Finite Group Databasebeta

← #29665229

Subgroups — #29665229

Order 15616.

674 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456959C211yesmaximal, characteristic, complemented
2#21455611C211yesmaximal, characteristic
3#461×D61C211yesmaximal, characteristic
4#21454840C211yesmaximal, characteristic
5#21445241C211yesmaximal, characteristic, complemented
6#21445240C211yesmaximal, characteristic, complemented
7#21445239C211yesmaximal, characteristic, complemented
8#21445195C211yesmaximal, characteristic, complemented
9#21445194C211yesmaximal, characteristic, complemented
10#21445193C211yesmaximal, characteristic, complemented
11#21445192C211yesmaximal, characteristic, complemented
12#21444588C211yesmaximal, characteristic, complemented
13#21444489C211yesmaximal, characteristic, complemented
14#21444475C211yesmaximal, characteristic, complemented
15C61×#1679C211yesmaximal, characteristic, complemented
16C2×SD16×D61—21no—
17#16840317C2211yescharacteristic
18C4⋊Q8×D61C2211yescharacteristic
19C4×D4×D61C2211yescharacteristic
20#16840160C2211yescharacteristic, complemented
21#16840158C2211yescharacteristic, complemented
22#16840112C2211yescharacteristic, complemented
23#16840091—21no—
24#16840091—21no—
25#16840065—21no—
26#16840064—21no—
27#16840053C2211yescharacteristic
28#16840052C2211yescharacteristic
29#16840045—21no—
30#16840045—21no—
31#16840039C2211yescharacteristic
32#16839968C2211yescharacteristic
33#16839967C2211yescharacteristic
34#16839966—21no—
35#16839965—21no—
36#16839964C2211yescharacteristic
37C8×D244C2211yescharacteristic
38D4×#92418C2211yescharacteristic
39#16839827C2211yescharacteristic
40C8×C22⋊D61—21no—
41#16839825—21no—
42#16839814C2211yescharacteristic
43#16839813C2211yescharacteristic
44#16839803—21no—
45#16839784C2211yescharacteristic
46C4⋊C8×D61C2211yescharacteristic
47#16839765—21no—
48#103×D61—21no—
49C2×#14519689—21no—
50C22⋊C8×D61—21no—
51#16839513C2211yescharacteristic, complemented
52#16839512C2211yescharacteristic, complemented
53#16839512C2211yescharacteristic, complemented
54#16839510C2211yescharacteristic, complemented
55#16839510C2211yescharacteristic, complemented
56#16839509C2211yescharacteristic, complemented
57#16839508C2211yescharacteristic, complemented
58#16839508C2211yescharacteristic, complemented
59#16839507C2211yescharacteristic, complemented
60C61×#487C2211yescharacteristic, complemented
61C61×#474C2211yescharacteristic
62C61×#461C2211yescharacteristic
63C8×D4×C61C2211yescharacteristic
64C61×#334C2211yescharacteristic, complemented
65C61×#332C2211yescharacteristic, complemented
66C61×#332C2211yescharacteristic, complemented
67C2×Q8×D61—21no—
68C2×D4×D61D411yescharacteristic
69C22×C4×D61—21no—
70C2×#11758190—21no—
71C2×#11758200—21no—
72C2×#11758201—21no—
73SD16×D61—44no—
74C2×#11758189—21no—
75C22×#92418—21no—
76C2×C8×D61—21no—
77C2×C8×D61—21no—
78C2×C8×D61—21no—
79#14519777C2311yescharacteristic
80#14519777C2311yescharacteristic
81#14519776—21no—
82#14519776—21no—
83#14519775—21no—
84#14519768—21no—
85#14519757—21no—
86#14519753—21no—
87Q8×Dic61—21no—
88#14519742—21no—
89C4×D244C2311yescharacteristic
90D4×Dic61D411yescharacteristic
91#14519739D411yescharacteristic
92C4×C22⋊D61—21no—
93#14519737—21no—
94#14519735—21no—
95C4⋊C4×D61—21no—
96C4⋊C4×D61—21no—
97C4⋊C4×D61D411yescharacteristic
98C22⋊C4×D61—21no—
99C42×D61C2311yescharacteristic
100#14519710—21no—
101#14519709—21no—
102#14519709—21no—
103#14519709—21no—
104#14519708—21no—
105#14519708—21no—
106#14519708—21no—
107C4⋊#92418C2311yescharacteristic
108C4⋊#92418C2311yescharacteristic
109C4⋊#92418C2311yescharacteristic
110#14519706—21no—
111#14519706—21no—
112#14519706D411yescharacteristic
113#14519706D411yescharacteristic
114#14519702—21no—
115#14519701—21no—
116#14519701—21no—
117#14519701—21no—
118#14519700—21no—
119#14519699—21no—
120#14519698—21no—
121#14519697—21no—
122C22⋊#92418—21no—
123#14519689—21no—
124#14519689—21no—
125#14519689—21no—
126#14519689D411yescharacteristic
127#14519689D411yescharacteristic
128C4×#92418C2311yescharacteristic
129C8×Dic61—21no—
130C2×SD16×C61—21no—
131C22×C8×C61—21no—
132C4⋊Q8×C61C2311yescharacteristic
133C4⋊Q8×C61C2311yescharacteristic
134C4×D4×C61C2311yescharacteristic
135#107×C61—21no—
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139#103×C61—21no—
140#103×C61—21no—
141#103×C61—21no—
142#102×C61—21no—
143C22⋊C8×C61—21no—
