Finite Group Databasebeta

← #29663980

Subgroups — #29663980

Order 15616.

754 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#486×D61C211yesmaximal, characteristic, complemented
2#21455301C211yesmaximal, characteristic, complemented
3#21455294C211yesmaximal, characteristic
4C8×#11758224C211yesmaximal, characteristic, complemented
5#21445266C211yesmaximal, characteristic, complemented
6#21445264C211yesmaximal, characteristic, complemented
7#21445262C211yesmaximal, characteristic, complemented
8#21445260C211yesmaximal, characteristic, complemented
9#21445258C211yesmaximal, characteristic, complemented
10#21445256C211yesmaximal, characteristic, complemented
11#21445254C211yesmaximal, characteristic, complemented
12#21444576C211yesmaximal, characteristic, complemented
13#21444489C211yesmaximal, characteristic, complemented
14#21444485C211yesmaximal, characteristic, complemented
15C61×#1681C211yesmaximal, characteristic, complemented
16C2×#14519806—21no—
17C2×#14519801—21no—
18C4⋊Q8×D61C2211yescharacteristic
19#127×D61C2211yescharacteristic
20C4×#11758224C2211yescharacteristic
21#16840110C2211yescharacteristic
22#16840109C2211yescharacteristic
23#16840108C2211yescharacteristic
24#16840107—21no—
25#16840107—21no—
26#16839973C2211yescharacteristic, complemented
27#16839971—21no—
28#16839969C2211yescharacteristic, complemented
29#16839967C2211yescharacteristic, complemented
30#16839965—21no—
31#16839963C2211yescharacteristic
32#16839961—21no—
33#16839959C2211yescharacteristic
34#16839957C2211yescharacteristic
35#16839955—21no—
36C8×Dic122C2211yescharacteristic, complemented
37#16839886C2211yescharacteristic, complemented
38D4×#92418C2211yescharacteristic, complemented
39C8×C22⋊D61—21no—
40#16839825—21no—
41#16839814C2211yescharacteristic
42#16839812—21no—
43#16839784C2211yescharacteristic
44#16839784C2211yescharacteristic
45#16839769—21no—
46#16839765—21no—
47#102×D61—21no—
48#102×D61—21no—
49C2×C8×Dic61—21no—
50C4×C8×D61C2211yescharacteristic
51#16839515C2211yescharacteristic, complemented
52#16839514C2211yescharacteristic, complemented
53#16839514C2211yescharacteristic, complemented
54#16839509C2211yescharacteristic, complemented
55#16839508C2211yescharacteristic, complemented
56#16839507C2211yescharacteristic, complemented
57#16839506C2211yescharacteristic
58#16839505C2211yescharacteristic
59#16839505C2211yescharacteristic
60C61×#486C2211yescharacteristic
61C61×#461C2211yescharacteristic, complemented
62C61×#459C2211yescharacteristic
63C8×D4×C61C2211yescharacteristic, complemented
64C61×#335C2211yescharacteristic, complemented
65C61×#332C2211yescharacteristic, complemented
66C61×#331C2211yescharacteristic
67C2×#11758224D411yescharacteristic
68C2×Q8×D61—21no—
69C2×D4×D61—21no—
70C2×D4×D61—21no—
71C2×D4×D61—21no—
72#14519806—44no—
73#14519801—44no—
74C2×Dic244—21no—
75C2×#11758202—21no—
76C2×#11758190—21no—
77C2×#11758200—21no—
78C2×#11758200—21no—
79C2×#11758199—21no—
80C2×#11758189—21no—
81C2×#11758189—21no—
82C22×#92418—21no—
83C2×C8×D61D411yescharacteristic
84C2×C8×D61D411yescharacteristic
85#14519777C2311yescharacteristic
86#14519776—21no—
87#14519776—21no—
88#14519775—21no—
89#14519774C2311yescharacteristic
90#14519773—21no—
91#14519773—21no—
92#14519773—21no—
93C4×Dic122C2311yescharacteristic
94#14519742D411yescharacteristic
95D4×Dic61D411yescharacteristic
96C4×C22⋊D61—21no—
97#14519737—21no—
98#14519735D411yescharacteristic
99#14519733—21no—
100C4⋊C4×D61—21no—
101C4⋊C4×D61—21no—
