Finite Group Databasebeta

← #29836761

Subgroups — #29836761

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#21458962C211yesmaximal, characteristic, complemented
2#21458957C211yesmaximal, characteristic, complemented
3#21457619C211yesmaximal, characteristic, complemented
4#21457607C211yesmaximal, characteristic, complemented
5#21448085C211yesmaximal, characteristic, complemented
6#21447950C211yesmaximal, characteristic, complemented
7#21447940C211yesmaximal, characteristic, complemented
8#21447895C211yesmaximal, characteristic, complemented
9#21447888C211yesmaximal, characteristic, complemented
10#21447791C211yesmaximal, characteristic, complemented
11#21447784C211yesmaximal, characteristic, complemented
12#21447777C211yesmaximal, characteristic, complemented
13#21447777C211yesmaximal, characteristic, complemented
14#21447662C211yesmaximal, characteristic, complemented
15C61×#2179C211yesmaximal, characteristic, complemented
16#16840576C2211yescharacteristic, complemented
17#16840574—21no—
18#16840567—21no—
19#16840564C2211yescharacteristic
20#16840564C2211yescharacteristic, complemented
21#16840564C2211yescharacteristic, complemented
22#16840204—21no—
23#16840202C2211yescharacteristic, complemented
24#16840199—21no—
25#16840199—21no—
26#16840197C2211yescharacteristic
27#16840197C2211yescharacteristic, complemented
28#16840197C2211yescharacteristic, complemented
29#16840196—21no—
30#16840195—21no—
31#16840193—21no—
32C2×#14519722C2211yescharacteristic, complemented
33C2×#14519722C2211yescharacteristic, complemented
34SD32×D61—21no—
35C2×D976C2211yescharacteristic, complemented
36C2×D976C2211yescharacteristic, complemented
37D16×D61—21no—
38#16840178C2211yescharacteristic, complemented
39#16840178C2211yescharacteristic, complemented
40#16840146C2211yescharacteristic, complemented
41#16840139C2211yescharacteristic, complemented
42#16840038C2211yescharacteristic, complemented
43#16840033C2211yescharacteristic
44#16840033C2211yescharacteristic, complemented
45#16840033C2211yescharacteristic, complemented
46#16840032—21no—
47#16840025—21no—
48#16839941—21no—
49#16839936—21no—
50#16839931—21no—
51#16839931—21no—
52#16839880C2211yescharacteristic
53#16839583C2211yescharacteristic, complemented
54#16839577C2211yescharacteristic, complemented
55#16839574C2211yescharacteristic, complemented
56#16839574C2211yescharacteristic, complemented
57#16839574C2211yescharacteristic, complemented
58#16839545C2211yescharacteristic, complemented
59#16839545C2211yescharacteristic, complemented
60C61×#508C2211yescharacteristic
61C61×#443C2211yescharacteristic, complemented
62C61×#443C2211yescharacteristic, complemented
63C61×#368C2211yescharacteristic, complemented
64C61×#359C2211yescharacteristic, complemented
65C61×#359C2211yescharacteristic, complemented
66C61×#346C2211yescharacteristic, complemented
67#14519824—21no—
68#14519823—21no—
69#14519823—21no—
70#14519823—21no—
71#14519810—21no—
72#14519810—41no—
73#14519807—21no—
74#14519806—41no—
75#14519805—21no—
76#14519805—21no—
77#14519805—21no—
78#14519805—41no—
79#14519805—41no—
80#14519805—41no—
81#14519804—41no—
82#14519804—41no—
83#14519804—41no—
84#14519802—21no—
85#14519802—21no—
86#14519802—21no—
87#14519800—21no—
88#14519800—21no—
89#14519800—21no—
90#14519799—41no—
91#14519799—41no—
92#14519799D411yescharacteristic
93#14519796—21no—
94C2×Dic244C2311yescharacteristic
95Q16×D61—21no—
96C2×#11758190—21no—
97C2×#11758190—41no—
98C2×D488—21no—
99C2×D488—41no—
100C2×D488C2311yescharacteristic
101C2×D488C2311yescharacteristic
