Finite Group Databasebeta

← #30612995

Subgroups — #30612995

Order 15616.

600 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462723C211yesmaximal, characteristic, complemented
2#21462709C211yesmaximal, characteristic
3#21461462C211yesmaximal, characteristic, complemented
4#21461461C211yesmaximal, characteristic, complemented
5#21461456C211yesmaximal, characteristic, complemented
6#21461453C211yesmaximal, characteristic, complemented
7#21461411C211yesmaximal, characteristic, complemented
8SD16⋊#92420C211yesmaximal, characteristic, complemented
9#21461403C211yesmaximal, characteristic, complemented
10#21461402C211yesmaximal, characteristic, complemented
11#21461381C211yesmaximal, characteristic, complemented
12#21461181C211yesmaximal, characteristic, complemented
13#21461178C211yesmaximal, characteristic
14#21461022C211yesmaximal, characteristic, complemented
15#21456373C211yesmaximal, characteristic
16#16840814—21no—
17#16840813C2211yescharacteristic
18#16840812—21no—
19#16840812C2211yescharacteristic
20#16840811C2211yescharacteristic
21Q8×#92420C2211yescharacteristic
22#16840797C2211yescharacteristic
23#16840796C2211yescharacteristic
24#16840794—21no—
25#16840791—21no—
26#16840790C2211yescharacteristic
27D4×#92420C2211yescharacteristic
28#16840786—21no—
29#16840786—21no—
30#16840783C2211yescharacteristic
31#16840783C2211yescharacteristic
32#16840778C2211yescharacteristic
33#16840778C2211yescharacteristic
34#16840736—21no—
35#16840735—21no—
36#16840625C2211yescharacteristic
37#16840625C2211yescharacteristic
38#16840624C2211yescharacteristic
39#16840624C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42Q8⋊#92420C2211yescharacteristic
43Q8⋊#92420C2211yescharacteristic
44#16840610C2211yescharacteristic
45#16840610C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48#16840603C2211yescharacteristic
49#16840603C2211yescharacteristic
50C8×#92420C2211yescharacteristic
51C8×#92420C2211yescharacteristic
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×D61⋊C8—21no—
70C22×#92420—21no—
71#14519844—21no—
72#14519844—21no—
73C4⋊#92420—21no—
74C4⋊#92420—21no—
75C4⋊#92420—21no—
76C4⋊#92420D411yescharacteristic
77C4⋊#92420D411yescharacteristic
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⋊#92420—21no—
89C22⋊#92420D411yescharacteristic
90C22⋊#92420D411yescharacteristic
91#14519832—21no—
92#14519832—21no—
93#14519832—21no—
94#14519832—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—81no—
162C2×#92420—21no—
163C2×#92420—21no—
164C2×#92420—21no—
165C2×#92420—21no—
166C2×#92420—21no—
167C2×#92420—21no—
168C2×#92420—81no—
169C2×#92420C2×D411yescharacteristic
170C2×#92420C2×D411yescharacteristic
171C2×#92420C2×D411yescharacteristic
172C2×#92420C2×D411yescharacteristic
173#11758213—81no—
174D61⋊C8—81no—
175SD16×C61—22no—
176C2×C8×C61—22no—
177C2×C8×C61C22×C411yescharacteristic
178C2×C8×C61C22×C411yescharacteristic
179C4⋊C4×C61—21no—
180C4⋊C4×C61C22×C411yescharacteristic
181C4⋊C4×C61C22×C411yescharacteristic
182C22⋊C4×C61—21no—
183C22⋊C4×C61—21no—
184C22⋊Dic61—21no—
185C22⋊Dic61—21no—
186#11758201—22no—
187#11758200—22no—
188#11758198—21no—
189#11758198—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61C22×C411yescharacteristic
192C4⋊Dic61C22×C411yescharacteristic
193#11758196—21no—
194#11758196—21no—
195#11758196—21no—
196#11758196—21no—
197#11758196—21no—
198#11758196—21no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C4×Dic61C22×C411yescharacteristic
202C4×Dic61C2×D411yescharacteristic
203C4×Dic61#4111yescharacteristic
204C4×Dic61C2411yescharacteristic
205C2×#92418—22no—
