Finite Group Databasebeta

← #30613271

Subgroups — #30613271

Order 15616.

650 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462770C211yesmaximal, characteristic, complemented
2#21462680C211yesmaximal, characteristic, complemented
3#21461453C211yesmaximal, characteristic, complemented
4#21461451C211yesmaximal, characteristic, complemented
5#21461446C211yesmaximal, characteristic, complemented
6#21461439C211yesmaximal, characteristic, complemented
7#21461439C211yesmaximal, characteristic, complemented
8#21461437C211yesmaximal, characteristic, complemented
9#21461403C211yesmaximal, characteristic, complemented
10#21461400C211yesmaximal, characteristic, complemented
11#21461394C211yesmaximal, characteristic, complemented
12#21461172C211yesmaximal, characteristic, complemented
13C2×#16840610C211yesmaximal, characteristic, complemented
14#21461024C211yesmaximal, characteristic, complemented
15#21455869C211yesmaximal, characteristic
16#16840813C2211yescharacteristic, complemented
17Q8×#92420C2211yescharacteristic, complemented
18#16840796C2211yescharacteristic
19#16840796C2211yescharacteristic
20#16840796C2211yescharacteristic, complemented
21#16840792—21no—
22#16840792—21no—
23#16840791—21no—
24#16840790C2211yescharacteristic
25#16840790C2211yescharacteristic
26#16840790C2211yescharacteristic, complemented
27#16840789—21no—
28#16840787—21no—
29#16840783C2211yescharacteristic
30#16840779C2211yescharacteristic
31#16840769—21no—
32C2×C4⋊#92420C2211yescharacteristic
33#16840733—21no—
34D61⋊(C22⋊C8)—21no—
35C2×C4×#92420C2211yescharacteristic
36#16840625C2211yescharacteristic, complemented
37#16840625C2211yescharacteristic, complemented
38#16840624C2211yescharacteristic, complemented
39#16840624C2211yescharacteristic, 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
50C8×#92420C2211yescharacteristic, 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×D61⋊C8—21no—
71C2×D61⋊C8—21no—
72C2×D61⋊C8—21no—
73C22×#92420—21no—
74C22×#92420—21no—
75#14519844—21no—
76#14519844D411yescharacteristic
77#14519844D411yescharacteristic
78C4⋊#92420—21no—
79C4⋊#92420—21no—
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⋊#92420D411yescharacteristic
92C22⋊#92420D411yescharacteristic
93#14519832—21no—
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—22no—
152C2×D244—21no—
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—
164C2×#92420—24no—
165C2×#92420—21no—
166C2×#92420—21no—
167C2×#92420—21no—
168C2×#92420—21no—
169C2×#92420—21no—
170C2×#92420—21no—
171C2×#92420—81no—
172C2×#92420C2×D411yescharacteristic
173C2×#92420C2×D411yescharacteristic
174C2×#92420C2×D411yescharacteristic
175C2×#92420C2×D411yescharacteristic
176#11758213—81no—
177#11758213—81no—
178#11758213—81no—
179D61⋊C8—81no—
180D61⋊C8—81no—
181D61⋊C8—81no—
182C2×C8×C61C22×C411yescharacteristic
183C2×C8×C61C22×C411yescharacteristic
184C4⋊C4×C61—21no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61C22×C411yescharacteristic
187C4⋊C4×C61C22×C411yescharacteristic
188C4⋊C4×C61C22×C411yescharacteristic
189C22⋊C4×C61—21no—
190#11758201—22no—
191#11758201—41no—
192#11758198—21no—
193#11758198—21no—
194#11758198—21no—
195#11758198—21no—
196#11758198—21no—
197#11758198—21no—
198#11758198—21no—
199#11758198—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61C22×C411yescharacteristic
203#11758196—21no—
204C4×Dic61—21no—
205C4×Dic61C22×C411yescharacteristic
206C4×Dic61C2×D411yescharacteristic
207C4×Dic61#4111yescharacteristic
208C4×Dic61C2411yescharacteristic
209C2×#92418C22×C411yescharacteristic
210C2×#92418C22×C411yescharacteristic
211D488—22no—
212D488—41no—
213C23×C61C4×D411yescharacteristic
214C22×D61—21no—
215C22×D61—21no—
216C22×D61—21no—
217C22×D61—42no—
218C22×D61—42no—
219C22×D61—81no—
220Q8×C61—21no—
221Q8×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—21no—
228C2×C4×C61—81no—
