Finite Group Databasebeta

← #14741683

Subgroups — #14741683

Order 2816.

784 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079564C211yesmaximal, characteristic, complemented
2#13079531C211yesmaximal, characteristic
3#13079171C211yesmaximal, characteristic, complemented
4#13078991C211yesmaximal, characteristic, complemented
5C2×#10622701C211yesmaximal, characteristic, complemented
6#13068273C212yesmaximal, complemented
7#13068252C212yesmaximal, complemented
8#13068229C212yesmaximal, complemented
9#13068220C212yesmaximal, complemented
10M16×C11⋊C8C211yesmaximal, characteristic, complemented
11C11×#3141C211yesmaximal, characteristic, complemented
12C11×#532C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#66927C2211yescharacteristic
15#10623001C2211yescharacteristic
16C11×#489—22no—
17C11×#487C2212yescomplemented
18C11×#486C2212yescomplemented
19C11×#417—22no—
20C4×C11×M16C2211yescharacteristic
21#10622841—22no—
22#10622744—22no—
23#10622706C2211yescharacteristic, complemented
24#10622705C2212yescomplemented
25#10622703—22no—
26#10622701—22no—
27#10622701C2212yes—
28#10622701C2212yes—
29#10622701C2212yes—
30#10622694C2212yescomplemented
31#10622692C2211yescharacteristic, complemented
32#10622689C2211yescharacteristic, complemented
33#10622686C2212yes—
34#10622683C2211yescharacteristic, complemented
35#10622654—22no—
36#10622649—22no—
37C4×#4324—22no—
38#10622628—22no—
39C2×#66873—22no—
40#10622538C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622326—22no—
43#10622307C2212yes—
44#10622307C2212yes—
45#10622093C2212yescomplemented
46C8×C11⋊C8C2212yescomplemented
47C2×C11×#41—21no—
48C22×Q8×C11—21no—
49C22×D44—21no—
50C22×D44—21no—
51C22×D44—21no—
52C2×C11×M16D412yes—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8C2312yes—
57C11×C4⋊Q8C2311yescharacteristic
58C11×#127C2311yescharacteristic
59C11×#124—21no—
60C11×#121—21no—
61C11×#121—21no—
62C4×D4×C11—21no—
63C4×D4×C11—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C42×C11C2311yescharacteristic
67C2×#4326—24no—
68C2×#4324—22no—
69C2×#4323—24no—
70#66979—21no—
71#66977—21no—
72#66977—21no—
73C22×C11⋊C8D412yes—
74#66927—21no—
75#66927—21no—
76#66927—21no—
77#66927C2312yes—
78#66923—21no—
79#66922C2311yescharacteristic
80#66922C2311yescharacteristic
81C4×Dic22—21no—
82C4×Dic22—21no—
83C11×#103—24no—
84C11×#102—24no—
85C11×#97D412yes—
86C4×C8×C11C2312yes—
87#66899—24no—
88#66896—22no—
89C22⋊(C11⋊C8)D412yes—
90#66885—24no—
91#66885—24no—
92#66874—22no—
93#66873—24no—
94#66873—24no—
95#66873—24no—
96#66872—22no—
97C4⋊(C11⋊C8)D412yes—
98C4×C11⋊C8D412yes—
99C4×C11⋊C8C2311yescharacteristic
100C4×C11⋊C8C2311yescharacteristic
101C4×C11⋊C8C2312yes—
102#19627—111nomaximal, Sylow
103C23×D11—41no—
104C11×#41—44no—
105C2×Q8×C11—22no—
106C2×Q8×C11—21no—
107C2×Q8×C11—41no—
108C2×Q8×C11—82no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—41no—
113C22×C4×C11—41no—
114C22×C4×C11—41no—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C2×D44—22no—
119C2×D44—22no—
120C2×D44—22no—
121C2×D44—44no—
122C2×D44—41no—
123C2×D44—41no—
124C2×D44—41no—
125C2×D44—44no—
126C2×D44—82no—
127C2×Dic22—21no—
128C2×Dic22—21no—
129C11×M16—24no—
130C2×C8×C11C2×D414yes—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—41no—
136C11×C4⋊C4—41no—
137C11×C22⋊C4—41no—
138C11×C22⋊C4—41no—
139C42×C11C2×D411yescharacteristic
140C42×C11C2×D411yescharacteristic
141C42×C11C2×D411yescharacteristic
142C42×C11C2411yescharacteristic
