Finite Group Databasebeta

← #29669885

Subgroups — #29669885

Order 15616.

626 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#21458694C211yesmaximal, characteristic, complemented
2#21458598C211yesmaximal, characteristic, complemented
3#21457643C211yesmaximal, characteristic
4#21445480C211yesmaximal, characteristic, complemented
5#21445356C211yesmaximal, characteristic, complemented
6#21445270C211yesmaximal, characteristic, complemented
7#21445233C211yesmaximal, characteristic, complemented
8#21445196C211yesmaximal, characteristic, complemented
9#21444998C211yesmaximal, characteristic
10#21444953C211yesmaximal, characteristic, complemented
11#21444951C211yesmaximal, characteristic, complemented
12#21444913C211yesmaximal, characteristic, complemented
13#21444655C211yesmaximal, characteristic, complemented
14SD16⋊#92418C211yesmaximal, characteristic, complemented
15C61×#3295C211yesmaximal, characteristic
16#16840490C2211yescharacteristic, complemented
17#16840469C2211yescharacteristic
18#16840161—21no—
19#16840158C2211yescharacteristic, complemented
20#16840141C2211yescharacteristic, complemented
21#16840129—21no—
22#16840113C2211yescharacteristic, complemented
23#16840108C2211yescharacteristic
24#16840108C2211yescharacteristic
25#16840078—21no—
26#16840072—21no—
27#16840066—21no—
28#16840062—21no—
29#16840057C2211yescharacteristic, complemented
30#16840054C2211yescharacteristic, complemented
31#16840052C2211yescharacteristic
32#16840042C2211yescharacteristic
33#16839989—21no—
34#16839967C2211yescharacteristic
35#16839965—21no—
36#16839959C2211yescharacteristic
37#16839913—21no—
38#16839892C2211yescharacteristic, complemented
39Q8×#92418C2211yescharacteristic, complemented
40#16839859—21no—
41C4×#11758200—21no—
42C4×#11758200C2211yescharacteristic
43D4×#92418C2211yescharacteristic
44C2×#14519698—21no—
45#16839515C2211yescharacteristic, complemented
46#16839512C2211yescharacteristic, complemented
47#16839511C2211yescharacteristic, complemented
48#16839510C2211yescharacteristic, complemented
49#16839509C2211yescharacteristic, complemented
50#16839506C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic, complemented
52#16839492C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55#16839483C2211yescharacteristic, complemented
56C61×#554C2211yescharacteristic
57D42×C61C2211yescharacteristic
58C61×#486C2211yescharacteristic
59C61×#481—21no—
60C61×#476C2211yescharacteristic
61C61×#465—21no—
62C61×#460C2211yescharacteristic
63C61×#450—21no—
64C4×SD16×C61C2211yescharacteristic
65C8×D4×C61C2211yescharacteristic
66C2×#102×C61—21no—
67C2×#11758202—41no—
68C2×#11758200—21no—
69C2×#11758200—21no—
70C2×#11758200D411yescharacteristic
71C22×#92418—21no—
72#14519777C2311yescharacteristic
73#14519777C2311yescharacteristic
74#14519775—21no—
75#14519769—21no—
76#14519768—21no—
77#14519767—41no—
78#14519756—21no—
79#14519754—41no—
80C4×Dic122—21no—
81C4×Dic122C2311yescharacteristic
82#14519742—21no—
83D4×Dic61—21no—
84C2×C4⋊Dic61—21no—
85#14519710—21no—
86#14519710—21no—
87#14519710—21no—
88#14519708—21no—
89#14519708—21no—
90#14519708—21no—
91#14519708D411yescharacteristic
92C4⋊#92418—21no—
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96#14519706—21no—
97#14519702—21no—
98#14519702—21no—
99#14519701—21no—
100#14519700—21no—
101#14519700—21no—
102#14519700D411yescharacteristic
103#14519698—21no—
