Finite Group Databasebeta

← #30613383

Subgroups — #30613383

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#21462719C211yesmaximal, characteristic, complemented
2#21462699C211yesmaximal, characteristic
3#21461461C211yesmaximal, characteristic, complemented
4#21461456C211yesmaximal, characteristic, complemented
5#21461449C211yesmaximal, characteristic, complemented
6#21461435C211yesmaximal, characteristic, complemented
7#21461427C211yesmaximal, characteristic, complemented
8#21461422C211yesmaximal, characteristic, complemented
9#21461410C211yesmaximal, characteristic, complemented
10#21461404C211yesmaximal, characteristic, complemented
11#21461390C211yesmaximal, characteristic, complemented
12#21461178C211yesmaximal, characteristic
13#21461123C211yesmaximal, characteristic, complemented
14#21461040C211yesmaximal, characteristic, complemented
15#21455847C211yesmaximal, characteristic
16#16840814—21no—
17#16840814—21no—
18#16840812C2211yescharacteristic
19#16840812C2211yescharacteristic
20#16840811C2211yescharacteristic
21#16840811C2211yescharacteristic
22#16840797C2211yescharacteristic
23#16840796C2211yescharacteristic
24#16840795—21no—
25#16840790C2211yescharacteristic
26#16840789—21no—
27D4×#92420C2211yescharacteristic
28#16840783C2211yescharacteristic
29#16840782—21no—
30#16840779C2211yescharacteristic
31#16840778—21no—
32#16840778C2211yescharacteristic
33#16840778C2211yescharacteristic
34#16840736—21no—
35#16840735—21no—
36#16840626C2211yescharacteristic
37#16840625C2211yescharacteristic
38#16840624C2211yescharacteristic
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#16840307C2211yescharacteristic
53C2×#14519742C2211yescharacteristic
54#16840080C411yescharacteristic
55#16840046C411yescharacteristic
56#16840046C411yescharacteristic
57#16839961C411yescharacteristic
58#16839961C411yescharacteristic
59#16839903C411yescharacteristic
60#16839900C411yescharacteristic
61#16839853C2211yescharacteristic
62#16839853C2211yescharacteristic
63#16839849C2211yescharacteristic
64#16839849C2211yescharacteristic
65#16839812C2211yescharacteristic
66C61×#481C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758217—21no—
69C2×D61⋊C8—21no—
70C22×#92420—21no—
71#14519844—21no—
72#14519844—21no—
73#14519844D411yescharacteristic
74#14519844D411yescharacteristic
75C4⋊#92420—21no—
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⋊#92420—21no—
89C22⋊#92420D411yescharacteristic
90C22⋊#92420D411yescharacteristic
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×#11758224—21no—
102C22×Dic122C2×C411yescharacteristic
103C2×#11758190C2×C411yescharacteristic
104C2×#11758190C2×C411yescharacteristic
105C2×#11758200C2×C411yescharacteristic
106C2×#11758200C2×C411yescharacteristic
107#14519776C2×C411yescharacteristic
108#14519773C2×C411yescharacteristic
109#14519763—21no—
110#14519751C2×C411yescharacteristic
111#14519749—21no—
112#14519742—21no—
113#14519742—21no—
114#14519742C2×C411yescharacteristic
115#14519742C2×C411yescharacteristic
116#14519742C2311yescharacteristic
117#14519742C2311yescharacteristic
118D4×Dic61C2311yescharacteristic
119#14519739C2311yescharacteristic
120#14519737—21no—
121C2×#11758196—21no—
122C2×C4×Dic61—21no—
123C2×C4×Dic61C2311yescharacteristic
124#14519708C2×C411yescharacteristic
125#14519708C2×C411yescharacteristic
126#14519706C2×C411yescharacteristic
127#14519706C2×C411yescharacteristic
128#14519702C2×C411yescharacteristic
