Finite Group Databasebeta

← #29670644

Subgroups — #29670644

Order 15616.

610 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458827C211yesmaximal, characteristic, complemented
2#21458477C211yesmaximal, characteristic, complemented
3#21457695C211yesmaximal, characteristic, complemented
4#21445455C211yesmaximal, characteristic, complemented
5#21445359C211yesmaximal, characteristic, complemented
6#21445275C211yesmaximal, characteristic, complemented
7#21445260C211yesmaximal, characteristic, complemented
8#21445172C211yesmaximal, characteristic
9#21445004C211yesmaximal, characteristic, complemented
10#21444940C211yesmaximal, characteristic, complemented
11#21444922C211yesmaximal, characteristic, complemented
12#21444889C211yesmaximal, characteristic, complemented
13#21444667C211yesmaximal, characteristic, complemented
14SD16⋊#92418C211yesmaximal, characteristic, complemented
15C61×#3373C211yesmaximal, characteristic, complemented
16#16840497C2211yescharacteristic
17#16840469C2211yescharacteristic
18#16840144—21no—
19#16840138C2211yescharacteristic
20#16840134C2211yescharacteristic
21#16840118—21no—
22#16840112C2211yescharacteristic
23#16840110C2211yescharacteristic
24#16840109C2211yescharacteristic
25#16840095—21no—
26#16840061—21no—
27#16840057C2211yescharacteristic
28#16840057C2211yescharacteristic
29#16840001—21no—
30#16839979—21no—
31#16839977—21no—
32#16839974—21no—
33#16839969C2211yescharacteristic
34#16839962C2211yescharacteristic
35#16839959C2211yescharacteristic
36#16839957C2211yescharacteristic
37#16839918—21no—
38Q8×#92418C2211yescharacteristic
39C8×Dic122C2211yescharacteristic
40C4×#11758202C2211yescharacteristic
41C4×#11758199—21no—
42#16839842—21no—
43D4×#92418C2211yescharacteristic
44C2×#14519701—21no—
45#16839515C2211yescharacteristic
46#16839514C2211yescharacteristic
47#16839510C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839506C2211yescharacteristic
50#16839505C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53#16839492C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55#16839483C2211yescharacteristic
56C61×#559C2211yescharacteristic
57D4×Q8×C61C2211yescharacteristic
58C61×#489—21no—
59C61×#486C2211yescharacteristic
60C61×#476—21no—
61C61×#475C2211yescharacteristic
62C61×#463—21no—
63C61×#459C2211yescharacteristic
64C61×#446C2211yescharacteristic
65C61×#442—21no—
66C4×SD16×C61C2211yescharacteristic
67C2×#11758202—21no—
68C2×#11758202D411yescharacteristic
69C2×#11758200—21no—
70C2×#11758200—41no—
71C2×#11758201—21no—
72C2×#11758199—21no—
73C2×#11758199—21no—
74C2×#11758199—21no—
75C22×#92418—21no—
76#14519777C2311yescharacteristic
77#14519774C2311yescharacteristic
78#14519768—21no—
79#14519766—21no—
80#14519765—21no—
81#14519762—41no—
82#14519756—21no—
83#14519754—41no—
84C4×Dic122C2311yescharacteristic
85C4×D244—21no—
86D4×Dic61—21no—
87#14519739—21no—
88C2×C4⋊Dic61—21no—
89#14519710—21no—
90#14519710—21no—
91#14519710D411yescharacteristic
92C4⋊#92418—21no—
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96#14519706—21no—
97#14519701—21no—
98#14519701—21no—
99#14519701—21no—
100#14519701—21no—
101#14519701—21no—
102#14519701D411yescharacteristic
103#14519700D411yescharacteristic
104#14519699—21no—
105#14519699—21no—
106#14519698—21no—
107#14519697—21no—
108#14519697—21no—