104#14519698—21no—
105#14519698—21no—
106#14519698—21no—
107#14519698—21no—
108#14519698—41no—
109#14519698D411yescharacteristic
110C22⋊#92418—21no—
111#14519687—21no—
112C4×#92418—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C22×D4×C61—21no—
116C22×D4×C61—21no—
117C2×SD16×C61—21no—
118C2×SD16×C61D411yescharacteristic
119C22×C8×C61—21no—
120C4⋊Q8×C61C2311yescharacteristic
121#127×C61C2311yescharacteristic
122#125×C61—21no—
123C22⋊Q8×C61—21no—
124C22⋊Q8×C61—41no—
125#121×C61—21no—
126#121×C61—21no—
127#120×C61—41no—
128C4×Q8×C61C2311yescharacteristic
129C4×D4×C61—21no—
130C4×D4×C61C2311yescharacteristic
131C4×D4×C61C2311yescharacteristic
132C2×C4⋊C4×C61—21no—
133#106×C61—21no—
134#106×C61D411yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136#103×C61D411yescharacteristic
137#102×C61—21no—
138#102×C61—21no—
139#102×C61—21no—
140#102×C61—21no—
141#102×C61D411yescharacteristic
142C22⋊C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C24×C61—41no—
145C2×Q8×C61—21no—
146C2×Q8×C61C2×D411yescharacteristic
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—41no—
151C2×D4×C61—41no—
152C2×D4×C61—42no—
153C2×D4×C61—42no—
154C2×D4×C61—81no—
155C2×D4×C61—81no—
156C2×D4×C61C2×D411yescharacteristic
157C2×D4×C61C2×D411yescharacteristic
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—41no—
161C22×Dic61—41no—
162C2×Dic122—21no—
163C2×Dic122—21no—
164C2×Dic122C2×D411yescharacteristic
165SD16×C61—22no—
166SD16×C61—81no—
167C2×C8×C61—21no—
168C2×C8×C61—81no—
169C2×C8×C61C2×D411yescharacteristic
170C2×C8×C61C2×D411yescharacteristic
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—41no—
175C4⋊C4×C61—41no—
176C4⋊C4×C61C2×D411yescharacteristic
177C4⋊C4×C61C2×D411yescharacteristic
178C4⋊C4×C61C2×D411yescharacteristic
179C22⋊C4×C61—21no—
180C22⋊C4×C61—21no—
181C22⋊C4×C61—41no—
182C22⋊C4×C61—41no—
183C42×C61—21no—
184C42×C61C2411yescharacteristic
185C22⋊Dic61—41no—
186#11758202—82no—
187#11758200—22no—
188#11758200—42no—
189#11758200—81no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—41no—
195C4⋊Dic61C2×D411yescharacteristic
196#11758196—21no—
197#11758196—41no—
198#11758196—41no—
199#11758196—41no—
200#11758196—41no—
201C4×Dic61—21no—
202C4×Dic61—41no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—81no—
208C2×#92418C2×D411yescharacteristic
209C2×#92418C2×D411yescharacteristic
210C23×C61—21no—
211C23×C61—21no—
212C23×C61—41no—
213C23×C61—82no—
214C23×C61—82no—
215C23×C61—161no—
216Q8×C61—21no—
217Q8×C61—21no—
218Q8×C61—81no—
219D4×C61—21no—
220D4×C61—21no—
221D4×C61—41no—
222D4×C61—41no—
223D4×C61—41no—
224D4×C61—41no—
225D4×C61—81no—
226D4×C61—82no—
227D4×C61—82no—
228D4×C61#13512yes—
229D4×C61#13712yes—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—161no—
240C2×C4×C61C22×D411yescharacteristic
241C2×C4×C61C22×D411yescharacteristic
242C2×C4×C61H(5,𝔽2)11yescharacteristic
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—161no—
248Dic122—21no—
249Dic122—21no—
250Dic122—41no—
251Dic122—41no—
252Dic122—81no—
253C8×C61—21no—
254C8×C61—21no—
255C8×C61—41no—
256#92418—21no—
257#92418—21no—
258#92418—41no—
259#92418—41no—
260#92418—41no—
261#92418—41no—
262#19790—611nomaximal, Sylow
263C22×C61—22no—
264C22×C61—22no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61—41no—
268C22×C61—41no—
269C22×C61—81no—
270C22×C61—81no—
271C22×C61—81no—
272C22×C61—164no—
