Finite Group Databasebeta

← #29676878

Subgroups — #29676878

Order 15616.

616 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#21458559C211yesmaximal, characteristic, complemented
2#21458052C211yesmaximal, characteristic
3#21458044C211yesmaximal, characteristic
4#21445422C211yesmaximal, characteristic, complemented
5#21445396C211yesmaximal, characteristic, complemented
6#21445391C211yesmaximal, characteristic, complemented
7#21445389C211yesmaximal, characteristic, complemented
8#21445387C211yesmaximal, characteristic, complemented
9#21445089C211yesmaximal, characteristic, complemented
10#21445087C211yesmaximal, characteristic, complemented
11#21444934C211yesmaximal, characteristic
12#21444897C211yesmaximal, characteristic, complemented
13#21444710C211yesmaximal, characteristic, complemented
14#21444709C211yesmaximal, characteristic, complemented
15C61×#3369C211yesmaximal, characteristic, complemented
16#16840485C2211yescharacteristic
17D4×D244C2211yescharacteristic
18#16840158C2211yescharacteristic, complemented
19#16840136C2211yescharacteristic
20#16840124—21no—
21#16840114C2211yescharacteristic, complemented
22#16840110C2211yescharacteristic
23#16840109C2211yescharacteristic
24#16840088—21no—
25#16840086—21no—
26#16840049C2211yescharacteristic
27#16840044—21no—
28#16840042C2211yescharacteristic
29#16840039C2211yescharacteristic
30#16840011—21no—
31#16840010—21no—
32#16839984—21no—
33#16839972C2211yescharacteristic, complemented
34#16839962C2211yescharacteristic
35#16839962C2211yescharacteristic
36#16839912—21no—
37#16839911—21no—
38#16839893C2211yescharacteristic, complemented
39#16839867—21no—
40C4×#11758201C2211yescharacteristic
41#16839841C2211yescharacteristic
42#16839840C2211yescharacteristic
43#16839766—21no—
44#16839765—21no—
45#16839513C2211yescharacteristic, complemented
46#16839512C2211yescharacteristic, complemented
47#16839511C2211yescharacteristic, complemented
48#16839508C2211yescharacteristic, complemented
49#16839507C2211yescharacteristic, complemented
50#16839505C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic, complemented
52Q8⋊#92418C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55C8×#92418C2211yescharacteristic, complemented
56Q82×C61C2211yescharacteristic, complemented
57C61×#556C2211yescharacteristic
58C61×#489—21no—
59C61×#487C2211yescharacteristic, complemented
60C61×#476C2211yescharacteristic
61C61×#475—21no—
62C61×#464—21no—
63C61×#462C2211yescharacteristic, complemented
64C61×#446C2211yescharacteristic, complemented
65C61×#441—21no—
66C4×SD16×C61C2211yescharacteristic
67C22×D244—21no—
68C2×D4×D61—21no—
69C2×#11758202—21no—
70C2×#11758201—21no—
71C2×#11758201—21no—
72C2×#11758201—41no—
73C2×#11758201D411yescharacteristic
74C2×#11758194—21no—
75C2×#11758189—21no—
76#14519777C2311yescharacteristic
77#14519774C2311yescharacteristic
78#14519772—41no—
79#14519765—21no—
80#14519753—21no—
81#14519752—21no—
82#14519751—21no—
83#14519747—41no—
84C4×Dic122—21no—
85C4×D244C2311yescharacteristic
86#14519735—21no—
87#14519710—21no—
88#14519710—21no—
89#14519708—21no—
90#14519708—41no—
91#14519708D411yescharacteristic
92C4⋊#92418—21no—
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96#14519701D411yescharacteristic
97#14519700—21no—
98#14519700—21no—
99#14519700—21no—
100#14519699—21no—
101#14519699—21no—
102#14519698—21no—
103#14519697—21no—
104#14519697—21no—
105#14519697—21no—
106#14519697—21no—
107#14519697—21no—
108#14519697—21no—
109#14519697D411yescharacteristic
110C22⋊#92418—21no—
111#14519689—21no—
112#14519688—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×Q16×C61—21no—
116C2×SD16×C61D411yescharacteristic
117C4⋊Q8×C61—21no—
118C4⋊Q8×C61—21no—
119C4⋊Q8×C61—41no—
120C4⋊Q8×C61C2311yescharacteristic
121C4⋊Q8×C61C2311yescharacteristic
122#126×C61—41no—
123#124×C61—21no—
124C22⋊Q8×C61—21no—
125C4×Q8×C61—21no—
126C4×Q8×C61—21no—
127C4×Q8×C61—21no—
128C4×Q8×C61C2311yescharacteristic
129C4×Q8×C61C2311yescharacteristic
130C4×D4×C61C2311yescharacteristic
131#117×C61—21no—
132#106×C61—21no—
133#106×C61D411yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136#103×C61—21no—
137#103×C61—21no—
138#103×C61—21no—
139#103×C61D411yescharacteristic
