Finite Group Databasebeta

← #29670374

Subgroups — #29670374

Order 15616.

632 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458466C211yesmaximal, characteristic, complemented
2#21458232C211yesmaximal, characteristic, complemented
3#21457643C211yesmaximal, characteristic, complemented
4#21445480C211yesmaximal, characteristic, complemented
5#21445394C211yesmaximal, characteristic, complemented
6#21445232C211yesmaximal, characteristic, complemented
7#21445226C211yesmaximal, characteristic, complemented
8#21445196C211yesmaximal, characteristic, complemented
9#21444998C211yesmaximal, characteristic, complemented
10#21444964C211yesmaximal, characteristic, complemented
11#21444951C211yesmaximal, characteristic, complemented
12#21444927C211yesmaximal, characteristic, complemented
13#21444660C211yesmaximal, characteristic, complemented
14#21444643C211yesmaximal, characteristic, complemented
15C61×#3325C211yesmaximal, characteristic
16#16840482C2211yescharacteristic, complemented
17#16840469C2211yescharacteristic
18#16840158C2211yescharacteristic, complemented
19#16840141C2211yescharacteristic, complemented
20#16840115—21no—
21#16840113C2211yescharacteristic, complemented
22#16840108C2211yescharacteristic
23#16840108C2211yescharacteristic
24#16840103—21no—
25#16840083—21no—
26#16840078—21no—
27#16840068—21no—
28#16840054C2211yescharacteristic, complemented
29#16840052C2211yescharacteristic
30#16840052C2211yescharacteristic, complemented
31#16840042C2211yescharacteristic
32#16839989—21no—
33#16839989—21no—
34#16839975—21no—
35#16839967C2211yescharacteristic
36#16839959C2211yescharacteristic
37#16839913—21no—
38C8×Dic122C2211yescharacteristic, complemented
39#16839853—21no—
40C4×#11758200C2211yescharacteristic
41D4×#92418C2211yescharacteristic
42D4×#92418C2211yescharacteristic, complemented
43#16839798—21no—
44C2×#14519698—21no—
45#16839513C2211yescharacteristic, complemented
46#16839512C2211yescharacteristic, complemented
47#16839511C2211yescharacteristic, complemented
48#16839510C2211yescharacteristic, complemented
49#16839509C2211yescharacteristic, complemented
50#16839506C2211yescharacteristic
51#16839492C2211yescharacteristic, complemented
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic, complemented
55#16839483C2211yescharacteristic, complemented
56C61×#555C2211yescharacteristic
57D42×C61C2211yescharacteristic
58C61×#486C2211yescharacteristic
59C61×#482—21no—
60C61×#476C2211yescharacteristic
61C61×#469—21no—
62C61×#459C2211yescharacteristic
63C61×#447—21no—
64C4×D8×C61C2211yescharacteristic
65C61×#436C2211yescharacteristic
66C61×#418—21no—
67C2×#11758202—41no—
68C2×#11758200—21no—
69C2×#11758200—21no—
70C2×#11758200D411yescharacteristic
71C22×#92418—21no—
72C22×#92418—21no—
73#14519777C2311yescharacteristic
74#14519777C2311yescharacteristic
75#14519770—41no—
76#14519768—21no—
77#14519764—21no—
78#14519756—21no—
79#14519756—21no—
80#14519754—41no—
81C4×Dic122C2311yescharacteristic
82#14519742—21no—
83D4×Dic61—21no—
84#14519736—21no—
85C2×C4⋊Dic61—21no—
86#14519710—21no—
87#14519710—21no—
88#14519708—21no—
89#14519708—21no—
90#14519708—21no—
91#14519708—21no—
92#14519708D411yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96#14519706—21no—
97#14519702—21no—
98#14519702—21no—
99#14519700—21no—
100#14519700—21no—
101#14519700D411yescharacteristic
102#14519698—21no—
103#14519698—21no—
104#14519698—21no—
105#14519698—21no—
106#14519698—21no—
107#14519698—21no—
108#14519698—41no—
109#14519698D411yescharacteristic
110C22⋊#92418—21no—
111C22⋊#92418—21no—
112C4×#92418C2311yescharacteristic
113C4×#92418C2311yescharacteristic
114C8×Dic61—21no—
115C22×D4×C61—21no—
116C22×D4×C61—21no—
117C2×D8×C61—21no—
118C2×D8×C61D411yescharacteristic
119C2×M16×C61—21no—
120C4⋊Q8×C61C2311yescharacteristic
121#127×C61C2311yescharacteristic
122#124×C61—41no—
123#121×C61—21no—
124#121×C61—21no—
125#121×C61—21no—
126#121×C61—21no—
127#120×C61—41no—
128C4×D4×C61C2311yescharacteristic
129C4×D4×C61C2311yescharacteristic
130C4×D4×C61C2311yescharacteristic
131#117×C61—21no—
132#117×C61—21no—
133#107×C61D411yescharacteristic
134#106×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136#102×C61—21no—
