Finite Group Databasebeta

← #29676550

Subgroups — #29676550

Order 15616.

616 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458846C211yesmaximal, characteristic, complemented
2#21458052C211yesmaximal, characteristic
3#21458044C211yesmaximal, characteristic
4#21445476C211yesmaximal, characteristic, complemented
5#21445389C211yesmaximal, characteristic, complemented
6#21445363C211yesmaximal, characteristic, complemented
7#21445306C211yesmaximal, characteristic, complemented
8#21445263C211yesmaximal, characteristic, complemented
9#21445089C211yesmaximal, characteristic, complemented
10#21445087C211yesmaximal, characteristic, complemented
11#21444997C211yesmaximal, characteristic
12#21444915C211yesmaximal, characteristic, complemented
13#21444722C211yesmaximal, characteristic, complemented
14#21444662C211yesmaximal, characteristic, complemented
15C61×#3364C211yesmaximal, characteristic, complemented
16#16840485C2211yescharacteristic
17D4×D244C2211yescharacteristic
18#16840158C2211yescharacteristic, complemented
19#16840154—21no—
20#16840141C2211yescharacteristic, complemented
21#16840110C2211yescharacteristic
22#16840110C2211yescharacteristic
23#16840109C2211yescharacteristic
24#16840088—21no—
25#16840086—21no—
26#16840042C2211yescharacteristic
27#16840039C2211yescharacteristic
28#16840011—21no—
29#16840010—21no—
30#16839984—21no—
31#16839972C2211yescharacteristic, complemented
32#16839969—21no—
33#16839964C2211yescharacteristic
34#16839962C2211yescharacteristic
35#16839962C2211yescharacteristic
36#16839912—21no—
37#16839911—21no—
38#16839893C2211yescharacteristic, complemented
39#16839867—21no—
40C4×#11758201C2211yescharacteristic
41#16839841C2211yescharacteristic
42#16839840C2211yescharacteristic
43#16839766—21no—
44#16839765—21no—
45#16839515C2211yescharacteristic, complemented
46#16839512C2211yescharacteristic, complemented
47#16839508C2211yescharacteristic, complemented
48#16839508C2211yescharacteristic, complemented
49#16839507C2211yescharacteristic, complemented
50#16839505C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic, complemented
52Q8⋊#92418C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55#16839483C2211yescharacteristic, complemented
56C61×#557C2211yescharacteristic, complemented
57C61×#556C2211yescharacteristic
58C61×#488—21no—
59C61×#487C2211yescharacteristic, complemented
60C61×#479—21no—
61C61×#474C2211yescharacteristic
62C61×#464—21no—
63C61×#462C2211yescharacteristic, complemented
64C8×Q8×C61C2211yescharacteristic, complemented
65C4×Q16×C61—21no—
66C4×SD16×C61C2211yescharacteristic
67C22×D244—21no—
68C2×D4×D61—21no—
69C2×#11758202—21no—
70C2×#11758202—21no—
71C2×#11758202—21no—
72C2×#11758201—21no—
73C2×#11758201—21no—
74C2×#11758201—21no—
75C2×#11758201D411yescharacteristic
76C2×#11758194—21no—
77C2×#11758189—21no—
78#14519777C2311yescharacteristic
79#14519774C2311yescharacteristic
80#14519772—41no—
81#14519765—21no—
82#14519753—21no—
83#14519752—21no—
84#14519751—21no—
85#14519747—41no—
86C4×Dic122—21no—
87C4×D244C2311yescharacteristic
88#14519735—21no—
89#14519710—21no—
90#14519710—21no—
91#14519708—41no—
92#14519708D411yescharacteristic
93C4⋊#92418—21no—
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519701—21no—
98#14519701D411yescharacteristic
99#14519700—21no—
100#14519699—21no—
101#14519699—21no—
102#14519698—21no—
103#14519697—21no—
104#14519697—21no—
105#14519697—21no—
106#14519697—21no—
107#14519697—21no—
108#14519697—41no—
109#14519697D411yescharacteristic
110C22⋊#92418—21no—
111#14519689—21no—
112#14519688—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×Q16×C61—21no—
116C2×SD16×C61D411yescharacteristic
117C4⋊Q8×C61—21no—
118C4⋊Q8×C61C2311yescharacteristic
119C4⋊Q8×C61C2311yescharacteristic
120#126×C61—41no—
121#125×C61—21no—
122#125×C61—41no—
123#124×C61—21no—
124C22⋊Q8×C61—21no—
125C4×Q8×C61—21no—
126C4×Q8×C61—21no—
127C4×Q8×C61—21no—
128C4×Q8×C61C2311yescharacteristic
129C4×Q8×C61C2311yescharacteristic
130C4×D4×C61C2311yescharacteristic
131#117×C61—21no—
132#107×C61—21no—
133#106×C61D411yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136#103×C61—21no—
137#103×C61—21no—
138#103×C61—21no—
