Finite Group Databasebeta

← #29669654

Subgroups — #29669654

Order 15616.

656 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458237C211yesmaximal, characteristic, complemented
2#21457749C211yesmaximal, characteristic, complemented
3#21457632C211yesmaximal, characteristic, complemented
4#21445469C211yesmaximal, characteristic, complemented
5#21445394C211yesmaximal, characteristic, complemented
6#21445254C211yesmaximal, characteristic, complemented
7#21445225C211yesmaximal, characteristic, complemented
8#21445216C211yesmaximal, characteristic, complemented
9#21445047C211yesmaximal, characteristic, complemented
10#21444968C211yesmaximal, characteristic, complemented
11#21444935C211yesmaximal, characteristic, complemented
12#21444901C211yesmaximal, characteristic, complemented
13#21444646C211yesmaximal, characteristic, complemented
14#21444643C211yesmaximal, characteristic, complemented
15C61×#3325C211yesmaximal, characteristic, complemented
16#16840477C2211yescharacteristic, complemented
17#16840416C2211yescharacteristic
18#16840165C2211yescharacteristic, complemented
19#16840134C2211yescharacteristic
20#16840113C2211yescharacteristic, complemented
21#16840112C2211yescharacteristic, complemented
22#16840108C2211yescharacteristic
23#16840105—21no—
24#16840086—21no—
25#16840083—21no—
26#16840073—21no—
27#16840052C2211yescharacteristic
28#16840052C2211yescharacteristic
29#16840049C2211yescharacteristic, complemented
30#16840042C2211yescharacteristic
31#16839996—21no—
32#16839996—21no—
33#16839990—21no—
34#16839967C2211yescharacteristic, complemented
35#16839954C2211yescharacteristic
36#16839904—21no—
37#16839896—21no—
38C4×#11758199C2211yescharacteristic
39C8×D244C2211yescharacteristic, complemented
40D4×#92418C2211yescharacteristic
41D4×#92418C2211yescharacteristic, complemented
42#16839798—21no—
43#16839755—21no—
44C2×#14519698—21no—
45#16839514C2211yescharacteristic, complemented
46#16839513C2211yescharacteristic, complemented
47#16839511C2211yescharacteristic, complemented
48#16839510C2211yescharacteristic, complemented
49#16839509C2211yescharacteristic, complemented
50#16839506C2211yescharacteristic
51D4⋊#92418C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic, complemented
54#16839489C2211yescharacteristic, complemented
55#16839483C2211yescharacteristic, complemented
56C61×#555C2211yescharacteristic
57D42×C61C2211yescharacteristic
58C61×#486C2211yescharacteristic
59C61×#482—21no—
60C61×#476C2211yescharacteristic
61C61×#469—21no—
62C61×#459C2211yescharacteristic
63C61×#447—21no—
64C4×D8×C61C2211yescharacteristic
65C61×#436C2211yescharacteristic
66C61×#418—21no—
67C2×#11758224—21no—
68C2×#11758200—21no—
69C2×#11758200—41no—
70C2×#11758199—21no—
71C2×#11758199D411yescharacteristic
72C22×#92418—21no—
73C22×#92418—21no—
74C2×C8×D61—21no—
75#14519777C2311yescharacteristic
76#14519777C2311yescharacteristic
77#14519763—41no—
78#14519761—41no—
79#14519757—21no—
80#14519751—21no—
81#14519751—21no—
82#14519748—21no—
83C4×D244C2311yescharacteristic
84#14519736—21no—
85#14519735—21no—
86C2×C4⋊Dic61—21no—
87#14519710—21no—
88#14519710—21no—
89#14519710—21no—
90#14519710D411yescharacteristic
91#14519708—21no—
92#14519708—21no—
93#14519708—21no—
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519702—21no—
98#14519702—21no—
99#14519701—41no—
100#14519700—21no—
101#14519698—21no—
102#14519698—21no—
103#14519698—21no—
104#14519698—21no—
105#14519698—21no—
106#14519698—21no—
107#14519698D411yescharacteristic
108#14519697—21no—
109#14519697D411yescharacteristic
110C22⋊#92418—21no—
111C22⋊#92418—21no—
112#14519689—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C22×D4×C61—21no—
116C22×D4×C61—21no—
117C2×D8×C61—21no—
118C2×D8×C61D411yescharacteristic
119C2×M16×C61—21no—
120C4⋊Q8×C61C2311yescharacteristic
121#127×C61C2311yescharacteristic
122#124×C61—41no—
123#121×C61—21no—
124#121×C61—21no—
125#121×C61—21no—
126#121×C61—21no—
127#120×C61—41no—
128C4×D4×C61C2311yescharacteristic
129C4×D4×C61C2311yescharacteristic
130C4×D4×C61C2311yescharacteristic
131#117×C61—21no—
132#117×C61—21no—
133#107×C61D411yescharacteristic
134#106×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136#102×C61—21no—
137#102×C61—21no—
138#102×C61—21no—
139#102×C61—21no—
