Finite Group Databasebeta

← #30612851

Subgroups — #30612851

Order 15616.

616 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462764C211yesmaximal, characteristic, complemented
2#21462684C211yesmaximal, characteristic, complemented
3#21461468C211yesmaximal, characteristic, complemented
4#21461463C211yesmaximal, characteristic, complemented
5#21461453C211yesmaximal, characteristic, complemented
6#21461451C211yesmaximal, characteristic, complemented
7#21461446C211yesmaximal, characteristic, complemented
8#21461439C211yesmaximal, characteristic, complemented
9#21461426C211yesmaximal, characteristic, complemented
10#21461419C211yesmaximal, characteristic, complemented
11#21461395C211yesmaximal, characteristic, complemented
12#21461146C211yesmaximal, characteristic, complemented
13#21461132C211yesmaximal, characteristic, complemented
14#21461040C211yesmaximal, characteristic, complemented
15#21455869C211yesmaximal, characteristic
16#16840813C2211yescharacteristic, complemented
17Q8×#92420C2211yescharacteristic, complemented
18#16840796—21no—
19#16840796—21no—
20#16840796C2211yescharacteristic
21#16840796C2211yescharacteristic
22#16840796C2211yescharacteristic
23#16840796C2211yescharacteristic
24#16840796C2211yescharacteristic, complemented
25#16840795—21no—
26#16840794—21no—
27#16840790C2211yescharacteristic, complemented
28#16840787—21no—
29#16840779C2211yescharacteristic
30#16840778C2211yescharacteristic
31#16840778C2211yescharacteristic
32#16840769—21no—
33#16840765C2211yescharacteristic
34#16840733—21no—
35#16840733—21no—
36#16840626C2211yescharacteristic, complemented
37#16840625C2211yescharacteristic, complemented
38#16840624C2211yescharacteristic, complemented
39#16840623C2211yescharacteristic, complemented
40Q8⋊#92420C2211yescharacteristic, complemented
41Q8⋊#92420C2211yescharacteristic, complemented
42#16840610C2211yescharacteristic
43#16840610C2211yescharacteristic
44#16840610C2211yescharacteristic
45#16840610C2211yescharacteristic
46#16840610C2211yescharacteristic, complemented
47#16840610C2211yescharacteristic, complemented
48#92420⋊C8C2211yescharacteristic, complemented
49#92420⋊C8C2211yescharacteristic, complemented
50#16840603C2211yescharacteristic, complemented
51C8×#92420C2211yescharacteristic, complemented
52#16840298C2211yescharacteristic
53C2×#14519739C2211yescharacteristic
54#16840080C411yescharacteristic
55#16840065C411yescharacteristic
56#16840065C411yescharacteristic
57#16839980C411yescharacteristic
58#16839980C411yescharacteristic
59#16839912C411yescharacteristic
60#16839898C411yescharacteristic
61#16839847C2211yescharacteristic
62#16839847C2211yescharacteristic
63#16839844C2211yescharacteristic
64#16839844C2211yescharacteristic
65#16839812C2211yescharacteristic
66C61×#484C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758213—21no—
69C2×#11758213—21no—
70C2×#11758213—21no—
71C2×#11758213—21no—
72C2×#11758217—21no—
73C2×D61⋊C8—21no—
74#14519844—21no—
75#14519844—21no—
76#14519844—21no—
77C4⋊#92420—21no—
78C4⋊#92420D411yescharacteristic
79C4⋊#92420D411yescharacteristic
80C4⋊#92420C2311yescharacteristic
81C4⋊#92420C2311yescharacteristic
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84#14519834—21no—
85#14519834—21no—
86#14519834—21no—
87#14519834—21no—
88#14519834—21no—
89#14519834—21no—
90C22⋊#92420—21no—
91C22⋊#92420—21no—
92C22⋊#92420D411yescharacteristic
93C22⋊#92420D411yescharacteristic
94#14519832—21no—
95C4×#92420—21no—
96C4×#92420—21no—
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C22×D244C2×C411yescharacteristic
102C22×C4×D61—21no—
103C2×#11758201C2×C411yescharacteristic
104C2×#11758201C2×C411yescharacteristic