139#103×C61D411yescharacteristic
140#102×C61—21no—
141#102×C61D411yescharacteristic
142C4×C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C23×D61—41no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61C2×D411yescharacteristic
148C2×Q8×C61C2×D411yescharacteristic
149C2×D4×C61C2×D411yescharacteristic
150C22×C4×C61—21no—
151C2×C22⋊D61—41no—
152D4×D61—42no—
153D4×D61—81no—
154C2×D244—21no—
155C2×D244—21no—
156C2×D244—21no—
157C2×D244—42no—
158C2×D244—41no—
159C2×D244—81no—
160C2×D244C2×D411yescharacteristic
161C2×C4×D61—21no—
162C2×Dic122—21no—
163Q16×C61—42no—
164SD16×C61—41no—
165C2×C8×C61—21no—
166C2×C8×C61C2×D411yescharacteristic
167C2×C8×C61C2×D411yescharacteristic
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—41no—
175C4⋊C4×C61—41no—
176C4⋊C4×C61—41no—
177C4⋊C4×C61—41no—
178C4⋊C4×C61C2×D411yescharacteristic
179C4⋊C4×C61C2×D411yescharacteristic
180C4⋊C4×C61C2×D411yescharacteristic
181C22⋊C4×C61—21no—
182C22⋊C4×C61—41no—
183C22⋊C4×C61—41no—
184C42×C61—21no—
185C42×C61—21no—
186C42×C61—41no—
187C42×C61—41no—
188C42×C61C2411yescharacteristic
189#11758202—42no—
190#11758202—81no—
191#11758202—81no—
192#11758201—41no—
193#11758201—81no—
194#11758201—81no—
195#11758201—81no—
196#11758198—21no—
197#11758198—41no—
198#11758198—41no—
199#11758198—41no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61C2×D411yescharacteristic
203#11758196—41no—
204C4×Dic61—41no—
205#11758194—81no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418C2×D411yescharacteristic
211C2×#92418C2×D411yescharacteristic
212#11758189—81no—
213C23×C61—21no—
214C22×D61—21no—
215C22×D61—41no—
216C22×D61—82no—
217C22×D61—82no—
218C22×D61—161no—
219Q8×C61—21no—
220Q8×C61—21no—
221Q8×C61—21no—
222Q8×C61—21no—
223Q8×C61—41no—
224Q8×C61—41no—
225Q8×C61—41no—
226Q8×C61—41no—
227D4×C61—21no—
228D4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61C22×D411yescharacteristic
239C2×C4×C61C22×D411yescharacteristic
240C2×C4×C61H(5,𝔽2)11yescharacteristic
241C22⋊D61—82no—
242C2×Dic61—21no—
243C2×Dic61—41no—
244D244—21no—
245D244—21no—
246D244—41no—
247D244—41no—
248D244—41no—
249D244—41no—
250D244—81no—
251D244—82no—
252C4×D61—41no—
253C4×D61—41no—
254Dic122—41no—
255Dic122—41no—
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#20267—611nomaximal, Sylow
266C22×C61—41no—
267C22×C61—41no—
268C22×C61—41no—
269C22×C61D4211yescharacteristic
270C2×D61—41no—
271C2×D61—41no—
272C2×D61—41no—
273C2×D61—81no—
274C2×D61—81no—
275C2×D61—81no—
276C2×D61—164no—
277C4×C61—21no—
278C4×C61—41no—
279C4×C61—41no—
280C4×C61—41no—
281C4×C61—41no—
282C4×C61—41no—
283C4×C61—81no—
284C4×C61—81no—
285C4×C61#57511yescharacteristic
286C4×C61#57511yescharacteristic
287C4×C61#57611yescharacteristic
288C4×C61#57711yescharacteristic
289Dic61—41no—
290Dic61—81no—
291#3398—611no—
292#3364D6111yescharacteristic, complemented
293#3324—611no—
294#3324—611no—
295#1720—611no—
296#1702—611no—
297#1699—611no—
298#1689—611no—
299#1682—611no—
300#1652—611no—
301#1652—611no—
302#1639—611no—
303#1626—611no—
304#1592—611no—
305#1583—611no—
306C2×C61—81no—
307C2×C61#326811yescharacteristic
308C2×C61#327511yescharacteristic
309C2×C61#328911yescharacteristic
310D61—81no—
311D61—161no—
312#557C2×D6111yescharacteristic, complemented
313#556—611no—
314#556C2×D6111yescharacteristic
315D42—611no—
316#498—611no—
317#497—1221no—
318#494—611no—
319#488—21no—
320#487C2×D6111yescharacteristic, complemented
321#486—611no—
322#486—611no—
323#486—611no—
324#482—1221no—
325#482—1221no—
326#479—21no—
327#474—611no—
328#474—611no—
329#474C2×D6111yescharacteristic
330#468—1221no—
331#468—1221no—
332#464—21no—
333#464—1221no—
334#462—611no—
335#462—1221no—
336#462C2×D6111yescharacteristic, complemented
337#461—611no—
338#460—611no—
339#460—611no—
340#450—1221no—
341#450—1221no—
342#446—611no—
343C8×Q8C2×D6111yescharacteristic, complemented
344#441—1221no—
345C4×Q16—21no—
346C4×SD16—611no—
347C4×SD16C2×D6111yescharacteristic
348#436—611no—
349#436—611no—
350#418—1221no—
351#418—1221no—
352#335—611no—
353#334—611no—
354#332—611no—
355#332—611no—
356#332—611no—
357#331—611no—
358Q8⋊C8—611no—
359Q8⋊C8—611no—
360D4⋊C8—611no—
361D4⋊C8—611no—
362#322—611no—
