Finite Group Databasebeta

← #29669883

Subgroups — #29669883

Order 15616.

626 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458693C211yesmaximal, characteristic, complemented
2#21458600C211yesmaximal, characteristic, complemented
3#21457640C211yesmaximal, characteristic
4#21457637C211yesmaximal, characteristic
5#21445482C211yesmaximal, characteristic, complemented
6#21445361C211yesmaximal, characteristic, complemented
7#21445273C211yesmaximal, characteristic, complemented
8#21445238C211yesmaximal, characteristic, complemented
9#21445196C211yesmaximal, characteristic, complemented
10#21445000C211yesmaximal, characteristic
11#21444950C211yesmaximal, characteristic, complemented
12#21444918C211yesmaximal, characteristic, complemented
13#21444658C211yesmaximal, characteristic, complemented
14#21444628C211yesmaximal, characteristic, complemented
15C61×#1632C211yesmaximal, characteristic, complemented
16#16840491C2211yescharacteristic, complemented
17#16840473C2211yescharacteristic
18D4×D244C2211yescharacteristic
19#16840163—21no—
20#16840158C2211yescharacteristic, complemented
21#16840132—21no—
22#16840114C2211yescharacteristic, complemented
23#16840110C2211yescharacteristic
24#16840110C2211yescharacteristic
25#16840109C2211yescharacteristic
26#16840082—21no—
27#16840080—21no—
28#16840071—21no—
29#16840066—21no—
30#16840065—21no—
31#16840054C2211yescharacteristic, complemented
32#16840049C2211yescharacteristic
33#16840043C2211yescharacteristic
34#16839993—21no—
35#16839992—21no—
36#16839967—21no—
37#16839967C2211yescharacteristic
38#16839963C2211yescharacteristic
39#16839962C2211yescharacteristic
40#16839914—21no—
41#16839912—21no—
42#16839893C2211yescharacteristic, complemented
43#16839886C2211yescharacteristic, complemented
44#16839862—21no—
45C4×#11758201C2211yescharacteristic
46C4×#11758200C2211yescharacteristic
47#16839847—21no—
48D4×#92418C2211yescharacteristic
49#16839827C2211yescharacteristic
50C2×#14519697—21no—
51#102×D61—21no—
52#16839514C2211yescharacteristic, complemented
53#16839512C2211yescharacteristic, complemented
54#16839511C2211yescharacteristic, complemented
55#16839509C2211yescharacteristic, complemented
56#16839505C2211yescharacteristic
57#16839494C2211yescharacteristic, complemented
58#16839491C2211yescharacteristic
59#16839484C2211yescharacteristic, complemented
60C61×#554C2211yescharacteristic
61C61×#494C2211yescharacteristic, complemented
62C61×#477C2211yescharacteristic, complemented
63C61×#476C2211yescharacteristic
64C61×#333C2211yescharacteristic, complemented
65C61×Q8⋊C8C2211yescharacteristic, complemented
66C61×D4⋊C8C2211yescharacteristic
67C22×D244—21no—
68C2×D4×D61—21no—
69C2×#11758190—21no—
70C2×#11758200—21no—
71C2×#11758200D411yescharacteristic
72C2×#11758201—21no—
73C2×#11758201D411yescharacteristic
74C22×#92418—21no—
75C2×C8×D61—21no—
76#14519777—21no—
77#14519777C2311yescharacteristic
78#14519774C2311yescharacteristic
79#14519768—21no—
80#14519768—21no—
81#14519768—41no—
82#14519757—21no—
83#14519753—41no—
84#14519752—21no—
85#14519751—21no—
86#14519747—41no—
87Q8×Dic61—21no—
88C4×Dic122—21no—
89C4×Dic122C2311yescharacteristic
90C4×D244C2311yescharacteristic
91#14519739—21no—
92C4⋊C4×D61—21no—
93#14519711—21no—
94#14519710—21no—
95#14519708—21no—
96#14519708—21no—
97#14519708—21no—
98#14519708D411yescharacteristic
99#14519708D411yescharacteristic
100C4⋊#92418—21no—
101C4⋊#92418C2311yescharacteristic
102C4⋊#92418C2311yescharacteristic
103#14519706—21no—
104#14519701D411yescharacteristic
105#14519700—21no—
106#14519700—21no—
107#14519700—21no—
108#14519700—21no—
109#14519700D411yescharacteristic
110#14519699—21no—
111#14519699—21no—
112#14519699—41no—
113#14519698D411yescharacteristic
114#14519697—21no—
115#14519697—21no—
116#14519697—21no—
117#14519697—21no—
118#14519697—21no—
119#14519697—21no—
120#14519697D411yescharacteristic
121C22⋊#92418—21no—
122#14519689—21no—
123#14519688—21no—
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C8×Dic61—21no—
127C2×Q16×C61—41no—
128C4⋊Q8×C61C2311yescharacteristic
129C4⋊Q8×C61C2311yescharacteristic
130#125×C61—21no—
131C22⋊Q8×C61—21no—
132C22⋊Q8×C61—41no—
133C4×Q8×C61C2311yescharacteristic
134C4×D4×C61—21no—
