Finite Group Databasebeta

← #14741702

Subgroups — #14741702

Order 2816.

1050 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079536C211yesmaximal, characteristic, complemented
2#13079191C211yesmaximal, characteristic, complemented
3#13079069C211yesmaximal, characteristic, complemented
4#13079066C211yesmaximal, characteristic, complemented
5C2×#10622686C211yesmaximal, characteristic, complemented
6#13068284C212yesmaximal, complemented
7#13068281C212yesmaximal, complemented
8#13068230C212yesmaximal, complemented
9#13068207C212yesmaximal, complemented
10#13066897C211yesmaximal, characteristic, complemented
11C11×#3205C211yesmaximal, characteristic, complemented
12C11×#532C2211yescharacteristic
13C2×C11×#127C2211yescharacteristic
14C2×#67002—22no—
15C2×#66985—22no—
16C22×#4323—22no—
17#10623008C2211yescharacteristic
18C2×#66927C2211yescharacteristic
19C11×#493C2212yescomplemented
20C11×#486C2212yescomplemented
21C11×#459—22no—
22C11×#447—22no—
23C11×#431C2211yescharacteristic
24#10622701C2211yescharacteristic, complemented
25#10622698C2212yescomplemented
26#10622691C2211yescharacteristic, complemented
27#10622689C2212yescomplemented
28#10622687—22no—
29#10622686—22no—
30#10622686C2212yes—
31#10622686C2212yes—
32#10622686C2212yescomplemented
33#10622686C2212yescomplemented
34#10622686C2211yescharacteristic, complemented
35#10622683C2211yescharacteristic, complemented
36#10622671—22no—
37#10622651—22no—
38C4×#4323—22no—
39C4×#4318C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622456—22no—
42#10622345—22no—
43#10622308C2212yescomplemented
44#10622307C2212yescomplemented
45#10622092C2212yescomplemented
46C8×C11⋊C8C2212yescomplemented
47C2×C11×#41—21no—
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11—21no—
51C2×#4339—21no—
52C22×D44—21no—
53C22×D44—21no—
54C22×D44—21no—
55C2×C11×D8—24no—
56C11×C4⋊Q8C2311yescharacteristic
57C11×#127—21no—
58C11×#127—21no—
59C11×#127—21no—
60C11×#127C2311yescharacteristic
61C11×#127C2312yes—
62C11×#124—21no—
63C11×#121—21no—
64C11×#121—21no—
65C4×D4×C11—21no—
66C4×D4×C11—21no—
67C2×C42×C11C2311yescharacteristic
68#67002—48no—
69C2×#4325—24no—
70C2×#4324—24no—
71#66985—48no—
72C2×#4323—24no—
73C2×#4323—24no—
74C2×#4323—24no—
75C2×#4323—24no—
76C2×#4323—22no—
77C2×#4323—48no—
78#66983—21no—
79#66983—21no—
80C2×#4318D412yes—
81C22×C11⋊C8D412yes—
82C2×D88—24no—
83#66928—21no—
84#66927—21no—
85#66927—21no—
86#66927—21no—
87#66927C2312yes—
88#66927C2311yescharacteristic
89C4×D44—21no—
90C4×D44—21no—
91#66922C2311yescharacteristic
92C11×C4⋊C8D412yes—
93C11×#102—24no—
94C11×C22⋊C8D412yes—
95C4×C8×C11C2312yes—
96#66896—22no—
97#66885—24no—
98#66873—22no—
99#66871—22no—
100#66867D412yes—
101C4×C11⋊C8D412yes—
102C4×C11⋊C8C2311yescharacteristic
103C4×C11⋊C8C2311yescharacteristic
104C4×C11⋊C8C2312yes—
105#19629—111nomaximal, Sylow
106C24×C11—41no—
107C23×D11—41no—
108C11×#41—44no—
109C2×Q8×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—22no—
112C2×D4×C11—21no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—21no—
116C2×D4×C11—44no—
117C2×D4×C11—41no—
118C2×D4×C11—41no—
119C2×D4×C11—41no—
120C2×D4×C11—41no—
121C2×D4×C11—44no—
122C2×D4×C11—82no—
123C22×C4×C11—41no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C2×C22⋊D11—41no—
128#4339—44no—
129C2×D44—21no—
130C2×D44—22no—
131C2×D44—21no—
132C2×D44—22no—
133C2×D44—22no—
134C2×D44—21no—
135C2×D44—44no—
136C2×D44—41no—
137C2×D44—41no—
138C2×D44—41no—
139C2×D44—44no—
140C2×D44—82no—