140#102×C61—21no—
141#102×C61D411yescharacteristic
142#97×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C23×D61—41no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—41no—
148C2×Q8×C61C2×D411yescharacteristic
149C2×Q8×C61C2×D411yescharacteristic
150C2×D4×C61C2×D411yescharacteristic
151C22×C4×C61—21no—
152C2×C22⋊D61—41no—
153D4×D61—42no—
154D4×D61—81no—
155C2×D244—21no—
156C2×D244—21no—
157C2×D244—21no—
158C2×D244—42no—
159C2×D244—41no—
160C2×D244—81no—
161C2×D244C2×D411yescharacteristic
162C2×C4×D61—21no—
163C2×Dic122—21no—
164Q16×C61—42no—
165SD16×C61—41no—
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—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—41no—
176C4⋊C4×C61—41no—
177C4⋊C4×C61—41no—
178C4⋊C4×C61C2×D411yescharacteristic
179C4⋊C4×C61C2×D411yescharacteristic
180C4⋊C4×C61C2×D411yescharacteristic
181C22⋊C4×C61—21no—
182C22⋊C4×C61—41no—
183C22⋊C4×C61—41no—
184C42×C61—21no—
185C42×C61—21no—
186C42×C61—41no—
187C42×C61—41no—
188C42×C61C2411yescharacteristic
189#11758202—42no—
190#11758201—41no—
191#11758201—82no—
192#11758201—81no—
193#11758201—81no—
194#11758198—21no—
195#11758198—41no—
196#11758198—41no—
197#11758198—41no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61C2×D411yescharacteristic
201#11758196—41no—
202C4×Dic61—41no—
203#11758194—81no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418C2×D411yescharacteristic
209C2×#92418C2×D411yescharacteristic
210#11758189—81no—
211C23×C61—21no—
212C22×D61—21no—
213C22×D61—41no—
214C22×D61—82no—
215C22×D61—82no—
216C22×D61—161no—
217Q8×C61—21no—
218Q8×C61—21no—
219Q8×C61—21no—
220Q8×C61—21no—
221Q8×C61—41no—
222Q8×C61—41no—
223Q8×C61—81no—
224Q8×C61—161no—
225D4×C61—21no—
226D4×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×C61C22×D411yescharacteristic
237C2×C4×C61C22×D411yescharacteristic
238C2×C4×C61H(5,𝔽2)11yescharacteristic
239C22⋊D61—82no—
240C2×Dic61—21no—
241C2×Dic61—41no—
242D244—21no—
243D244—21no—
244D244—41no—
245D244—41no—
246D244—41no—
247D244—41no—
248D244—81no—
249D244—82no—
250C4×D61—41no—
251C4×D61—41no—
252Dic122—41no—
253Dic122—41no—
254C8×C61—21no—
255C8×C61—21no—
256C8×C61—41no—
257#92418—22no—
258#92418—21no—
259#92418—21no—
260#92418—41no—
261#92418—41no—
262#92418—41no—
263#20289—611nomaximal, Sylow
264C22×C61—41no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61D4211yescharacteristic
268C2×D61—41no—
269C2×D61—41no—
270C2×D61—41no—
271C2×D61—81no—
272C2×D61—81no—
273C2×D61—81no—
274C2×D61—164no—
275C4×C61—21no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61—41no—
279C4×C61—41no—
280C4×C61—41no—
281C4×C61—81no—
282C4×C61—81no—
283C4×C61#57511yescharacteristic
284C4×C61#57511yescharacteristic
285C4×C61#57711yescharacteristic
286C4×C61#57711yescharacteristic
287Dic61—41no—
288Dic61—81no—
289#3369—611no—
290#3369D6111yescharacteristic, complemented
291#3324—611no—
292#3324—611no—
293#1708—611no—
294#1703—611no—
295#1703—611no—
296#1702—611no—
297#1702—611no—
298#1652—611no—
299#1652—611no—
300#1629—611no—
301#1623—611no—
302#1590—611no—
303#1590—611no—
304C2×C61—81no—
305C2×C61#327511yescharacteristic
306C2×C61#327511yescharacteristic
307C2×C61#329111yescharacteristic
308D61—81no—
309D61—161no—
310Q82C2×D6111yescharacteristic, complemented
311#556—611no—
312#556C2×D6111yescharacteristic
313D42—611no—
314#498—611no—
315#492—611no—
316#489—21no—
317#489—1221no—
318#487—611no—
319#487C2×D6111yescharacteristic, complemented
320#486—611no—
321#486—611no—
322#482—1221no—
323#482—1221no—
324#476—611no—
325#476C2×D6111yescharacteristic
326#475—21no—
327#475—1221no—
328#474—611no—
329#474—611no—
330#468—1221no—
331#468—1221no—
332#464—21no—
333#464—1221no—
334#462—611no—
335#462C2×D6111yescharacteristic, complemented
336#460—611no—
337#460—611no—
338#450—1221no—
339#450—1221no—
340#446—611no—
341#446C2×D6111yescharacteristic, complemented
342#441—21no—
343#441—1221no—
344C4×SD16—611no—
345C4×SD16C2×D6111yescharacteristic
346#436—611no—
347#436—611no—
348#418—1221no—
349#418—1221no—
350#334—611no—
351#334—611no—
352#333—611no—
353#332—611no—
354#332—611no—
355#331—611no—
356Q8⋊C8—611no—
357Q8⋊C8—611no—
358D4⋊C8—611no—
359D4⋊C8—611no—
360C82—611no—
