Finite Group Databasebeta

← #29676413

Subgroups — #29676413

Order 15616.

658 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458063C211yesmaximal, characteristic, complemented
2#21458044C211yesmaximal, characteristic, complemented
3#21457769C211yesmaximal, characteristic, complemented
4#21445456C211yesmaximal, characteristic, complemented
5#21445359C211yesmaximal, characteristic, complemented
6#21445350C211yesmaximal, characteristic, complemented
7#21445281C211yesmaximal, characteristic, complemented
8#21445258C211yesmaximal, characteristic, complemented
9#21445045C211yesmaximal, characteristic, complemented
10#21444991C211yesmaximal, characteristic, complemented
11#21444884C211yesmaximal, characteristic, complemented
12#21444872C211yesmaximal, characteristic, complemented
13#21444719C211yesmaximal, characteristic, complemented
14#21444649C211yesmaximal, characteristic, complemented
15C61×#3397C211yesmaximal, characteristic, complemented
16#16840477C2211yescharacteristic
17D4×D244C2211yescharacteristic
18#16840138C2211yescharacteristic
19#16840114C2211yescharacteristic, complemented
20#16840110C2211yescharacteristic
21#16840109C2211yescharacteristic
22#16840108C2211yescharacteristic, complemented
23#16840089—21no—
24#16840086—21no—
25#16840083—21no—
26#16840057C2211yescharacteristic, complemented
27#16840052C2211yescharacteristic
28#16840039C2211yescharacteristic
29#16840014—21no—
30#16840010—21no—
31#16839996—21no—
32#16839962C2211yescharacteristic
33#16839957C2211yescharacteristic
34#16839954C2211yescharacteristic
35#16839912—21no—
36#16839907—21no—
37#16839894—21no—
38C4×#11758201C2211yescharacteristic
39#16839841C2211yescharacteristic
40#16839840C2211yescharacteristic
41D4×#92418C2211yescharacteristic, complemented
42#16839766—21no—
43#16839765—21no—
44#16839758—21no—
45#16839515C2211yescharacteristic, complemented
46#16839514C2211yescharacteristic, complemented
47#16839510C2211yescharacteristic, complemented
48#16839508C2211yescharacteristic, complemented
49#16839506C2211yescharacteristic, complemented
50#16839505C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic, complemented
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic, complemented
54#16839489C2211yescharacteristic
55#16839484C2211yescharacteristic, complemented
56C61×#556C2211yescharacteristic
57C61×#550C2211yescharacteristic, complemented
58C61×#496—21no—
59C61×#492C2211yescharacteristic, complemented
60C61×#463—21no—
61C61×#461C2211yescharacteristic, complemented
62C61×#460—21no—
63C61×#459C2211yescharacteristic
64C61×#446C2211yescharacteristic, complemented
65C61×#440—21no—
66C4×D8×C61C2211yescharacteristic
67C22×D244—21no—
68C2×D4×D61—21no—
69C2×#11758201—21no—
70C2×#11758201D411yescharacteristic
71C2×#11758199—21no—
72C2×#11758199—21no—
73C2×#11758199—41no—
74C2×#11758194—21no—
75C2×#11758189—21no—
76C22×#92418—21no—
77#14519777C2311yescharacteristic
78#14519774C2311yescharacteristic
79#14519763—41no—
80#14519752—21no—
81#14519751—21no—
82#14519751—21no—
83#14519748—21no—
84#14519747—41no—
85C4×D244C2311yescharacteristic
86#14519736—21no—
87#14519735—21no—
88#14519710—21no—
89#14519710—21no—
90#14519708—21no—
91#14519708D411yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95#14519701—21no—
96#14519701D411yescharacteristic
97#14519700—41no—
98#14519699—21no—
99#14519699—21no—
100#14519698—21no—
101#14519698—21no—
102#14519698—21no—
103#14519698—21no—
104#14519697—21no—
105#14519697—21no—
106#14519697—21no—
107#14519697—21no—
108#14519697—21no—
109#14519697D411yescharacteristic
110C22⋊#92418—21no—
111C22⋊#92418—21no—
112#14519689—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×#41×C61—21no—
116C2×SD16×C61—21no—
117C2×SD16×C61—21no—
118C2×SD16×C61—21no—
119C2×D8×C61—21no—
120C2×D8×C61D411yescharacteristic
121C4⋊Q8×C61C2311yescharacteristic
122#127×C61—21no—
123#127×C61C2311yescharacteristic
124#126×C61—41no—
125#124×C61—21no—
126C22⋊Q8×C61—21no—
127#121×C61—21no—
128#121×C61—41no—
129C4×Q8×C61—21no—
130C4×Q8×C61C2311yescharacteristic
131C4×D4×C61—21no—
132C4×D4×C61C2311yescharacteristic
133C4×D4×C61C2311yescharacteristic
134#117×C61—21no—
135#107×C61D411yescharacteristic
136C4⋊C8×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
138#103×C61—21no—
139#102×C61—21no—
140#102×C61D411yescharacteristic
141#102×C61D411yescharacteristic
142#97×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C23×D61—41no—