144C4×C8×C61C2311yescharacteristic
145C23×D61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×D4×C61C2×D411yescharacteristic
149C22×C4×C61—21no—
150C2×C22⋊D61—21no—
151C22×Dic61—21no—
152Q8×D61—42no—
153Q8×D61—42no—
154D4×D61—22no—
155D4×D61SD1614yes—
156C2×D244C2×D411yescharacteristic
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—41no—
161C2×C4×D61—81no—
162C2×C4×D61—81no—
163C2×C4×D61C2×D411yescharacteristic
164C2×C4×D61C2×D411yescharacteristic
165C2×C4×D61#4111yescharacteristic
166C2×Dic122—21no—
167C2×Dic122—21no—
168C2×Dic122—41no—
169SD16×C61—42no—
170C2×C8×C61—21no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61—81no—
174C2×C8×C61C2×D411yescharacteristic
175C2×C8×C61C2×D411yescharacteristic
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61C2×D411yescharacteristic
181C22⋊C4×C61—21no—
182C42×C61C2411yescharacteristic
183C22⋊Dic61—21no—
184#11758201—42no—
185#11758200—42no—
186#11758198—21no—
187#11758198—21no—
188#11758198—41no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—41no—
194C4⋊Dic61C2×D411yescharacteristic
195#11758196—21no—
196#11758196—41no—
197#11758196—41no—
198#11758196—41no—
199C4×Dic61—41no—
200C4×Dic61C2×D411yescharacteristic
201C4×Dic61C2×D411yescharacteristic
202C4×Dic61#4111yescharacteristic
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—81no—
207C2×#92418C2×D411yescharacteristic
208C2×#92418C2×D411yescharacteristic
209#11758190—42no—
210#11758189—42no—
211C8×D61—42no—
212C8×D61—81no—
213C8×D61—81no—
214C23×C61—21no—
215C22×D61—21no—
216C22×D61—24no—
217C22×D61—81no—
218C22×D61—81no—
219C22×D61#12111yescharacteristic
220Q8×C61—41no—
221Q8×C61—41no—
222Q8×C61—41no—
223Q8×C61—41no—
224D4×C61—21no—
225D4×C61C2×SD1612yes—
226C2×C4×C61—21no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61C22×D411yescharacteristic
232C2×C4×C61C22×D411yescharacteristic
233C2×C4×C61C2×#4111yescharacteristic
234C22⋊D61—24no—
235C2×Dic61—21no—
236C2×Dic61—41no—
237C2×Dic61—41no—
238C2×Dic61—81no—
239C2×Dic61#12111yescharacteristic
240C2×Dic61#12111yescharacteristic
241C2×Dic61#12111yescharacteristic
242D244—21no—
243D244C2×SD1612yes—
244C4×D61—21no—
245C4×D61—21no—
246C4×D61—41no—
247C4×D61—41no—
248C4×D61—41no—
249C4×D61—81no—
250C4×D61—81no—
251C4×D61—82no—
252C4×D61C2×SD1612yes—
253C4×D61#13512yes—
254Dic122—41no—
255Dic122—41no—
256Dic122—82no—
257Dic122—81no—
258C8×C61—21no—
259C8×C61—21no—
260C8×C61—41no—
261C8×C61—41no—
262C8×C61—41no—
263#92418—21no—
264#92418—21no—
265#92418—41no—
266#92418—41no—
267#92418—41no—
268#19390—611nomaximal, Sylow
269C22×C61—22no—
270C22×C61—41no—
271C22×C61—41no—
272C22×C61C2×#12111yescharacteristic
273C2×D61—21no—
274C2×D61—21no—
275C2×D61—22no—
276C2×D61—41no—
277C2×D61—41no—
278C2×D61—84no—
279C2×D61#46512yes—
280C4×C61—21no—
281C4×C61—41no—
282C4×C61—81no—
283C4×C61—81no—
284C4×C61C22×SD1611yescharacteristic
285C4×C61C2×#13511yescharacteristic
286C4×C61#57711yescharacteristic
287C4×C61#57711yescharacteristic
288Dic61—21no—
289Dic61—21no—
290Dic61—41no—
291Dic61—81no—
292Dic61—81no—
293Dic61#46512yes—
294#3229—611no—
295#3077—611no—
296C2×#461—611no—
297#2972—611no—
298#1679—611no—
299#1679—611no—
300#1679—611no—
301#1679D6111yescharacteristic, complemented
302#1671—611no—
303#1671—611no—
304#1671—611no—
305#1671—611no—
306#1570—611no—
307#1546—611no—
308#1542—611no—
309C2×C61—42no—
310C2×C61#304211yescharacteristic
311C2×C61C2×#46511yescharacteristic
312C2×C61#306911yescharacteristic
313D61—22no—
314D61—42no—
315C22×SD16—1221no—
316#533—611no—
317C2×C4⋊Q8—611no—
318C2×C4×D4—611no—
319#498—611no—
320#498—611no—
321#487—611no—
322#487C2×D6111yescharacteristic, complemented
323#483—1221no—
324#483—1221no—
325#478—1221no—
326#478—1221no—
327#476—611no—
328#476—611no—
329#475—1221no—
330#475—1221no—
331#474—611no—
332#474C2×D6111yescharacteristic
333#461—611no—
334#461—611no—
335#461—611no—
336#461—1221no—
337#461—1221no—
338#461C2×D6111yescharacteristic
339C8×D4—611no—
340C8×D4—611no—
341C8×D4—611no—
342C8×D4—1221no—
343C8×D4—1221no—
344C8×D4C2×D6111yescharacteristic
345#431—611no—
346#431—611no—
347#428—1221no—
348#423—611no—
349C2×C4⋊C8—611no—
350#418—1221no—
351C2×#103—1221no—
352C2×C22⋊C8—1221no—
353C2×C22⋊C8—1221no—
354#334—611no—
355#334—611no—
356#334—611no—
357#334C2×D6111yescharacteristic, complemented
358#333—611no—
359#333—611no—
360#332—611no—
361#332—611no—
362#332—611no—
363#332—611no—
