Finite Group Databasebeta

← #29676548

Subgroups — #29676548

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#21458504C211yesmaximal, characteristic, complemented
2#21458052C211yesmaximal, characteristic
3#21458044C211yesmaximal, characteristic
4#21445482C211yesmaximal, characteristic, complemented
5#21445387C211yesmaximal, characteristic, complemented
6#21445368C211yesmaximal, characteristic, complemented
7#21445305C211yesmaximal, characteristic, complemented
8#21445265C211yesmaximal, characteristic, complemented
9#21445089C211yesmaximal, characteristic, complemented
10#21445087C211yesmaximal, characteristic, complemented
11#21444996C211yesmaximal, characteristic
12#21444915C211yesmaximal, characteristic, complemented
13#21444719C211yesmaximal, characteristic, complemented
14#21444663C211yesmaximal, characteristic, complemented
15C61×#3398C211yesmaximal, characteristic, complemented
16#16840485C2211yescharacteristic
17D4×D244C2211yescharacteristic
18#16840158C2211yescharacteristic, complemented
19#16840119—21no—
20#16840114C2211yescharacteristic, complemented
21#16840110C2211yescharacteristic
22#16840110C2211yescharacteristic
23#16840109C2211yescharacteristic
24#16840088—21no—
25#16840086—21no—
26#16840066—21no—
27#16840042C2211yescharacteristic
28#16840039C2211yescharacteristic
29#16840039C2211yescharacteristic
30#16840011—21no—
31#16840010—21no—
32#16839984—21no—
33#16839972C2211yescharacteristic, complemented
34#16839962C2211yescharacteristic
35#16839962C2211yescharacteristic
36#16839912—21no—
37#16839911—21no—
38Q8×#92418C2211yescharacteristic, complemented
39C4×#11758202—21no—
40C4×#11758201C2211yescharacteristic
41#16839841C2211yescharacteristic
42#16839840C2211yescharacteristic
43#16839766—21no—
44#16839765—21no—
45#16839514C2211yescharacteristic, complemented
46#16839513C2211yescharacteristic, complemented
47#16839508C2211yescharacteristic, complemented
48#16839508C2211yescharacteristic, complemented
49#16839507C2211yescharacteristic, complemented
50#16839505C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic, complemented
52Q8⋊#92418C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55#16839484C2211yescharacteristic, complemented
56C61×#557C2211yescharacteristic, complemented
57C61×#556C2211yescharacteristic
58C61×#497—21no—
59C61×#494C2211yescharacteristic, complemented
60C61×#464—21no—
61C61×#462—21no—
62C61×#462C2211yescharacteristic, complemented
63C61×#461C2211yescharacteristic
64C61×#446C2211yescharacteristic, complemented
65C61×#441—21no—
66C4×SD16×C61C2211yescharacteristic
67C22×D244—21no—
68C2×D4×D61—21no—
69C2×#11758202—21no—
70C2×#11758201—21no—
71C2×#11758201—21no—
72C2×#11758201D411yescharacteristic
73C2×#11758194—21no—
74C2×#11758189—21no—
75#14519777C2311yescharacteristic
76#14519774C2311yescharacteristic
77#14519772—41no—
78#14519765—21no—
79#14519753—21no—
80#14519752—21no—
81#14519751—21no—
82#14519747—41no—
83C4×Dic122—21no—
84C4×D244C2311yescharacteristic
85#14519735—21no—
86#14519710—21no—
87#14519710—21no—
88#14519710—21no—
89#14519708—41no—
90#14519708D411yescharacteristic
91C4⋊#92418—21no—
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95#14519701D411yescharacteristic
96#14519700—21no—
97#14519700—21no—
98#14519700—21no—
99#14519699—21no—
100#14519699—21no—
101#14519698—21no—
102#14519697—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—
112C4×#92418—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×Q16×C61—21no—
116C2×Q16×C61—21no—
117C2×Q16×C61—21no—
118C2×SD16×C61—21no—
119C2×SD16×C61D411yescharacteristic
120C4⋊Q8×C61—21no—
121C4⋊Q8×C61C2311yescharacteristic
122C4⋊Q8×C61C2311yescharacteristic
123#126×C61—41no—
124#125×C61—21no—
125#125×C61—41no—
126#124×C61—21no—
127C22⋊Q8×C61—21no—
128C4×Q8×C61—21no—
129C4×Q8×C61—21no—
130C4×Q8×C61—21no—
131C4×Q8×C61C2311yescharacteristic
132C4×Q8×C61C2311yescharacteristic