105C2×D488C2×C411yescharacteristic
106C2×D488C2×C411yescharacteristic
107#14519772—21no—
108#14519768C2×C411yescharacteristic
109#14519766C2×C411yescharacteristic
110#14519761—21no—
111#14519751C2×C411yescharacteristic
112Q8×Dic61C2311yescharacteristic
113#14519739—21no—
114#14519739—21no—
115#14519739C2×C411yescharacteristic
116#14519739C2×C411yescharacteristic
117#14519739C2311yescharacteristic
118#14519739C2311yescharacteristic
119#14519739C2311yescharacteristic
120#14519737—21no—
121#14519735—21no—
122C2×#11758198—21no—
123C2×C4×Dic61C2311yescharacteristic
124#14519708C2×C411yescharacteristic
125#14519708C2×C411yescharacteristic
126#14519706C2×C411yescharacteristic
127#14519706C2×C411yescharacteristic
128#14519699C2×C411yescharacteristic
129#14519699C2×C411yescharacteristic
130#14519697C2×C411yescharacteristic
131#14519697C2×C411yescharacteristic
132#14519697C2×C411yescharacteristic
133#14519697C2×C411yescharacteristic
134C22⋊#92418C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137C22⋊Q8×C61C2×C411yescharacteristic
138C2×C4⋊C4×C61C2×C411yescharacteristic
139#107×C61C2×C411yescharacteristic
140#107×C61C2×C411yescharacteristic
141#103×C61C2×C411yescharacteristic
142#103×C61C2×C411yescharacteristic
143C22⋊C8×C61C2×C411yescharacteristic
144C23×D61—21no—
145C2×Q8×C61C22×C411yescharacteristic
146C22×C4×C61—21no—
147C22×C4×C61C22×C411yescharacteristic
148C2×C22⋊D61—21no—
149C22×Dic61C2×D411yescharacteristic
150C22×Dic61#4111yescharacteristic
151C2×D244—21no—
152C2×D244—41no—
153C2×D244—41no—
154C2×D244C22×C411yescharacteristic
155C2×D244C22×C411yescharacteristic
156C2×D244C22×C411yescharacteristic
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—81no—
163C2×C4×D61—81no—
164#11758217—81no—
165C2×#92420—21no—
166C2×#92420—21no—
167C2×#92420—21no—
168C2×#92420—21no—
169C2×#92420—21no—
170C2×#92420—21no—
171C2×#92420C2×D411yescharacteristic
172C2×#92420C2×D411yescharacteristic
173C2×#92420C2×D411yescharacteristic
174C2×#92420C2×D411yescharacteristic
175#11758213—81no—
176#11758213—81no—
177#11758213—81no—
178#11758213—81no—
179#11758213—81no—
180D61⋊C8—81no—
181C2×C8×C61C22×C411yescharacteristic
182C2×C8×C61C22×C411yescharacteristic
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61C22×C411yescharacteristic
186C4⋊C4×C61C22×C411yescharacteristic
187C4⋊C4×C61C22×C411yescharacteristic
188C22⋊C4×C61—21no—
189#11758201—41no—
190#11758201—41no—
191#11758198—21no—
192#11758198—21no—
193#11758198—21no—
194#11758198—21no—
195#11758198—21no—
196#11758198—21no—
197#11758198—21no—
198#11758198—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61C22×C411yescharacteristic
202#11758196—21no—
203C4×Dic61—21no—
204C4×Dic61C22×C411yescharacteristic
205C4×Dic61C2×D411yescharacteristic
206C4×Dic61#4111yescharacteristic
207C4×Dic61C2411yescharacteristic
208C2×#92418C22×C411yescharacteristic
209C2×#92418C22×C411yescharacteristic
210D488—41no—
211D488—41no—
212C23×C61C4×D411yescharacteristic
213C22×D61—21no—
214C22×D61—21no—
215C22×D61—21no—
216C22×D61—42no—
217C22×D61—81no—
218C22×D61—81no—
219Q8×C61—21no—
220Q8×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—81no—
228C2×C4×C61C4×D411yescharacteristic
229C2×C4×C61C23×C411yescharacteristic
230C22⋊D61—81no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—41no—
235C2×Dic61C4×D411yescharacteristic
236C2×Dic61C4×D411yescharacteristic
237C2×Dic61C22×D411yescharacteristic
238C2×Dic61C2×#4111yescharacteristic
239D244—21no—
240D244—21no—
241D244—21no—
242D244—21no—
243D244—21no—
244D244—21no—
245D244—42no—
246C4×D61—41no—
247C4×D61—41no—
248C4×D61—41no—
249C4×D61—41no—
250C4×D61—41no—
251C4×D61—41no—
252C4×D61—81no—
253C4×D61—81no—
254#92420—21no—
