Finite Group Databasebeta

← #29665472

Subgroups — #29665472

Order 15616.

628 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456775C211yesmaximal, characteristic, complemented
2#21455964C211yesmaximal, characteristic
3#21455891C211yesmaximal, characteristic, complemented
4#21454928C211yesmaximal, characteristic, complemented
5#21445262C211yesmaximal, characteristic, complemented
6#21445255C211yesmaximal, characteristic, complemented
7#21445248C211yesmaximal, characteristic, complemented
8#21445241C211yesmaximal, characteristic, complemented
9#21445188C211yesmaximal, characteristic, complemented
10#21445183C211yesmaximal, characteristic, complemented
11#21445166C211yesmaximal, characteristic, complemented
12#21445159C211yesmaximal, characteristic, complemented
13#21444597C211yesmaximal, characteristic, complemented
14#21444517C211yesmaximal, characteristic, complemented
15C61×#1540C211yesmaximal, characteristic, complemented
16#16840319C2211yescharacteristic
17C4×#11758222C2211yescharacteristic
18#16840141C2211yescharacteristic
19#16840134C2211yescharacteristic
20#16840112C2211yescharacteristic
21#16840108C2211yescharacteristic
22#16840104—21no—
23#16840083—21no—
24#16840048C2211yescharacteristic
25#16840044C2211yescharacteristic
26#16840043C2211yescharacteristic
27#16840039C2211yescharacteristic
28#16839981—21no—
29#16839981—21no—
30#16839973C2211yescharacteristic
31#16839968C2211yescharacteristic
32#16839959C2211yescharacteristic
33#16839954C2211yescharacteristic
34#16839926—21no—
35#16839924—21no—
36#16839924—21no—
37#16839905—21no—
38#16839886C2211yescharacteristic
39#16839886C2211yescharacteristic
40#16839872—21no—
41#16839862—21no—
42C4×Dic244—21no—
43C4×#11758190—21no—
44#16839827C2211yescharacteristic
45#16839827C2211yescharacteristic
46C8×C22⋊D61—21no—
47C8×C22⋊D61—21no—
48#16839819C2211yescharacteristic
49#16839815C2211yescharacteristic
50#16839814—21no—
51C4⋊C8×D61—21no—
52#16839514C2211yescharacteristic
53#16839514C2211yescharacteristic
54#16839512C2211yescharacteristic
55#16839512C2211yescharacteristic
56#16839509C2211yescharacteristic
57#16839509C2211yescharacteristic
58#16839507C2211yescharacteristic
59#16839507C2211yescharacteristic
60C61×#532C2211yescharacteristic
61C61×#431C2211yescharacteristic
62C2×C4⋊C8×C61C2211yescharacteristic
63C61×#332C2211yescharacteristic
64C61×#332C2211yescharacteristic
65C61×#331C2211yescharacteristic
66C61×#331C2211yescharacteristic
67C2×#11758222D411yescharacteristic
68C2×Dic244—21no—
69C2×#11758202—21no—
70C2×#11758202—21no—
71C2×#11758190—21no—
72C2×#11758200—21no—
73C2×#11758200—21no—
74C2×#11758200—21no—
75C2×#11758199—21no—
76C2×C8×D61—21no—
77C2×C8×D61—21no—
78#14519777C2311yescharacteristic
79#14519777C2311yescharacteristic
80#14519769—21no—
81#14519756—21no—
82#14519756—21no—
83C4×Dic122—21no—
84C4×Dic122—21no—
85C4×Dic122D411yescharacteristic
86C4×Dic122C2311yescharacteristic
87C4×D244D411yescharacteristic
88C4×D244C2311yescharacteristic
89C4×C22⋊D61—21no—
90C4×C22⋊D61—21no—
91#14519736—21no—
92#14519736D411yescharacteristic
93#14519734—21no—
94C42×D61—21no—
95#14519711—21no—
96#14519710—21no—
97#14519709—21no—
98#14519708—21no—
99C4⋊#92418D411yescharacteristic
100C4⋊#92418D411yescharacteristic
101C4⋊#92418C2311yescharacteristic
102C4⋊#92418C2311yescharacteristic
103#14519706—21no—
104#14519706—21no—
