Finite Group Databasebeta

← #30612908

Subgroups — #30612908

Order 15616.

590 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462765C211yesmaximal, characteristic, complemented
2#21462742C211yesmaximal, characteristic, complemented
3#21461467C211yesmaximal, characteristic, complemented
4#21461465C211yesmaximal, characteristic, complemented
5#21461456C211yesmaximal, characteristic, complemented
6#21461454C211yesmaximal, characteristic, complemented
7#21461443C211yesmaximal, characteristic, complemented
8#21461441C211yesmaximal, characteristic, complemented
9#21461429C211yesmaximal, characteristic, complemented
10#21461423C211yesmaximal, characteristic, complemented
11#21461387C211yesmaximal, characteristic, complemented
12#21461155C211yesmaximal, characteristic, complemented
13#21461137C211yesmaximal, characteristic, complemented
14#21461037C211yesmaximal, characteristic, complemented
15#21455842C211yesmaximal, characteristic
16#16840812C2211yescharacteristic
17#16840812C2211yescharacteristic
18#16840812C2211yescharacteristic
19#16840811C2211yescharacteristic
20#16840797C2211yescharacteristic
21#16840797C2211yescharacteristic
22#16840796—21no—
23#16840796C2211yescharacteristic
24#16840794—21no—
25#16840794—21no—
26#16840792—21no—
27#16840790C2211yescharacteristic
28#16840787—21no—
29#16840782—21no—
30#16840780C2211yescharacteristic
31#16840769—21no—
32#16840766C2211yescharacteristic
33#16840765—21no—
34D61⋊(C4⋊C8)C2211yescharacteristic
35C4×#11758213C2211yescharacteristic
36#16840624C2211yescharacteristic
37#16840624C2211yescharacteristic
38#16840623C2211yescharacteristic
39#16840623C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42#16840612C2211yescharacteristic
43#16840612C2211yescharacteristic
44#16840610C2211yescharacteristic
45#16840610C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic
49#92420⋊C8C2211yescharacteristic
50#16840603C2211yescharacteristic
51C8×#92420C2211yescharacteristic
52#16840297C2211yescharacteristic
53C4×#11758224C2211yescharacteristic
54#16840106C411yescharacteristic
55#16840089C411yescharacteristic
56#16840066C411yescharacteristic
57#16839985C411yescharacteristic
58#16839977C411yescharacteristic
59#16839925C411yescharacteristic
60#16839908C411yescharacteristic
61#16839856C2211yescharacteristic
62#16839853C2211yescharacteristic
63#16839849C2211yescharacteristic
64#16839842C2211yescharacteristic
65#16839814C2211yescharacteristic
66C61×#478C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758213—21no—
69C2×#11758213—21no—
70C2×#11758217—21no—
71C2×#11758217—21no—
72C2×D61⋊C8—21no—
73C2×D61⋊C8—21no—
74#14519844—21no—
75#14519844—21no—
76#14519844D411yescharacteristic
77#14519844D411yescharacteristic
78C4⋊#92420—21no—
79C4⋊#92420—21no—
80C4⋊#92420—21no—
81C4⋊#92420—21no—
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84C4⋊#92420C2311yescharacteristic
85C4⋊#92420C2311yescharacteristic
86#14519834—21no—
87#14519834—21no—
88#14519834D411yescharacteristic
89#14519834D411yescharacteristic
90C22⋊#92420—21no—
91C22⋊#92420—21no—
92#14519832—21no—
93#14519832—21no—
94#14519832—21no—
95#14519832—21no—
96C4×#92420—21no—
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×#11758224C2×C411yescharacteristic
102C2×Dic244C2×C411yescharacteristic
103C2×#11758190C2×C411yescharacteristic
104C2×#11758200C2×C411yescharacteristic
105C2×#11758199C2×C411yescharacteristic
