Finite Group Databasebeta

← D61×#2212 #29834381

Subgroups — D61×#2212 #29834381

Order 15616.

706 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#510×D61C211yesmaximal, characteristic, complemented
2#509×D61C211yesmaximal, characteristic
3#495×D61C211yesmaximal, characteristic, complemented
4#443×D61C211yesmaximal, characteristic, complemented
5#21447891C211yesmaximal, characteristic, complemented
6#21447890C211yesmaximal, characteristic, complemented
7#21447889C211yesmaximal, characteristic, complemented
8#21447888C211yesmaximal, characteristic, complemented
9#21447887C211yesmaximal, characteristic, complemented
10#21447886C211yesmaximal, characteristic, complemented
11#21447885C211yesmaximal, characteristic, complemented
12#364×D61C211yesmaximal, characteristic, complemented
13#362×D61C211yesmaximal, characteristic, complemented
14#361×D61C211yesmaximal, characteristic, complemented
15C61×#2212C211yesmaximal, characteristic, complemented
16#135×D61C2211yescharacteristic
17C2×Q16×D61C2211yescharacteristic
18C2×SD16×D61—21no—
19C2×D8×D61C2211yescharacteristic
20#131×D61—21no—
21#124×D61—21no—
22#16840205C2211yescharacteristic, complemented
23#16840204—21no—
24#16840203C2211yescharacteristic, complemented
25#16840202C2211yescharacteristic, complemented
26#16840201—21no—
27#16840200C2211yescharacteristic
28#16840199—21no—
29#16840198C2211yescharacteristic
30#16840197C2211yescharacteristic
31#16840196—21no—
32Q32×D61—21no—
33SD32×D61—21no—
34SD32×D61—21no—
35D16×D61—21no—
36M32×D61C2211yescharacteristic
37M32×D61C2211yescharacteristic
38#16840147C2211yescharacteristic, complemented
39#16840146C2211yescharacteristic, complemented
40#16840145C2211yescharacteristic, complemented
41#16840144—21no—
42#16840143—21no—
43#16839880C2211yescharacteristic, complemented
44#16839879C2211yescharacteristic, complemented
45#16839878C2211yescharacteristic, complemented
46#16839877—21no—
47#16839876—21no—
48#108×D61C2211yescharacteristic
49#104×D61—21no—
50C4×C8×D61C2211yescharacteristic
51#16839583C2211yescharacteristic, complemented
52#16839582C2211yescharacteristic, complemented
53#16839582C2211yescharacteristic, complemented
54#16839579C2211yescharacteristic, complemented
55#16839578C2211yescharacteristic, complemented
56#16839577C2211yescharacteristic, complemented
57#16839576C2211yescharacteristic, complemented
58#16839575C2211yescharacteristic, complemented
59#16839574C2211yescharacteristic, complemented
60C61×#510C2211yescharacteristic, complemented
61C61×#509C2211yescharacteristic
62C61×#495C2211yescharacteristic, complemented
63C61×#443C2211yescharacteristic, complemented
64C61×#364C2211yescharacteristic, complemented
65C61×#362C2211yescharacteristic, complemented
66C61×#361C2211yescharacteristic, complemented
67#41×D61—21no—
68C2×Q8×D61—21no—
69C2×D4×D61—21no—
70#14519800D411yescharacteristic
71#14519799C2311yescharacteristic
72#14519798—21no—
73#14519797—21no—
74#14519796D411yescharacteristic
75C2×Dic244C2311yescharacteristic
76C2×#11758202—21no—
77Q16×D61—21no—
78Q16×D61—21no—
79Q16×D61—21no—
80Q16×D61—21no—
81Q16×D61D411yescharacteristic
82C2×#11758190—21no—
83C2×#11758200—21no—
84C2×#11758201—21no—
85SD16×D61—21no—
86SD16×D61—41no—
87SD16×D61—41no—
88SD16×D61—41no—
89SD16×D61—41no—
90C2×D488C2311yescharacteristic
91C2×#11758199—21no—
92D8×D61—21no—
93D8×D61—21no—
94D8×D61—21no—
95D8×D61—21no—
96D8×D61D411yescharacteristic
97#14519785—21no—
98#14519785—41no—
99#14519784—21no—
100#14519783—21no—
101#14519783—41no—
102M16×D61—21no—
103M16×D61—41no—
104C2×C8×D61—41no—
105C2×C8×D61D411yescharacteristic
106C2×C8×D61C2311yescharacteristic
107#14519766—21no—
108#14519765—21no—
109#14519764—21no—
110#14519763—42no—