105#14519702—21no—
106#14519702—21no—
107#14519702—21no—
108#14519701—21no—
109#14519701—21no—
110#14519700—21no—
111#14519699—21no—
112#14519698—21no—
113#14519698—21no—
114#14519698—21no—
115#14519698—21no—
116#14519697—21no—
117C22⋊#92418—21no—
118C22⋊#92418D411yescharacteristic
119C22⋊#92418D411yescharacteristic
120#14519689—21no—
121#14519689—21no—
122#14519688—21no—
123C4×#92418C2311yescharacteristic
124C4×#92418C2311yescharacteristic
125C8×Dic61—21no—
126C8×Dic61—21no—
127C2×#41×C61—21no—
128C22×C8×C61—21no—
129C4⋊Q8×C61C2311yescharacteristic
130#127×C61C2311yescharacteristic
131#124×C61—21no—
132#121×C61—21no—
133#121×C61—21no—
134C4×D4×C61—21no—
135C4×D4×C61—21no—
136C2×C42×C61C2311yescharacteristic
137C4⋊C8×C61—21no—
138C4⋊C8×C61C2311yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140C4⋊C8×C61C2311yescharacteristic
141C4⋊C8×C61C2311yescharacteristic
142C22⋊C8×C61—21no—
143C4×C8×C61—21no—
144#41×C61—81no—
145#41×C61—81no—
146C2×Q8×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—41no—
151C22×C4×C61—41no—
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61#4111yescharacteristic
155C2×C22⋊D61—21no—
156#11758222—22no—
157#11758222—22no—
158C2×D244C2×D411yescharacteristic
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×Dic122—21no—
163C2×Dic122—21no—
164C2×Dic122C2×D411yescharacteristic
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—81no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C22⋊C4×C61—41no—
173C22⋊C4×C61—41no—
174C42×C61C2×D411yescharacteristic
175C42×C61C2×D411yescharacteristic
176C42×C61#4111yescharacteristic
177C42×C61C2411yescharacteristic
178C22⋊Dic61—21no—
179C22⋊Dic61—41no—
180#11758202—81no—
181#11758202—81no—
182#11758200—42no—
183#11758200—81no—
184#11758200—81no—
185#11758199—42no—
186#11758198—21no—
187#11758198—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61C2×D411yescharacteristic
193C4⋊Dic61C2×D411yescharacteristic
194#11758196—21no—
195#11758196—21no—
196#11758196—41no—
197#11758196—41no—
198C4×Dic61—21no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C4×Dic61—41no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207C2×#92418C2×D411yescharacteristic
208Dic244—42no—
209#11758190—42no—
210C8×D61—81no—
211C8×D61—81no—
212C23×C61—41no—
213C23×C61#12111yescharacteristic
214C22×D61—21no—
215Q8×C61—41no—
216Q8×C61—41no—
217D4×C61—41no—
218D4×C61—41no—
219D4×C61—41no—
220D4×C61—41no—
221D4×C61—81no—
222D4×C61—82no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—82no—
230C2×C4×C61#12111yescharacteristic
231C2×C4×C61#12111yescharacteristic
232C2×C4×C61#12111yescharacteristic
233C2×C4×C61C22×D411yescharacteristic
234C2×C4×C61C22×D411yescharacteristic
235C2×C4×C61C2×#4111yescharacteristic
236C22⋊D61—24no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242D244—21no—
243D244#13512yes—
244C4×D61—24no—
245C4×D61—41no—
246C4×D61—41no—
247C4×D61—81no—
248Dic122—21no—
249Dic122—41no—
250Dic122—41no—
251Dic122—41no—
252Dic122—41no—
253Dic122#13512yes—
254C8×C61—41no—
255C8×C61—41no—
256C8×C61—41no—
257C8×C61—41no—
258#92418—21no—
259#92418—21no—
260#92418—21no—
261#92418—21no—
262#92418—41no—
263#92418—41no—
264#19413—611nomaximal, Sylow
265C22×C61—21no—
266C22×C61—21no—
267C22×C61—21no—
268C22×C61—81no—
269C22×C61—81no—
270C22×C61—81no—
271C22×C61C2×#12111yescharacteristic
272C2×D61—22no—
