Finite Group Databasebeta

← #29836813

Subgroups — #29836813

Order 15616.

646 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458970C211yesmaximal, characteristic, complemented
2#21458958C211yesmaximal, characteristic, complemented
3#21457606C211yesmaximal, characteristic, complemented
4#21448078C211yesmaximal, characteristic, complemented
5#21447942C211yesmaximal, characteristic, complemented
6#21447937C211yesmaximal, characteristic, complemented
7#21447888C211yesmaximal, characteristic, complemented
8#21447885C211yesmaximal, characteristic, complemented
9#21447790C211yesmaximal, characteristic, complemented
10#21447788C211yesmaximal, characteristic, complemented
11#21447783C211yesmaximal, characteristic, complemented
12#21447781C211yesmaximal, characteristic, complemented
13#21447698C211yesmaximal, characteristic, complemented
14#21447656C211yesmaximal, characteristic, complemented
15C61×#3290C211yesmaximal, characteristic, complemented
16#16840579C2211yescharacteristic, complemented
17#16840569—21no—
18#16840567C2211yescharacteristic
19#16840203—21no—
20#16840203C2211yescharacteristic, complemented
21#16840202—21no—
22#16840202C2211yescharacteristic, complemented
23#16840198—21no—
24#16840198C2211yescharacteristic
25#16840197—21no—
26#16840197C2211yescharacteristic
27#16840192—21no—
28#16840192—21no—
29#16840192C2211yescharacteristic
30C2×#14519723—21no—
31C2×#14519723C2211yescharacteristic, complemented
32C2×#14519721C2211yescharacteristic, complemented
33C2×#14519720C2211yescharacteristic, complemented
34C2×#14519718—21no—
35C2×#14519718C2211yescharacteristic
36#16840179C2211yescharacteristic
37#16840179C2211yescharacteristic, complemented
38#16840146C2211yescharacteristic, complemented
39#16840037C2211yescharacteristic
40#16840032C2211yescharacteristic, complemented
41#16840026—21no—
42#16839941—21no—
43#16839936—21no—
44#16839880C2211yescharacteristic, complemented
45#16839591C2211yescharacteristic, complemented
46#16839583C2211yescharacteristic, complemented
47#16839578C2211yescharacteristic, complemented
48#16839577C2211yescharacteristic, complemented
49#16839575C2211yescharacteristic, complemented
50#16839574C2211yescharacteristic, complemented
51#16839569C2211yescharacteristic, complemented
52#16839568C2211yescharacteristic, complemented
53#16839546C2211yescharacteristic
54#16839546C2211yescharacteristic, complemented
55C4×#11758185C2211yescharacteristic, complemented
56C61×#578C2211yescharacteristic, complemented
57C61×#577—21no—
58C61×#576C2211yescharacteristic
59C61×#495C2211yescharacteristic, complemented
60C61×#473C2211yescharacteristic
61C61×#472C2211yescharacteristic, complemented
62C61×#471—21no—
63C61×#455—21no—
64C61×#454—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#14519723D411yescharacteristic
94#14519721—21no—
95#14519721—21no—
96#14519721—41no—
97#14519721D411yescharacteristic
98#14519720—21no—
99#14519720—21no—
100#14519720—41no—
101#14519720D411yescharacteristic
102#14519718—21no—
103#14519718—21no—
104#14519718—21no—
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—
120H(5,𝔽2)×C61—21no—
121#137×C61—21no—
122#137×C61—21no—
123#137×C61—41no—
124#137×C61—41no—
125AGL(1,ℤ/8)×C61—21no—
126AGL(1,ℤ/8)×C61—21no—
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×Q16×C61—21no—
135C2×Q16×C61C2311yescharacteristic
136C2×SD16×C61—21no—
137C2×SD16×C61—41no—
138C2×D8×C61—21no—
139C2×D8×C61C2311yescharacteristic
140#131×C61—21no—
141#131×C61C2311yescharacteristic
142#131×C61C2311yescharacteristic
143#124×C61—21no—
144#108×C61D411yescharacteristic
145#108×C61C2311yescharacteristic
146#104×C61—21no—
147#104×C61D411yescharacteristic
148#104×C61D411yescharacteristic
149#101×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×C61—81no—
158#41×C61C2×D411yescharacteristic
159#41×C61C2×D411yescharacteristic
160C2×Q8×C61—21no—
