Finite Group Databasebeta

← #13079457

Subgroups — #13079457

Order 1408.

418 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623359C211yesmaximal, characteristic, complemented
2#10623158C211yesmaximal, characteristic, complemented
3C11×#452C211yesmaximal, characteristic, complemented
4#10622851C211yesmaximal, characteristic, complemented
5#10622802C211yesmaximal, characteristic, complemented
6#10622800C211yesmaximal, characteristic, complemented
7#10622787C211yesmaximal, characteristic, complemented
8#10622785C211yesmaximal, characteristic, complemented
9#10622658C211yesmaximal, characteristic, complemented
10#10622427C211yesmaximal, characteristic, complemented
11#10622425C211yesmaximal, characteristic, complemented
12#10622395C211yesmaximal, characteristic, complemented
13#10622392C211yesmaximal, characteristic, complemented
14#10622350C211yesmaximal, characteristic, complemented
15#10622339C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×#4343C2211yescharacteristic
18C22×C4×D11C2211yescharacteristic
19C2×C11×Q16C2211yescharacteristic, complemented
20C2×C11×SD16C2211yescharacteristic, complemented
21C11×C22⋊Q8C2211yescharacteristic
22#66999C2211yescharacteristic
23#66999C2211yescharacteristic
24#66999C2211yescharacteristic
25C2×#4325C2211yescharacteristic, complemented
26#66991C2211yescharacteristic
27#66991C2211yescharacteristic
28#66990—21no—
29#66988—21no—
30C2×#4323C2211yescharacteristic, complemented
31#66983C2211yescharacteristic
32C4×C22⋊D11—21no—
33C4×C22⋊D11—21no—
34#66979C2211yescharacteristic
35C2×#4313C2211yescharacteristic
36C2×#4313C2211yescharacteristic
37#66948C2211yescharacteristic
38#66947—21no—
39#66946—21no—
40#66945C2211yescharacteristic
41#66935—21no—
42(C22⋊D11)⋊C4—21no—
43C11×#103C2211yescharacteristic, complemented
44C11×#102C2211yescharacteristic, complemented
45C11×C22⋊C8C2211yescharacteristic
46#66899C2211yescharacteristic, complemented
47#66899C2211yescharacteristic, complemented
48#66899C2211yescharacteristic, complemented
49#66896C2211yescharacteristic, complemented
50C22⋊(C11⋊C8)C2211yescharacteristic
51#66885C2211yescharacteristic, complemented
52#66885C2211yescharacteristic, complemented
53(C2×D11)⋊C8C2211yescharacteristic
54(C2×D11)⋊C8C2211yescharacteristic
55#66882C2211yescharacteristic, complemented
56#66881C2211yescharacteristic, complemented
57#66872C2211yescharacteristic, complemented
58#66871C2211yescharacteristic, complemented
59C23×D11D411yescharacteristic
60C11×#41—41no—
61C11×#41—41no—
62C2×Q8×C11C2311yescharacteristic
63C2×Q8×C11C2311yescharacteristic
64C2×D4×C11—21no—
65C2×D4×C11C2311yescharacteristic
66C22×C4×C11—21no—
67C22×C4×C11C2311yescharacteristic
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70C2×C22⋊D11—21no—
71C22×Dic11D411yescharacteristic
72#4343—41no—
73#4343—41no—
74C2×D44—21no—
75C2×D44—21no—
76C2×D44C2311yescharacteristic
77C2×C4×D11—21no—
78C2×C4×D11—41no—
79C2×C4×D11—41no—
80C2×C4×D11D411yescharacteristic
81C2×C4×D11D411yescharacteristic
82C2×C4×D11C2311yescharacteristic
83C2×C4×D11C2311yescharacteristic
84C11×Q16—41no—
85C11×SD16—41no—
86C2×C8×C11C2311yescharacteristic
87C2×C8×C11C2311yescharacteristic
88C11×C4⋊C4—21no—
89C11×C4⋊C4C2311yescharacteristic
90C11×C22⋊C4—21no—
91C22⋊Dic11—21no—
92C22⋊Dic11—21no—
93C22⋊Dic11—21no—
94#4325—41no—
