Finite Group Databasebeta

← #14742994

Subgroups — #14742994

Order 2816.

814 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079549C211yesmaximal, characteristic, complemented
2#13079545C211yesmaximal, characteristic, complemented
3#13079536C211yesmaximal, characteristic, complemented
4#13079531C211yesmaximal, characteristic, complemented
5#13079531C211yesmaximal, characteristic, complemented
6#13068284C211yesmaximal, characteristic, complemented
7#13068281C211yesmaximal, characteristic, complemented
8#13068280C211yesmaximal, characteristic, complemented
9#13068258C211yesmaximal, characteristic, complemented
10#13068253C211yesmaximal, characteristic, complemented
11#13068252C211yesmaximal, characteristic, complemented
12#13068230C211yesmaximal, characteristic, complemented
13#13068229C211yesmaximal, characteristic, complemented
14#13066916C211yesmaximal, characteristic, complemented
15C11×#3207C211yesmaximal, characteristic, complemented
16C11×#532C2211yescharacteristic
17C11×#532C2211yescharacteristic
18#10623008C2211yescharacteristic
19C2×#66927C2211yescharacteristic
20C11×#493C2211yescharacteristic, complemented
21C11×#492C2211yescharacteristic, complemented
22C11×#487C2211yescharacteristic, complemented
23C11×#486C2211yescharacteristic, complemented
24C11×#463—22no—
25C11×#449—22no—
26C11×#431C2211yescharacteristic
27#10622851—22no—
28#10622706C2211yescharacteristic, complemented
29#10622701C2211yescharacteristic
30#10622701C2211yescharacteristic
31#10622701C2211yescharacteristic
32#10622701C2211yescharacteristic
33#10622701C2211yescharacteristic, complemented
34#10622698C2211yescharacteristic, complemented
35#10622694C2211yescharacteristic, complemented
36#10622689C2211yescharacteristic, complemented
37#10622686C2211yescharacteristic
38#10622686C2211yescharacteristic
39#10622686C2211yescharacteristic
40#10622686C2211yescharacteristic
41#10622686C2211yescharacteristic, complemented
42#10622686C2211yescharacteristic, complemented
43#10622683C2211yescharacteristic, complemented
44#10622670—22no—
45#10622650—22no—
46#10622649—22no—
47#10622649—22no—
48#10622629—22no—
49#10622628—22no—
50#10622628—22no—
51#10622538C2211yescharacteristic
52#10622538C2211yescharacteristic
53#10622456—22no—
54#10622345—22no—
55#10622308C2211yescharacteristic
56#10622308C2211yescharacteristic
57#10622307C2211yescharacteristic
58#10622307C2211yescharacteristic
59#10622093C2211yescharacteristic, complemented
60#10622092C2211yescharacteristic, complemented
61#10622092C2211yescharacteristic, complemented
62C8×C11⋊C8C2211yescharacteristic, complemented
63C2×C11×#41—21no—
64C2×C11×#41—21no—
65C2×#4339—21no—
66C22×D44—21no—
67C22×D44—21no—
68C22×D44—21no—
69C2×C11×SD16—22no—
70C2×C11×D8—22no—
71C11×C4⋊Q8C2311yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C11×#127C2311yescharacteristic
74C11×#127C2311yescharacteristic
75C11×#124—21no—
76C11×#124—21no—
77C11×#121—21no—
78C11×#121—21no—
79C11×#121—21no—
80C11×#121—21no—
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11—21no—
84C4×D4×C11—21no—
85C2×C42×C11C2311yescharacteristic
86C2×#4325—22no—
87C2×#4324—22no—
88C2×#4323—22no—
89C2×#4323—22no—
90C2×#4323—22no—
91C2×#4323—22no—
92C2×#4323—22no—
93C2×#4323—22no—
94#66983—21no—
95#66983—21no—
96C2×D88—22no—
97C2×D88—22no—
98#66928—21no—
99#66927—21no—
100#66927—21no—
101#66927—21no—
102#66927C2311yescharacteristic
103#66927C2311yescharacteristic
104#66927C2311yescharacteristic
105C4×D44—21no—
106C4×D44—21no—
107#66922C2311yescharacteristic
108C11×C4⋊C8D412yes—
109C11×#103—22no—
110C11×#102—22no—
111C11×C22⋊C8D412yes—
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114#66899—22no—
115#66896—22no—
116C22⋊(C11⋊C8)D412yes—
117C22⋊(C11⋊C8)D412yes—
118#66885—22no—
119#66885—22no—
120#66874—22no—
121#66873—22no—
122#66873—22no—
123#66873—22no—
124#66873—22no—
125#66873—22no—
126C4⋊(C11⋊C8)D412yes—
127C4⋊(C11⋊C8)D412yes—
128C4×C11⋊C8C2311yescharacteristic