273C22×C61D4211yescharacteristic
274C4×C61—21no—
275C4×C61—41no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61—41no—
279C4×C61—81no—
280C4×C61C2×#13511yescharacteristic
281C4×C61C2×#13711yescharacteristic
282C4×C61#57711yescharacteristic
283C4×C61#57711yescharacteristic
284Dic61—41no—
285Dic61—41no—
286Dic61—81no—
287Dic61—81no—
288#3381—611no—
289#3372—611no—
290#3295—611no—
291#3295D6111yescharacteristic
292#1720—611no—
293#1698—611no—
294#1683—611no—
295#1678—611no—
296#1671—611no—
297#1639—611no—
298#1632—611no—
299#1632—611no—
300#1626—611no—
301#1582—611no—
302SD16⋊C8—611no—
303C2×C61—42no—
304C2×C61—42no—
305C2×C61—161no—
306C2×C61#326611yescharacteristic
307C2×C61#328211yescharacteristic
308C2×C61#328811yescharacteristic
309#557—611no—
310#554—611no—
311#554C2×D6111yescharacteristic
312D42C2×D6111yescharacteristic
313#499—1221no—
314#498—611no—
315#494—611no—
316#491—1221no—
317#487—611no—
318#486—611no—
319#486—611no—
320#486C2×D6111yescharacteristic
321#481—21no—
322#481—1221no—
323#479—1221no—
324#479—1221no—
325#478—1221no—
326#477—611no—
327#477—611no—
328#476—611no—
329#476C2×D6111yescharacteristic
330#474—611no—
331#465—21no—
332#465—1221no—
333#461—611no—
334#461—1221no—
335#460—611no—
336#460C2×D6111yescharacteristic
337#450—21no—
338#450—1221no—
339#446—611no—
340C8×Q8—611no—
341#440—1221no—
342C4×SD16—611no—
343C4×SD16—1221no—
344C4×SD16C2×D6111yescharacteristic
345C8×D4—611no—
346C8×D4C2×D6111yescharacteristic
347C2×#102—21no—
348C2×#102—1221no—
349#335—611no—
350#334—611no—
351#333—611no—
352#333—611no—
353#332—611no—
354#331—611no—
355Q8⋊C8—611no—
356Q8⋊C8—611no—
357D4⋊C8—611no—
358D4⋊C8—611no—
359#322—611no—
360C61#1979011yescharacteristic, complemented, Sylow
361C22×D4—21no—
362C22×D4—21no—
363C2×Q16—2441no—
364C2×SD16—21no—
365C2×SD16—611no—
366C2×SD16—1221no—
367C2×SD16—1221no—
368C2×SD16C22⋊D6111yescharacteristic
369C22×C8—21no—
370C22×C8—1221no—
371C4⋊Q8—611no—
372C4⋊Q8—611no—
373C4⋊Q8—1221no—
374C4⋊Q8C22×D6111yescharacteristic
375#127C22×D6111yescharacteristic
376#125—21no—
377#125—1221no—
378#125—1221no—
379#125—2441no—
380C22⋊Q8—21no—
381C22⋊Q8—41no—
382C22⋊Q8—1221no—
383C22⋊Q8—2441no—
384#121—21no—
385#121—21no—
386#120—41no—
387C4×Q8—611no—
388C4×Q8—1221no—
389C4×Q8—1221no—
390C4×Q8C22×D6111yescharacteristic
391C4×D4—21no—
392C4×D4—1221no—
393C4×D4C22×D6111yescharacteristic
394C4×D4C22×D6111yescharacteristic
395C2×C4⋊C4—21no—
396C2×C4⋊C4—1221no—
397#107—1221no—
398#107—1221no—
399#107—1221no—
400#106—21no—
401#106—611no—
402#106—1221no—
403#106—1221no—
404#106—1221no—
405#106C22⋊D6111yescharacteristic
406C4⋊C8—611no—
407C4⋊C8—611no—
408C4⋊C8—611no—
409C4⋊C8—1221no—
410C4⋊C8—1221no—
411C4⋊C8C22×D6111yescharacteristic
412#103—611no—
413#103—1221no—
414#103—1221no—
415#103—1221no—
416#103—1221no—
417#103—1221no—
418#103C22⋊D6111yescharacteristic
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—611no—
424#102—1221no—
425#102—1221no—
426#102—1221no—
427#102—1221no—
428#102—1221no—
429#102—2441no—
430#102C22⋊D6111yescharacteristic
431C22⋊C8—21no—
432C22⋊C8—1221no—
433#97—1221no—
434C4×C8—611no—
435C4×C8—611no—
436C4×C8—1221no—
437C4×C8C22×D6111yescharacteristic
438C24—41no—
439C2×Q8—21no—
440C2×Q8—611no—
441C2×Q8—1221no—
442C2×Q8—1221no—
443C2×Q8C2×C22⋊D6111yescharacteristic
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—42no—
450C2×D4—42no—
