Finite Group Databasebeta

← #30613384

Subgroups — #30613384

Order 15616.

606 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#21462720C211yesmaximal, characteristic, complemented
2#21462702C211yesmaximal, characteristic
3#21461463C211yesmaximal, characteristic, complemented
4#21461453C211yesmaximal, characteristic, complemented
5#21461447C211yesmaximal, characteristic, complemented
6#21461437C211yesmaximal, characteristic, complemented
7#21461427C211yesmaximal, characteristic, complemented
8#21461425C211yesmaximal, characteristic, complemented
9#21461411C211yesmaximal, characteristic, complemented
10#21461404C211yesmaximal, characteristic, complemented
11#21461391C211yesmaximal, characteristic, complemented
12#21461180C211yesmaximal, characteristic
13#21461122C211yesmaximal, characteristic, complemented
14#21461041C211yesmaximal, characteristic, complemented
15#21455852C211yesmaximal, characteristic
16#16840814—21no—
17#16840814—21no—
18#16840813C2211yescharacteristic
19#16840813C2211yescharacteristic
20#16840811C2211yescharacteristic
21#16840811C2211yescharacteristic
22#16840796—21no—
23#16840796C2211yescharacteristic
24#16840796C2211yescharacteristic
25#16840790—21no—
26#16840790C2211yescharacteristic
27#16840790C2211yescharacteristic
28#16840785—21no—
29#16840784C2211yescharacteristic
30#16840781C2211yescharacteristic
31#16840781C2211yescharacteristic
32#16840780—21no—
33#16840780C2211yescharacteristic
34#16840737—21no—
35#16840737—21no—
36#16840626C2211yescharacteristic
37#16840625C2211yescharacteristic
38#16840624C2211yescharacteristic
39#16840623C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42Q8⋊#92420C2211yescharacteristic
43Q8⋊#92420C2211yescharacteristic
44#16840610C2211yescharacteristic
45#16840610C2211yescharacteristic
46#16840610C2211yescharacteristic
47#16840610C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic
49#92420⋊C8C2211yescharacteristic
50#16840603C2211yescharacteristic
51C8×#92420C2211yescharacteristic
52#16840313C2211yescharacteristic
53C4×Q8×D61C2211yescharacteristic
54#16840082C411yescharacteristic
55#16840082C411yescharacteristic
56#16840044C411yescharacteristic
57#16839963C411yescharacteristic
58#16839962C411yescharacteristic
59#16839902C411yescharacteristic
60#16839902C411yescharacteristic
61#16839849C2211yescharacteristic
62#16839849C2211yescharacteristic
63#16839847C2211yescharacteristic
64#16839847C2211yescharacteristic
65#16839814C2211yescharacteristic
66C61×#475C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758213—21no—
69C2×D61⋊C8—21no—
70C2×D61⋊C8—21no—
71#14519844—21no—
72#14519844—21no—
73#14519844—21no—
74#14519844—21no—
75#14519844—21no—
76C4⋊#92420D411yescharacteristic
77C4⋊#92420D411yescharacteristic
78C4⋊#92420C2311yescharacteristic
79C4⋊#92420C2311yescharacteristic
80C4⋊#92420C2311yescharacteristic
81C4⋊#92420C2311yescharacteristic
82#14519834—21no—
83#14519834—21no—
84#14519834—21no—
85#14519834—21no—
86#14519834—21no—
87#14519834—21no—
88#14519834—21no—
89#14519834D411yescharacteristic
90#14519834D411yescharacteristic
91#14519832—21no—
92#14519832—21no—
93#14519832—21no—
94C4×#92420—21no—
95C4×#92420—21no—
96C4×#92420—21no—
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×#11758226—21no—
102C2×Q8×D61C2×C411yescharacteristic
