Finite Group Databasebeta

← #29836783

Subgroups — #29836783

Order 15616.

652 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458962C211yesmaximal, characteristic, complemented
2#21457621C211yesmaximal, characteristic, complemented
3#21457616C211yesmaximal, characteristic, complemented
4#21448073C211yesmaximal, characteristic, complemented
5#21447949C211yesmaximal, characteristic, complemented
6#21447946C211yesmaximal, characteristic, complemented
7#21447898C211yesmaximal, characteristic, complemented
8#21447893C211yesmaximal, characteristic, complemented
9#21447790C211yesmaximal, characteristic, complemented
10#21447787C211yesmaximal, characteristic, complemented
11#21447783C211yesmaximal, characteristic, complemented
12#21447780C211yesmaximal, characteristic, complemented
13#21447700C211yesmaximal, characteristic, complemented
14#21447654C211yesmaximal, characteristic, complemented
15C61×#3416C211yesmaximal, characteristic, complemented
16#16840577—21no—
17#16840576C2211yescharacteristic, complemented
18#16840565—21no—
19#16840564C2211yescharacteristic
20#16840204—21no—
21#16840202C2211yescharacteristic
22#16840197C2211yescharacteristic, complemented
23#16840196—21no—
24#16840193—21no—
25C2×#14519722C2211yescharacteristic, complemented
26C2×#14519721C2211yescharacteristic, complemented
27C2×#14519720C2211yescharacteristic, complemented
28SD32×D61—21no—
29#16840178C2211yescharacteristic, complemented
30#16840140C2211yescharacteristic, complemented
31#16840137C2211yescharacteristic
32#16840037C2211yescharacteristic, complemented
33#16840035—21no—
34#16840034C2211yescharacteristic, complemented
35#16840032C2211yescharacteristic
36#16840030—21no—
37#16840029C2211yescharacteristic
38#16839945—21no—
39#16839943—21no—
40#16839930—21no—
41#16839928—21no—
42#16839879C2211yescharacteristic
43#16839879C2211yescharacteristic, complemented
44#16839877C2211yescharacteristic
45#16839592C2211yescharacteristic, complemented
46#16839582C2211yescharacteristic, complemented
47#16839579C2211yescharacteristic, complemented
48#16839578C2211yescharacteristic, complemented
49#16839576C2211yescharacteristic, complemented
50#16839575C2211yescharacteristic, complemented
51#16839569C2211yescharacteristic
52#16839569C2211yescharacteristic, complemented
53#16839547C2211yescharacteristic, complemented
54#16839546C2211yescharacteristic, complemented
55C16×Dic61C2211yescharacteristic, complemented
56C61×#578C2211yescharacteristic, complemented
57C61×#576C2211yescharacteristic
58C61×#510—21no—
59C61×#510C2211yescharacteristic
60C61×#509—21no—
61C61×#509C2211yescharacteristic, complemented
62C61×#508—21no—
63C61×#508C2211yescharacteristic
64C2×SD32×C61—21no—
65C2×SD32×C61C2211yescharacteristic, complemented
66C61×#504C2211yescharacteristic, complemented
67#14519824—21no—
68#14519823—21no—
69#14519808—21no—
70#14519808—41no—
71#14519807—21no—
72#14519807—21no—
73#14519807—41no—
74#14519806—41no—
75#14519804—41no—
76#14519803—21no—
77#14519803—41no—
78#14519802—21no—
79#14519802—21no—
80#14519802—41no—
81#14519800—21no—
82#14519797—41no—
83#14519797—41no—
84#14519797D411yescharacteristic
85#14519796—21no—
86C2×Dic244C2311yescharacteristic
87C2×#11758202—21no—
88C2×#11758202—41no—
89Q16×D61—21no—
90C2×D488C2311yescharacteristic
91C2×#11758199—21no—