111C22⋊C4×D61—42no—
112C42×D61D411yescharacteristic
113Dic488—21no—
114#14519723—21no—
115#14519723—21no—
116#14519722—21no—
117#14519722—21no—
118#14519721—21no—
119#14519721—21no—
120#14519720—21no—
121#14519720—21no—
122D976—21no—
123#14519718—21no—
124#14519718—21no—
125#14519717C2311yescharacteristic
126#14519717C2311yescharacteristic
127#14519716—21no—
128#14519716—21no—
129C16×D61—21no—
130C16×D61—21no—
131#14519713C2311yescharacteristic
132#14519712—21no—
133#14519705—21no—
134#14519704—21no—
135#14519703—21no—
136C4×#92418D411yescharacteristic
137C8×Dic61D411yescharacteristic
138C8×Dic61C2311yescharacteristic
139#135×C61C2311yescharacteristic
140C2×Q16×C61C2311yescharacteristic
141C2×SD16×C61—21no—
142C2×D8×C61C2311yescharacteristic
143#131×C61—21no—
144#124×C61—21no—
145Q32×C61—21no—
146SD32×C61—21no—
147SD32×C61—21no—
148D16×C61—21no—
149M32×C61C2311yescharacteristic
150M32×C61C2311yescharacteristic
151#108×C61C2311yescharacteristic
152#104×C61—21no—
153C4×C8×C61C2311yescharacteristic
154C23×D61—41no—
155#41×C61—21no—
156C2×Q8×C61—21no—
157C2×D4×C61—21no—
158C2×C22⋊D61—41no—
159#11758226—21no—
160Q8×D61—21no—
161Q8×D61—41no—
162Q8×D61—41no—
163Q8×D61—41no—
164Q8×D61—41no—
165#11758224—21no—
166#11758224—41no—
167D4×D61—21no—
168D4×D61—41no—
169D4×D61—41no—
170D4×D61—41no—
171D4×D61—41no—
172D4×D61—41no—
173#11758222—21no—
174#11758222—41no—
175C2×D244—21no—
176C2×C4×D61—21no—
177C2×C4×D61—41no—
178C2×C4×D61—41no—
179C2×C4×D61C2×D411yescharacteristic
180C2×Dic122—21no—
181C2×Dic122—41no—
182Q16×C61—21no—
183Q16×C61—21no—
184Q16×C61C2×D411yescharacteristic
185SD16×C61—21no—
186SD16×C61—41no—
187SD16×C61—41no—
188D8×C61—21no—
189D8×C61—21no—
190D8×C61C2×D411yescharacteristic
191M16×C61—21no—
192M16×C61—41no—
193C2×C8×C61—41no—
194C2×C8×C61C2×D411yescharacteristic
195C2×C8×C61C2411yescharacteristic
196C22⋊C4×C61—42no—
197C42×C61C2×D411yescharacteristic
198C22⋊Dic61—42no—
199#11758202—21no—
200#11758202—41no—
201#11758202—41no—
202#11758201—21no—
203#11758201—41no—
204#11758201—41no—
205#11758200—21no—
206#11758200—41no—
207#11758200—41no—
208#11758199—21no—
209#11758199—41no—
210#11758199—41no—
211#11758198—42no—
212#11758198—42no—
213C4×Dic61—21no—
214C4×Dic61C2×D411yescharacteristic
215#11758194—21no—
216#11758194—41no—
217C2×#92418—41no—
218C2×#92418C2×D411yescharacteristic
219C2×#92418C2×D411yescharacteristic
220Dic244—21no—
221Dic244—21no—
222Dic244C2×D411yescharacteristic
223D488—21no—
224D488—21no—
225D488C2×D411yescharacteristic
226#11758190—21no—
227#11758190—41no—
228#11758190—41no—
229#11758189—41no—
230#11758189—41no—
231#11758189—41no—
232C8×D61—41no—
233C8×D61—41no—
234C8×D61—41no—
235C8×D61D811yescharacteristic
236C8×D61D811yescharacteristic
237C8×D61D811yescharacteristic
238C8×D61D811yescharacteristic
239C8×D61C2×D411yescharacteristic
240C8×D61C2×D411yescharacteristic
241C8×D61#4111yescharacteristic
242C8×D61#4111yescharacteristic
243C16×C61—21no—
244C16×C61—21no—
245#11758185—21no—
246#11758185—21no—
247C23×C61—41no—
248C22×D61—41no—
249C22×D61—41no—
250C22×D61—84no—
251C22×D61—81no—
252C22×D61—81no—
253C22×D61AGL(1,ℤ/8)11yescharacteristic
254Q8×C61—21no—
255Q8×C61—41no—
256Q8×C61—41no—
257D4×C61—21no—
258D4×C61—41no—
259D4×C61—41no—
260D4×C61—41no—
261C2×C4×C61—21no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61C22×D411yescharacteristic
265C22⋊D61—41no—
266C22⋊D61—41no—
267C22⋊D61—41no—
268C22⋊D61—81no—
269C22⋊D61—81no—
270C2×Dic61—21no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61AGL(1,ℤ/8)11yescharacteristic
274D244—21no—
275D244—41no—
276D244—41no—
277D244—41no—
278C4×D61—42no—
279C4×D61—41no—
280C4×D61—41no—
281C4×D61—41no—
282C4×D61—81no—
283C4×D61—81no—