161C2×Q8×C61—41no—
162C2×Q8×C61—41no—
163C2×D4×C61—21no—
164C2×D4×C61—41no—
165C2×D4×C61—41no—
166C2×D4×C61—81no—
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—41no—
183Q16×C61—41no—
184Q16×C61D811yescharacteristic
185Q16×C61C2×D411yescharacteristic
186SD16×C61—21no—
187SD16×C61—41no—
188SD16×C61—41no—
189SD16×C61—41no—
190SD16×C61—41no—
191SD16×C61—41no—
192SD16×C61—41no—
193SD16×C61D811yescharacteristic
194SD16×C61D811yescharacteristic
195D8×C61—21no—
196D8×C61—21no—
197D8×C61—41no—
198D8×C61—41no—
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
212C22⋊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
240C23×C61—41no—
241C23×C61—81no—
242C22×D61—41no—
243C22×D61—81no—
244Q8×C61—21no—
245Q8×C61—41no—
246Q8×C61—41no—
247Q8×C61—81no—
248Q8×C61C2×D811yescharacteristic
249Q8×C61C2×D811yescharacteristic
250D4×C61—21no—
251D4×C61—21no—
252D4×C61—21no—
253D4×C61—41no—
254D4×C61—41no—
255D4×C61—41no—
256D4×C61—81no—
257D4×C61—81no—
258D4×C61—81no—
259D4×C61C2×D811yescharacteristic
260D4×C61C2×D811yescharacteristic
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
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#33859—611nomaximal, Sylow
295C22×C61—21no—
296C22×C61—21no—
297C22×C61—41no—
298C22×C61—81no—
299C22×C61—161no—
300C22×C61—321no—
301C22×C61#57611yescharacteristic
302C2×D61—41no—
303C2×D61—81no—
304C2×D61—161no—
305C2×D61—321no—
306C4×C61—21no—
307C4×C61—21no—
308C4×C61—41no—
309C4×C61—41no—
310C4×C61—81no—
311C4×C61D4211yescharacteristic
312C4×C61C22×D811yescharacteristic
313Dic61—41no—
314Dic61—81no—
315#3417—611no—
316#3415—611no—
317#3290—611no—
318#3290D6111yescharacteristic, complemented
319#2249—611no—
320#2222—611no—
321#2221—611no—
322#2212—611no—
323#2212—611no—
324#2194—611no—
325#2194—611no—
326#2193—611no—
327#2193—611no—
328#2178—611no—
329#2170—611no—
330C2×C61—21no—
331C2×C61—41no—
332C2×C61—41no—
333C2×C61—81no—
334C2×C61—161no—
335C2×C61D4×D811yescharacteristic
336D61—81no—
337D61—161no—
338#578—611no—
339#578C2×D6111yescharacteristic, complemented
340#577—21no—
341#577—1221no—
342#576—611no—
343#576C2×D6111yescharacteristic
344#510—611no—
345#510—611no—
346#510—1221no—
347#510—1221no—
348#509—611no—
349#509—611no—
350#509—1221no—
351#509—1221no—
352#508—611no—
353#508—1221no—
354#508—1221no—
355C2×Q32—611no—
356C2×Q32—1221no—
357C2×SD32—611no—
358C2×SD32—611no—
359C2×D16—611no—
360C2×D16—1221no—
361#504—611no—
362#504—611no—
363#495—611no—
364#495C2×D6111yescharacteristic, complemented
365#473—611no—
366#473C2×D6111yescharacteristic
367#472—611no—
368#472C2×D6111yescharacteristic, complemented
369#471—21no—
370#471—1221no—
371#455—21no—
372#455—1221no—
373#454—21no—
374#454—1221no—
375#443—611no—
376#443C2×D6111yescharacteristic
377#443C2×D6111yescharacteristic, complemented
378#368—611no—
379#364—611no—
380#362—611no—
381#362—611no—
382#361—611no—
383#361—611no—
384#359—611no—
385#359—611no—
386#350—611no—
387#350—611no—
388C4×C16—611no—
389C61#3385911yescharacteristic, complemented, Sylow
3902−1+4—21no—
3912−1+4—1221no—
392H(5,𝔽2)—21no—
393H(5,𝔽2)—1221no—
394#137—21no—
395#137—21no—
396#137—41no—
397#137—41no—
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)—41no—
405AGL(1,ℤ/8)—41no—
406AGL(1,ℤ/8)—1221no—
407AGL(1,ℤ/8)—1221no—
408AGL(1,ℤ/8)—2441no—
409AGL(1,ℤ/8)—2441no—
410#135—21no—
411#135—21no—
412#135—41no—
413#135—611no—
414#135—1221no—
415#135—1221no—
416#135—2441no—
417#135C22⋊D6111yescharacteristic
418#135C22×D6111yescharacteristic
419C2×Q16—21no—
420C2×Q16—611no—
421C2×Q16—1221no—
422C2×Q16C22×D6111yescharacteristic
423C2×SD16—21no—
424C2×SD16—41no—
425C2×SD16—1221no—
426C2×SD16—2441no—
427C2×D8—21no—
428C2×D8—611no—
429C2×D8—1221no—
430C2×D8C22×D6111yescharacteristic
431#131—21no—
432#131—1221no—
433#131C22×D6111yescharacteristic
434#131C22×D6111yescharacteristic
435#124—21no—
436#124—1221no—
437Q32—611no—
