Finite Group Databasebeta

← #29669886

Subgroups — #29669886

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#21458596C211yesmaximal, characteristic, complemented
2#21457645C211yesmaximal, characteristic
3#21457637C211yesmaximal, characteristic
4#21445477C211yesmaximal, characteristic, complemented
5#21445361C211yesmaximal, characteristic, complemented
6#21445268C211yesmaximal, characteristic, complemented
7#21445235C211yesmaximal, characteristic, complemented
8#21445191C211yesmaximal, characteristic, complemented
9#21444997C211yesmaximal, characteristic
10#21444953C211yesmaximal, characteristic, complemented
11#21444952C211yesmaximal, characteristic, complemented
12#21444915C211yesmaximal, characteristic, complemented
13#21444656C211yesmaximal, characteristic, complemented
14#21444629C211yesmaximal, characteristic, complemented
15C61×#3381C211yesmaximal, characteristic, complemented
16#16840472C2211yescharacteristic
17D4×D244C2211yescharacteristic
18#16840141C2211yescharacteristic, complemented
19#16840130—21no—
20#16840112C2211yescharacteristic, complemented
21#16840110C2211yescharacteristic
22#16840110C2211yescharacteristic
23#16840109C2211yescharacteristic
24#16840082—21no—
25#16840080—21no—
26#16840069—21no—
27#16840057C2211yescharacteristic, complemented
28#16840052C2211yescharacteristic
29#16840049C2211yescharacteristic
30#16839994—21no—
31#16839993—21no—
32#16839964—21no—
33#16839964C2211yescharacteristic
34#16839962C2211yescharacteristic
35#16839962C2211yescharacteristic
36#16839912—21no—
37#16839911—21no—
38#16839893C2211yescharacteristic, complemented
39#16839860—21no—
40C4×#11758201C2211yescharacteristic
41C8×D244C2211yescharacteristic
42D4×#92418C2211yescharacteristic
43C2×#14519697—21no—
44#102×D61—21no—
45#16839514C2211yescharacteristic, complemented
46#16839513C2211yescharacteristic, complemented
47#16839511C2211yescharacteristic, complemented
48#16839510C2211yescharacteristic, complemented
49#16839508C2211yescharacteristic, complemented
50#16839505C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic, complemented
52Q8⋊#92418C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55#16839484C2211yescharacteristic, complemented
56C61×#557C2211yescharacteristic, complemented
57C61×#554C2211yescharacteristic
58C61×#499—21no—
59C61×#498C2211yescharacteristic, complemented
60C61×#479—21no—
61C61×#478—21no—
62C61×#477C2211yescharacteristic, complemented
63C61×#474C2211yescharacteristic
64C8×Q8×C61C2211yescharacteristic, complemented
65C4×SD16×C61—21no—
66C4×SD16×C61C2211yescharacteristic
67C22×D244—21no—
68C2×D4×D61—21no—
69C2×#11758202—41no—
70C2×#11758201—21no—
71C2×#11758201—21no—
72C2×#11758201—21no—
73C2×#11758201D411yescharacteristic
74C22×#92418—21no—
75C2×C8×D61—21no—
76#14519777C2311yescharacteristic
77#14519774C2311yescharacteristic
78#14519769—21no—
79#14519755—41no—
80#14519753—21no—
81#14519752—21no—
82#14519751—21no—
83#14519747—41no—
84C4×D244—21no—
85C4×D244C2311yescharacteristic
86C4⋊C4×D61—21no—
87#14519710—21no—
88#14519708—21no—
89#14519708—21no—
90#14519708D411yescharacteristic
91C4⋊#92418—21no—
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95#14519701—21no—
96#14519701—21no—
97#14519701—21no—
98#14519701—21no—
99#14519701D411yescharacteristic
100#14519699—21no—
101#14519699—21no—
102#14519698—21no—
103#14519697—21no—
104#14519697—21no—
105#14519697—21no—
106#14519697—21no—
107#14519697—21no—
108#14519697—41no—
109#14519697D411yescharacteristic
110C22⋊#92418—21no—
111#14519689—21no—
112#14519688—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×SD16×C61D411yescharacteristic
116C4⋊Q8×C61—21no—
117C4⋊Q8×C61C2311yescharacteristic
118C4⋊Q8×C61C2311yescharacteristic
119#125×C61—21no—
120#125×C61—21no—
121#125×C61—41no—
122C22⋊Q8×C61—21no—
123C22⋊Q8×C61—41no—
124C4×Q8×C61—21no—
125C4×Q8×C61—21no—