95#4323—41no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4—21no—
100(C2×D11)⋊C4—21no—
101(C2×D11)⋊C4—21no—
102C4⋊Dic11C2311yescharacteristic
103C4⋊Dic11C2311yescharacteristic
104C4⋊Dic11C2311yescharacteristic
105Dic11⋊C4—21no—
106Dic11⋊C4—21no—
107Dic11⋊C4—21no—
108C4×Dic11—21no—
109C4×Dic11—21no—
110C2×C11⋊C8C2311yescharacteristic
111C2×C11⋊C8C2311yescharacteristic
112#4313—41no—
113#4313—41no—
114#3197—111nomaximal, Sylow
115C23×C11—21no—
116C23×C11C2×D411yescharacteristic
117C22×D11—21no—
118C22×D11—41no—
119C22×D11—41no—
120C22×D11—41no—
121C22×D11C2×D411yescharacteristic
122C22×D11C2×D411yescharacteristic
123Q8×C11—21no—
124Q8×C11—21no—
125Q8×C11—21no—
126Q8×C11—21no—
127D4×C11—21no—
128D4×C11—21no—
129D4×C11—42no—
130C2×C4×C11—21no—
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—42no—
139C22⋊D11—42no—
140C22⋊D11—42no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—41no—
145C2×Dic11C2×D411yescharacteristic
146C2×Dic11C2×D411yescharacteristic
147D44—21no—
148D44—21no—
149D44—42no—
150D44—42no—
151C4×D11—21no—
152C4×D11—21no—
153C4×D11—21no—
154C4×D11—21no—
155C4×D11—41no—
156C4×D11—41no—
157C4×D11—42no—
158C8×C11—21no—
159C8×C11—21no—
160C11⋊C8—21no—
161C11⋊C8—21no—
162#525—111no—
163#525—111no—
164#485—111no—
165#485—111no—
166#482—111no—
167#482—111no—
168#470—111no—
169#469—111no—
170#468—111no—
171#468—111no—
172#452—111no—
173#452D1111yescharacteristic, complemented
174#449—111no—
175#449—111no—
176#407—111no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11C22×D411yescharacteristic
184C2×D11—21no—
185C2×D11—21no—
186C2×D11—21no—
187C2×D11—21no—
188C2×D11—21no—
189C2×D11—21no—
190C2×D11—44no—
191C2×D11—41no—
192C2×D11—41no—
193C2×D11—41no—
194C4×C11—21no—
195C4×C11—41no—
196C4×C11—41no—
197C4×C11—41no—
198C4×C11H(5,𝔽2)11yescharacteristic
199C4×C11H(5,𝔽2)11yescharacteristic
200Dic11—21no—
201Dic11—21no—
202Dic11—41no—
203Dic11—41no—
204Dic11—41no—
205C2×#41—111no—
206C2×#41C2×D1111yescharacteristic
207C23×C4—111no—
208C2×Q16C2×D1111yescharacteristic, complemented
209C2×SD16—111no—
210C2×SD16C2×D1111yescharacteristic, complemented
211C2×D8—111no—
212C2×M16—111no—
213C2×M16—111no—
214#123—221no—
215#123—221no—
216C22⋊Q8—111no—
217C22⋊Q8—111no—
218C22⋊Q8—111no—
219C22⋊Q8C2×D1111yescharacteristic
220#121—111no—
221#121—111no—
222#121—111no—
223#121—111no—
224#120—221no—
225#120—221no—
226C4×D4—221no—
227C4×D4—221no—
228C4×D4—221no—
229C4×D4—221no—
230#117—111no—
231#117—111no—
232#107—111no—
233#107—111no—
234#106—111no—
235#106—111no—
236#103—111no—
237#103—111no—
238#103—111no—
239#103C2×D1111yescharacteristic, complemented
240#102—111no—
241#102—111no—
242#102—111no—
243#102C2×D1111yescharacteristic, complemented
244C22⋊C8—111no—
245C22⋊C8—111no—
246C22⋊C8—111no—
247C22⋊C8C2×D1111yescharacteristic
248C2×C11—41no—
249C2×C11—81no—
250C2×C11#53411yescharacteristic
251C2×C11#57511yescharacteristic
252C2×C11#57511yescharacteristic
253D11—41no—
254D11—41no—
255D11—81no—
256C24—111no—
257#41—41no—
258#41—41no—
259#41—441no—
260#41—441no—
261C2×Q8C22×D1111yescharacteristic
262C2×Q8C22×D1111yescharacteristic
263C2×D4—21no—
264C2×D4—111no—
265C2×D4—221no—
266C2×D4—221no—
267C2×D4—221no—
268C2×D4—221no—
269C2×D4—221no—
270C2×D4C22×D1111yescharacteristic
271C22×C4—21no—
272C22×C4—111no—
273C22×C4—111no—
274C22×C4—111no—
275C22×C4—111no—