102C2×C4×Dic61—21no—
103C42×D61C2311yescharacteristic
104C4⋊#92418C2311yescharacteristic
105C4⋊#92418C2311yescharacteristic
106C4⋊#92418C2311yescharacteristic
107#14519706—21no—
108#14519706—21no—
109#14519706—21no—
110#14519706—21no—
111#14519702—21no—
112#14519701—21no—
113#14519700—21no—
114#14519699—21no—
115#14519699—21no—
116#14519699—21no—
117#14519698—21no—
118#14519698—21no—
119#14519698—21no—
120#14519697—21no—
121#14519697—21no—
122#14519697—21no—
123C22⋊#92418—21no—
124#14519689—21no—
125C4×#92418C2311yescharacteristic
126C8×Dic61—21no—
127C8×Dic61—21no—
128C8×Dic61—21no—
129C8×Dic61D411yescharacteristic
130C8×Dic61D411yescharacteristic
131C2×SD16×C61—21no—
132C2×D8×C61—21no—
133C22×C8×C61—21no—
134C4⋊Q8×C61C2311yescharacteristic
135#127×C61C2311yescharacteristic
136C4×D4×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140#103×C61—21no—
141#102×C61—21no—
142#102×C61—21no—
143#102×C61—21no—
144C22⋊C8×C61—21no—
145C4×C8×C61C2311yescharacteristic
146C23×D61—41no—
147C2×Q8×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61C2×D411yescharacteristic
152C22×C4×C61—21no—
153C2×C22⋊D61—21no—
154C2×C22⋊D61—41no—
155C2×C22⋊D61—41no—
156C2×C22⋊D61—41no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159Q8×D61—42no—
160Q8×D61—42no—
161#11758224—22no—
162#11758224D814yes—
163D4×D61—42no—
164D4×D61—42no—
165D4×D61—42no—
166D4×D61—42no—
167D4×D61—82no—
168C2×D244—21no—
169C2×D244—21no—
170C2×D244—21no—
171C2×C4×D61—41no—
172C2×C4×D61C2×D411yescharacteristic
173C2×C4×D61C2×D411yescharacteristic
174C2×C4×D61#4111yescharacteristic
175C2×Dic122—21no—
176C2×Dic122—41no—
177C2×Dic122C2×D411yescharacteristic
178SD16×C61—42no—
179D8×C61—42no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61—42no—
184C2×C8×C61C2×D411yescharacteristic
185C2×C8×C61C2×D411yescharacteristic
186C4⋊C4×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61C2×D411yescharacteristic
189C22⋊C4×C61—21no—
190C42×C61C2411yescharacteristic
191C22⋊Dic61—21no—
192#11758202—42no—
193#11758200—42no—
194#11758200—42no—
195#11758199—42no—
196#11758198—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61C2×D411yescharacteristic
200#11758196—21no—
201#11758196—21no—
202#11758196—41no—
203#11758196—41no—
204C4×Dic61—21no—
205C4×Dic61—21no—
206C4×Dic61—21no—
207C4×Dic61C2×D411yescharacteristic
208C4×Dic61C2×D411yescharacteristic
209C4×Dic61#4111yescharacteristic
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—42no—
214C2×#92418C2×D411yescharacteristic
215C2×#92418C2×D411yescharacteristic
216Dic244—42no—
217#11758190—42no—
218#11758189—42no—
219#11758189—42no—
220C8×D61—41no—
221C8×D61—41no—
222C23×C61—21no—
223C23×C61—41no—
224C22×D61—41no—
225C22×D61—82no—
226C22×D61—82no—
227C22×D61—82no—
228C22×D61#12111yescharacteristic
229Q8×C61—41no—
230Q8×C61—41no—
231D4×C61—21no—
232D4×C61—41no—
233D4×C61—41no—
234D4×C61—41no—
235D4×C61—41no—
236D4×C61—81no—
237D4×C61C2×D812yes—
238C2×C4×C61—21no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61C22×D411yescharacteristic
243C2×C4×C61C22×D411yescharacteristic
244C2×C4×C61C2×#4111yescharacteristic
245C22⋊D61—24no—
246C22⋊D61—82no—
247C22⋊D61—82no—
248C22⋊D61—82no—
249C2×Dic61—21no—
250C2×Dic61—24no—
251C2×Dic61—21no—
252C2×Dic61—42no—
253C2×Dic61—41no—
254C2×Dic61#12111yescharacteristic
255C2×Dic61#12111yescharacteristic
256C2×Dic61#12111yescharacteristic
257D244—41no—
258D244—41no—
259D244—41no—
260D244—41no—
261D244—81no—
262C4×D61—21no—
263C4×D61—21no—
264C4×D61—22no—