135C4×D4×C61C2311yescharacteristic
136C2×C4⋊C4×C61—21no—
137#107×C61—21no—
138#106×C61—21no—
139C4⋊C8×C61C2311yescharacteristic
140C4⋊C8×C61C2311yescharacteristic
141#103×C61—21no—
142#102×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C23×D61—41no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61C2×D411yescharacteristic
148C2×D4×C61C2×D411yescharacteristic
149C22×C4×C61—21no—
150C22×C4×C61—41no—
151C2×C22⋊D61—41no—
152D4×D61—42no—
153D4×D61—81no—
154C2×D244—21no—
155C2×D244—21no—
156C2×D244—21no—
157C2×D244—42no—
158C2×D244—41no—
159C2×D244—81no—
160C2×D244C2×D411yescharacteristic
161C2×C4×D61—21no—
162C2×C4×D61—41no—
163C2×Dic122—21no—
164C2×Dic122C2×D411yescharacteristic
165Q16×C61—82no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—41no—
175C4⋊C4×C61—41no—
176C4⋊C4×C61C2×D411yescharacteristic
177C4⋊C4×C61C2×D411yescharacteristic
178C22⋊C4×C61—21no—
179C22⋊C4×C61—41no—
180C42×C61—21no—
181C42×C61C2411yescharacteristic
182#11758201—22no—
183#11758201—81no—
184#11758200—22no—
185#11758200—42no—
186#11758198—21no—
187#11758198—41no—
188#11758198—41no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—41no—
192C4⋊Dic61—41no—
193C4⋊Dic61—41no—
194C4⋊Dic61C2×D411yescharacteristic
195C4⋊Dic61C2×D411yescharacteristic
196#11758196—21no—
197#11758196—41no—
198#11758196—41no—
199C4×Dic61—21no—
200C4×Dic61—41no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—81no—
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207C2×#92418C2×D411yescharacteristic
208#11758190—81no—
209C8×D61—81no—
210C23×C61—21no—
211C22×D61—21no—
212C22×D61—41no—
213C22×D61—82no—
214C22×D61—82no—
215C22×D61—161no—
216Q8×C61—21no—
217Q8×C61—21no—
218Q8×C61—81no—
219Q8×C61—81no—
220D4×C61—21no—
221D4×C61#13512yes—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—161no—
230C2×C4×C61C22×D411yescharacteristic
231C2×C4×C61C22×D411yescharacteristic
232C2×C4×C61H(5,𝔽2)11yescharacteristic
233C22⋊D61—82no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—41no—
238D244—21no—
239D244—41no—
240D244—41no—
241D244—41no—
242D244—41no—
243D244—81no—
244D244—82no—
245D244#13712yes—
246C4×D61—41no—
247C4×D61—41no—
248C4×D61—161no—
249Dic122—21no—
250Dic122—21no—
251Dic122—41no—
252Dic122—41no—
253C8×C61—41no—
254C8×C61—41no—
255C8×C61—41no—
256#92418—21no—
257#92418—21no—
258#92418—21no—
259#92418—21no—
260#92418—41no—
261#92418—41no—
262#19790—611nomaximal, Sylow
263C22×C61—22no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61D4211yescharacteristic
267C2×D61—22no—
268C2×D61—41no—
269C2×D61—41no—
270C2×D61—81no—
271C2×D61—81no—
272C2×D61—81no—
273C2×D61—164no—
274C4×C61—21no—
275C4×C61—41no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61—81no—
279C4×C61—81no—
280C4×C61C2×#13511yescharacteristic
281C4×C61C2×#13711yescharacteristic
282C4×C61#57711yescharacteristic
283C4×C61#57711yescharacteristic
284Dic61—41no—
285Dic61—41no—
286Dic61—41no—
287Dic61—81no—
288#3381—611no—
289#3372—611no—
290#3295—611no—
291#3295—611no—
292#1720—611no—
293#1698—611no—
294#1683—611no—
295#1678—611no—
296#1671—611no—
297#1639—611no—
298#1632—611no—
299#1632D6111yescharacteristic, complemented
300#1626—611no—
301#1582—611no—
302SD16⋊C8—611no—
303C2×C61—42no—
304C2×C61#326611yescharacteristic
305C2×C61#328211yescharacteristic
306C2×C61#328811yescharacteristic
307D61—42no—
308D61—161no—
309#557—611no—
310#554—611no—
311#554C2×D6111yescharacteristic
312D42—611no—
313#499—1221no—
314#498—611no—
315#494C2×D6111yescharacteristic, complemented
316#491—1221no—
317#487—611no—
318#486—611no—
319#486—611no—
320#486—611no—
321#481—1221no—
322#481—1221no—
323#479—1221no—
324#479—1221no—
325#478—1221no—
326#477—611no—
327#477C2×D6111yescharacteristic, complemented
328#476—611no—
329#476C2×D6111yescharacteristic
330#474—611no—
331#465—1221no—
332#465—1221no—
333#461—611no—
334#461—1221no—
335#460—611no—
336#460—611no—
337#450—1221no—
338#450—1221no—
339#446—611no—
340C8×Q8—611no—
341#440—1221no—
342C4×SD16—611no—
343C4×SD16—611no—
344C4×SD16—1221no—
345C8×D4—611no—
346C8×D4—611no—
347C2×#102—1221no—
348C2×#102—1221no—
349#335—611no—
350#334—611no—
351#333—611no—
352#333C2×D6111yescharacteristic, complemented
353#332—611no—
354#331—611no—
355Q8⋊C8—611no—
