Finite Group Databasebeta

← #29669660

Subgroups — #29669660

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#21458063C211yesmaximal, characteristic, complemented
3#21457626C211yesmaximal, characteristic, complemented
4#21445473C211yesmaximal, characteristic, complemented
5#21445391C211yesmaximal, characteristic, complemented
6#21445258C211yesmaximal, characteristic, complemented
7#21445228C211yesmaximal, characteristic, complemented
8#21445216C211yesmaximal, characteristic, complemented
9#21445045C211yesmaximal, characteristic, complemented
10#21444970C211yesmaximal, characteristic, complemented
11#21444934C211yesmaximal, characteristic, complemented
12#21444902C211yesmaximal, characteristic, complemented
13#21444648C211yesmaximal, characteristic, complemented
14#21444643C211yesmaximal, characteristic, complemented
15C61×#3303C211yesmaximal, characteristic, complemented
16#16840477C2211yescharacteristic
17D4×D244C2211yescharacteristic
18#16840165C2211yescharacteristic, complemented
19#16840136C2211yescharacteristic
20#16840114C2211yescharacteristic, complemented
21#16840110C2211yescharacteristic
22#16840109C2211yescharacteristic
23#16840089—21no—
24#16840086—21no—
25#16840083—21no—
26#16840075—21no—
27#16840052C2211yescharacteristic
28#16840052C2211yescharacteristic, complemented
29#16840049C2211yescharacteristic
30#16840039C2211yescharacteristic
31#16840014—21no—
32#16839996—21no—
33#16839996—21no—
34#16839957C2211yescharacteristic
35#16839957C2211yescharacteristic
36#16839895—21no—
37#16839894—21no—
38C4×#11758199C2211yescharacteristic
39#16839841C2211yescharacteristic
40D4×#92418C2211yescharacteristic
41D4×#92418C2211yescharacteristic, complemented
42#16839798—21no—
43#16839765—21no—
44C2×#14519697—21no—
45#16839514C2211yescharacteristic, complemented
46#16839513C2211yescharacteristic, complemented
47#16839511C2211yescharacteristic, complemented
48#16839510C2211yescharacteristic, complemented
49#16839508C2211yescharacteristic, complemented
50#16839505C2211yescharacteristic
51D4⋊#92418C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic, complemented
54#16839489C2211yescharacteristic
55#16839483C2211yescharacteristic, complemented
56C61×#555C2211yescharacteristic, complemented
57C61×#547C2211yescharacteristic
58C61×#487C2211yescharacteristic, complemented
59C61×#485—21no—
60C61×#476C2211yescharacteristic
61C61×#465—21no—
62C61×#461C2211yescharacteristic, complemented
63C61×#449—21no—
64C4×D8×C61C2211yescharacteristic
65C8×D4×C61C2211yescharacteristic, complemented
66C61×#416—21no—
67C22×D244—21no—
68C2×D4×D61—21no—
69C2×#11758201—41no—
70C2×#11758199—21no—
71C2×#11758199—21no—
72C2×#11758199D411yescharacteristic
73C2×#11758189—21no—
74C22×#92418—21no—
75C22×#92418—21no—
76#14519777C2311yescharacteristic
77#14519774C2311yescharacteristic
78#14519763—41no—
79#14519752—21no—
80#14519751—21no—
81#14519751—21no—
82#14519748—21no—
83#14519747—41no—
84C4×D244C2311yescharacteristic
85#14519736—21no—
86#14519735—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#14519700—41no—
98#14519699—21no—
99#14519699—21no—
100#14519698—21no—
101#14519698—21no—
102#14519698D411yescharacteristic
103#14519697—21no—
104#14519697—21no—
105#14519697—21no—
106#14519697—21no—
107#14519697—21no—
108#14519697—21no—
109#14519697D411yescharacteristic
110C22⋊#92418—21no—
111C22⋊#92418—21no—
112#14519689—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×#41×C61—21no—
116C2×SD16×C61—21no—
117C2×D8×C61D411yescharacteristic
118C22×C8×C61—21no—
119C4⋊Q8×C61C2311yescharacteristic
120C4⋊Q8×C61C2311yescharacteristic
121#124×C61—41no—
122#123×C61—41no—
123C22⋊Q8×C61—21no—
124#121×C61—21no—
125#121×C61—21no—
126#121×C61—21no—
127C4×D4×C61C2311yescharacteristic
128C4×D4×C61C2311yescharacteristic
129C4×D4×C61C2311yescharacteristic
130#117×C61—21no—
131#117×C61—21no—
132C2×C4⋊C4×C61—21no—
133#107×C61D411yescharacteristic
134#106×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136#103×C61—21no—
137#103×C61—21no—
138#103×C61—21no—
139#102×C61—21no—
140#102×C61D411yescharacteristic
141#102×C61D411yescharacteristic
142C22⋊C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C23×D61—41no—
145#41×C61—42no—
146#41×C61—81no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×D4×C61—41no—
150C2×D4×C61—41no—
151C2×D4×C61C2×D411yescharacteristic
152C2×D4×C61C2×D411yescharacteristic
153C2×D4×C61C2×D411yescharacteristic
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—41no—
158C2×C22⋊D61—41no—
159C2×C22⋊D61—41no—
160D4×D61—42no—
161D4×D61—81no—
162C2×D244—21no—
163C2×D244—21no—
164C2×D244—21no—
165C2×D244—42no—
166C2×D244—41no—
167C2×D244—81no—
168C2×D244C2×D411yescharacteristic
169C2×C4×D61—21no—
170C2×Dic122—21no—
171SD16×C61—81no—
172D8×C61—22no—
173C2×C8×C61—21no—
174C2×C8×C61—81no—
175C2×C8×C61C2×D411yescharacteristic
176C2×C8×C61C2×D411yescharacteristic
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—41no—
182C4⋊C4×C61C2×D411yescharacteristic
183C4⋊C4×C61C2×D411yescharacteristic
184C4⋊C4×C61C2×D411yescharacteristic
185C22⋊C4×C61—21no—
186C22⋊C4×C61—21no—
187C22⋊C4×C61—21no—
188C22⋊C4×C61—41no—
189C22⋊C4×C61—41no—
190C22⋊C4×C61—41no—
191C42×C61—41no—
192C42×C61C2411yescharacteristic
193C22⋊Dic61—41no—
194#11758201—82no—
195#11758199—41no—
196#11758199—81no—
197#11758199—81no—
198#11758198—21no—
199#11758198—41no—
