Finite Group Databasebeta

← #13079376

Subgroups — #13079376

Order 1408.

472 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623137C211yesmaximal, characteristic, complemented
2D11×#121C211yesmaximal, characteristic, complemented
3C11×#466C211yesmaximal, characteristic, complemented
4#10622771C211yesmaximal, characteristic, complemented
5#10622769C211yesmaximal, characteristic, complemented
6#10622727C211yesmaximal, characteristic, complemented
7C2×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
8#10622654C211yesmaximal, characteristic, complemented
9#10622651C211yesmaximal, characteristic, complemented
10#10622498C211yesmaximal, characteristic, complemented
11#10622497C211yesmaximal, characteristic, complemented
12#10622394C211yesmaximal, characteristic, complemented
13#10622392C211yesmaximal, characteristic, complemented
14#10622390C211yesmaximal, characteristic, complemented
15#10622389C211yesmaximal, characteristic, complemented
16C2×#4341C2211yescharacteristic, complemented
17C2×D4×D11—21no—
18C2×D4×D11C2211yescharacteristic
19C22×C4×D11C2211yescharacteristic
20C2×C11×D8C2211yescharacteristic, complemented
21C22×C8×C11C2211yescharacteristic, complemented
22C11×#121C2211yescharacteristic
23C11×#121C2211yescharacteristic, complemented
24#66992—21no—
25#66991C2211yescharacteristic
26#66991C2211yescharacteristic
27#66990—21no—
28D4×Dic11—21no—
29C2×#4324C2211yescharacteristic, complemented
30C2×#4323C2211yescharacteristic, complemented
31#66983C2211yescharacteristic
32#66977C2211yescharacteristic, complemented
33C22×C11⋊C8C2211yescharacteristic, complemented
34C2×#4314C2211yescharacteristic, complemented
35#66950C2211yescharacteristic
36#66948C2211yescharacteristic
37#66945C2211yescharacteristic, complemented
38C4⋊C4×D11C2211yescharacteristic
39#66937—21no—
40#66936—21no—
41(C22⋊D11)⋊C4—21no—
42C22⋊C4×D11—21no—
43C11×#107C2211yescharacteristic, complemented
44C11×#102C2211yescharacteristic, complemented
45C11×#102C2211yescharacteristic, complemented
46#66896C2211yescharacteristic, complemented
47#66896C2211yescharacteristic, complemented
48#66885C2211yescharacteristic, complemented
49(C2×D11)⋊C8C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51(C2×D11)⋊C8C2211yescharacteristic, complemented
52(C2×D11)⋊C8C2211yescharacteristic, complemented
53#66881C2211yescharacteristic, complemented
54#66880C2211yescharacteristic, complemented
55#66874C2211yescharacteristic, complemented
56#66873C2211yescharacteristic, complemented
57#66872C2211yescharacteristic, complemented
58#66871C2211yescharacteristic, complemented
59C23×D11—21no—
60C23×D11D411yescharacteristic
61C2×D4×C11—21no—
62C2×D4×C11—21no—
63C2×D4×C11C2311yescharacteristic
64C2×D4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C2×C22⋊D11—21no—
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70C2×C22⋊D11—21no—
71C22×Dic11—21no—
72C22×Dic11D411yescharacteristic
73#4341—41no—
74#4341—41no—
75D4×D11—41no—
76D4×D11—41no—
77D4×D11—44no—
78C2×D44—21no—
79C2×D44C2311yescharacteristic
80C2×C4×D11—21no—
81C2×C4×D11—41no—
82C2×C4×D11—41no—
83C2×C4×D11D411yescharacteristic
84C2×C4×D11D411yescharacteristic
85C2×C4×D11C2311yescharacteristic
86C2×C4×D11C2311yescharacteristic
87C2×Dic22C2311yescharacteristic
88C11×D8—41no—
89C2×C8×C11—41no—
90C2×C8×C11C2311yescharacteristic
91C2×C8×C11C2311yescharacteristic
92C11×C4⋊C4C2311yescharacteristic
93C11×C4⋊C4C2311yescharacteristic
94C11×C22⋊C4—21no—
95C11×C22⋊C4—21no—
96C22⋊Dic11—21no—
97C22⋊Dic11—21no—
98C22⋊Dic11—21no—
99#4324—41no—
100#4323—41no—
101(C2×D11)⋊C4—21no—
102(C2×D11)⋊C4—21no—
103(C2×D11)⋊C4—21no—
104(C2×D11)⋊C4—21no—
