Finite Group Databasebeta

← #29665462

Subgroups — #29665462

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#21456771C211yesmaximal, characteristic, complemented
2#21455970C211yesmaximal, characteristic
3#21454930C211yesmaximal, characteristic, complemented
4#21445265C211yesmaximal, characteristic, complemented
5#21445258C211yesmaximal, characteristic, complemented
6#21445251C211yesmaximal, characteristic, complemented
7#21445244C211yesmaximal, characteristic, complemented
8#21445187C211yesmaximal, characteristic, complemented
9#21445182C211yesmaximal, characteristic, complemented
10#21445169C211yesmaximal, characteristic, complemented
11#21445162C211yesmaximal, characteristic, complemented
12#21444597C211yesmaximal, characteristic, complemented
13#21444519C211yesmaximal, characteristic, complemented
14#21444466C211yesmaximal, characteristic, complemented
15C61×#3107C211yesmaximal, characteristic, complemented
16#16840312C2211yescharacteristic
17#16840141C2211yescharacteristic
18#16840136C2211yescharacteristic
19#16840114C2211yescharacteristic
20#16840110C2211yescharacteristic
21#16840086—21no—
22#16840047C2211yescharacteristic
23#16840042C2211yescharacteristic
24#16839984—21no—
25#16839984—21no—
26#16839962C2211yescharacteristic
27#16839957C2211yescharacteristic
28#16839922—21no—
29#16839922—21no—
30#16839907—21no—
31Q8×#92418C2211yescharacteristic
32Q8×#92418C2211yescharacteristic
33#16839872—21no—
34#16839860—21no—
35D4×#92418—21no—
36D4×#92418—21no—
37D4×#92418C2211yescharacteristic
38D4×#92418C2211yescharacteristic
39#16839819C2211yescharacteristic
40#16839815—21no—
41#16839815C2211yescharacteristic
42C2×C4⋊#92418—21no—
43C2×C4⋊#92418C2211yescharacteristic
44#16839514C2211yescharacteristic
45#16839514C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839512C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839508C2211yescharacteristic
51#16839508C2211yescharacteristic
52#16839507C2211yescharacteristic
53#16839507C2211yescharacteristic
54#16839505C2211yescharacteristic
55#16839505C2211yescharacteristic
56C61×#533C2211yescharacteristic
57C4×#41×C61C2211yescharacteristic
58C61×#485—21no—
59C61×#475C2211yescharacteristic
60C61×#474C2211yescharacteristic
61C61×#462C2211yescharacteristic
62C61×#461C2211yescharacteristic
63C61×#452—21no—
64C4×Q16×C61—21no—
65C4×SD16×C61—21no—
66C61×#431C2211yescharacteristic
67C2×#11758222—21no—
68C2×#11758202—21no—
69C2×#11758202—21no—
70C2×#11758201—21no—
71C2×#11758201—21no—
72C2×#11758201—21no—
73C2×#11758199—21no—
74C22×#92418—21no—
75C22×#92418—21no—
76C22×#92418—21no—
77#14519777C2311yescharacteristic
78#14519774C2311yescharacteristic
79#14519765—21no—
80#14519751—21no—
81#14519751—21no—
82C4×D244—21no—
83C4×D244—21no—
84#14519710—21no—
85#14519708—21no—
86C4⋊#92418—21no—
87C4⋊#92418—21no—
88C4⋊#92418—21no—
89C4⋊#92418D411yescharacteristic
90C4⋊#92418D411yescharacteristic
91C4⋊#92418C2311yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95#14519701—21no—
96#14519700—21no—
97#14519700—21no—
98#14519698—21no—
99#14519697—21no—
