Finite Group Databasebeta

← #13080763

Subgroups — #13080763

Order 1408.

462 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623149C211yesmaximal, characteristic, complemented
2#10623140C211yesmaximal, characteristic, complemented
3C11×#466C211yesmaximal, characteristic, complemented
4#10622769C211yesmaximal, characteristic, complemented
5#10622763C211yesmaximal, characteristic, complemented
6C2×#66885C211yesmaximal, characteristic, complemented
7#10622724C211yesmaximal, characteristic, complemented
8#10622649C211yesmaximal, characteristic, complemented
9#10622647C211yesmaximal, characteristic, complemented
10#10622504C211yesmaximal, characteristic, complemented
11#10622498C211yesmaximal, characteristic, complemented
12#10622398C211yesmaximal, characteristic, complemented
13#10622395C211yesmaximal, characteristic, complemented
14#10622383C211yesmaximal, characteristic, complemented
15#10622377C211yesmaximal, characteristic, complemented
16C2×D4×D11—21no—
17C2×D4×D11C2211yescharacteristic
18C22×D44C2211yescharacteristic
19C2×C11×D8C2211yescharacteristic, complemented
20C22×C8×C11C2211yescharacteristic, complemented
21C11×#121C2211yescharacteristic
22C11×#121C2211yescharacteristic, complemented
23#66993C2211yescharacteristic
24#66992—21no—
25#66991C2211yescharacteristic, complemented
26#66990—21no—
27D4×Dic11—21no—
28D4×Dic11C2211yescharacteristic, complemented
29C2×#4323C2211yescharacteristic
30C2×#4323C2211yescharacteristic, complemented
31C4×C22⋊D11C2211yescharacteristic
32C2×C4⋊Dic11C2211yescharacteristic, complemented
33C2×#4313C2211yescharacteristic, complemented
34#66948C2211yescharacteristic
35#66946C2211yescharacteristic
36#66945C2211yescharacteristic, complemented
37#66943C2211yescharacteristic, complemented
38#66939—21no—
39#66937—21no—
40#66935—21no—
41#66932—21no—
42C11×#107C2211yescharacteristic, complemented
43C11×#102C2211yescharacteristic, complemented
44C11×#102C2211yescharacteristic, complemented
45#66896C2211yescharacteristic, complemented
46#66896C2211yescharacteristic, complemented
47C22⋊(C11⋊C8)C2211yescharacteristic, complemented
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50#66885C2211yescharacteristic, complemented
51#66885C2211yescharacteristic, complemented
52(C2×D11)⋊C8C2211yescharacteristic, complemented
53#66879C2211yescharacteristic, complemented
54Dic11⋊C8C2211yescharacteristic, complemented
55#66873C2211yescharacteristic
56#66873C2211yescharacteristic, complemented
57#66872C2211yescharacteristic, complemented
58#66872C2211yescharacteristic, complemented
59C23×D11—21no—
60C23×D11—21no—
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⋊D11D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73D4×D11—22no—
74D4×D11—41no—
75D4×D11—44no—
76C2×D44—21no—
77C2×D44—22no—
78C2×D44—21no—
79C2×D44—41no—
80C2×D44C2311yescharacteristic
81C2×D44C2311yescharacteristic
82C2×C4×D11—21no—
83C2×C4×D11C2311yescharacteristic
84C11×D8—41no—
85C2×C8×C11—41no—
86C2×C8×C11C2311yescharacteristic
87C2×C8×C11C2311yescharacteristic
88C11×C4⋊C4C2311yescharacteristic
89C11×C4⋊C4C2311yescharacteristic
90C11×C22⋊C4—21no—
91C11×C22⋊C4—21no—
92C22⋊Dic11—21no—
93C22⋊Dic11—21no—
94C22⋊Dic11D411yescharacteristic
95#4323—22no—
96#4323—41no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4—21no—
100(C2×D11)⋊C4D411yescharacteristic
101C4⋊Dic11—21no—
102C4⋊Dic11—21no—
103C4⋊Dic11C2311yescharacteristic
104C4⋊Dic11C2311yescharacteristic
105Dic11⋊C4—21no—
