Finite Group Databasebeta

← #29836755

Subgroups — #29836755

Order 15616.

656 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458966C211yesmaximal, characteristic, complemented
2#21458958C211yesmaximal, characteristic, complemented
3#21457606C211yesmaximal, characteristic, complemented
4#21448083C211yesmaximal, characteristic, complemented
5#21447947C211yesmaximal, characteristic, complemented
6#21447937C211yesmaximal, characteristic, complemented
7#21447892C211yesmaximal, characteristic, complemented
8#21447888C211yesmaximal, characteristic, complemented
9#21447790C211yesmaximal, characteristic, complemented
10#21447781C211yesmaximal, characteristic, complemented
11#21447776C211yesmaximal, characteristic, complemented
12#21447774C211yesmaximal, characteristic, complemented
13#21447703C211yesmaximal, characteristic, complemented
14#21447661C211yesmaximal, characteristic, complemented
15C61×#3292C211yesmaximal, characteristic, complemented
16#16840579C2211yescharacteristic, complemented
17#16840569—21no—
18#16840567C2211yescharacteristic, complemented
19#16840202—21no—
20#16840202C2211yescharacteristic, complemented
21#16840198—21no—
22#16840198—21no—
23#16840198C2211yescharacteristic, complemented
24#16840198C2211yescharacteristic, complemented
25#16840197—21no—
26#16840197C2211yescharacteristic
27#16840192—21no—
28#16840192—21no—
29#16840192C2211yescharacteristic
30C2×#14519721—21no—
31C2×#14519721C2211yescharacteristic, complemented
32C2×#14519721C2211yescharacteristic, complemented
33C2×#14519718—21no—
34C2×#14519718C2211yescharacteristic, complemented
35C2×#14519718C2211yescharacteristic, complemented
36#16840179C2211yescharacteristic, complemented
37#16840179C2211yescharacteristic, complemented
38#16840146C2211yescharacteristic, complemented
39#16840037C2211yescharacteristic, complemented
40#16840032C2211yescharacteristic, complemented
41#16840026—21no—
42#16839941—21no—
43#16839936—21no—
44#16839880C2211yescharacteristic, complemented
45#16839591C2211yescharacteristic, complemented
46#16839583C2211yescharacteristic, complemented
47#16839577C2211yescharacteristic, complemented
48#16839575C2211yescharacteristic, complemented
49#16839575C2211yescharacteristic, complemented
50#16839574C2211yescharacteristic, complemented
51#16839569C2211yescharacteristic, complemented
52#16839568C2211yescharacteristic, complemented
53#16839546C2211yescharacteristic, complemented
54#16839546C2211yescharacteristic, complemented
55#16839538C2211yescharacteristic, complemented
56C61×#576—21no—
57C61×#576C2211yescharacteristic
58C61×#576C2211yescharacteristic, complemented
59C61×#493C2211yescharacteristic, complemented
60C61×#472—21no—
61C61×#472C2211yescharacteristic
62C61×#472C2211yescharacteristic, complemented
63C61×#453—21no—
64C61×#453—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#14519723D411yescharacteristic, complemented
91#14519721—21no—
92#14519721—21no—
93#14519721—21no—
94#14519721—21no—
95#14519721—21no—
96#14519721—41no—
97#14519721D411yescharacteristic, complemented
98#14519720—21no—
99#14519720D411yescharacteristic, complemented
100#14519718—21no—
101#14519718—21no—
102#14519718—21no—
103#14519718—21no—
104#14519718—21no—
105#14519718—41no—
106#14519718D411yescharacteristic, complemented
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—
