Finite Group Databasebeta

← #29663835

Subgroups — #29663835

Order 15616.

694 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#21456404C211yesmaximal, characteristic, complemented
2#21455920C211yesmaximal, characteristic
3#21455917C211yesmaximal, characteristic
4C8×D4×D61C211yesmaximal, characteristic
5#21445243C211yesmaximal, characteristic, complemented
6#21445242C211yesmaximal, characteristic, complemented
7#21445239C211yesmaximal, characteristic, complemented
8#21445207C211yesmaximal, characteristic, complemented
9#21445206C211yesmaximal, characteristic, complemented
10#21445183C211yesmaximal, characteristic, complemented
11#21445182C211yesmaximal, characteristic, complemented
12#21444579C211yesmaximal, characteristic, complemented
13#21444518C211yesmaximal, characteristic, complemented
14#21444516C211yesmaximal, characteristic, complemented
15C61×#1679C211yesmaximal, characteristic, complemented
16C22×C8×D61—21no—
17#16840317C2211yescharacteristic
18#16840317C2211yescharacteristic
19C4×D4×D61C2211yescharacteristic
20#16840165C2211yescharacteristic, complemented
21#16840141C2211yescharacteristic, complemented
22#16840113C2211yescharacteristic, complemented
23#16840099—21no—
24#16840096—21no—
25#16840043C2211yescharacteristic
26#16840042C2211yescharacteristic
27#16840039C2211yescharacteristic
28#16840002—21no—
29#16840002—21no—
30#16839968C2211yescharacteristic
31#16839967C2211yescharacteristic
32#16839964C2211yescharacteristic
33#16839914—21no—
34#16839911—21no—
35#16839865—21no—
36#16839863—21no—
37#16839861—21no—
38#16839859—21no—
39#16839854—21no—
40#16839854—21no—
41C8×D244C2211yescharacteristic
42D4×#92418C2211yescharacteristic
43#16839827C2211yescharacteristic
44C8×C22⋊D61—21no—
45#16839825—21no—
46#16839818C2211yescharacteristic
47#16839818C2211yescharacteristic
48C4⋊C8×D61C2211yescharacteristic
49C22⋊C8×D61—21no—
50C4×C8×D61C2211yescharacteristic
51#16839514C2211yescharacteristic, complemented
52#16839514C2211yescharacteristic, complemented
53#16839513C2211yescharacteristic, complemented
54#16839509C2211yescharacteristic, complemented
55#16839509C2211yescharacteristic, complemented
56#16839508C2211yescharacteristic, complemented
57#16839508C2211yescharacteristic, complemented
58#16839507C2211yescharacteristic, complemented
59#16839507C2211yescharacteristic, complemented
60C61×#487C2211yescharacteristic, complemented
61C61×#474C2211yescharacteristic
62C61×#461C2211yescharacteristic
63C8×D4×C61C2211yescharacteristic
64C61×#334C2211yescharacteristic, complemented
65C61×#332C2211yescharacteristic, complemented
66C61×#332C2211yescharacteristic, complemented
67C2×D4×D61D411yescharacteristic
68C22×C4×D61—21no—
69C2×#11758202—21no—
70C2×#11758202—21no—
71C2×#11758190—21no—
72C2×#11758200—21no—
73C2×#11758201—21no—
74C22×#92418—21no—
75C2×C8×D61—21no—
76C2×C8×D61—21no—
77C2×C8×D61—21no—
78C2×C8×D61—44no—
79C2×C8×D61D411yescharacteristic
80C2×C8×D61D411yescharacteristic
81#14519777C2311yescharacteristic
82#14519777C2311yescharacteristic
83#14519768—21no—
84#14519768—21no—
85#14519757—21no—
86#14519757—21no—
87#14519753—21no—
88#14519753—21no—
89Q8×Dic61—21no—
90Q8×Dic61—21no—
91#14519742—21no—
92#14519742—21no—
93C4×D244C2311yescharacteristic
94D4×Dic61D411yescharacteristic
95#14519739D411yescharacteristic
96C4×C22⋊D61—21no—
97#14519737—21no—
98#14519735—21no—