102C2×D488C2311yescharacteristic
103D8×D61—21no—
104D8×D61—21no—
105D8×D61—21no—
106#14519783C2311yescharacteristic
107#14519783C2311yescharacteristic
108#14519774—21no—
109#14519765—21no—
110#14519723—21no—
111#14519722—21no—
112#14519722—21no—
113#14519722—41no—
114#14519721—21no—
115#14519720—21no—
116#14519720—21no—
117#14519720—21no—
118D976—21no—
119D976—21no—
120D976—41no—
121#14519718—21no—
122#14519718—21no—
123#14519718—21no—
124#14519717C2311yescharacteristic
125#14519717C2311yescharacteristic
126#14519716—21no—
127#14519716—21no—
128C16×D61—21no—
129C16×D61—21no—
130#14519713D411yescharacteristic
131#14519705D411yescharacteristic
132#14519705D411yescharacteristic
133#14519695—21no—
134#14519693—21no—
135#14519693—21no—
136#14519693—21no—
137#135×C61C2311yescharacteristic
138#135×C61C2311yescharacteristic
139#131×C61—21no—
140#131×C61—21no—
141Q32×C61D411yescharacteristic, complemented
142SD32×C61D411yescharacteristic, complemented
143SD32×C61D411yescharacteristic, complemented
144D16×C61D411yescharacteristic, complemented
145C2×C16×C61C2311yescharacteristic
146C2×C16×C61C2311yescharacteristic
147#108×C61C2311yescharacteristic
148#108×C61C2311yescharacteristic
149#104×C61—21no—
150#104×C61—21no—
151C4×C8×C61C2311yescharacteristic
152#41×C61—21no—
153#41×C61—21no—
154#11758226—41no—
155#11758226—41no—
156#11758226—41no—
157Q8×D61—41no—
158#11758224—41no—
159#11758224—81no—
160D4×D61—41no—
161D4×D61—41no—
162D4×D61—41no—
163D4×D61—81no—
164D4×D61—81no—
165D4×D61—81no—
166#11758222—41no—
167#11758222—41no—
168#11758222—41no—
169#11758222—41no—
170#11758222C2×D411yescharacteristic
171#11758222C2×D411yescharacteristic
172C2×D244—21no—
173C2×D244—21no—
174C2×D244—21no—
175C2×D244—41no—
176C2×D244—41no—
177C2×D244—41no—
178C2×D244—81no—
179C2×Dic122—21no—
180C2×Dic122—41no—
181Q16×C61C2×D411yescharacteristic
182Q16×C61C2×D411yescharacteristic
183SD16×C61—21no—
184SD16×C61—21no—
185D8×C61C2×D411yescharacteristic
186D8×C61C2×D411yescharacteristic
187M16×C61—21no—
188M16×C61—21no—
189M16×C61—41no—
190M16×C61—41no—
191C2×C8×C61—41no—
192C2×C8×C61—41no—
193C2×C8×C61C2×D411yescharacteristic
194C2×C8×C61C2411yescharacteristic
195C42×C61C2×D411yescharacteristic
196#11758202—41no—
197#11758201—41no—
198#11758201—41no—
199#11758201—41no—
200#11758200—41no—
201#11758199—41no—
202#11758199—41no—
203#11758199—41no—
204#11758198—81no—
205#11758194C2×D411yescharacteristic
206#11758194C2×D411yescharacteristic
207Dic244—21no—
208Dic244—21no—
209Dic244—41no—
210Dic244D811yescharacteristic
211D488—21no—
212D488—21no—
213D488—21no—
214D488—21no—
215D488—21no—
216D488—21no—
217D488—41no—
218D488—41no—
219D488—41no—
220D488—41no—
221D488—41no—
222D488D811yescharacteristic
223#11758190—41no—
224#11758190—41no—
225#11758190—41no—
226#11758190—41no—
227#11758190—41no—
228#11758190—41no—
229#11758190D811yescharacteristic
230#11758190D811yescharacteristic
231#11758189—21no—
232#11758189—21no—
233C8×D61—21no—
234C8×D61—21no—
235C16×C61—21no—
236C16×C61C2×D411yescharacteristic
237C16×C61C2×D411yescharacteristic
238#11758185—21no—
239#11758185—21no—
240C22×D61—41no—
241C22×D61—41no—
242C22×D61—41no—
243C22×D61—81no—
244C22×D61—81no—
245C22×D61—81no—
246Q8×C61—21no—
247Q8×C61—21no—
248D4×C61—21no—
249D4×C61—21no—
250D4×C61—41no—
251D4×C61—41no—
252C2×C4×C61—21no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61C22×D411yescharacteristic
256C22⋊D61—21no—
257C22⋊D61—21no—
258C22⋊D61—81no—
259C22⋊D61—81no—
260C22⋊D61—81no—
261C22⋊D61—81no—
262C2×Dic61—41no—
263C2×Dic61—81no—
