Finite Group Databasebeta

← #29663982

Subgroups — #29663982

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#21455303C211yesmaximal, characteristic, complemented
3#21455296C211yesmaximal, characteristic
4C8×#11758226C211yesmaximal, characteristic, complemented
5#21445265C211yesmaximal, characteristic, complemented
6#21445263C211yesmaximal, characteristic, complemented
7#21445261C211yesmaximal, characteristic, complemented
8#21445259C211yesmaximal, characteristic, complemented
9#21445257C211yesmaximal, characteristic, complemented
10#21445255C211yesmaximal, characteristic, complemented
11#21445253C211yesmaximal, characteristic, complemented
12#21444576C211yesmaximal, characteristic, complemented
13#21444489C211yesmaximal, characteristic, complemented
14#21444485C211yesmaximal, characteristic, complemented
15C61×#1682C211yesmaximal, characteristic, complemented
16C2×#14519809—21no—
17C2×#14519804—21no—
18C4⋊Q8×D61C2211yescharacteristic
19#127×D61C2211yescharacteristic
20C4×#11758226C2211yescharacteristic
21#16840110C2211yescharacteristic
22#16840109C2211yescharacteristic
23#16840108C2211yescharacteristic
24#16840107—21no—
25#16840107—21no—
26#16839972C2211yescharacteristic, complemented
27#16839970—21no—
28#16839968C2211yescharacteristic, complemented
29#16839966—21no—
30#16839964C2211yescharacteristic, complemented
31#16839962C2211yescharacteristic
32#16839960—21no—
33#16839958C2211yescharacteristic
34#16839956—21no—
35#16839954C2211yescharacteristic
36Q8×#92418C2211yescharacteristic, complemented
37C8×D244—21no—
38C8×D244C2211yescharacteristic, complemented
39#16839827—21no—
40#16839827C2211yescharacteristic, complemented
41#16839814—21no—
42#16839814C2211yescharacteristic
43#16839784C2211yescharacteristic
44#16839784C2211yescharacteristic
45#16839769—21no—
46#16839765—21no—
47#102×D61—21no—
48#102×D61—21no—
49C4×C8×D61—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×#462C2211yescharacteristic, complemented
62C61×#460C2211yescharacteristic
63C8×Q8×C61C2211yescharacteristic, complemented
64C61×#335C2211yescharacteristic, complemented
65C61×#332C2211yescharacteristic, complemented
66C61×#331C2211yescharacteristic
67C2×#11758226D411yescharacteristic
68C2×Q8×D61—21no—
69C2×D4×D61—21no—
70C2×D4×D61—21no—
71C2×D4×D61—21no—
72#14519809—44no—
73#14519804—44no—
74C2×#11758202—21no—
75C2×#11758190—21no—
76C2×#11758201—21no—
77C2×#11758201—21no—
78C2×D488—21no—
79C2×#11758199—21no—
80C2×#11758189—21no—
81C2×#11758189—21no—
82C2×C8×D61—21no—
83C2×C8×D61—21no—
84C2×C8×D61D411yescharacteristic
85C2×C8×D61D411yescharacteristic
86#14519777C2311yescharacteristic
87#14519776—21no—
88#14519776—21no—
89#14519775—21no—
90#14519774C2311yescharacteristic
91#14519773—21no—
92#14519773—21no—
93#14519773—21no—
94Q8×Dic61D411yescharacteristic
95C4×D244—21no—
96C4×D244C2311yescharacteristic
97#14519739—21no—
98#14519739D411yescharacteristic
99#14519735—21no—
100#14519735D411yescharacteristic
101C4⋊C4×D61—21no—
102C4⋊C4×D61—21no—
103C42×D61—21no—
104C42×D61C2311yescharacteristic
105C4⋊#92418—21no—
106C4⋊#92418C2311yescharacteristic