99#14519735—21no—
100C4⋊C4×D61D411yescharacteristic
101C22⋊C4×D61—21no—
102C42×D61C2311yescharacteristic
103#14519711—21no—
104#14519710—21no—
105#14519710—21no—
106#14519710—21no—
107#14519710—21no—
108C4⋊#92418C2311yescharacteristic
109C4⋊#92418C2311yescharacteristic
110C4⋊#92418C2311yescharacteristic
111#14519706—21no—
112#14519702—21no—
113#14519702—21no—
114#14519702—21no—
115#14519701—21no—
116#14519700—21no—
117#14519699—21no—
118#14519698—21no—
119#14519697—21no—
120C22⋊#92418—21no—
121#14519689—21no—
122#14519689—21no—
123#14519689—21no—
124#14519689—21no—
125#14519687—21no—
126#14519687—21no—
127C4×#92418C2311yescharacteristic
128C8×Dic61D411yescharacteristic
129C8×Dic61D411yescharacteristic
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—
152D4×D61—22no—
153D4×D61—22no—
154C2×D244C2×D411yescharacteristic
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—42no—
159C2×C4×D61—42no—
160C2×C4×D61C2×D411yescharacteristic
161C2×C4×D61C2×D411yescharacteristic
162C2×C4×D61#4111yescharacteristic
163C2×Dic122—21no—
164C2×Dic122—21no—
165SD16×C61—42no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—42no—
170C2×C8×C61C2×D411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61C2×D411yescharacteristic
177C22⋊C4×C61—21no—
178C42×C61C2411yescharacteristic
179C22⋊Dic61—21no—
180#11758202—42no—
181#11758202—42no—
182#11758201—42no—
183#11758200—42no—
184#11758198—21no—
185#11758198—21no—
186#11758198—41no—
187#11758198—41no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—41no—
193C4⋊Dic61—41no—
194C4⋊Dic61C2×D411yescharacteristic
195#11758196—21no—
196#11758196—41no—
197#11758196—41no—
198C4×Dic61—41no—
199C4×Dic61—41no—
200C4×Dic61C2×D411yescharacteristic
201C4×Dic61C2×D411yescharacteristic
202C4×Dic61#4111yescharacteristic
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—42no—
207C2×#92418C2×D411yescharacteristic
208C2×#92418C2×D411yescharacteristic
209#11758190—42no—
210C8×D61—22no—
211C8×D61—41no—
212C8×D61—42no—
213C8×D61—42no—
214C8×D61—42no—
215C23×C61—21no—
216C22×D61—24no—
217C22×D61—21no—
218C22×D61—42no—
219C22×D61—42no—
220C22×D61#12111yescharacteristic
221Q8×C61—41no—
222Q8×C61—41no—
223Q8×C61—41no—
224Q8×C61—41no—
225D4×C61—21no—
226D4×C61#13512yes—
227C2×C4×C61—21no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61C22×D411yescharacteristic
233C2×C4×C61C22×D411yescharacteristic
234C2×C4×C61C2×#4111yescharacteristic
235C22⋊D61—24no—
236C2×Dic61—21no—
237C2×Dic61—42no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61#12111yescharacteristic
241C2×Dic61#12111yescharacteristic
242C2×Dic61#12111yescharacteristic
243D244—21no—
244D244#13512yes—
245C4×D61—22no—
246C4×D61—21no—
247C4×D61—21no—
248C4×D61—21no—
249C4×D61—21no—
250C4×D61—42no—
251C4×D61—42no—
252C4×D61—41no—
253C4×D61—41no—
254Dic122—41no—
255Dic122—41no—
256Dic122—41no—
257Dic122—41no—
258C8×C61—21no—
259C8×C61—21no—
260C8×C61—41no—
261C8×C61—41no—
262C8×C61—41no—
263#92418—21no—
264#92418—41no—
265#92418—41no—
266#92418—41no—
267#92418AGL(1,ℤ/8)12yes—
268#19259—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—48no—
277C2×D61—41no—
278C2×D61—41no—
279C2×D61#47312yes—
280C4×C61—21no—
281C4×C61—41no—
282C4×C61—81no—
283C4×C61—81no—
284C4×C61C2×#13511yescharacteristic
285C4×C61C2×#13511yescharacteristic
286C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