264D244—41no—
265D244—41no—
266D244—41no—
267D244—41no—
268D244—41no—
269D244—41no—
270D244—81no—
271D244—81no—
272D244—81no—
273D244—162no—
274D244C2×D811yescharacteristic
275D244C2×D811yescharacteristic
276C4×D61—21no—
277C4×D61—21no—
278C4×D61—81no—
279C4×D61—81no—
280C4×D61—81no—
281C4×D61—81no—
282Dic122—41no—
283Dic122—41no—
284Dic122—81no—
285Dic122C2×D811yescharacteristic
286Dic122C2×D811yescharacteristic
287C8×C61—41no—
288C8×C61—41no—
289C8×C61C2×D811yescharacteristic
290C8×C61C2×D811yescharacteristic
291C8×C61C22×D411yescharacteristic
292C8×C61H(5,𝔽2)11yescharacteristic
293#92418—21no—
294#92418—21no—
295#33854—611nomaximal, Sylow
296C22×C61—41no—
297C22×C61—41no—
298C22×C61#57611yescharacteristic
299C2×D61—21no—
300C2×D61—21no—
301C2×D61—81no—
302C2×D61—81no—
303C2×D61—81no—
304C2×D61—161no—
305C2×D61—161no—
306C2×D61—161no—
307C2×D61—321no—
308C2×D61—321no—
309C2×D61—321no—
310C4×C61—41no—
311C4×C61—41no—
312C4×C61—41no—
313C4×C61D4211yescharacteristic
314C4×C61C22×D811yescharacteristic
315Dic61—21no—
316Dic61—21no—
317Dic61—81no—
318#3416—611no—
319#3415—611no—
320#3292—611no—
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#2179D6111yescharacteristic, complemented
332#2171—611no—
333C2×C61—21no—
334C2×C61—81no—
335C2×C61—81no—
336C2×C61D4×D811yescharacteristic
337D61—41no—
338D61—41no—
339D61—161no—
340D61—161no—
341D61—161no—
342#578—611no—
343#577—1221no—
344#576—611no—
345#576—611no—
346#576—611no—
347#576—1221no—
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—1221no—
357#508—1221no—
358#508C2×D6111yescharacteristic
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#493—611no—
369#473—611no—
370#472—611no—
371#472—611no—
372#472—611no—
373#472—1221no—
374#471—1221no—
375#455—1221no—
376#454—1221no—
377#453—1221no—
378#453—1221no—
379#443—611no—
380#443C2×D6111yescharacteristic, complemented
381#443C2×D6111yescharacteristic, complemented
382#368C2×D6111yescharacteristic, complemented
383#364—611no—
384#362—611no—
385#361—611no—
386#361—611no—
387#361—611no—
388#359C2×D6111yescharacteristic, complemented
389#359C2×D6111yescharacteristic, complemented
390#350—611no—
391#350—611no—
392#346C2×D6111yescharacteristic, complemented
393C61#3385411yescharacteristic, complemented, Sylow
3942−1+4—1221no—
395H(5,𝔽2)—1221no—
396H(5,𝔽2)—1221no—
397H(5,𝔽2)—1221no—
398#137—1221no—
399#137—1221no—
400#137—2441no—
401#137—2441no—
402AGL(1,ℤ/8)—1221no—
403AGL(1,ℤ/8)—1221no—
404AGL(1,ℤ/8)—1221no—
405AGL(1,ℤ/8)—1221no—
406AGL(1,ℤ/8)—1221no—
407AGL(1,ℤ/8)—1221no—
408AGL(1,ℤ/8)—2441no—
409AGL(1,ℤ/8)—2441no—
410AGL(1,ℤ/8)—2441no—
411AGL(1,ℤ/8)—2441no—
412AGL(1,ℤ/8)—2441no—
413AGL(1,ℤ/8)—2441no—
414#135—611no—
415#135—1221no—
416#135—1221no—
417#135—1221no—
418#135—1221no—
419#135—2441no—
420#135—2441no—
421#135C22×D6111yescharacteristic
422#135C22×D6111yescharacteristic
423C2×Q16—611no—
424C2×Q16—1221no—
425C2×SD16—1221no—
426C2×SD16—2441no—
427C2×D8—611no—
428C2×D8—611no—
429C2×D8—611no—
430C2×D8—1221no—
431C2×D8—1221no—
432C2×D8—1221no—
433C2×D8—1221no—
434C2×D8—2441no—
435#131—21no—
436#131—21no—
437#131—611no—
438#131—611no—
439#127—1221no—
440#124—1221no—
441Q32—1221no—
442Q32D24411yescharacteristic, complemented
443SD32—1221no—
444SD32—1221no—
445SD32—1221no—
446SD32—1221no—
447SD32—1221no—
448SD32—1221no—
449SD32—2441no—
450SD32D24411yescharacteristic, complemented
451SD32D24411yescharacteristic, complemented
452D16—1221no—
453D16—1221no—
454D16—1221no—
455D16—1221no—
456D16—1221no—
457D16—2441no—
458D16D24411yescharacteristic, complemented
