Finite Group Databasebeta

← #13079472

Subgroups — #13079472

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#10623160C211yesmaximal, characteristic, complemented
3C11×#450C211yesmaximal, characteristic, complemented
4#10622830C211yesmaximal, characteristic, complemented
5#10622787C211yesmaximal, characteristic, complemented
6#10622785C211yesmaximal, characteristic, complemented
7#10622785C211yesmaximal, characteristic, complemented
8#10622784C211yesmaximal, characteristic, complemented
9#10622658C211yesmaximal, characteristic, complemented
10#10622395C211yesmaximal, characteristic, complemented
11#10622390C211yesmaximal, characteristic, complemented
12#10622388C211yesmaximal, characteristic, complemented
13#10622387C211yesmaximal, characteristic, complemented
14#10622350C211yesmaximal, characteristic, complemented
15#10622340C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C2×#4343C2211yescharacteristic, complemented
18C2×#4339C2211yescharacteristic
19C2×C11×SD16C2211yescharacteristic
20C2×C11×SD16C2211yescharacteristic
21C11×C22⋊Q8C2211yescharacteristic
22#67006—21no—
23#67006—21no—
24#66999C2211yescharacteristic, complemented
25#66993—21no—
26#66991C2211yescharacteristic
27#66991C2211yescharacteristic
28#66991C2211yescharacteristic
29#66991C2211yescharacteristic
30#66989—21no—
31C2×#4323C2211yescharacteristic
32C2×#4323C2211yescharacteristic
33#66983C2211yescharacteristic
34#66979C2211yescharacteristic
35C2×#4313C2211yescharacteristic, complemented
36C2×C8×D11C2211yescharacteristic, complemented
37#66949—21no—
38#66948—21no—
39#66948C2211yescharacteristic, complemented
40C4⋊C4×D11C2211yescharacteristic, complemented
41#66937—21no—
42#66937—21no—
43C11×#102C2211yescharacteristic
44C11×#102C2211yescharacteristic
45C11×C22⋊C8C2211yescharacteristic
46#66899C2211yescharacteristic, complemented
47#66899C2211yescharacteristic, complemented
48#66896C2211yescharacteristic
49#66896C2211yescharacteristic
50C22⋊(C11⋊C8)C2211yescharacteristic
51#66885C2211yescharacteristic, complemented
52#66885C2211yescharacteristic, complemented
53(C2×D11)⋊C8C2211yescharacteristic, complemented
54(C2×D11)⋊C8C2211yescharacteristic, complemented
55#66882C2211yescharacteristic, complemented
56#66881C2211yescharacteristic, complemented
57#66872C2211yescharacteristic, complemented
58#66871C2211yescharacteristic, complemented
59C24×C11—21no—
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11—21no—
62C2×D4×C11—41no—
63C2×D4×C11—41no—
64C2×D4×C11C2311yescharacteristic
65C2×D4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70C2×C22⋊D11—21no—
71C2×C22⋊D11—21no—
72C2×C22⋊D11D411yescharacteristic
73C2×C22⋊D11D411yescharacteristic
74#4343—41no—
75#4343—41no—
76#4339—41no—
77#4339—41no—
78C2×D44—21no—
79C2×D44—21no—
80C2×D44D411yescharacteristic
81C2×D44C2311yescharacteristic
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11C2311yescharacteristic
85C2×C4×D11C2311yescharacteristic
86C2×Dic22D411yescharacteristic
87C11×SD16—41no—
88C11×SD16—41no—
89C2×C8×C11C2311yescharacteristic
90C2×C8×C11C2311yescharacteristic
91C11×C4⋊C4—21no—
92C11×C4⋊C4C2311yescharacteristic
93C11×C22⋊C4—21no—
94C22⋊Dic11—21no—
95C22⋊Dic11—21no—
96C22⋊Dic11—21no—
97C22⋊Dic11—21no—
98C22⋊Dic11—21no—
99#4323—41no—
100#4323—41no—
101(C2×D11)⋊C4—21no—
102(C2×D11)⋊C4—21no—
103(C2×D11)⋊C4—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—42no—
118C23×C11—81no—
119C23×C11—81no—
120C23×C11C2×D411yescharacteristic
121C22×D11—21no—
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—
131C2×C4×C11—21no—
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—81no—
140C22⋊D11—81no—
141C22⋊D11—81no—
142C22⋊D11—81no—
143C22⋊D11—81no—
144C2×Dic11—21no—
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11C2×D411yescharacteristic