265C4×D61—82no—
266C4×D61C2×D812yes—
267C4×D61#13512yes—
268Dic122—21no—
269Dic122—41no—
270Dic122—41no—
271Dic122—82no—
272Dic122C2×D812yes—
273C8×C61—21no—
274C8×C61—21no—
275C8×C61—41no—
276C8×C61—41no—
277C8×C61—41no—
278#92418—21no—
279#92418—21no—
280#92418—41no—
281#92418—41no—
282#92418—41no—
283#19276—611nomaximal, Sylow
284C22×C61—22no—
285C22×C61—41no—
286C22×C61—41no—
287C22×C61—81no—
288C22×C61—81no—
289C22×C61—81no—
290C22×C61C2×#12111yescharacteristic
291C2×D61—21no—
292C2×D61—21no—
293C2×D61—81no—
294C2×D61—81no—
295C2×D61—81no—
296C2×D61—164no—
297C2×D61#46612yes—
298C4×C61—21no—
299C4×C61—41no—
300C4×C61—81no—
301C4×C61C22×D811yescharacteristic
302C4×C61C2×#13511yescharacteristic
303C4×C61#57511yescharacteristic
304C4×C61#57511yescharacteristic
305Dic61—21no—
306Dic61—22no—
307Dic61—41no—
308Dic61—81no—
309Dic61#46612yes—
310Dic61#47112yes—
311C2×#486—611no—
312#3039—611no—
313#3038—611no—
314C8×#41—611no—
315#1682—611no—
316#1682—611no—
317#1682—611no—
318#1682—611no—
319#1681—611no—
320#1681—611no—
321#1681—611no—
322#1681D6111yescharacteristic, complemented
323#1567—611no—
324#1546—611no—
325#1545—611no—
326C2×C61—42no—
327C2×C61—161no—
328C2×C61#304011yescharacteristic
329C2×C61C2×#46611yescharacteristic
330C2×C61C2×#47111yescharacteristic
331D61—22no—
332D61—161no—
333C2×#137—1221no—
334C2×AGL(1,ℤ/8)—1221no—
335C2×C4⋊Q8—611no—
336C2×#127—611no—
337C4×#41—611no—
338#486—611no—
339#486—611no—
340#486—611no—
341#486—1221no—
342#486—1221no—
343#486C2×D6111yescharacteristic
344#462—611no—
345#462—611no—
346#462—1221no—
347#461—611no—
348#461—1221no—
349#461C2×D6111yescharacteristic, complemented
350#460—611no—
351#460—611no—
352#460—1221no—
353#459—611no—
354#459—1221no—
355#459C2×D6111yescharacteristic
356C8×Q8—611no—
357C8×Q8—611no—
358C8×D4—611no—
359C8×D4—1221no—
360C8×D4—1221no—
361C8×D4C2×D6111yescharacteristic, complemented
362#431—611no—
363#431—1221no—
364#423—611no—
365#423—611no—
366#419—1221no—
367#418—1221no—
368C2×#102—1221no—
369C2×#102—1221no—
370C2×C4×C8—611no—
371C2×C4×C8—1221no—
372#335—611no—
373#335—611no—
374#335—611no—
375#335C2×D6111yescharacteristic, complemented
376#332—611no—
377#332—611no—
378#332—611no—
379#332C2×D6111yescharacteristic, complemented
380#331—611no—
381#331—611no—
382#331—611no—
383#331C2×D6111yescharacteristic
384C61#1927611yescharacteristic, complemented, Sylow
385C2×#41—611no—
386C22×Q8—1221no—
387C22×D4—1221no—
388C22×D4—1221no—
389C22×D4—1221no—
390#137—2444no—
391AGL(1,ℤ/8)—2444no—
392C2×Q16—1221no—
393C2×Q16—1221no—
394C2×SD16—21no—
395C2×SD16—1221no—
396C2×SD16—1221no—
397C2×SD16—1221no—
398C2×D8—21no—
399C2×D8—1221no—
400C2×M16—1221no—
401C2×M16—1221no—
402C22×C8—21no—
403C22×C8—611no—
404C22×C8—611no—
405C22×C8—1221no—
406C4⋊Q8—611no—
407C4⋊Q8—1221no—
408C4⋊Q8—1221no—
409C4⋊Q8—1221no—
410C4⋊Q8C22×D6111yescharacteristic
411#127—611no—
412#127—1221no—
413#127—1221no—
414#127—1221no—
415#127C22×D6111yescharacteristic
416C4×Q8—611no—
417C4×Q8—611no—
418C4×D4—611no—
419C4×D4—1221no—
420C4×D4—1221no—
421C4×D4C22×D6111yescharacteristic
422#117—611no—
423#117—1221no—
424C2×C4⋊C4—1221no—
425C2×C4⋊C4—1221no—
426C2×C42—611no—
427C2×C42—1221no—
428C4⋊C8—611no—
429C4⋊C8—611no—
430C4⋊C8—611no—
431C4⋊C8—1221no—
432C4⋊C8—1221no—
433C4⋊C8—1221no—
434C4⋊C8—1221no—
435C4⋊C8C22×D6111yescharacteristic
436C4⋊C8C22×D6111yescharacteristic
437C4⋊C8C22×D6111yescharacteristic
438#103—21no—
439#103—1221no—
440#103—1221no—
441#103—1221no—