361C61#2028911yescharacteristic, complemented, Sylow
362C22×D4—1221no—
363C22×D4—1221no—
364C2×Q16—21no—
365C2×Q16—1221no—
366C2×SD16—611no—
367C2×SD16—1221no—
368C2×SD16—1221no—
369C2×SD16—2441no—
370C2×SD16C22⋊D6111yescharacteristic
371C2×M16—1221no—
372C2×M16—1221no—
373C4⋊Q8—21no—
374C4⋊Q8—21no—
375C4⋊Q8—41no—
376C4⋊Q8—611no—
377C4⋊Q8C22×D6111yescharacteristic
378C4⋊Q8C22×D6111yescharacteristic
379#127—611no—
380#126—41no—
381#126—2441no—
382#124—21no—
383#124—1221no—
384C22⋊Q8—21no—
385C22⋊Q8—1221no—
386#121—1221no—
387#121—1221no—
388#120—2441no—
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8—1221no—
393C4×Q8C22×D6111yescharacteristic
394C4×Q8C22×D6111yescharacteristic
395C4×D4—611no—
396C4×D4C22×D6111yescharacteristic
397#117—21no—
398#117—1221no—
399#107—1221no—
400#107—1221no—
401#106—21no—
402#106—611no—
403#106—1221no—
404#106—2441no—
405#106C22⋊D6111yescharacteristic
406C4⋊C8—21no—
407C4⋊C8—611no—
408C4⋊C8—611no—
409C4⋊C8—611no—
410C4⋊C8—1221no—
411C4⋊C8C22×D6111yescharacteristic
412#103—21no—
413#103—21no—
414#103—21no—
415#103—611no—
416#103—1221no—
417#103—1221no—
418#103—1221no—
419#103C22⋊D6111yescharacteristic
420#102—21no—
421#102—611no—
422#102—1221no—
423#102—1221no—
424#102—1221no—
425#102—1221no—
426#102—1221no—
427#102—1221no—
428#102—1221no—
429#102—1221no—
430#102—1221no—
431#102C22⋊D6111yescharacteristic
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434#97—21no—
435#97—1221no—
436C4×C8—611no—
437C4×C8—611no—
438C4×C8C22×D6111yescharacteristic
439C24—2441no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—41no—
443C2×Q8—1221no—
444C2×Q8D4×D6111yescharacteristic
445C2×Q8C2×C22⋊D6111yescharacteristic
446C2×D4—611no—
447C2×D4—1221no—
448C2×D4—1221no—
449C2×D4—1221no—
450C2×D4—4881no—
451C2×D4—4881no—
452C2×D4—2441no—
453C2×D4—2442no—
454C2×D4—2441no—
455C2×D4—2442no—
456C2×D4C2×C22⋊D6111yescharacteristic
457C22×C4—21no—
458C22×C4—1221no—
459Q16—42no—
460Q16—2442no—
461SD16—41no—
462SD16—4882no—
463SD16—4881no—
464SD16—4881no—
465SD16—2441no—
466M16—4881no—
467M16—4881no—
468C2×C8—21no—
469C2×C8—611no—
470C2×C8—611no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8—1221no—
474C2×C8—1221no—
475C2×C8C2×C22⋊D6111yescharacteristic
476C2×C8C2×C22⋊D6111yescharacteristic
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—611no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—2441no—
490C4⋊C4D4×D6111yescharacteristic
491C4⋊C4C2×C22⋊D6111yescharacteristic
492C4⋊C4C2×C22⋊D6111yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—1221no—
497C22⋊C4—2441no—
498C22⋊C4—2441no—
499C22⋊C4—2441no—
500C42—21no—
501C42—21no—
502C42—41no—
503C42—41no—
504C42—2441no—
505C42C23×D6111yescharacteristic
506C23—21no—
507C23—1221no—
508C23—9761no—
509C23—4882no—
510C23—4882no—
511C23—2441no—
512Q8—21no—
513Q8—21no—
514Q8—21no—
515Q8—21no—
516Q8—41no—
517Q8—41no—
518Q8—81no—
519Q8—161no—
520Q8—2441no—
521Q8—2441no—
522D4—21no—
523D4—21no—
524D4—1221no—
525D4—1221no—
526D4—4881no—
527D4—4882no—
528D4—4882no—
529D4—2441no—
530D4—2441no—
531D4—2441no—
532D4—2441no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—1221no—
543C2×C4—2441no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4C2×D4×D6111yescharacteristic
547C2×C4C22×C22⋊D6111yescharacteristic
548C2×C4#1451982211yescharacteristic
549C8—21no—
550C8—21no—
551C8—41no—
552C8—1222no—
553C8—1221no—
554C8—1221no—
555C8—2441no—
556C8—2441no—
557C8—2441no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—9764no—
562C22—4881no—
563C22—4881no—
564C22—4881no—
565C22—2441no—
566C22—2441no—
567C22—2441no—
568C22D4×C22⋊D6111yescharacteristic
569C4—21no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—81no—
576C4—81no—
577C4—4881no—
578C4—2441no—
579C4#1684056011yescharacteristic
580C4#1684056111yescharacteristic
581C4#1684057011yescharacteristic
582C4#1684057111yescharacteristic
583C2—81no—
584C2—9761no—
585C2—4881no—
586C2#2145744411yescharacteristic
587C2#2145745111yescharacteristic
588C2#2145761011yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3369C2
socleC22×C61D42
prime radicalD4×D244C22
hypercenter#3369D61
hypocenterC61#20289
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3369