255#92420—21no—
256#92420—21no—
257#92420—21no—
258#92420—41no—
259#92420—41no—
260#92420—41no—
261#92420—41no—
262#92420—41no—
263#92420—41no—
264C8×C61—21no—
265C8×C61—21no—
266#92418—21no—
267#92418—21no—
268#17946—611nomaximal, Sylow
269C22×C61—21no—
270C22×C61—21no—
271C22×C61—21no—
272C22×C61C2×C4×D411yescharacteristic
273C2×D61—41no—
274C2×D61—41no—
275C2×D61—41no—
276C2×D61—41no—
277C2×D61—41no—
278C2×D61—41no—
279C2×D61—41no—
280C2×D61—41no—
281C2×D61—41no—
282C2×D61—84no—
283C4×C61—21no—
284C4×C61—41no—
285C4×C61—41no—
286C4×C61—41no—
287C4×C61—41no—
288C4×C61#56811yescharacteristic
289C4×C61#56811yescharacteristic
290Dic61—21no—
291Dic61—21no—
292Dic61—21no—
293Dic61—41no—
294Dic61#57611yescharacteristic
295Dic61#57711yescharacteristic
296#3105—611no—
297#2993—611no—
298#2975—611no—
299#1594—611no—
300#1592—611no—
301#1590—611no—
302#1589—611no—
303#1588—611no—
304#1586—611no—
305#1583—611no—
306#1581—611no—
307#1574—611no—
308#1486—611no—
309#1482—611no—
310#1454—611no—
311C2×C61—41no—
312C2×C61#293011yescharacteristic
313C2×C61#294611yescharacteristic
314C2×C61#295711yescharacteristic
315D61—81no—
316D61—81no—
317D61—81no—
318#529—611no—
319C2×C4×D4—611no—
320#484#692311yescharacteristic
321#481—611no—
322#478—611no—
323#478—611no—
324#463—611no—
325#463—611no—
326#450—611no—
327#447—611no—
328#446—611no—
329C8×Q8—611no—
330C4×SD16—611no—
331C4×SD16—611no—
332C4×D8—611no—
333C4×D8—611no—
334#436—611no—
335#436—611no—
336#436—611no—
337#436—611no—
338#436—611no—
339#436—1221no—
340#436—1221no—
341#436—1221no—
342#435—1221no—
343C8×D4—611no—
344#433—1221no—
345#431—611no—
346#431—611no—
347#431—611no—
348#431—611no—
349#424—1221no—
350#423—611no—
351#407—1221no—
352#407—1221no—
353#335—611no—
354#335—611no—
355#334—611no—
356#334—611no—
357Q8⋊C8—611no—
358Q8⋊C8—611no—
359D4⋊C8—611no—
360D4⋊C8—611no—
361D4⋊C8—611no—
362D4⋊C8—611no—
363D4⋊C8—611no—
364D4⋊C8—611no—
365#322—611no—
366#322—611no—
367#322—611no—
368C82—611no—
369C61#1794611yescharacteristic, complemented, Sylow
370C22×D4—611no—
371C23×C4—1221no—
372C2×SD16—611no—
373C2×SD16—611no—
374C2×D8—611no—
375C2×D8—611no—
376C2×M16—1221no—
377C2×M16—1221no—
378C2×M16—1221no—
379C2×M16—1221no—
380C2×M16—1221no—
381C2×M16—1221no—
382C22×C8—1221no—
383#126—1221no—
384#125—611no—
385#124—611no—
386#123—1221no—
387C22⋊Q8C2×#692311yescharacteristic
388#121—611no—
389C4×Q8—611no—
390C4×D4—611no—
391C4×D4—611no—
392C4×D4—611no—
393C4×D4—611no—
394C4×D4—611no—
395C4×D4—1221no—
396C4×D4—1221no—
397C4×D4—1221no—
398#117—1221no—
399C2×C4⋊C4C2×#692311yescharacteristic
400C2×C22⋊C4—1221no—
401C2×C42—611no—
402#107C2×#692311yescharacteristic
403#107C2×#692311yescharacteristic
404#106—611no—
405#106—611no—
406C4⋊C8—611no—
407C4⋊C8—611no—
408C4⋊C8—611no—
409C4⋊C8—611no—
410C4⋊C8—611no—
411C4⋊C8—611no—
412C4⋊C8—611no—
413C4⋊C8—611no—
414C4⋊C8—1221no—
415C4⋊C8—1221no—
416C4⋊C8—1221no—
417C4⋊C8—1221no—
418#103C2×#692311yescharacteristic
419#103C2×#692311yescharacteristic
420#102—611no—
421#102—611no—
422#102—611no—
423#102—611no—
424#102—611no—
425#102—611no—
426C22⋊C8—611no—
427C22⋊C8—611no—
428C22⋊C8—611no—
429C22⋊C8—1221no—
430C22⋊C8—1221no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435C22⋊C8—1221no—
436C22⋊C8—1221no—
437C22⋊C8C2×#692311yescharacteristic
438#97—1221no—
439C4×C8—611no—
440C4×C8—611no—
441C4×C8—611no—
442C4×C8—611no—
443C4×C8—611no—
444C4×C8—611no—
445C4×C8—1221no—
446C4×C8—1221no—
447C24—1221no—
448C2×Q8C22×#692311yescharacteristic
449C2×D4—611no—
450C2×D4—611no—
451C2×D4—611no—
452C2×D4—1221no—
453C2×D4—1221no—
454C2×D4—2441no—
455C2×D4—2441no—
456C22×C4—21no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—1221no—