459M32—611no—
460M32—611no—
461M32—1221no—
462M32—1221no—
463C2×C16—1221no—
464C2×C16—1221no—
465C2×C16C22×D6111yescharacteristic
466C2×C16C22×D6111yescharacteristic
467#108—611no—
468#108C22×D6111yescharacteristic
469#108C22×D6111yescharacteristic
470#104—21no—
471#104—21no—
472#104—611no—
473#104—611no—
474#101—1221no—
475#100—1221no—
476#100—1221no—
477#100—1221no—
478C4×C8C22×D6111yescharacteristic
479#41—21no—
480#41—21no—
481#41—611no—
482#41—611no—
483#41—4881no—
484#41—2441no—
485#41—2441no—
486#41—2441no—
487#41—2441no—
488#41—2441no—
489#41—2441no—
490#41—2441no—
491#41—2441no—
492C2×Q8—1221no—
493C2×Q8—2441no—
494C2×Q8—2441no—
495C2×D4—1221no—
496C2×D4—1221no—
497C2×D4—1221no—
498C2×D4—4881no—
499C2×D4—4881no—
500C2×D4—4881no—
501C2×D4—4881no—
502C2×D4—2441no—
503C2×D4—2441no—
504C2×D4—2441no—
505C2×D4—2441no—
506C2×D4—2441no—
507C2×D4—2441no—
508Q16—611no—
509Q16—1221no—
510Q16—1221no—
511Q16—2441no—
512Q16—2441no—
513Q16C2×D24411yescharacteristic
514Q16C2×D24411yescharacteristic
515SD16—21no—
516SD16—21no—
517SD16—611no—
518SD16—611no—
519SD16—2441no—
520SD16—2441no—
521SD16—2441no—
522SD16—2441no—
523SD16—2441no—
524SD16—2441no—
525SD16—2441no—
526SD16—2441no—
527SD16—2441no—
528SD16—2441no—
529D8—611no—
530D8—1221no—
531D8—1221no—
532D8—1221no—
533D8—1221no—
534D8—1221no—
535D8—1221no—
536D8—2441no—
537D8—2441no—
538D8—2441no—
539D8—2441no—
540D8—2441no—
541D8—2441no—
542D8—2441no—
543D8—2441no—
544D8C2×D24411yescharacteristic
545D8C2×D24411yescharacteristic
546M16—21no—
547M16—21no—
548M16—41no—
549M16—41no—
550M16—611no—
551M16—611no—
552M16—1221no—
553M16—1221no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—1221no—
557C2×C8—1221no—
558C2×C8D4×D6111yescharacteristic
559C2×C8C23×D6111yescharacteristic
560C22⋊C4—4881no—
561C42D4×D6111yescharacteristic
562C16—21no—
563C16—1221no—
564C16—1221no—
565C16C2×D24411yescharacteristic
566C16C2×D24411yescharacteristic
567C23—4881no—
568C23—4881no—
569C23—4881no—
570C23—2441no—
571C23—2441no—
572C23—2441no—
573Q8—21no—
574Q8—21no—
575Q8—611no—
576Q8—611no—
577Q8—4881no—
578Q8—2441no—
579Q8—2441no—
580D4—21no—
581D4—21no—
582D4—41no—
583D4—41no—
584D4—611no—
585D4—611no—
586D4—1221no—
587D4—1221no—
588D4—9762no—
589D4—4881no—
590D4—4881no—
591D4—4881no—
592D4—4881no—
593D4—4881no—
594D4—4881no—
595D4—4881no—
596D4—2441no—
597D4—2441no—
598D4—2441no—
599D4—2441no—
600D4—2441no—
601D4—2441no—
602C2×C4—21no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—1221no—
606C2×C4—1221no—
607C2×C4—4881no—
608C2×C4—4881no—
609C2×C4—4881no—
610C2×C4—4881no—
611C2×C4—4881no—
612C2×C4—2441no—
613C2×C4C2×D4×D6111yescharacteristic
614C8—41no—
615C8—41no—
616C8—1221no—
617C8—1221no—
618C8D8×D6111yescharacteristic
619C8D8×D6111yescharacteristic
620C8C22×D24411yescharacteristic
621C8#1451982311yescharacteristic
622C22—41no—
623C22—41no—
624C22—1221no—
625C22—1221no—
626C22—19521no—
627C22—19521no—
628C22—19521no—
629C22—9761no—
630C22—9761no—
631C22—9761no—
632C22—4881no—
633C22—4881no—
634C22—4881no—
635C22#1684056411yescharacteristic
636C4—41no—
637C4—41no—
638C4—41no—
639C4—1221no—
640C4—1221no—
641C4—4881no—
642C4D4×D24411yescharacteristic
643C4C2×D8×D6111yescharacteristic
644C2—21no—
645C2—81no—
646C2—81no—
647C2—9761no—
648C2—9761no—
649C2—9761no—
650C2—2441no—
651C2—2441no—
652C2D8×D24411yescharacteristic
subgroupG/H
centerC2D8×D244
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2179C2
socleC2×C61D4×D8
hypercenter#2179D61
hypocenterC61#33854
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2179

