Finite Group Databasebeta

← #13079579

Subgroups — #13079579

Order 1408.

410 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#124C211yesmaximal, characteristic, complemented
2#10623088C211yesmaximal, characteristic, complemented
3C11×#463C211yesmaximal, characteristic, complemented
4#10622783C211yesmaximal, characteristic, complemented
5#10622781C211yesmaximal, characteristic, complemented
6#10622769C211yesmaximal, characteristic
7#10622768C211yesmaximal, characteristic, complemented
8#10622667C211yesmaximal, characteristic, complemented
9#10622629C211yesmaximal, characteristic, complemented
10#10622458C211yesmaximal, characteristic, complemented
11#10622446C211yesmaximal, characteristic, complemented
12#10622421C211yesmaximal, characteristic, complemented
13#10622413C211yesmaximal, characteristic, complemented
14#10622389C211yesmaximal, characteristic, complemented
15#10622381C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C2×D4×D11C2211yescharacteristic
18C2×C11×SD16C2211yescharacteristic, complemented
19C2×C11×D8C2211yescharacteristic
20C11×#124C2211yescharacteristic
21C4×D4×C11C2211yescharacteristic, complemented
22#67000C2211yescharacteristic
23C2×#4326C2211yescharacteristic, complemented
24#66991C2211yescharacteristic
25#66989C2211yescharacteristic
26#66989C2211yescharacteristic, complemented
27C2×#4324C2211yescharacteristic
28C2×#4324C2211yescharacteristic, complemented
29C2×#4323C2211yescharacteristic
30C4×C22⋊D11—21no—
31#66979—21no—
32C2×Dic44C2211yescharacteristic, complemented
33C2×#4314C2211yescharacteristic
34#66950C2211yescharacteristic
35#66943C2211yescharacteristic, complemented
36#66938—21no—
37#66938—21no—
38#66936—21no—
39C22⋊C4×D11—21no—
40C22⋊C4×D11—21no—
41#66932—21no—
42#66928C2211yescharacteristic
43C42×D11C2211yescharacteristic
44C4×Dic22C2211yescharacteristic, complemented
45C11×C4⋊C8C2211yescharacteristic, complemented
46C11×#103C2211yescharacteristic, complemented
47C11×#102C2211yescharacteristic
48#66899C2211yescharacteristic, complemented
49#66896C2211yescharacteristic
50#66885C2211yescharacteristic
51(C2×D11)⋊C8C2211yescharacteristic
52(C2×D11)⋊C8C2211yescharacteristic
53#66880C2211yescharacteristic, complemented
54C8×Dic11C2211yescharacteristic, complemented
55C8×Dic11C2211yescharacteristic, complemented
56#66874C2211yescharacteristic, complemented
57#66873C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C2×D4×C11C2311yescharacteristic
63C22×C4×C11—21no—
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66Q8×D11—41no—
67Q8×D11—41no—
68D4×D11—41no—
69D4×D11—41no—
70C2×D44C2311yescharacteristic
71C2×C4×D11—21no—
72C2×C4×D11D411yescharacteristic
73C2×C4×D11D411yescharacteristic
74C2×C4×D11C2311yescharacteristic
75C2×Dic22—21no—
76C2×Dic22C2311yescharacteristic
77C2×Dic22C2311yescharacteristic
78C11×SD16—41no—
79C11×D8—41no—
80C2×C8×C11C2311yescharacteristic
81C2×C8×C11C2311yescharacteristic
82C11×C4⋊C4C2311yescharacteristic
83C11×C22⋊C4—21no—
84C11×C22⋊C4—21no—
85C11×C22⋊C4—21no—
86C42×C11C2311yescharacteristic
87C22⋊Dic11—21no—
88C22⋊Dic11—21no—
89C22⋊Dic11—21no—
90C22⋊Dic11—21no—
91C22⋊Dic11—21no—
92#4326—41no—
93#4324—41no—
94#4324—41no—
95#4323—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—