92C2×#11758199—41no—
93D8×D61—21no—
94#14519784—21no—
95#14519784—21no—
96#14519783C2311yescharacteristic
97#14519775—21no—
98#14519773—21no—
99#14519723—21no—
100#14519722—21no—
101#14519722—21no—
102#14519721—21no—
103#14519721—41no—
104#14519720—21no—
105#14519720—41no—
106#14519718—21no—
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#14519695—21no—
120#14519694—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—
169Q8×D61—41no—
170#11758224—41no—
171#11758224—81no—
172D4×D61—41no—
173D4×D61—81no—
174#11758222—41no—
175#11758222—41no—
176#11758222C2×D411yescharacteristic
177C2×D244—21no—
178C2×D244—41no—
179C2×Dic122—21no—
180C2×Dic122—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#11758202—41no—
201#11758202—41no—
202#11758202—41no—
203#11758202—41no—
204#11758202D811yescharacteristic
205#11758201—41no—
206#11758201—41no—
207#11758201—41no—
208#11758201D811yescharacteristic
209#11758200—41no—
210#11758200—41no—
211#11758200—41no—
212#11758200D811yescharacteristic
213#11758199—41no—
214#11758199—41no—
215#11758199—41no—
216#11758199—41no—
217#11758199—41no—
218#11758199D811yescharacteristic
219#11758196—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
229Dic244—21no—
230Dic244—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—81no—
244Q8×C61—21no—
245Q8×C61—21no—
246Q8×C61—41no—
247Q8×C61—41no—
248Q8×C61—81no—
249Q8×C61C2×D811yescharacteristic
250D4×C61—21no—
251D4×C61—21no—
252D4×C61—21no—
253D4×C61—41no—
254D4×C61—41no—
255D4×C61—41no—
256D4×C61—41no—
257D4×C61—81no—
258D4×C61—81no—
259D4×C61—81no—
260D4×C61C2×D811yescharacteristic
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×C61C22×D411yescharacteristic
269C22⋊D61—21no—
270C22⋊D61—81no—
271C22⋊D61—81no—
272C22⋊D61—162no—
273C2×Dic61—21no—
274C2×Dic61—41no—
275C2×Dic61—81no—
276D244—41no—
277D244—41no—
278D244—81no—
279D244C2×D811yescharacteristic
280C4×D61—21no—
281C4×D61—81no—
282C4×D61—81no—
283Dic122—41no—
284Dic122—41no—
285Dic122—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#33856—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—161no—
306C2×D61—321no—
307C4×C61—21no—
308C4×C61—41no—
309C4×C61—41no—
310C4×C61—81no—
311C4×C61D4211yescharacteristic
312C4×C61C22×D811yescharacteristic
313Dic61—22no—
314Dic61—21no—
315Dic61—81no—
316#3416—611no—
317#3416D6111yescharacteristic, complemented
318#3293—611no—
319#3292—611no—
320#2248—611no—
321#2223—611no—
322#2223—611no—
323#2214—611no—
324#2213—611no—
325#2194—611no—
326#2194—611no—
327#2193—611no—
328#2193—611no—
329#2178—611no—
330#2170—611no—
331C2×C61—21no—
332C2×C61—41no—
333C2×C61—81no—
334C2×C61—81no—
335C2×C61—161no—
336C2×C61D4×D811yescharacteristic
337D61—41no—
338D61—161no—
339#578—611no—
340#578—1221no—
341#578C2×D6111yescharacteristic, complemented
342#576—611no—
343#576—1221no—
344#576C2×D6111yescharacteristic
345#510—21no—
346#510—611no—
347#510—1221no—
348#510C2×D6111yescharacteristic
349#509—21no—
350#509—611no—
351#509—1221no—
352#509C2×D6111yescharacteristic, complemented
353#508—21no—
354#508—1221no—
355#508C2×D6111yescharacteristic
356C2×SD32—21no—
357C2×SD32—611no—
358C2×SD32—611no—
359C2×SD32—611no—
360C2×SD32—1221no—
361C2×SD32C2×D6111yescharacteristic, complemented
362#504—611no—
363#504C2×D6111yescharacteristic, complemented
364#494—611no—
365#493—611no—
