Finite Group Databasebeta

← #29663999

Subgroups — #29663999

Order 15616.

630 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455975C211yesmaximal, characteristic, complemented
2#21455964C211yesmaximal, characteristic
3C8×#11758222C211yesmaximal, characteristic, complemented
4#21445274C211yesmaximal, characteristic, complemented
5#21445267C211yesmaximal, characteristic, complemented
6#21445260C211yesmaximal, characteristic, complemented
7#21445253C211yesmaximal, characteristic, complemented
8#21445246C211yesmaximal, characteristic, complemented
9#21445239C211yesmaximal, characteristic, complemented
10#21445232C211yesmaximal, characteristic, complemented
11#21445225C211yesmaximal, characteristic, complemented
12#21444582C211yesmaximal, characteristic, complemented
13#21444529C211yesmaximal, characteristic, complemented
14#21444524C211yesmaximal, characteristic, complemented
15C61×#3131C211yesmaximal, characteristic, complemented
16C4×#11758222C2211yescharacteristic
17#16840100—21no—
18#16840083—21no—
19#16840054C2211yescharacteristic
20#16840049C2211yescharacteristic
21#16840044C2211yescharacteristic
22#16840039C2211yescharacteristic
23#16839969C2211yescharacteristic
24#16839964C2211yescharacteristic
25#16839959C2211yescharacteristic
26#16839954C2211yescharacteristic
27#16839922—21no—
28#16839905—21no—
29C8×Dic122C2211yescharacteristic
30C8×Dic122C2211yescharacteristic
31#16839872—21no—
32#16839867—21no—
33#16839862—21no—
34#16839860—21no—
35C8×D244C2211yescharacteristic
36C8×D244C2211yescharacteristic
37C8×C22⋊D61—21no—
38C8×C22⋊D61—21no—
39#16839819C2211yescharacteristic
40#16839819C2211yescharacteristic
41#16839815C2211yescharacteristic
42#16839813—21no—
43C4×C8×D61—21no—
44#16839515C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839513C2211yescharacteristic
48#16839511C2211yescharacteristic
49#16839511C2211yescharacteristic
50#16839508C2211yescharacteristic
51#16839508C2211yescharacteristic
52#16839508C2211yescharacteristic
53#16839508C2211yescharacteristic
54#16839506C2211yescharacteristic
55#16839506C2211yescharacteristic
56C61×#533C2211yescharacteristic
57C61×#532C2211yescharacteristic
58C61×#488—21no—
59C61×#488—21no—
60C61×#487C2211yescharacteristic
61C61×#487C2211yescharacteristic
62C61×#486C2211yescharacteristic
63C61×#486C2211yescharacteristic
64C61×#416—21no—
65C61×#416—21no—
66C2×C4×C8×C61C2211yescharacteristic
67C2×#11758222D411yescharacteristic
68C2×#11758202—21no—
69C2×#11758200—21no—
70C2×#11758201—21no—
71C2×#11758199—21no—
72C2×C8×D61—21no—
73C2×C8×D61—21no—
74C4×Dic122D411yescharacteristic
75C4×Dic122C2311yescharacteristic
76C4×D244D411yescharacteristic
77C4×D244C2311yescharacteristic
78C4×C22⋊D61—21no—
79C4×C22⋊D61—21no—
80#14519736D411yescharacteristic
81#14519734—21no—
82C42×D61—21no—
83#14519710—21no—
84#14519710—21no—
85#14519708—21no—
86#14519708—21no—
87C4⋊#92418C2311yescharacteristic
88C4⋊#92418C2311yescharacteristic
89C4⋊#92418C2311yescharacteristic
90C4⋊#92418C2311yescharacteristic
91C4⋊#92418C2311yescharacteristic
92C4⋊#92418C2311yescharacteristic
93#14519706—21no—
94#14519706—21no—
95#14519701—21no—