105C4⋊Dic11—21no—
106C4⋊Dic11C2311yescharacteristic
107C4⋊Dic11C2311yescharacteristic
108Dic11⋊C4—21no—
109Dic11⋊C4—21no—
110C4×Dic11—21no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8C2311yescharacteristic
113C2×C11⋊C8C2311yescharacteristic
114#4314—41no—
115#3188—111nomaximal, Sylow
116C23×C11—21no—
117C23×C11—21no—
118C23×C11C2×D411yescharacteristic
119C22×D11—22no—
120C22×D11—22no—
121C22×D11—21no—
122C22×D11—41no—
123C22×D11—42no—
124C22×D11—42no—
125C22×D11—42no—
126C22×D11C2×D411yescharacteristic
127C22×D11C2×D411yescharacteristic
128D4×C11—21no—
129D4×C11—21no—
130D4×C11—21no—
131D4×C11—21no—
132D4×C11—42no—
133D4×C11—42no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11C2×D411yescharacteristic
139C2×C4×C11C2411yescharacteristic
140C22⋊D11—42no—
141C22⋊D11—42no—
142C22⋊D11—42no—
143C22⋊D11—42no—
144C22⋊D11—42no—
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—41no—
149C2×Dic11—42no—
150C2×Dic11C2×D411yescharacteristic
151C2×Dic11C2×D411yescharacteristic
152D44—21no—
153D44—21no—
154D44—42no—
155C4×D11—21no—
156C4×D11—21no—
157C4×D11—21no—
158C4×D11—21no—
159C4×D11—41no—
160C4×D11—41no—
161C4×D11—42no—
162Dic22—21no—
163Dic22—21no—
164C8×C11—21no—
165C8×C11—21no—
166C11⋊C8—21no—
167C11⋊C8—21no—
168#525—111no—
169C2×#121—111no—
170#484—111no—
171#482—111no—
172#482—111no—
173#481—111no—
174#466—111no—
175#466D1111yescharacteristic, complemented
176#465—111no—
177#465—111no—
178#450—111no—
179#449—111no—
180#449—111no—
181#447—111no—
182C2×C22⋊C8—111no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—41no—
186C22×C11—41no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11AGL(1,ℤ/8)12yes—
192C22×C11C22×D411yescharacteristic
193C2×D11—21no—
194C2×D11—21no—
195C2×D11—21no—
196C2×D11—21no—
197C2×D11—21no—
198C2×D11—44no—
199C2×D11—41no—
200C2×D11—41no—
201C2×D11—41no—
202C2×D11—84no—
203C2×D11#13512yes—
204C4×C11—21no—
205C4×C11—41no—
206C4×C11—41no—
207C4×C11H(5,𝔽2)11yescharacteristic
208C4×C11H(5,𝔽2)11yescharacteristic
209Dic11—21no—
210Dic11—21no—
211Dic11—41no—
212Dic11—41no—
213Dic11—41no—
214C2×#41—111no—
215C22×D4—111no—
216C22×D4—221no—
217C23×C4—111no—
218C2×SD16—111no—
219C2×SD16—111no—
220C2×D8—111no—
221C2×D8C2×D1111yescharacteristic, complemented
222C22×C8—111no—
223C22×C8C2×D1111yescharacteristic, complemented
224#123—221no—
225C22⋊Q8—111no—
226C22⋊Q8—111no—
227#121—111no—
228#121—111no—
229#121—111no—
230#121—111no—
231#121—221no—
232#121—221no—
233#121C2×D1111yescharacteristic
234#121C2×D1111yescharacteristic, complemented
235#120—221no—
236C4×D4—221no—
237C4×D4—221no—
238#117—111no—
239C2×C4⋊C4—111no—
240C2×C22⋊C4—221no—
241#107—111no—
242#107C2×D1111yescharacteristic, complemented
243#106—111no—
244#106—111no—
245#103—111no—
246#103—111no—
247#102—111no—
248#102—111no—
249#102—111no—
250#102—111no—
251#102C2×D1111yescharacteristic, complemented
252#102C2×D1111yescharacteristic, complemented
253C22⋊C8—111no—
254C22⋊C8—111no—
255C22⋊C8—111no—
256C22⋊C8—111no—
257C2×C11—22no—
258C2×C11—81no—
259C2×C11—81no—
260C2×C11#53411yescharacteristic
261C2×C11C2×#13511yescharacteristic
262C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
263D11—22no—
264D11—41no—
265D11—81no—
266C24—111no—
267C24—221no—
268#41—441no—
269#41—441no—
270C2×Q8—111no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—111no—
274C2×D4—221no—
275C2×D4—221no—
276C2×D4—221no—
277C2×D4—221no—
278C2×D4—221no—
279C2×D4—221no—
280C2×D4—441no—
281C2×D4—441no—
282C2×D4—444no—
283C2×D4C22×D1111yescharacteristic
284C2×D4C22×D1111yescharacteristic
285C22×C4—111no—
286C22×C4—111no—
287C22×C4—111no—
288C22×C4—111no—
289C22×C4—111no—
290C22×C4—221no—