107C4⋊#92418C2311yescharacteristic
108C4⋊#92418C2311yescharacteristic
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—
123#14519689—21no—
124#14519689—21no—
125#14519689—21no—
126C4×#92418—21no—
127C4×#92418C2311yescharacteristic
128C8×Dic61—21no—
129C8×Dic61D411yescharacteristic
130C8×Dic61D411yescharacteristic
131C2×Q16×C61—21no—
132C2×SD16×C61—21no—
133C4⋊Q8×C61C2311yescharacteristic
134#127×C61C2311yescharacteristic
135C4×Q8×C61C2311yescharacteristic
136C4⋊C8×C61—21no—
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—
144C4×C8×C61—21no—
145C4×C8×C61C2311yescharacteristic
146C23×D61—41no—
147C2×Q8×C61—21no—
148C2×Q8×C61C2×D411yescharacteristic
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×C22⋊D61—41no—
153C2×C22⋊D61—41no—
154C2×C22⋊D61—41no—
155#11758226—22no—
156#11758226D814yes—
157Q8×D61—42no—
158Q8×D61—42no—
159D4×D61—42no—
160D4×D61—42no—
161D4×D61—42no—
162D4×D61—42no—
163D4×D61—82no—
164C2×D244—21no—
165C2×D244—21no—
166C2×D244—21no—
167C2×D244—21no—
168C2×D244C2×D411yescharacteristic
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×C4×D61—41no—
173C2×C4×D61C2×D411yescharacteristic
174C2×C4×D61C2×D411yescharacteristic
175C2×C4×D61#4111yescharacteristic
176C2×Dic122—21no—
177C2×Dic122—41no—
178Q16×C61—42no—
179SD16×C61—42no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61C2×D411yescharacteristic
184C2×C8×C61C2×D411yescharacteristic
185C4⋊C4×C61—21no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61C2×D411yescharacteristic
189C42×C61—21no—
190C42×C61C2411yescharacteristic
191#11758202—42no—
192#11758201—42no—
193#11758201—42no—
194#11758199—42no—
195#11758198—21no—
196#11758198—21no—
197#11758198—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61C2×D411yescharacteristic
202#11758196—41no—
203#11758196—41no—
204C4×Dic61—21no—
205C4×Dic61—21no—
206C4×Dic61C2×D411yescharacteristic
207C4×Dic61C2×D411yescharacteristic
208C4×Dic61#4111yescharacteristic
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418C2×D411yescharacteristic
213C2×#92418C2×D411yescharacteristic
214D488—42no—
215#11758190—42no—
216#11758189—42no—
217#11758189—42no—
218C8×D61—41no—
219C8×D61—41no—
220C8×D61—42no—
221C8×D61—42no—
222C23×C61—41no—
223C22×D61—21no—
224C22×D61—41no—
225C22×D61—82no—
226C22×D61—82no—
227C22×D61—82no—
228C22×D61#12111yescharacteristic
229Q8×C61—21no—
230Q8×C61—41no—
231Q8×C61—41no—
232Q8×C61C2×D812yes—
233D4×C61—41no—
234D4×C61—41no—
235D4×C61—41no—
236D4×C61—41no—
237D4×C61—81no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—41no—
241C2×C4×C61C22×D411yescharacteristic
242C2×C4×C61C22×D411yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C22⋊D61—82no—
245C22⋊D61—82no—
246C22⋊D61—82no—
247C2×Dic61—21no—
248C2×Dic61—41no—
249C2×Dic61#12111yescharacteristic
250C2×Dic61#12111yescharacteristic
251C2×Dic61#12111yescharacteristic
252D244—24no—
253D244—21no—
254D244—41no—
255D244—41no—
256D244—41no—
257D244—41no—
258D244—81no—
259D244C2×D812yes—
260C4×D61—21no—
261C4×D61—21no—
262C4×D61—24no—
263C4×D61—22no—
264C4×D61—41no—
265C4×D61—41no—
266C4×D61—42no—
267C4×D61—82no—
268C4×D61C2×D812yes—
269C4×D61#13512yes—