100#14519697—21no—
101#14519697—21no—
102#14519697—21no—
103C22⋊#92418—21no—
104C22⋊#92418—21no—
105C22⋊#92418—21no—
106C22⋊#92418D411yescharacteristic
107C22⋊#92418D411yescharacteristic
108#14519688—21no—
109C4×#92418—21no—
110C4×#92418—21no—
111C4×#92418C2311yescharacteristic
112C4×#92418C2311yescharacteristic
113C2×#41×C61D411yescharacteristic
114C2×Q16×C61—21no—
115C2×SD16×C61—21no—
116C4⋊Q8×C61C2311yescharacteristic
117C4⋊Q8×C61C2311yescharacteristic
118#125×C61—21no—
119C22⋊Q8×C61—21no—
120C22⋊Q8×C61—21no—
121C4×Q8×C61—21no—
122C4×Q8×C61—21no—
123C4×Q8×C61D411yescharacteristic
124C4×Q8×C61C2311yescharacteristic
125C4×D4×C61—21no—
126C4×D4×C61—21no—
127C4×D4×C61D411yescharacteristic
128C4×D4×C61C2311yescharacteristic
129#117×C61—21no—
130#117×C61—21no—
131#117×C61D411yescharacteristic
132C2×C42×C61—21no—
133C2×C42×C61C2311yescharacteristic
134#107×C61—21no—
135#106×C61—21no—
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138#103×C61—21no—
139#103×C61—21no—
140#103×C61—21no—
141#102×C61—21no—
142C22⋊C8×C61—21no—
143C4×C8×C61—21no—
144#41×C61—22no—
145#41×C61—22no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61C2×D411yescharacteristic
149C2×D4×C61—21no—
150C2×D4×C61C2×D411yescharacteristic
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61#4111yescharacteristic
157C2×C22⋊D61—41no—
158#11758222—81no—
159#11758222—81no—
160C2×D244—21no—
161C2×D244—21no—
162C2×D244—21no—
163C2×C4×D61—41no—
164C2×Dic122—21no—
165Q16×C61—42no—
166SD16×C61—42no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—41no—
176C4⋊C4×C61—41no—
177C4⋊C4×C61C2×D411yescharacteristic
178C4⋊C4×C61C2×D411yescharacteristic
179C22⋊C4×C61—21no—
180C22⋊C4×C61—21no—
181C22⋊C4×C61—21no—
182C22⋊C4×C61—41no—
183C42×C61—21no—
184C42×C61—21no—
185C42×C61—21no—
186C42×C61—41no—
187C42×C61C2×D411yescharacteristic
188C42×C61C2×D411yescharacteristic
189C42×C61#4111yescharacteristic
190C42×C61C2411yescharacteristic
191#11758202—81no—
192#11758202—81no—
193#11758201—42no—
194#11758201—81no—
195#11758201—81no—
196#11758199—42no—
197#11758198—41no—
198#11758198—41no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—81no—
206C2×#92418—81no—
207C2×#92418—81no—
208C2×#92418C2×D411yescharacteristic
209C2×#92418C2×D411yescharacteristic
210C2×#92418C2×D411yescharacteristic
211C2×#92418C2×D411yescharacteristic
212C23×C61—21no—
213C23×C61#12111yescharacteristic
214C22×D61—41no—
215Q8×C61—21no—
216Q8×C61—41no—
217Q8×C61—41no—
218Q8×C61—41no—
219Q8×C61—41no—
220Q8×C61#13512yes—
221D4×C61—24no—
222D4×C61—21no—
223D4×C61#13512yes—
224C2×C4×C61—24no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—81no—
238C2×C4×C61#12111yescharacteristic
239C2×C4×C61#12111yescharacteristic
240C2×C4×C61#12111yescharacteristic
241C2×C4×C61C22×D411yescharacteristic
242C2×C4×C61C22×D411yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C22⋊D61—82no—
245C2×Dic61—41no—
246D244—41no—
247D244—41no—
248D244—41no—
249D244—41no—
250D244—81no—
251C4×D61—82no—
252Dic122—41no—
253Dic122—41no—
254C8×C61—41no—
255C8×C61—41no—
256#92418—21no—