106#14519772—21no—
107#14519765C2×C411yescharacteristic
108#14519762—21no—
109#14519757C2×C411yescharacteristic
110#14519752C2×C411yescharacteristic
111C4×Dic122C2×C411yescharacteristic
112#14519742C2311yescharacteristic
113#14519742C2311yescharacteristic
114D4×Dic61C2311yescharacteristic
115#14519739—21no—
116#14519739C2311yescharacteristic
117C4×C22⋊D61—21no—
118#14519737—21no—
119#14519735—21no—
120#14519735C2×C411yescharacteristic
121#14519733—21no—
122C2×C4×Dic61—21no—
123C42×D61C2311yescharacteristic
124#14519710C2×C411yescharacteristic
125#14519708C2×C411yescharacteristic
126C4⋊#92418C2×C411yescharacteristic
127#14519702C2×C411yescharacteristic
128#14519700C2×C411yescharacteristic
129#14519700C2×C411yescharacteristic
130#14519700C2×C411yescharacteristic
131#14519699C2×C411yescharacteristic
132#14519697C2×C411yescharacteristic
133#14519689C2×C411yescharacteristic
134#14519689C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137#125×C61C2×C411yescharacteristic
138C4×D4×C61C2×C411yescharacteristic
139#107×C61C2×C411yescharacteristic
140#106×C61C2×C411yescharacteristic
141C4⋊C8×C61C2×C411yescharacteristic
142#102×C61C2×C411yescharacteristic
143#102×C61C2×C411yescharacteristic
144C2×D4×C61C22×C411yescharacteristic
145C22×C4×C61—21no—
146C2×C22⋊D61—21no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149#11758224—41no—
150#11758224—41no—
151C2×D244—21no—
152C2×D244C22×C411yescharacteristic
153C2×C4×D61—21no—
154C2×C4×D61C22×C411yescharacteristic
155C2×C4×D61C2×D411yescharacteristic
156C2×C4×D61#4111yescharacteristic
157C2×Dic122C22×C411yescharacteristic
158C2×Dic122C22×C411yescharacteristic
159#11758217—81no—
160#11758217—81no—
161C2×#92420—21no—
162C2×#92420—21no—
163C2×#92420—21no—
164C2×#92420—21no—
165C2×#92420—21no—
166C2×#92420—21no—
167C2×#92420C2×D411yescharacteristic
168C2×#92420C2×D411yescharacteristic
169C2×#92420C2×D411yescharacteristic
170C2×#92420C2×D411yescharacteristic
171#11758213—42no—
172#11758213—81no—
173#11758213—81no—
174D61⋊C8—81no—
175D61⋊C8—81no—
176C2×C8×C61C22×C411yescharacteristic
177C2×C8×C61C22×C411yescharacteristic
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61C22×C411yescharacteristic
181C4⋊C4×C61C22×C411yescharacteristic
182C4⋊C4×C61C22×C411yescharacteristic
183C22⋊C4×C61—21no—
184C42×C61C22×C411yescharacteristic
185C22⋊Dic61—21no—
186#11758200—41no—
187#11758199—41no—
188#11758198—21no—
189#11758198—21no—
190#11758198—21no—
191#11758198—21no—
192#11758198—21no—
193#11758198—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61C22×C411yescharacteristic
196#11758196—21no—
197#11758196—21no—
198#11758196—21no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C4×Dic61—21no—
203C4×Dic61C2×D411yescharacteristic
204C4×Dic61#4111yescharacteristic
205C4×Dic61C2411yescharacteristic
206C2×#92418C22×C411yescharacteristic
207C2×#92418C22×C411yescharacteristic
208Dic244—41no—
209#11758190—41no—
210C23×C61—21no—
211C22×D61—21no—
212C22×D61C4×D411yescharacteristic
213D4×C61—21no—
214D4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—81no—
219C2×C4×C61C4×D411yescharacteristic
220C2×C4×C61C4×D411yescharacteristic
221C2×C4×C61C23×C411yescharacteristic
222C22⋊D61—42no—
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—42no—
227C2×Dic61—41no—
228C2×Dic61—41no—
229C2×Dic61C4×D411yescharacteristic
230C2×Dic61C22×D411yescharacteristic
