Finite Group Databasebeta

← #13079474

Subgroups — #13079474

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#10623160C211yesmaximal, characteristic, complemented
2#10623056C211yesmaximal, characteristic, complemented
3C11×#485C211yesmaximal, characteristic, complemented
4#10622659C211yesmaximal, characteristic, complemented
5#10622616C211yesmaximal, characteristic, complemented
6#10622496C211yesmaximal, characteristic, complemented
7#10622495C211yesmaximal, characteristic, complemented
8#10622478C211yesmaximal, characteristic, complemented
9#10622476C211yesmaximal, characteristic, complemented
10#10622425C211yesmaximal, characteristic, complemented
11#10622424C211yesmaximal, characteristic, complemented
12#10622424C211yesmaximal, characteristic, complemented
13#10622420C211yesmaximal, characteristic, complemented
14#10622345C211yesmaximal, characteristic, complemented
15#10622340C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic, complemented
17C2×#4339C2211yescharacteristic
18C22×D44C2211yescharacteristic
19C11×C22⋊Q8C2211yescharacteristic
20C11×#117C2211yescharacteristic
21#66999C2211yescharacteristic, complemented
22C2×#4325C2211yescharacteristic
23C2×#4325C2211yescharacteristic
24#66983C2211yescharacteristic
25C2×D88C2211yescharacteristic
26C2×D88C2211yescharacteristic
27C2×#4313C2211yescharacteristic, complemented
28C2×C8×D11C2211yescharacteristic, complemented
29#66949—21no—
30#66948—21no—
31#66948C2211yescharacteristic
32#66948C2211yescharacteristic
33#66948C2211yescharacteristic
34#66948C2211yescharacteristic
35#66948C2211yescharacteristic, complemented
36C4⋊C4×D11C2211yescharacteristic, complemented
37#66937—21no—
38#66937—21no—
39#66935—21no—
40#66935—21no—
41#66928—21no—
42#66927—21no—
43C11×#107C2211yescharacteristic, complemented
44C11×#106C2211yescharacteristic, complemented
45C11×#103C2211yescharacteristic, complemented
46C11×#103C2211yescharacteristic, complemented
47C11×C22⋊C8C2211yescharacteristic
48C22⋊(C11⋊C8)C2211yescharacteristic
49#66885C2211yescharacteristic
50#66885C2211yescharacteristic
51(C2×D11)⋊C8C2211yescharacteristic, complemented
52(C2×D11)⋊C8C2211yescharacteristic, complemented
53#66873C2211yescharacteristic
54#66873C2211yescharacteristic
55#66873C2211yescharacteristic, complemented
56#66873C2211yescharacteristic, complemented
57#66872C2211yescharacteristic, complemented
58#66871C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×Q8×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C2×C22⋊D11D411yescharacteristic
64C2×C22⋊D11D411yescharacteristic
65#4343—41no—
66#4343—41no—
67#4339—41no—
68#4339—41no—
69C2×D44—21no—
70C2×D44—21no—
71C2×D44—21no—
72C2×D44—21no—
73C2×D44—21no—
74C2×D44—21no—
75C2×D44—21no—
76C2×D44—41no—
77C2×D44—41no—
78C2×D44D411yescharacteristic
79C2×D44C2311yescharacteristic
80C2×D44C2311yescharacteristic
81C2×D44C2311yescharacteristic
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11C2311yescharacteristic
85C2×C4×D11C2311yescharacteristic
86C2×Dic22D411yescharacteristic
87C2×C8×C11C2311yescharacteristic
88C2×C8×C11C2311yescharacteristic
89C11×C4⋊C4—21no—
90C11×C4⋊C4C2311yescharacteristic
91C11×C4⋊C4C2311yescharacteristic
92C11×C4⋊C4C2311yescharacteristic
93C11×C22⋊C4—21no—
94C11×C22⋊C4—21no—
95C42×C11—21no—
96#4325—41no—
97#4325—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—
103(C2×D11)⋊C4—21no—
104(C2×D11)⋊C4—21no—
105C4⋊Dic11C2311yescharacteristic
106Dic11⋊C4—21no—
107Dic11⋊C4—21no—
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110D88—41no—
111D88—41no—
112#4313—41no—
113C8×D11—41no—
114#3198—111nomaximal, Sylow
115C23×C11C2×D411yescharacteristic
116C22×D11—21no—
117C22×D11—21no—
118C22×D11—21no—
119C22×D11—42no—
120C22×D11—81no—
121C22×D11—81no—
122C22×D11C2×D411yescharacteristic
123C22×D11C2×D411yescharacteristic
124Q8×C11—21no—
125Q8×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11C2×D411yescharacteristic
133C2×C4×C11C2411yescharacteristic
134C22⋊D11—41no—
135C22⋊D11—41no—
136C22⋊D11—81no—
137C2×Dic11—21no—
138C2×Dic11C2×D411yescharacteristic
139C2×Dic11C2×D411yescharacteristic
140D44—21no—
141D44—21no—
142D44—21no—
143D44—21no—
144D44—21no—
145D44—21no—
146D44—41no—
147D44—42no—
148D44—42no—
149D44—81no—
150D44—81no—
151D44—81no—
152D44—81no—
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#485D1111yescharacteristic, complemented