284C4×D61#12111yescharacteristic
285C4×D61#12111yescharacteristic
286C4×D61C2×D811yescharacteristic
287C4×D61C2×D811yescharacteristic
288Dic122—21no—
289Dic122—41no—
290Dic122—41no—
291Dic122—41no—
292Dic122—81no—
293Dic122—81no—
294C8×C61—41no—
295C8×C61C2×D811yescharacteristic
296C8×C61C2×D811yescharacteristic
297C8×C61C22×D411yescharacteristic
298C8×C61C2×#4111yescharacteristic
299#92418—41no—
300#92418#12111yescharacteristic
301#92418#12111yescharacteristic
302#92418C2×D811yescharacteristic
303#92418C2×D811yescharacteristic
304C2×#2212—611nomaximal, Sylow
305C22×C61—41no—
306C22×C61—82no—
307C22×C61—81no—
308C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
309C2×D61—22no—
310C2×D61—41no—
311C2×D61—82no—
312C2×D61—82no—
313C2×D61—81no—
314C2×D61—162no—
315C2×D61—162no—
316C2×D61#45911yescharacteristic
317C2×D61#45911yescharacteristic
318C4×C61—41no—
319C4×C61—41no—
320C4×C61—81no—
321C4×C61C2×#12111yescharacteristic
322C4×C61C22×D811yescharacteristic
323Dic61—41no—
324Dic61—41no—
325Dic61—81no—
326Dic61#45911yescharacteristic
327Dic61#45911yescharacteristic
328C2×#510—611no—
329C2×#509—611no—
330C2×#495—611no—
331C2×#443—611no—
332#2212—611no—
333#2212—611no—
334#2212—611no—
335#2212—611no—
336#2212—611no—
337#2212—611no—
338#2212—611no—
339#2212D6111yescharacteristic, direct product factor
340C2×#364—611no—
341C2×#362—611no—
342C2×#361—611no—
343C2×C61—21no—
344C2×C61—81no—
345C2×C61—161no—
346C2×C61C2×#45911yescharacteristic
347D61—21no—
348D61—81no—
349D61—161no—
350D61#221212yesdirect product factor
351C2×#135—611no—
352C22×Q16—611no—
353C22×SD16—1221no—
354C22×D8—611no—
355C2×#131—1221no—
356C2×#124—1221no—
357#510—611no—
358#510—611no—
359#510—611no—
360#510—1221no—
361#510—1221no—
362#510C2×D6111yescharacteristic, complemented
363#509—611no—
364#509—611no—
365#509—611no—
366#509—1221no—
367#509—1221no—
368#509C2×D6111yescharacteristic
369C2×Q32—1221no—
370C2×SD32—1221no—
371C2×SD32—1221no—
372C2×D16—1221no—
373C2×M32—611no—
374C2×M32—611no—
375#495—611no—
376#495—611no—
377#495—611no—
378#495—1221no—
379#495—1221no—
380#495C2×D6111yescharacteristic, complemented
381#443—611no—
382#443—611no—
383#443—611no—
384#443—1221no—
385#443—1221no—
386#443C2×D6111yescharacteristic, complemented
387C2×#108—611no—
388C2×#104—1221no—
389C2×C4×C8—611no—
390#364—611no—
391#364—611no—
392#364—611no—
393#364C2×D6111yescharacteristic, complemented
394#362—611no—
395#362—611no—
396#362—611no—
397#362C2×D6111yescharacteristic, complemented
398#361—611no—
399#361—611no—
400#361—611no—
401#361C2×D6111yescharacteristic, complemented
402C61C2×#221211yescharacteristic, complemented, Sylow
403C2×#41—1221no—
404C22×Q8—1221no—
405C22×D4—1221no—
406#135—611no—
407#135—611no—
408#135—611no—
409#135—1221no—
410#135—1221no—
411#135C22×D6111yescharacteristic
412C2×Q16—611no—
413C2×Q16—611no—
414C2×Q16—1221no—
415C2×Q16—1221no—
416C2×Q16—1221no—
417C2×Q16—1221no—
418C2×Q16—1221no—
419C2×Q16C22×D6111yescharacteristic
420C2×SD16—21no—
421C2×SD16—1221no—
422C2×SD16—1221no—
423C2×SD16—1221no—
424C2×SD16—1221no—
425C2×SD16—2441no—
426C2×SD16—2441no—
427C2×SD16—2441no—
428C2×SD16—2441no—
429C2×D8—611no—
430C2×D8—611no—
431C2×D8—1221no—
432C2×D8—1221no—
433C2×D8—1221no—
434C2×D8—1221no—
435C2×D8—1221no—
436C2×D8C22×D6111yescharacteristic
437#131—21no—
438#131—1221no—
439#131—1221no—
440#131—1221no—
441#131—2441no—
442#131—2441no—
443C2×M16—1221no—
444C2×M16—2441no—
445C22×C8—611no—
446C22×C8—611no—
447C22×C8—2441no—
448#124—21no—
449#124—1221no—
450#124—1221no—
451#124—1221no—
452#124—2442no—
453C2×C22⋊C4—2442no—
454C2×C42—611no—
455Q32—21no—
456Q32—1221no—
457Q32—1221no—
458Q32—1221no—
459SD32—21no—
460SD32—21no—
461SD32—1221no—
462SD32—1221no—
463SD32—1221no—