363C61#2026711yescharacteristic, complemented, Sylow
364C22×D4—1221no—
365C22×D4—1221no—
366C2×Q16—21no—
367C2×Q16—1221no—
368C2×Q16—1221no—
369C2×Q16—1221no—
370C2×SD16—611no—
371C2×SD16—1221no—
372C2×SD16—1221no—
373C2×SD16—1221no—
374C2×SD16C22⋊D6111yescharacteristic
375C2×M16—1221no—
376C2×M16—1221no—
377C4⋊Q8—21no—
378C4⋊Q8—611no—
379C4⋊Q8C22×D6111yescharacteristic
380C4⋊Q8C22×D6111yescharacteristic
381#127—611no—
382#126—41no—
383#126—2441no—
384#125—21no—
385#125—41no—
386#124—21no—
387#124—1221no—
388C22⋊Q8—21no—
389C22⋊Q8—1221no—
390#121—1221no—
391#121—1221no—
392#120—2441no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8—21no—
396C4×Q8—1221no—
397C4×Q8C22×D6111yescharacteristic
398C4×Q8C22×D6111yescharacteristic
399C4×D4—611no—
400C4×D4C22×D6111yescharacteristic
401#117—21no—
402#117—1221no—
403#107—21no—
404#107—1221no—
405#107—1221no—
406#106—611no—
407#106—2441no—
408#106C22⋊D6111yescharacteristic
409C4⋊C8—21no—
410C4⋊C8—611no—
411C4⋊C8—611no—
412C4⋊C8—611no—
413C4⋊C8—1221no—
414C4⋊C8C22×D6111yescharacteristic
415#103—21no—
416#103—21no—
417#103—21no—
418#103—611no—
419#103—1221no—
420#103—1221no—
421#103C22⋊D6111yescharacteristic
422#102—21no—
423#102—611no—
424#102—1221no—
425#102—1221no—
426#102—1221no—
427#102—1221no—
428#102—1221no—
429#102—1221no—
430#102—1221no—
431#102—1221no—
432#102—2441no—
433#102C22⋊D6111yescharacteristic
434C22⋊C8—1221no—
435C22⋊C8—1221no—
436#97—1221no—
437C4×C8—21no—
438C4×C8—611no—
439C4×C8—611no—
440C4×C8C22×D6111yescharacteristic
441C24—2441no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—1221no—
445C2×Q8D4×D6111yescharacteristic
446C2×Q8C2×C22⋊D6111yescharacteristic
447C2×D4—611no—
448C2×D4—1221no—
449C2×D4—1221no—
450C2×D4—1221no—
451C2×D4—4881no—
452C2×D4—4881no—
453C2×D4—2441no—
454C2×D4—2442no—
455C2×D4—2441no—
456C2×D4—2442no—
457C2×D4C2×C22⋊D6111yescharacteristic
458C22×C4—21no—
459C22×C4—1221no—
460Q16—42no—
461Q16—4881no—
462Q16—4881no—
463Q16—2442no—
464SD16—41no—
465SD16—4881no—
466SD16—4881no—
467SD16—4881no—
468SD16—2441no—
469M16—4881no—
470M16—4881no—
471C2×C8—21no—
472C2×C8—611no—
473C2×C8—611no—
474C2×C8—1221no—
475C2×C8—1221no—
476C2×C8—1221no—
477C2×C8—1221no—
478C2×C8C2×C22⋊D6111yescharacteristic
479C2×C8C2×C22⋊D6111yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—611no—
491C4⋊C4—1221no—
492C4⋊C4—1221no—
493C4⋊C4—2441no—
494C4⋊C4D4×D6111yescharacteristic
495C4⋊C4C2×C22⋊D6111yescharacteristic
496C4⋊C4C2×C22⋊D6111yescharacteristic
497C22⋊C4—21no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—1221no—
501C22⋊C4—2441no—
502C22⋊C4—2441no—
503C22⋊C4—2441no—
504C42—21no—
505C42—21no—
506C42—41no—
507C42—41no—
508C42—2441no—
509C42C23×D6111yescharacteristic
510C23—21no—
511C23—1221no—
512C23—9761no—
513C23—4882no—
514C23—4882no—
515C23—2441no—
516Q8—21no—
517Q8—21no—
518Q8—21no—
519Q8—21no—
520Q8—41no—
521Q8—41no—
522Q8—41no—
523Q8—41no—
524Q8—2441no—
525Q8—2441no—
526D4—21no—
527D4—21no—
528D4—1221no—
529D4—1221no—
530D4—4881no—
531D4—4882no—
532D4—4882no—
533D4—2441no—
534D4—2441no—
535D4—2441no—
536D4—2441no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—1221no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4C2×D4×D6111yescharacteristic
551C2×C4C22×C22⋊D6111yescharacteristic
552C2×C4#1451982211yescharacteristic
553C8—21no—
554C8—21no—
555C8—41no—
556C8—1221no—
557C8—1221no—
558C8—2441no—
559C8—2441no—
560C8—2441no—
561C8—2441no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—9764no—
566C22—4881no—
567C22—4881no—
568C22—4881no—
569C22—2441no—
570C22—2441no—
571C22—2441no—
572C22D4×C22⋊D6111yescharacteristic
573C4—21no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—81no—
580C4—81no—
581C4—4881no—
582C4—2441no—
583C4#1684055911yescharacteristic
584C4#1684056011yescharacteristic
585C4#1684056411yescharacteristic
586C4#1684057011yescharacteristic
587C2—81no—
588C2—9761no—
589C2—4881no—
590C2#2145735911yescharacteristic
591C2#2145745111yescharacteristic
592C2#2145759011yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3364C2
socleC22×C61D42
prime radicalD4×D244C22
hypercenter#3364D61
hypocenterC61#20267
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3364

