Finite Group Databasebeta

← #13079470

Subgroups — #13079470

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#10623361C211yesmaximal, characteristic, complemented
3C11×#408C211yesmaximal, characteristic, complemented
4#10622748C211yesmaximal, characteristic, complemented
5#10622747C211yesmaximal, characteristic, complemented
6#10622728C211yesmaximal, characteristic, complemented
7#10622727C211yesmaximal, characteristic, complemented
8#10622350C211yesmaximal, characteristic, complemented
9#10622349C211yesmaximal, characteristic, complemented
10#10622348C211yesmaximal, characteristic, complemented
11#10622347C211yesmaximal, characteristic, complemented
12#10622347C211yesmaximal, characteristic, complemented
13#10622345C211yesmaximal, characteristic, complemented
14#10622344C211yesmaximal, characteristic, complemented
15#10622336C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×#4339C2211yescharacteristic, complemented
18C22×D44C2211yescharacteristic
19C2×C11×M16C2211yescharacteristic, complemented
20C22×C8×C11C2211yescharacteristic, complemented
21#67000—21no—
22#66999—21no—
23#66993—21no—
24#66992—21no—
25#66992—21no—
26#66991—21no—
27#66990—21no—
28#66990—21no—
29#66983C2211yescharacteristic
30#66983C2211yescharacteristic
31#66983C2211yescharacteristic
32#66983C2211yescharacteristic
33#66983C2211yescharacteristic
34#66983C2211yescharacteristic, complemented
35#66979C2211yescharacteristic
36C2×C4⋊Dic11C2211yescharacteristic, complemented
37#66977C2211yescharacteristic
38#66977C2211yescharacteristic, complemented
39C2×D88C2211yescharacteristic
40C2×D88C2211yescharacteristic
41C2×#4314C2211yescharacteristic
42C2×#4314C2211yescharacteristic
43C11×C22⋊C8C2211yescharacteristic
44C11×C22⋊C8C2211yescharacteristic
45C11×C22⋊C8C2211yescharacteristic, complemented
46C11×C22⋊C8C2211yescharacteristic, complemented
47#66885C2211yescharacteristic
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50#66885C2211yescharacteristic
51#66885C2211yescharacteristic, complemented
52#66885C2211yescharacteristic, complemented
53#66882C2211yescharacteristic, complemented
54#66882C2211yescharacteristic, complemented
55#66881C2211yescharacteristic, complemented
56#66881C2211yescharacteristic, complemented
57#66880C2211yescharacteristic, complemented
58#66880C2211yescharacteristic, complemented
59C23×D11—21no—
60C11×#41—41no—
61C11×#41—41no—
62C2×Q8×C11D411yescharacteristic
63C2×D4×C11D411yescharacteristic
64C2×D4×C11D411yescharacteristic
65C2×D4×C11D411yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
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⋊D11—21no—
75C2×C22⋊D11—21no—
76C22×Dic11—21no—
77#4339—41no—
78#4339—41no—
79C2×D44—21no—
80C2×D44—41no—
81C2×D44—41no—
82C2×D44C2311yescharacteristic
83C2×D44C2311yescharacteristic
84C2×D44C2311yescharacteristic
85C2×C4×D11—21no—
86C2×Dic22C2311yescharacteristic
87C11×M16—41no—
88C2×C8×C11—41no—
89C2×C8×C11C2311yescharacteristic
90C2×C8×C11C2311yescharacteristic
91C2×C8×C11C2311yescharacteristic
92C2×C8×C11C2311yescharacteristic
93C22⋊Dic11—21no—
94C22⋊Dic11—21no—
95C22⋊Dic11—21no—
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⋊Dic11—21no—
103C4⋊Dic11C2311yescharacteristic
104C4⋊Dic11C2311yescharacteristic
105C4⋊Dic11C2311yescharacteristic
106C4⋊Dic11C2311yescharacteristic
107Dic11⋊C4—21no—
108Dic11⋊C4—21no—
109C4×Dic11—21no—
110D88—41no—
111D88—41no—
112#4314—41no—
113#4314—41no—
114#3198—111nomaximal, Sylow
115C23×C11C2×D411yescharacteristic
116C23×C11C2×D411yescharacteristic
117C23×C11C2×D411yescharacteristic
118C22×D11—21no—
119C22×D11—21no—
120C22×D11—21no—
121C22×D11—42no—
122C22×D11—81no—
123C22×D11—81no—
124Q8×C11—41no—
125D4×C11—41no—
126D4×C11—41no—
127D4×C11—41no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11C2×D411yescharacteristic
135C2×C4×C11C2×D411yescharacteristic
136C2×C4×C11C2×D411yescharacteristic
137C2×C4×C11C2411yescharacteristic
138C22⋊D11—42no—
139C22⋊D11—81no—
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—21no—
150C2×Dic11—81no—
151D44—21no—
152D44—21no—
153D44—21no—
154D44—21no—
155D44—21no—
156D44—21no—
157D44—42no—
158C4×D11—42no—
159Dic22—21no—
160Dic22—21no—
161C8×C11—21no—
162C8×C11—21no—
163C8×C11—21no—
164C8×C11—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#447—111no—
179#408D1111yescharacteristic, complemented
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11C22×D411yescharacteristic
190C2×D11—41no—
191C2×D11—41no—
192C2×D11—41no—
193C2×D11—41no—
194C2×D11—41no—
195C2×D11—41no—
196C2×D11—41no—
197C2×D11—41no—