356Q8⋊C8C2×D6111yescharacteristic, complemented
357D4⋊C8—611no—
358D4⋊C8C2×D6111yescharacteristic
359#322—611no—
360C61#1979011yescharacteristic, complemented, Sylow
361C22×D4—1221no—
362C22×D4—1221no—
363C2×Q16—41no—
364C2×SD16—611no—
365C2×SD16—611no—
366C2×SD16—1221no—
367C2×SD16—1221no—
368C2×SD16—1221no—
369C22×C8—1221no—
370C22×C8—1221no—
371C4⋊Q8—611no—
372C4⋊Q8—1221no—
373C4⋊Q8C22×D6111yescharacteristic
374C4⋊Q8C22×D6111yescharacteristic
375#127—611no—
376#125—21no—
377#125—1221no—
378#125—1221no—
379#125—2441no—
380C22⋊Q8—21no—
381C22⋊Q8—41no—
382C22⋊Q8—1221no—
383C22⋊Q8—2441no—
384#121—1221no—
385#121—1221no—
386#120—2441no—
387C4×Q8—611no—
388C4×Q8—1221no—
389C4×Q8—1221no—
390C4×Q8C22×D6111yescharacteristic
391C4×D4—21no—
392C4×D4—611no—
393C4×D4—1221no—
394C4×D4C22×D6111yescharacteristic
395C2×C4⋊C4—21no—
396C2×C4⋊C4—1221no—
397#107—21no—
398#107—1221no—
399#107—1221no—
400#106—21no—
401#106—611no—
402#106—611no—
403#106—1221no—
404#106—1221no—
405#106—1221no—
406C4⋊C8—611no—
407C4⋊C8—611no—
408C4⋊C8—1221no—
409C4⋊C8—1221no—
410C4⋊C8C22×D6111yescharacteristic
411C4⋊C8C22×D6111yescharacteristic
412#103—21no—
413#103—611no—
414#103—611no—
415#103—1221no—
416#103—1221no—
417#103—1221no—
418#103—1221no—
419#102—21no—
420#102—611no—
421#102—611no—
422#102—1221no—
423#102—1221no—
424#102—1221no—
425#102—1221no—
426#102—1221no—
427#102—1221no—
428#102—1221no—
429#102—1221no—
430#102—2441no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433#97—1221no—
434C4×C8—611no—
435C4×C8—611no—
436C4×C8—1221no—
437C4×C8C22×D6111yescharacteristic
438C24—2441no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—611no—
442C2×Q8—1221no—
443C2×Q8D4×D6111yescharacteristic
444C2×D4—611no—
445C2×D4—1221no—
446C2×D4—1221no—
447C2×D4—1221no—
448C2×D4—4881no—
449C2×D4—4881no—
450C2×D4—2441no—
451C2×D4—2442no—
452C2×D4—2441no—
453C2×D4—2442no—
454C2×D4D4×D6111yescharacteristic
455C22×C4—21no—
456C22×C4—41no—
457C22×C4—1221no—
458C22×C4—2441no—
459Q16—82no—
460SD16—1222no—
461SD16—1222no—
462SD16—4881no—
463SD16—4881no—
464SD16—2442no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—611no—
469C2×C8—611no—
470C2×C8—611no—
471C2×C8—611no—
472C2×C8—1221no—
473C2×C8—1221no—
474C2×C8—4881no—
475C2×C8—4881no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—611no—
484C4⋊C4—611no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—2441no—
489C4⋊C4—2441no—
490C4⋊C4—2441no—
491C4⋊C4—2441no—
492C4⋊C4—2441no—
493C4⋊C4D4×D6111yescharacteristic
494C4⋊C4D4×D6111yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—41no—
497C22⋊C4—1221no—
498C22⋊C4—2441no—
499C22⋊C4—2441no—
500C42—21no—
501C42—1221no—
502C42—2441no—
503C42C23×D6111yescharacteristic
504C23—21no—
505C23—1221no—
506C23—9761no—
507C23—4882no—
508C23—4882no—
509C23—2441no—
510Q8—21no—
511Q8—21no—
512Q8—81no—
513Q8—81no—
514Q8—1221no—
515Q8—1221no—
516Q8—2441no—
517Q8—2441no—
518D4—21no—
519D4—612no—
520D4—1221no—
521D4—4881no—
522D4—4882no—
523D4—4882no—
524D4—2441no—
525D4—2441no—
526D4—2441no—
527D4—2441no—
528D4#1451980012yes—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—161no—
537C2×C4—1221no—
538C2×C4—1221no—
539C2×C4—1221no—
540C2×C4—9761no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4C2×D4×D6111yescharacteristic
545C2×C4C2×D4×D6111yescharacteristic
546C2×C4#1451982211yescharacteristic
547C8—41no—
548C8—41no—
549C8—41no—
550C8—1221no—
551C8—1221no—
552C8—1221no—
553C8—1221no—
554C8—2441no—
555C8—2441no—
556C22—22no—
557C22—41no—
558C22—41no—
559C22—1222no—
560C22—9764no—
561C22—4881no—
562C22—4881no—
563C22—4881no—
564C22—2441no—
565C22—2441no—
566C22#1684039411yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4—4881no—
574C4—2441no—
575C4—2441no—
576C4—2441no—
577C4C2×#1451980011yescharacteristic
578C4#137×D6111yescharacteristic
579C4#1684056911yescharacteristic
580C4#1684057111yescharacteristic
581C2—42no—
582C2—9761no—
583C2—2442no—
584C2#2145732711yescharacteristic
585C2#2145751911yescharacteristic
586C2#2145758011yescharacteristic
subgroupG/H
centerC22#16840394
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1632C2
socleC22×C61D42
prime radicalD4×D244C22
hypercenter#1632D61
hypocenterC61#19790
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1632