464SD32—1221no—
465SD32—1221no—
466SD32—1221no—
467D16—21no—
468D16—1221no—
469D16—1221no—
470D16—1221no—
471M32—611no—
472M32—611no—
473M32—1221no—
474M32—1221no—
475M32C22×D6111yescharacteristic
476M32C22×D6111yescharacteristic
477C2×C16—1221no—
478C2×C16—1221no—
479#108—611no—
480#108—1221no—
481#108C22×D6111yescharacteristic
482#104—21no—
483#104—1221no—
484#104—1221no—
485#104—1221no—
486C4×C8—611no—
487C4×C8—611no—
488C4×C8—611no—
489C4×C8C22×D6111yescharacteristic
490C24—2441no—
491#41—21no—
492#41—1221no—
493#41—1221no—
494#41—1221no—
495#41—2441no—
496#41—2441no—
497C2×Q8—21no—
498C2×Q8—1221no—
499C2×Q8—1221no—
500C2×Q8—2441no—
501C2×Q8—2441no—
502C2×Q8—2441no—
503C2×Q8—2441no—
504C2×Q8—2441no—
505C2×D4—21no—
506C2×D4—1221no—
507C2×D4—1221no—
508C2×D4—2441no—
509C2×D4—2441no—
510C2×D4—2441no—
511C2×D4—2441no—
512C2×D4—2441no—
513C2×D4—2441no—
514C22×C4—611no—
515C22×C4—1221no—
516C22×C4—2441no—
517C22×C4—2441no—
518Q16—21no—
519Q16—21no—
520Q16—611no—
521Q16—1221no—
522Q16—1221no—
523Q16—1221no—
524Q16—2441no—
525Q16—2441no—
526Q16D4×D6111yescharacteristic
527SD16—21no—
528SD16—41no—
529SD16—41no—
530SD16—1221no—
531SD16—1221no—
532SD16—1221no—
533SD16—2441no—
534SD16—2441no—
535SD16—2441no—
536SD16—2441no—
537SD16—2441no—
538SD16—2441no—
539D8—21no—
540D8—21no—
541D8—611no—
542D8—1221no—
543D8—1221no—
544D8—1221no—
545D8—2441no—
546D8—2441no—
547D8D4×D6111yescharacteristic
548M16—21no—
549M16—41no—
550M16—1221no—
551M16—2441no—
552M16—2441no—
553M16—2441no—
554M16—2441no—
555C2×C8—41no—
556C2×C8—611no—
557C2×C8—611no—
558C2×C8—611no—
559C2×C8—611no—
560C2×C8—611no—
561C2×C8—611no—
562C2×C8—611no—
563C2×C8—611no—
564C2×C8—611no—
565C2×C8—611no—
566C2×C8—2441no—
567C2×C8—2441no—
568C2×C8—2441no—
569C2×C8—2441no—
570C2×C8D4×D6111yescharacteristic
571C2×C8C23×D6111yescharacteristic
572C22⋊C4—42no—
573C22⋊C4—2442no—
574C22⋊C4—2442no—
575C22⋊C4—2442no—
576C42—611no—
577C42—1221no—
578C42D4×D6111yescharacteristic
579C16—21no—
580C16—21no—
581C16—1221no—
582C16—1221no—
583C23—41no—
584C23—611no—
585C23—4881no—
586C23—4881no—
587C23—4884no—
588C23—2441no—
589C23—2441no—
590Q8—21no—
591Q8—41no—
592Q8—41no—
593Q8—1221no—
594Q8—4881no—
595Q8—4881no—
596Q8—2441no—
597Q8—2441no—
598Q8—2441no—
599D4—21no—
600D4—41no—
601D4—41no—
602D4—41no—
603D4—1221no—
604D4—4881no—
605D4—4881no—
606D4—2441no—
607D4—2441no—
608D4—2441no—
609D4—2441no—
610D4—2441no—
611D4—2441no—
612C2×C4—21no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—611no—
616C2×C4—611no—
617C2×C4—611no—
618C2×C4—611no—
619C2×C4—611no—
620C2×C4—1221no—
621C2×C4—4881no—
622C2×C4—4881no—
623C2×C4—2441no—
624C2×C4—2441no—
625C2×C4—2442no—
626C2×C4—2441no—
627C2×C4—2441no—
628C2×C4—2441no—
629C2×C4C2×D4×D6111yescharacteristic
630C8—41no—
631C8—611no—
632C8—611no—
633C8—611no—
634C8—611no—
635C8—2441no—
636C8D8×D6111yescharacteristic
637C8D8×D6111yescharacteristic
638C8C2×D4×D6111yescharacteristic
639C8#41×D6111yescharacteristic
640C22—41no—
641C22—82no—
642C22—81no—
643C22—611no—
644C22—611no—
645C22—1222no—
646C22—9762no—
647C22—9762no—
648C22—4882no—
649C22—4882no—
650C22—4881no—
651C22—2441no—
652C22AGL(1,ℤ/8)×D6111yescharacteristic
653C4—41no—
654C4—41no—
655C4—81no—
656C4—611no—
657C4—611no—
658C4—4881no—
659C4—2441no—
660C4—2441no—
661C4#121×D6111yescharacteristic
662C4C2×D8×D6111yescharacteristic
663C2—21no—
664C2—81no—
665C2—161no—
666C2—612no—
667C2—1221no—
668C2—9761no—
669C2—4881no—
670C2#459×D6111yescharacteristic
subgroupG/H
centerC2#459×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2212C2
socleC2×C61C2×#459
prime radical#509×D61C2
hypercenter#2212D61
hypocenterC61C2×#2212
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2212