141C2×C4×D11—41no—
142C2×Dic22—21no—
143C11×D8—84no—
144C2×C8×C11C2×D414yes—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C22⋊C4—41no—
148C11×C22⋊C4—41no—
149C42×C11C2×D411yescharacteristic
150C42×C11C2×D411yescharacteristic
151C42×C11C2×D411yescharacteristic
152C42×C11C2411yescharacteristic
153#4325—48no—
154#4324—48no—
155#4323—48no—
156#4323—48no—
157#4323—48no—
158#4323—44no—
159#4323—48no—
160(C2×D11)⋊C4—41no—
161(C2×D11)⋊C4—41no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164#4318D818yescomplemented
165C2×C11⋊C8—24no—
166C2×C11⋊C8C2×D412yes—
167C2×C11⋊C8C2×D414yes—
168C2×C11⋊C8C2×D412yes—
169D88—84no—
170#3205—111no—
171#3205D1111yescharacteristic, complemented
172#3169—111no—
173#3151—111no—
174#3151—111no—
175C2×#493—111no—
176#1721—112no—
177#1721—112no—
178#1712—112no—
179#1706—112no—
180C8×M16—111no—
181C23×C11—41no—
182C23×C11—42no—
183C23×C11—82no—
184C23×C11—82no—
185C23×C11—82no—
186C23×C11#12711yescharacteristic
187C22×D11—41no—
188C22×D11—42no—
189C22×D11—82no—
190C22×D11—82no—
191C22×D11—82no—
192Q8×C11—42no—
193D4×C11—42no—
194D4×C11—44no—
195D4×C11—44no—
196D4×C11—42no—
197D4×C11—42no—
198D4×C11—44no—
199D4×C11—82no—
200D4×C11—82no—
201D4×C11—82no—
202D4×C11—82no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—41no—
206C2×C4×C11—82no—
207C2×C4×C11#12711yescharacteristic
208C2×C4×C11#12711yescharacteristic
209C2×C4×C11#12711yescharacteristic
210C2×C4×C11C2×D814yes—
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C22⋊D11—82no—
215C2×Dic11—41no—
216D44—42no—
217D44—44no—
218D44—44no—
219D44—42no—
220D44—42no—
221D44—44no—
222D44—82no—
223D44—82no—
224D44—82no—
225C4×D11—82no—
226Dic22—42no—
227C8×C11—24no—
228C11⋊C8—22no—
229C11⋊C8C2×D818yescomplemented
230C11⋊C8AGL(1,ℤ/8)14yescomplemented
231C2×AGL(1,ℤ/8)—222no—
232C2×AGL(1,ℤ/8)—222no—
233C22×D8—222no—
234#532—111no—
235#532C2×D1111yescharacteristic
236C2×#127—111no—
237C2×#127C2×D1111yescharacteristic
238#500—111no—
239#496—222no—
240#496—222no—
241#493—112no—
242#493—112no—
243#493—112no—
244#493—112no—
245#493—111no—
246#493—112no—
247#493—222no—
248#493C2×D1112yescomplemented
249#492—112no—
250#492—112no—
251#486—111no—
252#486—111no—
253#486—112no—
254#486C2×D1112yescomplemented
255#466—222no—
256#459—22no—
257#459—222no—
258#447—22no—
259#447—222no—
260C4×D8—222no—
261#431C2×D1111yescharacteristic
262C4×M16—111no—
263C2×C4×C8—111no—
264#322—112no—
265C82—112no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—81no—
269C22×C11—82no—
270C22×C11—82no—
271C22×C11—81no—
272C22×C11—82no—
273C22×C11—81no—
274C22×C11—164no—
275C22×C11#49312yes—
276C22×C11C2×#12711yescharacteristic
277C2×D11—82no—
278C2×D11—81no—
279C2×D11—82no—
280C2×D11—81no—
281C2×D11—82no—
282C2×D11—81no—
283C2×D11—164no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—81no—
287C4×C11#49312yes—
288C4×C11C22×D812yes—
289C4×C11C2×AGL(1,ℤ/8)12yes—
290C4×C11#57612yes—
291Dic11—81no—
292C2×#41—21no—
293C2×#41—221no—
294C22×D4—21no—
295C22×D4—21no—
296C22×D4—21no—
297C22×D4—221no—
298C22×D4—221no—
299C22×D4—221no—
300AGL(1,ℤ/8)—448no—
301AGL(1,ℤ/8)—448no—
302C2×SD16—224no—
303C2×SD16—224no—
304C2×D8—24no—
305C2×D8—224no—
306C2×D8—224no—
307C2×D8—224no—
308C2×D8—224no—
309C2×D8—222no—
310C2×D8—224no—
311C2×D8—448no—
312C2×M16—112no—
313C22×C8—112no—
314C4⋊Q8—111no—
315C4⋊Q8C22×D1111yescharacteristic
316#127—21no—
317#127—21no—
318#127—21no—
319#127—112no—
320#127—111no—
321#127—221no—
322#127—221no—