145#41×C61—42no—
146#41×C61—81no—
147C2×Q8×C61—21no—
148C2×Q8×C61C2×D411yescharacteristic
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—41no—
153C2×D4×C61—41no—
154C2×D4×C61C2×D411yescharacteristic
155C2×D4×C61C2×D411yescharacteristic
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—41no—
159C2×C22⋊D61—41no—
160C2×C22⋊D61—41no—
161D4×D61—42no—
162D4×D61—81no—
163C2×D244—21no—
164C2×D244—21no—
165C2×D244—21no—
166C2×D244—42no—
167C2×D244—41no—
168C2×D244—81no—
169C2×D244C2×D411yescharacteristic
170C2×C4×D61—21no—
171C2×Dic122—21no—
172SD16×C61—42no—
173SD16×C61—81no—
174SD16×C61—81no—
175D8×C61—41no—
176D8×C61—81no—
177C2×C8×C61—21no—
178C2×C8×C61C2×D411yescharacteristic
179C2×C8×C61C2×D411yescharacteristic
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—41no—
184C4⋊C4×C61C2×D411yescharacteristic
185C4⋊C4×C61C2×D411yescharacteristic
186C4⋊C4×C61C2×D411yescharacteristic
187C22⋊C4×C61—21no—
188C22⋊C4×C61—21no—
189C22⋊C4×C61—41no—
190C22⋊C4×C61—41no—
191C22⋊C4×C61—41no—
192C42×C61—21no—
193C42×C61—41no—
194C42×C61C2411yescharacteristic
195C22⋊Dic61—41no—
196#11758201—41no—
197#11758201—81no—
198#11758199—81no—
199#11758199—81no—
200#11758199—82no—
201#11758198—21no—
202#11758198—41no—
203#11758198—41no—
204C4⋊Dic61—21no—
205C4⋊Dic61—21no—
206C4⋊Dic61C2×D411yescharacteristic
207C4×Dic61—41no—
208#11758194—81no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—81no—
214C2×#92418C2×D411yescharacteristic
215C2×#92418C2×D411yescharacteristic
216#11758189—81no—
217C23×C61—21no—
218C23×C61—21no—
219C23×C61—41no—
220C22×D61—21no—
221C22×D61—41no—
222C22×D61—82no—
223C22×D61—82no—
224C22×D61—161no—
225Q8×C61—21no—
226Q8×C61—21no—
227Q8×C61—41no—
228Q8×C61—41no—
229D4×C61—21no—
230D4×C61—21no—
231D4×C61—21no—
232D4×C61—21no—
233D4×C61—41no—
234D4×C61—41no—
235D4×C61—41no—
236D4×C61—41no—
237D4×C61—81no—
238D4×C61—82no—
239D4×C61—161no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—82no—
250C2×C4×C61C22×D411yescharacteristic
251C2×C4×C61C22×D411yescharacteristic
252C2×C4×C61H(5,𝔽2)11yescharacteristic
253C22⋊D61—82no—
254C22⋊D61—161no—
255C2×Dic61—21no—
256C2×Dic61—41no—
257D244—21no—
258D244—21no—
259D244—41no—
260D244—41no—
261D244—41no—
262D244—41no—
263D244—81no—
264D244—82no—
265C4×D61—41no—
266C4×D61—41no—
267Dic122—81no—
268C8×C61—21no—
269C8×C61—21no—
270C8×C61—41no—
271#92418—21no—
272#92418—21no—
273#92418—41no—
274#92418—41no—
275#92418—41no—
276#92418—41no—
277#20258—611nomaximal, Sylow
278C22×C61—41no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—81no—
285C22×C61—81no—
286C22×C61—81no—
287C22×C61D4211yescharacteristic
288C2×D61—41no—
289C2×D61—41no—
290C2×D61—41no—
291C2×D61—81no—
292C2×D61—81no—
293C2×D61—81no—
294C2×D61—164no—
295C4×C61—21no—
296C4×C61—41no—
297C4×C61—41no—
298C4×C61—41no—
299C4×C61—41no—
300C4×C61—81no—
301C4×C61#57511yescharacteristic
302C4×C61#57511yescharacteristic
303C4×C61#57611yescharacteristic
304C4×C61#57611yescharacteristic
305Dic61—41no—
306Dic61—81no—
307#3397D6111yescharacteristic, complemented
308#3325—611no—
309#3324—611no—
310#3305—611no—
311#1717—611no—
312#1698—611no—
313#1697—611no—
314#1685—611no—
315#1681—611no—
316#1646—611no—
317#1638—611no—
318#1621—611no—
319#1619—611no—
320#1592—611no—
321#1581—611no—
322C2×C61—81no—
323C2×C61—81no—
324C2×C61—161no—
325C2×C61#326811yescharacteristic
326C2×C61#327311yescharacteristic
327C2×C61#328811yescharacteristic
328D61—81no—
329D61—161no—
330#556C2×D6111yescharacteristic
331#555—611no—
332#550C2×D6111yescharacteristic, complemented
333D42—611no—
334#496—21no—
335#493—611no—
336#492C2×D6111yescharacteristic, complemented
337#487—611no—
338#486—611no—
339#486—611no—
340#486—611no—
341#482—1221no—
342#482—1221no—
343#482—1221no—
344#477—611no—
345#476—611no—
346#474—611no—
347#469—1221no—
348#468—1221no—
349#466—1221no—
350#463—21no—
351#461C2×D6111yescharacteristic, complemented
352#460—21no—
353#460—611no—
354#459—611no—
355#459—611no—
356#459C2×D6111yescharacteristic
357#450—1221no—
358#449—1221no—
359#447—1221no—
360#446C2×D6111yescharacteristic, complemented
361#440—21no—
362C4×SD16—611no—
363C4×D8C2×D6111yescharacteristic
364#436—611no—
365#436—611no—
366C8×D4—611no—
367#418—1221no—
368#418—1221no—
369#416—1221no—
370#335—611no—
371#335—611no—
372#333—611no—
373#332—611no—
374#331—611no—
375#331—611no—
376Q8⋊C8—611no—
377D4⋊C8—611no—
378D4⋊C8—611no—
379D4⋊C8—611no—