126C4×Q8×C61C2311yescharacteristic
127C4×Q8×C61C2311yescharacteristic
128C4×D4×C61—21no—
129C4×D4×C61C2311yescharacteristic
130C2×C4⋊C4×C61—21no—
131#107×C61—21no—
132#107×C61—21no—
133#106×C61—21no—
134#106×C61—21no—
135#106×C61D411yescharacteristic
136C4⋊C8×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
138#103×C61—21no—
139#103×C61D411yescharacteristic
140#102×C61—21no—
141#102×C61D411yescharacteristic
142C4×C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C23×D61—41no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61C2×D411yescharacteristic
148C2×Q8×C61C2×D411yescharacteristic
149C2×D4×C61C2×D411yescharacteristic
150C22×C4×C61—21no—
151C22×C4×C61—41no—
152C2×C22⋊D61—41no—
153D4×D61—42no—
154D4×D61—81no—
155C2×D244—21no—
156C2×D244—21no—
157C2×D244—21no—
158C2×D244—42no—
159C2×D244—41no—
160C2×D244—81no—
161C2×D244C2×D411yescharacteristic
162C2×C4×D61—21no—
163C2×C4×D61—41no—
164C2×Dic122—21no—
165SD16×C61—22no—
166C2×C8×C61—21no—
167C2×C8×C61C2×D411yescharacteristic
168C2×C8×C61C2×D411yescharacteristic
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—41no—
176C4⋊C4×C61—41no—
177C4⋊C4×C61—41no—
178C4⋊C4×C61—41no—
179C4⋊C4×C61—41no—
180C4⋊C4×C61C2×D411yescharacteristic
181C4⋊C4×C61C2×D411yescharacteristic
182C4⋊C4×C61C2×D411yescharacteristic
183C22⋊C4×C61—21no—
184C22⋊C4×C61—41no—
185C42×C61—21no—
186C42×C61—21no—
187C42×C61—41no—
188C42×C61C2411yescharacteristic
189#11758202—82no—
190#11758201—22no—
191#11758201—42no—
192#11758201—81no—
193#11758201—81no—
194#11758198—21no—
195#11758198—41no—
196#11758198—41no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61C2×D411yescharacteristic
200#11758196—41no—
201#11758196—41no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—81no—
207C2×#92418C2×D411yescharacteristic
208C2×#92418C2×D411yescharacteristic
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—21no—
219Q8×C61—21no—
220Q8×C61—41no—
221Q8×C61—41no—
222Q8×C61—81no—
223D4×C61—21no—
224D4×C61#13712yes—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—161no—
235C2×C4×C61C22×D411yescharacteristic
236C2×C4×C61C22×D411yescharacteristic
237C2×C4×C61H(5,𝔽2)11yescharacteristic
238C22⋊D61—82no—
239C2×Dic61—21no—
240C2×Dic61—41no—
241D244—21no—
242D244—41no—
243D244—41no—
244D244—41no—
245D244—41no—
246D244—81no—
247D244—82no—
248D244#13512yes—
249C4×D61—41no—
250C4×D61—41no—
251C4×D61—161no—
252Dic122—81no—
253C8×C61—21no—
254C8×C61—21no—
255C8×C61—41no—
256#92418—21no—
257#92418—21no—
258#92418—41no—
259#92418—41no—
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—41no—
279C4×C61—41no—
280C4×C61—81no—
281C4×C61—81no—
282C4×C61C2×#13511yescharacteristic
283C4×C61C2×#13711yescharacteristic
284C4×C61#57711yescharacteristic
285C4×C61#57711yescharacteristic
286Dic61—41no—
287Dic61—81no—
288#3381D6111yescharacteristic, complemented
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#1632—611no—
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#557C2×D6111yescharacteristic, complemented
310#554—611no—
311#554C2×D6111yescharacteristic
312D42—611no—
313#499—21no—
314#498C2×D6111yescharacteristic, complemented
315#494—611no—
316#491—1221no—
317#487—611no—
318#486—611no—
319#486—611no—
320#486—611no—
321#481—1221no—
322#481—1221no—
323#479—21no—
324#479—1221no—
325#478—21no—
326#477—611no—
327#477C2×D6111yescharacteristic, complemented
328#476—611no—
329#476—611no—
330#474C2×D6111yescharacteristic
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×Q8C2×D6111yescharacteristic, complemented
341#440—1221no—
342C4×SD16—21no—
343C4×SD16—611no—
344C4×SD16C2×D6111yescharacteristic
345C8×D4—611no—
346C8×D4—611no—
347C2×#102—1221no—
348C2×#102—1221no—
349#335—611no—
350#334—611no—
351#333—611no—
352#333—611no—
353#332—611no—
354#331—611no—
355Q8⋊C8—611no—
356Q8⋊C8—611no—
357D4⋊C8—611no—
358D4⋊C8—611no—
359#322—611no—
