Finite Group Databasebeta

← #29834594

Subgroups — #29834594

Order 15616.

656 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840196C211yesmaximal, characteristic, complemented
2#21458920C211yesmaximal, characteristic, complemented
3#21455537C211yesmaximal, characteristic, complemented
4#472×D61C211yesmaximal, characteristic, complemented
5#21447950C211yesmaximal, characteristic, complemented
6#21447949C211yesmaximal, characteristic, complemented
7#21447948C211yesmaximal, characteristic, complemented
8#21447947C211yesmaximal, characteristic, complemented
9#21447938C211yesmaximal, characteristic, complemented
10#21447937C211yesmaximal, characteristic, complemented
11#21447936C211yesmaximal, characteristic, complemented
12#21447612C211yesmaximal, characteristic, complemented
13#21447565C211yesmaximal, characteristic, complemented
14#361×D61C211yesmaximal, characteristic, complemented
15C61×#2221C211yesmaximal, characteristic, complemented
16#16840558—21no—
17AGL(1,ℤ/8)×D61—21no—
18C2×#14519796C2211yescharacteristic
19C2×D8×D61C2211yescharacteristic
20#131×D61C2211yescharacteristic
21#16840196—21no—
22#16840196—21no—
23#16840196—21no—
24#16840196—21no—
25C2×#14519722C2211yescharacteristic, complemented
26C2×#14519721C2211yescharacteristic, complemented
27C2×#14519718C2211yescharacteristic, complemented
28#16840180—21no—
29#16840180C2211yescharacteristic, complemented
30#16840179C2211yescharacteristic, complemented
31#16840178—21no—
32#16840178C2211yescharacteristic, complemented
33C2×#14519716—21no—
34C2×#14519716C2211yescharacteristic
35M32×D61—21no—
36M32×D61C2211yescharacteristic
37#16840038C2211yescharacteristic, complemented
38#16840037C2211yescharacteristic, complemented
39#16840033C2211yescharacteristic
40#16840032C2211yescharacteristic
41#16840031—21no—
42#16840030—21no—
43#16840029C2211yescharacteristic
44#16840029C2211yescharacteristic, complemented
45#16840024—21no—
46#16840023—21no—
47#108×D61C2211yescharacteristic
48#108×D61C2211yescharacteristic
49#16839743—21no—
50#100×D61—21no—
51#16839592C2211yescharacteristic, complemented
52#16839591C2211yescharacteristic, complemented
53#16839591C2211yescharacteristic, complemented
54#16839579C2211yescharacteristic, complemented
55#16839577C2211yescharacteristic, complemented
56#16839576C2211yescharacteristic, complemented
57#16839575C2211yescharacteristic, complemented
58#16839575C2211yescharacteristic, complemented
59#16839574C2211yescharacteristic, complemented
60C2×D16×C61C2211yescharacteristic, complemented
61C61×#504C2211yescharacteristic, complemented
62C61×#472C2211yescharacteristic
63C61×#472C2211yescharacteristic, complemented
64C61×#368C2211yescharacteristic, complemented
65C61×#361C2211yescharacteristic, complemented
66C61×#361C2211yescharacteristic, complemented
67C2×#11758224—21no—
68#41×D61D411yescharacteristic
69C2×D4×D61—21no—
70#14519810—21no—
71#14519807—21no—
72#14519806—41no—
73#14519805—21no—
74#14519804—41no—
75#14519803—21no—
76#14519803—21no—
77#14519802—21no—
78#14519801—41no—
79#14519801—41no—
80#14519798—41no—
81#14519796—21no—
82#14519796—21no—
83#14519796—21no—
84#14519796—21no—
85#14519796—41no—
86C2×Dic244C2311yescharacteristic
87C2×#11758200—21no—
88SD16×D61—41no—
89C2×D488C2311yescharacteristic
90C2×#11758199—21no—
91D8×D61—21no—
92D8×D61—21no—
93D8×D61—21no—
94D8×D61—21no—
95D8×D61—41no—
96#14519785—21no—
97#14519785D411yescharacteristic
98#14519784D411yescharacteristic
99#14519783—21no—
100#14519783C2311yescharacteristic
101M16×D61—21no—
102M16×D61—21no—
103M16×D61—21no—
104M16×D61D411yescharacteristic
105C2×C8×D61—21no—
