Finite Group Databasebeta

← #30613784

Subgroups — #30613784

Order 15616.

604 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462728C211yesmaximal, characteristic, complemented
2#21462699C211yesmaximal, characteristic
3#21461463C211yesmaximal, characteristic, complemented
4#21461460C211yesmaximal, characteristic, complemented
5#21461428C211yesmaximal, characteristic, complemented
6#21461427C211yesmaximal, characteristic, complemented
7#21461424C211yesmaximal, characteristic, complemented
8#21461423C211yesmaximal, characteristic, complemented
9#21461410C211yesmaximal, characteristic, complemented
10#21461409C211yesmaximal, characteristic, complemented
11#21461368C211yesmaximal, characteristic, complemented
12#21461141C211yesmaximal, characteristic, complemented
13#21461138C211yesmaximal, characteristic
14#21461028C211yesmaximal, characteristic, complemented
15#21456373C211yesmaximal, characteristic
16#16840814—21no—
17#16840813C2211yescharacteristic
18#16840812C2211yescharacteristic
19#16840811—21no—
20#16840811C2211yescharacteristic
21Q8×#92420C2211yescharacteristic
22#16840797C2211yescharacteristic
23#16840796C2211yescharacteristic
24#16840795—21no—
25#16840790C2211yescharacteristic
26#16840789—21no—
27D4×#92420C2211yescharacteristic
28#16840786—21no—
29#16840786—21no—
30#16840779C2211yescharacteristic
31#16840778C2211yescharacteristic
32#16840778C2211yescharacteristic
33#16840736—21no—
34#16840735—21no—
35C4×#11758217C2211yescharacteristic
36#16840626C2211yescharacteristic
37#16840626C2211yescharacteristic
38#16840624C2211yescharacteristic
39#16840624C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42Q8⋊#92420C2211yescharacteristic
43Q8⋊#92420C2211yescharacteristic
44#16840610C2211yescharacteristic
45#16840610C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic
49#92420⋊C8C2211yescharacteristic
50#16840603C2211yescharacteristic
51#16840603C2211yescharacteristic
52#16840314C2211yescharacteristic
53#16840307C2211yescharacteristic
54#16840159C411yescharacteristic
55#16840133C411yescharacteristic
56#16840111C411yescharacteristic
57#16840107C411yescharacteristic
58#16839993C411yescharacteristic
59#16839991C411yescharacteristic
60#16839989C411yescharacteristic
61#16839853C2211yescharacteristic
62SD16×Dic61C2211yescharacteristic
63#16839849C2211yescharacteristic
64#16839847C2211yescharacteristic
65C2×C8×Dic61C2211yescharacteristic
66C61×#465C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758217—21no—
69C2×#11758217—21no—
70C2×D61⋊C8—21no—
71C22×#92420—21no—
72#14519844—21no—
73#14519844—21no—
74#14519844D411yescharacteristic
75#14519844D411yescharacteristic
76C4⋊#92420—21no—
77C4⋊#92420—21no—
78C4⋊#92420C2311yescharacteristic
79C4⋊#92420C2311yescharacteristic
80C4⋊#92420C2311yescharacteristic
81C4⋊#92420C2311yescharacteristic
82#14519834—21no—
83#14519834—21no—
84C22⋊#92420—21no—
85C22⋊#92420—21no—
86C22⋊#92420—21no—
87C22⋊#92420—21no—
88C22⋊#92420D411yescharacteristic
89C22⋊#92420D411yescharacteristic
90#14519832—21no—
91#14519832—21no—
92#14519832—21no—
93C4×#92420—21no—
94C4×#92420—21no—
95C4×#92420—21no—
96C4×#92420—21no—
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×#11758224—21no—
102C2×#11758190C2×C411yescharacteristic
103C2×#11758200C2×C411yescharacteristic
104C2×#11758201C2×C411yescharacteristic
105C22×#92418C2×C411yescharacteristic
106#14519776C2×C411yescharacteristic
107#14519776C2×C411yescharacteristic