109#14519697—41no—
110C22⋊#92418—21no—
111C4×#92418—21no—
112C4×#92418C2311yescharacteristic
113C4×#92418C2311yescharacteristic
114C8×Dic61—21no—
115C22×Q8×C61—21no—
116C2×SD16×C61D411yescharacteristic
117C2×D8×C61—21no—
118C4⋊Q8×C61—21no—
119C4⋊Q8×C61C2311yescharacteristic
120#127×C61C2311yescharacteristic
121#124×C61—21no—
122#124×C61—21no—
123#123×C61—41no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—41no—
126C4×Q8×C61C2311yescharacteristic
127C4×Q8×C61C2311yescharacteristic
128C4×D4×C61—21no—
129C4×D4×C61—21no—
130C4×D4×C61—21no—
131C4×D4×C61C2311yescharacteristic
132#106×C61—21no—
133#106×C61D411yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136#103×C61—21no—
137#103×C61D411yescharacteristic
138#102×C61—21no—
139#102×C61—21no—
140#102×C61—21no—
141#102×C61D411yescharacteristic
142#97×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—41no—
146C2×Q8×C61—42no—
147C2×Q8×C61—81no—
148C2×Q8×C61C2×D411yescharacteristic
149C2×Q8×C61C2×D411yescharacteristic
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61C2×D411yescharacteristic
154C22×C4×C61—21no—
155C22×C4×C61—41no—
156C22×C4×C61—41no—
157C22×Dic61—41no—
158C2×D244—21no—
159C2×D244—21no—
160C2×D244—21no—
161C2×C4×D61—41no—
162C2×Dic122—21no—
163C2×Dic122C2×D411yescharacteristic
164SD16×C61—22no—
165D8×C61—42no—
166C2×C8×C61—21no—
167C2×C8×C61C2×D411yescharacteristic
168C2×C8×C61C2×D411yescharacteristic
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—41no—
174C4⋊C4×C61C2×D411yescharacteristic
175C4⋊C4×C61C2×D411yescharacteristic
176C4⋊C4×C61C2×D411yescharacteristic
177C22⋊C4×C61—21no—
178C22⋊C4×C61—41no—
179C22⋊C4×C61—41no—
180C22⋊C4×C61—41no—
181C22⋊C4×C61—41no—
182C42×C61—21no—
183C42×C61—21no—
184C42×C61C2411yescharacteristic
185C22⋊Dic61—41no—
186#11758202—41no—
187#11758202—81no—
188#11758201—81no—
189#11758200—81no—
190#11758200—82no—
191#11758199—42no—
192#11758199—42no—
193#11758199—81no—
194#11758198—41no—
195#11758198—41no—
196#11758198—41no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—41no—
200C4⋊Dic61C2×D411yescharacteristic
201#11758196—21no—
202#11758196—41no—
203C4×Dic61—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—81no—
209C2×#92418C2×D411yescharacteristic
210C2×#92418C2×D411yescharacteristic
211C23×C61—21no—
212C23×C61—41no—
213C22×D61—41no—
214Q8×C61—21no—
215Q8×C61—21no—
216Q8×C61—21no—
217Q8×C61—21no—
218Q8×C61—41no—
219Q8×C61—41no—
220Q8×C61—82no—
221D4×C61—21no—
222D4×C61—41no—
223D4×C61—41no—
224D4×C61—41no—
225D4×C61—41no—
226D4×C61—81no—
227D4×C61#13512yes—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—82no—
237C2×C4×C61—161no—
238C2×C4×C61C22×D411yescharacteristic
239C2×C4×C61C22×D411yescharacteristic
240C2×C4×C61H(5,𝔽2)11yescharacteristic
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—41no—
244C2×Dic61—161no—
245D244—41no—
246D244—41no—
247D244—41no—
248D244—41no—
249D244—81no—
250C4×D61—161no—
251Dic122—21no—
252Dic122—21no—
253Dic122—81no—
254C8×C61—21no—
255C8×C61—21no—
256C8×C61—41no—
257#92418—21no—
258#92418—21no—
259#92418—41no—
260#92418—41no—
261#92418—41no—
262#92418—41no—
263#19841—611nomaximal, Sylow
264C22×C61—22no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61—81no—
268C22×C61—81no—
269C22×C61—81no—
270C22×C61D4211yescharacteristic
271C2×D61—81no—
272C2×D61—81no—