360C61#1979011yescharacteristic, complemented, Sylow
361C22×D4—1221no—
362C22×D4—1221no—
363C2×Q16—2441no—
364C2×SD16—611no—
365C2×SD16—1221no—
366C2×SD16—1221no—
367C2×SD16—1221no—
368C2×SD16C22⋊D6111yescharacteristic
369C22×C8—1221no—
370C22×C8—1221no—
371C4⋊Q8—21no—
372C4⋊Q8—611no—
373C4⋊Q8C22×D6111yescharacteristic
374C4⋊Q8C22×D6111yescharacteristic
375#127—611no—
376#125—21no—
377#125—21no—
378#125—41no—
379#125—1221no—
380C22⋊Q8—21no—
381C22⋊Q8—41no—
382C22⋊Q8—1221no—
383C22⋊Q8—2441no—
384#121—1221no—
385#121—1221no—
386#120—2441no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8C22×D6111yescharacteristic
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—21no—
399#107—1221no—
400#106—21no—
401#106—21no—
402#106—611no—
403#106—1221no—
404#106—1221no—
405#106C22⋊D6111yescharacteristic
406C4⋊C8—21no—
407C4⋊C8—611no—
408C4⋊C8—611no—
409C4⋊C8—611no—
410C4⋊C8—1221no—
411C4⋊C8C22×D6111yescharacteristic
412#103—21no—
413#103—611no—
414#103—1221no—
415#103—1221no—
416#103—1221no—
417#103—1221no—
418#103C22⋊D6111yescharacteristic
419#102—21no—
420#102—611no—
421#102—1221no—
422#102—1221no—
423#102—1221no—
424#102—1221no—
425#102—1221no—
426#102—1221no—
427#102—1221no—
428#102—1221no—
429#102—2441no—
430#102C22⋊D6111yescharacteristic
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433#97—1221no—
434C4×C8—21no—
435C4×C8—611no—
436C4×C8—611no—
437C4×C8C22×D6111yescharacteristic
438C24—2441no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—1221no—
442C2×Q8D4×D6111yescharacteristic
443C2×Q8C2×C22⋊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×D4C2×C22⋊D6111yescharacteristic
455C22×C4—21no—
456C22×C4—41no—
457C22×C4—1221no—
458C22×C4—2441no—
459Q16—4882no—
460SD16—22no—
461SD16—1222no—
462SD16—4881no—
463SD16—4881no—
464SD16—2442no—
465C2×C8—21no—
466C2×C8—611no—
467C2×C8—611no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8—4881no—
473C2×C8—4881no—
474C2×C8C2×C22⋊D6111yescharacteristic
475C2×C8C2×C22⋊D6111yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—611no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C4⋊C4—2441no—
491C4⋊C4—2441no—
492C4⋊C4D4×D6111yescharacteristic
493C4⋊C4C2×C22⋊D6111yescharacteristic
494C4⋊C4C2×C22⋊D6111yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—41no—
497C22⋊C4—1221no—
498C22⋊C4—2441no—
499C22⋊C4—2441no—
500C42—21no—
501C42—21no—
502C42—41no—
503C42C23×D6111yescharacteristic
504C23—21no—
505C23—1221no—
506C23—9761no—
507C23—4882no—
508C23—4882no—
509C23—2441no—
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—21no—
514Q8—41no—
515Q8—41no—
516Q8—81no—
517Q8—4881no—
518D4—21no—
519D4—612no—
520D4—1221no—
521D4—4881no—
522D4—4882no—
523D4—4882no—
524D4—2441no—
525D4—2441no—
526D4—2441no—
527D4—2441no—
528D4#1451980812yes—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—161no—
539C2×C4—1221no—
540C2×C4—9761no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4C2×D4×D6111yescharacteristic
545C2×C4C22×C22⋊D6111yescharacteristic
546C2×C4#1451982211yescharacteristic
547C8—21no—
548C8—21no—
549C8—41no—
550C8—1221no—
551C8—1221no—
552C8—2441no—
553C8—2441no—
554C8—2441no—
555C8—2441no—
556C22—22no—
557C22—41no—
558C22—41no—
559C22—1222no—
560C22—9764no—
561C22—4881no—
562C22—4881no—
563C22—4881no—
564C22—2441no—
565C22—2441no—
566C22D4×C22⋊D6111yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—81no—
574C4—81no—
575C4—4881no—
576C4—2441no—
577C4#135×D6111yescharacteristic
578C4C2×#1451980811yescharacteristic
579C4#1684056911yescharacteristic
580C4#1684057011yescharacteristic
581C2—42no—
582C2—9761no—
583C2—2442no—
584C2#2145733011yescharacteristic
585C2#2145752011yescharacteristic
586C2#2145758111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3381C2
socleC22×C61D42
prime radicalD4×D244C22
hypercenter#3381D61
hypocenterC61#19790
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3381