200#11758198—41no—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
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
213#11758189—81no—
214C23×C61—21no—
215C23×C61—21no—
216C23×C61—21no—
217C22×D61—21no—
218C22×D61—41no—
219C22×D61—82no—
220C22×D61—82no—
221C22×D61—161no—
222Q8×C61—41no—
223Q8×C61—41no—
224Q8×C61—81no—
225D4×C61—21no—
226D4×C61—21no—
227D4×C61—21no—
228D4×C61—21no—
229D4×C61—21no—
230D4×C61—82no—
231D4×C61—161no—
232D4×C61#13512yes—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—82no—
245C2×C4×C61C22×D411yescharacteristic
246C2×C4×C61C22×D411yescharacteristic
247C2×C4×C61H(5,𝔽2)11yescharacteristic
248C22⋊D61—82no—
249C22⋊D61—161no—
250C2×Dic61—21no—
251C2×Dic61—41no—
252D244—21no—
253D244—21no—
254D244—41no—
255D244—41no—
256D244—41no—
257D244—41no—
258D244—81no—
259D244—82no—
260C4×D61—41no—
261C4×D61—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×C61D4211yescharacteristic
283C2×D61—41no—
284C2×D61—41no—
285C2×D61—41no—
286C2×D61—81no—
287C2×D61—81no—
288C2×D61—81no—
289C2×D61—164no—
290C4×C61—21no—
291C4×C61—41no—
292C4×C61—41no—
293C4×C61—41no—
294C4×C61—81no—
295C4×C61—81no—
296C4×C61C2×#13511yescharacteristic
297C4×C61#57511yescharacteristic
298C4×C61#57611yescharacteristic
299C4×C61#57711yescharacteristic
300Dic61—41no—
301Dic61—81no—
302#3341—611no—
303#3325—611no—
304#3303D6111yescharacteristic, complemented
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#326711yescharacteristic
321C2×C61#328011yescharacteristic
322C2×C61#328811yescharacteristic
323D61—81no—
324D61—161no—
325#555—611no—
326#555C2×D6111yescharacteristic, complemented
327#547C2×D6111yescharacteristic
328D42—611no—
329#500—611no—
330#492—611no—
331#487—611no—
332#487C2×D6111yescharacteristic, complemented
333#486—611no—
334#486—611no—
335#485—21no—
336#482—1221no—
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—1221no—
346#466—1221no—
347#466—1221no—
348#465—21no—
349#461C2×D6111yescharacteristic, complemented
350#459—611no—
351#459—611no—
352#449—21no—
353#447—1221no—
354#447—1221no—
355C4×D8—611no—
356C4×D8C2×D6111yescharacteristic
357#436—611no—
358C8×D4—611no—
359C8×D4—611no—
360C8×D4C2×D6111yescharacteristic, complemented
361#427—1221no—
362#418—1221no—
363#416—21no—
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—21no—
378C22×D4—1221no—
379C22×D4—1221no—
380C2×SD16—21no—
381C2×SD16—2441no—
382C2×D8—611no—
383C2×D8—1221no—
384C2×D8—1221no—
385C2×D8C22⋊D6111yescharacteristic
386C2×M16—1221no—
387C22×C8—21no—
388C22×C8—1221no—
389C22×C8—1221no—
390C4⋊Q8—611no—
391C4⋊Q8C22×D6111yescharacteristic
392C4⋊Q8C22×D6111yescharacteristic
393#127—611no—
394#124—41no—
395#124—2441no—
396#123—41no—
397C22⋊Q8—21no—
398#121—21no—
399#121—21no—
400#121—21no—
401#121—1221no—
402#121—1221no—
403#121—1221no—
404#121—1221no—
405#120—2441no—
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—21no—
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—21no—
429#103—21no—
430#103—21no—
431#103—2441no—
432#102—21no—
433#102—611no—
434#102—611no—
435#102—1221no—
436#102—1221no—
437#102—1221no—
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—2441no—
455#41—42no—
456#41—81no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—1221no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—611no—
463C2×D4—1221no—
464C2×D4—1221no—
465C2×D4—1221no—
466C2×D4—4881no—
467C2×D4—4881no—
468C2×D4—2441no—
469C2×D4—2442no—
470C2×D4—2441no—
471C2×D4—2441no—
472C2×D4—2442no—
473C2×D4D4×D6111yescharacteristic
474C2×D4C2×C22⋊D6111yescharacteristic
475C2×D4C2×C22⋊D6111yescharacteristic
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—41no—
480C22×C4—1221no—
481SD16—81no—
482SD16—4882no—
483D8—22no—
484D8—4881no—
485D8—4881no—
486D8—2441no—
487M16—4881no—
488C2×C8—21no—
489C2×C8—81no—
490C2×C8—611no—
491C2×C8—611no—
492C2×C8—1221no—
493C2×C8—1221no—
494C2×C8—1221no—
495C2×C8—1221no—
496C2×C8—4881no—
497C2×C8—2442no—
498C2×C8C2×C22⋊D6111yescharacteristic
499C2×C8C2×C22⋊D6111yescharacteristic
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—41no—
505C4⋊C4—611no—
506C4⋊C4—1221no—
507C4⋊C4—1221no—
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—1221no—
528C23—9761no—
529C23—4882no—
530C23—4882no—
531C23—2441no—
532Q8—41no—
533Q8—41no—
534Q8—81no—
535Q8—4881no—
536D4—21no—
537D4—21no—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—82no—
542D4—161no—
543D4—1221no—
544D4—1221no—
545D4—9761no—
546D4—4881no—
547D4—4882no—
548D4—4882no—
549D4—2441no—
550D4—2441no—
551D4—2441no—
552D4—2441no—
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—41no—
565C2×C4—82no—
566C2×C4—1221no—
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—9764no—
592C22—4881no—
593C22—4881no—
594C22—4881no—
595C22—2441no—
596C22—2441no—
597C22—2441no—
598C22D4×C22⋊D6111yescharacteristic
599C4—21no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—81no—
604C4—81no—
605C4—4881no—
606C4—2441no—
607C4C2×#1451979711yescharacteristic
608C4#1684055911yescharacteristic
609C4#1684056511yescharacteristic
610C4#1684056911yescharacteristic
611C2—42no—
612C2—81no—
613C2—81no—
614C2—9761no—
615C2—4881no—
616C2#2145734411yescharacteristic
617C2#2145750011yescharacteristic
618C2#2145758111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3303C2
socleC22×C61D42
hypercenter#3303D61
hypocenterC61#19775
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3303