119H(5,𝔽2)×C61—21no—
120H(5,𝔽2)×C61—21no—
121AGL(1,ℤ/8)×C61—21no—
122AGL(1,ℤ/8)×C61—21no—
123AGL(1,ℤ/8)×C61—21no—
124AGL(1,ℤ/8)×C61—21no—
125AGL(1,ℤ/8)×C61—41no—
126AGL(1,ℤ/8)×C61—41no—
127AGL(1,ℤ/8)×C61—41no—
128AGL(1,ℤ/8)×C61—41no—
129#135×C61—21no—
130#135×C61—21no—
131#135×C61—41no—
132#135×C61D411yescharacteristic
133#135×C61C2311yescharacteristic
134C2×D8×C61—21no—
135C2×D8×C61—21no—
136C2×D8×C61—21no—
137C2×D8×C61—41no—
138C2×D8×C61C2311yescharacteristic
139C2×D8×C61C2311yescharacteristic
140#131×C61—21no—
141#131×C61C2311yescharacteristic
142#131×C61C2311yescharacteristic
143#127×C61—21no—
144#108×C61D411yescharacteristic
145#108×C61C2311yescharacteristic
146#104×C61—21no—
147#104×C61D411yescharacteristic
148#104×C61D411yescharacteristic
149#100×C61—21no—
150#100×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×C61C2×D411yescharacteristic
158#41×C61C2×D411yescharacteristic
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—41no—
162C2×D4×C61—41no—
163C2×D4×C61—41no—
164C2×D4×C61—41no—
165C2×D4×C61—81no—
166C2×D4×C61—81no—
167C2×D4×C61—81no—
168#11758226—41no—
169Q8×D61—41no—
170#11758224—41no—
171#11758224—81no—
172D4×D61—41no—
173D4×D61—81no—
174#11758222—21no—
175#11758222—41no—
176#11758222—41no—
177C2×D244—21no—
178C2×D244—41no—
179C2×Dic122—21no—
180C2×Dic122—41no—
181Q16×C61D811yescharacteristic
182Q16×C61C2×D411yescharacteristic
183SD16×C61—21no—
184SD16×C61—41no—
185SD16×C61—41no—
186SD16×C61—41no—
187SD16×C61—41no—
188SD16×C61D811yescharacteristic
189SD16×C61D811yescharacteristic
190D8×C61—21no—
191D8×C61—21no—
192D8×C61—21no—
193D8×C61—21no—
194D8×C61—41no—
195D8×C61—41no—
196D8×C61—41no—
197D8×C61—41no—
198D8×C61—41no—
199D8×C61—41no—
200D8×C61D811yescharacteristic
201D8×C61C2×D411yescharacteristic
202M16×C61—21no—
203M16×C61—21no—
204M16×C61—21no—
205M16×C61—41no—
206M16×C61C2×D411yescharacteristic
207M16×C61C2×D411yescharacteristic
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—41no—
211C2×C8×C61C2×D411yescharacteristic
212C2×C8×C61C2411yescharacteristic
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
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—81no—
243C23×C61—81no—
244C22×D61—41no—
245C22×D61—81no—
246Q8×C61—21no—
247Q8×C61C2×D811yescharacteristic
248Q8×C61C2×D811yescharacteristic
249D4×C61—21no—
250D4×C61—21no—
251D4×C61—21no—
252D4×C61—41no—
253D4×C61—41no—
254D4×C61—41no—
255D4×C61—41no—
256D4×C61—41no—
257D4×C61—81no—
258D4×C61—81no—
259D4×C61—81no—
260D4×C61—81no—
261D4×C61—162no—
262D4×C61C2×D811yescharacteristic
263D4×C61C2×D811yescharacteristic
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—41no—
268C2×C4×C61—81no—
269C2×C4×C61—81no—
270C2×C4×C61C22×D411yescharacteristic
271C22⋊D61—41no—
272C22⋊D61—81no—
273C22⋊D61—81no—
274C2×Dic61—41no—
275C2×Dic61—81no—
276D244—21no—
277D244—41no—
278D244—41no—
279D244—81no—
280C4×D61—41no—
281C4×D61—81no—
282C4×D61—81no—
283Dic122—21no—
284Dic122—41no—
285Dic122—41no—
286Dic122—81no—
287C8×C61—21no—
288C8×C61—21no—
289C8×C61—41no—
290C8×C61C2×D811yescharacteristic
291C8×C61C2×D811yescharacteristic
292C8×C61C22×D411yescharacteristic
293C8×C61H(5,𝔽2)11yescharacteristic
294#92418—41no—
295#33854—611nomaximal, Sylow
296C22×C61—21no—
297C22×C61—21no—
298C22×C61—41no—
299C22×C61—81no—
300C22×C61—81no—
301C22×C61—161no—
302C22×C61—161no—