101C4⋊Dic11—21no—
102C4⋊Dic11—21no—
103C4⋊Dic11C2311yescharacteristic
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106C4×Dic11—21no—
107C4×Dic11D411yescharacteristic
108C4×Dic11D411yescharacteristic
109C4×Dic11C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111C2×C11⋊C8C2311yescharacteristic
112Dic44—41no—
113#4314—41no—
114#3211—111nomaximal, Sylow
115C23×C11—21no—
116C23×C11—21no—
117C22×D11—21no—
118C22×D11—42no—
119C22×D11—42no—
120C22×D11—42no—
121C22×D11C2×D411yescharacteristic
122Q8×C11—21no—
123Q8×C11—21no—
124D4×C11—21no—
125D4×C11—21no—
126D4×C11—21no—
127D4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—42no—
131C2×C4×C11C2×D411yescharacteristic
132C2×C4×C11C2×D411yescharacteristic
133C2×C4×C11C2411yescharacteristic
134C22⋊D11—42no—
135C22⋊D11—42no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11C2×D411yescharacteristic
140C2×Dic11C2×D411yescharacteristic
141C2×Dic11C2×D411yescharacteristic
142D44—21no—
143D44—21no—
144C4×D11—22no—
145C4×D11—21no—
146C4×D11—21no—
147C4×D11—41no—
148C4×D11—42no—
149Dic22—21no—
150Dic22—21no—
151Dic22—21no—
152Dic22—21no—
153Dic22—42no—
154C8×C11—21no—
155C8×C11—21no—
156C11⋊C8—21no—
157C11⋊C8—21no—
158#529—111no—
159C2×#124—111no—
160#495—111no—
161#495—111no—
162#488—111no—
163#488—111no—
164#464—111no—
165#464—111no—
166#463—111no—
167#463D1111yescharacteristic, complemented
168#451—111no—
169#450—111no—
170#448—111no—
171#447—111no—
172#431—111no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11C22×D411yescharacteristic
180C2×D11—21no—
181C2×D11—21no—
182C2×D11—41no—
183C2×D11—41no—
184C2×D11—41no—
185C2×D11—84no—
186C2×D11#13512yes—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11H(5,𝔽2)11yescharacteristic
192C4×C11H(5,𝔽2)11yescharacteristic
193Dic11—21no—
194Dic11—21no—
195Dic11—21no—
196Dic11—41no—
197Dic11—41no—
198Dic11—41no—
199C22×Q8—111no—
200C22×D4—111no—
201C2×Q16—111no—
202C2×Q16—111no—
203C2×SD16—111no—
204C2×SD16—111no—
205C2×SD16—111no—
206C2×SD16C2×D1111yescharacteristic, complemented
207C2×D8—111no—
208C2×D8C2×D1111yescharacteristic
209#126—221no—
210#125—111no—
211#124—111no—
212#124—111no—
213#124—111no—
214#124—111no—
215#124—221no—
216#124—221no—
217#124C2×D1111yescharacteristic
218#123—221no—
219C22⋊Q8—111no—
220#121—111no—
221C4×Q8—111no—
222C4×D4—221no—
223C4×D4C2×D1111yescharacteristic, complemented
224#117—221no—
225C2×C22⋊C4—221no—
226C2×C22⋊C4—221no—
227C2×C42—111no—
228C4⋊C8—111no—
229C4⋊C8C2×D1111yescharacteristic, complemented
230#103—111no—
231#103—111no—
232#103—111no—
233#103C2×D1111yescharacteristic, complemented
234#102—111no—
235#102—111no—
236#102—111no—
237#102C2×D1111yescharacteristic
238C22⋊C8—111no—
239C22⋊C8—111no—
240C4×C8—111no—
241C4×C8—111no—
242C2×C11—81no—
243C2×C11—81no—
244C2×C11#53511yescharacteristic
245C2×C11C2×#13511yescharacteristic
246C2×C11#57511yescharacteristic
247D11—22no—
248D11—81no—
249C24—221no—
250C2×Q8—111no—
251C2×Q8—111no—
252C2×Q8—221no—
253C2×Q8—441no—
254C2×Q8—441no—
255C2×Q8C22×D1111yescharacteristic
256C2×D4—111no—
257C2×D4—221no—
258C2×D4—221no—
259C2×D4—441no—
260C2×D4—441no—
261C2×D4C22×D1111yescharacteristic
262C2×D4C22×D1111yescharacteristic
263C22×C4—21no—
264C22×C4—111no—
265C22×C4—111no—
266C22×C4—111no—