229C2×C4×C61C4×D411yescharacteristic
230C2×C4×C61C23×C411yescharacteristic
231C22⋊D61—42no—
232C2×Dic61—22no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61C4×D411yescharacteristic
237C2×Dic61C4×D411yescharacteristic
238C2×Dic61C22×D411yescharacteristic
239C2×Dic61C2×#4111yescharacteristic
240D244—21no—
241D244—21no—
242D244—21no—
243D244—21no—
244D244—21no—
245D244—42no—
246D244#13112yes—
247C4×D61—41no—
248C4×D61—41no—
249C4×D61—41no—
250C4×D61—41no—
251C4×D61—41no—
252C4×D61—41no—
253C4×D61—81no—
254C4×D61—81no—
255#92420—22no—
256#92420—22no—
257#92420—21no—
258#92420—21no—
259#92420—21no—
260#92420—21no—
261#92420—41no—
262#92420—41no—
263#92420—41no—
264#92420—41no—
265C8×C61—21no—
266C8×C61—21no—
267#92418—21no—
268#92418—21no—
269#18014—611nomaximal, Sylow
270C22×C61—21no—
271C22×C61—21no—
272C22×C61#44312yes—
273C22×C61C2×C4×D411yescharacteristic
274C2×D61—22no—
275C2×D61—41no—
276C2×D61—41no—
277C2×D61—41no—
278C2×D61—41no—
279C2×D61—41no—
280C2×D61—41no—
281C2×D61—41no—
282C2×D61—41no—
283C2×D61—84no—
284C4×C61—21no—
285C4×C61—41no—
286C4×C61—41no—
287C4×C61—41no—
288C4×C61—41no—
289C4×C61C2×#13111yescharacteristic
290C4×C61#56811yescharacteristic
291Dic61—21no—
292Dic61—21no—
293Dic61—21no—
294Dic61—41no—
295Dic61#57611yescharacteristic
296Dic61#57711yescharacteristic
297#3105—611no—
298#2994—611no—
299#2974—611no—
300#1590—611no—
301#1589—611no—
302#1588—611no—
303#1586—611no—
304#1586—611no—
305#1585—611no—
306C8×SD16—611no—
307C8×D8—611no—
308#1573—611no—
309#1494—611no—
310C2×D4⋊C8—611no—
311#1450—611no—
312C2×C61—22no—
313C2×C61#293311yescharacteristic
314C2×C61#294611yescharacteristic
315C2×C61C2×#44311yescharacteristic
316D61—42no—
317D61—81no—
318D61—81no—
319#529—611no—
320C2×C4×D4—611no—
321#484#692311yescharacteristic
322#481—611no—
323#478—611no—
324#478—611no—
325#463—611no—
326#463—611no—
327#450—611no—
328#447—611no—
329#446—611no—
330C8×Q8—611no—
331C4×SD16—611no—
332C4×SD16—611no—
333C4×D8—611no—
334C4×D8—611no—
335#436—611no—
336#436—611no—
337#436—611no—
338#435—1221no—
339#435—1221no—
340#435—1221no—
341C8×D4—611no—
342C8×D4—611no—
343C8×D4—611no—
344C8×D4—1221no—
345#433—1221no—
346#432—611no—
347#431—611no—
348#431—611no—
349#424—1221no—
350C2×C4⋊C8—611no—
351#407—1221no—
352C2×C22⋊C8—1221no—
353C2×C4×C8—611no—
354#335—611no—
355#335—611no—
356#334—611no—
357#334—611no—
358Q8⋊C8—611no—
359Q8⋊C8—611no—
360D4⋊C8—611no—
361D4⋊C8—611no—
362D4⋊C8—611no—
363D4⋊C8—611no—
364D4⋊C8—611no—
365D4⋊C8—611no—
366#322—611no—
367#322—611no—
368C82—611no—
369C82—611no—
370C61#1801411yescharacteristic, complemented, Sylow
371C22×D4—611no—
372C23×C4—1221no—
373C2×SD16—611no—
374C2×SD16—611no—
375C2×D8—611no—
376C2×D8—611no—
377C2×M16—1221no—
378C2×M16—1221no—
379C2×M16—1221no—
380C22×C8—1221no—
381C22×C8—1221no—
382C22×C8—1221no—
383C22×C8—1221no—
384C22×C8—1221no—
385#126—1221no—
386#125—611no—
387#124—611no—
388#123—1221no—
389C22⋊Q8C2×#692311yescharacteristic
390#121—611no—
391C4×Q8—611no—
392C4×D4—611no—
393C4×D4—611no—
394C4×D4—611no—
395C4×D4—611no—
396C4×D4—611no—
397C4×D4—1221no—
398C4×D4—1221no—
399C4×D4—1221no—
400#117—1221no—
401C2×C4⋊C4C2×#692311yescharacteristic
402C2×C22⋊C4—1221no—
403C2×C42—611no—
404#107C2×#692311yescharacteristic
405#107C2×#692311yescharacteristic
406#106—611no—
407#106—611no—
408C4⋊C8—611no—
409C4⋊C8—611no—
410C4⋊C8—611no—
411C4⋊C8—611no—
412C4⋊C8—611no—
413C4⋊C8—611no—
414C4⋊C8—611no—
415C4⋊C8—611no—
416C4⋊C8—1221no—
417C4⋊C8—1221no—
418C4⋊C8—1221no—
419#103C2×#692311yescharacteristic
420#103C2×#692311yescharacteristic
421#102—611no—
422#102—611no—
423#102—611no—
424#102—611no—
425#102—611no—
426#102—611no—
427C22⋊C8—611no—
428C22⋊C8—611no—
429C22⋊C8—611no—
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—
439#97—1221no—
440C4×C8—611no—
441C4×C8—611no—
442C4×C8—611no—
443C4×C8—611no—
444C4×C8—611no—
445C4×C8—611no—
