Finite Group Databasebeta

← #29836775

Subgroups — #29836775

Order 15616.

640 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458970C211yesmaximal, characteristic, complemented
2#21458963C211yesmaximal, characteristic, complemented
3#21457606C211yesmaximal, characteristic, complemented
4#21448088C211yesmaximal, characteristic, complemented
5#21447951C211yesmaximal, characteristic, complemented
6#21447942C211yesmaximal, characteristic, complemented
7#21447897C211yesmaximal, characteristic, complemented
8#21447888C211yesmaximal, characteristic, complemented
9#21447797C211yesmaximal, characteristic, complemented
10#21447795C211yesmaximal, characteristic, complemented
11#21447788C211yesmaximal, characteristic, complemented
12#21447783C211yesmaximal, characteristic, complemented
13#21447703C211yesmaximal, characteristic, complemented
14#21447661C211yesmaximal, characteristic, complemented
15C61×#3293C211yesmaximal, characteristic, complemented
16#16840579C2211yescharacteristic
17#16840569—21no—
18#16840567C2211yescharacteristic
19#16840203—21no—
20#16840203—21no—
21#16840203C2211yescharacteristic
22#16840203C2211yescharacteristic
23#16840202—21no—
24#16840202C2211yescharacteristic, complemented
25#16840197—21no—
26#16840197C2211yescharacteristic
27#16840192—21no—
28#16840192—21no—
29#16840192C2211yescharacteristic
30C2×#14519723—21no—
31C2×#14519723C2211yescharacteristic, complemented
32C2×#14519723C2211yescharacteristic, complemented
33C2×#14519720—21no—
34C2×#14519720C2211yescharacteristic
35C2×#14519720C2211yescharacteristic
36#16840179C2211yescharacteristic
37#16840179C2211yescharacteristic, complemented
38#16840146C2211yescharacteristic
39#16840037C2211yescharacteristic
40#16840032C2211yescharacteristic
41#16840026—21no—
42#16839941—21no—
43#16839936—21no—
44#16839880C2211yescharacteristic
45#16839591C2211yescharacteristic, complemented
46#16839583C2211yescharacteristic, complemented
47#16839578C2211yescharacteristic, complemented
48#16839578C2211yescharacteristic, complemented
49#16839577C2211yescharacteristic, complemented
50#16839574C2211yescharacteristic
51#16839569C2211yescharacteristic, complemented
52#16839568C2211yescharacteristic
53#16839546C2211yescharacteristic
54#16839546C2211yescharacteristic, complemented
55#16839538C2211yescharacteristic, complemented
56C61×#578—21no—
57C61×#578C2211yescharacteristic
58C61×#578C2211yescharacteristic, complemented
59C61×#494C2211yescharacteristic, complemented
60C61×#473—21no—
61C61×#473C2211yescharacteristic
62C61×#473C2211yescharacteristic, complemented
63C61×#456—21no—
64C61×#456—21no—
65C61×#443C2211yescharacteristic
66C61×#443C2211yescharacteristic, complemented
67#14519824—21no—
68#14519823—21no—
69#14519810—21no—
70#14519810—41no—
71#14519809—41no—
72#14519807—21no—
73#14519805—21no—
74#14519805—41no—
75#14519802—21no—
76#14519801—41no—
77#14519799—21no—
78#14519799—21no—
79#14519799C2311yescharacteristic
80#14519798—41no—
81C2×Dic244—21no—
82C2×Dic244C2311yescharacteristic
83C2×#11758190—21no—
84SD16×D61—41no—
85C2×D488—21no—
86C2×D488C2311yescharacteristic
87#14519783—21no—
88#14519765—21no—
89#14519723—21no—
90#14519723—21no—
91#14519723—21no—
92#14519723—21no—
93#14519723—21no—
94#14519723—41no—
95#14519723D411yescharacteristic
96#14519721—21no—
97#14519721D411yescharacteristic
98#14519720—21no—
99#14519720—21no—
100#14519720—21no—
101#14519720—21no—
102#14519720—21no—
103#14519720—41no—
104#14519720D411yescharacteristic
105#14519718—21no—
