Finite Group Databasebeta

← #29836753

Subgroups — #29836753

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#21458957C211yesmaximal, characteristic, complemented
2#21457616C211yesmaximal, characteristic, complemented
3#21457605C211yesmaximal, characteristic, complemented
4#21448084C211yesmaximal, characteristic, complemented
5#21447946C211yesmaximal, characteristic, complemented
6#21447939C211yesmaximal, characteristic, complemented
7#21447893C211yesmaximal, characteristic, complemented
8#21447890C211yesmaximal, characteristic, complemented
9#21447787C211yesmaximal, characteristic, complemented
10#21447783C211yesmaximal, characteristic, complemented
11#21447776C211yesmaximal, characteristic, complemented
12#21447773C211yesmaximal, characteristic, complemented
13#21447705C211yesmaximal, characteristic, complemented
14#21447659C211yesmaximal, characteristic, complemented
15C61×#3416C211yesmaximal, characteristic, complemented
16#16840570—21no—
17#16840565—21no—
18#16840564C2211yescharacteristic
19#16840564C2211yescharacteristic, complemented
20#16840199—21no—
21#16840199—21no—
22#16840197C2211yescharacteristic
23#16840197C2211yescharacteristic, complemented
24#16840195—21no—
25C2×#14519720C2211yescharacteristic, complemented
26C2×D976C2211yescharacteristic, complemented
27C2×#14519718C2211yescharacteristic, complemented
28D16×D61—21no—
29#16840178C2211yescharacteristic, complemented
30#16840147C2211yescharacteristic, complemented
31#16840137C2211yescharacteristic, complemented
32#16840034C2211yescharacteristic, complemented
33#16840032C2211yescharacteristic, complemented
34#16840032C2211yescharacteristic, complemented
35#16840030—21no—
36#16840029C2211yescharacteristic
37#16840027—21no—
38#16839938—21no—
39#16839935—21no—
40#16839930—21no—
41#16839928—21no—
42#16839879C2211yescharacteristic, complemented
43#16839879C2211yescharacteristic, complemented
44#16839877C2211yescharacteristic
45#16839592C2211yescharacteristic, complemented
46#16839582C2211yescharacteristic, complemented
47#16839578C2211yescharacteristic, complemented
48#16839576C2211yescharacteristic, complemented
49#16839576C2211yescharacteristic, complemented
50#16839575C2211yescharacteristic, complemented
51#16839569C2211yescharacteristic, complemented
52#16839569C2211yescharacteristic, complemented
53#16839547C2211yescharacteristic, complemented
54#16839546C2211yescharacteristic, complemented
55#16839537C2211yescharacteristic, complemented
56C61×#578C2211yescharacteristic, complemented
57C61×#576C2211yescharacteristic, complemented
58C61×#510—21no—
59C61×#510C2211yescharacteristic, complemented
60C61×#509—21no—
61C61×#509C2211yescharacteristic, complemented
62C61×#508—21no—
63C61×#508C2211yescharacteristic
64C2×SD32×C61—21no—
65C2×SD32×C61C2211yescharacteristic, complemented
66C61×#504C2211yescharacteristic, complemented
67#14519823—21no—
68#14519823—21no—
69#14519808—21no—
70#14519808—41no—
71#14519804—41no—
72#14519804—41no—
73#14519803—21no—
74#14519803—41no—
75#14519802—21no—
76#14519802—21no—
77#14519802—21no—
78#14519802—21no—
79#14519802—41no—
80#14519802—41no—
81#14519800—21no—
82#14519800—21no—