366#473—611no—
367#473—611no—
368#473—1221no—
369#472—611no—
370#472—611no—
371#472—1221no—
372#456—1221no—
373#456—1221no—
374#453—1221no—
375#453—1221no—
376#443—611no—
377#443—611no—
378#443—611no—
379#368—611no—
380#364—611no—
381#362—611no—
382#362—611no—
383#361—611no—
384#361—611no—
385#359—611no—
386#359—611no—
387#350—611no—
388#350—611no—
389C4×C16—611no—
390C61#3385611yescharacteristic, complemented, Sylow
3912−1+4—21no—
3922−1+4—1221no—
393H(5,𝔽2)—21no—
394H(5,𝔽2)—1221no—
395#137—21no—
396#137—41no—
397#137—1221no—
398#137—1221no—
399#137—1221no—
400#137—2441no—
401#137—2441no—
402#137—2441no—
403AGL(1,ℤ/8)—21no—
404AGL(1,ℤ/8)—41no—
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—
411#135—21no—
412#135—21no—
413#135—611no—
414#135—1221no—
415#135—1221no—
416#135—2441no—
417#135—2441no—
418#135C22×D6111yescharacteristic
419#135C22×D6111yescharacteristic
420C2×Q16—21no—
421C2×Q16—611no—
422C2×Q16—1221no—
423C2×Q16—1221no—
424C2×Q16—2441no—
425C2×Q16C22×D6111yescharacteristic
426C2×D8—21no—
427C2×D8—611no—
428C2×D8—1221no—
429C2×D8—1221no—
430C2×D8—2441no—
431C2×D8C22×D6111yescharacteristic
432#131—611no—
433#131—1221no—
434#131—1221no—
435#131C22×D6111yescharacteristic
436C4⋊Q8—1221no—
437#127—1221no—
438Q32—21no—
439Q32—1221no—
440Q32C22⋊D6111yescharacteristic, complemented
441SD32—21no—
442SD32—21no—
443SD32—21no—
444SD32—21no—
445SD32—1221no—
446SD32—1221no—
447SD32—1221no—
448SD32—1221no—
449SD32—2441no—
450SD32—2441no—
451SD32C22⋊D6111yescharacteristic, complemented
452SD32C22⋊D6111yescharacteristic, complemented
453D16—21no—
454D16—1221no—
455D16C22⋊D6111yescharacteristic, complemented
456M32—21no—
457M32—611no—
458M32—1221no—
459M32C22×D6111yescharacteristic
460C2×C16—21no—
461C2×C16—611no—
462C2×C16—1221no—
463C2×C16C22×D6111yescharacteristic
464#108—611no—
465#108—611no—
466#108—611no—
467#104—611no—
468#104—611no—
469#104—1221no—
470#104—1221no—
471#101—1221no—
472#101—1221no—
473#100—1221no—
474#100—1221no—
475C4×C8—611no—
476#41—21no—
477#41—21no—
478#41—41no—
479#41—41no—
480#41—41no—
481#41—41no—
482#41—81no—
483#41—611no—
484#41—4881no—
485#41—2441no—
486#41—2441no—
487#41—2441no—
488#41—2441no—
489#41D4×D6111yescharacteristic
490C2×Q8—21no—
491C2×Q8—41no—
492C2×Q8—41no—
493C2×Q8—1221no—
494C2×Q8—2441no—
495C2×Q8—2441no—
496C2×D4—21no—
497C2×D4—41no—
498C2×D4—41no—
499C2×D4—81no—
500C2×D4—1221no—
501C2×D4—4881no—
502C2×D4—4881no—
503C2×D4—2441no—
504C2×D4—2441no—
505Q16—21no—
506Q16—21no—
507Q16—41no—
508Q16—611no—
509Q16—1221no—
510Q16—1221no—
511Q16—2441no—
512Q16—2441no—
513Q16—2441no—
514Q16—2441no—
515Q16—2441no—
516Q16C2×C22⋊D6111yescharacteristic
517Q16C2×C22⋊D6111yescharacteristic
518SD16—21no—
519SD16—21no—
520SD16—41no—
521SD16—41no—
522SD16—611no—
523SD16—611no—
524SD16—2441no—
525SD16—2441no—
526SD16—2441no—
527SD16—2441no—
528SD16—2441no—
529SD16—2441no—
530D8—21no—
531D8—21no—
532D8—41no—
533D8—611no—
534D8—1221no—
535D8—1221no—
536D8—2441no—
537D8—2441no—
538D8—2441no—
539D8—2441no—
540D8—2441no—
541D8C2×C22⋊D6111yescharacteristic
542D8C2×C22⋊D6111yescharacteristic
543M16—21no—
544M16—611no—
545M16—1221no—
546M16—1221no—
547M16—1221no—
548M16—2441no—
549M16—2441no—
550M16D4×D6111yescharacteristic
551C2×C8—21no—
552C2×C8—611no—
553C2×C8—1221no—
554C2×C8—2441no—
555C2×C8—2441no—
