Finite Group Databasebeta

← #30613378

Subgroups — #30613378

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#21462721C211yesmaximal, characteristic, complemented
2#21462700C211yesmaximal, characteristic
3#21461460C211yesmaximal, characteristic, complemented
4#21461456C211yesmaximal, characteristic, complemented
5#21461448C211yesmaximal, characteristic, complemented
6#21461434C211yesmaximal, characteristic, complemented
7#21461428C211yesmaximal, characteristic, complemented
8#21461422C211yesmaximal, characteristic, complemented
9SD16⋊#92420C211yesmaximal, characteristic, complemented
10SD16×#92420C211yesmaximal, characteristic, complemented
11#21461391C211yesmaximal, characteristic, complemented
12#21461179C211yesmaximal, characteristic
13#21461122C211yesmaximal, characteristic, complemented
14#21461041C211yesmaximal, characteristic, complemented
15#21455849C211yesmaximal, characteristic
16#16840812—21no—
17#16840812—21no—
18#16840812C2211yescharacteristic
19#16840812C2211yescharacteristic
20Q8×#92420C2211yescharacteristic
21Q8×#92420C2211yescharacteristic
22#16840797—21no—
23#16840797C2211yescharacteristic
24#16840797C2211yescharacteristic
25D4×#92420—21no—
26D4×#92420C2211yescharacteristic
27D4×#92420C2211yescharacteristic
28#16840784—21no—
29#16840784C2211yescharacteristic
30#16840781—21no—
31#16840781C2211yescharacteristic
32#16840781C2211yescharacteristic
33#16840780C2211yescharacteristic
34#16840735—21no—
35#16840735—21no—
36#16840626C2211yescharacteristic
37#16840625C2211yescharacteristic
38#16840624C2211yescharacteristic
39#16840623C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42Q8⋊#92420C2211yescharacteristic
43Q8⋊#92420C2211yescharacteristic
44D4⋊#92420C2211yescharacteristic
45D4⋊#92420C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic
49#92420⋊C8C2211yescharacteristic
50#16840603C2211yescharacteristic
51C8×#92420C2211yescharacteristic
52#16840310C2211yescharacteristic
53C4×Q8×D61C2211yescharacteristic
54#16840079C411yescharacteristic
55#16840079C411yescharacteristic
56#16840048C411yescharacteristic
57#16840047C411yescharacteristic
58#16839959C411yescharacteristic
59#16839899C411yescharacteristic
60#16839899C411yescharacteristic
61#16839853C2211yescharacteristic
62#16839853C2211yescharacteristic
63SD16×Dic61C2211yescharacteristic
64SD16×Dic61C2211yescharacteristic
65#16839814C2211yescharacteristic
66C61×#460C411yescharacteristic
67C2×#11758217—21no—
68C2×#11758217—21no—
69C22×#92420—21no—
70C22×#92420—21no—
71#14519844—21no—
72C4⋊#92420—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—
84#14519834—21no—
85#14519834D411yescharacteristic
86#14519834D411yescharacteristic
87C22⋊#92420—21no—
88C22⋊#92420—21no—
89C22⋊#92420—21no—
90C22⋊#92420—21no—
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—
102C2×Q8×D61C2×C411yescharacteristic
103C2×#11758200C2×C411yescharacteristic
104C2×#11758200C2×C411yescharacteristic
105#14519777C2×C411yescharacteristic
106#14519764—21no—
107#14519748—21no—
108#14519748C2×C411yescharacteristic
109#14519748C2×C411yescharacteristic
110Q8×Dic61C2311yescharacteristic
111C4×Dic122—21no—
112C4×Dic122C2×C411yescharacteristic
113#14519742—21no—
114#14519742C2311yescharacteristic
115D4×Dic61—21no—
116D4×Dic61C2311yescharacteristic
117D4×Dic61C2311yescharacteristic
118C4⋊C4×D61—21no—
119C4⋊C4×D61C2×C411yescharacteristic
120C42×D61—21no—
121C42×D61C2311yescharacteristic