303C22×C61—321no—
304C22×C61—321no—
305C22×C61#57611yescharacteristic
306C2×D61—41no—
307C2×D61—81no—
308C2×D61—161no—
309C2×D61—321no—
310C4×C61—21no—
311C4×C61—21no—
312C4×C61—41no—
313C4×C61—41no—
314C4×C61D4211yescharacteristic
315C4×C61C22×D811yescharacteristic
316Dic61—41no—
317Dic61—81no—
318#3416—611no—
319#3415—611no—
320#3292D6111yescharacteristic, complemented
321#3290—611no—
322#2250—611no—
323#2223—611no—
324#2221—611no—
325#2213—611no—
326#2212—611no—
327#2194—611no—
328#2193—611no—
329#2192—611no—
330#2192—611no—
331#2179—611no—
332#2171—611no—
333C2×C61—21no—
334C2×C61—41no—
335C2×C61—41no—
336C2×C61—81no—
337C2×C61—161no—
338C2×C61—161no—
339C2×C61D4×D811yescharacteristic
340D61—81no—
341D61—161no—
342#578—611no—
343#577—1221no—
344#576—21no—
345#576—611no—
346#576C2×D6111yescharacteristic
347#576C2×D6111yescharacteristic, complemented
348#510—611no—
349#510—1221no—
350#509—611no—
351#509—611no—
352#509—611no—
353#509—1221no—
354#509—1221no—
355#509—1221no—
356#508—611no—
357#508—1221no—
358#508—1221no—
359C2×SD32—611no—
360C2×SD32—611no—
361C2×SD32—1221no—
362C2×D16—611no—
363C2×D16—611no—
364C2×D16—1221no—
365#504—611no—
366#504—611no—
367#495—611no—
368#493C2×D6111yescharacteristic, complemented
369#473—611no—
370#472—21no—
371#472—611no—
372#472C2×D6111yescharacteristic
373#472C2×D6111yescharacteristic, complemented
374#471—1221no—
375#455—1221no—
376#454—1221no—
377#453—21no—
378#453—21no—
379#443—611no—
380#443C2×D6111yescharacteristic
381#443C2×D6111yescharacteristic, complemented
382#368—611no—
383#364—611no—
384#362—611no—
385#361—611no—
386#361—611no—
387#361—611no—
388#359—611no—
389#359—611no—
390#350—611no—
391#350—611no—
392#346—611no—
393C61#3385411yescharacteristic, complemented, Sylow
3942−1+4—1221no—
395H(5,𝔽2)—21no—
396H(5,𝔽2)—21no—
397H(5,𝔽2)—1221no—
398#137—1221no—
399#137—1221no—
400#137—2441no—
401#137—2441no—
402AGL(1,ℤ/8)—21no—
403AGL(1,ℤ/8)—21no—
404AGL(1,ℤ/8)—21no—
405AGL(1,ℤ/8)—21no—
406AGL(1,ℤ/8)—41no—
407AGL(1,ℤ/8)—41no—
408AGL(1,ℤ/8)—41no—
409AGL(1,ℤ/8)—41no—
410AGL(1,ℤ/8)—1221no—
411AGL(1,ℤ/8)—1221no—
412AGL(1,ℤ/8)—2441no—
413AGL(1,ℤ/8)—2441no—
414#135—21no—
415#135—21no—
416#135—41no—
417#135—611no—
418#135—1221no—
419#135—1221no—
420#135—2441no—
421#135C22⋊D6111yescharacteristic
422#135C22×D6111yescharacteristic
423C2×Q16—611no—
424C2×Q16—1221no—
425C2×SD16—1221no—
426C2×SD16—2441no—
427C2×D8—21no—
428C2×D8—21no—
429C2×D8—21no—
430C2×D8—41no—
431C2×D8—611no—
432C2×D8—1221no—
433C2×D8C22×D6111yescharacteristic
434C2×D8C22×D6111yescharacteristic
435#131—21no—
436#131—1221no—
437#131C22×D6111yescharacteristic
438#131C22×D6111yescharacteristic
439#127—21no—
440#124—1221no—
441Q32—611no—
442Q32—1221no—
443SD32—611no—
444SD32—611no—
445SD32—1221no—
446SD32—1221no—
447SD32—1221no—
448SD32—1221no—
449SD32—1221no—
450SD32—1221no—
451SD32—2441no—
452D16—611no—
453D16—1221no—
454D16—1221no—
455D16—1221no—
456D16—1221no—
457D16—1221no—
458D16—2441no—
459M32—611no—
460M32—611no—
461M32—1221no—
462M32—1221no—
463C2×C16—611no—
464C2×C16—611no—
465C2×C16—1221no—
466C2×C16—1221no—
467#108—611no—
468#108C22⋊D6111yescharacteristic
469#108C22×D6111yescharacteristic
470#104—21no—
471#104—1221no—
472#104C22⋊D6111yescharacteristic
473#104C22⋊D6111yescharacteristic
474#101—1221no—
475#100—21no—
476#100—21no—
