Finite Group Databasebeta

← #29665466

Subgroups — #29665466

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#21456777C211yesmaximal, characteristic, complemented
2#21455970C211yesmaximal, characteristic
3#21455890C211yesmaximal, characteristic, complemented
4#21445263C211yesmaximal, characteristic, complemented
5#21445256C211yesmaximal, characteristic, complemented
6#21445249C211yesmaximal, characteristic, complemented
7#21445242C211yesmaximal, characteristic, complemented
8#21445189C211yesmaximal, characteristic, complemented
9#21445184C211yesmaximal, characteristic, complemented
10#21445167C211yesmaximal, characteristic, complemented
11#21445160C211yesmaximal, characteristic, complemented
12#21444599C211yesmaximal, characteristic, complemented
13#21444517C211yesmaximal, characteristic, complemented
14#21444469C211yesmaximal, characteristic, complemented
15C61×#2988C211yesmaximal, characteristic, complemented
16#16840319C2211yescharacteristic
17#16840312C2211yescharacteristic
18#16840142C2211yescharacteristic
19#16840135C2211yescharacteristic
20#16840113C2211yescharacteristic
21#16840109C2211yescharacteristic
22#16840103—21no—
23#16840086—21no—
24#16840047C2211yescharacteristic
25#16840047C2211yescharacteristic
26#16840042C2211yescharacteristic
27#16840042C2211yescharacteristic
28#16839985—21no—
29#16839985—21no—
30#16839972C2211yescharacteristic
31#16839967C2211yescharacteristic
32#16839962C2211yescharacteristic
33#16839957C2211yescharacteristic
34#16839926—21no—
35#16839926—21no—
36#16839924—21no—
37#16839907—21no—
38#16839872—21no—
39#16839860—21no—
40C4×#11758202—21no—
41C4×#11758200—21no—
42#16839819C2211yescharacteristic
43#16839815C2211yescharacteristic
44#16839515C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839513C2211yescharacteristic
48#16839509C2211yescharacteristic
49#16839509C2211yescharacteristic
50#16839509C2211yescharacteristic
51#16839509C2211yescharacteristic
52#16839507C2211yescharacteristic
53#16839507C2211yescharacteristic
54#16839505C2211yescharacteristic
55#16839505C2211yescharacteristic
56C4×#41×C61C2211yescharacteristic
57C8×Q8×C61C2211yescharacteristic
58C8×Q8×C61C2211yescharacteristic
59C8×D4×C61—21no—
60C8×D4×C61—21no—
61C8×D4×C61C2211yescharacteristic
62C8×D4×C61C2211yescharacteristic
63C61×#431—21no—
64C61×#431C2211yescharacteristic
65C2×C4⋊C8×C61—21no—
66C2×C4⋊C8×C61C2211yescharacteristic
67C2×#11758222—21no—
68C2×Dic244—21no—
69C2×Dic244—21no—
70C2×#11758202—21no—
71C2×#11758190—21no—
72C2×#11758190—21no—
73C2×#11758200—21no—
74C2×#11758201—21no—
75C2×#11758199—21no—
76#14519777C2311yescharacteristic
77#14519777C2311yescharacteristic
78#14519777C2311yescharacteristic
79#14519774C2311yescharacteristic
80#14519769—21no—
81#14519765—21no—
82#14519756—21no—
83#14519756—21no—
84#14519751—21no—
85#14519751—21no—
86C4×Dic122—21no—
87C4×Dic122—21no—
88C4×D244—21no—
89C4×D244—21no—
90#14519736—21no—
91#14519710—21no—
92#14519710—21no—
93#14519708—21no—
94#14519708—21no—
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99#14519702—21no—
100#14519702—21no—
101#14519701—21no—
102#14519701—21no—
103#14519700—21no—
104#14519700—21no—
105#14519699—21no—
106#14519699—21no—
107#14519698—21no—
108#14519698—21no—
109#14519697—21no—
110#14519697—21no—
111C22⋊#92418—21no—
112C22⋊#92418—21no—
113#14519688—21no—
114C4×#92418—21no—
115C2×#41×C61D411yescharacteristic
116C22×C8×C61—21no—
117C22×C8×C61—21no—
118C22×C8×C61—21no—
119C4×Q8×C61D411yescharacteristic
120C4×Q8×C61C2311yescharacteristic
121C4×D4×C61—21no—
122C4×D4×C61—21no—
123C4×D4×C61D411yescharacteristic
124C4×D4×C61C2311yescharacteristic
125#117×C61—21no—
126#117×C61D411yescharacteristic
127C2×C42×C61—21no—
128C2×C42×C61C2311yescharacteristic
129C4⋊C8×C61—21no—
130C4⋊C8×C61—21no—
131C4⋊C8×C61—21no—
132C4⋊C8×C61D411yescharacteristic
133C4⋊C8×C61D411yescharacteristic
134C4⋊C8×C61C2311yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C22⋊C8×C61—21no—