273C2×D61—41no—
274C2×D61—41no—
275C4×C61—21no—
276C4×C61—21no—
277C4×C61—21no—
278C4×C61—21no—
279C4×C61—81no—
280C4×C61C2×#13511yescharacteristic
281C4×C61C2×#13511yescharacteristic
282C4×C61#57611yescharacteristic
283C4×C61#57711yescharacteristic
284Dic61—22no—
285Dic61—41no—
286Dic61—41no—
287Dic61—81no—
288Dic61—81no—
289#3210—611no—
290#3115—611no—
291#3107—611no—
292#2988—611no—
293#1682—611no—
294#1681—611no—
295#1680—611no—
296#1679—611no—
297#1670—611no—
298#1669—611no—
299#1666—611no—
300#1665—611no—
301#1572—611no—
302#1552—611no—
303#1540D6111yescharacteristic, complemented
304C2×C61—41no—
305C2×C61—161no—
306C2×C61#304511yescharacteristic
307C2×C61#305011yescharacteristic
308C2×C61#306911yescharacteristic
309D61—42no—
310#533—611no—
311#532C2×D6111yescharacteristic
312C4×#41—611no—
313#494—611no—
314#492—611no—
315#487—611no—
316#486—611no—
317#485—1221no—
318#482—1221no—
319#475—611no—
320#475—611no—
321#474—611no—
322#474—611no—
323#464—1221no—
324#464—1221no—
325#462—611no—
326#461—611no—
327#460—611no—
328#459—611no—
329#452—1221no—
330#452—1221no—
331#452—1221no—
332#449—1221no—
333C8×Q8—611no—
334C8×Q8—611no—
335#442—1221no—
336#440—1221no—
337C4×Q16—1221no—
338C4×SD16—1221no—
339C8×D4—611no—
340C8×D4—611no—
341C8×D4—1221no—
342C8×D4—1221no—
343#432—611no—
344#431—611no—
345#431—1221no—
346#431C2×D6111yescharacteristic
347C2×C4⋊C8—1221no—
348C2×C4⋊C8C2×D6111yescharacteristic
349#335—611no—
350#335—611no—
351#334—611no—
352#334—611no—
353#332—611no—
354#332—611no—
355#332—611no—
356#332—611no—
357#332C2×D6111yescharacteristic
358#332C2×D6111yescharacteristic
359#331C2×D6111yescharacteristic
360#331C2×D6111yescharacteristic
361C61#1941311yescharacteristic, complemented, Sylow
362C2×#41—21no—
363C2×#41—611no—
364C2×Q16—1221no—
365C2×Q16—1221no—
366C2×Q16—1221no—
367C2×SD16—1221no—
368C2×SD16—1221no—
369C2×SD16—1221no—
370C2×SD16—1221no—
371C2×D8—1221no—
372C22×C8—21no—
373C22×C8—1221no—
374C22×C8—1221no—
375C4⋊Q8—611no—
376C4⋊Q8—611no—
377C4⋊Q8C22×D6111yescharacteristic
378#127C22×D6111yescharacteristic
379#125—1221no—
380#124—21no—
381C22⋊Q8—1221no—
382C22⋊Q8—1221no—
383#121—21no—
384#121—21no—
385C4×Q8—611no—
386C4×Q8—611no—
387C4×Q8—1221no—
388C4×Q8—1221no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—611no—
392C4×D4—611no—
393C4×D4—1221no—
394C4×D4—1221no—
395#117—611no—
396#117—1221no—
397#117—1221no—
398C2×C42—1221no—
399C2×C42C22×D6111yescharacteristic
400#107—1221no—
401#107—1221no—
402#106—1221no—
403#106—1221no—
404C4⋊C8—21no—
405C4⋊C8—611no—
406C4⋊C8—611no—
407C4⋊C8—611no—
408C4⋊C8—611no—
409C4⋊C8—1221no—
410C4⋊C8—1221no—
411C4⋊C8C22×D6111yescharacteristic
412C4⋊C8C22×D6111yescharacteristic
413C4⋊C8C22×D6111yescharacteristic
414C4⋊C8C22×D6111yescharacteristic
415#103—1221no—
416#103—1221no—
417#103—1221no—
418#103—1221no—
419#103—1221no—
420#103—1221no—
421#102—1221no—
422#102—1221no—
423#102—1221no—
424#102—1221no—
425#102—1221no—
426#102—1221no—
427C22⋊C8—21no—
428C22⋊C8—611no—
429C22⋊C8—611no—
430C22⋊C8—1221no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433#97—1221no—
434C4×C8—21no—
435C4×C8—611no—
436C4×C8—611no—
437C4×C8—1221no—
438C4×C8—1221no—
439#41—81no—
440#41—81no—
441#41—1222no—
442#41—1222no—
443C2×Q8—21no—
444C2×Q8—611no—
445C2×Q8—1221no—
446C2×Q8—1221no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4—611no—