323#127—221no—
324#127C22×D1112yes—
325#127C22×D1111yescharacteristic
326#124—21no—
327#124—221no—
328#121—21no—
329#121—21no—
330#121—221no—
331#121—221no—
332C4×D4—21no—
333C4×D4—21no—
334C4×D4—221no—
335C4×D4—221no—
336C2×C42C22×D1111yescharacteristic
337#107—222no—
338C4⋊C8C22⋊D1112yes—
339#102—24no—
340#102—222no—
341#102—222no—
342#102—224no—
343C22⋊C8C22⋊D1112yes—
344#97—112no—
345C4×C8—112no—
346C4×C8—111no—
347C4×C8—112no—
348C4×C8—111no—
349C4×C8C22×D1112yes—
350C2×C11—22no—
351C2×C11—161no—
352C2×C11—162no—
353C2×C11C2×#49311yescharacteristic
354C2×C11#315111yescharacteristic
355C2×C11#315511yescharacteristic
356D11—161no—
357D11—162no—
358C24—41no—
359C24—441no—
360#41—44no—
361#41—444no—
362C2×Q8—21no—
363C2×Q8—221no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—21no—
370C2×D4—44no—
371C2×D4—41no—
372C2×D4—44no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—82no—
377C2×D4—221no—
378C2×D4—221no—
379C2×D4—222no—
380C2×D4—222no—
381C2×D4—222no—
382C2×D4—221no—
383C2×D4—444no—
384C2×D4—441no—
385C2×D4—444no—
386C2×D4—441no—
387C2×D4—441no—
388C2×D4—441no—
389C2×D4—882no—
390C22×C4—41no—
391C22×C4—441no—
392C22×C4D4×D1111yescharacteristic
393C22×C4D4×D1111yescharacteristic
394C22×C4C2×C22⋊D1111yescharacteristic
395SD16—448no—
396SD16—448no—
397D8—84no—
398D8—448no—
399D8—448no—
400D8—448no—
401D8—444no—
402D8—448no—
403D8—884no—
404M16—118no—
405C2×C8—112no—
406C2×C8—114no—
407C2×C8—112no—
408C2×C8—224no—
409C2×C8C2×C22⋊D1114yes—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—221no—
413C4⋊C4—221no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—441no—
417C22⋊C4—441no—
418C42D4×D1111yescharacteristic
419C42D4×D1111yescharacteristic
420C42C2×C22⋊D1111yescharacteristic
421C42C23×D1111yescharacteristic
422C11#1962911yescharacteristic, complemented, Sylow
423C23—41no—
424C23—42no—
425C23—82no—
426C23—82no—
427C23—82no—
428C23—441no—
429C23—442no—
430C23—882no—
431C23—882no—
432C23—882no—
433C23#6699311yescharacteristic
434Q8—42no—
435Q8—442no—
436D4—42no—
437D4—44no—
438D4—44no—
439D4—42no—
440D4—42no—
441D4—44no—
442D4—82no—
443D4—82no—
444D4—82no—
445D4—82no—
446D4—442no—
447D4—444no—
448D4—444no—
449D4—442no—
450D4—442no—
451D4—444no—
452D4—882no—
453D4—882no—
454D4—882no—
455D4—882no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—41no—
459C2×C4—82no—
460C2×C4—441no—
461C2×C4—882no—
462C2×C4D8×D1114yes—
463C2×C4#6699311yescharacteristic
464C2×C4#6699311yescharacteristic
465C2×C4#6699311yescharacteristic
466C2×C4C2×D4×D1111yescharacteristic
467C2×C4C2×D4×D1111yescharacteristic
468C2×C4C22×C22⋊D1111yescharacteristic
469C8—24no—
470C8—118no—
471C8—114no—
472C8—222no—
473C22—21no—
474C22—21no—
475C22—82no—
476C22—81no—
477C22—82no—
478C22—81no—
479C22—81no—
480C22—82no—
481C22—164no—
482C22—882no—
483C22—881no—
484C22—882no—
485C22—881no—
486C22—881no—
487C22—882no—
488C22—1764no—
489C22#1062276412yes—
490C22C2×#6699311yescharacteristic
491C4—21no—
492C4—21no—
493C4—81no—
494C4—881no—
495C4#1062276412yes—
496C4C2×D8×D1112yes—
497C4D11×AGL(1,ℤ/8)12yes—
498C4#1062336612yes—
499C2—22no—
500C2—162no—
501C2—161no—
502C2—1762no—
503C2—1761no—
504C2C2×#1062276411yescharacteristic
505C2#1307906411yescharacteristic
506C2#1307909911yescharacteristic
subgroupG/H
centerC22C2×#66993
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3205C2
socleC22×C11C2×#127
hypercenter#3205D11
hypocenterC11#19629
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3205