137C22⋊C8×C61—21no—
138C22⋊C8×C61D411yescharacteristic
139C22⋊C8×C61D411yescharacteristic
140C4×C8×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144#41×C61—22no—
145#41×C61—22no—
146C2×Q8×C61C2×D411yescharacteristic
147C2×D4×C61—21no—
148C2×D4×C61C2×D411yescharacteristic
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61#4111yescharacteristic
155C2×C22⋊D61—41no—
156#11758222—81no—
157#11758222—81no—
158C2×D244—21no—
159C2×D244—21no—
160C2×D244—21no—
161C2×C4×D61—41no—
162C2×Dic122—21no—
163C2×Dic122—21no—
164C2×Dic122—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—81no—
168C2×C8×C61—81no—
169C2×C8×C61—81no—
170C2×C8×C61C2×D411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172C2×C8×C61C2×D411yescharacteristic
173C2×C8×C61C2×D411yescharacteristic
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61C2×D411yescharacteristic
177C4⋊C4×C61C2×D411yescharacteristic
178C22⋊C4×C61—21no—
179C22⋊C4×C61—21no—
180C22⋊C4×C61—21no—
181C42×C61—21no—
182C42×C61—21no—
183C42×C61—21no—
184C42×C61C2×D411yescharacteristic
185C42×C61C2×D411yescharacteristic
186C42×C61#4111yescharacteristic
187C42×C61C2411yescharacteristic
188C22⋊Dic61—41no—
189#11758202—42no—
190#11758201—42no—
191#11758200—42no—
192#11758199—42no—
193#11758198—41no—
194#11758198—41no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201#11758196—41no—
202#11758196—41no—
203C4×Dic61—41no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208Dic244—81no—
209Dic244—81no—
210#11758190—81no—
211#11758190—81no—
212C23×C61—21no—
213C23×C61#12111yescharacteristic
214C22×D61—41no—
215Q8×C61—21no—
216Q8×C61#13512yes—
217D4×C61—24no—
218D4×C61—21no—
219D4×C61#13512yes—
220C2×C4×C61—24no—
221C2×C4×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—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—81no—
232C2×C4×C61#12111yescharacteristic
233C2×C4×C61#12111yescharacteristic
234C2×C4×C61#12111yescharacteristic
235C2×C4×C61C22×D411yescharacteristic
236C2×C4×C61C22×D411yescharacteristic
237C2×C4×C61C2×#4111yescharacteristic
238C22⋊D61—82no—
239C2×Dic61—41no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242D244—41no—
243D244—41no—
244D244—41no—
245D244—41no—
246D244—81no—
247C4×D61—82no—
248Dic122—41no—
249Dic122—41no—
250Dic122—41no—
251Dic122—41no—
252Dic122—41no—
253Dic122—41no—
254C8×C61—21no—
255C8×C61—21no—
256C8×C61—21no—
257C8×C61—21no—
258C8×C61—41no—
259C8×C61—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—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×C61C2×#13511yescharacteristic
283C4×C61C2×#13511yescharacteristic
284C4×C61#57611yescharacteristic
285C4×C61#57711yescharacteristic
286Dic61—81no—
287Dic61—81no—
288Dic61—81no—
289#3210—611no—
290#3115—611no—
291#3107—611no—
292#2988D6111yescharacteristic, complemented
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#533—611no—
311#532—611no—
312C4×#41C2×D6111yescharacteristic
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×Q8C2×D6111yescharacteristic
334C8×Q8C2×D6111yescharacteristic
335#442—1221no—
336#440—1221no—
337C4×Q16—1221no—
338C4×SD16—1221no—
339C8×D4—21no—
340C8×D4—21no—
341C8×D4C2×D6111yescharacteristic
342C8×D4C2×D6111yescharacteristic
343#432—611no—
344#431—21no—
345#431—611no—
346#431C2×D6111yescharacteristic
347C2×C4⋊C8—21no—
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#332—611no—
358#332—611no—
359#331—611no—
360#331—611no—
361C61#1941311yescharacteristic, complemented, Sylow
362C2×#41—1221no—
363C2×#41D24411yescharacteristic
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—21no—
374C22×C8—21no—
375C4⋊Q8—611no—
376C4⋊Q8—611no—
377C4⋊Q8—611no—
378#127—611no—
379#125—1221no—
380#124—1221no—
381C22⋊Q8—1221no—
382C22⋊Q8—1221no—
383#121—1221no—
384#121—1221no—
385C4×Q8—1221no—
386C4×Q8—1221no—
387C4×Q8D24411yescharacteristic
388C4×Q8C22×D6111yescharacteristic
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—1221no—
392C4×D4—1221no—
393C4×D4D24411yescharacteristic