446C4×C8—1221no—
447C4×C8—1221no—
448C24—1221no—
449C2×Q8C22×#692311yescharacteristic
450C2×D4—611no—
451C2×D4—611no—
452C2×D4—611no—
453C2×D4—1222no—
454C2×D4—1221no—
455C2×D4—1221no—
456C2×D4—2441no—
457C22×C4—21no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4—4881no—
466C22×C4—4881no—
467C22×C4C22×#692311yescharacteristic
468SD16—1222no—
469SD16—2441no—
470D8—1222no—
471D8—2441no—
472M16—4881no—
473M16—4881no—
474M16—4881no—
475C2×C8—611no—
476C2×C8—611no—
477C2×C8—611no—
478C2×C8—611no—
479C2×C8—611no—
480C2×C8—611no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—1224no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—4881no—
489C2×C8—4881no—
490C2×C8—4881no—
491C2×C8—4881no—
492C2×C8C22×#692311yescharacteristic
493C2×C8C22×#692311yescharacteristic
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—611no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4—1221no—
500C4⋊C4C22×#692311yescharacteristic
501C4⋊C4C22×#692311yescharacteristic
502C4⋊C4C22×#692311yescharacteristic
503C22⋊C4—21no—
504C22⋊C4—1221no—
505C22⋊C4—1221no—
506C22⋊C4—1221no—
507C22⋊C4—1221no—
508C22⋊C4—1221no—
509C22⋊C4—1221no—
510C22⋊C4—1221no—
511C22⋊C4—1221no—
512C42—611no—
513C42—611no—
514C42—611no—
515C42—611no—
516C42—1221no—
517C23—1221no—
518C23—1221no—
519C23—1221no—
520C23—4881no—
521C23—2442no—
522C23—2442no—
523C23D4×#692311yescharacteristic
524Q8—21no—
525Q8—21no—
526D4—612no—
527D4—1221no—
528D4—1221no—
529D4—1221no—
530D4—1221no—
531D4—1221no—
532D4—2442no—
533D4—2442no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—81no—
541C2×C4—611no—
542C2×C4—611no—
543C2×C4—611no—
544C2×C4—611no—
545C2×C4—1221no—
546C2×C4—1221no—
547C2×C4—1222no—
548C2×C4—1221no—
549C2×C4—4881no—
550C2×C4—4881no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4—2441no—
557C2×C4D4×#692311yescharacteristic
558C2×C4C23×#692311yescharacteristic
559C8—21no—
560C8—21no—
561C8—1221no—
562C8—1221no—
563C8—1221no—
564C8—1221no—
565C8—1222no—
566C8—1222no—
567C8—1221no—
568C8—1221no—
569C8—2441no—
570C8—2441no—
571C8—2441no—
572C8—2441no—
573C22—21no—
574C22—21no—
575C22—1222no—
576C22—4884no—
577C22—2441no—
578C22—2441no—
579C22—2441no—
580C22—2441no—
581C22—2441no—
582C22—2441no—
583C22—2441no—
584C22—2441no—
585C22#1684080612yes—
586C22C2×D4×#692311yescharacteristic
587C4—21no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—611no—
593C4—611no—
594C4—1221no—
595C4—1221no—
596C4—1221no—
597C4—2441no—
598C4D61⋊#13111yescharacteristic
599C4#1684084111yescharacteristic
600C2—22no—
601C2—4881no—
602C2—4881no—
603C2—2442no—
604C2#2146255311yescharacteristic
605C2#2146257611yescharacteristic
606C2C2×#1684080611yescharacteristic
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#18014
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. #21462770C2semidirect
2. #21462680C2semidirect
3. #21461453C2semidirect
4. #21461451C2semidirect
5. #21461446C2semidirect
6. #21461439C2semidirect
7. #21461439C2semidirect
8. #21461437C2semidirect
9. #21461403C2semidirect
10. #21461400C2semidirect
11. #21461394C2semidirect
12. #21461172C2semidirect
13. C2×#16840610C2semidirect
14. #21461024C2semidirect
16. #16840813C22semidirect
17. Q8×#92420C22semidirect
20. #16840796C22semidirect
26. #16840790C22semidirect
36. #16840625C22semidirect
37. #16840625C22semidirect
38. #16840624C22semidirect
39. #16840624C22semidirect
40. Q8⋊#92420C22semidirect
41. Q8⋊#92420C22semidirect
46. #16840610C22semidirect
47. #16840610C22semidirect
48. #92420⋊C8C22semidirect
49. #92420⋊C8C22semidirect
50. C8×#92420C22semidirect
51. C8×#92420C22semidirect
370. C61#18014semidirect

Maximal subgroups

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

subgroupindex
#214627702
#214626802
#214614532
#214614512
#214614462
#214614392
#214614372
#214614032
#214614002
#214613942
#214611722
C2×#168406102
#214610242
#214558692
#1801461