276C22×C4—111no—
277C22×C4—221no—
278C22×C4—441no—
279C22×C4—441no—
280C22×C4C22×D1111yescharacteristic
281Q16—41no—
282SD16—41no—
283SD16—441no—
284D8—441no—
285M16—441no—
286M16—441no—
287C2×C8—111no—
288C2×C8—111no—
289C2×C8C22×D1111yescharacteristic
290C2×C8C22×D1111yescharacteristic
291C4⋊C4—21no—
292C4⋊C4—111no—
293C4⋊C4—111no—
294C4⋊C4—111no—
295C4⋊C4—221no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C4⋊C4C22×D1111yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—221no—
301C22⋊C4—221no—
302C22⋊C4—221no—
303C22⋊C4—221no—
304C22⋊C4—221no—
305C22⋊C4—221no—
306C22⋊C4—221no—
307C22⋊C4—221no—
308C22⋊C4—221no—
309C42—221no—
310C42—221no—
311C11#319711yescharacteristic, complemented, Sylow
312C23—21no—
313C23—111no—
314C23—111no—
315C23—221no—
316C23—441no—
317C23—441no—
318C23—441no—
319C23D4×D1111yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—21no—
323Q8—21no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—221no—
328D4—221no—
329D4—442no—
330D4—442no—
331D4—442no—
332D4—442no—
333D4—442no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—111no—
341C2×C4—111no—
342C2×C4—221no—
343C2×C4—221no—
344C2×C4—221no—
345C2×C4—221no—
346C2×C4—221no—
347C2×C4—221no—
348C2×C4—221no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—442no—
352C2×C4—441no—
353C2×C4D4×D1111yescharacteristic
354C2×C4C23×D1111yescharacteristic
355C8—21no—
356C8—21no—
357C8—221no—
358C8—221no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—221no—
366C22—221no—
367C22—221no—
368C22—221no—
369C22—221no—
370C22—221no—
371C22—444no—
372C22—441no—
373C22—441no—
374C22—441no—
375C22C2×D4×D1111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—221no—
381C4—221no—
382C4—441no—
383C4—441no—
384C4—441no—
385C4#6703711yescharacteristic
386C4#6703711yescharacteristic
387C2—41no—
388C2—81no—
389C2—441no—
390C2—441no—
391C2—881no—
392C2#1062312011yescharacteristic
393C2#1062329911yescharacteristic
394C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#452C2
socleC22×C11C22×D4
hypercenter#452D11
hypocenterC11#3197
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #10623359C2semidirect
2. #10623158C2semidirect
3. C11×#452C2semidirect
4. #10622851C2semidirect
5. #10622802C2semidirect
6. #10622800C2semidirect
7. #10622787C2semidirect
8. #10622785C2semidirect
9. #10622658C2semidirect
10. #10622427C2semidirect
11. #10622425C2semidirect
12. #10622395C2semidirect
13. #10622392C2semidirect
14. #10622350C2semidirect
15. #10622339C2semidirect
19. C2×C11×Q16C22semidirect
20. C2×C11×SD16C22semidirect
25. C2×#4325C22semidirect
30. C2×#4323C22semidirect
43. C11×#103C22semidirect
44. C11×#102C22semidirect
46. #66899C22semidirect
47. #66899C22semidirect
48. #66899C22semidirect
49. #66896C22semidirect
51. #66885C22semidirect
52. #66885C22semidirect
55. #66882C22semidirect
56. #66881C22semidirect
57. #66872C22semidirect
58. #66871C22semidirect
173. #452D11semidirect
208. C2×Q16C2×D11semidirect
210. C2×SD16C2×D11semidirect
239. #103C2×D11semidirect
243. #102C2×D11semidirect
311. C11#3197semidirect

Maximal subgroups

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

subgroupindex
#106233592
#106231582
C11×#4522
#106228512
#106228022
#106228002
#106227872
#106227852
#106226582
#106224272
#106224252
#106223952
#106223922
#106223502
#106223392
#319711