Complements

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

NH ≅ G/Ntype
1. #13079536C2semidirect
2. #13079191C2semidirect
3. #13079069C2semidirect
4. #13079066C2semidirect
5. C2×#10622686C2semidirect
6. #13068284C2semidirect
7. #13068281C2semidirect
8. #13068230C2semidirect
9. #13068207C2semidirect
10. #13066897C2semidirect
11. C11×#3205C2semidirect
19. C11×#493C22semidirect
20. C11×#486C22semidirect
24. #10622701C22semidirect
25. #10622698C22semidirect
26. #10622691C22semidirect
27. #10622689C22semidirect
32. #10622686C22semidirect
33. #10622686C22semidirect
34. #10622686C22semidirect
35. #10622683C22semidirect
43. #10622308C22semidirect
44. #10622307C22semidirect
45. #10622092C22semidirect
46. C8×C11⋊C8C22semidirect
164. #4318D8semidirect
171. #3205D11semidirect
229. C11⋊C8C2×D8semidirect
230. C11⋊C8AGL(1,ℤ/8)semidirect
248. #493C2×D11semidirect
254. #486C2×D11semidirect
422. C11#19629semidirect

Maximal subgroups

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

subgroupindex
#130795362
#130791912
#130790692
#130790662
C2×#106226862
#130682842
#130682812
#130682302
#130682072
#130668972
C11×#32052
#1962911