140#102×C61D411yescharacteristic
141#102×C61D411yescharacteristic
142C22⋊C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C24×C61—41no—
145C2×Q8×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—41no—
150C2×D4×C61—41no—
151C2×D4×C61—42no—
152C2×D4×C61—42no—
153C2×D4×C61—41no—
154C2×D4×C61—81no—
155C2×D4×C61—81no—
156C2×D4×C61C2×D411yescharacteristic
157C2×D4×C61C2×D411yescharacteristic
158C2×D4×C61C2×D411yescharacteristic
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C2×C22⋊D61—41no—
163C2×C22⋊D61—41no—
164C22×Dic61—41no—
165#11758224—42no—
166#11758224—81no—
167C2×D244C2×D411yescharacteristic
168C2×C4×D61—21no—
169C2×Dic122—21no—
170C2×Dic122—21no—
171D8×C61—22no—
172D8×C61—81no—
173M16×C61—81no—
174C2×C8×C61—21no—
175C2×C8×C61C2×D411yescharacteristic
176C2×C8×C61C2×D411yescharacteristic
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61C2×D411yescharacteristic
180C4⋊C4×C61C2×D411yescharacteristic
181C4⋊C4×C61C2×D411yescharacteristic
182C22⋊C4×C61—21no—
183C22⋊C4×C61—21no—
184C22⋊C4×C61—21no—
185C22⋊C4×C61—41no—
186C22⋊C4×C61—41no—
187C22⋊C4×C61—41no—
188C42×C61—41no—
189C42×C61C2411yescharacteristic
190C22⋊Dic61—41no—
191#11758200—81no—
192#11758200—82no—
193#11758199—41no—
194#11758199—81no—
195#11758198—21no—
196#11758198—41no—
197#11758198—41no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61—41no—
203C4⋊Dic61C2×D411yescharacteristic
204C4×Dic61—41no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—42no—
210C2×#92418—81no—
211C2×#92418C2×D411yescharacteristic
212C2×#92418C2×D411yescharacteristic
213C8×D61—81no—
214C23×C61—21no—
215C23×C61—21no—
216C23×C61—21no—
217C23×C61—41no—
218C23×C61—82no—
219C23×C61—82no—
220C23×C61—161no—
221C22×D61—21no—
222Q8×C61—81no—
223D4×C61—21no—
224D4×C61—21no—
225D4×C61—21no—
226D4×C61—21no—
227D4×C61—21no—
228D4×C61—41no—
229D4×C61—41no—
230D4×C61—41no—
231D4×C61—41no—
232D4×C61—81no—
233D4×C61—82no—
234D4×C61—82no—
235D4×C61—161no—
236D4×C61#13512yes—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61C22×D411yescharacteristic
248C2×C4×C61C22×D411yescharacteristic
249C2×C4×C61H(5,𝔽2)11yescharacteristic
250C22⋊D61—82no—
251C22⋊D61—161no—
252C2×Dic61—21no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—82no—
256D244—21no—
257D244—21no—
258C4×D61—41no—
259C4×D61—41no—
260Dic122—41no—
261Dic122—41no—
262Dic122—81no—
263C8×C61—21no—
264C8×C61—21no—
265C8×C61—41no—
266#92418—21no—
267#92418—21no—
268#92418—41no—
269#92418—41no—
270#92418—41no—
271#92418—41no—
272#19775—611nomaximal, Sylow
273C22×C61—22no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61—81no—
283C22×C61—81no—
284C22×C61—81no—
285C22×C61—164no—
286C22×C61D4211yescharacteristic
287C2×D61—41no—
288C2×D61—41no—
289C2×D61—41no—
290C4×C61—21no—
291C4×C61—41no—
292C4×C61—41no—
293C4×C61—41no—
294C4×C61—81no—
295C4×C61C2×#13511yescharacteristic
296C4×C61#57511yescharacteristic
297C4×C61#57611yescharacteristic
298C4×C61#57711yescharacteristic
299Dic61—41no—
300Dic61—81no—
301Dic61—81no—
302#3341—611no—
303#3325D6111yescharacteristic, complemented
304#3303—611no—
305#3294—611no—
306#1719—611no—
307#1703—611no—
308#1681—611no—
309#1677—611no—
310#1675—611no—
311#1646—611no—
312#1635—611no—
313#1629—611no—
314#1624—611no—
315#1581—611no—
316#1580—611no—
317C2×C61—42no—
318C2×C61—81no—
319C2×C61—81no—
320C2×C61—161no—
321C2×C61#326711yescharacteristic
322C2×C61#328011yescharacteristic
323C2×C61#328811yescharacteristic
324D61—81no—
325#555—611no—
326#555C2×D6111yescharacteristic
327#547—611no—
328D42C2×D6111yescharacteristic
329#500—611no—
330#492—611no—
331#487—611no—
332#487—611no—
333#486—611no—
334#486C2×D6111yescharacteristic
335#485—1221no—
336#482—21no—
337#482—1221no—
338#482—1221no—
339#480—1221no—
340#476—611no—
341#476—611no—
342#476—611no—
343#476C2×D6111yescharacteristic
344#474—611no—
345#469—21no—
346#466—1221no—
347#466—1221no—
348#465—1221no—
349#461—611no—
350#459—611no—
351#459C2×D6111yescharacteristic
352#449—1221no—
353#447—21no—
354#447—1221no—
355C4×D8—611no—
356C4×D8C2×D6111yescharacteristic
357#436C2×D6111yescharacteristic
358C8×D4—611no—
359C8×D4—611no—
360C8×D4—611no—
361#427—1221no—
362#418—21no—
363#416—1221no—
364C2×#102—1221no—
365#335—611no—
366#334—611no—
367#333—611no—