Complements

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

NH ≅ G/Ntype
1. #21458693C2semidirect
2. #21458600C2semidirect
5. #21445482C2semidirect
6. #21445361C2semidirect
7. #21445273C2semidirect
8. #21445238C2semidirect
9. #21445196C2semidirect
11. #21444950C2semidirect
12. #21444918C2semidirect
13. #21444658C2semidirect
14. #21444628C2semidirect
15. C61×#1632C2semidirect
16. #16840491C22semidirect
20. #16840158C22semidirect
22. #16840114C22semidirect
31. #16840054C22semidirect
42. #16839893C22semidirect
43. #16839886C22semidirect
52. #16839514C22semidirect
53. #16839512C22semidirect
54. #16839511C22semidirect
55. #16839509C22semidirect
57. #16839494C22semidirect
59. #16839484C22semidirect
61. C61×#494C22semidirect
62. C61×#477C22semidirect
64. C61×#333C22semidirect
65. C61×Q8⋊C8C22semidirect
299. #1632D61semidirect
315. #494C2×D61semidirect
327. #477C2×D61semidirect
352. #333C2×D61semidirect
356. Q8⋊C8C2×D61semidirect
360. C61#19790semidirect

Maximal subgroups

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

subgroupindex
#214586932
#214586002
#214576402
#214576372
#214454822
#214453612
#214452732
#214452382
#214451962
#214450002
#214449502
#214449182
#214446582
#214446282
C61×#16322
#1979061