Finite Group Databasebeta

← #13079467

Subgroups — #13079467

Order 1408.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623364C211yesmaximal, characteristic, complemented
2#10623138C211yesmaximal, characteristic, complemented
3C11×#449C211yesmaximal, characteristic, complemented
4#10622851C211yesmaximal, characteristic, complemented
5#10622784C211yesmaximal, characteristic, complemented
6#10622782C211yesmaximal, characteristic, complemented
7#10622772C211yesmaximal, characteristic, complemented
8#10622769C211yesmaximal, characteristic, complemented
9#10622646C211yesmaximal, characteristic, complemented
10#10622428C211yesmaximal, characteristic, complemented
11#10622425C211yesmaximal, characteristic, complemented
12#10622392C211yesmaximal, characteristic, complemented
13#10622388C211yesmaximal, characteristic, complemented
14#10622348C211yesmaximal, characteristic, complemented
15#10622340C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic, complemented
17C2×D4×D11C2211yescharacteristic
18C2×#4339C2211yescharacteristic
19C2×C11×SD16C2211yescharacteristic
20C2×C11×D8C2211yescharacteristic
21C11×#121C2211yescharacteristic
22#66999C2211yescharacteristic
23#66999C2211yescharacteristic, complemented
24C2×#4325C2211yescharacteristic
25#66993—21no—
26#66992—21no—
27#66992—21no—
28#66991C2211yescharacteristic
29#66991C2211yescharacteristic
30#66991C2211yescharacteristic, complemented
31#66990—21no—
32C2×#4323C2211yescharacteristic
33#66983—21no—
34#66983C2211yescharacteristic
35C2×C4⋊Dic11C2211yescharacteristic, complemented
36#66977—21no—
37C2×#4313C2211yescharacteristic, complemented
38C2×C8×D11C2211yescharacteristic, complemented
39#66948C2211yescharacteristic
40#66945C2211yescharacteristic
41#66938—21no—
42#66935—21no—
43C11×#103C2211yescharacteristic, complemented
44C11×#102C2211yescharacteristic, complemented
45C11×C22⋊C8C2211yescharacteristic, complemented
46#66899C2211yescharacteristic, complemented
47#66896C2211yescharacteristic
48#66896C2211yescharacteristic
49#66896C2211yescharacteristic, complemented
50C22⋊(C11⋊C8)C2211yescharacteristic, complemented
51#66885C2211yescharacteristic
52#66885C2211yescharacteristic
53(C2×D11)⋊C8C2211yescharacteristic
54(C2×D11)⋊C8C2211yescharacteristic
55#66881C2211yescharacteristic, complemented
56#66881C2211yescharacteristic, complemented
57#66871C2211yescharacteristic, complemented
58#66871C2211yescharacteristic, complemented
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—
73C2×C22⋊D11—21no—
74C2×C22⋊D11D411yescharacteristic
75C2×C22⋊D11D411yescharacteristic
76C22×Dic11—21no—
77D4×D11—41no—
78D4×D11—41no—
79#4339—41no—
80#4339—41no—
81C2×D44—21no—
82C2×D44D411yescharacteristic
83C2×D44C2311yescharacteristic
84C2×C4×D11C2311yescharacteristic
85C2×C4×D11C2311yescharacteristic
86C2×Dic22D411yescharacteristic
87C11×SD16—41no—
88C11×D8—41no—
89C2×C8×C11C2311yescharacteristic
90C2×C8×C11C2311yescharacteristic
91C11×C4⋊C4C2311yescharacteristic
92C11×C22⋊C4—21no—
93C22⋊Dic11—21no—
94C22⋊Dic11—21no—
95C22⋊Dic11—21no—
96#4325—41no—
97#4323—41no—
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4—21no—
100(C2×D11)⋊C4—21no—
101(C2×D11)⋊C4—21no—
102(C2×D11)⋊C4—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11C2311yescharacteristic
105C4⋊Dic11C2311yescharacteristic
106C4⋊Dic11C2311yescharacteristic
