Finite Group Databasebeta

← #13079464

Subgroups — #13079464

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#10623336C211yesmaximal, characteristic, complemented
2#10623139C211yesmaximal, characteristic, complemented
3C11×#447C211yesmaximal, characteristic, complemented
4#10622831C211yesmaximal, characteristic, complemented
5#10622772C211yesmaximal, characteristic, complemented
6#10622771C211yesmaximal, characteristic, complemented
7#10622771C211yesmaximal, characteristic, complemented
8#10622770C211yesmaximal, characteristic, complemented
9#10622648C211yesmaximal, characteristic, complemented
10#10622393C211yesmaximal, characteristic, complemented
11#10622391C211yesmaximal, characteristic, complemented
12#10622390C211yesmaximal, characteristic, complemented
13#10622387C211yesmaximal, characteristic, complemented
14#10622340C211yesmaximal, characteristic, complemented
15#10622336C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C2×#4341C2211yescharacteristic, complemented
18C2×#4339C2211yescharacteristic
19C2×C11×D8C2211yescharacteristic
20C2×C11×D8C2211yescharacteristic
21C11×#121C2211yescharacteristic
22#67006—21no—
23#67006—21no—
24#66993—21no—
25#66992—21no—
26#66991—21no—
27#66991C2211yescharacteristic
28#66991C2211yescharacteristic
29#66991C2211yescharacteristic
30#66991C2211yescharacteristic
31#66991C2211yescharacteristic, complemented
32#66989—21no—
33C2×#4324C2211yescharacteristic
34C2×#4324C2211yescharacteristic
35#66979C2211yescharacteristic
36#66977C2211yescharacteristic
37C2×#4313C2211yescharacteristic, complemented
38C2×C8×D11C2211yescharacteristic, complemented
39#66950C2211yescharacteristic, complemented
40C4⋊C4×D11C2211yescharacteristic, complemented
41#66937—21no—
42#66931—21no—
43C11×#102C2211yescharacteristic
44C11×#102C2211yescharacteristic
45C11×C22⋊C8C2211yescharacteristic
46#66896C2211yescharacteristic
47#66896C2211yescharacteristic
48#66896C2211yescharacteristic, complemented
49#66896C2211yescharacteristic, complemented
50C22⋊(C11⋊C8)C2211yescharacteristic
51(C2×D11)⋊C8C2211yescharacteristic, complemented
52(C2×D11)⋊C8C2211yescharacteristic, complemented
53#66882C2211yescharacteristic, complemented
54#66881C2211yescharacteristic, complemented
55#66880C2211yescharacteristic, complemented
56#66880C2211yescharacteristic, complemented
57#66872C2211yescharacteristic, complemented
58#66871C2211yescharacteristic, complemented
59C24×C11—21no—
60C2×D4×C11—21no—
61C2×D4×C11—21no—
62C2×D4×C11—41no—
63C2×D4×C11—41no—
64C2×D4×C11C2311yescharacteristic
65C2×D4×C11C2311yescharacteristic
66C2×D4×C11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
68C2×C22⋊D11—21no—
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—
77#4341—41no—
78#4341—41no—
79#4339—41no—
80#4339—41no—
81C2×D44D411yescharacteristic
82C2×C4×D11—21no—
83C2×C4×D11C2311yescharacteristic
84C2×C4×D11C2311yescharacteristic
85C2×Dic22D411yescharacteristic
86C2×Dic22C2311yescharacteristic
87C11×D8—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—
96C22⋊Dic11—21no—
97C22⋊Dic11—21no—
98C22⋊Dic11—21no—
99C22⋊Dic11—21no—
100#4324—41no—
101#4324—41no—
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×C11—21no—
118C23×C11—42no—
119C23×C11—81no—
120C23×C11—81no—
121C23×C11C2×D411yescharacteristic
122C22×D11C2×D411yescharacteristic
123C22×D11C2×D411yescharacteristic
124D4×C11—21no—
125D4×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×C11C2×D411yescharacteristic
136C2×C4×C11C2411yescharacteristic
137C22⋊D11—41no—
138C22⋊D11—41no—
139C22⋊D11—42no—
140C22⋊D11—81no—
141C22⋊D11—81no—
142C22⋊D11—81no—
143C22⋊D11—81no—
144C22⋊D11—81no—
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11—42no—
150C2×Dic11C2×D411yescharacteristic
151C2×Dic11C2×D411yescharacteristic
152D44—41no—
153C4×D11—21no—
154C4×D11—21no—
155C4×D11—21no—
156C4×D11—21no—
157C4×D11—81no—
158Dic22—21no—
159Dic22—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#449—111no—