108#14519775C2×C411yescharacteristic
109#14519773C2×C411yescharacteristic
110#14519767—21no—
111#14519763—21no—
112#14519756C2×C411yescharacteristic
113#14519754—21no—
114#14519751C2×C411yescharacteristic
115#14519749—21no—
116Q8×Dic61C2311yescharacteristic
117#14519742—21no—
118#14519742C2311yescharacteristic
119D4×Dic61C2311yescharacteristic
120#14519739C2311yescharacteristic
121#14519737—21no—
122#14519733—21no—
123C2×C4×Dic61C2311yescharacteristic
124#14519709C2×C411yescharacteristic
125#14519708C2×C411yescharacteristic
126#14519708C2×C411yescharacteristic
127#14519702C2×C411yescharacteristic
128#14519701C2×C411yescharacteristic
129#14519700C2×C411yescharacteristic
130#14519699C2×C411yescharacteristic
131#14519698C2×C411yescharacteristic
132#14519697C2×C411yescharacteristic
133C8×Dic61C2×C411yescharacteristic
134C8×Dic61C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137C2×SD16×C61C2×C411yescharacteristic
138C22×C8×C61C2×C411yescharacteristic
139C22⋊Q8×C61C2×C411yescharacteristic
140#121×C61C2×C411yescharacteristic
141#106×C61C2×C411yescharacteristic
142#103×C61C2×C411yescharacteristic
143#102×C61C2×C411yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C2×D4×C61—21no—
146C2×D4×C61C22×C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C2×C22⋊D61—21no—
149C2×C22⋊D61—21no—
150C2×C22⋊D61—21no—
151C22×Dic61—21no—
152C22×Dic61C2×D411yescharacteristic
153C22×Dic61#4111yescharacteristic
154#11758224—81no—
155#11758224—81no—
156C2×D244C22×C411yescharacteristic
157C2×C4×D61—21no—
158C2×Dic122—21no—
159C2×Dic122—21no—
160C2×Dic122C22×C411yescharacteristic
161#11758217—42no—
162#11758217—81no—
163C2×#92420—21no—
164C2×#92420—21no—
165C2×#92420—21no—
166C2×#92420—21no—
167C2×#92420—21no—
168C2×#92420—21no—
169C2×#92420—81no—
170C2×#92420C2×D411yescharacteristic
171C2×#92420C2×D411yescharacteristic
172C2×#92420C2×D411yescharacteristic
173C2×#92420C2×D411yescharacteristic
174#11758213—81no—
175D61⋊C8—81no—
176SD16×C61—41no—
177C2×C8×C61—41no—
178C2×C8×C61C22×C411yescharacteristic
179C2×C8×C61C22×C411yescharacteristic
180C4⋊C4×C61—21no—
181C4⋊C4×C61C22×C411yescharacteristic
182C4⋊C4×C61C22×C411yescharacteristic
183C22⋊C4×C61—21no—
184C22⋊C4×C61—21no—
185C22⋊Dic61—21no—
186C22⋊Dic61—21no—
187#11758201—22no—
188#11758200—22no—
189#11758198—21no—
190#11758198—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61C22×C411yescharacteristic
193C4⋊Dic61C22×C411yescharacteristic
194#11758196—21no—
195#11758196—21no—
196#11758196—21no—
197#11758196—21no—
198#11758196—21no—
199#11758196—21no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C4×Dic61C22×C411yescharacteristic
203C4×Dic61C2×D411yescharacteristic
204C4×Dic61#4111yescharacteristic
205C4×Dic61C2411yescharacteristic
206C2×#92418—22no—
207C2×#92418C22×C411yescharacteristic
208C2×#92418C22×C411yescharacteristic
209#11758190—41no—
210C23×C61—21no—
211C23×C61C4×D411yescharacteristic
212C22×D61—21no—
213Q8×C61—21no—
214Q8×C61—21no—
215D4×C61—21no—
216D4×C61—21no—
217D4×C61—81no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61C4×D411yescharacteristic
224C2×C4×C61C23×C411yescharacteristic
225C22⋊D61—42no—
226C22⋊D61—81no—
227C22⋊D61—81no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—22no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—41no—
235C2×Dic61—41no—
236C2×Dic61C4×D411yescharacteristic
237C2×Dic61C4×D411yescharacteristic
238C2×Dic61C22×D411yescharacteristic