106Dic11⋊C4D411yescharacteristic
107C4×Dic11—21no—
108C4×Dic11C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111#4313—41no—
112#3318—111nomaximal, Sylow
113C23×C11—21no—
114C23×C11—21no—
115C23×C11C2×D411yescharacteristic
116C22×D11—21no—
117C22×D11—21no—
118C22×D11—42no—
119C22×D11—42no—
120C22×D11—42no—
121C22×D11—42no—
122C22×D11—81no—
123C22×D11—81no—
124C22×D11C2×D411yescharacteristic
125D4×C11—21no—
126D4×C11—21no—
127D4×C11—21no—
128D4×C11—21no—
129D4×C11—42no—
130D4×C11—42no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11C2×D411yescharacteristic
136C2×C4×C11C2411yescharacteristic
137C22⋊D11—22no—
138C22⋊D11—42no—
139C22⋊D11—42no—
140C22⋊D11—81no—
141C22⋊D11—81no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—81no—
145C2×Dic11—81no—
146C2×Dic11C2×D411yescharacteristic
147C2×Dic11C2×D411yescharacteristic
148C2×Dic11C2×D411yescharacteristic
149D44—21no—
150D44—21no—
151D44—21no—
152D44—42no—
153D44—42no—
154D44#4112yes—
155C4×D11—21no—
156C4×D11—21no—
157C4×D11—42no—
158C8×C11—21no—
159C8×C11—21no—
160C11⋊C8—21no—
161C11⋊C8—21no—
162#553—111no—
163D42—111no—
164#490—111no—
165#482—111no—
166#481—111no—
167#478—111no—
168#469—111no—
169#466D1111yescharacteristic, complemented
170#459—111no—
171#447—111no—
172#447—111no—
173#442—111no—
174#435—111no—
175#418—111no—
176C2×#102—111no—
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×C11AGL(1,ℤ/8)12yes—
186C22×C11C22×D411yescharacteristic
187C2×D11—22no—
188C2×D11—21no—
189C2×D11—21no—
190C2×D11—21no—
191C2×D11—41no—
192C2×D11—41no—
193C2×D11—41no—
194C2×D11—41no—
195C2×D11—41no—
196C2×D11—84no—
197C2×D11—84no—
198C4×C11—21no—
199C4×C11—41no—
200C4×C11—41no—
201C4×C11C2×#4111yescharacteristic
202C4×C11H(5,𝔽2)11yescharacteristic
203Dic11—21no—
204Dic11—21no—
205Dic11—21no—
206Dic11—41no—
207Dic11—41no—
208C22×D4—111no—
209C22×D4—111no—
210C22×D4—221no—
211C2×D8—111no—
212C2×D8—111no—
213C2×D8C2×D1111yescharacteristic, complemented
214C2×M16—111no—
215C22×C8C2×D1111yescharacteristic, complemented
216#127—111no—
217#126—221no—
218#125—111no—
219#123—221no—
220#121—111no—
221#121—111no—
222#121—221no—
223#121—221no—
224#121C2×D1111yescharacteristic
225#121C2×D1111yescharacteristic, complemented
226#120—221no—
227#120—221no—
228C4×D4—111no—
229C4×D4—111no—
230C4×D4—111no—
231C4×D4—221no—
232#117—111no—
233C2×C4⋊C4—111no—
234#107C2×D1111yescharacteristic, complemented
235#106—111no—
236#106—111no—
237C4⋊C8—111no—
238#102—111no—
239#102—111no—
240#102—111no—
241#102—111no—
242#102—111no—
243#102—111no—
244#102—111no—
245#102—111no—
246#102C2×D1111yescharacteristic, complemented
247#102C2×D1111yescharacteristic, complemented
248C22⋊C8—111no—
249C22⋊C8—111no—
250#97—111no—
251C2×C11—22no—
252C2×C11—81no—
253C2×C11—81no—
254C2×C11#54611yescharacteristic
255C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
256C2×C11#57611yescharacteristic
257D11—41no—
258D11—42no—
259D11—81no—
260C24—221no—
261C24—221no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—111no—
265C2×D4—111no—
266C2×D4—111no—
267C2×D4—222no—
268C2×D4—221no—
269C2×D4—221no—
270C2×D4—221no—
271C2×D4—221no—
272C2×D4—222no—
273C2×D4—221no—
274C2×D4—221no—
275C2×D4—441no—
276C2×D4—441no—
277C2×D4—444no—
278C2×D4C22×D1111yescharacteristic
279C2×D4C22×D1111yescharacteristic
280C22×C4—111no—
281C22×C4—221no—
282C22×C4—221no—
283C22×C4—221no—
284C22×C4C22×D1111yescharacteristic
285D8—41no—
286D8—222no—
287D8—441no—
288M16—441no—
289C2×C8—41no—
290C2×C8—111no—
