Finite Group Databasebeta

← #13079708

Subgroups — #13079708

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
1#10623361C211yesmaximal, characteristic, complemented
2#10623134C211yesmaximal, characteristic, complemented
3C11×#449C211yesmaximal, characteristic, complemented
4#10622852C211yesmaximal, characteristic, complemented
5#10622781C211yesmaximal, characteristic, complemented
6#10622778C211yesmaximal, characteristic, complemented
7#10622767C211yesmaximal, characteristic, complemented
8#10622763C211yesmaximal, characteristic, complemented
9#10622649C211yesmaximal, characteristic, complemented
10#10622411C211yesmaximal, characteristic, complemented
11#10622408C211yesmaximal, characteristic, complemented
12#10622375C211yesmaximal, characteristic, complemented
13#10622373C211yesmaximal, characteristic, complemented
14#10622344C211yesmaximal, characteristic, complemented
15#10622333C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C22×D44C2211yescharacteristic
18C2×C11×SD16C2211yescharacteristic, complemented
19C2×C11×D8C2211yescharacteristic, complemented
20C11×#121C2211yescharacteristic
21#67000C2211yescharacteristic
22#67000C2211yescharacteristic
23C2×#4326C2211yescharacteristic, complemented
24#66993C2211yescharacteristic
25#66993C2211yescharacteristic
26#66990—21no—
27#66990—21no—
28#66989—21no—
29#66989C2211yescharacteristic, complemented
30#66988—21no—
31D4×Dic11C2211yescharacteristic, complemented
32C2×#4324C2211yescharacteristic, complemented
33C2×#4323C2211yescharacteristic
34C2×#4323C2211yescharacteristic
35#66983—21no—
36#66983—21no—
37#66979C2211yescharacteristic
38#66977C2211yescharacteristic
39C2×#4314C2211yescharacteristic
40C2×#4314C2211yescharacteristic
41#66941C2211yescharacteristic, complemented
42#66940C2211yescharacteristic, complemented
43#66932—21no—
44#66931—21no—
45C11×#103C2211yescharacteristic, complemented
46C11×#102C2211yescharacteristic, complemented
47C11×C22⋊C8C2211yescharacteristic
48#66899C2211yescharacteristic, complemented
49#66896C2211yescharacteristic, complemented
50C22⋊(C11⋊C8)C2211yescharacteristic
51#66885C2211yescharacteristic
52#66885C2211yescharacteristic
53#66879C2211yescharacteristic, complemented
54Dic11⋊C8C2211yescharacteristic, complemented
55Dic11⋊C8C2211yescharacteristic, complemented
56C8×Dic11C2211yescharacteristic, complemented
57#66873C2211yescharacteristic
58#66873C2211yescharacteristic
59C23×D11—21no—
60C11×#41—41no—
61C11×#41—41no—
62C2×Q8×C11C2311yescharacteristic
63C2×D4×C11—21no—
64C2×D4×C11—21no—
65C2×D4×C11C2311yescharacteristic
66C2×D4×C11C2311yescharacteristic
67C22×C4×C11—21no—
68C22×C4×C11C2311yescharacteristic
69C2×C22⋊D11—21no—
70C2×C22⋊D11—21no—
71C2×C22⋊D11—21no—
72C2×C22⋊D11—21no—
73C22×Dic11—21no—
74C2×D44—21no—
75C2×D44—41no—
76C2×D44—41no—
77C2×D44C2311yescharacteristic
78C2×D44C2311yescharacteristic
79C2×Dic22—21no—
80C2×Dic22C2311yescharacteristic
81C11×SD16—41no—
82C11×D8—41no—
83C2×C8×C11C2311yescharacteristic
84C2×C8×C11C2311yescharacteristic
85C11×C4⋊C4C2311yescharacteristic
86C11×C22⋊C4—21no—
87C22⋊Dic11—21no—
88C22⋊Dic11—21no—
89C22⋊Dic11—21no—
90C22⋊Dic11—21no—
91C22⋊Dic11D411yescharacteristic
92C22⋊Dic11D411yescharacteristic
93#4326—41no—
94#4324—41no—
95#4323—41no—