96#14519701—21no—
97#14519700—21no—
98#14519700—21no—
99#14519698—21no—
100#14519698—21no—
101#14519697—21no—
102#14519697—21no—
103C22⋊#92418—21no—
104C22⋊#92418—21no—
105C22⋊#92418—21no—
106#14519689—21no—
107#14519689—21no—
108#14519688—21no—
109#14519688—21no—
110C4×#92418—21no—
111C8×Dic61—21no—
112C8×Dic61—21no—
113C2×#41×C61—21no—
114C22×C8×C61D411yescharacteristic
115C22×C8×C61D411yescharacteristic
116C4⋊Q8×C61C2311yescharacteristic
117C4⋊Q8×C61C2311yescharacteristic
118C4⋊Q8×C61C2311yescharacteristic
119#127×C61C2311yescharacteristic
120#125×C61—21no—
121#124×C61—21no—
122C22⋊Q8×C61—21no—
123C22⋊Q8×C61—21no—
124#121×C61—21no—
125#121×C61—21no—
126C4×Q8×C61—21no—
127C4×Q8×C61—21no—
128C4×D4×C61—21no—
129C4×D4×C61—21no—
130#117×C61—21no—
131C2×C42×C61C2311yescharacteristic
132#103×C61—21no—
133#103×C61—21no—
134#103×C61—21no—
135#103×C61—21no—
136#102×C61—21no—
137#102×C61—21no—
138#102×C61—21no—
139#102×C61—21no—
140C4×C8×C61D411yescharacteristic
141C4×C8×C61D411yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144#41×C61—42no—
145#41×C61—42no—
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
165C2×C8×C61—41no—
166C2×C8×C61—41no—
167C2×C8×C61C2×D411yescharacteristic
168C2×C8×C61C2×D411yescharacteristic
169C2×C8×C61C2×D411yescharacteristic
170C2×C8×C61C2×D411yescharacteristic
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—41no—
178C4⋊C4×C61—41no—
179C22⋊C4×C61—41no—
180C22⋊C4×C61—41no—
181C22⋊C4×C61—41no—
182C42×C61—41no—
183C42×C61C2×D411yescharacteristic
184C42×C61C2×D411yescharacteristic
185C42×C61#4111yescharacteristic
186C42×C61C2411yescharacteristic
187C22⋊Dic61—21no—
188#11758202—42no—
189#11758201—42no—
190#11758200—42no—
191#11758199—42no—
192#11758198—21no—
193#11758198—21no—
194C4⋊Dic61C2×D411yescharacteristic
195C4⋊Dic61C2×D411yescharacteristic
196#11758196—21no—
197#11758196—21no—
198C4×Dic61—21no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C8×D61—42no—
208C8×D61—42no—
209C23×C61—41no—
210C23×C61#12111yescharacteristic
211C22×D61—21no—
212Q8×C61—41no—
213Q8×C61—41no—
214Q8×C61—41no—
215Q8×C61—41no—
216Q8×C61—81no—
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—41no—
230C2×C4×C61—41no—
231C2×C4×C61—82no—
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—24no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242D244—21no—
243D244#13512yes—
244C4×D61—24no—
245C4×D61—42no—
246C4×D61—41no—
247C4×D61—41no—
248Dic122—21no—
249Dic122#13512yes—
250C8×C61—21no—
251C8×C61—21no—
252C8×C61—21no—
253C8×C61—21no—
254#92418—41no—
255#92418—41no—
256#92418—41no—
257#92418—41no—
258#92418—41no—
259#92418—41no—
260#19278—611nomaximal, Sylow
261C22×C61—21no—
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—81no—
265C22×C61—81no—
266C22×C61—81no—
267C22×C61C2×#12111yescharacteristic
268C2×D61—22no—
269C2×D61—41no—
270C2×D61—41no—
271C4×C61—21no—
272C4×C61—21no—
273C4×C61—21no—
274C4×C61—21no—
275C4×C61—81no—
276C4×C61—81no—
277C4×C61—81no—
278C4×C61C2×#13511yescharacteristic
279C4×C61C2×#13511yescharacteristic
280C4×C61#57511yescharacteristic
281C4×C61#57511yescharacteristic
282Dic61—22no—
283Dic61—41no—
284Dic61—41no—