83#14519797—41no—
84#14519797—41no—
85#14519797D411yescharacteristic
86C2×#11758201—21no—
87C2×#11758201—41no—
88C2×D488C2311yescharacteristic
89C2×D488C2311yescharacteristic
90C2×#11758199—21no—
91C2×#11758199—41no—
92D8×D61—21no—
93D8×D61—21no—
94#14519784—21no—
95#14519784—21no—
96#14519783C2311yescharacteristic
97#14519773—21no—
98#14519766—21no—
99#14519720—21no—
100#14519720—21no—
101#14519720—41no—
102D976—21no—
103D976—21no—
104#14519718—21no—
105#14519718—21no—
106#14519718—41no—
107#14519717C2311yescharacteristic
108#14519716—21no—
109C2×#11758185C2311yescharacteristic
110C16×D61—21no—
111#14519713C2311yescharacteristic
112#14519713C2311yescharacteristic
113#14519712D411yescharacteristic
114#14519704—21no—
115#14519704—21no—
116#14519704D411yescharacteristic
117#14519703D411yescharacteristic
118#14519696—21no—
119#14519694—21no—
120#14519693—21no—
121#14519693—21no—
122C8×Dic61C2311yescharacteristic
1232−1+4×C61—21no—
124H(5,𝔽2)×C61—21no—
125#137×C61—21no—
126#137×C61—41no—
127AGL(1,ℤ/8)×C61—21no—
128AGL(1,ℤ/8)×C61—41no—
129#135×C61—21no—
130#135×C61—21no—
131#135×C61C2311yescharacteristic
132#135×C61C2311yescharacteristic
133C2×Q16×C61—21no—
134C2×Q16×C61C2311yescharacteristic
135C2×D8×C61—21no—
136C2×D8×C61C2311yescharacteristic
137#131×C61C2311yescharacteristic
138Q32×C61—21no—
139Q32×C61D411yescharacteristic, complemented
140SD32×C61—21no—
141SD32×C61—21no—
142SD32×C61—21no—
143SD32×C61—21no—
144SD32×C61D411yescharacteristic, complemented
145SD32×C61D411yescharacteristic, complemented
146D16×C61—21no—
147D16×C61D411yescharacteristic, complemented
148M32×C61—21no—
149M32×C61C2311yescharacteristic
150C2×C16×C61—21no—
151C2×C16×C61C2311yescharacteristic
152#41×C61—21no—
153#41×C61—21no—
154#41×C61—41no—
155#41×C61—41no—
156#41×C61—41no—
157#41×C61—41no—
158#41×C61—81no—
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—
167C2×C22⋊D61—81no—
168#11758226—41no—
169#11758226—41no—
170D4×D61—41no—
171D4×D61—41no—
172D4×D61—81no—
173D4×D61—81no—
174#11758222—41no—
175#11758222—41no—
176#11758222C2×D411yescharacteristic
177C2×D244—21no—
178C2×D244—21no—
179C2×D244—41no—
180C2×D244—41no—
181Q16×C61—21no—
182Q16×C61—21no—
183Q16×C61—41no—
184Q16×C61C2×D411yescharacteristic
185Q16×C61C2×D411yescharacteristic
186SD16×C61—21no—
187SD16×C61—21no—
188SD16×C61—41no—
189SD16×C61—41no—
190D8×C61—21no—
191D8×C61—21no—
192D8×C61—41no—
193D8×C61C2×D411yescharacteristic
194D8×C61C2×D411yescharacteristic
195M16×C61—21no—
196M16×C61C2×D411yescharacteristic
197C2×C8×C61—21no—
198C2×C8×C61C2411yescharacteristic
199#11758202—41no—
200#11758202D811yescharacteristic
201#11758201—41no—
202#11758201—41no—
203#11758201—41no—
204#11758201—41no—
205#11758201—41no—
206#11758201—41no—
207#11758201—41no—
208#11758201D811yescharacteristic
209#11758200—41no—
210#11758200D811yescharacteristic
211#11758199—41no—
212#11758199—41no—
213#11758199—41no—
214#11758199—41no—
215#11758199—41no—
216#11758199—41no—
217#11758199—41no—
218#11758199D811yescharacteristic
219#11758198—81no—
220C4×Dic61C2×D411yescharacteristic
221#11758194—21no—
222#11758194—21no—
223#11758194—41no—
224#11758194—41no—