107Dic11⋊C4—21no—
108Dic11⋊C4—21no—
109C4×Dic11—21no—
110C2×C11⋊C8C2311yescharacteristic
111C2×C11⋊C8C2311yescharacteristic
112#4313—41no—
113C8×D11—41no—
114#3198—111nomaximal, Sylow
115C23×C11—21no—
116C23×C11—21no—
117C23×C11C2×D411yescharacteristic
118C22×D11—21no—
119C22×D11—42no—
120C22×D11—81no—
121C22×D11—81no—
122C22×D11C2×D411yescharacteristic
123C22×D11C2×D411yescharacteristic
124Q8×C11—21no—
125Q8×C11—21no—
126D4×C11—21no—
127D4×C11—21no—
128D4×C11—21no—
129D4×C11—21no—
130D4×C11—42no—
131D4×C11—81no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—42no—
137C2×C4×C11C2×D411yescharacteristic
138C2×C4×C11C2411yescharacteristic
139C22⋊D11—41no—
140C22⋊D11—41no—
141C22⋊D11—42no—
142C22⋊D11—81no—
143C22⋊D11—81no—
144C22⋊D11—81no—
145C22⋊D11—81no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11—81no—
150C2×Dic11C2×D411yescharacteristic
151C2×Dic11C2×D411yescharacteristic
152D44—21no—
153D44—21no—
154D44—41no—
155D44—81no—
156C4×D11—21no—
157C4×D11—21no—
158C4×D11—21no—
159C4×D11—21no—
160Dic22—41no—
161C8×C11—21no—
162C8×C11—21no—
163C11⋊C8—21no—
164C11⋊C8—21no—
165#537—111no—
166#535—111no—
167#485—111no—
168#482—111no—
169#481—111no—
170#480—111no—
171#469—111no—
172#468—111no—
173#466—111no—
174#465—111no—
175#450—111no—
176#449—111no—
177#449D1111yescharacteristic, complemented
178#447—111no—
179#408—111no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11—41no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11C22×D411yescharacteristic
190C2×D11—21no—
191C2×D11—21no—
192C2×D11—21no—
193C2×D11—21no—
194C2×D11—21no—
195C2×D11—21no—
196C2×D11—41no—
197C2×D11—41no—
198C2×D11—41no—
199C2×D11—84no—
200C4×C11—21no—
201C4×C11—41no—
202C4×C11—41no—
203C4×C11H(5,𝔽2)11yescharacteristic
204C4×C11H(5,𝔽2)11yescharacteristic
205Dic11—21no—
206Dic11—21no—
207Dic11—41no—
208Dic11—41no—
209Dic11—41no—
210C2×#41—111no—
211C2×#41C2×D1111yescharacteristic, complemented
212C22×D4—111no—
213C2×SD16—111no—
214C2×SD16C2×D1111yescharacteristic
215C2×D8—111no—
216C2×D8C2×D1111yescharacteristic
217C2×M16—111no—
218C22×C8—111no—
219#127—221no—
220#124—221no—
221C22⋊Q8—111no—
222C22⋊Q8—111no—
223C22⋊Q8—221no—
224#121—111no—
225#121—111no—
226#121—111no—
227#121—111no—
228#121—111no—
229#121—221no—
230#121—221no—
231#121—221no—
232#121C2×D1111yescharacteristic
233#120—221no—
234#120—221no—
235#117—111no—
236C2×C4⋊C4—111no—
237#107—111no—
238#107—111no—
239#106—111no—
240#106—111no—
241#103—111no—
242#103C2×D1111yescharacteristic, complemented
243#102—111no—
244#102—111no—
245#102—111no—
246#102—111no—
247#102—111no—
248#102C2×D1111yescharacteristic, complemented
249C22⋊C8—111no—
250C22⋊C8—111no—
251C22⋊C8—111no—
252C22⋊C8C2×D1111yescharacteristic, complemented
253C2×C11—41no—
254C2×C11—81no—
255C2×C11—81no—
256C2×C11#53411yescharacteristic
257C2×C11#57611yescharacteristic
258C2×C11#57711yescharacteristic
259D11—41no—
260D11—41no—
261D11—81no—
262C24—221no—
263#41—41no—
264#41—41no—
265#41—441no—
266#41—441no—
267C2×Q8—111no—
268C2×Q8C22×D1111yescharacteristic
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—111no—
272C2×D4—111no—
273C2×D4—111no—
274C2×D4—111no—
275C2×D4—221no—
276C2×D4—221no—
277C2×D4—221no—
278C2×D4—221no—
279C2×D4—221no—
280C2×D4—221no—
281C2×D4—441no—
282C2×D4—441no—
283C2×D4C22×D1111yescharacteristic