285#3131D6111yescharacteristic, complemented
286#3116—611no—
287#3115—611no—
288C8×#41—611no—
289#1684—611no—
290#1683—611no—
291#1682—611no—
292#1681—611no—
293#1680—611no—
294#1679—611no—
295#1678—611no—
296#1677—611no—
297#1568—611no—
298#1554—611no—
299#1553—611no—
300C2×C61—41no—
301C2×C61—161no—
302C2×C61#304011yescharacteristic
303C2×C61#305011yescharacteristic
304C2×C61#306711yescharacteristic
305D61—42no—
306#533C2×D6111yescharacteristic
307#532C2×D6111yescharacteristic
308C4×#41—611no—
309#488—21no—
310#488—21no—
311#487C2×D6111yescharacteristic
312#487C2×D6111yescharacteristic
313#486C2×D6111yescharacteristic
314#486C2×D6111yescharacteristic
315#485—1221no—
316#482—1221no—
317#477—611no—
318#476—611no—
319#475—611no—
320#474—611no—
321#462—611no—
322#461—611no—
323#460—611no—
324#459—611no—
325#452—1221no—
326#449—1221no—
327C8×Q8—611no—
328C8×Q8—611no—
329#442—1221no—
330#441—1221no—
331#440—1221no—
332#440—1221no—
333C8×D4—611no—
334C8×D4—611no—
335C8×D4—1221no—
336C8×D4—1221no—
337#432—611no—
338#432—611no—
339#431—611no—
340#431—1221no—
341#416—21no—
342#416—21no—
343C2×C4×C8—1221no—
344C2×C4×C8C2×D6111yescharacteristic
345#335—611no—
346#335—611no—
347#334—611no—
348#334—611no—
349#333—611no—
350#333—611no—
351#332—611no—
352#332—611no—
353#332—611no—
354#332—611no—
355#331—611no—
356#331—611no—
357C61#1927811yescharacteristic, complemented, Sylow
358C2×#41—21no—
359C2×#41—611no—
360C2×Q16—1221no—
361C2×SD16—1221no—
362C2×SD16—1221no—
363C2×D8—1221no—
364C22×C8—1221no—
365C22×C8—1221no—
366C22×C8C22⋊D6111yescharacteristic
367C22×C8C22⋊D6111yescharacteristic
368C4⋊Q8C22×D6111yescharacteristic
369C4⋊Q8C22×D6111yescharacteristic
370C4⋊Q8C22×D6111yescharacteristic
371#127C22×D6111yescharacteristic
372#125—21no—
373#124—21no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376#121—21no—
377#121—21no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8—611no—
381C4×Q8—611no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—611no—
385C4×D4—611no—
386C4×D4—1221no—
387C4×D4—1221no—
388#117—21no—
389#117—611no—
390#117—1221no—
391C2×C42—1221no—
392C2×C42C22×D6111yescharacteristic
393#107—1221no—
394#107—1221no—
395#106—1221no—
396#106—1221no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—611no—
400C4⋊C8—611no—
401C4⋊C8—611no—
402C4⋊C8—611no—
403C4⋊C8—1221no—
404C4⋊C8—1221no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—1221no—
410#103—1221no—
411#103—1221no—
412#103—1221no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—1221no—
418#102—1221no—
419#102—1221no—
420#102—1221no—
421C22⋊C8—1221no—
422C22⋊C8—1221no—
423C22⋊C8—1221no—
424C22⋊C8—1221no—
425C22⋊C8—1221no—
426#97—1221no—
427#97—1221no—
428C4×C8—1221no—
429C4×C8—1221no—
430C4×C8—1221no—
431C4×C8C22⋊D6111yescharacteristic
432C4×C8C22⋊D6111yescharacteristic
433C4×C8C22×D6111yescharacteristic
434C4×C8C22×D6111yescharacteristic
435#41—42no—
436#41—42no—
437#41—1222no—
438#41—1222no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—611no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—41no—
447C2×D4—611no—
448C2×D4—1221no—
449C22×C4—41no—
450C22×C4—1221no—