464C22×C4—4881no—
465C22×C4—4881no—
466C22×C4C22×#692311yescharacteristic
467SD16—2441no—
468SD16—2441no—
469D8—2441no—
470D8—2441no—
471M16—4881no—
472M16—4881no—
473M16—4881no—
474M16—4881no—
475M16—4881no—
476M16—4881no—
477C2×C8—611no—
478C2×C8—611no—
479C2×C8—611no—
480C2×C8—611no—
481C2×C8—611no—
482C2×C8—611no—
483C2×C8—1221no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—1221no—
489C2×C8—4881no—
490C2×C8C22×#692311yescharacteristic
491C2×C8C22×#692311yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—611no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4C22×#692311yescharacteristic
499C4⋊C4C22×#692311yescharacteristic
500C4⋊C4C22×#692311yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—1221no—
503C22⋊C4—1221no—
504C22⋊C4—1221no—
505C22⋊C4—1221no—
506C22⋊C4—1221no—
507C22⋊C4—1221no—
508C22⋊C4—1221no—
509C22⋊C4—1221no—
510C42—611no—
511C42—611no—
512C42—611no—
513C42—611no—
514C42—1221no—
515C23—1221no—
516C23—1221no—
517C23—1221no—
518C23—4881no—
519C23—4881no—
520C23—2442no—
521C23D4×#692311yescharacteristic
522Q8—21no—
523Q8—21no—
524D4—1221no—
525D4—1221no—
526D4—1221no—
527D4—1221no—
528D4—1221no—
529D4—1221no—
530D4—4881no—
531D4—2442no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—81no—
539C2×C4—611no—
540C2×C4—611no—
541C2×C4—611no—
542C2×C4—611no—
543C2×C4—1221no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—4881no—
547C2×C4—4881no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4—2441no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4D4×#692311yescharacteristic
556C2×C4C23×#692311yescharacteristic
557C8—21no—
558C8—21no—
559C8—1221no—
560C8—1221no—
561C8—1221no—
562C8—1221no—
563C8—1221no—
564C8—1221no—
565C8—2441no—
566C8—2441no—
567C8—2441no—
568C8—2441no—
569C8—2441no—
570C8—2441no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—4884no—
575C22—2441no—
576C22—2441no—
577C22—2441no—
578C22—2441no—
579C22—2441no—
580C22—2441no—
581C22—2441no—
582C22—2441no—
583C22—2441no—
584C22C2×D4×#692311yescharacteristic
585C4—21no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4—611no—
591C4—611no—
592C4—1221no—
593C4—1221no—
594C4—1221no—
595C4—2441no—
596C4#1684084111yescharacteristic
597C4#1684084111yescharacteristic
598C2—41no—
599C2—4881no—
600C2—4881no—
601C2—4881no—
602C2#2146254011yescharacteristic
603C2#2146257611yescharacteristic
604C2#2146259911yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#484C4
socleC22×C61C2×C4×D4
prime radical#16839898C4
cosocleC4×Dic61C24
hypercenter#484#6923
hypocenterC61#17946
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #21462764C2semidirect
2. #21462684C2semidirect
3. #21461468C2semidirect
4. #21461463C2semidirect
5. #21461453C2semidirect
6. #21461451C2semidirect
7. #21461446C2semidirect
8. #21461439C2semidirect
9. #21461426C2semidirect
10. #21461419C2semidirect
11. #21461395C2semidirect
12. #21461146C2semidirect
13. #21461132C2semidirect
14. #21461040C2semidirect
16. #16840813C22semidirect
17. Q8×#92420C22semidirect
24. #16840796C22semidirect
27. #16840790C22semidirect
36. #16840626C22semidirect
37. #16840625C22semidirect
38. #16840624C22semidirect
39. #16840623C22semidirect
40. Q8⋊#92420C22semidirect
41. Q8⋊#92420C22semidirect
46. #16840610C22semidirect
47. #16840610C22semidirect
48. #92420⋊C8C22semidirect
49. #92420⋊C8C22semidirect
50. #16840603C22semidirect
51. C8×#92420C22semidirect
369. C61#17946semidirect

Maximal subgroups

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

subgroupindex
#214627642
#214626842
#214614682
#214614632
#214614532
#214614512
#214614462
#214614392
#214614262
#214614192
#214613952
#214611462
#214611322
#214610402
#214558692
#1794661