Finite Group Databasebeta

← #13080573

Subgroups — #13080573

Order 1408.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623337C211yesmaximal, characteristic, complemented
2#10623038C211yesmaximal, characteristic, complemented
3C2×C11×#102C211yesmaximal, characteristic, complemented
4#10622830C211yesmaximal, characteristic, complemented
5#10622727C211yesmaximal, characteristic, complemented
6#10622724C211yesmaximal, characteristic, complemented
7#10622584C211yesmaximal, characteristic, complemented
8#10622400C211yesmaximal, characteristic, complemented
9#10622398C211yesmaximal, characteristic, complemented
10#10622395C211yesmaximal, characteristic, complemented
11#10622394C211yesmaximal, characteristic, complemented
12#10622390C211yesmaximal, characteristic, complemented
13#10622384C211yesmaximal, characteristic, complemented
14#10622378C211yesmaximal, characteristic, complemented
15#10622374C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C2×#4341C2211yescharacteristic
18C2×#4339—21no—
19C22×C8×C11C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic
21#67006—21no—
22C2×C22⋊Dic11—21no—
23#66992—21no—
24#66991C2211yescharacteristic
25#66989C2211yescharacteristic
26#66988—21no—
27D4×Dic11C2211yescharacteristic
28C2×#4323C2211yescharacteristic
29C2×#4323C2211yescharacteristic
30#66983C2211yescharacteristic
31#66982—21no—
32C4×C22⋊D11C2211yescharacteristic
33#66977C2211yescharacteristic
34C2×#4314C2211yescharacteristic, complemented
35C2×#4313C2211yescharacteristic, complemented
36#66949—21no—
37#66948C2211yescharacteristic, complemented
38#66947—21no—
39#66946C2211yescharacteristic, complemented
40C4⋊C4×D11C2211yescharacteristic, complemented
41#66941C2211yescharacteristic, complemented
42C11×#102C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×#102C2211yescharacteristic
45C11×#102C2211yescharacteristic
46#66896C2211yescharacteristic
47#66896C2211yescharacteristic
48C22⋊(C11⋊C8)C2211yescharacteristic
49#66885C2211yescharacteristic, complemented
50(C2×D11)⋊C8C2211yescharacteristic, complemented
51#66881C2211yescharacteristic, complemented
52#66880C2211yescharacteristic, complemented
53#66879C2211yescharacteristic, complemented
54Dic11⋊C8C2211yescharacteristic, complemented
55#66874C2211yescharacteristic, complemented
56#66874C2211yescharacteristic, complemented
57#66872C2211yescharacteristic, complemented
58#66872C2211yescharacteristic, complemented
59C24×C11—21no—
60C2×D4×C11—22no—
61C2×D4×C11—21no—
62C2×D4×C11—41no—
63C2×D4×C11C2311yescharacteristic
64C2×D4×C11C2311yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11C2311yescharacteristic
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70C2×C22⋊D11D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73#4341—22no—
74#4341—41no—
75#4339—44no—
76C2×D44—21no—
77C2×D44C2311yescharacteristic
78C2×C4×D11—21no—
79C2×C4×D11—21no—
80C2×C4×D11C2311yescharacteristic
81C2×Dic22—21no—
82C2×Dic22C2311yescharacteristic
83C2×C8×C11—41no—
84C2×C8×C11C2311yescharacteristic
85C2×C8×C11C2311yescharacteristic
86C11×C4⋊C4—21no—
87C11×C4⋊C4C2311yescharacteristic
88C11×C4⋊C4C2311yescharacteristic
89C22⋊Dic11—21no—
90C22⋊Dic11—21no—
91C22⋊Dic11—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⋊Dic11C2311yescharacteristic