129C4×C11⋊C8C2311yescharacteristic
130C4×C11⋊C8C2311yescharacteristic
131C4×C11⋊C8C2311yescharacteristic
132#19743—111nomaximal, Sylow
133C23×D11—41no—
134C11×#41—82no—
135C11×#41—82no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—41no—
145C2×D4×C11—41no—
146C22×C4×C11—41no—
147C22×C4×C11—41no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C2×C22⋊D11—41no—
152#4339—82no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—41no—
163C2×D44—41no—
164C2×D44—41no—
165C2×D44—82no—
166C2×D44—82no—
167C2×D44—82no—
168C2×C4×D11—41no—
169C2×Dic22—21no—
170C11×SD16—82no—
171C11×D8—82no—
172C2×C8×C11C2×D412yes—
173C2×C8×C11C2×D412yes—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C22⋊C4—41no—
179C11×C22⋊C4—41no—
180C11×C22⋊C4—41no—
181C11×C22⋊C4—41no—
182C42×C11C2×D411yescharacteristic
183C42×C11C2×D411yescharacteristic
184C42×C11C2×D411yescharacteristic
185C42×C11C2411yescharacteristic
186#4325—82no—
187#4324—82no—
188#4323—82no—
189#4323—82no—
190#4323—82no—
191#4323—82no—
192#4323—82no—
193#4323—82no—
194(C2×D11)⋊C4—41no—
195(C2×D11)⋊C4—41no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C2×C11⋊C8C2×D412yes—
199C2×C11⋊C8C2×D412yes—
200C2×C11⋊C8C2×D412yes—
201C2×C11⋊C8C2×D412yes—
202D88—82no—
203D88—82no—
204#3207—111no—
205#3207—111no—
206#3207D1111yescharacteristic, complemented
207#3205—111no—
208#3205—111no—
209#3205—111no—
210#1721—111no—
211#1721—111no—
212#1721—111no—
213#1717—111no—
214#1717—111no—
215#1717—111no—
216#1712—111no—
217#1711—111no—
218#1454—111no—
219C23×C11—41no—
220C23×C11—41no—
221C23×C11#12711yescharacteristic
222C22×D11—41no—
223C22×D11—41no—
224C22×D11—41no—
225C22×D11—82no—
226C22×D11—82no—
227C22×D11—82no—
228Q8×C11—42no—
229Q8×C11—42no—
230D4×C11—42no—
231D4×C11—42no—
232D4×C11—42no—
233D4×C11—42no—
234D4×C11—42no—
235D4×C11—42no—
236D4×C11—82no—
237D4×C11—82no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—82no—
244C2×C4×C11—82no—
245C2×C4×C11#12711yescharacteristic
246C2×C4×C11#12711yescharacteristic
247C2×C4×C11#12711yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C22⋊D11—82no—
252C2×Dic11—41no—
253D44—42no—
254D44—42no—
255D44—42no—
256D44—42no—
257D44—42no—
258D44—42no—
259D44—42no—
260D44—42no—
261D44—42no—
262D44—82no—
263D44—82no—
264D44—82no—
265C4×D11—82no—
266Dic22—42no—
267C8×C11—22no—
268C8×C11—22no—
269C11⋊C8—22no—
270C11⋊C8—22no—
271C11⋊C8—22no—
272C11⋊C8—22no—
273#532—111no—
274#532C2×D1111yescharacteristic
275#532C2×D1111yescharacteristic
276C2×#127—111no—
277#493—111no—
278#493—111no—
279#493—111no—
280#493—111no—
281#493—111no—
282#493—111no—
283#493—111no—
284#493—111no—
285#493C2×D1111yescharacteristic, complemented
286#492—111no—
287#492—111no—
288#492C2×D1111yescharacteristic, complemented
289#487—111no—
290#487—111no—
291#487C2×D1111yescharacteristic, complemented
292#486—111no—
293#486—111no—
294#486—111no—
295#486—111no—
296#486—111no—
297#486—111no—
298#486—111no—
299#486—111no—
300#486C2×D1111yescharacteristic, complemented
301#463—22no—
302#463—222no—
303#463—222no—
304#459—222no—
305#459—222no—
306#459—222no—
307#449—22no—
308#449—222no—
309#449—222no—
310#447—222no—
311#447—222no—
312#447—222no—
313#431—111no—
314#431—111no—
315#431C2×D1111yescharacteristic
316#322—111no—
317#322—111no—
318#322—111no—
319C82—111no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—81no—
324C22×C11—81no—
325C22×C11—81no—
326C22×C11—81no—
327C22×C11—81no—
328C22×C11—81no—
329C22×C11C2×#12711yescharacteristic
330C2×D11—81no—
331C2×D11—81no—
332C2×D11—81no—
333C2×D11—81no—
334C2×D11—81no—
335C2×D11—81no—
336C2×D11—81no—
337C2×D11—81no—
338C2×D11—81no—
339C2×D11—164no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—81no—
344C4×C11—81no—
345C4×C11#57612yes—
346C4×C11#57612yes—
347C4×C11#57612yes—
348Dic11—81no—
349C2×#41—21no—
350C2×#41—21no—
351C2×#41—221no—
352C22×D4—221no—
353C22×D4—221no—
354C22×D4—221no—
355C2×SD16—22no—
356C2×SD16—222no—
357C2×SD16—222no—
358C2×D8—22no—
359C2×D8—222no—