239C2×Dic61C2×#4111yescharacteristic
240D244—21no—
241D244—21no—
242C4×D61—41no—
243C4×D61—41no—
244Dic122—21no—
245Dic122—21no—
246Dic122—42no—
247Dic122—81no—
248#92420—21no—
249#92420—21no—
250#92420—21no—
251#92420—21no—
252#92420—41no—
253#92420—41no—
254#92420—41no—
255#92420—41no—
256#92420—41no—
257#92420—41no—
258C8×C61—21no—
259C8×C61—21no—
260#92418—21no—
261#92418#13112yes—
262#18089—611nomaximal, Sylow
263C22×C61—21no—
264C22×C61—21no—
265C22×C61—21no—
266C22×C61—41no—
267C22×C61—41no—
268C22×C61—41no—
269C22×C61C2×C4×D411yescharacteristic
270C2×D61—41no—
271C2×D61—41no—
272C2×D61—41no—
273C4×C61—21no—
274C4×C61—41no—
275C4×C61—41no—
276C4×C61—41no—
277C4×C61C2×#13111yescharacteristic
278C4×C61#56811yescharacteristic
279Dic61—21no—
280Dic61—21no—
281Dic61—41no—
282Dic61—41no—
283Dic61—41no—
284Dic61#44412yes—
285Dic61#57711yescharacteristic
286Dic61#57711yescharacteristic
287#3167—611no—
288#2986—611no—
289#2979—611no—
290#1592—611no—
291#1592—611no—
292#1583—611no—
293#1583—611no—
294#1582—611no—
295#1582—611no—
296SD16⋊C8—611no—
297SD16⋊C8—611no—
298#1564—611no—
299#1485—611no—
300#1484—611no—
301#1451—611no—
302C2×C61—41no—
303C2×C61—81no—
304C2×C61#293511yescharacteristic
305C2×C61#294911yescharacteristic
306C2×C61C2×#44411yescharacteristic
307D61—81no—
308#533—611no—
309#532—611no—
310#498—611no—
311#492—611no—
312#487—611no—
313#486—611no—
314#465—611no—
315#465—611no—
316#465—611no—
317#465#692311yescharacteristic
318#446—611no—
319#446—611no—
320#446—1221no—
321C8×Q8—611no—
322C8×Q8—611no—
323C8×Q8—1221no—
324C4×SD16—611no—
325C4×SD16—611no—
326C4×SD16—611no—
327C4×SD16—611no—
328#436—611no—
329#436—611no—
330#436—1221no—
331C8×D4—611no—
332C8×D4—611no—
333C8×D4—1221no—
334#433—1221no—
335#433—1221no—
336#431—611no—
337#431—611no—
338#431—611no—
339#408—1221no—
340#408—1221no—
341C4×M16—611no—
342C2×C4×C8—611no—
343#335—611no—
344#335—611no—
345#334—611no—
346#334—611no—
347Q8⋊C8—611no—
348Q8⋊C8—611no—
349Q8⋊C8—611no—
350Q8⋊C8—611no—
351D4⋊C8—611no—
352D4⋊C8—611no—
353D4⋊C8—611no—
354D4⋊C8—611no—
355#322—611no—
356#322—611no—
357#322—611no—
358#322—611no—
359C61#1808911yescharacteristic, complemented, Sylow
360C2×#41—1221no—
361C2×SD16—611no—
362C2×SD16—611no—
363C2×SD16—611no—
364C2×SD16C2×#692311yescharacteristic
365C2×M16—1221no—
366C2×M16—1221no—
367C2×M16—1221no—
368C22×C8—611no—
369C22×C8—1221no—
370C22×C8—1221no—
371C22×C8C2×#692311yescharacteristic
372C4⋊Q8—611no—
373C4⋊Q8—611no—
374C4⋊Q8—611no—
375#127—611no—
376#125—1221no—
377#124—1221no—
378C22⋊Q8—611no—
379C22⋊Q8—1221no—
380C22⋊Q8C2×#692311yescharacteristic
381#121—611no—
382#121—1221no—
383#121C2×#692311yescharacteristic
384C4×Q8—611no—
385C4×Q8—611no—
386C4×Q8—1221no—
387C4×D4—611no—
388C4×D4—611no—
389C4×D4—1221no—
390#117—1221no—
391C2×C42—611no—
392#106—611no—
393#106—611no—
394#106—611no—
395#106C2×#692311yescharacteristic
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—611no—
400C4⋊C8—611no—
401C4⋊C8—611no—
402C4⋊C8—1221no—
403C4⋊C8—1221no—
404C4⋊C8—1221no—
405C4⋊C8—1221no—
406#103—611no—
407#103—611no—
408#103—611no—
409#103C2×#692311yescharacteristic
410#102—611no—
411#102—611no—
412#102—611no—
413#102C2×#692311yescharacteristic
414C22⋊C8—611no—
415C22⋊C8—611no—
416C22⋊C8—1221no—
417C22⋊C8—1221no—
418C22⋊C8—1221no—
419C22⋊C8—1221no—
420C22⋊C8—1221no—
421C22⋊C8—1221no—
422#97—1221no—
423#97—1221no—
424#97—1221no—