442#102—21no—
443#102—21no—
444#102—21no—
445#102—1221no—
446#102—1221no—
447#102—1221no—
448#102—1221no—
449#102—1221no—
450#102—1221no—
451#102—1221no—
452#102—1221no—
453#102—1221no—
454C22⋊C8—21no—
455C22⋊C8—1221no—
456C22⋊C8—1221no—
457C4×C8—611no—
458C4×C8—611no—
459C4×C8—611no—
460C4×C8—1221no—
461C4×C8—1221no—
462C4×C8—1221no—
463C4×C8C22×D6111yescharacteristic
464C24—2441no—
465#41—614no—
466#41—1222no—
467C2×Q8—21no—
468C2×Q8—611no—
469C2×Q8—1221no—
470C2×Q8—2441no—
471C2×Q8—2442no—
472C2×Q8—2442no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—1221no—
477C2×D4—1221no—
478C2×D4—1221no—
479C2×D4—1221no—
480C2×D4—4882no—
481C2×D4—2442no—
482C2×D4—2442no—
483C2×D4—2441no—
484C2×D4—2441no—
485C2×D4—2441no—
486C2×D4—2442no—
487C2×D4—2442no—
488C2×D4D4×D6111yescharacteristic
489C22×C4—21no—
490C22×C4—611no—
491C22×C4—611no—
492C22×C4—611no—
493C22×C4—1221no—
494C22×C4—1221no—
495C22×C4—2441no—
496Q16—2442no—
497Q16—2442no—
498SD16—42no—
499SD16—2442no—
500SD16—2442no—
501SD16—2442no—
502D8—42no—
503D8—2442no—
504M16—2442no—
505M16—2442no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—42no—
510C2×C8—611no—
511C2×C8—611no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—1221no—
515C2×C8—2441no—
516C2×C8—2441no—
517C2×C8—2442no—
518C2×C8D4×D6111yescharacteristic
519C2×C8D4×D6111yescharacteristic
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—611no—
523C4⋊C4—1221no—
524C4⋊C4—1221no—
525C4⋊C4—1221no—
526C4⋊C4—1221no—
527C4⋊C4—2441no—
528C4⋊C4—2441no—
529C4⋊C4D4×D6111yescharacteristic
530C22⋊C4—21no—
531C22⋊C4—1221no—
532C22⋊C4—1221no—
533C42—611no—
534C42—611no—
535C42—611no—
536C42—1221no—
537C42—1221no—
538C42—1221no—
539C42C23×D6111yescharacteristic
540C23—21no—
541C23—41no—
542C23—611no—
543C23—4882no—
544C23—4882no—
545C23—4882no—
546C23—2441no—
547Q8—41no—
548Q8—41no—
549Q8—612no—
550Q8—1221no—
551Q8—4882no—
552Q8—2441no—
553Q8—2441no—
554D4—21no—
555D4—41no—
556D4—41no—
557D4—41no—
558D4—41no—
559D4—81no—
560D4—1224no—
561D4—4881no—
562D4—4882no—
563D4—4882no—
564D4—4882no—
565D4—2441no—
566D4—2441no—
567D4—2441no—
568D4—2441no—
569D4D8×D6112yes—
570C2×C4—21no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—611no—
575C2×C4—611no—
576C2×C4—612no—
577C2×C4—612no—
578C2×C4—611no—
579C2×C4—1222no—
580C2×C4—1224no—
581C2×C4—1221no—
582C2×C4—1221no—
583C2×C4—1221no—
584C2×C4—1221no—
585C2×C4—4882no—
586C2×C4—2442no—
587C2×C4—2441no—
588C2×C4C2×D4×D6111yescharacteristic
589C2×C4C2×D4×D6111yescharacteristic
590C2×C4#41×D6111yescharacteristic
591C8—21no—
592C8—21no—
593C8—41no—
594C8—41no—
595C8—41no—
596C8—1221no—
597C8—1221no—
598C8—2441no—
599C8—2441no—
600C8—2441no—
601C22—22no—
602C22—41no—
603C22—41no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—612no—
608C22—1221no—
609C22—1221no—
610C22—9764no—
611C22—4881no—
612C22—4881no—
613C22—4881no—
614C22#121×D6111yescharacteristic
615C4—21no—
616C4—41no—
617C4—81no—
618C4—612no—
619C4—612no—
620C4—1222no—
621C4—1221no—
622C4—4881no—
623C4—2441no—
624C4C2×D8×D6111yescharacteristic
625C4#135×D6111yescharacteristic
626C4#1684055811yescharacteristic
627C4#1684055911yescharacteristic
628C2—42no—
629C2—161no—
630C2—1222no—
631C2—9761no—
632C2#2145530811yescharacteristic
633C2#466×D6111yescharacteristic
634C2#471×D6111yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1681C2
socleC22×C61C2×#121
prime radical#21455294C2
hypercenter#1681D61
hypocenterC61#19276
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1681