Complements

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

NH ≅ G/Ntype
1. #21458596C2semidirect
4. #21445477C2semidirect
5. #21445361C2semidirect
6. #21445268C2semidirect
7. #21445235C2semidirect
8. #21445191C2semidirect
10. #21444953C2semidirect
11. #21444952C2semidirect
12. #21444915C2semidirect
13. #21444656C2semidirect
14. #21444629C2semidirect
15. C61×#3381C2semidirect
18. #16840141C22semidirect
20. #16840112C22semidirect
27. #16840057C22semidirect
38. #16839893C22semidirect
45. #16839514C22semidirect
46. #16839513C22semidirect
47. #16839511C22semidirect
48. #16839510C22semidirect
49. #16839508C22semidirect
51. Q8⋊#92418C22semidirect
52. Q8⋊#92418C22semidirect
55. #16839484C22semidirect
56. C61×#557C22semidirect
59. C61×#498C22semidirect
62. C61×#477C22semidirect
64. C8×Q8×C61C22semidirect
288. #3381D61semidirect
309. #557C2×D61semidirect
314. #498C2×D61semidirect
327. #477C2×D61semidirect
340. C8×Q8C2×D61semidirect
360. C61#19790semidirect

Maximal subgroups

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

subgroupindex
#214585962
#214576452
#214576372
#214454772
#214453612
#214452682
#214452352
#214451912
#214449972
#214449532
#214449522
#214449152
#214446562
#214446292
C61×#33812
#1979061