133C4×D4×C61C2311yescharacteristic
134#117×C61—21no—
135#106×C61D411yescharacteristic
136C4⋊C8×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
138#103×C61—21no—
139#103×C61—21no—
140#103×C61D411yescharacteristic
141#102×C61D411yescharacteristic
142#97×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—
164Q16×C61—81no—
165Q16×C61—81no—
166SD16×C61—41no—
167SD16×C61—81no—
168C2×C8×C61—21no—
169C2×C8×C61C2×D411yescharacteristic
170C2×C8×C61C2×D411yescharacteristic
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—41no—
178C4⋊C4×C61—41no—
179C4⋊C4×C61—41no—
180C4⋊C4×C61—41no—
181C4⋊C4×C61C2×D411yescharacteristic
182C4⋊C4×C61C2×D411yescharacteristic
183C4⋊C4×C61C2×D411yescharacteristic
184C22⋊C4×C61—21no—
185C22⋊C4×C61—41no—
186C22⋊C4×C61—41no—
187C42×C61—21no—
188C42×C61—21no—
189C42×C61—41no—
190C42×C61—41no—
191C42×C61C2411yescharacteristic
192#11758202—42no—
193#11758201—41no—
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#3398D6111yescharacteristic, complemented
292#3364—611no—
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—21no—
318#494C2×D6111yescharacteristic, complemented
319#488—1221no—
320#487—611no—
321#486—611no—
322#486—611no—
323#486—611no—
324#482—1221no—
325#482—1221no—
326#479—1221no—
327#474—611no—
328#474—611no—
329#474—611no—
330#468—1221no—
331#468—1221no—
332#464—21no—
333#464—1221no—
334#462—21no—
335#462—611no—
336#462C2×D6111yescharacteristic, complemented
337#461C2×D6111yescharacteristic
338#460—611no—
339#460—611no—
340#450—1221no—
341#450—1221no—
342#446C2×D6111yescharacteristic, complemented
343C8×Q8—611no—
344#441—21no—
345C4×Q16—1221no—
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—21no—
368C2×Q16—21no—
369C2×Q16—1221no—
370C2×SD16—21no—
371C2×SD16—611no—
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—1221no—
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—611no—
418#103—1221no—
419#103—1221no—
420#103—1221no—
421#103C22⋊D6111yescharacteristic
422#102—611no—
423#102—1221no—
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—21no—
437C4×C8—611no—
438C4×C8—611no—
439C4×C8—1221no—
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—81no—
462Q16—81no—
463Q16—2442no—
464SD16—41no—
465SD16—81no—
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#1684056011yescharacteristic
584C4#1684056111yescharacteristic
585C4#1684056511yescharacteristic
586C4#1684057111yescharacteristic
587C2—81no—
588C2—9761no—
589C2—4881no—
590C2#2145736011yescharacteristic
591C2#2145744411yescharacteristic
592C2#2145759011yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3398C2
socleC22×C61D42
prime radicalD4×D244C22
hypercenter#3398D61
hypocenterC61#20267
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3398

Complements

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

NH ≅ G/Ntype
1. #21458504C2semidirect
4. #21445482C2semidirect
5. #21445387C2semidirect
6. #21445368C2semidirect
7. #21445305C2semidirect
8. #21445265C2semidirect
9. #21445089C2semidirect
10. #21445087C2semidirect
12. #21444915C2semidirect
13. #21444719C2semidirect
14. #21444663C2semidirect
15. C61×#3398C2semidirect
18. #16840158C22semidirect
20. #16840114C22semidirect
33. #16839972C22semidirect
38. Q8×#92418C22semidirect
45. #16839514C22semidirect
46. #16839513C22semidirect
47. #16839508C22semidirect
48. #16839508C22semidirect
49. #16839507C22semidirect
51. Q8⋊#92418C22semidirect
52. Q8⋊#92418C22semidirect
55. #16839484C22semidirect
56. C61×#557C22semidirect
59. C61×#494C22semidirect
62. C61×#462C22semidirect
64. C61×#446C22semidirect
291. #3398D61semidirect
312. #557C2×D61semidirect
318. #494C2×D61semidirect
336. #462C2×D61semidirect
342. #446C2×D61semidirect
363. C61#20267semidirect

Maximal subgroups

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

subgroupindex
#214585042
#214580522
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