137#102×C61—21no—
138#102×C61—21no—
139#102×C61—21no—
140#102×C61D411yescharacteristic
141#102×C61D411yescharacteristic
142C22⋊C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C24×C61—41no—
145C2×Q8×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—41no—
150C2×D4×C61—41no—
151C2×D4×C61—42no—
152C2×D4×C61—42no—
153C2×D4×C61—41no—
154C2×D4×C61—81no—
155C2×D4×C61—81no—
156C2×D4×C61C2×D411yescharacteristic
157C2×D4×C61C2×D411yescharacteristic
158C2×D4×C61C2×D411yescharacteristic
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×Dic61—41no—
163C2×Dic122—21no—
164C2×Dic122—21no—
165C2×Dic122C2×D411yescharacteristic
166D8×C61—22no—
167D8×C61—81no—
168M16×C61—81no—
169C2×C8×C61—21no—
170C2×C8×C61C2×D411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61C2×D411yescharacteristic
175C4⋊C4×C61C2×D411yescharacteristic
176C4⋊C4×C61C2×D411yescharacteristic
177C22⋊C4×C61—21no—
178C22⋊C4×C61—21no—
179C22⋊C4×C61—21no—
180C22⋊C4×C61—41no—
181C22⋊C4×C61—41no—
182C22⋊C4×C61—41no—
183C42×C61—41no—
184C42×C61C2411yescharacteristic
185C22⋊Dic61—41no—
186C22⋊Dic61—41no—
187C22⋊Dic61—41no—
188#11758202—82no—
189#11758200—41no—
190#11758200—42no—
191#11758200—81no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—41no—
197C4⋊Dic61C2×D411yescharacteristic
198#11758196—21no—
199#11758196—41no—
200#11758196—41no—
201C4×Dic61—21no—
202C4×Dic61—41no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—42no—
208C2×#92418—81no—
209C2×#92418C2×D411yescharacteristic
210C2×#92418C2×D411yescharacteristic
211C23×C61—21no—
212C23×C61—21no—
213C23×C61—21no—
214C23×C61—41no—
215C23×C61—82no—
216C23×C61—82no—
217C23×C61—161no—
218Q8×C61—81no—
219D4×C61—21no—
220D4×C61—21no—
221D4×C61—21no—
222D4×C61—21no—
223D4×C61—21no—
224D4×C61—41no—
225D4×C61—41no—
226D4×C61—41no—
227D4×C61—41no—
228D4×C61—81no—
229D4×C61—82no—
230D4×C61—82no—
231D4×C61—161no—
232D4×C61#13512yes—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61C22×D411yescharacteristic
244C2×C4×C61C22×D411yescharacteristic
245C2×C4×C61H(5,𝔽2)11yescharacteristic
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—161no—
251Dic122—21no—
252Dic122—21no—
253Dic122—41no—
254Dic122—41no—
255Dic122—81no—
256C8×C61—21no—
257C8×C61—21no—
258C8×C61—41no—
259#92418—21no—
260#92418—21no—
261#92418—41no—
262#92418—41no—
263#92418—41no—
264#92418—41no—
265#19823—611nomaximal, Sylow
266C22×C61—22no—
267C22×C61—41no—
268C22×C61—41no—
269C22×C61—41no—
270C22×C61—41no—
271C22×C61—41no—
272C22×C61—41no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—81no—
276C22×C61—81no—
277C22×C61—81no—
278C22×C61—164no—
279C22×C61D4211yescharacteristic
280C4×C61—21no—
281C4×C61—41no—
282C4×C61—41no—
283C4×C61—41no—
284C4×C61—81no—
285C4×C61C2×#13511yescharacteristic
286C4×C61#57511yescharacteristic
287C4×C61#57711yescharacteristic
288C4×C61#57711yescharacteristic
289Dic61—41no—
290Dic61—41no—
291Dic61—81no—
292Dic61—81no—
293#3360—611no—
294#3340—611no—
295#3325D6111yescharacteristic
296#3295—611no—
297#1720—611no—
298#1703—611no—
299#1678—611no—
300#1677—611no—
301#1671—611no—
302#1639—611no—
303#1634—611no—
304#1632—611no—
305#1628—611no—
306#1583—611no—
307#1580—611no—
308C2×C61—42no—
309C2×C61—81no—
310C2×C61—81no—
311C2×C61—161no—
312C2×C61#326711yescharacteristic
313C2×C61#328211yescharacteristic
314C2×C61#328811yescharacteristic
315#556—611no—
316#555C2×D6111yescharacteristic
317#554—611no—
318D42C2×D6111yescharacteristic
319#498—611no—
320#494—611no—
321#488—1221no—
322#487—611no—
323#486—611no—
324#486—611no—
325#486C2×D6111yescharacteristic
326#485—1221no—
327#482—21no—
328#482—1221no—
329#481—1221no—
330#479—1221no—
331#477—611no—
332#476—611no—
333#476—611no—
334#476C2×D6111yescharacteristic
335#474—611no—
336#469—21no—
337#465—1221no—
338#465—1221no—
339#463—1221no—
340#461—611no—
341#460—611no—
342#459C2×D6111yescharacteristic
343#450—1221no—
344#447—21no—
345C8×Q8—611no—
346C4×SD16—611no—
347C4×SD16—1221no—
348C4×D8C2×D6111yescharacteristic
349#436C2×D6111yescharacteristic
350C8×D4—611no—
351C8×D4—611no—
352#427—1221no—
353#418—21no—
354C2×#102—1221no—
355#334—611no—
356#334—611no—
357#333—611no—
358#333—611no—