270Dic122—41no—
271Dic122—41no—
272Dic122—82no—
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—81no—
285C22×C61—81no—
286C22×C61—81no—
287C22×C61C2×#12111yescharacteristic
288C2×D61—21no—
289C2×D61—21no—
290C2×D61—22no—
291C2×D61—41no—
292C2×D61—41no—
293C2×D61—81no—
294C2×D61—81no—
295C2×D61—81no—
296C2×D61—164no—
297C2×D61#46612yes—
298C4×C61—22no—
299C4×C61—21no—
300C4×C61—41no—
301C4×C61—81no—
302C4×C61C22×D811yescharacteristic
303C4×C61C2×#13511yescharacteristic
304C4×C61#57511yescharacteristic
305C4×C61#57511yescharacteristic
306Dic61—21no—
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#1682D6111yescharacteristic, complemented
319#1681—611no—
320#1681—611no—
321#1681—611no—
322#1681—611no—
323#1567—611no—
324#1546—611no—
325#1545—611no—
326C2×C61—161no—
327C2×C61#304011yescharacteristic
328C2×C61C2×#46611yescharacteristic
329C2×C61C2×#47111yescharacteristic
330D61—22no—
331D61—42no—
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—1221no—
346#462C2×D6111yescharacteristic, complemented
347#461—611no—
348#461—611no—
349#461—1221no—
350#460—611no—
351#460—1221no—
352#460C2×D6111yescharacteristic
353#459—611no—
354#459—611no—
355#459—1221no—
356C8×Q8—611no—
357C8×Q8C2×D6111yescharacteristic, complemented
358C8×D4—611no—
359C8×D4—611no—
360C8×D4—1221no—
361C8×D4—1221no—
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—21no—
393C2×Q16—1221no—
394C2×SD16—21no—
395C2×SD16—1221no—
396C2×SD16—1221no—
397C2×SD16—1221no—
398C2×D8—1221no—
399C2×D8—1221no—
400C2×M16—1221no—
401C2×M16—1221no—
402C22×C8—611no—
403C22×C8—611no—
404C22×C8—1221no—
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×Q8C22×D6111yescharacteristic
418C4×D4—611no—
419C4×D4—611no—
420C4×D4—1221no—
421C4×D4—1221no—
422#117—611no—
423#117—1221no—
424C2×C4⋊C4—1221no—
425C2×C4⋊C4—1221no—
426C2×C42—611no—
427C2×C42—1221no—
428C4⋊C8—21no—
429C4⋊C8—611no—
430C4⋊C8—611no—
431C4⋊C8—611no—
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—1221no—
455C22⋊C8—1221no—
456C22⋊C8—1221no—
457C4×C8—21no—
458C4×C8—611no—
459C4×C8—611no—
460C4×C8—611no—
461C4×C8—1221no—
462C4×C8—1221no—
463C4×C8C22×D6111yescharacteristic
464C24—2441no—
465#41—614no—
466#41—1222no—
467C2×Q8—21no—
468C2×Q8—1221no—
469C2×Q8—2441no—
470C2×Q8—2442no—
471C2×Q8—2442no—
472C2×Q8D4×D6111yescharacteristic
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—611no—
477C2×D4—1221no—
478C2×D4—1221no—
479C2×D4—1221no—
480C2×D4—1221no—
481C2×D4—4882no—
482C2×D4—2442no—
483C2×D4—2442no—
484C2×D4—2441no—
485C2×D4—2441no—
486C2×D4—2441no—
487C2×D4—2442no—
488C2×D4—2442no—
489C22×C4—611no—
490C22×C4—611no—
491C22×C4—611no—
492C22×C4—1221no—
493C22×C4—1221no—
494C22×C4—1221no—
495C22×C4—2441no—
496Q16—42no—
497Q16—2442no—
498SD16—42no—
499SD16—2442no—
500SD16—2442no—
501SD16—2442no—
502D8—2442no—
503D8—2442no—
504M16—2442no—
505M16—2442no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—611no—
510C2×C8—611no—
511C2×C8—1221no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—2441no—
515C2×C8—2441no—
516C2×C8—2442no—
517C2×C8—2442no—
518C2×C8D4×D6111yescharacteristic