477#100—1221no—
478C4×C8C22×D6111yescharacteristic
479#41—21no—
480#41—41no—
481#41—41no—
482#41—41no—
483#41—41no—
484#41—1221no—
485#41—4881no—
486#41—2441no—
487#41—2441no—
488#41—2441no—
489#41—2441no—
490#41C2×C22⋊D6111yescharacteristic
491#41C2×C22⋊D6111yescharacteristic
492C2×Q8—1221no—
493C2×Q8—2441no—
494C2×Q8—2441no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—41no—
498C2×D4—41no—
499C2×D4—41no—
500C2×D4—41no—
501C2×D4—81no—
502C2×D4—81no—
503C2×D4—81no—
504C2×D4—1221no—
505C2×D4—4881no—
506C2×D4—2441no—
507C2×D4—2441no—
508Q16—611no—
509Q16—1221no—
510Q16—1221no—
511Q16—2441no—
512Q16—2441no—
513Q16#1175819911yescharacteristic
514Q16D4×D6111yescharacteristic
515SD16—21no—
516SD16—41no—
517SD16—41no—
518SD16—41no—
519SD16—41no—
520SD16—1221no—
521SD16—2441no—
522SD16—2441no—
523SD16—2441no—
524SD16—2441no—
525SD16—2441no—
526SD16—2441no—
527SD16#1175819911yescharacteristic
528SD16#1175819911yescharacteristic
529D8—21no—
530D8—21no—
531D8—21no—
532D8—21no—
533D8—41no—
534D8—41no—
535D8—41no—
536D8—41no—
537D8—41no—
538D8—41no—
539D8—611no—
540D8—1221no—
541D8—1221no—
542D8—2441no—
543D8—2441no—
544D8#1175819911yescharacteristic
545D8D4×D6111yescharacteristic
546M16—21no—
547M16—21no—
548M16—21no—
549M16—41no—
550M16—1221no—
551M16—2441no—
552M16C2×C22⋊D6111yescharacteristic
553M16C2×C22⋊D6111yescharacteristic
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—41no—
557C2×C8—2441no—
558C2×C8C2×C22⋊D6111yescharacteristic
559C2×C8C23×D6111yescharacteristic
560C22⋊C4—4881no—
561C42C2×C22⋊D6111yescharacteristic
562C16—611no—
563C16—611no—
564C16—1221no—
565C16—1221no—
566C16—1221no—
567C23—41no—
568C23—41no—
569C23—81no—
570C23—81no—
571C23—4881no—
572C23—2441no—
573Q8—21no—
574Q8—1221no—
575Q8—4881no—
576Q8—2441no—
577Q8—2441no—
578Q8C2×#1175819911yescharacteristic
579Q8C2×#1175819911yescharacteristic
580D4—21no—
581D4—21no—
582D4—21no—
583D4—41no—
584D4—41no—
585D4—41no—
586D4—41no—
587D4—41no—
588D4—81no—
589D4—81no—
590D4—81no—
591D4—81no—
592D4—162no—
593D4—1221no—
594D4—4881no—
595D4—4881no—
596D4—4881no—
597D4—2441no—
598D4—2441no—
599D4—2441no—
600D4C2×#1175819911yescharacteristic
601D4C2×#1175819911yescharacteristic
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—41no—
606C2×C4—81no—
607C2×C4—81no—
608C2×C4—4881no—
609C2×C4—4881no—
610C2×C4—4881no—
611C2×C4—2441no—
612C2×C4—2441no—
613C2×C4C22×C22⋊D6111yescharacteristic
614C8—21no—
615C8—21no—
616C8—41no—
617C8—2441no—
618C8C2×#1175819911yescharacteristic
619C8C2×#1175819911yescharacteristic
620C8C2×D4×D6111yescharacteristic
621C8#1451982211yescharacteristic
622C22—21no—
623C22—21no—
624C22—41no—
625C22—81no—
626C22—81no—
627C22—161no—
628C22—161no—
629C22—321no—
630C22—321no—
631C22—19521no—
632C22—9761no—
633C22—4881no—
634C22—2441no—
635C22#1684056511yescharacteristic
636C4—21no—
637C4—21no—
638C4—41no—
639C4—41no—
640C4—4881no—
641C4—2441no—
642C4D4×C22⋊D6111yescharacteristic
643C4C22×#1175819911yescharacteristic
644C2—21no—
645C2—41no—
646C2—41no—
647C2—81no—
648C2—161no—
649C2—161no—
650C2—9761no—
651C2—4881no—
652C2D4×#1175819911yescharacteristic
subgroupG/H
centerC2D4×#11758199
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#3292C2
socleC2×C61D4×D8
hypercenter#3292D61
hypocenterC61#33854
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443 ◁ #3292