291C2×C8—111no—
292C2×C8C22×D1111yescharacteristic
293C2×C8C22×D1111yescharacteristic
294C4⋊C4—111no—
295C4⋊C4—111no—
296C4⋊C4—111no—
297C4⋊C4—221no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4C22×D1111yescharacteristic
301C4⋊C4C22×D1111yescharacteristic
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—111no—
305C22⋊C4—111no—
306C22⋊C4—221no—
307C22⋊C4—221no—
308C22⋊C4—221no—
309C22⋊C4—221no—
310C22⋊C4—221no—
311C42—111no—
312C42—221no—
313C11#331811yescharacteristic, complemented, Sylow
314C23—21no—
315C23—21no—
316C23—111no—
317C23—221no—
318C23—221no—
319C23—442no—
320C23—442no—
321C23—442no—
322C23—442no—
323C23—881no—
324C23—881no—
325C23D4×D1111yescharacteristic
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—42no—
332D4—112no—
333D4—222no—
334D4—221no—
335D4—221no—
336D4—221no—
337D4—442no—
338D4—442no—
339D4—442no—
340D4—442no—
341D4—881no—
342D4—881no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—111no—
348C2×C4—111no—
349C2×C4—111no—
350C2×C4—221no—
351C2×C4—221no—
352C2×C4—221no—
353C2×C4—221no—
354C2×C4—442no—
355C2×C4—881no—
356C2×C4—881no—
357C2×C4D4×D1111yescharacteristic
358C2×C4C23×D1111yescharacteristic
359C8—21no—
360C8—21no—
361C8—221no—
362C8—221no—
363C22—21no—
364C22—21no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—221no—
372C22—221no—
373C22—221no—
374C22—222no—
375C22—441no—
376C22—441no—
377C22—441no—
378C22—441no—
379C22—441no—
380C22—884no—
381C22—884no—
382C22#6696412yes—
383C22C2×D4×D1111yescharacteristic
384C4—21no—
385C4—41no—
386C4—41no—
387C4—221no—
388C4—221no—
389C4—221no—
390C4—441no—
391C4—441no—
392C4#6703711yescharacteristic
393C4#41×D1111yescharacteristic
394C2—22no—
395C2—81no—
396C2—81no—
397C2—441no—
398C2—442no—
399C2—881no—
400C2#1062314111yescharacteristic
401C2C2×#6696411yescharacteristic
402C2#1062330011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#466C2
socleC22×C11C22×D4
hypercenter#466D11
hypocenterC11#3318
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. #10623149C2semidirect
2. #10623140C2semidirect
3. C11×#466C2semidirect
4. #10622769C2semidirect
5. #10622763C2semidirect
6. C2×#66885C2semidirect
7. #10622724C2semidirect
8. #10622649C2semidirect
9. #10622647C2semidirect
10. #10622504C2semidirect
11. #10622498C2semidirect
12. #10622398C2semidirect
13. #10622395C2semidirect
14. #10622383C2semidirect
15. #10622377C2semidirect
19. C2×C11×D8C22semidirect
20. C22×C8×C11C22semidirect
22. C11×#121C22semidirect
25. #66991C22semidirect
28. D4×Dic11C22semidirect
30. C2×#4323C22semidirect
32. C2×C4⋊Dic11C22semidirect
33. C2×#4313C22semidirect
36. #66945C22semidirect
37. #66943C22semidirect
42. C11×#107C22semidirect
43. C11×#102C22semidirect
44. C11×#102C22semidirect
45. #66896C22semidirect
46. #66896C22semidirect
47. C22⋊(C11⋊C8)C22semidirect
50. #66885C22semidirect
51. #66885C22semidirect
52. (C2×D11)⋊C8C22semidirect
53. #66879C22semidirect
54. Dic11⋊C8C22semidirect
56. #66873C22semidirect
57. #66872C22semidirect
58. #66872C22semidirect
169. #466D11semidirect
213. C2×D8C2×D11semidirect
215. C22×C8C2×D11semidirect
225. #121C2×D11semidirect
234. #107C2×D11semidirect
246. #102C2×D11semidirect
247. #102C2×D11semidirect
313. C11#3318semidirect

Maximal subgroups

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

subgroupindex
#106231492
#106231402
C11×#4662
#106227692
#106227632
C2×#668852
#106227242
#106226492
#106226472
#106225042
#106224982
#106223982
#106223952
#106223832
#106223772
#331811