106C2×C8×D61C2311yescharacteristic
107#14519722—21no—
108#14519722—21no—
109#14519721—21no—
110#14519721—21no—
111#14519718—21no—
112#14519718—21no—
113#14519717—21no—
114#14519717C2311yescharacteristic
115#14519716—21no—
116#14519716—21no—
117#14519716—21no—
118#14519716D411yescharacteristic
119#14519716D411yescharacteristic
120#14519716D411yescharacteristic
121#14519716D411yescharacteristic
122C2×#11758185—21no—
123C2×#11758185C2311yescharacteristic
124C16×D61—21no—
125C16×D61—21no—
126C16×D61—21no—
127#14519713C2311yescharacteristic
128#14519713C2311yescharacteristic
129#14519712—21no—
130#14519712—21no—
131#14519695—21no—
132#14519695—21no—
133#14519694—21no—
134#14519694—21no—
135#14519693—21no—
136#14519693—21no—
137AGL(1,ℤ/8)×C61—21no—
138AGL(1,ℤ/8)×C61—21no—
139C2×D8×C61C2311yescharacteristic
140C2×D8×C61C2311yescharacteristic
141#131×C61C2311yescharacteristic
142D16×C61—21no—
143D16×C61—21no—
144M32×C61—21no—
145M32×C61C2311yescharacteristic
146C2×C16×C61—21no—
147C2×C16×C61C2311yescharacteristic
148#108×C61C2311yescharacteristic
149#108×C61C2311yescharacteristic
150#100×C61—21no—
151#100×C61—21no—
152C23×D61—41no—
153#41×C61C2×D411yescharacteristic
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×C22⋊D61—41no—
157C2×C22⋊D61—41no—
158C22×Dic61—41no—
159#11758226D811yescharacteristic
160Q8×D61D811yescharacteristic
161#11758224—21no—
162#11758224—41no—
163#11758224—41no—
164#11758224—41no—
165#11758224—41no—
166#11758224D811yescharacteristic
167D4×D61—21no—
168D4×D61—41no—
169D4×D61—41no—
170D4×D61—41no—
171D4×D61—41no—
172D4×D61D811yescharacteristic
173#11758222—21no—
174#11758222C2×D411yescharacteristic
175C2×D244—21no—
176C2×C4×D61—21no—
177C2×C4×D61C2×D411yescharacteristic
178C2×Dic122—21no—
179SD16×C61—41no—
180SD16×C61—41no—
181D8×C61—21no—
182D8×C61—21no—
183D8×C61—21no—
184D8×C61—21no—
185D8×C61—41no—
186D8×C61—41no—
187M16×C61—21no—
188M16×C61—21no—
189M16×C61—21no—
190M16×C61C2×D411yescharacteristic
191C2×C8×C61—21no—
192C2×C8×C61C2411yescharacteristic
193#11758202—41no—
194#11758201—41no—
195#11758200—41no—
196#11758200—41no—
197#11758200—41no—
198#11758200—41no—
199#11758200—41no—
200#11758199—41no—
201#11758199—41no—
202#11758199—41no—
203#11758199—41no—
204#11758199—41no—
205#11758194—21no—
206#11758194—21no—
207#11758194—21no—
208#11758194C2×D411yescharacteristic
209C2×#92418—21no—
210C2×#92418C2×D411yescharacteristic
211Dic244—21no—
212Dic244—21no—
213Dic244—41no—
214D488—21no—
215D488—21no—
216D488—41no—
217#11758190—41no—
218#11758190—41no—
219#11758189—21no—
220#11758189—21no—
221#11758189—21no—
222#11758189—41no—
223#11758189—41no—
224C8×D61—21no—
225C8×D61—21no—
226C8×D61—21no—
227C8×D61—41no—
228C8×D61—41no—
229C8×D61C2×D411yescharacteristic
230C8×D61C2×D411yescharacteristic
231C8×D61#4111yescharacteristic
232C8×D61#4111yescharacteristic
233C16×C61—21no—
234C16×C61C2×D411yescharacteristic
235C16×C61C2×D411yescharacteristic
236#11758185—21no—
237#11758185C2×D411yescharacteristic
238#11758185C2×D411yescharacteristic
239C23×C61—41no—
240C23×C61—41no—
241C22×D61—21no—
242C22×D61—41no—
243C22×D61—81no—
244C22×D61—81no—
245C22×D61—162no—
246C22×D61#13511yescharacteristic
247Q8×C61C2×D811yescharacteristic
248D4×C61—21no—
249D4×C61—41no—
250D4×C61—41no—
251D4×C61—41no—
252D4×C61—41no—
253D4×C61C2×D811yescharacteristic
254C2×C4×C61—21no—
255C2×C4×C61C22×D411yescharacteristic
256C22⋊D61—21no—
257C22⋊D61—21no—
258C22⋊D61—21no—
259C22⋊D61—81no—
260C22⋊D61—81no—
261C22⋊D61—81no—
262C22⋊D61—81no—
263C2×Dic61—21no—
264C2×Dic61—41no—
265C2×Dic61—81no—
266C2×Dic61—81no—
267C2×Dic61#13511yescharacteristic