364#332C2×D6111yescharacteristic, complemented
365#332C2×D6111yescharacteristic, complemented
366C61#1939011yescharacteristic, complemented, Sylow
367C22×Q8—1221no—
368C22×D4—611no—
369C23×C4—1221no—
370C2×SD16—21no—
371C2×SD16—1221no—
372C2×SD16—1221no—
373C2×SD16—1221no—
374C2×SD16—2444no—
375C2×M16—1221no—
376C22×C8—21no—
377C22×C8—1221no—
378C22×C8—1221no—
379C22×C8—1221no—
380C22×C8—1221no—
381C4⋊Q8—611no—
382C4⋊Q8—611no—
383C4⋊Q8—1221no—
384C4⋊Q8—1221no—
385C4⋊Q8—1221no—
386C4⋊Q8C22×D6111yescharacteristic
387C4⋊Q8C22×D6111yescharacteristic
388#125—1221no—
389C22⋊Q8—1221no—
390C22⋊Q8—1221no—
391C4×Q8—1221no—
392C4×Q8—1221no—
393C4×D4—611no—
394C4×D4—611no—
395C4×D4—611no—
396C4×D4—1221no—
397C4×D4—1221no—
398C4×D4C22×D6111yescharacteristic
399#117—1221no—
400C2×C4⋊C4—611no—
401C2×C4⋊C4—1221no—
402C2×C4⋊C4—1221no—
403C2×C22⋊C4—1221no—
404C2×C42—611no—
405#107—21no—
406#107—1221no—
407#106—1221no—
408#106—1221no—
409#106—1221no—
410#106—1221no—
411#106—1221no—
412#106—1221no—
413C4⋊C8—611no—
414C4⋊C8—611no—
415C4⋊C8—611no—
416C4⋊C8—611no—
417C4⋊C8—611no—
418C4⋊C8—1221no—
419C4⋊C8—1221no—
420C4⋊C8C22×D6111yescharacteristic
421C4⋊C8C22×D6111yescharacteristic
422C4⋊C8C22×D6111yescharacteristic
423#103—21no—
424#103—21no—
425#103—21no—
426#103—1221no—
427#103—1221no—
428#103—1221no—
429#103—1221no—
430#103—1221no—
431#102—21no—
432#102—1221no—
433#102—1221no—
434#102—1221no—
435C22⋊C8—21no—
436C22⋊C8—611no—
437C22⋊C8—611no—
438C22⋊C8—1221no—
439C22⋊C8—1221no—
440C22⋊C8—1221no—
441C22⋊C8—1221no—
442C4×C8—611no—
443C4×C8—1221no—
444C4×C8C22×D6111yescharacteristic
445C24—1221no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—1221no—
449C2×Q8—1221no—
450C2×Q8—2441no—
451C2×Q8—2442no—
452C2×Q8—2442no—
453C2×D4—614no—
454C2×D4—611no—
455C2×D4—1222no—
456C2×D4—1221no—
457C2×D4D4×D6111yescharacteristic
458C22×C4—21no—
459C22×C4—611no—
460C22×C4—611no—
461C22×C4—611no—
462C22×C4—1221no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4—1221no—
466C22×C4—4881no—
467C22×C4—4881no—
468C22×C4—2441no—
469SD16—42no—
470SD16—2442no—
471SD16—2442no—
472SD16—2442no—
473M16—2442no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—81no—
478C2×C8—611no—
479C2×C8—611no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—4881no—
484C2×C8—4881no—
485C2×C8—4881no—
486C2×C8—2442no—
487C2×C8D4×D6111yescharacteristic
488C2×C8D4×D6111yescharacteristic
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—611no—
494C4⋊C4—1221no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4—2441no—
500C4⋊C4—2441no—
501C4⋊C4—2441no—
502C4⋊C4—2441no—
503C4⋊C4D4×D6111yescharacteristic
504C22⋊C4—21no—
505C22⋊C4—1221no—
506C22⋊C4—1221no—
507C22⋊C4—1221no—
508C22⋊C4—2441no—
509C42—611no—
510C42—611no—
511C42—611no—
512C42—2441no—
513C42C23×D6111yescharacteristic
514C23—21no—
515C23—611no—
516C23—1224no—
517C23—1221no—
518C23—4881no—
519C23—4881no—
520Q8—41no—
521Q8—41no—
522Q8—41no—
523Q8—41no—
524Q8—4881no—
525Q8—4882no—
526Q8—2441no—
527Q8—2441no—
528D4—21no—
529D4—612no—
530D4—1224no—
531D4—1221no—
532D4SD16×D6112yes—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—611no—
539C2×C4—612no—
540C2×C4—612no—
541C2×C4—611no—
542C2×C4—611no—
543C2×C4—1221no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—4881no—
547C2×C4—4881no—
548C2×C4—4882no—
549C2×C4—4881no—
550C2×C4—2441no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4C2×D4×D6111yescharacteristic
556C2×C4C2×D4×D6111yescharacteristic
557C2×C4#41×D6111yescharacteristic
558C8—21no—
559C8—21no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—1221no—
564C8—1221no—
565C8—2441no—
566C8—2441no—
567C8—2441no—
568C22—22no—
569C22—41no—
570C22—41no—
571C22—612no—
572C22—1221no—
573C22—1221no—
574C22—1222no—
575C22—4884no—
576C22—2441no—
577C22—2441no—
578C22#121×D6111yescharacteristic
579C4—21no—
580C4—41no—
581C4—81no—
582C4—81no—
583C4—612no—
584C4—1221no—
585C4—1221no—
586C4—4881no—
587C4—4881no—
588C4—2441no—
589C4C2×SD16×D6111yescharacteristic
590C4#135×D6111yescharacteristic
591C4#1684056911yescharacteristic
592C4#1684057211yescharacteristic
593C2—42no—
594C2—1222no—
595C2—2442no—
596C2#2145532911yescharacteristic
597C2#465×D6111yescharacteristic
598C2#2145555411yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1679C2
socleC22×C61C2×#121
prime radicalC2×D4×D61D4
hypercenter#1679D61
hypocenterC61#19390
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1679