143C22⋊Dic11—41no—
144#4326—84no—
145#4324—44no—
146#4323—84no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153C4×Dic11—41no—
154C2×C11⋊C8—42no—
155C2×C11⋊C8C2×D412yes—
156C2×C11⋊C8C2×D412yes—
157C2×C11⋊C8C2×D414yes—
158#3209—111no—
159#3205—111no—
160#3167—111no—
161#3141D1111yescharacteristic, complemented
162#3138—111no—
163C2×#486—111no—
164#1720—112no—
165#1717—112no—
166#1711—112no—
167#1709—112no—
168C8×M16—111no—
169C23×C11—41no—
170C23×C11#12711yescharacteristic
171C22×D11—42no—
172C22×D11—82no—
173C22×D11—82no—
174C22×D11—82no—
175Q8×C11—42no—
176Q8×C11—44no—
177Q8×C11—82no—
178D4×C11—42no—
179D4×C11—42no—
180D4×C11—42no—
181D4×C11—82no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—41no—
185C2×C4×C11—42no—
186C2×C4×C11—82no—
187C2×C4×C11—82no—
188C2×C4×C11#12711yescharacteristic
189C2×C4×C11#12711yescharacteristic
190C2×C4×C11#12711yescharacteristic
191C2×C4×C11#13514yes—
192C2×C4×C11C22×D411yescharacteristic
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C22×D411yescharacteristic
195C2×Dic11—41no—
196C2×Dic11—41no—
197D44—44no—
198D44—44no—
199D44—44no—
200D44—82no—
201D44—82no—
202D44—82no—
203Dic22—42no—
204Dic22—42no—
205C8×C11—24no—
206C11⋊C8—22no—
207C11⋊C8—22no—
208C11⋊C8—24no—
209#533—111no—
210#532C2×D1111yescharacteristic
211C2×C4⋊Q8C2×D1111yescharacteristic
212C2×#127—111no—
213#498—111no—
214#494—112no—
215#493—112no—
216#492—111no—
217#490—222no—
218#489—22no—
219#487—111no—
220#487—112no—
221#487C2×D1112yescomplemented
222#486—112no—
223#486—112no—
224#486—112no—
225#486—111no—
226#486—112no—
227#486—112no—
228#486—222no—
229#486C2×D1112yescomplemented
230#465—222no—
231#462—222no—
232#459—222no—
233#451—222no—
234#447—222no—
235C4×SD16—222no—
236#431—111no—
237#418—222no—
238#417—22no—
239C2×#102—222no—
240C4×M16C2×D1111yescharacteristic
241C2×C4×C8—111no—
242#322—112no—
243C82—112no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—81no—
247C22×C11—81no—
248C22×C11—81no—
249C22×C11#49512yes—
250C22×C11C2×#12711yescharacteristic
251C2×D11—82no—
252C2×D11—82no—
253C2×D11—82no—
254C2×D11—164no—
255C4×C11—21no—
256C4×C11—21no—
257C4×C11—81no—
258C4×C11—82no—
259C4×C11#49512yes—
260C4×C11C2×#13512yes—
261C4×C11#57512yes—
262C4×C11#57612yes—
263Dic11—81no—
264Dic11—81no—
265C2×#41—21no—
266C22×Q8—21no—
267C22×D4—221no—
268C22×D4—221no—
269C22×D4—221no—
270C2×Q16—224no—
271C2×SD16—222no—
272C2×D8—224no—
273C2×M16C22⋊D1112yes—
274C22×C8—112no—
275C4⋊Q8—21no—
276C4⋊Q8—21no—
277C4⋊Q8—21no—
278C4⋊Q8—111no—
279C4⋊Q8—111no—
280C4⋊Q8C22×D1112yes—
281C4⋊Q8C22×D1111yescharacteristic
282#127—112no—
283#127—221no—
284#127—221no—
285#127—221no—
286#127C22×D1111yescharacteristic
287#125—221no—
288#124—21no—
289C22⋊Q8—221no—
290C22⋊Q8—221no—
291#121—21no—
292#121—21no—
293C4×Q8—221no—
294C4×Q8—221no—
295C4×D4—21no—
296C4×D4—21no—
297#117—221no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C42C22×D1111yescharacteristic
301#106—222no—
302C4⋊C8—112no—
303#103—24no—
304#103—222no—
305#103—224no—
306#102—24no—
307#102—224no—
308#102—224no—
309#102—224no—
310#102—222no—
311#102—224no—
312#102—224no—
313C22⋊C8—112no—
314#97C22⋊D1112yes—
315C4×C8—112no—
316C4×C8—111no—
317C4×C8—112no—
318C4×C8—111no—
319C4×C8C22×D1112yes—
320C2×C11—22no—
321C2×C11—161no—
322C2×C11C2×#49511yescharacteristic
323C2×C11#315311yescharacteristic
324C2×C11#315511yescharacteristic
325D11—162no—
326C24—441no—
327#41—44no—
328C2×Q8—22no—
329C2×Q8—21no—