106#14519718D411yescharacteristic
107#14519717—21no—
108#14519717—21no—
109#14519717C2311yescharacteristic
110#14519717C2311yescharacteristic
111C2×#11758185—21no—
112C2×#11758185—21no—
113C2×#11758185C2311yescharacteristic
114C2×#11758185C2311yescharacteristic
115#14519713C2311yescharacteristic
116#14519705—21no—
117#14519695—21no—
118#14519693—21no—
1192−1+4×C61—21no—
1202−1+4×C61—21no—
121#137×C61—21no—
122#137×C61—21no—
123#137×C61—21no—
124#137×C61—21no—
125#137×C61—41no—
126#137×C61—41no—
127#137×C61—41no—
128#137×C61—41no—
129#135×C61—21no—
130#135×C61—21no—
131#135×C61—41no—
132#135×C61D411yescharacteristic
133#135×C61C2311yescharacteristic
134C2×Q16×C61—21no—
135C2×Q16×C61—21no—
136C2×Q16×C61—21no—
137C2×Q16×C61—41no—
138C2×Q16×C61C2311yescharacteristic
139C2×Q16×C61C2311yescharacteristic
140#131×C61—21no—
141#131×C61C2311yescharacteristic
142#131×C61C2311yescharacteristic
143C4⋊Q8×C61—21no—
144#108×C61D411yescharacteristic
145#108×C61C2311yescharacteristic
146#104×C61—21no—
147#104×C61D411yescharacteristic
148#104×C61D411yescharacteristic
149#101×C61—21no—
150#101×C61—21no—
151C4×C8×C61C2311yescharacteristic
152#41×C61—21no—
153#41×C61—41no—
154#41×C61—41no—
155#41×C61—41no—
156#41×C61—41no—
157#41×C61—81no—
158#41×C61—81no—
159#41×C61C2×D411yescharacteristic
160#41×C61C2×D411yescharacteristic
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—41no—
164C2×Q8×C61—41no—
165C2×Q8×C61—41no—
166C2×Q8×C61—41no—
167#11758226—41no—
168Q8×D61—41no—
169#11758224—41no—
170#11758224—81no—
171D4×D61—41no—
172D4×D61—81no—
173#11758222—21no—
174#11758222—41no—
175#11758222—41no—
176C2×D244—21no—
177C2×D244—41no—
178C2×Dic122—21no—
179C2×Dic122—41no—
180Q16×C61—21no—
181Q16×C61—21no—
182Q16×C61—21no—
183Q16×C61—21no—
184Q16×C61—41no—
185Q16×C61—41no—
186Q16×C61—41no—
187Q16×C61—41no—
188Q16×C61—41no—
189Q16×C61—41no—
190Q16×C61D811yescharacteristic
191Q16×C61C2×D411yescharacteristic
192SD16×C61—21no—
193SD16×C61—41no—
194SD16×C61—41no—
195SD16×C61—41no—
196SD16×C61—41no—
197SD16×C61D811yescharacteristic
198SD16×C61D811yescharacteristic
199D8×C61D811yescharacteristic
200D8×C61C2×D411yescharacteristic
201M16×C61—21no—
202M16×C61—21no—
203M16×C61—21no—
204M16×C61—41no—
205M16×C61C2×D411yescharacteristic
206M16×C61C2×D411yescharacteristic
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—41no—
210C2×C8×C61C2×D411yescharacteristic
211C2×C8×C61C2411yescharacteristic
212C4⋊C4×C61—81no—
213C42×C61C2×D411yescharacteristic
214#11758202—41no—
215#11758201—41no—
216#11758200—41no—
217#11758199—41no—
218#11758198—81no—
219#11758194—21no—
220Dic244—21no—
221Dic244—21no—
222Dic244—41no—
223Dic244C2×D411yescharacteristic
224D488—21no—
225D488—21no—
226D488—41no—
227D488C2×D411yescharacteristic
228#11758190—21no—
229#11758190—41no—
230#11758190—41no—
231#11758190—41no—
232#11758190—41no—
233#11758189—41no—
234C8×D61—41no—
235#11758185—21no—
236#11758185—21no—
237#11758185—21no—
238#11758185C2×D411yescharacteristic
239#11758185C2×D411yescharacteristic
240C22×D61—41no—
241C22×D61—81no—
242Q8×C61—21no—
243Q8×C61—41no—
244Q8×C61—41no—
245Q8×C61—41no—
246Q8×C61—41no—
247Q8×C61—81no—
248Q8×C61—81no—
249Q8×C61C2×D811yescharacteristic
250Q8×C61C2×D811yescharacteristic
251D4×C61—21no—
252D4×C61—21no—
253D4×C61—21no—
254D4×C61—41no—
255D4×C61—81no—
256D4×C61—81no—
257D4×C61C2×D811yescharacteristic
258D4×C61C2×D811yescharacteristic
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—81no—
266C2×C4×C61—81no—
267C2×C4×C61—81no—
268C2×C4×C61—81no—
