Finite Group Databasebeta

← #29665460

Subgroups — #29665460

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#21455964C211yesmaximal, characteristic
2#21455884C211yesmaximal, characteristic, complemented
3#21454927C211yesmaximal, characteristic, complemented
4#21445260C211yesmaximal, characteristic, complemented
5#21445253C211yesmaximal, characteristic, complemented
6#21445246C211yesmaximal, characteristic, complemented
7#21445239C211yesmaximal, characteristic, complemented
8#21445186C211yesmaximal, characteristic, complemented
9#21445181C211yesmaximal, characteristic, complemented
10#21445164C211yesmaximal, characteristic, complemented
11#21445157C211yesmaximal, characteristic, complemented
12#21444599C211yesmaximal, characteristic, complemented
13#21444519C211yesmaximal, characteristic, complemented
14#21444468C211yesmaximal, characteristic, complemented
15C61×#3210C211yesmaximal, characteristic, complemented
16C4×#11758222C2211yescharacteristic
17#16840100—21no—
18#16840083—21no—
19#16840044C2211yescharacteristic
20#16840044C2211yescharacteristic
21#16840039C2211yescharacteristic
22#16840039C2211yescharacteristic
23#16839969C2211yescharacteristic
24#16839964C2211yescharacteristic
25#16839959C2211yescharacteristic
26#16839954C2211yescharacteristic
27#16839922—21no—
28#16839905—21no—
29C8×Dic122C2211yescharacteristic
30C8×Dic122C2211yescharacteristic
31#16839872—21no—
32#16839862—21no—
33C4×#11758202—21no—
34C4×#11758201—21no—
35C8×D244C2211yescharacteristic
36C8×D244C2211yescharacteristic
37#16839825—21no—
38#16839825—21no—
39#16839819C2211yescharacteristic
40#16839815C2211yescharacteristic
41#16839814—21no—
42C2×C4⋊#92418C2211yescharacteristic
43C4⋊C8×D61—21no—
44#16839515C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839513C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839508C2211yescharacteristic
51#16839508C2211yescharacteristic
52#16839508C2211yescharacteristic
53#16839508C2211yescharacteristic
54#16839506C2211yescharacteristic
55#16839506C2211yescharacteristic
56C61×#533C2211yescharacteristic
57C61×#532C2211yescharacteristic
58C61×#494C2211yescharacteristic
59C61×#492C2211yescharacteristic
60C61×#487C2211yescharacteristic
61C61×#486C2211yescharacteristic
62C61×#464—21no—
63C61×#464—21no—
64C61×#452—21no—
65C61×#452—21no—
66C61×#431C2211yescharacteristic
67C2×#11758222D411yescharacteristic
68C2×#11758202—21no—
69C2×#11758200—21no—
70C2×#11758201—21no—
71C2×#11758199—21no—
72C22×#92418—21no—
73C2×C8×D61—21no—
74C2×C8×D61—21no—
75C4×Dic122D411yescharacteristic
76C4×Dic122C2311yescharacteristic
77C4×D244D411yescharacteristic
78C4×D244C2311yescharacteristic
79C4×C22⋊D61—21no—
80C4×C22⋊D61—21no—
81#14519736D411yescharacteristic
82#14519734—21no—
83C42×D61—21no—
84#14519710—21no—
85#14519710—21no—
86#14519708—21no—
87#14519708—21no—
88C4⋊#92418—21no—
89C4⋊#92418C2311yescharacteristic
90C4⋊#92418C2311yescharacteristic
91C4⋊#92418C2311yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95#14519706—21no—
96#14519706—21no—
97#14519701—21no—
98#14519701—21no—
99#14519700—21no—
100#14519700—21no—
101#14519698—21no—
102#14519698—21no—
103#14519697—21no—
104#14519697—21no—
105C22⋊#92418—21no—
106C22⋊#92418—21no—
107#14519689—21no—
108#14519689—21no—
109#14519688—21no—
110C4×#92418—21no—
111C8×Dic61—21no—
112C8×Dic61—21no—
113C2×#41×C61—21no—
114C2×Q16×C61—21no—
115C2×Q16×C61—21no—
116C2×SD16×C61—21no—
117C2×SD16×C61—21no—
118C4⋊Q8×C61C2311yescharacteristic
119C4⋊Q8×C61C2311yescharacteristic
120C4⋊Q8×C61C2311yescharacteristic
121#127×C61C2311yescharacteristic
122#125×C61—21no—
123#124×C61—21no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—21no—
126#121×C61—21no—
127#121×C61—21no—
128C4×Q8×C61—21no—
129C4×Q8×C61—21no—
130C4×D4×C61—21no—
131C4×D4×C61—21no—
132#117×C61—21no—
133C2×C42×C61C2311yescharacteristic
134C4⋊C8×C61D411yescharacteristic
135C4⋊C8×C61D411yescharacteristic
136#103×C61—21no—
137#103×C61—21no—
138#102×C61—21no—
139#102×C61—21no—
140C22⋊C8×C61D411yescharacteristic