225#11758194C2×D411yescharacteristic
226C2×#92418—41no—
227C2×#92418—41no—
228C2×#92418C2×D411yescharacteristic
229D488—21no—
230D488—21no—
231D488—21no—
232D488—21no—
233#11758189—21no—
234C8×D61—21no—
235C16×C61—21no—
236C16×C61C2×D411yescharacteristic
237C16×C61C2×D411yescharacteristic
238#11758185—21no—
239#11758185—21no—
240C23×C61—41no—
241C23×C61—81no—
242C22×D61—41no—
243C22×D61—41no—
244C22×D61—81no—
245C22×D61—81no—
246Q8×C61—21no—
247Q8×C61—21no—
248Q8×C61—41no—
249Q8×C61—41no—
250Q8×C61—81no—
251Q8×C61C2×D811yescharacteristic
252D4×C61—21no—
253D4×C61—21no—
254D4×C61—21no—
255D4×C61—41no—
256D4×C61—41no—
257D4×C61—41no—
258D4×C61—41no—
259D4×C61—81no—
260D4×C61—81no—
261D4×C61—81no—
262D4×C61C2×D811yescharacteristic
263C2×C4×C61—21no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61—81no—
268C2×C4×C61—81no—
269C2×C4×C61—81no—
270C2×C4×C61C22×D411yescharacteristic
271C22⋊D61—21no—
272C22⋊D61—81no—
273C22⋊D61—81no—
274C22⋊D61—162no—
275C2×Dic61—21no—
276D244—41no—
277D244—41no—
278D244—41no—
279D244—41no—
280D244—81no—
281D244—81no—
282D244C2×D811yescharacteristic
283C4×D61—21no—
284C4×D61—81no—
285C4×D61—81no—
286Dic122C2×D811yescharacteristic
287C8×C61—21no—
288C8×C61C22×D411yescharacteristic
289C8×C61H(5,𝔽2)11yescharacteristic
290#92418—21no—
291#92418—41no—
292#92418—41no—
293#92418C2×D811yescharacteristic
294#92418C2×D811yescharacteristic
295#33854—611nomaximal, Sylow
296C22×C61—21no—
297C22×C61—41no—
298C22×C61—41no—
299C22×C61—81no—
300C22×C61—161no—
301C22×C61—321no—
302C22×C61#57611yescharacteristic
303C2×D61—21no—
304C2×D61—81no—
305C2×D61—81no—
306C2×D61—161no—
307C2×D61—161no—
308C2×D61—321no—
309C2×D61—321no—
310C4×C61—21no—
311C4×C61—41no—
312C4×C61—41no—
313C4×C61—81no—
314C4×C61D4211yescharacteristic
315C4×C61C22×D811yescharacteristic
316Dic61—21no—
317Dic61—41no—
318#3416D6111yescharacteristic, complemented
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#2179—611no—
332#2171—611no—
333C2×C61—21no—
334C2×C61—41no—
335C2×C61—81no—
336C2×C61—81no—
337C2×C61—161no—
338C2×C61D4×D811yescharacteristic
339D61—41no—
340D61—161no—
341D61—161no—
342#578C2×D6111yescharacteristic, complemented
343#577—1221no—
344#576—611no—
345#576—611no—
346#576—1221no—
347#576C2×D6111yescharacteristic, complemented
348#510—21no—
349#510C2×D6111yescharacteristic, complemented
350#509—21no—
351#509—611no—
352#509—611no—
353#509—1221no—
354#509—1221no—
355#509C2×D6111yescharacteristic, complemented
356#508—21no—
357#508—1221no—
358#508C2×D6111yescharacteristic
359C2×SD32—21no—
360C2×SD32—611no—
361C2×SD32C2×D6111yescharacteristic, complemented
362C2×D16—611no—
363C2×D16—611no—
364C2×D16—1221no—
365#504—611no—
366#504C2×D6111yescharacteristic, complemented
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#443—611no—
381#443—611no—
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—21no—
395H(5,𝔽2)—21no—
396H(5,𝔽2)—1221no—
397H(5,𝔽2)—1221no—
398#137—21no—
399#137—41no—
400#137—1221no—
401#137—2441no—
402AGL(1,ℤ/8)—21no—
403AGL(1,ℤ/8)—41no—
404AGL(1,ℤ/8)—1221no—
405AGL(1,ℤ/8)—1221no—
406AGL(1,ℤ/8)—1221no—
407AGL(1,ℤ/8)—1221no—
408AGL(1,ℤ/8)—1221no—
