semidirect
13. #10622646C2semidirect
14. #10622616C2semidirect
15. #10622609C2semidirect
18. C2×#4339C22semidirect
37. #66983C22semidirect
38. C2×C4⋊Dic11C22semidirect
40. #66977C22semidirect
41. C2×#4318C22semidirect
42. C22×C11⋊C8C22semidirect
49. C22⋊(C11⋊C8)C22semidirect
50. C22⋊(C11⋊C8)C22semidirect
51. #66874C22semidirect
52. #66874C22semidirect
53. #66873C22semidirect
54. #66873C22semidirect
55. #66872C22semidirect
56. #66872C22semidirect
57. #66871C22semidirect
58. #66871C22semidirect
166. #535D11semidirect
317. C11#3198semidirect

Maximal subgroups

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

subgroupindex
C11×#5352
#106233642
#106228472
#106228312
#106228302
#106226552
#106226542
#106226522
#106226512
#106226502
#106226472
#106226462
#106226162
#106226092
#319811