Complements

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

NH ≅ G/Ntype
1. #21458846C2semidirect
4. #21445476C2semidirect
5. #21445389C2semidirect
6. #21445363C2semidirect
7. #21445306C2semidirect
8. #21445263C2semidirect
9. #21445089C2semidirect
10. #21445087C2semidirect
12. #21444915C2semidirect
13. #21444722C2semidirect
14. #21444662C2semidirect
15. C61×#3364C2semidirect
18. #16840158C22semidirect
20. #16840141C22semidirect
31. #16839972C22semidirect
38. #16839893C22semidirect
45. #16839515C22semidirect
46. #16839512C22semidirect
47. #16839508C22semidirect
48. #16839508C22semidirect
49. #16839507C22semidirect
51. Q8⋊#92418C22semidirect
52. Q8⋊#92418C22semidirect
55. #16839483C22semidirect
56. C61×#557C22semidirect
59. C61×#487C22semidirect
63. C61×#462C22semidirect
64. C8×Q8×C61C22semidirect
292. #3364D61semidirect
312. #557C2×D61semidirect
320. #487C2×D61semidirect
336. #462C2×D61semidirect
343. C8×Q8C2×D61semidirect
363. C61#20267semidirect

Maximal subgroups

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

subgroupindex
#214588462
#214580522
#214580442
#214454762
#214453892
#214453632
#214453062
#214452632
#214450892
#214450872
#214449972
#214449152
#214447222
#214446622
C61×#33642
#2026761