129#14519702C2×C411yescharacteristic
130#14519700C2×C411yescharacteristic
131#14519700C2×C411yescharacteristic
132#14519697C2×C411yescharacteristic
133#14519697C2×C411yescharacteristic
134C22⋊#92418C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137#121×C61C2×C411yescharacteristic
138C2×C4⋊C4×C61C2×C411yescharacteristic
139#106×C61C2×C411yescharacteristic
140#106×C61C2×C411yescharacteristic
141#102×C61C2×C411yescharacteristic
142#102×C61C2×C411yescharacteristic
143C22⋊C8×C61C2×C411yescharacteristic
144C2×D4×C61—21no—
145C2×D4×C61C22×C411yescharacteristic
146C22×C4×C61—21no—
147C22×C4×C61C22×C411yescharacteristic
148C2×C22⋊D61—21no—
149C2×C22⋊D61—21no—
150C2×C22⋊D61—21no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61C2×D411yescharacteristic
154C22×Dic61#4111yescharacteristic
155#11758224—81no—
156#11758224—81no—
157C2×D244C22×C411yescharacteristic
158C2×C4×D61—21no—
159C2×Dic122—22no—
160C2×Dic122—21no—
161C2×Dic122—21no—
162C2×Dic122—41no—
163C2×Dic122C22×C411yescharacteristic
164C2×Dic122C22×C411yescharacteristic
165#11758217—81no—
166C2×#92420—21no—
167C2×#92420—21no—
168C2×#92420—21no—
169C2×#92420—21no—
170C2×#92420—21no—
171C2×#92420—21no—
172C2×#92420—81no—
173C2×#92420C2×D411yescharacteristic
174C2×#92420C2×D411yescharacteristic
175C2×#92420C2×D411yescharacteristic
176C2×#92420C2×D411yescharacteristic
177#11758213—81no—
178D61⋊C8—81no—
179C2×C8×C61C22×C411yescharacteristic
180C2×C8×C61C22×C411yescharacteristic
181C4⋊C4×C61—21no—
182C4⋊C4×C61C22×C411yescharacteristic
183C4⋊C4×C61C22×C411yescharacteristic
184C4⋊C4×C61C22×C411yescharacteristic
185C22⋊C4×C61—21no—
186C22⋊Dic61—21no—
187#11758200—22no—
188#11758200—41no—
189#11758198—21no—
190#11758198—21no—
191C4⋊Dic61C22×C411yescharacteristic
192#11758196—21no—
193#11758196—21no—
194#11758196—21no—
195#11758196—21no—
196#11758196—21no—
197C4×Dic61—21no—
198C4×Dic61—21no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C4×Dic61C22×C411yescharacteristic
202C4×Dic61C2×D411yescharacteristic
203C4×Dic61#4111yescharacteristic
204C4×Dic61C2411yescharacteristic
205C2×#92418C22×C411yescharacteristic
206C2×#92418C22×C411yescharacteristic
207#11758190—22no—
208#11758190—41no—
209C23×C61—21no—
210C23×C61C4×D411yescharacteristic
211C22×D61—21no—
212D4×C61—21no—
213D4×C61—21no—
214D4×C61—81no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—42no—
221C2×C4×C61C4×D411yescharacteristic
222C2×C4×C61C23×C411yescharacteristic
223C22⋊D61—42no—
224C22⋊D61—81no—
225C22⋊D61—81no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—41no—
232C2×Dic61—42no—
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—21no—
246Dic122—42no—
247Dic122—81no—
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×C61—21no—
265C22×C61—21no—
266C22×C61—21no—
267C22×C61—41no—
268C22×C61—41no—
269C22×C61—41no—
270C22×C61C2×C4×D411yescharacteristic
271C2×D61—41no—
272C2×D61—41no—
273C2×D61—41no—
274C4×C61—21no—
275C4×C61—41no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61C2×#13111yescharacteristic
279C4×C61#56811yescharacteristic
280Dic61—22no—
281Dic61—21no—
282Dic61—21no—
283Dic61—21no—
284Dic61—41no—
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—41no—
304C2×C61—81no—
305C2×C61#293311yescharacteristic
306C2×C61#294911yescharacteristic
307C2×C61#295511yescharacteristic
308D61—81no—
309#532—611no—
310C2×C4×Q8—611no—
311#481—611no—
312#481#692311yescharacteristic