268D244—21no—
269D244—41no—
270D244—41no—
271D244C2×D811yescharacteristic
272C4×D61—21no—
273C4×D61—21no—
274C4×D61—21no—
275C4×D61#12111yescharacteristic
276C4×D61#12111yescharacteristic
277C4×D61C2×D811yescharacteristic
278C4×D61C2×D811yescharacteristic
279Dic122—21no—
280Dic122—41no—
281Dic122—41no—
282Dic122C2×D811yescharacteristic
283C8×C61—21no—
284C8×C61—41no—
285C8×C61—41no—
286C8×C61C22×D411yescharacteristic
287C8×C61C2×#4111yescharacteristic
288#92418—21no—
289#92418—41no—
290#92418—41no—
291#92418#12111yescharacteristic
292#92418#12111yescharacteristic
293#33618—611nomaximal, Sylow
294C22×C61—21no—
295C22×C61—81no—
296C22×C61—81no—
297C22×C61—161no—
298C22×C61—161no—
299C22×C61C2×#13511yescharacteristic
300C2×D61—21no—
301C2×D61—41no—
302C2×D61—81no—
303C2×D61—81no—
304C2×D61—162no—
305C2×D61—162no—
306C2×D61—161no—
307C2×D61#46611yescharacteristic
308C2×D61#46611yescharacteristic
309C4×C61—21no—
310C4×C61C2×#12111yescharacteristic
311C4×C61C22×D811yescharacteristic
312Dic61—21no—
313Dic61—81no—
314Dic61#46611yescharacteristic
315Dic61#46611yescharacteristic
316C2×#509—611no—
317#3407—611no—
318#3067—611no—
319C2×#472—611no—
320#2223—611no—
321#2223—611no—
322#2223—611no—
323#2223—611no—
324#2221—611no—
325#2221—611no—
326#2221—611no—
327#2221D6111yescharacteristic, complemented
328#2161—611no—
329#2148—611no—
330C2×#361—611no—
331C2×C61—21no—
332C2×C61—41no—
333C2×C61—161no—
334C2×C61—161no—
335C2×C61C2×#46611yescharacteristic
336D61—21no—
337D61—21no—
338D61—41no—
339D61—161no—
340#575—1221no—
341C2×AGL(1,ℤ/8)—1221no—
342C2×#135—611no—
343C22×D8—611no—
344C2×#131—611no—
345#509—1221no—
346#509—1221no—
347#509—1221no—
348#509—1221no—
349C2×SD32—611no—
350C2×SD32—611no—
351C2×D16—611no—
352C2×D16C2×D6111yescharacteristic, complemented
353#504—611no—
354#504—611no—
355#504—611no—
356#504—1221no—
357#504—1221no—
358#504C2×D6111yescharacteristic, complemented
359C2×M32—611no—
360C2×M32—611no—
361C2×M32—1221no—
362C2×M32—1221no—
363#473—611no—
364#473—611no—
365#472—611no—
366#472—611no—
367#472—611no—
368#472—611no—
369#472—1221no—
370#472—1221no—
371#472C2×D6111yescharacteristic
372#472C2×D6111yescharacteristic, complemented
373#471—1221no—
374#471—1221no—
375C2×#108—611no—
376C2×#108—611no—
377#413—1221no—
378C2×#100—1221no—
379#368—611no—
380#368—611no—
381#368—611no—
382#368C2×D6111yescharacteristic, complemented
383#362—611no—
384#362—611no—
385#361—611no—
386#361—611no—
387#361—611no—
388#361—611no—
389#361C2×D6111yescharacteristic, complemented
390#361C2×D6111yescharacteristic, complemented
391C61#3361811yescharacteristic, complemented, Sylow
392C2×#41—611no—
393C2×#41—1221no—
394C22×D4—1221no—
395#137—1221no—
396#137—1221no—
397#137—2441no—
398AGL(1,ℤ/8)—21no—
399AGL(1,ℤ/8)—21no—
400AGL(1,ℤ/8)—1221no—
401AGL(1,ℤ/8)—1221no—
402AGL(1,ℤ/8)—1221no—
403AGL(1,ℤ/8)—1221no—
404AGL(1,ℤ/8)—2441no—
405AGL(1,ℤ/8)—2441no—
406AGL(1,ℤ/8)—2441no—
407#135—1221no—
408#135—1221no—
409#135—1221no—
410#135—1221no—
411#135—2441no—
412#135—2441no—
413C2×Q16—611no—
414C2×SD16—1221no—
415C2×SD16—2441no—
416C2×D8—611no—
417C2×D8—1221no—
418C2×D8—1221no—
419C2×D8—1221no—
420C2×D8—1221no—
421C2×D8—1221no—
422C2×D8—2441no—
423C2×D8C22×D6111yescharacteristic
424C2×D8C22×D6111yescharacteristic
425#131—611no—
426#131—611no—
427#131—611no—
428#131—1221no—
429#131—1221no—
430#131C22×D6111yescharacteristic
431C2×M16—611no—
432C2×M16—1221no—
433C2×M16—1221no—
434C2×M16—1221no—
435C22×C8—611no—
436C22×C8—1221no—
437SD32—1221no—
438SD32—1221no—
439SD32—1221no—
440SD32—1221no—
441D16—21no—
442D16—21no—
443D16—1221no—