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—21no—
415#135—21no—
416#135—611no—
417#135—1221no—
418#135—1221no—
419#135—2441no—
420#135—2441no—
421#135C22×D6111yescharacteristic
422#135C22×D6111yescharacteristic
423C2×Q16—21no—
424C2×Q16C22×D6111yescharacteristic
425C2×SD16—1221no—
426C2×SD16—2441no—
427C2×D8—21no—
428C2×D8—611no—
429C2×D8—611no—
430C2×D8—1221no—
431C2×D8—1221no—
432C2×D8—1221no—
433C2×D8—2441no—
434C2×D8C22×D6111yescharacteristic
435#131—611no—
436#131—1221no—
437#131—1221no—
438#131C22×D6111yescharacteristic
439#127—1221no—
440#124—1221no—
441Q32—21no—
442Q32C22⋊D6111yescharacteristic, complemented
443SD32—21no—
444SD32—21no—
445SD32—21no—
446SD32—21no—
447SD32—1221no—
448SD32—1221no—
449SD32—2441no—
450SD32C22⋊D6111yescharacteristic, complemented
451SD32C22⋊D6111yescharacteristic, complemented
452D16—21no—
453D16—1221no—
454D16—1221no—
455D16—1221no—
456D16—1221no—
457D16—2441no—
458D16C22⋊D6111yescharacteristic, complemented
459M32—21no—
460M32—611no—
461M32—1221no—
462M32C22×D6111yescharacteristic
463C2×C16—21no—
464C2×C16—611no—
465C2×C16—1221no—
466C2×C16C22×D6111yescharacteristic
467#108—611no—
468#108—611no—
469#108—611no—
470#104—611no—
471#104—611no—
472#104—1221no—
473#104—1221no—
474#101—1221no—
475#100—1221no—
476#100—1221no—
477#100—1221no—
478C4×C8—611no—
479#41—21no—
480#41—21no—
481#41—41no—
482#41—41no—
483#41—41no—
484#41—41no—
485#41—81no—
486#41—611no—
487#41—2441no—
488#41—2441no—
489#41—2441no—
490#41—2441no—
491#41D4×D6111yescharacteristic
492C2×Q8—21no—
493C2×Q8—41no—
494C2×Q8—41no—
495C2×D4—21no—
496C2×D4—41no—
497C2×D4—41no—
498C2×D4—81no—
499C2×D4—1221no—
500C2×D4—1221no—
501C2×D4—4881no—
502C2×D4—4881no—
503C2×D4—4881no—
504C2×D4—2441no—
505C2×D4—2441no—
506C2×D4—2441no—
507C2×D4—2441no—
508Q16—21no—
509Q16—21no—
510Q16—41no—
511Q16—611no—
512Q16—2441no—
513Q16C2×C22⋊D6111yescharacteristic
514Q16C2×C22⋊D6111yescharacteristic
515SD16—21no—
516SD16—21no—
517SD16—41no—
518SD16—41no—
519SD16—611no—
520SD16—611no—
521SD16—2441no—
522SD16—2441no—
523SD16—2441no—
524SD16—2441no—
525SD16—2441no—
526SD16—2441no—
527SD16—2441no—
528SD16—2441no—
529D8—21no—
530D8—21no—
531D8—41no—
532D8—611no—
533D8—1221no—
534D8—1221no—
535D8—1221no—
536D8—1221no—
537D8—2441no—
538D8—2441no—
539D8—2441no—
540D8—2441no—
541D8—2441no—
542D8—2441no—
543D8—2441no—
544D8C2×C22⋊D6111yescharacteristic
545D8C2×C22⋊D6111yescharacteristic
546M16—21no—
547M16—611no—
548M16—1221no—
549M16—1221no—
550M16—1221no—
551M16—2441no—
552M16—2441no—
553M16D4×D6111yescharacteristic
554C2×C8—21no—
555C2×C8—611no—
556C2×C8—1221no—
557C2×C8—2441no—
558C2×C8—2441no—
559C2×C8C23×D6111yescharacteristic
560C22⋊C4—4881no—
561C42—611no—
562C16—21no—
563C16—1221no—
564C16—1221no—
565C16C2×C22⋊D6111yescharacteristic
566C16C2×C22⋊D6111yescharacteristic
567C23—41no—
568C23—81no—
569C23—4881no—
570C23—4881no—
571C23—2441no—
572C23—2441no—
573Q8—21no—
574Q8—21no—
575Q8—41no—
576Q8—41no—
577Q8—81no—
578Q8—611no—
579Q8D8×D6111yescharacteristic
580D4—21no—
581D4—21no—
582D4—21no—
583D4—41no—
584D4—41no—
585D4—41no—
586D4—41no—
587D4—81no—
588D4—81no—
589D4—81no—
590D4—611no—
591D4—1221no—