273C2×D61—81no—
274C4×C61—21no—
275C4×C61—41no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61—41no—
279C4×C61—41no—
280C4×C61—81no—
281C4×C61C2×#13511yescharacteristic
282C4×C61#57511yescharacteristic
283C4×C61#57611yescharacteristic
284C4×C61#57811yescharacteristic
285Dic61—41no—
286Dic61—41no—
287Dic61—81no—
288#3396—611no—
289#3373D6111yescharacteristic, complemented
290#3361—611no—
291#3299—611no—
292#1717—611no—
293#1698—611no—
294#1684—611no—
295#1682—611no—
296#1667—611no—
297#1640—611no—
298#1630—611no—
299#1627—611no—
300#1622—611no—
301#1584—611no—
302SD16⋊C8—611no—
303C2×C61—42no—
304C2×C61—161no—
305C2×C61#326811yescharacteristic
306C2×C61#328511yescharacteristic
307C2×C61#328811yescharacteristic
308D61—161no—
309#559—611no—
310#559C2×D6111yescharacteristic
311#554—611no—
312D4×Q8C2×D6111yescharacteristic
313#495—1221no—
314#493—611no—
315#492—611no—
316#489—21no—
317#488—1221no—
318#487—611no—
319#486—611no—
320#486—611no—
321#486C2×D6111yescharacteristic
322#484—1221no—
323#478—1221no—
324#477—611no—
325#477—611no—
326#476—21no—
327#475C2×D6111yescharacteristic
328#467—1221no—
329#463—21no—
330#463—1221no—
331#463—1221no—
332#463—1221no—
333#462—611no—
334#460—611no—
335#460—611no—
336#459—611no—
337#459C2×D6111yescharacteristic
338#451—1221no—
339#446C2×D6111yescharacteristic
340C8×Q8—611no—
341C8×Q8—611no—
342#442—21no—
343C4×Q16—611no—
344C4×SD16C2×D6111yescharacteristic
345C4×D8—1221no—
346C4×D8—1221no—
347C8×D4—611no—
348C2×#103—1221no—
349#335—611no—
350#335—611no—
351#333—611no—
352#332—611no—
353#331—611no—
354#331—611no—
355Q8⋊C8—611no—
356Q8⋊C8—611no—
357Q8⋊C8—611no—
358D4⋊C8—611no—
359#322—611no—
360C61#1984111yescharacteristic, complemented, Sylow
361C22×Q8—21no—
362C2×Q16—611no—
363C2×Q16—1221no—
364C2×SD16—1221no—
365C2×SD16—1221no—
366C2×SD16—2441no—
367C2×SD16C22⋊D6111yescharacteristic
368C2×D8—21no—
369C2×D8—1221no—
370C2×D8—1221no—
371C2×D8—1221no—
372C22×C8—1221no—
373C4⋊Q8—21no—
374C4⋊Q8—611no—
375C4⋊Q8C22×D6111yescharacteristic
376#127—611no—
377#127C22×D6111yescharacteristic
378#125—1221no—
379#124—21no—
380#124—21no—
381#124—1221no—
382#124—1221no—
383#123—41no—
384#123—2441no—
385C22⋊Q8—21no—
386C22⋊Q8—41no—
387C22⋊Q8—1221no—
388C22⋊Q8—2441no—
389C4×Q8—611no—
390C4×Q8C22×D6111yescharacteristic
391C4×Q8C22×D6111yescharacteristic
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—1221no—
396C4×D4—1221no—
397C4×D4—1221no—
398C4×D4C22×D6111yescharacteristic
399C2×C4⋊C4—1221no—
400#107—611no—
401#107—1221no—
402#107—1221no—
403#106—21no—
404#106C22⋊D6111yescharacteristic
405C4⋊C8—21no—
406C4⋊C8—611no—
407C4⋊C8—611no—
408C4⋊C8—611no—
409C4⋊C8—1221no—
410C4⋊C8—1221no—
411C4⋊C8C22×D6111yescharacteristic
412#103—21no—
413#103—611no—
414#103—611no—
415#103—1221no—
416#103—1221no—
417#103—1221no—
418#103—1221no—
419#103—1221no—
420#103C22⋊D6111yescharacteristic
421#102—21no—
422#102—21no—
423#102—21no—
424#102—1221no—
425#102—1221no—
426#102—1221no—
427#102—1221no—
428#102—1221no—
429#102—2441no—
430#102C22⋊D6111yescharacteristic
431C22⋊C8—1221no—
432#97—21no—
433C4×C8—611no—
434C4×C8—611no—
435C4×C8—1221no—
436C4×C8—1221no—
437C4×C8C22×D6111yescharacteristic
438C2×Q8—21no—
439C2×Q8—41no—
440C2×Q8—42no—
441C2×Q8—81no—
442C2×Q8—611no—
443C2×Q8—1221no—
444C2×Q8D4×D6111yescharacteristic