444D16—1221no—
445M32—21no—
446M32—611no—
447M32—611no—
448M32—611no—
449M32—611no—
450M32—611no—
451M32—1221no—
452M32—1221no—
453M32—1221no—
454M32—1221no—
455M32C22×D6111yescharacteristic
456C2×C16—21no—
457C2×C16—611no—
458C2×C16—1221no—
459C2×C16—1221no—
460C2×C16—1221no—
461C2×C16—1221no—
462C2×C16C22×D6111yescharacteristic
463#108—611no—
464#108—611no—
465#108—1221no—
466#108—1221no—
467#108C22×D6111yescharacteristic
468#108C22×D6111yescharacteristic
469#101—1221no—
470#101—1221no—
471#100—21no—
472#100—21no—
473#100—1221no—
474#100—1221no—
475#100—1221no—
476#100—1221no—
477C24—2441no—
478#41—611no—
479#41—611no—
480#41—611no—
481#41—1221no—
482#41—1221no—
483#41—2441no—
484#41—2441no—
485#41—2441no—
486#41—2441no—
487#41D4×D6111yescharacteristic
488C2×Q8—611no—
489C2×Q8—1221no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—611no—
493C2×D4—1221no—
494C2×D4—1221no—
495C2×D4—2441no—
496C2×D4—2441no—
497C2×D4—2441no—
498C2×D4—2441no—
499C2×D4—2441no—
500C2×D4—2441no—
501C22×C4—611no—
502C22×C4—1221no—
503C22×C4—2441no—
504Q16—1221no—
505Q16—1221no—
506Q16—2441no—
507Q16—2441no—
508SD16—41no—
509SD16—41no—
510SD16—2441no—
511SD16—2441no—
512SD16—2441no—
513SD16—2441no—
514SD16—2441no—
515SD16—2441no—
516SD16—2441no—
517SD16—2441no—
518D8—21no—
519D8—21no—
520D8—21no—
521D8—21no—
522D8—41no—
523D8—41no—
524D8—1221no—
525D8—1221no—
526D8—2441no—
527D8—2441no—
528D8—2441no—
529D8—2441no—
530D8—2441no—
531D8—2441no—
532M16—21no—
533M16—21no—
534M16—21no—
535M16—611no—
536M16—1221no—
537M16—1221no—
538M16—1221no—
539M16—1221no—
540M16—1221no—
541M16—1221no—
542M16—2441no—
543M16—2441no—
544M16D4×D6111yescharacteristic
545C2×C8—21no—
546C2×C8—611no—
547C2×C8—611no—
548C2×C8—611no—
549C2×C8—611no—
550C2×C8—611no—
551C2×C8—1221no—
552C2×C8—1221no—
553C2×C8—1221no—
554C2×C8—1221no—
555C2×C8—2441no—
556C2×C8—2441no—
557C2×C8C23×D6111yescharacteristic
558C16—21no—
559C16—611no—
560C16—611no—
561C16—1221no—
562C16D4×D6111yescharacteristic
563C16D4×D6111yescharacteristic
564C23—41no—
565C23—41no—
566C23—611no—
567C23—1221no—
568C23—9762no—
569C23—4881no—
570C23—4881no—
571C23—2441no—
572Q8—611no—
573Q8—1221no—
574Q8—2441no—
575Q8—2441no—
576Q8D8×D6111yescharacteristic
577D4—21no—
578D4—41no—
579D4—41no—
580D4—41no—
581D4—41no—
582D4—611no—
583D4—1221no—
584D4—1221no—
585D4—1221no—
586D4—1221no—
587D4—4881no—
588D4—4881no—
589D4—4881no—
590D4—4881no—
591D4—2441no—
592D4—2441no—
593D4D8×D6111yescharacteristic
594C2×C4—21no—
595C2×C4—611no—
596C2×C4—611no—
597C2×C4—611no—
598C2×C4—611no—
599C2×C4—611no—
600C2×C4—1221no—
601C2×C4—1221no—
602C2×C4—1221no—
603C2×C4—1221no—
604C2×C4—4881no—
605C2×C4—4881no—
606C2×C4—2441no—
607C2×C4C2×D4×D6111yescharacteristic
608C8—21no—
609C8—41no—
610C8—41no—
611C8—611no—
612C8—611no—
613C8—1221no—
614C8—2441no—
615C8—2441no—
616C8C2×D4×D6111yescharacteristic
617C8#41×D6111yescharacteristic
618C22—21no—
619C22—81no—
620C22—81no—
621C22—161no—
622C22—161no—
623C22—611no—
624C22—611no—
625C22—1221no—
626C22—9761no—
627C22—9762no—
628C22—9762no—
629C22—4881no—
630C22—4881no—
631C22—2441no—
632C22#135×D6111yescharacteristic
633C4—21no—
634C4—611no—
635C4—611no—
636C4—1221no—
637C4—4881no—
638C4#121×D6111yescharacteristic
639C4C2×D8×D6111yescharacteristic
640C2—21no—
641C2—41no—
642C2—161no—
643C2—161no—
644C2—1221no—
645C2—1221no—
646C2—9761no—
647C2—2441no—
648C2#466×D6111yescharacteristic
subgroupG/H
centerC2#466×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2221C2
socleC2×C61C2×#466
hypercenter#2221D61
hypocenterC61#33618
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #2221