592D4—9762no—
593D4—4881no—
594D4—4881no—
595D4—4881no—
596D4—4881no—
597D4—2441no—
598D4—2441no—
599D4—2441no—
600D4—2441no—
601D4D8×D6111yescharacteristic
602C2×C4—21no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—81no—
607C2×C4—81no—
608C2×C4—81no—
609C2×C4—1221no—
610C2×C4—1221no—
611C2×C4—4881no—
612C2×C4—4881no—
613C2×C4C2×D4×D6111yescharacteristic
614C8—21no—
615C8—611no—
616C8—611no—
617C8—1221no—
618C8—2441no—
619C8—2441no—
620C8C22×C22⋊D6111yescharacteristic
621C8#1451982211yescharacteristic
622C22—21no—
623C22—41no—
624C22—41no—
625C22—81no—
626C22—161no—
627C22—321no—
628C22—1221no—
629C22—19521no—
630C22—19521no—
631C22—9761no—
632C22—9761no—
633C22—4881no—
634C22—4881no—
635C22#1684056311yescharacteristic
636C4—21no—
637C4—41no—
638C4—41no—
639C4—81no—
640C4—1221no—
641C4—2441no—
642C4D4×C22⋊D6111yescharacteristic
643C4C2×D8×D6111yescharacteristic
644C2—21no—
645C2—41no—
646C2—81no—
647C2—81no—
648C2—161no—
649C2—9761no—
650C2—9761no—
651C2—2441no—
652C2D8×C22⋊D6111yescharacteristic
subgroupG/H
centerC2D8×C22⋊D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#3416C2
socleC2×C61D4×D8
hypercenter#3416D61
hypocenterC61#33854
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #3416

Complements

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

NH ≅ G/Ntype
1. #21458957C2semidirect
2. #21457616C2semidirect
3. #21457605C2semidirect
4. #21448084C2semidirect
5. #21447946C2semidirect
6. #21447939C2semidirect
7. #21447893C2semidirect
8. #21447890C2semidirect
9. #21447787C2semidirect
10. #21447783C2semidirect
11. #21447776C2semidirect
12. #21447773C2semidirect
13. #21447705C2semidirect
14. #21447659C2semidirect
15. C61×#3416C2semidirect
19. #16840564C22semidirect
23. #16840197C22semidirect
25. C2×#14519720C22semidirect
26. C2×D976C22semidirect
27. C2×#14519718C22semidirect
29. #16840178C22semidirect
30. #16840147C22semidirect
31. #16840137C22semidirect
32. #16840034C22semidirect
33. #16840032C22semidirect
34. #16840032C22semidirect
42. #16839879C22semidirect
43. #16839879C22semidirect
45. #16839592C22semidirect
46. #16839582C22semidirect
47. #16839578C22semidirect
48. #16839576C22semidirect
49. #16839576C22semidirect
50. #16839575C22semidirect
51. #16839569C22semidirect
52. #16839569C22semidirect
53. #16839547C22semidirect
54. #16839546C22semidirect
55. #16839537C22semidirect
56. C61×#578C22semidirect
57. C61×#576C22semidirect
59. C61×#510C22semidirect
61. C61×#509C22semidirect
65. C2×SD32×C61C22semidirect
66. C61×#504C22semidirect
139. Q32×C61D4semidirect
144. SD32×C61D4semidirect
145. SD32×C61D4semidirect
147. D16×C61D4semidirect
318. #3416D61semidirect
342. #578C2×D61semidirect
347. #576C2×D61semidirect
349. #510C2×D61semidirect
355. #509C2×D61semidirect
361. C2×SD32C2×D61semidirect
366. #504C2×D61semidirect
393. C61#33854semidirect
442. Q32C22⋊D61semidirect
450. SD32C22⋊D61semidirect
451. SD32C22⋊D61semidirect
458. D16C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214589572
#214576162
#214576052
#214480842
#214479462
#214479392
#214478932
#214478902
#214477872
#214477832
#214477762
#214477732
#214477052
#214476592
C61×#34162
#3385461