445C2×Q8C2×C22⋊D6111yescharacteristic
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—1221no—
450C2×D4—1221no—
451C2×D4—1221no—
452C2×D4C2×C22⋊D6111yescharacteristic
453C22×C4—21no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—2441no—
457C22×C4—2441no—
458Q16—4881no—
459Q16—2441no—
460SD16—22no—
461SD16—4881no—
462SD16—4882no—
463SD16—4881no—
464D8—42no—
465D8—4881no—
466D8—2442no—
467D8—2442no—
468C2×C8—21no—
469C2×C8—611no—
470C2×C8—611no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8—1221no—
474C2×C8—1221no—
475C2×C8—4881no—
476C2×C8C2×C22⋊D6111yescharacteristic
477C2×C8C2×C22⋊D6111yescharacteristic
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—41no—
483C4⋊C4—611no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—2441no—
488C4⋊C4—2441no—
489C4⋊C4D4×D6111yescharacteristic
490C4⋊C4C2×C22⋊D6111yescharacteristic
491C4⋊C4C2×C22⋊D6111yescharacteristic
492C22⋊C4—21no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—2441no—
498C22⋊C4—2441no—
499C22⋊C4—2441no—
500C22⋊C4—2441no—
501C42—21no—
502C42—21no—
503C42—1221no—
504C42C23×D6111yescharacteristic
505C23—21no—
506C23—41no—
507C23—2441no—
508Q8—21no—
509Q8—21no—
510Q8—21no—
511Q8—21no—
512Q8—41no—
513Q8—41no—
514Q8—82no—
515Q8—1221no—
516Q8—1221no—
517Q8—4881no—
518D4—21no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—81no—
524D4—4881no—
525D4—2441no—
526D4—2441no—
527D4—2441no—
528D4—2441no—
529D4#1451979712yes—
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—82no—
539C2×C4—161no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—9761no—
543C2×C4—9761no—
544C2×C4—2441no—
545C2×C4C2×D4×D6111yescharacteristic
546C2×C4C22×C22⋊D6111yescharacteristic
547C2×C4#1451982211yescharacteristic
548C8—21no—
549C8—21no—
550C8—41no—
551C8—1221no—
552C8—1221no—
553C8—2441no—
554C8—2441no—
555C8—2441no—
556C8—2441no—
557C22—22no—
558C22—41no—
559C22—41no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—4881no—
564C22—4881no—
565C22—4881no—
566C22D4×C22⋊D6111yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—81no—
574C4—4881no—
575C4—2441no—
576C4—2441no—
577C4C2×#1451979711yescharacteristic
578C4#1684055811yescharacteristic
579C4#1684056611yescharacteristic
580C4#1684057711yescharacteristic
581C2—42no—
582C2—161no—
583C2—9761no—
584C2#2145735311yescharacteristic
585C2#2145755611yescharacteristic
586C2#2145758111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3373C2
socleC22×C61D42
prime radical#21445172C2
hypercenter#3373D61
hypocenterC61#19841
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3373

Complements

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

NH ≅ G/Ntype
1. #21458827C2semidirect
2. #21458477C2semidirect
3. #21457695C2semidirect
4. #21445455C2semidirect
5. #21445359C2semidirect
6. #21445275C2semidirect
7. #21445260C2semidirect
9. #21445004C2semidirect
10. #21444940C2semidirect
11. #21444922C2semidirect
12. #21444889C2semidirect
13. #21444667C2semidirect
14. SD16⋊#92418C2semidirect
15. C61×#3373C2semidirect
289. #3373D61semidirect
360. C61#19841semidirect

Maximal subgroups

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

subgroupindex
#214588272
#214584772
#214576952
#214454552
#214453592
#214452752
#214452602
#214451722
#214450042
#214449402
#214449222
#214448892
#214446672
SD16⋊#924182
C61×#33732
#1984161