141C22⋊C8×C61D411yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144#41×C61—81no—
145#41×C61—81no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—41no—
153C22×C4×C61—41no—
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61#4111yescharacteristic
157C2×C22⋊D61—21no—
158#11758222—22no—
159#11758222—22no—
160C2×D244C2×D411yescharacteristic
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×Dic122C2×D411yescharacteristic
165Q16×C61—81no—
166Q16×C61—81no—
167SD16×C61—81no—
168SD16×C61—81no—
169C2×C8×C61C2×D411yescharacteristic
170C2×C8×C61C2×D411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172C2×C8×C61C2×D411yescharacteristic
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—41no—
180C4⋊C4×C61—41no—
181C22⋊C4×C61—41no—
182C22⋊C4×C61—41no—
183C22⋊C4×C61—41no—
184C42×C61—41no—
185C42×C61C2×D411yescharacteristic
186C42×C61C2×D411yescharacteristic
187C42×C61#4111yescharacteristic
188C42×C61C2411yescharacteristic
189C22⋊Dic61—21no—
190#11758202—42no—
191#11758201—42no—
192#11758200—42no—
193#11758199—42no—
194#11758198—21no—
195#11758198—21no—
196C4⋊Dic61C2×D411yescharacteristic
197C4⋊Dic61C2×D411yescharacteristic
198#11758196—21no—
199#11758196—21no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C4×Dic61—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—81no—
210C8×D61—81no—
211C8×D61—81no—
212C23×C61—41no—
213C23×C61#12111yescharacteristic
214C22×D61—21no—
215Q8×C61—41no—
216Q8×C61—41no—
217Q8×C61—41no—
218Q8×C61—41no—
219Q8×C61—41no—
220Q8×C61—41no—
221D4×C61—41no—
222D4×C61—41no—
223D4×C61—41no—
224D4×C61—41no—
225D4×C61—81no—
226D4×C61—82no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—82no—
236C2×C4×C61#12111yescharacteristic
237C2×C4×C61#12111yescharacteristic
238C2×C4×C61#12111yescharacteristic
239C2×C4×C61C22×D411yescharacteristic
240C2×C4×C61C22×D411yescharacteristic
241C2×C4×C61C2×#4111yescharacteristic
242C22⋊D61—24no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246D244—21no—
247D244#13512yes—
248C4×D61—24no—
249C4×D61—41no—
250C4×D61—41no—
251C4×D61—81no—
252Dic122—21no—
253Dic122#13512yes—
254C8×C61—21no—
255C8×C61—21no—
256C8×C61—21no—
257C8×C61—21no—
258#92418—41no—
259#92418—41no—
260#92418—41no—
261#92418—41no—
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×C61—81no—
281C4×C61—81no—
282C4×C61C2×#13511yescharacteristic
283C4×C61C2×#13511yescharacteristic
284C4×C61#57611yescharacteristic
285C4×C61#57711yescharacteristic
286Dic61—22no—
287Dic61—41no—
288Dic61—41no—
289#3210D6111yescharacteristic, complemented
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#1540—611no—
304C2×C61—41no—
305C2×C61—161no—
306C2×C61#304511yescharacteristic
307C2×C61#305011yescharacteristic
308C2×C61#306911yescharacteristic
309D61—42no—
310#533C2×D6111yescharacteristic
311#532C2×D6111yescharacteristic
312C4×#41—611no—
313#494C2×D6111yescharacteristic
314#492C2×D6111yescharacteristic
315#487C2×D6111yescharacteristic
316#486C2×D6111yescharacteristic
317#485—1221no—
318#482—1221no—
319#475—611no—
320#475—611no—
321#474—611no—
322#474—611no—
323#464—21no—
324#464—21no—
325#462—611no—
326#461—611no—
327#460—611no—
328#459—611no—
329#452—21no—
330#452—21no—
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—611no—
348C2×C4⋊C8—1221no—
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#332—611no—
358#332—611no—
359#331—611no—
360#331—611no—
361C61#1941311yescharacteristic, complemented, Sylow
362C2×#41—21no—
363C2×#41—611no—
364C2×Q16—21no—
365C2×Q16—21no—
366C2×Q16—1221no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—1221no—
370C2×SD16—1221no—
371C2×D8—1221no—
372C22×C8—1221no—
373C22×C8—1221no—
374C22×C8—1221no—
375C4⋊Q8C22×D6111yescharacteristic
376C4⋊Q8C22×D6111yescharacteristic
377C4⋊Q8C22×D6111yescharacteristic
378#127C22×D6111yescharacteristic
379#125—21no—
380#124—21no—
381C22⋊Q8—21no—
382C22⋊Q8—21no—
383#121—21no—
384#121—21no—
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8—611no—
388C4×Q8—611no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—611no—
392C4×D4—611no—
393C4×D4—1221no—
394C4×D4—1221no—