Complements

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

NH ≅ G/Ntype
1. C2×#16840196C2semidirect
2. #21458920C2semidirect
3. #21455537C2semidirect
4. #472×D61C2semidirect
5. #21447950C2semidirect
6. #21447949C2semidirect
7. #21447948C2semidirect
8. #21447947C2semidirect
9. #21447938C2semidirect
10. #21447937C2semidirect
11. #21447936C2semidirect
12. #21447612C2semidirect
13. #21447565C2semidirect
14. #361×D61C2semidirect
15. C61×#2221C2semidirect
25. C2×#14519722C22semidirect
26. C2×#14519721C22semidirect
27. C2×#14519718C22semidirect
29. #16840180C22semidirect
30. #16840179C22semidirect
32. #16840178C22semidirect
37. #16840038C22semidirect
38. #16840037C22semidirect
44. #16840029C22semidirect
51. #16839592C22semidirect
52. #16839591C22semidirect
53. #16839591C22semidirect
54. #16839579C22semidirect
55. #16839577C22semidirect
56. #16839576C22semidirect
57. #16839575C22semidirect
58. #16839575C22semidirect
59. #16839574C22semidirect
60. C2×D16×C61C22semidirect
61. C61×#504C22semidirect
63. C61×#472C22semidirect
64. C61×#368C22semidirect
65. C61×#361C22semidirect
66. C61×#361C22semidirect
327. #2221D61semidirect
352. C2×D16C2×D61semidirect
358. #504C2×D61semidirect
372. #472C2×D61semidirect
382. #368C2×D61semidirect
389. #361C2×D61semidirect
390. #361C2×D61semidirect
391. C61#33618semidirect

Maximal subgroups

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

subgroupindex
C2×#168401962
#214589202
#214555372
#472×D612
#214479502
#214479492
#214479482
#214479472
#214479382
#214479372
#214479362
#214476122
#214475652
#361×D612
C61×#22212
#3361861