Complements

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

NH ≅ G/Ntype
1. #21458237C2semidirect
2. #21458063C2semidirect
3. #21457626C2semidirect
4. #21445473C2semidirect
5. #21445391C2semidirect
6. #21445258C2semidirect
7. #21445228C2semidirect
8. #21445216C2semidirect
9. #21445045C2semidirect
10. #21444970C2semidirect
11. #21444934C2semidirect
12. #21444902C2semidirect
13. #21444648C2semidirect
14. #21444643C2semidirect
15. C61×#3303C2semidirect
18. #16840165C22semidirect
20. #16840114C22semidirect
28. #16840052C22semidirect
41. D4×#92418C22semidirect
45. #16839514C22semidirect
46. #16839513C22semidirect
47. #16839511C22semidirect
48. #16839510C22semidirect
49. #16839508C22semidirect
52. D4⋊#92418C22semidirect
53. D4⋊#92418C22semidirect
55. #16839483C22semidirect
56. C61×#555C22semidirect
58. C61×#487C22semidirect
62. C61×#461C22semidirect
65. C8×D4×C61C22semidirect
304. #3303D61semidirect
326. #555C2×D61semidirect
332. #487C2×D61semidirect
349. #461C2×D61semidirect
360. C8×D4C2×D61semidirect
376. C61#19775semidirect

Maximal subgroups

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

subgroupindex
#214582372
#214580632
#214576262
#214454732
#214453912
#214452582
#214452282
#214452162
#214450452
#214449702
#214449342
#214449022
#214446482
#214446432
C61×#33032
#1977561