451C22×C4—1221no—
452C22×C4—1221no—
453C22×C4D4×D6111yescharacteristic
454C22×C4#1175822411yescharacteristic
455C22×C4C2×C22⋊D6111yescharacteristic
456Q16—2442no—
457SD16—2442no—
458SD16—2442no—
459D8—2442no—
460C2×C8—41no—
461C2×C8—41no—
462C2×C8—1221no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—2442no—
469C2×C8—2442no—
470C2×C8C2×C22⋊D6111yescharacteristic
471C2×C8C2×C22⋊D6111yescharacteristic
472C2×C8C2×C22⋊D6111yescharacteristic
473C2×C8C2×C22⋊D6111yescharacteristic
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4—611no—
483C4⋊C4—611no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—1221no—
490C22⋊C4—1221no—
491C22⋊C4—1221no—
492C42—41no—
493C42—1221no—
494C42—1221no—
495C42—1221no—
496C42D4×D6111yescharacteristic
497C42#1175822411yescharacteristic
498C42C2×C22⋊D6111yescharacteristic
499C42C23×D6111yescharacteristic
500C23—41no—
501C23—1221no—
502C23#1451974811yescharacteristic
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—81no—
508Q8—612no—
509Q8—1221no—
510D4—41no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—81no—
515D4—82no—
516D4—612no—
517D4—1224no—
518D4—1221no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—82no—
528C2×C4—1224no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—2442no—
533C2×C4—2441no—
534C2×C4—2441no—
535C2×C4#1451974811yescharacteristic
536C2×C4#1451974811yescharacteristic
537C2×C4#1451974811yescharacteristic
538C2×C4C2×D4×D6111yescharacteristic
539C2×C4C22×C22⋊D6111yescharacteristic
540C2×C4C2×#1175822411yescharacteristic
541C8—21no—
542C8—21no—
543C8—21no—
544C8—21no—
545C8—2441no—
546C8—2441no—
547C8—2441no—
548C8—2441no—
549C8—2441no—
550C8—2441no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—1222no—
558C22—2441no—
559C22—2441no—
560C22C2×#1451974811yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—81no—
566C4—81no—
567C4—81no—
568C4—1222no—
569C4—2441no—
570C4—2441no—
571C4#135×D6111yescharacteristic
572C4#135×D6111yescharacteristic
573C4#1684056011yescharacteristic
574C4#1684056011yescharacteristic
575C2—41no—
576C2—161no—
577C2—2442no—
578C2#2145530911yescharacteristic
579C2#2145539611yescharacteristic
580C2#2145553511yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3131C2
socleC22×C61C2×#121
prime radical#21455964C2
hypercenter#3131D61
hypocenterC61#19278
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3131

Complements

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

NH ≅ G/Ntype
1. #21455975C2semidirect
3. C8×#11758222C2semidirect
4. #21445274C2semidirect
5. #21445267C2semidirect
6. #21445260C2semidirect
7. #21445253C2semidirect
8. #21445246C2semidirect
9. #21445239C2semidirect
10. #21445232C2semidirect
11. #21445225C2semidirect
12. #21444582C2semidirect
13. #21444529C2semidirect
14. #21444524C2semidirect
15. C61×#3131C2semidirect
285. #3131D61semidirect
357. C61#19278semidirect

Maximal subgroups

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

subgroupindex
#214559752
#214559642
C8×#117582222
#214452742
#214452672
#214452602
#214452532
#214452462
#214452392
#214452322
#214452252
#214445822
#214445292
#214445242
C61×#31312
#1927861