102C4⋊Dic11C2311yescharacteristic
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106Dic11⋊C4D411yescharacteristic
107C4×Dic11C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110#4314—41no—
111#4313—41no—
112#3306—111nomaximal, Sylow
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—42no—
116C23×C11—42no—
117C23×C11—81no—
118C23×C11C2×D411yescharacteristic
119C22×D11—21no—
120C22×D11C2×D411yescharacteristic
121D4×C11—21no—
122D4×C11—21no—
123D4×C11—21no—
124D4×C11—42no—
125D4×C11#4112yescomplemented
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—42no—
131C2×C4×C11C2×D411yescharacteristic
132C2×C4×C11C2411yescharacteristic
133C22⋊D11—22no—
134C22⋊D11—42no—
135C22⋊D11—42no—
136C22⋊D11—81no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—42no—
141C2×Dic11—81no—
142C2×Dic11C2×D411yescharacteristic
143C2×Dic11C2×D411yescharacteristic
144C2×Dic11C2×D411yescharacteristic
145D44—21no—
146D44—21no—
147D44—42no—
148C4×D11—21no—
149C4×D11—21no—
150C4×D11—42no—
151C4×D11—42no—
152Dic22—21no—
153Dic22—21no—
154Dic22—42no—
155C8×C11—21no—
156C8×C11—21no—
157C11⋊C8—21no—
158C11⋊C8—21no—
159#547—111no—
160#546—111no—
161#489—111no—
162#483—111no—
163#481—111no—
164#476—111no—
165#469—111no—
166#465—111no—
167#463—111no—
168#449—111no—
169#447—111no—
170#442—111no—
171#435—111no—
172#417—111no—
173C2×#102D1111yescharacteristic, complemented
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—22no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—84no—
183C22×C11AGL(1,ℤ/8)12yes—
184C22×C11C22×D411yescharacteristic
185C2×D11—21no—
186C2×D11—21no—
187C2×D11—21no—
188C2×D11—41no—
189C2×D11—41no—
190C2×D11—41no—
191C4×C11—21no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11C2×#4111yescharacteristic
195C4×C11H(5,𝔽2)11yescharacteristic
196Dic11—21no—
197Dic11—21no—
198Dic11—21no—
199Dic11—41no—
200Dic11—41no—
201Dic11—41no—
202C2×#41—111no—
203C2×#41—221no—
204C22×D4C2×D1111yescharacteristic
205C2×SD16—111no—
206C2×D8—111no—
207C2×D8—111no—
208C2×M16—111no—
209C22×C8C2×D1111yescharacteristic
210C4⋊Q8—111no—
211#124—111no—
212#123—221no—
213#123—221no—
214#123—221no—
215C22⋊Q8—111no—
216C22⋊Q8—221no—
217#121—111no—
218#121—111no—
219#121—111no—
220#121—221no—
221#120—221no—
222C4×D4—111no—
223C4×D4—111no—
224C4×D4—111no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4C2×D1111yescharacteristic
227C2×C22⋊C4—221no—
228#106—111no—
229#106—111no—
230#106—111no—
231C4⋊C8—111no—
232#103—111no—
233#103—111no—
234#103—111no—
235#102—111no—
236#102—111no—
237#102—111no—
238#102C2×D1111yescharacteristic
239#102C2×D1111yescharacteristic
240#102C2×D1111yescharacteristic
241#102C2×D1111yescharacteristic
242C22⋊C8—111no—
243C22⋊C8—111no—
244#97—111no—
245C2×C11—22no—
246C2×C11—42no—
247C2×C11—81no—
248C2×C11#54611yescharacteristic
249C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
250C2×C11#57711yescharacteristic
251D11—41no—
252D11—81no—
253C24—21no—
254#41—222no—
255#41—444no—
256#41—441no—
257C2×Q8—111no—
258C2×Q8—221no—
259C2×D4—22no—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4—111no—
263C2×D4—111no—
264C2×D4—221no—
265C2×D4—221no—
266C2×D4—221no—
267C2×D4—221no—
268C2×D4C22×D1111yescharacteristic
269C2×D4C22×D1111yescharacteristic
270C22×C4—21no—
271C22×C4—111no—