556C2×C8C23×D6111yescharacteristic
557C4⋊C4—4881no—
558C42—611no—
559C16—21no—
560C16—1221no—
561C16—1221no—
562C16C2×C22⋊D6111yescharacteristic
563C16C2×C22⋊D6111yescharacteristic
564C23—41no—
565C23—81no—
566C23—4881no—
567C23—2441no—
568Q8—21no—
569Q8—21no—
570Q8—41no—
571Q8—41no—
572Q8—81no—
573Q8—611no—
574Q8—4881no—
575Q8—2441no—
576Q8—2441no—
577Q8D8×D6111yescharacteristic
578D4—21no—
579D4—21no—
580D4—21no—
581D4—41no—
582D4—41no—
583D4—41no—
584D4—41no—
585D4—81no—
586D4—81no—
587D4—81no—
588D4—611no—
589D4—1221no—
590D4—9762no—
591D4—4881no—
592D4—4881no—
593D4—4881no—
594D4—2441no—
595D4—2441no—
596D4D8×D6111yescharacteristic
597C2×C4—21no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—81no—
602C2×C4—81no—
603C2×C4—81no—
604C2×C4—1221no—
605C2×C4—1221no—
606C2×C4—4881no—
607C2×C4—4881no—
608C2×C4—4881no—
609C2×C4—2441no—
610C2×C4C2×D4×D6111yescharacteristic
611C8—21no—
612C8—611no—
613C8—611no—
614C8—1221no—
615C8—2441no—
616C8—2441no—
617C8C22×C22⋊D6111yescharacteristic
618C8#1451982211yescharacteristic
619C22—21no—
620C22—41no—
621C22—41no—
622C22—81no—
623C22—161no—
624C22—321no—
625C22—1221no—
626C22—19521no—
627C22—9761no—
628C22—4881no—
629C22#1684056311yescharacteristic
630C4—21no—
631C4—41no—
632C4—41no—
633C4—81no—
634C4—1222no—
635C4—1221no—
636C4—4881no—
637C4D4×C22⋊D6111yescharacteristic
638C4C2×D8×D6111yescharacteristic
639C2—21no—
640C2—41no—
641C2—81no—
642C2—81no—
643C2—161no—
644C2—9761no—
645C2—2441no—
646C2D8×C22⋊D6111yescharacteristic
subgroupG/H
centerC2D8×C22⋊D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#3416C2
socleC2×C61D4×D8
hypercenter#3416D61
hypocenterC61#33856
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. #21458962C2semidirect
2. #21457621C2semidirect
3. #21457616C2semidirect
4. #21448073C2semidirect
5. #21447949C2semidirect
6. #21447946C2semidirect
7. #21447898C2semidirect
8. #21447893C2semidirect
9. #21447790C2semidirect
10. #21447787C2semidirect
11. #21447783C2semidirect
12. #21447780C2semidirect
13. #21447700C2semidirect
14. #21447654C2semidirect
15. C61×#3416C2semidirect
17. #16840576C22semidirect
22. #16840197C22semidirect
25. C2×#14519722C22semidirect
26. C2×#14519721C22semidirect
27. C2×#14519720C22semidirect
29. #16840178C22semidirect
30. #16840140C22semidirect
32. #16840037C22semidirect
34. #16840034C22semidirect
43. #16839879C22semidirect
45. #16839592C22semidirect
46. #16839582C22semidirect
47. #16839579C22semidirect
48. #16839578C22semidirect
49. #16839576C22semidirect
50. #16839575C22semidirect
52. #16839569C22semidirect
53. #16839547C22semidirect
54. #16839546C22semidirect
55. C16×Dic61C22semidirect
56. C61×#578C22semidirect
61. C61×#509C22semidirect
65. C2×SD32×C61C22semidirect
66. C61×#504C22semidirect
139. Q32×C61D4semidirect
144. SD32×C61D4semidirect
145. SD32×C61D4semidirect
147. D16×C61D4semidirect
317. #3416D61semidirect
341. #578C2×D61semidirect
352. #509C2×D61semidirect
361. C2×SD32C2×D61semidirect
363. #504C2×D61semidirect
390. C61#33856semidirect
440. Q32C22⋊D61semidirect
451. SD32C22⋊D61semidirect
452. SD32C22⋊D61semidirect
455. D16C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214589622
#214576212
#214576162
#214480732
#214479492
#214479462
#214478982
#214478932
#214477902
#214477872
#214477832
#214477802
#214477002
#214476542
C61×#34162
#3385661