103C2×#11758190C2×C411yescharacteristic
104C2×#11758190C2×C411yescharacteristic
105C2×#11758201C2×C411yescharacteristic
106C2×#11758201C2×C411yescharacteristic
107#14519774C2×C411yescharacteristic
108#14519766—21no—
109#14519752—21no—
110#14519752C2×C411yescharacteristic
111#14519752C2×C411yescharacteristic
112Q8×Dic61C2311yescharacteristic
113C4×Dic122—21no—
114C4×Dic122C2×C411yescharacteristic
115#14519742—21no—
116#14519742C2311yescharacteristic
117#14519739—21no—
118#14519739C2311yescharacteristic
119#14519739C2311yescharacteristic
120C4⋊C4×D61—21no—
121C4⋊C4×D61C2×C411yescharacteristic
122C42×D61—21no—
123C42×D61C2311yescharacteristic
124#14519708C2×C411yescharacteristic
125#14519708C2×C411yescharacteristic
126C4⋊#92418C2×C411yescharacteristic
127#14519700C2×C411yescharacteristic
128#14519700C2×C411yescharacteristic
129#14519699C2×C411yescharacteristic
130#14519699C2×C411yescharacteristic
131#14519697C2×C411yescharacteristic
132#14519697C2×C411yescharacteristic
133#14519689C2×C411yescharacteristic
134#14519689C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137C4⋊Q8×C61C2×C411yescharacteristic
138C4×Q8×C61C2×C411yescharacteristic
139#106×C61C2×C411yescharacteristic
140#106×C61C2×C411yescharacteristic
141C4⋊C8×C61C2×C411yescharacteristic
142#103×C61C2×C411yescharacteristic
143#103×C61C2×C411yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61C22×C411yescharacteristic
146#11758226—81no—
147#11758226—81no—
148Q8×D61—22no—
149Q8×D61—41no—
150C2×D244—21no—
151C2×D244—21no—
152C2×D244—21no—
153C2×D244—21no—
154C2×D244C22×C411yescharacteristic
155C2×D244C22×C411yescharacteristic
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61C22×C411yescharacteristic
161C2×C4×D61C2×D411yescharacteristic
162C2×C4×D61#4111yescharacteristic
163C2×Dic122—21no—
164C2×Dic122C22×C411yescharacteristic
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—
177D61⋊C8—81no—
178D61⋊C8—81no—
179C2×C8×C61C22×C411yescharacteristic
180C2×C8×C61C22×C411yescharacteristic
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61C22×C411yescharacteristic
184C4⋊C4×C61C22×C411yescharacteristic
185C4⋊C4×C61C22×C411yescharacteristic
186C42×C61—21no—
187C42×C61C22×C411yescharacteristic
188#11758201—41no—
189#11758201—41no—
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×Dic61C2×D411yescharacteristic
203C4×Dic61#4111yescharacteristic
204C4×Dic61C2411yescharacteristic
205C2×#92418C22×C411yescharacteristic
206C2×#92418C22×C411yescharacteristic
207#11758190—22no—
208#11758190—22no—
209C22×D61—21no—
210C22×D61—21no—
211C22×D61C4×D411yescharacteristic
212Q8×C61—21no—
213Q8×C61—21no—
214Q8×C61—81no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61C4×D411yescharacteristic
220C2×C4×C61C4×D411yescharacteristic
221C2×C4×C61C23×C411yescharacteristic
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61C4×D411yescharacteristic
225C2×Dic61C22×D411yescharacteristic
226C2×Dic61C2×#4111yescharacteristic
227D244—21no—
228D244—21no—
229D244—21no—
230D244—21no—
231D244—42no—
232D244—81no—
233D244—81no—
234D244—81no—
235C4×D61—21no—
236C4×D61—21no—
237C4×D61—21no—
238C4×D61—21no—
239C4×D61—41no—
240C4×D61—42no—
241C4×D61—42no—
242C4×D61—41no—
243C4×D61—41no—
244C4×D61—41no—
245C4×D61—41no—
246Dic122—21no—
247Dic122—42no—