272C22×C4—221no—
273C22×C4—221no—
274C22×C4—221no—
275C22×C4—221no—
276C22×C4C22×D1111yescharacteristic
277SD16—441no—
278D8—222no—
279D8—441no—
280M16—441no—
281C2×C8—41no—
282C2×C8—111no—
283C2×C8—111no—
284C2×C8C22×D1111yescharacteristic
285C2×C8C22×D1111yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—111no—
288C4⋊C4—111no—
289C4⋊C4—111no—
290C4⋊C4—221no—
291C4⋊C4—221no—
292C4⋊C4—221no—
293C4⋊C4C22×D1111yescharacteristic
294C4⋊C4C22×D1111yescharacteristic
295C22⋊C4—111no—
296C22⋊C4—111no—
297C22⋊C4—221no—
298C22⋊C4—221no—
299C22⋊C4—221no—
300C22⋊C4—221no—
301C22⋊C4—221no—
302C22⋊C4—221no—
303C22⋊C4—221no—
304C22⋊C4—221no—
305C42—111no—
306C11#330611yescharacteristic, complemented, Sylow
307C23—21no—
308C23—21no—
309C23—42no—
310C23—42no—
311C23—81no—
312C23—111no—
313C23—221no—
314C23D4×D1111yescharacteristic
315Q8—221no—
316Q8—221no—
317Q8—442no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—222no—
323D4—221no—
324D4—221no—
325D4—442no—
326D4—442no—
327D4—442no—
328D4—881no—
329D4#433912yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—111no—
336C2×C4—111no—
337C2×C4—111no—
338C2×C4—221no—
339C2×C4—221no—
340C2×C4—221no—
341C2×C4—221no—
342C2×C4—221no—
343C2×C4—442no—
344C2×C4—442no—
345C2×C4—442no—
346C2×C4—881no—
347C2×C4D4×D1111yescharacteristic
348C2×C4C23×D1111yescharacteristic
349C8—21no—
350C8—21no—
351C8—221no—
352C8—221no—
353C22—21no—
354C22—21no—
355C22—22no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—84no—
362C22—221no—
363C22—221no—
364C22—221no—
365C22—441no—
366C22—441no—
367C22—441no—
368C22#6696412yes—
369C22C2×D4×D1111yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—221no—
374C4—221no—
375C4—221no—
376C4—441no—
377C4—441no—
378C4—441no—
379C4C2×#433911yescharacteristic
380C4#6703711yescharacteristic
381C2—22no—
382C2—42no—
383C2—81no—
384C2—441no—
385C2—881no—
386C2#1062302111yescharacteristic
387C2C2×#6696411yescharacteristic
388C2#1062329311yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×#102C2
socleC22×C11C22×D4
hypercenterC2×#102D11
hypocenterC11#3306
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #10623337C2semidirect
2. #10623038C2semidirect
3. C2×C11×#102C2semidirect
4. #10622830C2semidirect
5. #10622727C2semidirect
6. #10622724C2semidirect
7. #10622584C2semidirect
8. #10622400C2semidirect
9. #10622398C2semidirect
10. #10622395C2semidirect
11. #10622394C2semidirect
12. #10622390C2semidirect
13. #10622384C2semidirect
14. #10622378C2semidirect
15. #10622374C2semidirect
34. C2×#4314C22semidirect
35. C2×#4313C22semidirect
37. #66948C22semidirect
39. #66946C22semidirect
40. C4⋊C4×D11C22semidirect
41. #66941C22semidirect
49. #66885C22semidirect
50. (C2×D11)⋊C8C22semidirect
51. #66881C22semidirect
52. #66880C22semidirect
53. #66879C22semidirect
54. Dic11⋊C8C22semidirect
55. #66874C22semidirect
56. #66874C22semidirect
57. #66872C22semidirect
58. #66872C22semidirect
125. D4×C11#41semidirect
173. C2×#102D11semidirect
306. C11#3306semidirect
329. D4#4339semidirect

Maximal subgroups

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

subgroupindex
#106233372
#106230382
C2×C11×#1022
#106228302
#106227272
#106227242
#106225842
#106224002
#106223982
#106223952
#106223942
#106223902
#106223842
#106223782
#106223742
#330611