395#117—21no—
396#117—611no—
397#117—1221no—
398C2×C42—1221no—
399C2×C42C22×D6111yescharacteristic
400#107—1221no—
401#107—1221no—
402#106—1221no—
403#106—1221no—
404C4⋊C8—611no—
405C4⋊C8—611no—
406C4⋊C8—611no—
407C4⋊C8—611no—
408C4⋊C8—611no—
409C4⋊C8—611no—
410C4⋊C8—1221no—
411C4⋊C8—1221no—
412C4⋊C8—1221no—
413C4⋊C8C22⋊D6111yescharacteristic
414C4⋊C8C22⋊D6111yescharacteristic
415#103—21no—
416#103—21no—
417#103—1221no—
418#103—1221no—
419#103—1221no—
420#103—1221no—
421#102—21no—
422#102—21no—
423#102—1221no—
424#102—1221no—
425#102—1221no—
426#102—1221no—
427C22⋊C8—1221no—
428C22⋊C8—1221no—
429C22⋊C8—1221no—
430C22⋊C8—1221no—
431C22⋊C8C22⋊D6111yescharacteristic
432C22⋊C8C22⋊D6111yescharacteristic
433#97—1221no—
434C4×C8—1221no—
435C4×C8—1221no—
436C4×C8—1221no—
437C4×C8C22×D6111yescharacteristic
438C4×C8C22×D6111yescharacteristic
439#41—81no—
440#41—81no—
441#41—1222no—
442#41—1222no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—611no—
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×C4D4×D6111yescharacteristic
458C22×C4#1175822411yescharacteristic
459C22×C4C2×C22⋊D6111yescharacteristic
460Q16—81no—
461Q16—81no—
462Q16—2442no—
463SD16—81no—
464SD16—81no—
465SD16—2442no—
466SD16—2442no—
467D8—2442no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8—1221no—
474C2×C8—4881no—
475C2×C8—4881no—
476C2×C8—4881no—
477C2×C8C2×C22⋊D6111yescharacteristic
478C2×C8C2×C22⋊D6111yescharacteristic
479C2×C8C2×C22⋊D6111yescharacteristic
480C2×C8C2×C22⋊D6111yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—611no—
490C4⋊C4—611no—
491C4⋊C4—1221no—
492C4⋊C4—1221no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—1221no—
497C22⋊C4—1221no—
498C22⋊C4—1221no—
499C42—41no—
500C42—1221no—
501C42—1221no—
502C42—1221no—
503C42D4×D6111yescharacteristic
504C42#1175822411yescharacteristic
505C42C2×C22⋊D6111yescharacteristic
506C42C23×D6111yescharacteristic
507C23—41no—
508C23—1221no—
509C23#1451974811yescharacteristic
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—612no—
517Q8—1221no—
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—41no—
534C2×C4—41no—
535C2×C4—82no—
536C2×C4—1224no—
537C2×C4—1221no—
538C2×C4—1221no—
539C2×C4—1221no—
540C2×C4—4881no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4#1451974811yescharacteristic
544C2×C4#1451974811yescharacteristic
545C2×C4#1451974811yescharacteristic
546C2×C4C2×D4×D6111yescharacteristic
547C2×C4C22×C22⋊D6111yescharacteristic
548C2×C4C2×#1175822411yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—21no—
553C8—2441no—
554C8—2441no—
555C8—2441no—
556C8—2441no—
557C8—2441no—
558C8—2441no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—1222no—
566C22—2441no—
567C22—2441no—
568C22C2×#1451974811yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—1222no—
577C4—2441no—
578C4—2441no—
579C4#135×D6111yescharacteristic
580C4#135×D6111yescharacteristic
581C4#1684056511yescharacteristic
582C4#1684057311yescharacteristic
583C2—41no—
584C2—161no—
585C2—2442no—
586C2#2145535411yescharacteristic
587C2#2145539611yescharacteristic
588C2#2145555211yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3210C2
socleC22×C61C2×#121
prime radical#21455964C2
hypercenter#3210D61
hypocenterC61#19413
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3210

Complements

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

NH ≅ G/Ntype
2. #21455884C2semidirect
3. #21454927C2semidirect
4. #21445260C2semidirect
5. #21445253C2semidirect
6. #21445246C2semidirect
7. #21445239C2semidirect
8. #21445186C2semidirect
9. #21445181C2semidirect
10. #21445164C2semidirect
11. #21445157C2semidirect
12. #21444599C2semidirect
13. #21444519C2semidirect
14. #21444468C2semidirect
15. C61×#3210C2semidirect
289. #3210D61semidirect
361. C61#19413semidirect

Maximal subgroups

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

subgroupindex
#214559642
#214558842
#214549272
#214452602
#214452532
#214452462
#214452392
#214451862
#214451812
#214451642
#214451572
#214445992
#214445192
#214444682
C61×#32102
#1941361