313#475—611no—
314#475—611no—
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⋊Q8—611no—
372#127—611no—
373#124—1221no—
374#121—611no—
375#121—1221no—
376#121C2×#692311yescharacteristic
377C4×Q8—611no—
378C4×Q8—611no—
379C4×Q8—611no—
380C4×Q8—611no—
381C4×Q8—1221no—
382C4×Q8—1221no—
383C4×D4—611no—
384C4×D4—611no—
385C4×D4—1221no—
386C2×C4⋊C4—1221no—
387C2×C4⋊C4C2×#692311yescharacteristic
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—611no—
402C4⋊C8—1221no—
403C4⋊C8—1221no—
404C4⋊C8—1221no—
405C4⋊C8—1221no—
406C4⋊C8—1221no—
407#103—611no—
408#103—611no—
409#103—611no—
410#103—611no—
411#102—611no—
412#102—611no—
413#102C2×#692311yescharacteristic
414#102C2×#692311yescharacteristic
415C22⋊C8—611no—
416C22⋊C8—611no—
417C22⋊C8—611no—
418C22⋊C8—1221no—
419C22⋊C8—1221no—
420C22⋊C8—1221no—
421C22⋊C8—1221no—
422C22⋊C8—1221no—
423C22⋊C8—1221no—
424C22⋊C8—1221no—
425C22⋊C8C2×#692311yescharacteristic
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—611no—
441C2×Q8—611no—
442C2×Q8—1221no—
443C2×Q8—1222no—
444C2×Q8—1221no—
445C2×Q8—2441no—
446C2×D4—21no—
447C2×D4—611no—
448C2×D4—1221no—
449C2×D4—1221no—
450C2×D4—1221no—
451C2×D4C22×#692311yescharacteristic
452C22×C4—21no—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—1221no—
456C22×C4—1221no—
457C22×C4—1221no—
458C22×C4C22×#692311yescharacteristic
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—611no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4C22×#692311yescharacteristic
489C4⋊C4C22×#692311yescharacteristic
490C4⋊C4C22×#692311yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—1221no—
493C22⋊C4—1221no—
494C22⋊C4—1221no—
495C42—611no—
496C42—611no—
497C42—611no—
498C42—611no—
499C42—1221no—
500C42—1221no—
501C42—1221no—
502C42—1221no—
503C23—21no—
504C23—1221no—
505C23D4×#692311yescharacteristic
506Q8—612no—
507Q8—1221no—
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—42no—
526C2×C4—611no—
527C2×C4—611no—
528C2×C4—611no—
529C2×C4—611no—
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×C4—2441no—
540C2×C4—2442no—
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—21no—
558C22—21no—
559C22—21no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—2441no—
564C22—2441no—
565C22—2441no—
566C22C2×D4×#692311yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—611no—
572C4—611no—
573C4—1222no—
574C4—1221no—
575C4—1221no—
576C4—1221no—
577C4—2441no—
578C4—2441no—
579C4D61⋊#13111yescharacteristic
580C4#1684084111yescharacteristic
581C2—41no—
582C2—81no—
583C2—4881no—
584C2#2146255311yescharacteristic
585C2#2146257911yescharacteristic
586C2#2146259111yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#481C4
socleC22×C61C2×C4×D4
prime radical#16840307C22
cosocleC4×Dic61C24
hypercenter#481#6923
hypocenterC61#18030
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #21462719C2semidirect
3. #21461461C2semidirect
4. #21461456C2semidirect
5. #21461449C2semidirect
6. #21461435C2semidirect
7. #21461427C2semidirect
8. #21461422C2semidirect
9. #21461410C2semidirect
10. #21461404C2semidirect
11. #21461390C2semidirect
13. #21461123C2semidirect
14. #21461040C2semidirect
360. C61#18030semidirect

Maximal subgroups

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

subgroupindex
#214627192
#214626992
#214614612
#214614562
#214614492
#214614352
#214614272
#214614222
#214614102
#214614042
#214613902
#214611782
#214611232
#214610402
#214558472
#1803061