359#332—611no—
360#331—611no—
361Q8⋊C8—611no—
362D4⋊C8—611no—
363D4⋊C8—611no—
364D4⋊C8—611no—
365#322—611no—
366C61#1982311yescharacteristic, complemented, Sylow
367C22×D4—21no—
368C22×D4—21no—
369C2×Q16—2441no—
370C2×SD16—611no—
371C2×SD16—1221no—
372C2×SD16—1221no—
373C2×D8—21no—
374C2×D8C22⋊D6111yescharacteristic
375C2×M16—21no—
376C22×C8—1221no—
377C22×C8—1221no—
378C4⋊Q8—611no—
379C4⋊Q8—611no—
380C4⋊Q8C22×D6111yescharacteristic
381#127C22×D6111yescharacteristic
382#126—2441no—
383#125—1221no—
384#124—41no—
385#124—1221no—
386C22⋊Q8—1221no—
387C22⋊Q8—1221no—
388C22⋊Q8—2441no—
389#121—21no—
390#121—21no—
391#121—21no—
392#121—21no—
393#120—41no—
394C4×Q8—611no—
395C4×Q8—1221no—
396C4×D4—1221no—
397C4×D4C22×D6111yescharacteristic
398C4×D4C22×D6111yescharacteristic
399C4×D4C22×D6111yescharacteristic
400#117—21no—
401#117—21no—
402#117—1221no—
403C2×C4⋊C4—1221no—
404#107—1221no—
405#107—1221no—
406#107C22⋊D6111yescharacteristic
407#106—21no—
408#106—611no—
409#106—1221no—
410#106—1221no—
411#106—1221no—
412#106—1221no—
413C4⋊C8—611no—
414C4⋊C8—611no—
415C4⋊C8—611no—
416C4⋊C8—1221no—
417C4⋊C8C22×D6111yescharacteristic
418#103—611no—
419#103—1221no—
420#103—1221no—
421#103—1221no—
422#103—1221no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—611no—
428#102—1221no—
429#102—1221no—
430#102—1221no—
431#102—1221no—
432#102—1221no—
433#102—1221no—
434#102—2441no—
435#102C22⋊D6111yescharacteristic
436#102C22⋊D6111yescharacteristic
437C22⋊C8—21no—
438C22⋊C8—1221no—
439C22⋊C8—1221no—
440C4×C8—611no—
441C4×C8—611no—
442C4×C8—1221no—
443C4×C8C22×D6111yescharacteristic
444C24—41no—
445C2×Q8—21no—
446C2×Q8—611no—
447C2×Q8—1221no—
448C2×Q8—1221no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—42no—
455C2×D4—42no—
456C2×D4—41no—
457C2×D4—81no—
458C2×D4—81no—
459C2×D4D4×D6111yescharacteristic
460C2×D4C2×C22⋊D6111yescharacteristic
461C2×D4C2×C22⋊D6111yescharacteristic
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—2441no—
466Q16—4882no—
467SD16—4881no—
468SD16—2441no—
469SD16—2442no—
470D8—22no—
471D8—81no—
472M16—81no—
473C2×C8—21no—
474C2×C8—611no—
475C2×C8—611no—
476C2×C8—1221no—
477C2×C8—1221no—
478C2×C8—1221no—
479C2×C8—1221no—
480C2×C8—4881no—
481C2×C8—2442no—
482C2×C8C2×C22⋊D6111yescharacteristic
483C2×C8C2×C22⋊D6111yescharacteristic
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—611no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C4⋊C4—1221no—
491C4⋊C4—1221no—
492C4⋊C4—2441no—
493C4⋊C4—2441no—
494C4⋊C4—2441no—
495C4⋊C4D4×D6111yescharacteristic
496C4⋊C4C2×C22⋊D6111yescharacteristic
497C4⋊C4C2×C22⋊D6111yescharacteristic
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—2441no—
505C22⋊C4—2441no—
506C22⋊C4—2441no—
507C42—41no—
508C42—1221no—
509C42—2441no—
510C42C23×D6111yescharacteristic
511C23—21no—
512C23—21no—
513C23—21no—
514C23—41no—
515C23—82no—
516C23—82no—
517C23—161no—
518Q8—81no—
519Q8—1221no—
520Q8—1221no—
521Q8—4881no—
522Q8—2441no—
523Q8—2441no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—81no—
534D4—82no—
535D4—82no—
536D4—161no—
537D4#1451979712yes—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—1221no—
549C2×C4—1221no—
550C2×C4—9761no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4C2×D4×D6111yescharacteristic
554C2×C4C22×C22⋊D6111yescharacteristic
555C2×C4#1451982211yescharacteristic
556C8—21no—
557C8—21no—
558C8—41no—
559C8—1221no—
560C8—1221no—
561C8—2441no—
562C8—2441no—
563C8—2441no—
564C8—2441no—
565C22—22no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—164no—
578C22D4×C22⋊D6111yescharacteristic
579C4—21no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—81no—
584C4—4881no—
585C4—4881no—
586C4—2441no—
587C4—2441no—
588C4C2×#1451979711yescharacteristic
589C4#1684055811yescharacteristic
590C4#1684057211yescharacteristic
591C4#1684057311yescharacteristic
592C2—42no—
593C2—81no—
594C2—81no—
595C2—161no—
596C2#2145733811yescharacteristic
597C2#2145752211yescharacteristic
598C2#2145758311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
Fitting, prime radicalC61×#3325C2
socleC22×C61D42
hypercenter#3325D61
hypocenterC61#19823
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3325