248Dic122#13112yes—
249#92420—21no—
250#92420—21no—
251#92420—21no—
252#92420—21no—
253#92420—41no—
254#92420—41no—
255#92420—41no—
256#92420—41no—
257#92420—41no—
258#92420—41no—
259C8×C61—21no—
260C8×C61—21no—
261#92418—21no—
262#92418—21no—
263#18030—611nomaximal, Sylow
264C22×C61C2×C4×D411yescharacteristic
265C2×D61—21no—
266C2×D61—21no—
267C2×D61—21no—
268C2×D61—41no—
269C2×D61—41no—
270C2×D61—41no—
271C2×D61—41no—
272C2×D61—41no—
273C2×D61—41no—
274C4×C61—21no—
275C4×C61—21no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61—41no—
279C4×C61—41no—
280C4×C61C2×#13111yescharacteristic
281C4×C61#56811yescharacteristic
282Dic61—22no—
283Dic61—21no—
284Dic61—21no—
285Dic61—41no—
286Dic61#57711yescharacteristic
287Dic61#57711yescharacteristic
288#3103—611no—
289#2984—611no—
290#2979—611no—
291#1592—611no—
292#1590—611no—
293#1588—611no—
294#1585—611no—
295#1583—611no—
296#1582—611no—
297SD16⋊C8—611no—
298C8×SD16—611no—
299#1572—611no—
300#1496—611no—
301#1479—611no—
302#1454—611no—
303C2×C61#293311yescharacteristic
304C2×C61#294911yescharacteristic
305C2×C61#295511yescharacteristic
306D61—41no—
307D61—81no—
308D61—81no—
309#532—611no—
310C2×C4×Q8—611no—
311#481—611no—
312#481—611no—
313#475—611no—
314#475#692311yescharacteristic
315#460—611no—
316#460—611no—
317#448—611no—
318#448—611no—
319#446—611no—
320#446—611no—
321#446—1221no—
322#446—1221no—
323C8×Q8—611no—
324C8×Q8—611no—
325C4×SD16—611no—
326C4×SD16—611no—
327C4×SD16—611no—
328C4×SD16—611no—
329#436—611no—
330#436—611no—
331#436—1221no—
332C8×D4—611no—
333C8×D4—611no—
334C8×D4—1221no—
335#432—611no—
336#432—1221no—
337#431—611no—
338#431—611no—
339#431—611no—
340#431—611no—
341#431—1221no—
342#408—1221no—
343#408—1221no—
344#335—611no—
345#335—611no—
346#334—611no—
347#334—611no—
348Q8⋊C8—611no—
349Q8⋊C8—611no—
350Q8⋊C8—611no—
351Q8⋊C8—611no—
352D4⋊C8—611no—
353D4⋊C8—611no—
354D4⋊C8—611no—
355D4⋊C8—611no—
356#322—611no—
357#322—611no—
358#322—611no—
359C82—611no—
360C61#1803011yescharacteristic, complemented, Sylow
361C2×#41—1221no—
362C22×Q8—611no—
363C2×SD16—611no—
364C2×SD16—611no—
365C2×SD16—611no—
366C2×SD16—611no—
367C2×M16—1221no—
368C2×M16—1221no—
369C22×C8—1221no—
370C22×C8—1221no—
371C4⋊Q8C2×#692311yescharacteristic
372#127—611no—
373#124—1221no—
374#121—611no—
375#121—611no—
376#121—1221no—
377C4×Q8—611no—
378C4×Q8—611no—
379C4×Q8—611no—
380C4×Q8—1221no—
381C4×Q8—1221no—
382C4×Q8C2×#692311yescharacteristic
383C4×D4—611no—
384C4×D4—611no—
385C4×D4—1221no—
386C2×C4⋊C4—611no—
387C2×C4⋊C4—1221no—
388C2×C42—611no—
389C2×C42—1221no—
390#106—611no—
391#106—611no—
392#106C2×#692311yescharacteristic
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⋊C8C2×#692311yescharacteristic
407#103—611no—
408#103—611no—
409#103C2×#692311yescharacteristic
410#103C2×#692311yescharacteristic
411#102—611no—
412#102—611no—
413#102—611no—
414#102—611no—
415C22⋊C8—611no—
416C22⋊C8—611no—
417C22⋊C8—611no—
418C22⋊C8—611no—
419C22⋊C8—1221no—
420C22⋊C8—1221no—
421C22⋊C8—1221no—
422C22⋊C8—1221no—
423C22⋊C8—1221no—
424C22⋊C8—1221no—
425C22⋊C8—1221no—
426#97—1221no—
427#97—1221no—
428#97—1221no—
429C4×C8—611no—
430C4×C8—611no—
431C4×C8—611no—
432C4×C8—611no—
433C4×C8—611no—
434C4×C8—611no—
435C4×C8—1221no—
436C4×C8—1221no—
437C4×C8—1221no—
438#41—4881no—