257#92418—21no—
258#92418—21no—
259#92418—21no—
260#92418—41no—
261#92418—41no—
262#92418—41no—
263#92418—41no—
264#19413—611nomaximal, Sylow
265C22×C61—21no—
266C22×C61—21no—
267C22×C61—22no—
268C22×C61—21no—
269C22×C61—41no—
270C22×C61—41no—
271C22×C61C2×#12111yescharacteristic
272C2×D61—81no—
273C2×D61—81no—
274C2×D61—81no—
275C4×C61—21no—
276C4×C61—21no—
277C4×C61—22no—
278C4×C61—21no—
279C4×C61—21no—
280C4×C61—41no—
281C4×C61—41no—
282C4×C61—81no—
283C4×C61—81no—
284C4×C61C2×#13511yescharacteristic
285C4×C61C2×#13511yescharacteristic
286C4×C61#57611yescharacteristic
287C4×C61#57711yescharacteristic
288Dic61—81no—
289#3210—611no—
290#3115—611no—
291#3107D6111yescharacteristic, complemented
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—42no—
306C2×C61#304511yescharacteristic
307C2×C61#305011yescharacteristic
308C2×C61#306911yescharacteristic
309D61—161no—
310#533C2×D6111yescharacteristic
311#532—611no—
312C4×#41C2×D6111yescharacteristic
313#494—611no—
314#492—611no—
315#487—611no—
316#486—611no—
317#485—21no—
318#482—1221no—
319#475—611no—
320#475C2×D6111yescharacteristic
321#474—611no—
322#474C2×D6111yescharacteristic
323#464—1221no—
324#464—1221no—
325#462C2×D6111yescharacteristic
326#461C2×D6111yescharacteristic
327#460—611no—
328#459—611no—
329#452—21no—
330#452—1221no—
331#452—1221no—
332#449—1221no—
333C8×Q8—611no—
334C8×Q8—611no—
335#442—1221no—
336#440—1221no—
337C4×Q16—21no—
338C4×SD16—21no—
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—1221no—
363C2×#41C22⋊D6111yescharacteristic
364C2×Q16—21no—
365C2×Q16—1221no—
366C2×Q16—1221no—
367C2×SD16—21no—
368C2×SD16—1221no—
369C2×SD16—1221no—
370C2×SD16—1221no—
371C2×D8—1221no—
372C22×C8—1221no—
373C22×C8—1221no—
374C22×C8—1221no—
375C4⋊Q8—611no—
376C4⋊Q8C22×D6111yescharacteristic
377C4⋊Q8C22×D6111yescharacteristic
378#127—611no—
379#125—21no—
380#124—1221no—
381C22⋊Q8—21no—
382C22⋊Q8—21no—
383#121—1221no—
384#121—1221no—
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8C22⋊D6111yescharacteristic
388C4×Q8C22×D6111yescharacteristic
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—1221no—
392C4×D4—1221no—
393C4×D4C22⋊D6111yescharacteristic
394C4×D4C22×D6111yescharacteristic
395#117—21no—
396#117—21no—
397#117C22⋊D6111yescharacteristic
398C2×C42—21no—
399C2×C42C22×D6111yescharacteristic
400#107—21no—
401#107—1221no—
402#106—21no—
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—21no—
418#103—1221no—
419#103—1221no—
420#103—1221no—
421#102—21no—
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—22no—
440#41—22no—
441#41—4881no—
442#41—4881no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—1221no—
446C2×Q8C2×C22⋊D6111yescharacteristic
447C2×D4—21no—
448C2×D4—1221no—
449C2×D4—1221no—
450C2×D4—1221no—
451C2×D4—2441no—
452C2×D4C2×C22⋊D6111yescharacteristic
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—2441no—
457C22×C4D4×D6111yescharacteristic
458C22×C4#1175822411yescharacteristic
459C22×C4C2×C22⋊D6111yescharacteristic
460Q16—42no—
461Q16—4881no—
462Q16—4881no—
463SD16—42no—