Complements

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

NH ≅ G/Ntype
1. #21458559C2semidirect
4. #21445422C2semidirect
5. #21445396C2semidirect
6. #21445391C2semidirect
7. #21445389C2semidirect
8. #21445387C2semidirect
9. #21445089C2semidirect
10. #21445087C2semidirect
12. #21444897C2semidirect
13. #21444710C2semidirect
14. #21444709C2semidirect
15. C61×#3369C2semidirect
18. #16840158C22semidirect
21. #16840114C22semidirect
33. #16839972C22semidirect
38. #16839893C22semidirect
45. #16839513C22semidirect
46. #16839512C22semidirect
47. #16839511C22semidirect
48. #16839508C22semidirect
49. #16839507C22semidirect
51. Q8⋊#92418C22semidirect
52. Q8⋊#92418C22semidirect
55. C8×#92418C22semidirect
56. Q82×C61C22semidirect
59. C61×#487C22semidirect
63. C61×#462C22semidirect
64. C61×#446C22semidirect
290. #3369D61semidirect
310. Q82C2×D61semidirect
319. #487C2×D61semidirect
335. #462C2×D61semidirect
341. #446C2×D61semidirect
361. C61#20289semidirect

Maximal subgroups

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

subgroupindex
#214585592
#214580522
#214580442
#214454222
#214453962
#214453912
#214453892
#214453872
#214450892
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C61×#33692
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