Complements

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

NH ≅ G/Ntype
1. #21458966C2semidirect
2. #21458958C2semidirect
3. #21457606C2semidirect
4. #21448083C2semidirect
5. #21447947C2semidirect
6. #21447937C2semidirect
7. #21447892C2semidirect
8. #21447888C2semidirect
9. #21447790C2semidirect
10. #21447781C2semidirect
11. #21447776C2semidirect
12. #21447774C2semidirect
13. #21447703C2semidirect
14. #21447661C2semidirect
15. C61×#3292C2semidirect
16. #16840579C22semidirect
18. #16840567C22semidirect
20. #16840202C22semidirect
23. #16840198C22semidirect
24. #16840198C22semidirect
31. C2×#14519721C22semidirect
32. C2×#14519721C22semidirect
34. C2×#14519718C22semidirect
35. C2×#14519718C22semidirect
36. #16840179C22semidirect
37. #16840179C22semidirect
38. #16840146C22semidirect
39. #16840037C22semidirect
40. #16840032C22semidirect
44. #16839880C22semidirect
45. #16839591C22semidirect
46. #16839583C22semidirect
47. #16839577C22semidirect
48. #16839575C22semidirect
49. #16839575C22semidirect
50. #16839574C22semidirect
51. #16839569C22semidirect
52. #16839568C22semidirect
53. #16839546C22semidirect
54. #16839546C22semidirect
55. #16839538C22semidirect
58. C61×#576C22semidirect
59. C61×#493C22semidirect
62. C61×#472C22semidirect
66. C61×#443C22semidirect
90. #14519723D4semidirect
97. #14519721D4semidirect
99. #14519720D4semidirect
106. #14519718D4semidirect
320. #3292D61semidirect
347. #576C2×D61semidirect
368. #493C2×D61semidirect
373. #472C2×D61semidirect
381. #443C2×D61semidirect
393. C61#33854semidirect

Maximal subgroups

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

subgroupindex
#214589662
#214589582
#214576062
#214480832
#214479472
#214479372
#214478922
#214478882
#214477902
#214477812
#214477762
#214477742
#214477032
#214476612
C61×#32922
#3385461