464SD16—4881no—
465SD16—4881no—
466SD16—2442no—
467D8—2442no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—611no—
471C2×C8—611no—
472C2×C8—611no—
473C2×C8—611no—
474C2×C8—1221no—
475C2×C8—1221no—
476C2×C8—1221no—
477C2×C8—1221no—
478C2×C8—4881no—
479C2×C8—4881no—
480C2×C8—4881no—
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—1221no—
490C4⋊C4—1221no—
491C4⋊C4C2×C22⋊D6111yescharacteristic
492C4⋊C4C2×C22⋊D6111yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—41no—
497C22⋊C4—2441no—
498C22⋊C4—2441no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—41no—
503C42D4×D6111yescharacteristic
504C42#1175822411yescharacteristic
505C42C2×C22⋊D6111yescharacteristic
506C42C23×D6111yescharacteristic
507C23—21no—
508C23—2441no—
509C23#1451974911yescharacteristic
510Q8—21no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—2441no—
516Q8—2441no—
517Q8#1451979712yes—
518D4—24no—
519D4—21no—
520D4—4881no—
521D4—4882no—
522D4—2441no—
523D4—2441no—
524D4—2441no—
525D4—2441no—
526D4#1451979712yes—
527C2×C4—24no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—81no—
541C2×C4—4882no—
542C2×C4—2441no—
543C2×C4#1451974911yescharacteristic
544C2×C4#1451974911yescharacteristic
545C2×C4#1451974911yescharacteristic
546C2×C4C2×D4×D6111yescharacteristic
547C2×C4C22×C22⋊D6111yescharacteristic
548C2×C4C2×#1175822411yescharacteristic
549C8—41no—
550C8—41no—
551C8—1221no—
552C8—1221no—
553C8—1221no—
554C8—1221no—
555C8—2441no—
556C8—2441no—
557C8—2441no—
558C8—2441no—
559C22—21no—
560C22—22no—
561C22—21no—
562C22—21no—
563C22—41no—
564C22—41no—
565C22—4881no—
566C22—4881no—
567C22—4881no—
568C22C2×#1451974911yescharacteristic
569C4—21no—
570C4—22no—
571C4—21no—
572C4—21no—
573C4—21no—
574C4—41no—
575C4—41no—
576C4—81no—
577C4—81no—
578C4—4881no—
579C4C2×#1451979711yescharacteristic
580C4C2×#1451979711yescharacteristic
581C4#1684056411yescharacteristic
582C4#1684056911yescharacteristic
583C2—41no—
584C2—42no—
585C2—9761no—
586C2#2145535611yescharacteristic
587C2#2145539711yescharacteristic
588C2#2145555311yescharacteristic
subgroupG/H
centerC22C2×#14519749
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3107C2
socleC22×C61C2×#121
prime radical#21455970C2
hypercenter#3107D61
hypocenterC61#19413
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3107

Complements

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

NH ≅ G/Ntype
1. #21456771C2semidirect
3. #21454930C2semidirect
4. #21445265C2semidirect
5. #21445258C2semidirect
6. #21445251C2semidirect
7. #21445244C2semidirect
8. #21445187C2semidirect
9. #21445182C2semidirect
10. #21445169C2semidirect
11. #21445162C2semidirect
12. #21444597C2semidirect
13. #21444519C2semidirect
14. #21444466C2semidirect
15. C61×#3107C2semidirect
291. #3107D61semidirect
361. C61#19413semidirect

Maximal subgroups

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

subgroupindex
#214567712
#214559702
#214549302
#214452652
#214452582
#214452512
#214452442
#214451872
#214451822
#214451692
#214451622
#214445972
#214445192
#214444662
C61×#31072
#1941361