439#41—4881no—
440C2×Q8—21no—
441C2×Q8—611no—
442C2×Q8—1221no—
443C2×Q8—1222no—
444C2×Q8—2441no—
445C2×Q8C22×#692311yescharacteristic
446C2×D4—611no—
447C2×D4—611no—
448C2×D4—1221no—
449C2×D4—1221no—
450C2×D4—1221no—
451C2×D4—1221no—
452C22×C4—611no—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—1221no—
456C22×C4—1221no—
457C22×C4—1221no—
458C22×C4—1221no—
459SD16—1222no—
460SD16—1222no—
461SD16—2441no—
462SD16—2441no—
463M16—4881no—
464M16—4881no—
465C2×C8—611no—
466C2×C8—611no—
467C2×C8—611no—
468C2×C8—611no—
469C2×C8—611no—
470C2×C8—611no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8—1221no—
474C2×C8—1221no—
475C2×C8—1221no—
476C2×C8—1221no—
477C2×C8—4881no—
478C2×C8—4881no—
479C2×C8C22×#692311yescharacteristic
480C2×C8C22×#692311yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—611no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4C22×#692311yescharacteristic
489C4⋊C4C22×#692311yescharacteristic
490C4⋊C4C22×#692311yescharacteristic
491C22⋊C4—1221no—
492C22⋊C4—1221no—
493C22⋊C4—1221no—
494C22⋊C4—1221no—
495C42—21no—
496C42—611no—
497C42—611no—
498C42—611no—
499C42—1221no—
500C42—1221no—
501C42—1221no—
502C42C22×#692311yescharacteristic
503C23—611no—
504C23—1221no—
505C23—1221no—
506Q8—21no—
507Q8—21no—
508Q8—81no—
509Q8—612no—
510Q8—1221no—
511Q8—2442no—
512D4—1221no—
513D4—1221no—
514D4—1221no—
515D4—1221no—
516D4—4881no—
517D4—4881no—
518D4—4881no—
519D4—2442no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
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—1221no—
533C2×C4—2441no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4—2442no—
539C2×C4—2442no—
540C2×C4D4×#692311yescharacteristic
541C2×C4D4×#692311yescharacteristic
542C2×C4C23×#692311yescharacteristic
543C8—21no—
544C8—21no—
545C8—1221no—
546C8—1221no—
547C8—1221no—
548C8—1221no—
549C8—1221no—
550C8—1221no—
551C8—2441no—
552C8—2441no—
553C8—2441no—
554C8—2441no—
555C8—2441no—
556C8—2441no—
557C22—1221no—
558C22—1221no—
559C22—1221no—
560C22—2441no—
561C22—2441no—
562C22—2441no—
563C22—2441no—
564C22—2441no—
565C22—2441no—
566C22C2×D4×#692311yescharacteristic
567C4—21no—
568C4—21no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—611no—
574C4—611no—
575C4—1221no—
576C4—1222no—
577C4—1221no—
578C4—2441no—
579C4D61⋊#13111yescharacteristic
580C4#1684084211yescharacteristic
581C2—4881no—
582C2—4881no—
583C2—2441no—
584C2#2146255411yescharacteristic
585C2#2146257911yescharacteristic
586C2#2146259211yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#475C4
socleC22×C61C2×C4×D4
prime radical#16840313C22
cosocleC4×Dic61C24
hypercenter#475#6923
hypocenterC61#18030
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #21462720C2semidirect
3. #21461463C2semidirect
4. #21461453C2semidirect
5. #21461447C2semidirect
6. #21461437C2semidirect
7. #21461427C2semidirect
8. #21461425C2semidirect
9. #21461411C2semidirect
10. #21461404C2semidirect
11. #21461391C2semidirect
13. #21461122C2semidirect
14. #21461041C2semidirect
360. C61#18030semidirect

Maximal subgroups

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

subgroupindex
#214627202
#214627022
#214614632
#214614532
#214614472
#214614372
#214614272
#214614252
#214614112
#214614042
#214613912
#214611802
#214611222
#214610412
#214558522
#1803061