360C2×D8—222no—
361C2×D8—222no—
362C2×D8—222no—
363C2×D8—222no—
364C2×D8—222no—
365C2×D8—222no—
366C2×D8—222no—
367C4⋊Q8—111no—
368C4⋊Q8C22×D1111yescharacteristic
369C4⋊Q8C22×D1111yescharacteristic
370#127—111no—
371#127—111no—
372#127—111no—
373#127—221no—
374#127—221no—
375#127—221no—
376#127C22×D1111yescharacteristic
377#127C22×D1111yescharacteristic
378#124—21no—
379#124—21no—
380#124—221no—
381#121—21no—
382#121—21no—
383#121—21no—
384#121—21no—
385#121—221no—
386#121—221no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—221no—
392C4×D4—221no—
393C2×C42C22×D1111yescharacteristic
394C4⋊C8—112no—
395C4⋊C8—112no—
396C4⋊C8C22⋊D1112yes—
397#103—22no—
398#103—222no—
399#103—222no—
400#102—22no—
401#102—222no—
402#102—222no—
403#102—222no—
404#102—222no—
405#102—222no—
406#102—222no—
407#102—222no—
408#102—222no—
409C22⋊C8—112no—
410C22⋊C8—112no—
411C22⋊C8C22⋊D1112yes—
412C4×C8—111no—
413C4×C8—111no—
414C4×C8—111no—
415C4×C8—111no—
416C4×C8C22×D1111yescharacteristic
417C4×C8C22×D1111yescharacteristic
418C2×C11—41no—
419C2×C11—161no—
420C2×C11—161no—
421C2×C11#315511yescharacteristic
422C2×C11#315511yescharacteristic
423C2×C11#315511yescharacteristic
424D11—161no—
425D11—161no—
426D11—161no—
427C24—441no—
428#41—82no—
429#41—82no—
430#41—882no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—221no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—221no—
443C2×D4—221no—
444C2×D4—221no—
445C2×D4—221no—
446C2×D4—221no—
447C2×D4—221no—
448C2×D4—221no—
449C2×D4—221no—
450C2×D4—221no—
451C2×D4—441no—
452C2×D4—441no—
453C2×D4—441no—
454C2×D4—441no—
455C2×D4—882no—
456C2×D4—882no—
457C2×D4—882no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—441no—
461C22×C4D4×D1111yescharacteristic
462C22×C4D4×D1111yescharacteristic
463C22×C4C2×C22⋊D1111yescharacteristic
464SD16—82no—
465SD16—882no—
466SD16—882no—
467D8—82no—
468D8—882no—
469D8—882no—
470D8—882no—
471D8—882no—
472D8—882no—
473D8—882no—
474D8—882no—
475D8—882no—
476C2×C8—112no—
477C2×C8—112no—
478C2×C8—112no—
479C2×C8—112no—
480C2×C8C2×C22⋊D1112yes—
481C2×C8C2×C22⋊D1112yes—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4—441no—
493C22⋊C4—441no—
494C42D4×D1111yescharacteristic
495C42D4×D1111yescharacteristic
496C42C2×C22⋊D1111yescharacteristic
497C42C23×D1111yescharacteristic
498C11#1974311yescharacteristic, complemented, Sylow
499C23—41no—
500C23—41no—
501C23—441no—
502C23—441no—
503C23—441no—
504C23—882no—
505C23—882no—
506C23—882no—
507C23#6699311yescharacteristic
508Q8—42no—
509Q8—42no—
510Q8—442no—
511D4—42no—
512D4—42no—
513D4—42no—
514D4—42no—
515D4—42no—
516D4—42no—
517D4—82no—
518D4—82no—
519D4—442no—
520D4—442no—
521D4—442no—
522D4—442no—
523D4—442no—
524D4—442no—
525D4—442no—
526D4—442no—
527D4—442no—
528D4—882no—
529D4—882no—
530D4—882no—
531D4—882no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—82no—
538C2×C4—82no—
539C2×C4—441no—
540C2×C4—882no—
541C2×C4#6699311yescharacteristic
542C2×C4#6699311yescharacteristic
543C2×C4#6699311yescharacteristic
544C2×C4C2×D4×D1111yescharacteristic
545C2×C4C2×D4×D1111yescharacteristic
546C2×C4C22×C22⋊D1111yescharacteristic
547C8—22no—
548C8—22no—
549C8—222no—
550C8—222no—
551C8—222no—
552C8—222no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—881no—
563C22—881no—
564C22—881no—
565C22—881no—
566C22—881no—
567C22—881no—
568C22—881no—
569C22—881no—
570C22—881no—
571C22—1764no—
572C22C2×#6699311yescharacteristic
573C4—21no—
574C4—21no—
575C4—21no—
576C4—81no—
577C4—81no—
578C4—881no—
579C4#1062330012yes—
580C4#1062330512yes—
581C4#1062336612yes—
582C2—41no—
583C2—161no—
584C2—161no—
585C2—1761no—
586C2—1761no—
587C2—1761no—
588C2#1307909911yescharacteristic
589C2#1307910111yescharacteristic
590C2#1307910311yescharacteristic
subgroupG/H
centerC22C2×#66993
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3207C2
socleC22×C11C2×#127
hypercenter#3207D11
hypocenterC11#19743
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3207