269C2×C4×C61C22×D411yescharacteristic
270C22⋊D61—41no—
271C22⋊D61—81no—
272C22⋊D61—81no—
273C2×Dic61—41no—
274C2×Dic61—81no—
275D244—21no—
276D244—41no—
277D244—41no—
278D244—81no—
279C4×D61—41no—
280C4×D61—81no—
281C4×D61—81no—
282Dic122—21no—
283Dic122—41no—
284Dic122—41no—
285Dic122—81no—
286C8×C61—21no—
287C8×C61—21no—
288C8×C61—41no—
289C8×C61C2×D811yescharacteristic
290C8×C61C2×D811yescharacteristic
291C8×C61C22×D411yescharacteristic
292C8×C61H(5,𝔽2)11yescharacteristic
293#92418—41no—
294#33855—611nomaximal, Sylow
295C22×C61—21no—
296C22×C61—21no—
297C22×C61—41no—
298C22×C61#57611yescharacteristic
299C2×D61—41no—
300C2×D61—81no—
301C2×D61—161no—
302C2×D61—321no—
303C4×C61—21no—
304C4×C61—21no—
305C4×C61—41no—
306C4×C61—41no—
307C4×C61—81no—
308C4×C61—81no—
309C4×C61D4211yescharacteristic
310C4×C61C22×D811yescharacteristic
311Dic61—41no—
312Dic61—81no—
313#3417—611no—
314#3416—611no—
315#3293D6111yescharacteristic, complemented
316#3290—611no—
317#2251—611no—
318#2223—611no—
319#2222—611no—
320#2214—611no—
321#2212—611no—
322#2195—611no—
323#2195—611no—
324#2194—611no—
325#2193—611no—
326#2179—611no—
327#2171—611no—
328C2×C61—21no—
329C2×C61—41no—
330C2×C61—41no—
331C2×C61—81no—
332C2×C61D4×D811yescharacteristic
333D61—81no—
334D61—161no—
335#578—21no—
336#578—611no—
337#578C2×D6111yescharacteristic
338#578C2×D6111yescharacteristic, complemented
339#577—1221no—
340#576—611no—
341#510—611no—
342#510—611no—
343#510—611no—
344#510—1221no—
345#510—1221no—
346#510—1221no—
347#509—611no—
348#509—1221no—
349#508—611no—
350#508—1221no—
351#508—1221no—
352C2×Q32—611no—
353C2×Q32—611no—
354C2×Q32—1221no—
355C2×SD32—611no—
356C2×SD32—611no—
357C2×SD32—1221no—
358#504—611no—
359#504—611no—
360#495—611no—
361#494C2×D6111yescharacteristic, complemented
362#473—21no—
363#473—611no—
364#473C2×D6111yescharacteristic
365#473C2×D6111yescharacteristic, complemented
366#472—611no—
367#471—1221no—
368#456—21no—
369#456—21no—
370#455—1221no—
371#454—1221no—
372#443—611no—
373#443C2×D6111yescharacteristic
374#443C2×D6111yescharacteristic, complemented
375#368—611no—
376#364—611no—
377#362—611no—
378#362—611no—
379#362—611no—
380#361—611no—
381#359—611no—
382#359—611no—
383#350—611no—
384#350—611no—
385#346—611no—
386C61#3385511yescharacteristic, complemented, Sylow
3872−1+4—21no—
3882−1+4—21no—
3892−1+4—1221no—
390H(5,𝔽2)—1221no—
391#137—21no—
392#137—21no—
393#137—21no—
394#137—21no—
395#137—41no—
396#137—41no—
397#137—41no—
398#137—41no—
399#137—1221no—
400#137—1221no—
401#137—2441no—
402#137—2441no—
403AGL(1,ℤ/8)—1221no—
404AGL(1,ℤ/8)—1221no—
405AGL(1,ℤ/8)—2441no—
406AGL(1,ℤ/8)—2441no—
407#135—21no—
408#135—21no—
409#135—41no—
410#135—611no—
411#135—1221no—
412#135—1221no—
413#135—2441no—
414#135C22⋊D6111yescharacteristic
415#135C22×D6111yescharacteristic
416C2×Q16—21no—
417C2×Q16—21no—
418C2×Q16—21no—
419C2×Q16—41no—
420C2×Q16—611no—
421C2×Q16—1221no—
422C2×Q16C22×D6111yescharacteristic
423C2×Q16C22×D6111yescharacteristic
424C2×SD16—1221no—
425C2×SD16—2441no—
426C2×D8—611no—
427C2×D8—1221no—
428#131—21no—
429#131—1221no—
430#131C22×D6111yescharacteristic
431#131C22×D6111yescharacteristic
432C4⋊Q8—21no—
433#124—1221no—
434Q32—611no—
435Q32—1221no—
436Q32—1221no—
437Q32—1221no—
438Q32—1221no—
439Q32—1221no—
440Q32—2441no—
441SD32—611no—
442SD32—611no—
443SD32—1221no—
444SD32—1221no—
445SD32—1221no—
446SD32—1221no—
447SD32—1221no—
448SD32—1221no—
449SD32—2441no—
450D16—611no—
451D16—1221no—
452M32—611no—
453M32—611no—
454M32—1221no—
455M32—1221no—