122#14519709C2×C411yescharacteristic
123#14519709C2×C411yescharacteristic
124#14519708C2×C411yescharacteristic
125#14519708C2×C411yescharacteristic
126C4⋊#92418C2×C411yescharacteristic
127#14519702C2×C411yescharacteristic
128#14519702C2×C411yescharacteristic
129#14519701C2×C411yescharacteristic
130#14519701C2×C411yescharacteristic
131#14519698C2×C411yescharacteristic
132#14519698C2×C411yescharacteristic
133#14519689C2×C411yescharacteristic
134#14519689C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137C2×SD16×C61C2×C411yescharacteristic
138C2×SD16×C61C2×C411yescharacteristic
139#127×C61C2×C411yescharacteristic
140C4×Q8×C61C2×C411yescharacteristic
141C4⋊C8×C61C2×C411yescharacteristic
142#102×C61C2×C411yescharacteristic
143#102×C61C2×C411yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61C22×C411yescharacteristic
148C2×D4×C61C22×C411yescharacteristic
149C2×C22⋊D61—21no—
150C2×C22⋊D61—21no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153Q8×D61—22no—
154Q8×D61—41no—
155#11758224—81no—
156#11758224—81no—
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61C22×C411yescharacteristic
160C2×C4×D61C2×D411yescharacteristic
161C2×C4×D61#4111yescharacteristic
162C2×Dic122—21no—
163C2×Dic122—21no—
164C2×Dic122C22×C411yescharacteristic
165#11758217—81no—
166#11758217—81no—
167C2×#92420—21no—
168C2×#92420—21no—
169C2×#92420—21no—
170C2×#92420—21no—
171C2×#92420—21no—
172C2×#92420—21no—
173C2×#92420—81no—
174C2×#92420—81no—
175C2×#92420C2×D411yescharacteristic
176C2×#92420C2×D411yescharacteristic
177C2×#92420C2×D411yescharacteristic
178C2×#92420C2×D411yescharacteristic
179SD16×C61—22no—
180SD16×C61—22no—
181C2×C8×C61C22×C411yescharacteristic
182C2×C8×C61C22×C411yescharacteristic
183C4⋊C4×C61—21no—
184C4⋊C4×C61C22×C411yescharacteristic
185C42×C61—21no—
186C42×C61C22×C411yescharacteristic
187C22⋊Dic61—21no—
188C22⋊Dic61—21no—
189C22⋊Dic61—21no—
190C22⋊Dic61—21no—
191#11758200—41no—
192#11758200—41no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61C22×C411yescharacteristic
196C4⋊Dic61C22×C411yescharacteristic
197C4⋊Dic61C22×C411yescharacteristic
198#11758196—21no—
199#11758196—21no—
200#11758196—21no—
201C4×Dic61—21no—
202C4×Dic61—21no—
203C4×Dic61—21no—
204C4×Dic61C2×D411yescharacteristic
205C4×Dic61#4111yescharacteristic
206C4×Dic61C2411yescharacteristic
207C2×#92418C22×C411yescharacteristic
208C2×#92418C22×C411yescharacteristic
209C23×C61—21no—
210C23×C61—21no—
211C22×D61C4×D411yescharacteristic
212Q8×C61—21no—
213Q8×C61#13112yes—
214D4×C61—21no—
215D4×C61—21no—
216D4×C61—21no—
217D4×C61—21no—
218D4×C61—42no—
219D4×C61—81no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61C4×D411yescharacteristic
223C2×C4×C61C4×D411yescharacteristic
224C2×C4×C61C23×C411yescharacteristic
225C22⋊D61—81no—
226C22⋊D61—81no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—41no—
232C2×Dic61—41no—
233C2×Dic61—41no—
234C2×Dic61—41no—
235C2×Dic61C4×D411yescharacteristic
236C2×Dic61C22×D411yescharacteristic
237C2×Dic61C2×#4111yescharacteristic
238C4×D61—21no—
239C4×D61—21no—
240C4×D61—21no—
241C4×D61—21no—
242C4×D61—41no—
243C4×D61—42no—
244C4×D61—42no—
245Dic122—21no—
246Dic122—21no—
247Dic122—42no—
248Dic122—81no—
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—41no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61—41no—
268C22×C61—41no—
269C22×C61—41no—
270C22×C61C2×C4×D411yescharacteristic
271C2×D61—21no—