Complements

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

NH ≅ G/Ntype
1. #13079549C2semidirect
2. #13079545C2semidirect
3. #13079536C2semidirect
4. #13079531C2semidirect
5. #13079531C2semidirect
6. #13068284C2semidirect
7. #13068281C2semidirect
8. #13068280C2semidirect
9. #13068258C2semidirect
10. #13068253C2semidirect
11. #13068252C2semidirect
12. #13068230C2semidirect
13. #13068229C2semidirect
14. #13066916C2semidirect
15. C11×#3207C2semidirect
20. C11×#493C22semidirect
21. C11×#492C22semidirect
22. C11×#487C22semidirect
23. C11×#486C22semidirect
28. #10622706C22semidirect
33. #10622701C22semidirect
34. #10622698C22semidirect
35. #10622694C22semidirect
36. #10622689C22semidirect
41. #10622686C22semidirect
42. #10622686C22semidirect
43. #10622683C22semidirect
59. #10622093C22semidirect
60. #10622092C22semidirect
61. #10622092C22semidirect
62. C8×C11⋊C8C22semidirect
206. #3207D11semidirect
285. #493C2×D11semidirect
288. #492C2×D11semidirect
291. #487C2×D11semidirect
300. #486C2×D11semidirect
498. C11#19743semidirect

Maximal subgroups

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

subgroupindex
#130795492
#130795452
#130795362
#130795312
#130682842
#130682812
#130682802
#130682582
#130682532
#130682522
#130682302
#130682292
#130669162
C11×#32072
#1974311