Complements

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

NH ≅ G/Ntype
1. #21458466C2semidirect
2. #21458232C2semidirect
3. #21457643C2semidirect
4. #21445480C2semidirect
5. #21445394C2semidirect
6. #21445232C2semidirect
7. #21445226C2semidirect
8. #21445196C2semidirect
9. #21444998C2semidirect
10. #21444964C2semidirect
11. #21444951C2semidirect
12. #21444927C2semidirect
13. #21444660C2semidirect
14. #21444643C2semidirect
16. #16840482C22semidirect
18. #16840158C22semidirect
19. #16840141C22semidirect
21. #16840113C22semidirect
28. #16840054C22semidirect
30. #16840052C22semidirect
38. C8×Dic122C22semidirect
42. D4×#92418C22semidirect
45. #16839513C22semidirect
46. #16839512C22semidirect
47. #16839511C22semidirect
48. #16839510C22semidirect
49. #16839509C22semidirect
51. #16839492C22semidirect
54. D4⋊#92418C22semidirect
55. #16839483C22semidirect
366. C61#19823semidirect

Maximal subgroups

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

subgroupindex
#214584662
#214582322
#214576432
#214454802
#214453942
#214452322
#214452262
#214451962
#214449982
#214449642
#214449512
#214449272
#214446602
#214446432
C61×#33252
#1982361