272C2×D61—21no—
273C2×D61—21no—
274C4×C61—22no—
275C4×C61—21no—
276C4×C61—21no—
277C4×C61—41no—
278C4×C61C2×#13111yescharacteristic
279C4×C61#56811yescharacteristic
280Dic61—21no—
281Dic61—21no—
282Dic61—41no—
283Dic61—41no—
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—81no—
304C2×C61—81no—
305C2×C61#293311yescharacteristic
306C2×C61#294911yescharacteristic
307C2×C61#295511yescharacteristic
308D61—41no—
309#532—611no—
310C2×C4×Q8—611no—
311#481—611no—
312#481—611no—
313#475—611no—
314#475—611no—
315#460—611no—
316#460#692311yescharacteristic
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×SD16C2×#692311yescharacteristic
366C2×SD16C2×#692311yescharacteristic
367C2×M16—1221no—
368C2×M16—1221no—
369C22×C8—1221no—
370C22×C8—1221no—
371C4⋊Q8—611no—
372#127C2×#692311yescharacteristic
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#106—611no—
393#106—611no—
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#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—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—611no—
441C2×Q8—1221no—
442C2×Q8—1221no—
443C2×Q8—1222no—
444C2×Q8—2441no—
445C2×Q8C22×#692311yescharacteristic
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—1221no—
449C2×D4—1221no—
450C2×D4C22×#692311yescharacteristic
451C2×D4C22×#692311yescharacteristic
452C22×C4—611no—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—1221no—
456C22×C4—1221no—
457C22×C4—1221no—
458C22×C4—1221no—
459SD16—22no—
460SD16—22no—
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—611no—
484C4⋊C4—611no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
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—21no—
504C23—21no—
505C23—611no—
506Q8—21no—
507Q8—1221no—
508Q8—1221no—
509Q8—4881no—
510Q8—2442no—
511Q8#1451986412yes—
512D4—21no—
513D4—21no—
514D4—21no—
515D4—21no—
516D4—42no—
517D4—81no—
518D4—4881no—
519D4—4881no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—611no—
523C2×C4—611no—
524C2×C4—611no—
525C2×C4—1221no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—1221no—
533C2×C4—2441no—
534C2×C4—2442no—
535C2×C4—2442no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4—2441no—
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—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—1221no—
564C22—1221no—
565C22—1221no—
566C22C2×D4×#692311yescharacteristic
567C4—22no—
568C4—21no—
569C4—21no—
570C4—41no—
571C4—611no—
572C4—611no—
573C4—1221no—
574C4—1221no—
575C4—2441no—
576C4—2441no—
577C4—2441no—
578C4—2441no—
579C4C2×#1451986411yescharacteristic
580C4#1684084111yescharacteristic
581C2—81no—
582C2—81no—
583C2—2441no—
584C2#2146254911yescharacteristic
585C2#2146257911yescharacteristic
586C2#2146259111yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#460C4
socleC22×C61C2×C4×D4
prime radical#16840310C22
cosocleC4×Dic61C24
hypercenter#460#6923
hypocenterC61#18030
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #21462721C2semidirect
3. #21461460C2semidirect
4. #21461456C2semidirect
5. #21461448C2semidirect
6. #21461434C2semidirect
7. #21461428C2semidirect
8. #21461422C2semidirect
9. SD16⋊#92420C2semidirect
10. SD16×#92420C2semidirect
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
#214627212
#214627002
#214614602
#214614562
#214614482
#214614342
#214614282
#214614222
SD16⋊#924202
SD16×#924202
#214613912
#214611792
#214611222
#214610412
#214558492
#1803061