519C2×C8D4×D6111yescharacteristic
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—611no—
524C4⋊C4—1221no—
525C4⋊C4—1221no—
526C4⋊C4—1221no—
527C4⋊C4—2441no—
528C4⋊C4—2441no—
529C4⋊C4D4×D6111yescharacteristic
530C22⋊C4—1221no—
531C22⋊C4—1221no—
532C22⋊C4—1221no—
533C42—21no—
534C42—611no—
535C42—611no—
536C42—611no—
537C42—1221no—
538C42—1221no—
539C42C23×D6111yescharacteristic
540C23—41no—
541C23—611no—
542C23—1221no—
543C23—4882no—
544C23—4882no—
545C23—4882no—
546C23—2441no—
547Q8—21no—
548Q8—41no—
549Q8—41no—
550Q8—4882no—
551Q8—2441no—
552Q8—2441no—
553Q8D8×D6112yes—
554D4—41no—
555D4—41no—
556D4—41no—
557D4—41no—
558D4—81no—
559D4—612no—
560D4—1224no—
561D4—1221no—
562D4—4881no—
563D4—4882no—
564D4—4882no—
565D4—4882no—
566D4—2441no—
567D4—2441no—
568D4—2441no—
569D4—2441no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—41no—
573C2×C4—611no—
574C2×C4—611no—
575C2×C4—612no—
576C2×C4—612no—
577C2×C4—611no—
578C2×C4—1222no—
579C2×C4—1224no—
580C2×C4—1221no—
581C2×C4—1221no—
582C2×C4—1221no—
583C2×C4—4882no—
584C2×C4—2442no—
585C2×C4—2441no—
586C2×C4—2441no—
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—81no—
602C22—81no—
603C22—81no—
604C22—612no—
605C22—1221no—
606C22—1221no—
607C22—1222no—
608C22—9764no—
609C22—4881no—
610C22—4881no—
611C22—4881no—
612C22—2441no—
613C22—2441no—
614C22#121×D6111yescharacteristic
615C4—22no—
616C4—21no—
617C4—41no—
618C4—81no—
619C4—612no—
620C4—612no—
621C4—1221no—
622C4—4881no—
623C4—2441no—
624C4C2×D8×D6111yescharacteristic
625C4#135×D6111yescharacteristic
626C4#1684055911yescharacteristic
627C4#1684056111yescharacteristic
628C2—161no—
629C2—1222no—
630C2—9761no—
631C2—2442no—
632C2#2145531011yescharacteristic
633C2#466×D6111yescharacteristic
634C2#471×D6111yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1682C2
socleC22×C61C2×#121
prime radical#21455296C2
hypercenter#1682D61
hypocenterC61#19276
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1682

Complements

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

NH ≅ G/Ntype
1. #486×D61C2semidirect
2. #21455303C2semidirect
4. C8×#11758226C2semidirect
5. #21445265C2semidirect
6. #21445263C2semidirect
7. #21445261C2semidirect
8. #21445259C2semidirect
9. #21445257C2semidirect
10. #21445255C2semidirect
11. #21445253C2semidirect
12. #21444576C2semidirect
13. #21444489C2semidirect
14. #21444485C2semidirect
15. C61×#1682C2semidirect
26. #16839972C22semidirect
28. #16839968C22semidirect
30. #16839964C22semidirect
36. Q8×#92418C22semidirect
38. C8×D244C22semidirect
40. #16839827C22semidirect
51. #16839515C22semidirect
52. #16839514C22semidirect
53. #16839514C22semidirect
54. #16839509C22semidirect
55. #16839508C22semidirect
56. #16839507C22semidirect
61. C61×#462C22semidirect
63. C8×Q8×C61C22semidirect
64. C61×#335C22semidirect
65. C61×#332C22semidirect
318. #1682D61semidirect
346. #462C2×D61semidirect
357. C8×Q8C2×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
#214553032
#214552962
C8×#117582262
#214452652
#214452632
#214452612
#214452592
#214452572
#214452552
#214452532
#214445762
#214444892
#214444852
C61×#16822
#1927661