206C2×#92418C22×C411yescharacteristic
207C2×#92418C22×C411yescharacteristic
208#11758190—22no—
209C23×C61—21no—
210C23×C61C4×D411yescharacteristic
211C22×D61—21no—
212Q8×C61—21no—
213Q8×C61—21no—
214D4×C61—21no—
215D4×C61—21no—
216D4×C61—81no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61C4×D411yescharacteristic
223C2×C4×C61C23×C411yescharacteristic
224C22⋊D61—81no—
225C22⋊D61—81no—
226C22⋊D61—81no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—41no—
233C2×Dic61—41no—
234C2×Dic61—41no—
235C2×Dic61C4×D411yescharacteristic
236C2×Dic61C4×D411yescharacteristic
237C2×Dic61C22×D411yescharacteristic
238C2×Dic61C2×#4111yescharacteristic
239D244—21no—
240D244—21no—
241C4×D61—41no—
242C4×D61—41no—
243Dic122—21no—
244Dic122—21no—
245Dic122—81no—
246Dic122—81no—
247#92420—21no—
248#92420—21no—
249#92420—21no—
250#92420—21no—
251#92420—41no—
252#92420—41no—
253#92420—41no—
254#92420—41no—
255#92420—41no—
256#92420—41no—
257C8×C61—21no—
258C8×C61#13112yes—
259#92418—21no—
260#92418#13112yes—
261#17971—611nomaximal, Sylow
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—21no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61—41no—
268C22×C61C2×C4×D411yescharacteristic
269C2×D61—41no—
270C2×D61—41no—
271C2×D61—41no—
272C4×C61—21no—
273C4×C61—41no—
274C4×C61—41no—
275C4×C61—41no—
276C4×C61C2×#13111yescharacteristic
277C4×C61C2×#13111yescharacteristic
278Dic61—21no—
279Dic61—21no—
280Dic61—21no—
281Dic61—41no—
282Dic61—41no—
283Dic61—41no—
284Dic61#57711yescharacteristic
285Dic61#57711yescharacteristic
286#3167—611no—
287#2985—611no—
288#2981—611no—
289#1592—611no—
290#1592—611no—
291#1590—611no—
292#1590—611no—
293SD16⋊C8—611no—
294SD16⋊C8—611no—
295C8×SD16—611no—
296C8×SD16—611no—
297#1568—611no—
298#1497—611no—
299#1496—611no—
300#1450—611no—
301C2×C61—41no—
302C2×C61—81no—
303C2×C61#293111yescharacteristic
304C2×C61#294911yescharacteristic
305C2×C61#295711yescharacteristic
306D61—81no—
307#533—611no—
308#532—611no—
309#498—611no—
310#492—611no—
311#487—611no—
312#486—611no—
313#465—611no—
314#465—611no—
315#465—611no—
316#465#692311yescharacteristic
317#446—611no—
318#446—611no—
319#446—1221no—
320#446—1221no—
321C8×Q8—611no—
322C8×Q8—611no—
323C4×SD16—611no—
324C4×SD16—611no—
325C4×SD16—611no—
326C4×SD16—611no—
327#436—611no—
328#436—611no—
329#435—1221no—
330#435—1221no—
331C8×D4—611no—
332C8×D4—611no—
333#433—1221no—
334#433—1221no—
335#432—611no—
336#432—611no—
337#431—611no—
338#431—611no—
339#408—1221no—
340#408—1221no—
341C2×C4×C8—611no—
342#335—611no—
343#335—611no—
344#334—611no—
345#334—611no—
346Q8⋊C8—611no—
347Q8⋊C8—611no—
348Q8⋊C8—611no—
349Q8⋊C8—611no—
350D4⋊C8—611no—
351D4⋊C8—611no—
352D4⋊C8—611no—
353D4⋊C8—611no—
354#322—611no—
355#322—611no—
356C82—611no—
357C82—611no—
358C61#1797111yescharacteristic, complemented, Sylow
359C2×#41—1221no—
360C2×SD16—611no—
361C2×SD16—611no—
362C2×SD16—611no—
363C2×SD16C2×#692311yescharacteristic
364C2×M16—1221no—
365C2×M16—1221no—
366C22×C8—611no—
367C22×C8—1221no—
368C22×C8—1221no—
369C22×C8C2×#692311yescharacteristic
370C4⋊Q8—611no—
371C4⋊Q8—611no—
372C4⋊Q8—611no—
373#127—611no—
374#125—1221no—
375#124—1221no—
376C22⋊Q8—611no—
377C22⋊Q8—1221no—
378C22⋊Q8C2×#692311yescharacteristic
379#121—611no—
380#121—1221no—
381#121C2×#692311yescharacteristic
382C4×Q8—611no—
383C4×Q8—611no—
384C4×Q8—1221no—
385C4×D4—611no—
386C4×D4—611no—
387C4×D4—1221no—
388#117—1221no—
389C2×C42—611no—
390#106—611no—
391#106—611no—
392#106—611no—
393#106C2×#692311yescharacteristic
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—611no—
400C4⋊C8—1221no—