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#408—111no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11C22×D411yescharacteristic
184C2×D11—21no—
185C2×D11—21no—
186C2×D11—21no—
187C2×D11—21no—
188C2×D11—21no—
189C2×D11—21no—
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—41no—
202C4×C11—41no—
203C4×C11—41no—
204C4×C11—41no—
205C4×C11H(5,𝔽2)11yescharacteristic
206C4×C11H(5,𝔽2)11yescharacteristic
207Dic11—21no—
208Dic11—21no—
209Dic11—41no—
210C2×#41—111no—
211C2×#41—111no—
212C22×D4—111no—
213C2×SD16—111no—
214C2×SD16—111no—
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#117C2×D1111yescharacteristic
236C2×C4⋊C4—111no—
237#107—111no—
238#107C2×D1111yescharacteristic, complemented
239#106—111no—
240#106C2×D1111yescharacteristic, complemented
241#103C2×D1111yescharacteristic, complemented
242#103C2×D1111yescharacteristic, complemented
243#102—111no—
244#102—111no—
245#102—111no—
246#102—111no—
247#102—111no—
248#102—111no—
249C22⋊C8—111no—
250C22⋊C8—111no—
251C22⋊C8—111no—
252C22⋊C8C2×D1111yescharacteristic
253C2×C11—41no—
254C2×C11#53411yescharacteristic
255C2×C11#57611yescharacteristic
256C2×C11#57711yescharacteristic
257D11—41no—
258D11—41no—
259D11—81no—
260D11—81no—
261D11—81no—
262C24—221no—
263#41—441no—
264#41—441no—
265#41—441no—
266#41—441no—
267C2×Q8—111no—
268C2×Q8C22×D1111yescharacteristic
269C2×D4—111no—
270C2×D4—111no—
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—221no—
282C2×D4—221no—
283C2×D4—441no—
284C2×D4—441no—
285C22×C4—111no—
286C22×C4—111no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4C22×D1111yescharacteristic
290SD16—441no—
291SD16—441no—
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—221no—
303C4⋊C4—221no—
304C4⋊C4C22×D1111yescharacteristic
305C4⋊C4C22×D1111yescharacteristic
306C4⋊C4C22×D1111yescharacteristic
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—221no—
310C22⋊C4—221no—
311C22⋊C4—221no—
312C22⋊C4—221no—
313C22⋊C4—221no—
314C22⋊C4—221no—
315C22⋊C4—221no—
316C42—21no—
317C11#319811yescharacteristic, complemented, Sylow
318C23—111no—
319C23—111no—
320C23—221no—
321C23—221no—
322C23—221no—
323C23—442no—
324C23—881no—
325C23—881no—
326C23D4×D1111yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—441no—
330D4—221no—
331D4—221no—
332D4—221no—
333D4—221no—
334D4—221no—
335D4—221no—
336D4—441no—
337D4—442no—
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—21no—
352C2×C4—21no—
353C2×C4—111no—
354C2×C4—111no—
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—221no—
372C22—221no—
373C22—221no—
374C22—221no—
375C22—221no—
376C22—221no—
377C22—441no—
378C22—441no—
379C22—441no—
380C22—441no—
381C22—441no—
382C22—441no—
383C22—441no—
384C22—441no—
385C22—441no—
386C22—884no—
387C22C2×D4×D1111yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—41no—
393C4—221no—
394C4—221no—
395C4—441no—
396C4#6704211yescharacteristic
397C4#6704211yescharacteristic
398C2—41no—
399C2—441no—
400C2—441no—
401C2—881no—
402C2—881no—
403C2—881no—
404C2#1062318411yescharacteristic
405C2#1062330011yescharacteristic
406C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#485C2
socleC22×C11C22×D4
hypercenter#485D11
hypocenterC11#3198
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #10623160C2semidirect
2. #10623056C2semidirect
3. C11×#485C2semidirect
4. #10622659C2semidirect
5. #10622616C2semidirect
6. #10622496C2semidirect
7. #10622495C2semidirect
8. #10622478C2semidirect
9. #10622476C2semidirect
10. #10622425C2semidirect
11. #10622424C2semidirect
12. #10622424C2semidirect
13. #10622420C2semidirect
14. #10622345C2semidirect
15. #10622340C2semidirect
16. C2×#4343C22semidirect
21. #66999C22semidirect
27. C2×#4313C22semidirect
28. C2×C8×D11C22semidirect
35. #66948C22semidirect
36. C4⋊C4×D11C22semidirect
43. C11×#107C22semidirect
44. C11×#106C22semidirect
45. C11×#103C22semidirect
46. C11×#103C22semidirect
51. (C2×D11)⋊C8C22semidirect
52. (C2×D11)⋊C8C22semidirect
55. #66873C22semidirect
56. #66873C22semidirect
57. #66872C22semidirect
58. #66871C22semidirect
167. #485D11semidirect
238. #107C2×D11semidirect
240. #106C2×D11semidirect
241. #103C2×D11semidirect
242. #103C2×D11semidirect
317. C11#3198semidirect

Maximal subgroups

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

subgroupindex
#106231602
#106230562
C11×#4852
#106226592
#106226162
#106224962
#106224952
#106224782
#106224762
#106224252
#106224242
#106224202
#106223452
#106223402
#319811