425C4×C8—611no—
426C4×C8—611no—
427C4×C8—611no—
428C4×C8—611no—
429C4×C8—611no—
430C4×C8—611no—
431C4×C8—611no—
432C4×C8—611no—
433C4×C8—1221no—
434C4×C8—1221no—
435C4×C8—1221no—
436C4×C8—1221no—
437#41—4881no—
438#41—4881no—
439C2×Q8—611no—
440C2×Q8—1221no—
441C2×Q8—1221no—
442C2×Q8C22×#692311yescharacteristic
443C2×D4—21no—
444C2×D4—611no—
445C2×D4—1221no—
446C2×D4—1221no—
447C2×D4—1221no—
448C2×D4C22×#692311yescharacteristic
449C22×C4—611no—
450C22×C4—611no—
451C22×C4—1221no—
452C22×C4—1221no—
453C22×C4C22×#692311yescharacteristic
454SD16—41no—
455SD16—1222no—
456SD16—1222no—
457SD16—2441no—
458M16—4881no—
459M16—4881no—
460M16—2442no—
461C2×C8—41no—
462C2×C8—611no—
463C2×C8—611no—
464C2×C8—611no—
465C2×C8—611no—
466C2×C8—611no—
467C2×C8—611no—
468C2×C8—1222no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8—1221no—
474C2×C8—1221no—
475C2×C8—4881no—
476C2×C8—4881no—
477C2×C8C22×#692311yescharacteristic
478C2×C8C22×#692311yescharacteristic
479C4⋊C4—21no—
480C4⋊C4—611no—
481C4⋊C4—611no—
482C4⋊C4—1221no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4C22×#692311yescharacteristic
490C4⋊C4C22×#692311yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—1221no—
494C22⋊C4—1221no—
495C22⋊C4—1221no—
496C22⋊C4—1221no—
497C42—611no—
498C42—611no—
499C42—611no—
500C42—611no—
501C42—1221no—
502C42—1221no—
503C23—21no—
504C23—1221no—
505C23D4×#692311yescharacteristic
506Q8—21no—
507Q8—21no—
508Q8—1221no—
509Q8—1221no—
510Q8—4881no—
511Q8—2442no—
512D4—21no—
513D4—21no—
514D4—81no—
515D4—1221no—
516D4—1221no—
517D4—4881no—
518D4—4881no—
519D4—2442no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—611no—
526C2×C4—611no—
527C2×C4—611no—
528C2×C4—611no—
529C2×C4—1222no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—1221no—
533C2×C4—1221no—
534C2×C4—1221no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4D4×#692311yescharacteristic
540C2×C4C23×#692311yescharacteristic
541C8—21no—
542C8—21no—
543C8—612no—
544C8—1221no—
545C8—1221no—
546C8—1221no—
547C8—1221no—
548C8—1221no—
549C8—2441no—
550C8—2441no—
551C8—2441no—
552C8—2441no—
553C8—2441no—
554C8—2441no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—2441no—
562C22—2441no—
563C22—2441no—
564C22C2×D4×#692311yescharacteristic
565C4—21no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—611no—
570C4—611no—
571C4—612no—
572C4—1221no—
573C4—1221no—
574C4—2441no—
575C4—2441no—
576C4—2441no—
577C4D61⋊#13111yescharacteristic
578C4#1684084011yescharacteristic
579C2—41no—
580C2—81no—
581C2—4881no—
582C2#2146256311yescharacteristic
583C2#2146257911yescharacteristic
584C2D61⋊#44411yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#465C4
socleC22×C61C2×C4×D4
prime radical#16840307C22
cosocleC4×Dic61C24
hypercenter#465#6923
hypocenterC61#18089
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #21462728C2semidirect
3. #21461463C2semidirect
4. #21461460C2semidirect
5. #21461428C2semidirect
6. #21461427C2semidirect
7. #21461424C2semidirect
8. #21461423C2semidirect
9. #21461410C2semidirect
10. #21461409C2semidirect
11. #21461368C2semidirect
12. #21461141C2semidirect
14. #21461028C2semidirect
359. C61#18089semidirect

Maximal subgroups

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

subgroupindex
#214627282
#214626992
#214614632
#214614602
#214614282
#214614272
#214614242
#214614232
#214614102
#214614092
#214613682
#214611412
#214611382
#214610282
#214563732
#1808961