96#4323—41no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4—21no—
100(C2×D11)⋊C4—21no—
101C4⋊Dic11D411yescharacteristic
102C4⋊Dic11D411yescharacteristic
103C4⋊Dic11C2311yescharacteristic
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106Dic11⋊C4—21no—
107C4×Dic11—21no—
108C4×Dic11C2311yescharacteristic
109C4×Dic11C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111C2×C11⋊C8C2311yescharacteristic
112#4314—41no—
113#4314—41no—
114#3224—111nomaximal, Sylow
115C23×C11—21no—
116C23×C11—21no—
117C23×C11C2×D411yescharacteristic
118C22×D11—21no—
119C22×D11—21no—
120C22×D11—42no—
121C22×D11—81no—
122C22×D11—81no—
123Q8×C11—21no—
124Q8×C11—21no—
125D4×C11—21no—
126D4×C11—21no—
127D4×C11—21no—
128D4×C11—21no—
129D4×C11—42no—
130D4×C11—81no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—42no—
136C2×C4×C11C2×D411yescharacteristic
137C2×C4×C11C2411yescharacteristic
138C22⋊D11—81no—
139C22⋊D11—81no—
140C22⋊D11—81no—
141C22⋊D11—81no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—81no—
145C2×Dic11C2×D411yescharacteristic
146C2×Dic11C2×D411yescharacteristic
147C2×Dic11C2×D411yescharacteristic
148C2×Dic11C2×D411yescharacteristic
149D44—21no—
150D44—21no—
151D44—21no—
152D44—21no—
153D44—42no—
154Dic22—21no—
155Dic22—21no—
156Dic22—81no—
157C8×C11—21no—
158C8×C11—21no—
159C11⋊C8—21no—
160C11⋊C8—21no—
161#542—111no—
162#535—111no—
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#449D1111yescharacteristic, complemented
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×C11C22×D411yescharacteristic
186C2×D11—41no—
187C2×D11—41no—
188C2×D11—41no—
189C2×D11—41no—
190C2×D11—41no—
191C2×D11—41no—
192C2×D11—84no—
193C4×C11—21no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11H(5,𝔽2)11yescharacteristic
197C4×C11H(5,𝔽2)11yescharacteristic
198Dic11—21no—
199Dic11—21no—
200Dic11—21no—
201Dic11—21no—
202Dic11—41no—
203Dic11—41no—
204C2×#41C2×D1111yescharacteristic
205C22×D4—111no—
206C2×Q16—111no—
207C2×SD16—111no—
208C2×SD16—111no—
209C2×SD16—111no—
210C2×SD16C2×D1111yescharacteristic, complemented
211C2×D8—111no—
212C2×D8—111no—
213C2×D8C2×D1111yescharacteristic, complemented
214C4⋊Q8—111no—
215#127—111no—
216#127—111no—
217#126—221no—
218#124—111no—
219#124—111no—
220#124—111no—
221#124—221no—
222#123—221no—
223C22⋊Q8—111no—
224C22⋊Q8—221no—
225#121—221no—
226#121—221no—
227#121C2×D1111yescharacteristic
228#120—221no—
229#120—221no—
230C4×Q8—111no—
231C4×D4—111no—
232#117—111no—
233C4⋊C8—111no—
234C4⋊C8—111no—
235#103—111no—
236#103C2×D1111yescharacteristic, complemented
237#102—111no—
238#102—111no—
239#102—111no—
240#102—111no—
241#102—111no—
242#102C2×D1111yescharacteristic, complemented
243C22⋊C8—111no—
244C22⋊C8C2×D1111yescharacteristic
245#97—111no—
246C4×C8—111no—
247C2×C11—41no—
248C2×C11—81no—
249C2×C11—81no—
250C2×C11#53511yescharacteristic
251C2×C11#57611yescharacteristic
252C2×C11#57711yescharacteristic
253D11—81no—
254D11—81no—
255C24—221no—
256#41—41no—
257#41—41no—
258C2×Q8—111no—
259C2×Q8—221no—
260C2×Q8C22×D1111yescharacteristic
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—111no—
264C2×D4—111no—
265C2×D4—221no—
266C2×D4—221no—
267C2×D4—221no—
268C2×D4—221no—
269C2×D4—221no—
270C2×D4—441no—
271C2×D4—441no—
272C2×D4C22×D1111yescharacteristic
273C2×D4C22×D1111yescharacteristic