456C2×C16—611no—
457C2×C16—611no—
458C2×C16—1221no—
459C2×C16—1221no—
460#108—611no—
461#108C22⋊D6111yescharacteristic
462#108C22×D6111yescharacteristic
463#104—21no—
464#104—1221no—
465#104C22⋊D6111yescharacteristic
466#104C22⋊D6111yescharacteristic
467#101—21no—
468#101—21no—
469#101—1221no—
470#100—1221no—
471C4×C8C22×D6111yescharacteristic
472#41—21no—
473#41—41no—
474#41—41no—
475#41—41no—
476#41—41no—
477#41—81no—
478#41—81no—
479#41—1221no—
480#41—4881no—
481#41—2441no—
482#41—2441no—
483#41—2441no—
484#41—2441no—
485#41C2×C22⋊D6111yescharacteristic
486#41C2×C22⋊D6111yescharacteristic
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—41no—
490C2×Q8—41no—
491C2×Q8—41no—
492C2×Q8—41no—
493C2×Q8—1221no—
494C2×Q8—2441no—
495C2×Q8—2441no—
496C2×D4—1221no—
497C2×D4—4881no—
498C2×D4—2441no—
499C2×D4—2441no—
500Q16—21no—
501Q16—21no—
502Q16—21no—
503Q16—21no—
504Q16—41no—
505Q16—41no—
506Q16—41no—
507Q16—41no—
508Q16—41no—
509Q16—41no—
510Q16—611no—
511Q16—1221no—
512Q16—1221no—
513Q16—2441no—
514Q16—2441no—
515Q16#1175819911yescharacteristic
516Q16D4×D6111yescharacteristic
517SD16—21no—
518SD16—41no—
519SD16—41no—
520SD16—41no—
521SD16—41no—
522SD16—1221no—
523SD16—2441no—
524SD16—2441no—
525SD16—2441no—
526SD16—2441no—
527SD16—2441no—
528SD16—2441no—
529SD16#1175819911yescharacteristic
530SD16#1175819911yescharacteristic
531D8—611no—
532D8—1221no—
533D8—1221no—
534D8—2441no—
535D8—2441no—
536D8#1175819911yescharacteristic
537D8D4×D6111yescharacteristic
538M16—21no—
539M16—21no—
540M16—21no—
541M16—41no—
542M16—1221no—
543M16—2441no—
544M16C2×C22⋊D6111yescharacteristic
545M16C2×C22⋊D6111yescharacteristic
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—41no—
549C2×C8—2441no—
550C2×C8C2×C22⋊D6111yescharacteristic
551C2×C8C23×D6111yescharacteristic
552C4⋊C4—81no—
553C22⋊C4—4881no—
554C42C2×C22⋊D6111yescharacteristic
555C16—611no—
556C16—611no—
557C16—1221no—
558C16—1221no—
559C16—1221no—
560C23—4881no—
561C23—2441no—
562Q8—21no—
563Q8—41no—
564Q8—41no—
565Q8—41no—
566Q8—41no—
567Q8—81no—
568Q8—81no—
569Q8—1221no—
570Q8—4881no—
571Q8—2441no—
572Q8—2441no—
573Q8C2×#1175819911yescharacteristic
574Q8C2×#1175819911yescharacteristic
575D4—21no—
576D4—21no—
577D4—21no—
578D4—41no—
579D4—81no—
580D4—81no—
581D4—1221no—
582D4—4881no—
583D4—4881no—
584D4—4881no—
585D4—2441no—
586D4—2441no—
587D4—2441no—
588D4C2×#1175819911yescharacteristic
589D4C2×#1175819911yescharacteristic
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—81no—
597C2×C4—81no—
598C2×C4—81no—
599C2×C4—81no—
600C2×C4—4881no—
601C2×C4—4881no—
602C2×C4—4881no—
603C2×C4—2441no—
604C2×C4—2441no—
605C2×C4C22×C22⋊D6111yescharacteristic
606C8—21no—
607C8—21no—
608C8—41no—
609C8—2441no—
610C8C2×#1175819911yescharacteristic
611C8C2×#1175819911yescharacteristic
612C8C2×D4×D6111yescharacteristic
613C8#1451982211yescharacteristic
614C22—21no—
615C22—21no—
616C22—41no—
617C22—19521no—
618C22—9761no—
619C22—4881no—
620C22—2441no—
621C22#1684056511yescharacteristic
622C4—21no—
623C4—21no—
624C4—41no—
625C4—41no—
626C4—81no—
627C4—81no—
628C4—4881no—
629C4—2441no—
630C4D4×C22⋊D6111yescharacteristic
631C4C22×#1175819911yescharacteristic
632C2—21no—
633C2—41no—
634C2—41no—
635C2—81no—
636C2—9761no—
637C2—4881no—
638C2D4×#1175819911yescharacteristic
subgroupG/H
centerC2D4×#11758199
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#3293C2
socleC2×C61D4×D8
hypercenter#3293D61
hypocenterC61#33855
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443 ◁ #3293