380#322—611no—
381C61#2025811yescharacteristic, complemented, Sylow
382C2×#41—21no—
383C22×D4—1221no—
384C22×D4—1221no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×SD16—21no—
388C2×SD16—611no—
389C2×SD16—1221no—
390C2×D8—21no—
391C2×D8—1221no—
392C2×D8—1221no—
393C2×D8—2441no—
394C2×D8C22⋊D6111yescharacteristic
395C2×M16—1221no—
396C2×M16—1221no—
397C22×C8—1221no—
398C4⋊Q8—611no—
399C4⋊Q8C22×D6111yescharacteristic
400#127—21no—
401#127—611no—
402#127C22×D6111yescharacteristic
403#126—41no—
404#124—21no—
405#124—2441no—
406C22⋊Q8—21no—
407#121—21no—
408#121—41no—
409#121—1221no—
410#121—1221no—
411#121—1221no—
412#121—1221no—
413#120—2441no—
414C4×Q8—21no—
415C4×Q8C22×D6111yescharacteristic
416C4×D4—21no—
417C4×D4—611no—
418C4×D4C22×D6111yescharacteristic
419C4×D4C22×D6111yescharacteristic
420#117—21no—
421#117—1221no—
422#117—1221no—
423#107—1221no—
424#107—1221no—
425#107C22⋊D6111yescharacteristic
426#106—611no—
427#106—1221no—
428C4⋊C8—21no—
429C4⋊C8—611no—
430C4⋊C8—611no—
431C4⋊C8—611no—
432C4⋊C8C22×D6111yescharacteristic
433#103—21no—
434#103—611no—
435#103—1221no—
436#103—2441no—
437#102—21no—
438#102—611no—
439#102—1221no—
440#102—1221no—
441#102—1221no—
442#102—1221no—
443#102—1221no—
444#102—1221no—
445#102—1221no—
446#102—1221no—
447#102—1221no—
448#102—1221no—
449#102—1221no—
450#102C22⋊D6111yescharacteristic
451#102C22⋊D6111yescharacteristic
452C22⋊C8—1221no—
453C22⋊C8—1221no—
454C22⋊C8—1221no—
455#97—21no—
456C4×C8—611no—
457C4×C8—611no—
458C4×C8C22×D6111yescharacteristic
459C24—2441no—
460#41—42no—
461#41—81no—
462C2×Q8—21no—
463C2×Q8—1221no—
464C2×Q8D4×D6111yescharacteristic
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—611no—
471C2×D4—1221no—
472C2×D4—1221no—
473C2×D4—1221no—
474C2×D4—4881no—
475C2×D4—4881no—
476C2×D4—2441no—
477C2×D4—2442no—
478C2×D4—2441no—
479C2×D4—2442no—
480C2×D4—2441no—
481C2×D4C2×C22⋊D6111yescharacteristic
482C2×D4C2×C22⋊D6111yescharacteristic
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—41no—
486C22×C4—1221no—
487SD16—42no—
488SD16—81no—
489SD16—81no—
490SD16—4881no—
491SD16—2441no—
492D8—41no—
493D8—81no—
494D8—4881no—
495D8—4881no—
496D8—4882no—
497M16—4881no—
498M16—4881no—
499C2×C8—21no—
500C2×C8—611no—
501C2×C8—611no—
502C2×C8—1221no—
503C2×C8—1221no—
504C2×C8—1221no—
505C2×C8—1221no—
506C2×C8—4881no—
507C2×C8C2×C22⋊D6111yescharacteristic
508C2×C8C2×C22⋊D6111yescharacteristic
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—41no—
513C4⋊C4—611no—
514C4⋊C4—1221no—
515C4⋊C4—1221no—
516C4⋊C4D4×D6111yescharacteristic
517C4⋊C4C2×C22⋊D6111yescharacteristic
518C4⋊C4C2×C22⋊D6111yescharacteristic
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—1221no—
525C22⋊C4—2441no—
526C22⋊C4—2441no—
527C22⋊C4—2441no—
528C42—21no—
529C42—41no—
530C42—2441no—
531C42C23×D6111yescharacteristic
532C23—21no—
533C23—21no—
534C23—41no—
535C23—1221no—
536C23—9761no—
537C23—4882no—
538C23—4882no—
539C23—2441no—
540Q8—21no—
541Q8—21no—
542Q8—41no—
543Q8—41no—
544Q8—4881no—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—21no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—81no—
554D4—82no—
555D4—161no—
556D4—1221no—
557D4—1221no—
558D4—9761no—
559D4—4881no—
560D4—4882no—
561D4—4882no—
562D4—2441no—
563D4—2441no—
564D4—2441no—
565D4—2441no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—82no—
576C2×C4—1221no—
577C2×C4—2441no—
578C2×C4—2441no—
579C2×C4—2441no—
580C2×C4C2×D4×D6111yescharacteristic
581C2×C4C22×C22⋊D6111yescharacteristic
582C2×C4#1451982211yescharacteristic
583C8—21no—
584C8—21no—
585C8—41no—
586C8—1221no—
587C8—1221no—
588C8—2441no—
589C8—2441no—
590C8—2441no—
591C8—2441no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—9764no—
602C22—4881no—
603C22—4881no—
604C22—4881no—
605C22—2441no—
606C22—2441no—
607C22—2441no—
608C22D4×C22⋊D6111yescharacteristic
609C4—21no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—41no—
614C4—81no—
615C4—4881no—
616C4—2441no—
617C4#1684055811yescharacteristic
618C4#1684056011yescharacteristic
619C4#1684056511yescharacteristic
620C4#1684056611yescharacteristic
621C2—81no—
622C2—81no—
623C2—161no—
624C2—9761no—
625C2—4881no—
626C2#2145736011yescharacteristic
627C2#2145742411yescharacteristic
628C2#2145758111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3397C2
socleC22×C61D42
hypercenter#3397D61
hypocenterC61#20258
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3397