274C22×C4—21no—
275C22×C4—221no—
276C22×C4C22×D1111yescharacteristic
277Q16—441no—
278SD16—41no—
279SD16—441no—
280SD16—441no—
281SD16—441no—
282D8—41no—
283D8—441no—
284D8—441no—
285C2×C8—111no—
286C2×C8—111no—
287C2×C8C22×D1111yescharacteristic
288C2×C8C22×D1111yescharacteristic
289C4⋊C4—111no—
290C4⋊C4—111no—
291C4⋊C4—111no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C4⋊C4—221no—
295C4⋊C4C22×D1111yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—111no—
298C22⋊C4—111no—
299C22⋊C4—221no—
300C22⋊C4—221no—
301C22⋊C4—221no—
302C22⋊C4—221no—
303C22⋊C4—221no—
304C22⋊C4—221no—
305C22⋊C4—221no—
306C22⋊C4—221no—
307C42—111no—
308C42—111no—
309C42—221no—
310C11#322411yescharacteristic, complemented, Sylow
311C23—21no—
312C23—21no—
313C23—221no—
314C23—221no—
315C23—442no—
316C23—881no—
317C23—881no—
318C23D4×D1111yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—221no—
322Q8—221no—
323Q8—881no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—42no—
329D4—81no—
330D4—221no—
331D4—221no—
332D4—221no—
333D4—221no—
334D4—442no—
335D4—881no—
336D4—881no—
337D4—881no—
338D4—881no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—111no—
345C2×C4—111no—
346C2×C4—111no—
347C2×C4—111no—
348C2×C4—221no—
349C2×C4—221no—
350C2×C4—881no—
351C2×C4D4×D1111yescharacteristic
352C2×C4C23×D1111yescharacteristic
353C8—21no—
354C8—21no—
355C8—221no—
356C8—221no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—441no—
367C22—441no—
368C22—441no—
369C22—441no—
370C22—441no—
371C22—441no—
372C22—884no—
373C22C2×D4×D1111yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—221no—
378C4—221no—
379C4—221no—
380C4—221no—
381C4—441no—
382C4—441no—
383C4#6703711yescharacteristic
384C4#6703711yescharacteristic
385C2—41no—
386C2—81no—
387C2—81no—
388C2—881no—
389C2—881no—
390C2#1062312311yescharacteristic
391C2#1062330111yescharacteristic
392C2#1062330511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#449C2
socleC22×C11C22×D4
hypercenter#449D11
hypocenterC11#3224
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #10623361C2semidirect
2. #10623134C2semidirect
3. C11×#449C2semidirect
4. #10622852C2semidirect
5. #10622781C2semidirect
6. #10622778C2semidirect
7. #10622767C2semidirect
8. #10622763C2semidirect
9. #10622649C2semidirect
10. #10622411C2semidirect
11. #10622408C2semidirect
12. #10622375C2semidirect
13. #10622373C2semidirect
14. #10622344C2semidirect
15. #10622333C2semidirect
18. C2×C11×SD16C22semidirect
19. C2×C11×D8C22semidirect
23. C2×#4326C22semidirect
29. #66989C22semidirect
31. D4×Dic11C22semidirect
32. C2×#4324C22semidirect
41. #66941C22semidirect
42. #66940C22semidirect
45. C11×#103C22semidirect
46. C11×#102C22semidirect
48. #66899C22semidirect
49. #66896C22semidirect
53. #66879C22semidirect
54. Dic11⋊C8C22semidirect
55. Dic11⋊C8C22semidirect
56. C8×Dic11C22semidirect
173. #449D11semidirect
210. C2×SD16C2×D11semidirect
213. C2×D8C2×D11semidirect
236. #103C2×D11semidirect
242. #102C2×D11semidirect
310. C11#3224semidirect

Maximal subgroups

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

subgroupindex
#106233612
#106231342
C11×#4492
#106228522
#106227812
#106227782
#106227672
#106227632
#106226492
#106224112
#106224082
#106223752
#106223732
#106223442
#106223332
#322411