291C22×C4—221no—
292C22×C4—441no—
293C22×C4—441no—
294C22×C4C22×D1111yescharacteristic
295SD16—441no—
296SD16—441no—
297D8—41no—
298D8—441no—
299C2×C8—41no—
300C2×C8—111no—
301C2×C8—111no—
302C2×C8—441no—
303C2×C8C22×D1111yescharacteristic
304C2×C8C22×D1111yescharacteristic
305C4⋊C4—111no—
306C4⋊C4—111no—
307C4⋊C4—221no—
308C4⋊C4—221no—
309C4⋊C4—221no—
310C4⋊C4C22×D1111yescharacteristic
311C4⋊C4C22×D1111yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—221no—
315C22⋊C4—221no—
316C22⋊C4—221no—
317C22⋊C4—221no—
318C22⋊C4—221no—
319C22⋊C4—221no—
320C22⋊C4—221no—
321C42—221no—
322C11#318811yescharacteristic, complemented, Sylow
323C23—21no—
324C23—21no—
325C23—111no—
326C23—111no—
327C23—222no—
328C23—222no—
329C23—221no—
330C23—441no—
331C23—442no—
332C23—442no—
333C23—442no—
334C23D4×D1111yescharacteristic
335Q8—221no—
336Q8—221no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—42no—
343D4—221no—
344D4—221no—
345D4—442no—
346D4—442no—
347D4—442no—
348D4—442no—
349D4—442no—
350D4—442no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—111no—
356C2×C4—111no—
357C2×C4—221no—
358C2×C4—221no—
359C2×C4—221no—
360C2×C4—221no—
361C2×C4—221no—
362C2×C4—221no—
363C2×C4—221no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—442no—
367C2×C4—441no—
368C2×C4—442no—
369C2×C4D4×D1111yescharacteristic
370C2×C4C23×D1111yescharacteristic
371C8—21no—
372C8—21no—
373C8—221no—
374C8—221no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—112no—
384C22—221no—
385C22—221no—
386C22—221no—
387C22—221no—
388C22—221no—
389C22—444no—
390C22—441no—
391C22—441no—
392C22—441no—
393C22—884no—
394C22#6696412yes—
395C22C2×D4×D1111yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—221no—
400C4—221no—
401C4—441no—
402C4—441no—
403C4—441no—
404C4#6703711yescharacteristic
405C4#6704211yescharacteristic
406C2—22no—
407C2—81no—
408C2—81no—
409C2—222no—
410C2—441no—
411C2—881no—
412C2#1062313611yescharacteristic
413C2C2×#6696411yescharacteristic
414C2D11×#13511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#466C2
socleC22×C11C22×D4
hypercenter#466D11
hypocenterC11#3188
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #10623137C2semidirect
2. D11×#121C2semidirect
3. C11×#466C2semidirect
4. #10622771C2semidirect
5. #10622769C2semidirect
6. #10622727C2semidirect
7. C2×(C2×D11)⋊C8C2semidirect
8. #10622654C2semidirect
9. #10622651C2semidirect
10. #10622498C2semidirect
11. #10622497C2semidirect
12. #10622394C2semidirect
13. #10622392C2semidirect
14. #10622390C2semidirect
15. #10622389C2semidirect
16. C2×#4341C22semidirect
20. C2×C11×D8C22semidirect
21. C22×C8×C11C22semidirect
23. C11×#121C22semidirect
29. C2×#4324C22semidirect
30. C2×#4323C22semidirect
32. #66977C22semidirect
33. C22×C11⋊C8C22semidirect
34. C2×#4314C22semidirect
37. #66945C22semidirect
43. C11×#107C22semidirect
44. C11×#102C22semidirect
45. C11×#102C22semidirect
46. #66896C22semidirect
47. #66896C22semidirect
48. #66885C22semidirect
51. (C2×D11)⋊C8C22semidirect
52. (C2×D11)⋊C8C22semidirect
53. #66881C22semidirect
54. #66880C22semidirect
55. #66874C22semidirect
56. #66873C22semidirect
57. #66872C22semidirect
58. #66871C22semidirect
175. #466D11semidirect
221. C2×D8C2×D11semidirect
223. C22×C8C2×D11semidirect
234. #121C2×D11semidirect
242. #107C2×D11semidirect
251. #102C2×D11semidirect
252. #102C2×D11semidirect
322. C11#3188semidirect

Maximal subgroups

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

subgroupindex
#106231372
D11×#1212
C11×#4662
#106227712
#106227692
#106227272
C2×(C2×D11)⋊C82
#106226542
#106226512
#106224982
#106224972
#106223942
#106223922
#106223902
#106223892
#318811