Complements

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

NH ≅ G/Ntype
1. #21458970C2semidirect
2. #21458963C2semidirect
3. #21457606C2semidirect
4. #21448088C2semidirect
5. #21447951C2semidirect
6. #21447942C2semidirect
7. #21447897C2semidirect
8. #21447888C2semidirect
9. #21447797C2semidirect
10. #21447795C2semidirect
11. #21447788C2semidirect
12. #21447783C2semidirect
13. #21447703C2semidirect
14. #21447661C2semidirect
15. C61×#3293C2semidirect
24. #16840202C22semidirect
31. C2×#14519723C22semidirect
32. C2×#14519723C22semidirect
37. #16840179C22semidirect
45. #16839591C22semidirect
46. #16839583C22semidirect
47. #16839578C22semidirect
48. #16839578C22semidirect
49. #16839577C22semidirect
51. #16839569C22semidirect
54. #16839546C22semidirect
55. #16839538C22semidirect
58. C61×#578C22semidirect
59. C61×#494C22semidirect
62. C61×#473C22semidirect
66. C61×#443C22semidirect
315. #3293D61semidirect
338. #578C2×D61semidirect
361. #494C2×D61semidirect
365. #473C2×D61semidirect
374. #443C2×D61semidirect
386. C61#33855semidirect

Maximal subgroups

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

subgroupindex
#214589702
#214589632
#214576062
#214480882
#214479512
#214479422
#214478972
#214478882
#214477972
#214477952
#214477882
#214477832
#214477032
#214476612
C61×#32932
#3385561