Complements

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

NH ≅ G/Ntype
1. #21458962C2semidirect
2. #21458957C2semidirect
3. #21457619C2semidirect
4. #21457607C2semidirect
5. #21448085C2semidirect
6. #21447950C2semidirect
7. #21447940C2semidirect
8. #21447895C2semidirect
9. #21447888C2semidirect
10. #21447791C2semidirect
11. #21447784C2semidirect
12. #21447777C2semidirect
13. #21447777C2semidirect
14. #21447662C2semidirect
15. C61×#2179C2semidirect
16. #16840576C22semidirect
20. #16840564C22semidirect
21. #16840564C22semidirect
23. #16840202C22semidirect
27. #16840197C22semidirect
28. #16840197C22semidirect
32. C2×#14519722C22semidirect
33. C2×#14519722C22semidirect
35. C2×D976C22semidirect
36. C2×D976C22semidirect
38. #16840178C22semidirect
39. #16840178C22semidirect
40. #16840146C22semidirect
41. #16840139C22semidirect
42. #16840038C22semidirect
44. #16840033C22semidirect
45. #16840033C22semidirect
53. #16839583C22semidirect
54. #16839577C22semidirect
55. #16839574C22semidirect
56. #16839574C22semidirect
57. #16839574C22semidirect
58. #16839545C22semidirect
59. #16839545C22semidirect
61. C61×#443C22semidirect
62. C61×#443C22semidirect
63. C61×#368C22semidirect
64. C61×#359C22semidirect
65. C61×#359C22semidirect
66. C61×#346C22semidirect
141. Q32×C61D4semidirect
142. SD32×C61D4semidirect
143. SD32×C61D4semidirect
144. D16×C61D4semidirect
331. #2179D61semidirect
380. #443C2×D61semidirect
381. #443C2×D61semidirect
382. #368C2×D61semidirect
388. #359C2×D61semidirect
389. #359C2×D61semidirect
392. #346C2×D61semidirect
393. C61#33854semidirect
442. Q32D244semidirect
450. SD32D244semidirect
451. SD32D244semidirect
458. D16D244semidirect

Maximal subgroups

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

subgroupindex
#214589622
#214589572
#214576192
#214576072
#214480852
#214479502
#214479402
#214478952
#214478882
#214477912
#214477842
#214477772
#214476622
C61×#21792
#3385461