178#447D1111yescharacteristic, complemented
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×C11—41no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—84no—
193C22×C11C22×D411yescharacteristic
194C2×D11—21no—
195C2×D11—21no—
196C2×D11—21no—
197C2×D11—21no—
198C2×D11—21no—
199C2×D11—21no—
200C4×C11—21no—
201C4×C11—41no—
202C4×C11H(5,𝔽2)11yescharacteristic
203C4×C11H(5,𝔽2)11yescharacteristic
204Dic11—21no—
205Dic11—21no—
206Dic11—41no—
207Dic11—41no—
208Dic11—41no—
209Dic11—41no—
210C2×#41—111no—
211C2×#41—111no—
212C22×D4C2×D1111yescharacteristic
213C2×SD16—111no—
214C2×SD16—111no—
215C2×D8C2×D1111yescharacteristic
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#103—111no—
243#102—111no—
244#102—111no—
245#102—111no—
246#102—111no—
247#102C2×D1111yescharacteristic
248#102C2×D1111yescharacteristic
249C22⋊C8—111no—
250C22⋊C8—111no—
251C22⋊C8—111no—
252C22⋊C8C2×D1111yescharacteristic
253C2×C11—41no—
254C2×C11—81no—
255C2×C11—81no—
256C2×C11—81no—
257C2×C11#53411yescharacteristic
258C2×C11#57611yescharacteristic
259C2×C11#57711yescharacteristic
260D11—41no—
261D11—41no—
262C24—21no—
263#41—441no—
264#41—441no—
265#41—441no—
266#41—441no—
267C2×Q8—111no—
268C2×Q8—111no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—111no—
274C2×D4—111no—
275C2×D4—111no—
276C2×D4—221no—
277C2×D4—221no—
278C2×D4—221no—
279C2×D4—221no—
280C2×D4—221no—
281C2×D4—221no—
282C2×D4C22×D1111yescharacteristic
283C2×D4C22×D1111yescharacteristic
284C2×D4C22×D1111yescharacteristic
285C22×C4—111no—
286C22×C4—111no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4C22×D1111yescharacteristic
290SD16—441no—
291SD16—441no—
292D8—41no—
293D8—41no—
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—21no—
321C23—42no—
322C23—81no—
323C23—81no—
324C23—111no—
325C23—111no—
326C23D4×D1111yescharacteristic
327Q8—221no—
328Q8—221no—
329Q8—441no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—42no—
337D4—81no—
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—111no—
351C2×C4—111no—
352C2×C4—221no—
353C2×C4—221no—
354C2×C4—221no—
355C2×C4—221no—
356C2×C4—221no—
357C2×C4—221no—
358C2×C4—221no—
359C2×C4—221no—
360C2×C4—442no—
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—41no—
378C22—41no—
379C22—41no—
380C22—84no—
381C22—221no—
382C22—221no—
383C22—221no—
384C22—221no—
385C22—221no—
386C22—221no—
387C22C2×D4×D1111yescharacteristic
388C4—21no—
389C4—41no—
390C4—221no—
391C4—221no—
392C4—441no—
393C4—441no—
394C4—441no—
395C4—441no—
396C4#6703711yescharacteristic
397C4#6703711yescharacteristic
398C2—41no—
399C2—81no—
400C2—81no—
401C2—81no—
402C2—441no—
403C2—441no—
404C2#1062312011yescharacteristic
405C2#1062328811yescharacteristic
406C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#447C2
socleC22×C11C22×D4
hypercenter#447D11
hypocenterC11#3198
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #10623336C2semidirect
2. #10623139C2semidirect
3. C11×#447C2semidirect
4. #10622831C2semidirect
5. #10622772C2semidirect
6. #10622771C2semidirect
7. #10622771C2semidirect
8. #10622770C2semidirect
9. #10622648C2semidirect
10. #10622393C2semidirect
11. #10622391C2semidirect
12. #10622390C2semidirect
13. #10622387C2semidirect
14. #10622340C2semidirect
15. #10622336C2semidirect
17. C2×#4341C22semidirect
31. #66991C22semidirect
37. C2×#4313C22semidirect
38. C2×C8×D11C22semidirect
39. #66950C22semidirect
40. C4⋊C4×D11C22semidirect
48. #66896C22semidirect
49. #66896C22semidirect
51. (C2×D11)⋊C8C22semidirect
52. (C2×D11)⋊C8C22semidirect
53. #66882C22semidirect
54. #66881C22semidirect
55. #66880C22semidirect
56. #66880C22semidirect
57. #66872C22semidirect
58. #66871C22semidirect
178. #447D11semidirect
317. C11#3198semidirect

Maximal subgroups

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

subgroupindex
#106233362
#106231392
C11×#4472
#106228312
#106227722
#106227712
#106227702
#106226482
#106223932
#106223912
#106223902
#106223872
#106223402
#106223362
#319811