267C22×C4—221no—
268Q16—441no—
269Q16—441no—
270SD16—41no—
271SD16—441no—
272SD16—441no—
273SD16—441no—
274D8—41no—
275D8—441no—
276C2×C8—111no—
277C2×C8—111no—
278C2×C8C22×D1111yescharacteristic
279C2×C8C22×D1111yescharacteristic
280C4⋊C4—111no—
281C4⋊C4—221no—
282C4⋊C4—221no—
283C4⋊C4—221no—
284C4⋊C4—221no—
285C4⋊C4C22×D1111yescharacteristic
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—221no—
290C22⋊C4—221no—
291C22⋊C4—221no—
292C22⋊C4—221no—
293C22⋊C4—221no—
294C22⋊C4—221no—
295C22⋊C4—221no—
296C22⋊C4—221no—
297C22⋊C4—221no—
298C22⋊C4—221no—
299C42—111no—
300C42—111no—
301C42—111no—
302C42—221no—
303C42C22×D1111yescharacteristic
304C11#321111yescharacteristic, complemented, Sylow
305C23—21no—
306C23—21no—
307C23—111no—
308C23—221no—
309C23—442no—
310C23—442no—
311C23—442no—
312Q8—21no—
313Q8—21no—
314Q8—221no—
315Q8—221no—
316Q8—221no—
317Q8—221no—
318Q8—442no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—21no—
323D4—221no—
324D4—221no—
325D4—442no—
326D4—442no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—111no—
331C2×C4—111no—
332C2×C4—111no—
333C2×C4—222no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—221no—
339C2×C4—441no—
340C2×C4—442no—
341C2×C4D4×D1111yescharacteristic
342C2×C4D4×D1111yescharacteristic
343C2×C4C23×D1111yescharacteristic
344C8—21no—
345C8—21no—
346C8—221no—
347C8—221no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—112no—
355C22—221no—
356C22—221no—
357C22—441no—
358C22—441no—
359C22—441no—
360C22—884no—
361C22C2×D4×D1111yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—221no—
367C4—221no—
368C4—221no—
369C4—441no—
370C4—441no—
371C4—441no—
372C4#6703711yescharacteristic
373C4#6704211yescharacteristic
374C2—81no—
375C2—81no—
376C2—222no—
377C2—881no—
378C2#1062313811yescharacteristic
379C2D11×#13511yescharacteristic
380C2#1062330411yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#463C2
socleC22×C11C22×D4
prime radical#10622769C2
hypercenter#463D11
hypocenterC11#3211
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. D11×#124C2semidirect
2. #10623088C2semidirect
3. C11×#463C2semidirect
4. #10622783C2semidirect
5. #10622781C2semidirect
7. #10622768C2semidirect
8. #10622667C2semidirect
9. #10622629C2semidirect
10. #10622458C2semidirect
11. #10622446C2semidirect
12. #10622421C2semidirect
13. #10622413C2semidirect
14. #10622389C2semidirect
15. #10622381C2semidirect
18. C2×C11×SD16C22semidirect
21. C4×D4×C11C22semidirect
23. C2×#4326C22semidirect
26. #66989C22semidirect
28. C2×#4324C22semidirect
32. C2×Dic44C22semidirect
35. #66943C22semidirect
44. C4×Dic22C22semidirect
45. C11×C4⋊C8C22semidirect
46. C11×#103C22semidirect
48. #66899C22semidirect
53. #66880C22semidirect
54. C8×Dic11C22semidirect
55. C8×Dic11C22semidirect
56. #66874C22semidirect
58. C4⋊(C11⋊C8)C22semidirect
167. #463D11semidirect
206. C2×SD16C2×D11semidirect
223. C4×D4C2×D11semidirect
229. C4⋊C8C2×D11semidirect
233. #103C2×D11semidirect
304. C11#3211semidirect

Maximal subgroups

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

subgroupindex
D11×#1242
#106230882
C11×#4632
#106227832
#106227812
#106227692
#106227682
#106226672
#106226292
#106224582
#106224462
#106224212
#106224132
#106223892
#106223812
#321111