401C4⋊C8—1221no—
402C4⋊C8—1221no—
403C4⋊C8—1221no—
404C4⋊C8—1221no—
405#103—611no—
406#103—611no—
407#103—611no—
408#103C2×#692311yescharacteristic
409#102—611no—
410#102—611no—
411#102—611no—
412#102C2×#692311yescharacteristic
413C22⋊C8—611no—
414C22⋊C8—611no—
415C22⋊C8—1221no—
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—
425#97—1221no—
426C4×C8—611no—
427C4×C8—611no—
428C4×C8—611no—
429C4×C8—611no—
430C4×C8—611no—
431C4×C8—611no—
432C4×C8—611no—
433C4×C8—611no—
434C4×C8—1221no—
435C4×C8—1221no—
436#41—4881no—
437#41—4881no—
438C2×Q8—611no—
439C2×Q8—1221no—
440C2×Q8—1221no—
441C2×Q8C22×#692311yescharacteristic
442C2×D4—21no—
443C2×D4—611no—
444C2×D4—1221no—
445C2×D4—1221no—
446C2×D4—1221no—
447C2×D4C22×#692311yescharacteristic
448C22×C4—611no—
449C22×C4—611no—
450C22×C4—1221no—
451C22×C4—1221no—
452C22×C4C22×#692311yescharacteristic
453SD16—22no—
454SD16—1222no—
455SD16—1222no—
456SD16—1222no—
457M16—4881no—
458M16—4881no—
459C2×C8—22no—
460C2×C8—611no—
461C2×C8—611no—
462C2×C8—611no—
463C2×C8—611no—
464C2×C8—611no—
465C2×C8—611no—
466C2×C8—1222no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8—4881no—
474C2×C8—4881no—
475C2×C8C22×#692311yescharacteristic
476C2×C8C22×#692311yescharacteristic
477C4⋊C4—21no—
478C4⋊C4—611no—
479C4⋊C4—611no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4C22×#692311yescharacteristic
488C4⋊C4C22×#692311yescharacteristic
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—1221no—
492C22⋊C4—1221no—
493C22⋊C4—1221no—
494C22⋊C4—1221no—
495C42—611no—
496C42—611no—
497C42—611no—
498C42—611no—
499C42—1221no—
500C42—1221no—
501C23—21no—
502C23—1221no—
503C23D4×#692311yescharacteristic
504Q8—21no—
505Q8—21no—
506Q8—1221no—
507Q8—1221no—
508Q8—4881no—
509Q8—4881no—
510D4—21no—
511D4—21no—
512D4—81no—
513D4—1221no—
514D4—1221no—
515D4—4881no—
516D4—4881no—
517D4—4881no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—611no—
524C2×C4—611no—
525C2×C4—611no—
526C2×C4—611no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—2441no—
533C2×C4—2441no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4D4×#692311yescharacteristic
538C2×C4C23×#692311yescharacteristic
539C8—21no—
540C8—612no—
541C8—1221no—
542C8—1221no—
543C8—1221no—
544C8—1221no—
545C8—1221no—
546C8—2441no—
547C8—2441no—
548C8—2441no—
549C8—2441no—
550C8—2441no—
551C8—2441no—
552C8#1451986412yes—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—2441no—
560C22—2441no—
561C22—2441no—
562C22C2×D4×#692311yescharacteristic
563C4—21no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—611no—
568C4—611no—
569C4—1221no—
570C4—1221no—
571C4—1221no—
572C4—2441no—
573C4—2441no—
574C4—2441no—
575C4C2×#1451986411yescharacteristic
576C4D61⋊#13111yescharacteristic
577C2—41no—
578C2—81no—
579C2—4881no—
580C2#2146254211yescharacteristic
581C2#2146257911yescharacteristic
582C2#2146259611yescharacteristic
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#17971
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. #21462723C2semidirect
3. #21461462C2semidirect
4. #21461461C2semidirect
5. #21461456C2semidirect
6. #21461453C2semidirect
7. #21461411C2semidirect
8. SD16⋊#92420C2semidirect
9. #21461403C2semidirect
10. #21461402C2semidirect
11. #21461381C2semidirect
12. #21461181C2semidirect
14. #21461022C2semidirect
358. C61#17971semidirect

Maximal subgroups

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

subgroupindex
#214627232
#214627092
#214614622
#214614612
#214614562
#214614532
#214614112
SD16⋊#924202
#214614032
#214614022
#214613812
#214611812
#214611782
#214610222
#214563732
#1797161