284C2×D4C22×D1111yescharacteristic
285C22×C4—21no—
286C22×C4—111no—
287C22×C4—111no—
288C22×C4—221no—
289C22×C4C22×D1111yescharacteristic
290SD16—41no—
291SD16—441no—
292D8—41no—
293D8—441no—
294M16—441no—
295C2×C8—111no—
296C2×C8—111no—
297C2×C8—441no—
298C2×C8C22×D1111yescharacteristic
299C2×C8C22×D1111yescharacteristic
300C4⋊C4—111no—
301C4⋊C4—111no—
302C4⋊C4—111no—
303C4⋊C4—221no—
304C4⋊C4—221no—
305C4⋊C4—221no—
306C4⋊C4C22×D1111yescharacteristic
307C22⋊C4—21no—
308C22⋊C4—221no—
309C22⋊C4—221no—
310C22⋊C4—221no—
311C22⋊C4—221no—
312C22⋊C4—221no—
313C22⋊C4—221no—
314C22⋊C4—221no—
315C22⋊C4—221no—
316C42—221no—
317C11#319811yescharacteristic, complemented, Sylow
318C23—21no—
319C23—21no—
320C23—111no—
321C23—111no—
322C23—221no—
323C23—442no—
324C23—881no—
325C23—881no—
326C23D4×D1111yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—441no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—42no—
335D4—81no—
336D4—221no—
337D4—221no—
338D4—441no—
339D4—441no—
340D4—441no—
341D4—442no—
342D4—881no—
343D4—881no—
344D4—881no—
345D4—881no—
346D4—881no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—42no—
352C2×C4—111no—
353C2×C4—111no—
354C2×C4—221no—
355C2×C4—221no—
356C2×C4—221no—
357C2×C4—221no—
358C2×C4—221no—
359C2×C4—221no—
360C2×C4—221no—
361C2×C4—881no—
362C2×C4D4×D1111yescharacteristic
363C2×C4C23×D1111yescharacteristic
364C8—21no—
365C8—21no—
366C8—221no—
367C8—221no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—221no—
378C22—221no—
379C22—221no—
380C22—221no—
381C22—221no—
382C22—221no—
383C22—441no—
384C22—441no—
385C22—441no—
386C22—884no—
387C22C2×D4×D1111yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—221no—
392C4—221no—
393C4—441no—
394C4—441no—
395C4—441no—
396C4#6703711yescharacteristic
397C4#6703711yescharacteristic
398C2—41no—
399C2—81no—
400C2—81no—
401C2—441no—
402C2—441no—
403C2—881no—
404C2#1062312011yescharacteristic
405C2#1062330111yescharacteristic
406C2#1062330511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#449C2
socleC22×C11C22×D4
hypercenter#449D11
hypocenterC11#3198
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. #10623364C2semidirect
2. #10623138C2semidirect
3. C11×#449C2semidirect
4. #10622851C2semidirect
5. #10622784C2semidirect
6. #10622782C2semidirect
7. #10622772C2semidirect
8. #10622769C2semidirect
9. #10622646C2semidirect
10. #10622428C2semidirect
11. #10622425C2semidirect
12. #10622392C2semidirect
13. #10622388C2semidirect
14. #10622348C2semidirect
15. #10622340C2semidirect
16. C2×C11×#41C22semidirect
23. #66999C22semidirect
30. #66991C22semidirect
35. C2×C4⋊Dic11C22semidirect
37. C2×#4313C22semidirect
38. C2×C8×D11C22semidirect
43. C11×#103C22semidirect
44. C11×#102C22semidirect
45. C11×C22⋊C8C22semidirect
46. #66899C22semidirect
49. #66896C22semidirect
50. C22⋊(C11⋊C8)C22semidirect
55. #66881C22semidirect
56. #66881C22semidirect
57. #66871C22semidirect
58. #66871C22semidirect
177. #449D11semidirect
211. C2×#41C2×D11semidirect
242. #103C2×D11semidirect
248. #102C2×D11semidirect
252. C22⋊C8C2×D11semidirect
317. C11#3198semidirect

Maximal subgroups

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

subgroupindex
#106233642
#106231382
C11×#4492
#106228512
#106227842
#106227822
#106227722
#106227692
#106226462
#106224282
#106224252
#106223922
#106223882
#106223482
#106223402
#319811