438Q32—1221no—
439Q32—1221no—
440Q32—1221no—
441Q32—1221no—
442SD32—611no—
443SD32—611no—
444SD32—1221no—
445SD32—1221no—
446SD32—1221no—
447SD32—1221no—
448SD32—2441no—
449SD32—2441no—
450D16—611no—
451D16—1221no—
452D16—1221no—
453D16—1221no—
454D16—1221no—
455M32—611no—
456M32—611no—
457M32—1221no—
458M32—1221no—
459C2×C16—611no—
460C2×C16—611no—
461C2×C16—1221no—
462C2×C16—1221no—
463#108—611no—
464#108C22⋊D6111yescharacteristic
465#108C22×D6111yescharacteristic
466#104—21no—
467#104—1221no—
468#104C22⋊D6111yescharacteristic
469#104C22⋊D6111yescharacteristic
470#101—21no—
471#101—1221no—
472#100—21no—
473#100—1221no—
474C4×C8C22×D6111yescharacteristic
475#41—21no—
476#41—41no—
477#41—41no—
478#41—41no—
479#41—41no—
480#41—81no—
481#41—1221no—
482#41—4881no—
483#41—2441no—
484#41—2441no—
485#41—2441no—
486#41—2441no—
487#41C2×C22⋊D6111yescharacteristic
488#41C2×C22⋊D6111yescharacteristic
489C2×Q8—21no—
490C2×Q8—41no—
491C2×Q8—41no—
492C2×Q8—1221no—
493C2×Q8—2441no—
494C2×Q8—2441no—
495C2×D4—21no—
496C2×D4—41no—
497C2×D4—41no—
498C2×D4—81no—
499C2×D4—1221no—
500C2×D4—4881no—
501C2×D4—2441no—
502C2×D4—2441no—
503Q16—21no—
504Q16—21no—
505Q16—41no—
506Q16—41no—
507Q16—611no—
508Q16—1221no—
509Q16—1221no—
510Q16—2441no—
511Q16—2441no—
512Q16#1175819911yescharacteristic
513Q16D4×D6111yescharacteristic
514SD16—21no—
515SD16—41no—
516SD16—41no—
517SD16—41no—
518SD16—41no—
519SD16—41no—
520SD16—41no—
521SD16—1221no—
522SD16—2441no—
523SD16—2441no—
524SD16—2441no—
525SD16—2441no—
526SD16—2441no—
527SD16—2441no—
528SD16#1175819911yescharacteristic
529SD16#1175819911yescharacteristic
530D8—21no—
531D8—21no—
532D8—41no—
533D8—41no—
534D8—611no—
535D8—1221no—
536D8—1221no—
537D8—2441no—
538D8—2441no—
539D8#1175819911yescharacteristic
540D8D4×D6111yescharacteristic
541M16—21no—
542M16—21no—
543M16—21no—
544M16—41no—
545M16—1221no—
546M16—2441no—
547M16C2×C22⋊D6111yescharacteristic
548M16C2×C22⋊D6111yescharacteristic
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—41no—
552C2×C8—2441no—
553C2×C8C2×C22⋊D6111yescharacteristic
554C2×C8C23×D6111yescharacteristic
555C22⋊C4—81no—
556C22⋊C4—4881no—
557C42C2×C22⋊D6111yescharacteristic
558C16—611no—
559C16—611no—
560C16—1221no—
561C16—1221no—
562C16—1221no—
563C23—41no—
564C23—81no—
565C23—4881no—
566C23—2441no—
567Q8—21no—
568Q8—41no—
569Q8—41no—
570Q8—81no—
571Q8—1221no—
572Q8—4881no—
573Q8—2441no—
574Q8—2441no—
575Q8C2×#1175819911yescharacteristic
576Q8C2×#1175819911yescharacteristic
577D4—21no—
578D4—21no—
579D4—21no—
580D4—41no—
581D4—41no—
582D4—41no—
583D4—81no—
584D4—81no—
585D4—81no—
586D4—1221no—
587D4—4881no—
588D4—4881no—
589D4—4881no—
590D4—2441no—
591D4—2441no—
592D4—2441no—
593D4C2×#1175819911yescharacteristic
594D4C2×#1175819911yescharacteristic
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—81no—
601C2×C4—81no—
602C2×C4—81no—
603C2×C4—4881no—
604C2×C4—4881no—
605C2×C4—4881no—
606C2×C4—2441no—
607C2×C4—2441no—
608C2×C4C22×C22⋊D6111yescharacteristic
609C8—21no—
610C8—21no—
611C8—41no—
612C8—2441no—
613C8C2×#1175819911yescharacteristic
614C8C2×#1175819911yescharacteristic
615C8C2×D4×D6111yescharacteristic
616C8#1451982211yescharacteristic
617C22—21no—
618C22—21no—
619C22—41no—
620C22—81no—
621C22—161no—
622C22—321no—
623C22—19521no—
624C22—9761no—
625C22—4881no—
626C22—2441no—
627C22#1684056511yescharacteristic
628C4—21no—
629C4—21no—
630C4—41no—
631C4—41no—
632C4—81no—
633C4—4881no—
634C4—2441no—
635C4D4×C22⋊D6111yescharacteristic
636C4C22×#1175819911yescharacteristic
637C2—21no—
638C2—41no—
639C2—41no—
640C2—81no—
641C2—161no—
642C2—9761no—
643C2—4881no—
644C2D4×#1175819911yescharacteristic
subgroupG/H
centerC2D4×#11758199
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#3290C2
socleC2×C61D4×D8
hypercenter#3290D61
hypocenterC61#33859
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443 ◁ #3290