Complements

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

NH ≅ G/Ntype
1. #510×D61C2semidirect
3. #495×D61C2semidirect
4. #443×D61C2semidirect
5. #21447891C2semidirect
6. #21447890C2semidirect
7. #21447889C2semidirect
8. #21447888C2semidirect
9. #21447887C2semidirect
10. #21447886C2semidirect
11. #21447885C2semidirect
12. #364×D61C2semidirect
13. #362×D61C2semidirect
14. #361×D61C2semidirect
15. C61×#2212C2semidirect
22. #16840205C22semidirect
24. #16840203C22semidirect
25. #16840202C22semidirect
38. #16840147C22semidirect
39. #16840146C22semidirect
40. #16840145C22semidirect
43. #16839880C22semidirect
44. #16839879C22semidirect
45. #16839878C22semidirect
51. #16839583C22semidirect
52. #16839582C22semidirect
53. #16839582C22semidirect
54. #16839579C22semidirect
55. #16839578C22semidirect
56. #16839577C22semidirect
57. #16839576C22semidirect
58. #16839575C22semidirect
59. #16839574C22semidirect
60. C61×#510C22semidirect
62. C61×#495C22semidirect
63. C61×#443C22semidirect
64. C61×#364C22semidirect
65. C61×#362C22semidirect
66. C61×#361C22semidirect
339. #2212D61direct (N × H)
350. D61#2212direct (N × H)
362. #510C2×D61semidirect
380. #495C2×D61semidirect
386. #443C2×D61semidirect
393. #364C2×D61semidirect
397. #362C2×D61semidirect
401. #361C2×D61semidirect
402. C61C2×#2212semidirect

Maximal subgroups

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

subgroupindex
#510×D612
#509×D612
#495×D612
#443×D612
#214478912
#214478902
#214478892
#214478882
#214478872
#214478862
#214478852
#364×D612
#362×D612
#361×D612
C61×#22122
C2×#221261