451C2×D4—81no—
452C2×D4—81no—
453C2×D4D4×D6111yescharacteristic
454C2×D4C2×C22⋊D6111yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—41no—
458C22×C4—2441no—
459Q16—4882no—
460SD16—22no—
461SD16—81no—
462SD16—1222no—
463SD16—4881no—
464SD16—2442no—
465C2×C8—21no—
466C2×C8—81no—
467C2×C8—611no—
468C2×C8—611no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8—4881no—
474C2×C8C2×C22⋊D6111yescharacteristic
475C2×C8C2×C22⋊D6111yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4—611no—
482C4⋊C4—1221no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—2441no—
488C4⋊C4—2441no—
489C4⋊C4—2441no—
490C4⋊C4—2441no—
491C4⋊C4—2441no—
492C4⋊C4D4×D6111yescharacteristic
493C4⋊C4C2×C22⋊D6111yescharacteristic
494C4⋊C4C2×C22⋊D6111yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—2441no—
500C42—21no—
501C42—1221no—
502C42—2441no—
503C42C23×D6111yescharacteristic
504C23—21no—
505C23—21no—
506C23—41no—
507C23—82no—
508C23—82no—
509C23—161no—
510Q8—21no—
511Q8—21no—
512Q8—81no—
513Q8—1221no—
514Q8—1221no—
515Q8—4881no—
516Q8—2441no—
517Q8—2441no—
518D4—21no—
519D4—21no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—81no—
525D4—82no—
526D4—82no—
527D4#1451979712yes—
528D4#1451980612yes—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—161no—
539C2×C4—1221no—
540C2×C4—1221no—
541C2×C4—9761no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4C2×D4×D6111yescharacteristic
545C2×C4C22×C22⋊D6111yescharacteristic
546C2×C4#1451982211yescharacteristic
547C8—21no—
548C8—21no—
549C8—41no—
550C8—1221no—
551C8—1221no—
552C8—2441no—
553C8—2441no—
554C8—2441no—
555C8—2441no—
556C22—22no—
557C22—22no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—164no—
566C22D4×C22⋊D6111yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—4881no—
574C4—4881no—
575C4—2441no—
576C4—2441no—
577C4C2×#1451979711yescharacteristic
578C4C2×#1451980611yescharacteristic
579C4#1684056811yescharacteristic
580C4#1684057311yescharacteristic
581C2—42no—
582C2—42no—
583C2—161no—
584C2#2145732911yescharacteristic
585C2#2145752211yescharacteristic
586C2#2145758311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3295C2
socleC22×C61D42
prime radicalD42×C61C22
hypercenter#3295D61
hypocenterC61#19790
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3295

Complements

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

NH ≅ G/Ntype
1. #21458694C2semidirect
2. #21458598C2semidirect
4. #21445480C2semidirect
5. #21445356C2semidirect
6. #21445270C2semidirect
7. #21445233C2semidirect
8. #21445196C2semidirect
10. #21444953C2semidirect
11. #21444951C2semidirect
12. #21444913C2semidirect
13. #21444655C2semidirect
14. SD16⋊#92418C2semidirect
16. #16840490C22semidirect
19. #16840158C22semidirect
20. #16840141C22semidirect
22. #16840113C22semidirect
29. #16840057C22semidirect
30. #16840054C22semidirect
38. #16839892C22semidirect
39. Q8×#92418C22semidirect
45. #16839515C22semidirect
46. #16839512C22semidirect
47. #16839511C22semidirect
48. #16839510C22semidirect
49. #16839509C22semidirect
51. Q8⋊#92418C22semidirect
52. #16839492C22semidirect
55. #16839483C22semidirect
360. C61#19790semidirect

Maximal subgroups

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

subgroupindex
#214586942
#214585982
#214576432
#214454802
#214453562
#214452702
#214452332
#214451962
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