Complements

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

NH ≅ G/Ntype
1. #21458970C2semidirect
2. #21458958C2semidirect
3. #21457606C2semidirect
4. #21448078C2semidirect
5. #21447942C2semidirect
6. #21447937C2semidirect
7. #21447888C2semidirect
8. #21447885C2semidirect
9. #21447790C2semidirect
10. #21447788C2semidirect
11. #21447783C2semidirect
12. #21447781C2semidirect
13. #21447698C2semidirect
14. #21447656C2semidirect
15. C61×#3290C2semidirect
16. #16840579C22semidirect
20. #16840203C22semidirect
22. #16840202C22semidirect
31. C2×#14519723C22semidirect
32. C2×#14519721C22semidirect
33. C2×#14519720C22semidirect
37. #16840179C22semidirect
38. #16840146C22semidirect
40. #16840032C22semidirect
44. #16839880C22semidirect
45. #16839591C22semidirect
46. #16839583C22semidirect
47. #16839578C22semidirect
48. #16839577C22semidirect
49. #16839575C22semidirect
50. #16839574C22semidirect
51. #16839569C22semidirect
52. #16839568C22semidirect
54. #16839546C22semidirect
55. C4×#11758185C22semidirect
56. C61×#578C22semidirect
59. C61×#495C22semidirect
61. C61×#472C22semidirect
66. C61×#443C22semidirect
318. #3290D61semidirect
339. #578C2×D61semidirect
364. #495C2×D61semidirect
368. #472C2×D61semidirect
377. #443C2×D61semidirect
389. C61#33859semidirect

Maximal subgroups

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

subgroupindex
#214589702
#214589582
#214576062
#214480782
#214479422
#214479372
#214478882
#214478852
#214477902
#214477882
#214477832
#214477812
#214476982
#214476562
C61×#32902
#3385961