Complements

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

NH ≅ G/Ntype
1. #21458063C2semidirect
2. #21458044C2semidirect
3. #21457769C2semidirect
4. #21445456C2semidirect
5. #21445359C2semidirect
6. #21445350C2semidirect
7. #21445281C2semidirect
8. #21445258C2semidirect
9. #21445045C2semidirect
10. #21444991C2semidirect
11. #21444884C2semidirect
12. #21444872C2semidirect
13. #21444719C2semidirect
14. #21444649C2semidirect
15. C61×#3397C2semidirect
19. #16840114C22semidirect
22. #16840108C22semidirect
26. #16840057C22semidirect
41. D4×#92418C22semidirect
45. #16839515C22semidirect
46. #16839514C22semidirect
47. #16839510C22semidirect
48. #16839508C22semidirect
49. #16839506C22semidirect
51. Q8⋊#92418C22semidirect
53. D4⋊#92418C22semidirect
55. #16839484C22semidirect
57. C61×#550C22semidirect
59. C61×#492C22semidirect
61. C61×#461C22semidirect
64. C61×#446C22semidirect
307. #3397D61semidirect
332. #550C2×D61semidirect
336. #492C2×D61semidirect
351. #461C2×D61semidirect
360. #446C2×D61semidirect
381. C61#20258semidirect

Maximal subgroups

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

subgroupindex
#214580632
#214580442
#214577692
#214454562
#214453592
#214453502
#214452812
#214452582
#214450452
#214449912
#214448842
#214448722
#214447192
#214446492
C61×#33972
#2025861