368#333—611no—
369#332—611no—
370#331—611no—
371D4⋊C8—611no—
372D4⋊C8—611no—
373D4⋊C8—611no—
374D4⋊C8—611no—
375#322—611no—
376C61#1977511yescharacteristic, complemented, Sylow
377C2×#41—1221no—
378C22×D4—21no—
379C22×D4—21no—
380C2×SD16—1221no—
381C2×SD16—2441no—
382C2×D8—21no—
383C2×D8—611no—
384C2×D8—1221no—
385C2×D8C22⋊D6111yescharacteristic
386C2×M16—21no—
387C22×C8—1221no—
388C22×C8—1221no—
389C22×C8—1221no—
390C4⋊Q8—611no—
391C4⋊Q8—611no—
392C4⋊Q8C22×D6111yescharacteristic
393#127C22×D6111yescharacteristic
394#124—41no—
395#124—2441no—
396#123—2441no—
397C22⋊Q8—1221no—
398#121—21no—
399#121—21no—
400#121—21no—
401#121—21no—
402#121—1221no—
403#121—1221no—
404#121—1221no—
405#120—41no—
406C4×D4—611no—
407C4×D4C22×D6111yescharacteristic
408C4×D4C22×D6111yescharacteristic
409C4×D4C22×D6111yescharacteristic
410#117—21no—
411#117—21no—
412#117—1221no—
413#117—1221no—
414C2×C4⋊C4—1221no—
415#107—611no—
416#107—1221no—
417#107—1221no—
418#107—1221no—
419#107C22⋊D6111yescharacteristic
420#106—21no—
421#106—1221no—
422#106—1221no—
423#106—1221no—
424C4⋊C8—611no—
425C4⋊C8—611no—
426C4⋊C8—611no—
427C4⋊C8C22×D6111yescharacteristic
428#103—1221no—
429#103—1221no—
430#103—1221no—
431#103—2441no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—611no—
437#102—611no—
438#102—1221no—
439#102—1221no—
440#102—1221no—
441#102—1221no—
442#102—1221no—
443#102—1221no—
444#102—1221no—
445#102C22⋊D6111yescharacteristic
446#102C22⋊D6111yescharacteristic
447C22⋊C8—21no—
448C22⋊C8—1221no—
449C22⋊C8—1221no—
450C22⋊C8—1221no—
451C4×C8—611no—
452C4×C8—611no—
453C4×C8C22×D6111yescharacteristic
454C24—41no—
455#41—4881no—
456#41—2442no—
457C2×Q8—21no—
458C2×Q8—1221no—
459C2×Q8—1221no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4—41no—
468C2×D4—81no—
469C2×D4—81no—
470C2×D4—611no—
471C2×D4—2441no—
472C2×D4—2441no—
473C2×D4D4×D6111yescharacteristic
474C2×D4C2×C22⋊D6111yescharacteristic
475C2×D4C2×C22⋊D6111yescharacteristic
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—1221no—
480C22×C4—2441no—
481SD16—4881no—
482SD16—4882no—
483D8—22no—
484D8—81no—
485D8—4881no—
486D8—2441no—
487M16—81no—
488C2×C8—21no—
489C2×C8—611no—
490C2×C8—611no—
491C2×C8—1221no—
492C2×C8—1221no—
493C2×C8—1221no—
494C2×C8—1221no—
495C2×C8—4881no—
496C2×C8—4881no—
497C2×C8—2442no—
498C2×C8C2×C22⋊D6111yescharacteristic
499C2×C8C2×C22⋊D6111yescharacteristic
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—611no—
503C4⋊C4—1221no—
504C4⋊C4—1221no—
505C4⋊C4—1221no—
506C4⋊C4—1221no—
507C4⋊C4—2441no—
508C4⋊C4D4×D6111yescharacteristic
509C4⋊C4C2×C22⋊D6111yescharacteristic
510C4⋊C4C2×C22⋊D6111yescharacteristic
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—1221no—
518C22⋊C4—2441no—
519C22⋊C4—2441no—
520C22⋊C4—2441no—
521C42—41no—
522C42—2441no—
523C42C23×D6111yescharacteristic
524C23—21no—
525C23—21no—
526C23—21no—
527C23—41no—
528C23—82no—
529C23—82no—
530C23—161no—
531C23—1221no—
532Q8—81no—
533Q8—4881no—
534Q8—2441no—
535Q8—2441no—
536D4—21no—
537D4—21no—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—81no—
546D4—82no—
547D4—82no—
548D4—161no—
549D4—1221no—
550D4—1221no—
551D4—9761no—
552D4—4882no—
553D4#1451979712yes—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—1221no—
565C2×C4—4882no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4C2×D4×D6111yescharacteristic
571C2×C4C22×C22⋊D6111yescharacteristic
572C2×C4#1451982211yescharacteristic
573C8—21no—
574C8—21no—
575C8—41no—
576C8—1221no—
577C8—1221no—
578C8—2441no—
579C8—2441no—
580C8—2441no—
581C8—2441no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—164no—
595C22—2441no—
596C22—2441no—
597C22—2441no—
598C22D4×C22⋊D6111yescharacteristic
599C4—21no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—81no—
604C4—4881no—
605C4—4881no—
606C4—2441no—
607C4C2×#1451979711yescharacteristic
608C4#1684055811yescharacteristic
609C4#1684056511yescharacteristic
610C4#1684057211yescharacteristic
611C2—42no—
612C2—81no—
613C2—81no—
614C2—161no—
615C2—4881no—
616C2#2145733811yescharacteristic
617C2#2145750011yescharacteristic
618C2#2145758311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3325C2
socleC22×C61D42
hypercenter#3325D61
hypocenterC61#19775
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3325