231C2×Dic61C2×#4111yescharacteristic
232D244—21no—
233D244—21no—
234D244—81no—
235C4×D61—21no—
236C4×D61—21no—
237C4×D61—21no—
238C4×D61—21no—
239C4×D61—41no—
240C4×D61—41no—
241C4×D61—41no—
242Dic122—21no—
243Dic122—21no—
244Dic122—21no—
245Dic122—21no—
246#92420—22no—
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—
256C8×C61—21no—
257C8×C61—21no—
258#92418—21no—
259#92418—21no—
260#17955—611nomaximal, Sylow
261C22×C61—41no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61C2×C4×D411yescharacteristic
265C2×D61—21no—
266C2×D61—21no—
267C2×D61—21no—
268C2×D61—41no—
269C2×D61—41no—
270C2×D61—41no—
271C4×C61—21no—
272C4×C61—21no—
273C4×C61—41no—
274C4×C61—41no—
275C4×C61—41no—
276C4×C61#56811yescharacteristic
277C4×C61#56811yescharacteristic
278Dic61—21no—
279Dic61—21no—
280Dic61—41no—
281Dic61—41no—
282Dic61—41no—
283Dic61#57711yescharacteristic
284Dic61#57711yescharacteristic
285#3102—611no—
286#2993—611no—
287#2989—611no—
288#1594—611no—
289#1593—611no—
290#1590—611no—
291#1590—611no—
292#1587—611no—
293#1586—611no—
294#1583—611no—
295#1582—611no—
296#1570—611no—
297#1489—611no—
298#1483—611no—
299#1453—611no—
300C2×C61—81no—
301C2×C61#293011yescharacteristic
302C2×C61#295211yescharacteristic
303C2×C61#295611yescharacteristic
304D61—41no—
305D61—81no—
306#529—611no—
307C4×#41—611no—
308#485—611no—
309#482—611no—
310#479—611no—
311#478#692311yescharacteristic
312#464—611no—
313#463—611no—
314#452—611no—
315#449—611no—
316#446—611no—
317#446—611no—
318#446—611no—
319C8×Q8—611no—
320C4×Q16—611no—
321C4×SD16—611no—
322C4×SD16—611no—
323C4×D8—611no—
324#436—611no—
325#436—611no—
326#436—611no—
327#436—1221no—
328#435—1221no—
329#435—1221no—
330#435—1221no—
331C8×D4—611no—
332#433—1221no—
333#432—1221no—
334#431—611no—
335#431—611no—
336#424—1221no—
337#423—611no—
338#423—1221no—
339C2×C4⋊C8—611no—
340C4×M16—611no—
341#334—611no—
342#334—611no—
343#334—611no—
344#334—611no—
345Q8⋊C8—611no—
346Q8⋊C8—611no—
347Q8⋊C8—611no—
348Q8⋊C8—611no—
349D4⋊C8—611no—
350D4⋊C8—611no—
351D4⋊C8—611no—
352D4⋊C8—611no—
353#322—611no—
354#322—611no—
355#322—611no—
356C82—611no—
357C61#1795511yescharacteristic, complemented, Sylow
358C2×#41—611no—
359C2×Q16—611no—
360C2×SD16—611no—
361C2×SD16—611no—
362C2×D8—611no—
363C2×M16—1221no—
364C2×M16—1221no—
365C2×M16—1221no—
366C2×M16—1221no—
367C2×M16—1221no—
368C22×C8—1221no—
369C22×C8—1221no—
370#126—1221no—
371#125C2×#692311yescharacteristic
372#124—611no—
373#123—1221no—
374C22⋊Q8—611no—
375#121—611no—
376C4×Q8—611no—
377C4×Q8—611no—
378C4×Q8—611no—
379C4×D4—611no—
380C4×D4—611no—
381C4×D4—1221no—
382C4×D4—1221no—
383C4×D4—1221no—
384C4×D4C2×#692311yescharacteristic
385#117—611no—
386#117—1221no—
387#117—1221no—
388C2×C42—611no—
389C2×C42—1221no—
390#107—611no—
391#107C2×#692311yescharacteristic
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—611no—
401C4⋊C8—1221no—
402C4⋊C8—1221no—
403C4⋊C8—1221no—
404C4⋊C8—1221no—
405C4⋊C8—1221no—
406C4⋊C8—1221no—
407C4⋊C8C2×#692311yescharacteristic
408#103—611no—
409#103—611no—
410#103—611no—
411#103—611no—
412#102—611no—
413#102—611no—
414#102C2×#692311yescharacteristic
415#102C2×#692311yescharacteristic
416C22⋊C8—611no—
417C22⋊C8—611no—
418C22⋊C8—611no—
419C22⋊C8—611no—
420C22⋊C8—1221no—
421C22⋊C8—1221no—
422C22⋊C8—1221no—
423C22⋊C8—1221no—
424#97—1221no—
425#97—1221no—
426#97—1221no—
427#97—1221no—
428C4×C8—611no—
429C4×C8—611no—