Complements

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

NH ≅ G/Ntype
1. #21456959C2semidirect
5. #21445241C2semidirect
6. #21445240C2semidirect
7. #21445239C2semidirect
8. #21445195C2semidirect
9. #21445194C2semidirect
10. #21445193C2semidirect
11. #21445192C2semidirect
12. #21444588C2semidirect
13. #21444489C2semidirect
14. #21444475C2semidirect
15. C61×#1679C2semidirect
20. #16840160C22semidirect
21. #16840158C22semidirect
22. #16840112C22semidirect
51. #16839513C22semidirect
52. #16839512C22semidirect
53. #16839512C22semidirect
54. #16839510C22semidirect
55. #16839510C22semidirect
56. #16839509C22semidirect
57. #16839508C22semidirect
58. #16839508C22semidirect
59. #16839507C22semidirect
60. C61×#487C22semidirect
64. C61×#334C22semidirect
65. C61×#332C22semidirect
66. C61×#332C22semidirect
301. #1679D61semidirect
322. #487C2×D61semidirect
357. #334C2×D61semidirect
364. #332C2×D61semidirect
365. #332C2×D61semidirect
366. C61#19390semidirect

Maximal subgroups

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

subgroupindex
#214569592
#214556112
#461×D612
#214548402
#214452412
#214452402
#214452392
#214451952
#214451942
#214451932
#214451922
#214445882
#214444892
#214444752
C61×#16792
#1939061