148C2×Dic11C2×D411yescharacteristic
149D44—21no—
150D44—21no—
151D44—41no—
152D44—42no—
153D44—81no—
154C4×D11—21no—
155C4×D11—21no—
156C4×D11—21no—
157C4×D11—21no—
158C4×D11—42no—
159C4×D11—81no—
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#450D1111yescharacteristic, complemented
176#449—111no—
177#449—111no—
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×C11—84no—
190C22×C11C22×D411yescharacteristic
191C2×D11—21no—
192C2×D11—21no—
193C2×D11—21no—
194C2×D11—21no—
195C2×D11—21no—
196C2×D11—21no—
197C2×D11—41no—
198C2×D11—41no—
199C2×D11—41no—
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×#41—111no—
212C22×D4C2×D1111yescharacteristic
213C2×SD16C2×D1111yescharacteristic
214C2×SD16C2×D1111yescharacteristic
215C2×D8—111no—
216C2×D8—111no—
217C2×M16—111no—
218C22×C8—111no—
219#127—221no—
220#124—221no—
221C22⋊Q8—111no—
222C22⋊Q8—221no—
223C22⋊Q8C2×D1111yescharacteristic
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#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#53411yescharacteristic
257C2×C11#57611yescharacteristic
258C2×C11#57711yescharacteristic
259D11—41no—
260D11—41no—
261D11—81no—
262C24—21no—
263#41—441no—
264#41—441no—
265#41—441no—
266#41—441no—
267C2×Q8—111no—
268C2×Q8C22×D1111yescharacteristic
269C2×D4—21no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—111no—
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×D4—221no—
283C2×D4C22×D1111yescharacteristic
284C2×D4C22×D1111yescharacteristic
285C22×C4—111no—
286C22×C4—111no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4C22×D1111yescharacteristic
290SD16—41no—
291SD16—41no—
292D8—441no—
293D8—441no—
294M16—441no—
295C2×C8—111no—
296C2×C8—111no—
297C2×C8—441no—
298C2×C8C22×D1111yescharacteristic
299C2×C8C22×D1111yescharacteristic
300C4⋊C4—21no—
301C4⋊C4—111no—
302C4⋊C4—111no—
303C4⋊C4—111no—
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—42no—
321C23—81no—
322C23—81no—
323C23—111no—
324C23—111no—
325C23—221no—
326C23D4×D1111yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—441no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—42no—
335D4—221no—
336D4—221no—
337D4—441no—
338D4—442no—
339D4—441no—
340D4—441no—
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—111no—
352C2×C4—111no—
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—84no—
378C22—221no—
379C22—221no—
380C22—221no—
381C22—221no—
382C22—221no—
383C22—221no—
384C22—441no—
385C22—441no—
386C22—441no—
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#1062329311yescharacteristic
406C2#1062330511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#450C2
socleC22×C11C22×D4
hypercenter#450D11
hypocenterC11#3198
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #10623336C2semidirect
2. #10623160C2semidirect
3. C11×#450C2semidirect
4. #10622830C2semidirect
5. #10622787C2semidirect
6. #10622785C2semidirect
7. #10622785C2semidirect
8. #10622784C2semidirect
9. #10622658C2semidirect
10. #10622395C2semidirect
11. #10622390C2semidirect
12. #10622388C2semidirect
13. #10622387C2semidirect
14. #10622350C2semidirect
15. #10622340C2semidirect
17. C2×#4343C22semidirect
24. #66999C22semidirect
35. C2×#4313C22semidirect
36. C2×C8×D11C22semidirect
39. #66948C22semidirect
40. C4⋊C4×D11C22semidirect
46. #66899C22semidirect
47. #66899C22semidirect
51. #66885C22semidirect
52. #66885C22semidirect
53. (C2×D11)⋊C8C22semidirect
54. (C2×D11)⋊C8C22semidirect
55. #66882C22semidirect
56. #66881C22semidirect
57. #66872C22semidirect
58. #66871C22semidirect
175. #450D11semidirect
317. C11#3198semidirect

Maximal subgroups

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

subgroupindex
#106233362
#106231602
C11×#4502
#106228302
#106227872
#106227852
#106227842
#106226582
#106223952
#106223902
#106223882
#106223872
#106223502
#106223402
#319811