430C4×C8—611no—
431C4×C8—611no—
432C4×C8—611no—
433C4×C8—611no—
434C4×C8—1221no—
435#41—2441no—
436#41—2441no—
437C2×Q8—611no—
438C2×Q8—611no—
439C2×D4—611no—
440C2×D4—1221no—
441C2×D4—1221no—
442C2×D4C22×#692311yescharacteristic
443C22×C4—21no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—611no—
447C22×C4—1221no—
448C22×C4—1221no—
449C22×C4—1221no—
450Q16—2441no—
451SD16—2441no—
452SD16—2441no—
453D8—2441no—
454M16—4881no—
455M16—4881no—
456M16—4881no—
457M16—4881no—
458M16—2442no—
459C2×C8—611no—
460C2×C8—611no—
461C2×C8—611no—
462C2×C8—611no—
463C2×C8—611no—
464C2×C8—611no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8—4881no—
472C2×C8—4881no—
473C2×C8C22×#692311yescharacteristic
474C2×C8C22×#692311yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—611no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4C22×#692311yescharacteristic
483C4⋊C4C22×#692311yescharacteristic
484C4⋊C4C22×#692311yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—1221no—
487C22⋊C4—1221no—
488C22⋊C4—1221no—
489C22⋊C4—1221no—
490C22⋊C4—1221no—
491C22⋊C4—1221no—
492C22⋊C4—1221no—
493C42—611no—
494C42—611no—
495C42—611no—
496C42—1221no—
497C42—1221no—
498C42—1221no—
499C42—1221no—
500C42C22×#692311yescharacteristic
501C23—21no—
502C23—611no—
503C23—1221no—
504Q8—1221no—
505Q8—1221no—
506Q8—1221no—
507Q8—1221no—
508D4—21no—
509D4—21no—
510D4—1221no—
511D4—1221no—
512D4—4881no—
513D4—2442no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—81no—
518C2×C4—611no—
519C2×C4—611no—
520C2×C4—611no—
521C2×C4—1221no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—2441no—
529C2×C4—2441no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4—2441no—
533C2×C4—2442no—
534C2×C4D4×#692311yescharacteristic
535C2×C4D4×#692311yescharacteristic
536C2×C4C23×#692311yescharacteristic
537C8—21no—
538C8—21no—
539C8—1221no—
540C8—1221no—
541C8—1221no—
542C8—1221no—
543C8—1222no—
544C8—1221no—
545C8—1221no—
546C8—2441no—
547C8—2441no—
548C8—2441no—
549C8—2441no—
550C8—2441no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—1221no—
555C22—1221no—
556C22—1221no—
557C22—2441no—
558C22—2441no—
559C22—2441no—
560C22C2×D4×#692311yescharacteristic
561C4—21no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—611no—
567C4—611no—
568C4—1221no—
569C4—1221no—
570C4—2441no—
571C4—2441no—
572C4—2441no—
573C4#1684084111yescharacteristic
574C4#1684084211yescharacteristic
575C2—81no—
576C2—4881no—
577C2—2441no—
578C2#2146253911yescharacteristic
579C2#2146258211yescharacteristic
580C2#2146259311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#478C4
socleC22×C61C2×C4×D4
prime radical#16839908C4
cosocleC4×Dic61C24
hypercenter#478#6923
hypocenterC61#17955
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #21462765C2semidirect
2. #21462742C2semidirect
3. #21461467C2semidirect
4. #21461465C2semidirect
5. #21461456C2semidirect
6. #21461454C2semidirect
7. #21461443C2semidirect
8. #21461441C2semidirect
9. #21461429C2semidirect
10. #21461423C2semidirect
11. #21461387C2semidirect
12. #21461155C2semidirect
13. #21461137C2semidirect
14. #21461037C2semidirect
357. C61#17955semidirect

Maximal subgroups

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

subgroupindex
#214627652
#214627422
#214614672
#214614652
#214614562
#214614542
#214614432
#214614412
#214614292
#214614232
#214613872
#214611552
#214611372
#214610372
#214558422
#1795561