394C4×D4C22×D6111yescharacteristic
395#117—21no—
396#117—1221no—
397#117D24411yescharacteristic
398C2×C42—21no—
399C2×C42C22×D6111yescharacteristic
400#107—1221no—
401#107—1221no—
402#106—1221no—
403#106—1221no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8—611no—
408C4⋊C8—611no—
409C4⋊C8—611no—
410C4⋊C8—611no—
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—21no—
429C22⋊C8—1221no—
430C22⋊C8—1221no—
431C22⋊C8C22⋊D6111yescharacteristic
432C22⋊C8C22⋊D6111yescharacteristic
433#97—1221no—
434C4×C8—21no—
435C4×C8—21no—
436C4×C8—1221no—
437C4×C8C22×D6111yescharacteristic
438C4×C8C22×D6111yescharacteristic
439#41—22no—
440#41—22no—
441#41—4881no—
442#41—4881no—
443C2×Q8—1221no—
444C2×Q8—1221no—
445C2×Q8—1221no—
446C2×Q8C2×D24411yescharacteristic
447C2×D4—21no—
448C2×D4—1221no—
449C2×D4—1221no—
450C2×D4—1221no—
451C2×D4—2441no—
452C2×D4C2×D24411yescharacteristic
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—2441no—
457C22×C4C2×D24411yescharacteristic
458C22×C4#1175822211yescharacteristic
459C22×C4C2×C22⋊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—81no—
471C2×C8—81no—
472C2×C8—81no—
473C2×C8—1221no—
474C2×C8—1221no—
475C2×C8—1221no—
476C2×C8—1221no—
477C2×C8C2×C22⋊D6111yescharacteristic
478C2×C8C2×C22⋊D6111yescharacteristic
479C2×C8C2×C22⋊D6111yescharacteristic
480C2×C8C2×C22⋊D6111yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—2441no—
490C4⋊C4—2441no—
491C4⋊C4C2×D24411yescharacteristic
492C4⋊C4C2×D24411yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—2441no—
497C22⋊C4—2441no—
498C22⋊C4—2441no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—2441no—
503C42C2×D24411yescharacteristic
504C42#1175822211yescharacteristic
505C42C2×C22⋊D6111yescharacteristic
506C42C23×D6111yescharacteristic
507C23—21no—
508C23—2441no—
509C23#1451975111yescharacteristic
510Q8—21no—
511Q8—2441no—
512Q8—2441no—
513Q8—2441no—
514Q8—2441no—
515Q8—2441no—
516Q8—2441no—
517Q8#1451979912yes—
518D4—24no—
519D4—21no—
520D4—4881no—
521D4—4882no—
522D4—2441no—
523D4—2441no—
524D4—2441no—
525D4—2441no—
526D4#1451979912yes—
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—81no—
539C2×C4—4882no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4#1451975111yescharacteristic
544C2×C4#1451975111yescharacteristic
545C2×C4#1451975111yescharacteristic
546C2×C4C22×C22⋊D6111yescharacteristic
547C2×C4C22×D24411yescharacteristic
548C2×C4C2×#1175822211yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—21no—
553C8—41no—
554C8—41no—
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×#1451975111yescharacteristic
569C4—21no—
570C4—22no—
571C4—21no—
572C4—21no—
573C4—21no—
574C4—41no—
575C4—41no—
576C4—4881no—
577C4—4881no—
578C4—4881no—
579C4C2×#1451979911yescharacteristic
580C4C2×#1451979911yescharacteristic
581C4#1684056511yescharacteristic
582C4#1684057011yescharacteristic
583C2—41no—
584C2—42no—
585C2—9761no—
586C2#2145535811yescharacteristic
587C2#2145540011yescharacteristic
588C2#2145555611yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#2988C2
socleC22×C61C2×#121
prime radical#21455970C2
hypercenter#2988D61
hypocenterC61#19413
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2988

Complements

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

NH ≅ G/Ntype
1. #21456777C2semidirect
3. #21455890C2semidirect
4. #21445263C2semidirect
5. #21445256C2semidirect
6. #21445249C2semidirect
7. #21445242C2semidirect
8. #21445189C2semidirect
9. #21445184C2semidirect
10. #21445167C2semidirect
11. #21445160C2semidirect
12. #21444599C2semidirect
13. #21444517C2semidirect
14. #21444469C2semidirect
15. C61×#2988C2semidirect
292. #2988D61semidirect
361. C61#19413semidirect

Maximal subgroups

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

subgroupindex
#214567772
#214559702
#214558902
#214452632
#214452562
#214452492
#214452422
#214451892
#214451842
#214451672
#214451602
#214445992
#214445172
#214444692
C61×#29882
#1941361