Complements

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

NH ≅ G/Ntype
1. #486×D61C2semidirect
2. #21455301C2semidirect
4. C8×#11758224C2semidirect
5. #21445266C2semidirect
6. #21445264C2semidirect
7. #21445262C2semidirect
8. #21445260C2semidirect
9. #21445258C2semidirect
10. #21445256C2semidirect
11. #21445254C2semidirect
12. #21444576C2semidirect
13. #21444489C2semidirect
14. #21444485C2semidirect
15. C61×#1681C2semidirect
26. #16839973C22semidirect
28. #16839969C22semidirect
29. #16839967C22semidirect
36. C8×Dic122C22semidirect
37. #16839886C22semidirect
38. D4×#92418C22semidirect
51. #16839515C22semidirect
52. #16839514C22semidirect
53. #16839514C22semidirect
54. #16839509C22semidirect
55. #16839508C22semidirect
56. #16839507C22semidirect
61. C61×#461C22semidirect
63. C8×D4×C61C22semidirect
64. C61×#335C22semidirect
65. C61×#332C22semidirect
322. #1681D61semidirect
349. #461C2×D61semidirect
361. C8×D4C2×D61semidirect
375. #335C2×D61semidirect
379. #332C2×D61semidirect
384. C61#19276semidirect

Maximal subgroups

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

subgroupindex
#486×D612
#214553012
#214552942
C8×#117582242
#214452662
#214452642
#214452622
#214452602
#214452582
#214452562
#214452542
#214445762
#214444892
#214444852
C61×#16812
#1927661