452C2×D4—1221no—
453C22×C4—41no—
454C22×C4—1221no—
455C22×C4—1221no—
456C22×C4—1221no—
457C22×C4#1175822211yescharacteristic
458C22×C4D4×D6111yescharacteristic
459C22×C4D4×D6111yescharacteristic
460Q16—4881no—
461Q16—4881no—
462Q16—2442no—
463SD16—4881no—
464SD16—4881no—
465SD16—2442no—
466SD16—2442no—
467D8—2442no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—81no—
473C2×C8—611no—
474C2×C8—611no—
475C2×C8—611no—
476C2×C8—611no—
477C2×C8—1221no—
478C2×C8—1221no—
479C2×C8—4881no—
480C2×C8—4881no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—611no—
484C4⋊C4—611no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C4⋊C4—1221no—
491C4⋊C4—2441no—
492C4⋊C4—2441no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—1221no—
496C22⋊C4—1221no—
497C22⋊C4—1221no—
498C22⋊C4—2441no—
499C42—1221no—
500C42—1221no—
501C42—1221no—
502C42—2441no—
503C42#1175822211yescharacteristic
504C42D4×D6111yescharacteristic
505C42D4×D6111yescharacteristic
506C42C23×D6111yescharacteristic
507C23—41no—
508C23—1221no—
509C23#1451975011yescharacteristic
510Q8—41no—
511Q8—41no—
512Q8—612no—
513Q8—1221no—
514Q8—2441no—
515Q8—2441no—
516Q8—2441no—
517Q8—2441no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—81no—
523D4—82no—
524D4—612no—
525D4—1224no—
526D4—1221no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—82no—
534C2×C4—1224no—
535C2×C4—1221no—
536C2×C4—1221no—
537C2×C4—1221no—
538C2×C4—4881no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4#1451975011yescharacteristic
544C2×C4#1451975011yescharacteristic
545C2×C4#1451975011yescharacteristic
546C2×C4C2×D4×D6111yescharacteristic
547C2×C4C2×D4×D6111yescharacteristic
548C2×C4C2×#1175822211yescharacteristic
549C8—41no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—1221no—
554C8—1221no—
555C8—1221no—
556C8—1221no—
557C8—2441no—
558C8—2441no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—1222no—
566C22—2441no—
567C22—2441no—
568C22C2×#1451975011yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—81no—
574C4—1222no—
575C4—4881no—
576C4—4881no—
577C4—2441no—
578C4—2441no—
579C4#135×D6111yescharacteristic
580C4#135×D6111yescharacteristic
581C4#1684056311yescharacteristic
582C4#1684056811yescharacteristic
583C2—41no—
584C2—161no—
585C2—2442no—
586C2#2145536311yescharacteristic
587C2#2145539911yescharacteristic
588C2#2145555911yescharacteristic
subgroupG/H
centerC22C2×#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1540C2
socleC22×C61C2×#121
prime radical#21455964C2
hypercenter#1540D61
hypocenterC61#19413
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1540

Complements

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

NH ≅ G/Ntype
1. #21456775C2semidirect
3. #21455891C2semidirect
4. #21454928C2semidirect
5. #21445262C2semidirect
6. #21445255C2semidirect
7. #21445248C2semidirect
8. #21445241C2semidirect
9. #21445188C2semidirect
10. #21445183C2semidirect
11. #21445166C2semidirect
12. #21445159C2semidirect
13. #21444597C2semidirect
14. #21444517C2semidirect
15. C61×#1540C2semidirect
303. #1540D61semidirect
361. C61#19413semidirect

Maximal subgroups

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

subgroupindex
#214567752
#214559642
#214558912
#214549282
#214452622
#214452552
#214452482
#214452412
#214451882
#214451832
#214451662
#214451592
#214445972
#214445172
C61×#15402
#1941361