330C2×Q8—41no—
331C2×Q8—82no—
332C2×Q8—221no—
333C2×Q8—221no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4—21no—
337C2×D4—41no—
338C2×D4—222no—
339C2×D4—222no—
340C2×D4—222no—
341C2×D4—444no—
342C2×D4—441no—
343C2×D4—441no—
344C2×D4—441no—
345C2×D4—444no—
346C2×D4—882no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4D4×D1111yescharacteristic
350C22×C4D4×D1111yescharacteristic
351C22×C4C2×C22⋊D1111yescharacteristic
352Q16—884no—
353SD16—444no—
354D8—884no—
355M16—24no—
356C2×C8—112no—
357C2×C8—112no—
358C2×C8—114no—
359C2×C8—442no—
360C2×C8C2×C22⋊D1114yes—
361C4⋊C4—22no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—22no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—221no—
368C4⋊C4—221no—
369C4⋊C4—221no—
370C4⋊C4—221no—
371C4⋊C4—441no—
372C4⋊C4—441no—
373C22⋊C4—41no—
374C22⋊C4—41no—
375C22⋊C4—441no—
376C42—441no—
377C42D4×D1111yescharacteristic
378C42D4×D1111yescharacteristic
379C42C2×C22⋊D1111yescharacteristic
380C42C23×D1111yescharacteristic
381C11#1962711yescharacteristic, complemented, Sylow
382C23—41no—
383C23—442no—
384C23—882no—
385C23—882no—
386C23—882no—
387C23#6699311yescharacteristic
388Q8—44no—
389Q8—42no—
390Q8—82no—
391Q8—442no—
392Q8—442no—
393D4—42no—
394D4—42no—
395D4—42no—
396D4—82no—
397D4—444no—
398D4—444no—
399D4—444no—
400D4—882no—
401D4—882no—
402D4—882no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—41no—
406C2×C4—42no—
407C2×C4—82no—
408C2×C4—82no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4#6699311yescharacteristic
412C2×C4#6699311yescharacteristic
413C2×C4#6699311yescharacteristic
414C2×C4#6700314yes—
415C2×C4C2×D4×D1111yescharacteristic
416C2×C4C2×D4×D1111yescharacteristic
417C2×C4C22×C22⋊D1111yescharacteristic
418C8—24no—
419C8—224no—
420C8—222no—
421C8—222no—
422C22—21no—
423C22—21no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22—882no—
428C22—882no—
429C22—882no—
430C22—1764no—
431C22#1062267212yes—
432C22C2×#6699311yescharacteristic
433C4—21no—
434C4—21no—
435C4—82no—
436C4—81no—
437C4—881no—
438C4—881no—
439C4#1062267212yes—
440C4#1062330512yes—
441C4#1062330812yes—
442C4C2×#6700312yes—
443C2—22no—
444C2—161no—
445C2—1762no—
446C2C2×#1062267211yescharacteristic
447C2#1307908311yescharacteristic
448C2#1307910111yescharacteristic
subgroupG/H
centerC22C2×#66993
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3141C2
socleC22×C11C2×#127
prime radical#13079531C2
hypercenter#3141D11
hypocenterC11#19627
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3141

Complements

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

NH ≅ G/Ntype
1. #13079564C2semidirect
3. #13079171C2semidirect
4. #13078991C2semidirect
5. C2×#10622701C2semidirect
6. #13068273C2semidirect
7. #13068252C2semidirect
8. #13068229C2semidirect
9. #13068220C2semidirect
10. M16×C11⋊C8C2semidirect
11. C11×#3141C2semidirect
17. C11×#487C22semidirect
18. C11×#486C22semidirect
23. #10622706C22semidirect
24. #10622705C22semidirect
30. #10622694C22semidirect
31. #10622692C22semidirect
32. #10622689C22semidirect
34. #10622683C22semidirect
45. #10622093C22semidirect
46. C8×C11⋊C8C22semidirect
161. #3141D11semidirect
221. #487C2×D11semidirect
229. #486C2×D11semidirect
381. C11#19627semidirect

Maximal subgroups

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

subgroupindex
#130795642
#130795312
#130791712
#130789912
C2×#106227012
#130682732
#130682522
#130682292
#130682202
M16×C11⋊C82
C11×#31412
#1962711