198C2×D11—41no—
199C2×D11—84no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11H(5,𝔽2)11yescharacteristic
204C4×C11H(5,𝔽2)11yescharacteristic
205Dic11—41no—
206Dic11—41no—
207Dic11—41no—
208Dic11—41no—
209Dic11—41no—
210C2×#41—111no—
211C2×#41C2×D1111yescharacteristic
212C22×D4—111no—
213C2×SD16—111no—
214C2×SD16—111no—
215C2×D8—111no—
216C2×D8—111no—
217C2×M16C2×D1111yescharacteristic, complemented
218C22×C8C2×D1111yescharacteristic, complemented
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—111no—
230#121—221no—
231#121—221no—
232#121—221no—
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#102—111no—
248#102—111no—
249C22⋊C8C2×D1111yescharacteristic
250C22⋊C8C2×D1111yescharacteristic
251C22⋊C8C2×D1111yescharacteristic, complemented
252C22⋊C8C2×D1111yescharacteristic, complemented
253C2×C11—41no—
254C2×C11—41no—
255C2×C11—41no—
256C2×C11#53411yescharacteristic
257C2×C11#57611yescharacteristic
258C2×C11#57711yescharacteristic
259D11—81no—
260D11—81no—
261D11—81no—
262C24—221no—
263#41—41no—
264#41—41no—
265#41—441no—
266#41—441no—
267C2×Q8—111no—
268C2×Q8D4411yescharacteristic
269C2×D4—111no—
270C2×D4—111no—
271C2×D4—111no—
272C2×D4—221no—
273C2×D4—221no—
274C2×D4—221no—
275C2×D4—221no—
276C2×D4—221no—
277C2×D4—221no—
278C2×D4—221no—
279C2×D4—221no—
280C2×D4—441no—
281C2×D4—441no—
282C2×D4D4411yescharacteristic
283C2×D4D4411yescharacteristic
284C2×D4D4411yescharacteristic
285C22×C4—221no—
286C22×C4—221no—
287C22×C4C22×D1111yescharacteristic
288C22×C4C22×D1111yescharacteristic
289C22×C4C22×D1111yescharacteristic
290SD16—441no—
291SD16—441no—
292D8—441no—
293D8—441no—
294M16—41no—
295C2×C8—41no—
296C2×C8C22×D1111yescharacteristic
297C2×C8C22×D1111yescharacteristic
298C2×C8C22×D1111yescharacteristic
299C2×C8C22×D1111yescharacteristic
300C4⋊C4—111no—
301C4⋊C4—111no—
302C4⋊C4—111no—
303C4⋊C4—111no—
304C4⋊C4—221no—
305C4⋊C4—221no—
306C4⋊C4—221no—
307C22⋊C4—221no—
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—221no—
319C23—221no—
320C23—221no—
321C23—442no—
322C23—881no—
323C23—881no—
324C23C2×D4411yescharacteristic
325C23C2×D4411yescharacteristic
326C23C2×D4411yescharacteristic
327Q8—41no—
328Q8—221no—
329Q8—221no—
330D4—41no—
331D4—41no—
332D4—41no—
333D4—221no—
334D4—221no—
335D4—221no—
336D4—221no—
337D4—221no—
338D4—221no—
339D4—442no—
340D4—442no—
341D4—881no—
342D4—881no—
343D4—881no—
344D4—881no—
345D4—881no—
346D4—881no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—221no—
354C2×C4—221no—
355C2×C4—221no—
356C2×C4—221no—
357C2×C4—221no—
358C2×C4—442no—
359C2×C4—881no—
360C2×C4C2×D4411yescharacteristic
361C2×C4C2×D4411yescharacteristic
362C2×C4C2×D4411yescharacteristic
363C2×C4C23×D1111yescharacteristic
364C8—21no—
365C8—21no—
366C8—21no—
367C8—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—441no—
378C22—441no—
379C22—441no—
380C22—441no—
381C22—441no—
382C22—441no—
383C22—441no—
384C22—441no—
385C22—441no—
386C22—884no—
387C22C22×D4411yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—441no—
392C4—441no—
393C4—441no—
394C4—441no—
395C4—441no—
396C4#6703711yescharacteristic
397C4#6703711yescharacteristic
398C2—41no—
399C2—41no—
400C2—41no—
401C2—881no—
402C2—881no—
403C2—881no—
404C2#1062302411yescharacteristic
405C2#1062328211yescharacteristic
406C2#1062328311yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#408C2
socleC22×C11C22×D4
hypercenter#408D11
hypocenterC11#3198
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #10623364C2semidirect
2. #10623361C2semidirect
3. C11×#408C2semidirect
4. #10622748C2semidirect
5. #10622747C2semidirect
6. #10622728C2semidirect
7. #10622727C2semidirect
8. #10622350C2semidirect
9. #10622349C2semidirect
10. #10622348C2semidirect
11. #10622347C2semidirect
12. #10622347C2semidirect
13. #10622345C2semidirect
14. #10622344C2semidirect
15. #10622336C2semidirect
17. C2×#4339C22semidirect
19. C2×C11×M16C22semidirect
20. C22×C8×C11C22semidirect
34. #66983C22semidirect
36. C2×C4⋊Dic11C22semidirect
38. #66977C22semidirect
45. C11×C22⋊C8C22semidirect
46. C11×C22⋊C8C22semidirect
51. #66885C22semidirect
52. #66885C22semidirect
53. #66882C22semidirect
54. #66882C22semidirect
55. #66881C22semidirect
56. #66881C22semidirect
57. #66880C22semidirect
58. #66880C22semidirect
179. #408D11semidirect
217. C2×M16C2×D11semidirect
218. C22×C8C2×D11semidirect
251. C22⋊C8C2×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
#106233612
C11×#4082
#106227482
#106227472
#106227282
#106227272
#106223502
#106223492
#106223482
#106223472
#106223452
#106223442
#106223362
#319811