Complements

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

NH ≅ G/Ntype
1. #21458237C2semidirect
2. #21457749C2semidirect
3. #21457632C2semidirect
4. #21445469C2semidirect
5. #21445394C2semidirect
6. #21445254C2semidirect
7. #21445225C2semidirect
8. #21445216C2semidirect
9. #21445047C2semidirect
10. #21444968C2semidirect
11. #21444935C2semidirect
12. #21444901C2semidirect
13. #21444646C2semidirect
14. #21444643C2semidirect
15. C61×#3325C2semidirect
16. #16840477C22semidirect
18. #16840165C22semidirect
20. #16840113C22semidirect
21. #16840112C22semidirect
29. #16840049C22semidirect
34. #16839967C22semidirect
39. C8×D244C22semidirect
41. D4×#92418C22semidirect
45. #16839514C22semidirect
46. #16839513C22semidirect
47. #16839511C22semidirect
48. #16839510C22semidirect
49. #16839509C22semidirect
53. D4⋊#92418C22semidirect
54. #16839489C22semidirect
55. #16839483C22semidirect
303. #3325D61semidirect
376. C61#19775semidirect

Maximal subgroups

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

subgroupindex
#214582372
#214577492
#214576322
#214454692
#214453942
#214452542
#214452252
#214452162
#214450472
#214449682
#214449352
#214449012
#214446462
#214446432
C61×#33252
#1977561