287C4×C61#57511yescharacteristic
288Dic61—21no—
289Dic61—21no—
290Dic61—21no—
291Dic61—41no—
292Dic61—81no—
293Dic61—81no—
294#3170—611no—
295#3110—611no—
296#3110—611no—
297C2×C8×D4—611no—
298#1679—611no—
299#1679—611no—
300#1679—611no—
301#1679D6111yescharacteristic, complemented
302#1673—611no—
303#1673—611no—
304#1669—611no—
305#1669—611no—
306#1568—611no—
307#1552—611no—
308#1552—611no—
309C2×C61—42no—
310C2×C61#303611yescharacteristic
311C2×C61#305011yescharacteristic
312C2×C61C2×#47311yescharacteristic
313D61—22no—
314D61—42no—
315C23×C8—1221no—
316#533—611no—
317#533—611no—
318C2×C4×D4—611no—
319#500—611no—
320#494—611no—
321#487—611no—
322#487C2×D6111yescharacteristic, complemented
323#484—1221no—
324#484—1221no—
325#474—611no—
326#474—611no—
327#474—611no—
328#474C2×D6111yescharacteristic
329#467—1221no—
330#467—1221no—
331#461—611no—
332#461—611no—
333#461—611no—
334#461C2×D6111yescharacteristic
335#450—1221no—
336#450—1221no—
337#440—1221no—
338#440—1221no—
339#440—1221no—
340#440—1221no—
341C4×Q16—1221no—
342C4×Q16—1221no—
343C8×D4—611no—
344C8×D4—611no—
345C8×D4—611no—
346C8×D4—1221no—
347C8×D4—1221no—
348C8×D4C2×D6111yescharacteristic
349#432—611no—
350#432—611no—
351C2×C4⋊C8—611no—
352C2×C22⋊C8—1221no—
353C2×C4×C8—611no—
354#335—611no—
355#335—611no—
356#334—611no—
357#334C2×D6111yescharacteristic, complemented
358#332—611no—
359#332—611no—
360#332—611no—
361#332—611no—
362#332—611no—
363#332—611no—
364#332C2×D6111yescharacteristic, complemented
365#332C2×D6111yescharacteristic, complemented
366C61#1925911yescharacteristic, complemented, Sylow
367C22×D4—611no—
368C23×C4—1221no—
369C2×Q16—1221no—
370C2×Q16—1221no—
371C2×SD16—21no—
372C2×SD16—1221no—
373C2×SD16—1221no—
374C2×SD16—1221no—
375C22×C8—21no—
376C22×C8—611no—
377C22×C8—611no—
378C22×C8—1221no—
379C22×C8—1221no—
380C22×C8—1221no—
381C22×C8—1221no—
382C22×C8—2444no—
383C4⋊Q8—611no—
384C4⋊Q8—611no—
385C4⋊Q8C22×D6111yescharacteristic
386C4⋊Q8C22×D6111yescharacteristic
387#125—1221no—
388#125—1221no—
389C22⋊Q8—1221no—
390C22⋊Q8—1221no—
391C22⋊Q8—1221no—
392C22⋊Q8—1221no—
393C4×Q8—1221no—
394C4×Q8—1221no—
395C4×Q8—1221no—
396C4×Q8—1221no—
397C4×D4—611no—
398C4×D4—611no—
399C4×D4—611no—
400C4×D4—1221no—
401C4×D4—1221no—
402C4×D4C22×D6111yescharacteristic
403#117—1221no—
404#117—1221no—
405C2×C4⋊C4—611no—
406C2×C22⋊C4—1221no—
407C2×C42—611no—
408#107—21no—
409#107—1221no—
410#107—1221no—
411#107—1221no—
412#107—1221no—
413#107—1221no—
414C4⋊C8—611no—
415C4⋊C8—611no—
416C4⋊C8—611no—
417C4⋊C8—1221no—
418C4⋊C8C22×D6111yescharacteristic
419C4⋊C8C22×D6111yescharacteristic
420C4⋊C8C22×D6111yescharacteristic
421#103—21no—
422#103—21no—
423#103—21no—
424#103—1221no—
425#103—1221no—
426#103—1221no—
427#103—1221no—
428#103—1221no—
429#102—21no—
430#102—1221no—
431#102—1221no—
432#102—1221no—
433C22⋊C8—21no—
434C22⋊C8—1221no—
435C22⋊C8—1221no—
436C22⋊C8—1221no—
437C22⋊C8—1221no—
438C22⋊C8—1221no—
439#97—1221no—
440#97—1221no—
441C4×C8—611no—
442C4×C8—611no—
443C4×C8—611no—
444C4×C8C22×D6111yescharacteristic
445C24—1221no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—1221no—
449C2×Q8—1221no—
450C2×D4—611no—
451C2×D4—1221no—
452C2×D4—1222no—
453C2×D4—1222no—
454C2×D4D4×D6111yescharacteristic
455C22×C4—21no—
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—2442no—
464C22×C4—2442no—
465Q16—2442no—
466Q16—2442no—
467SD16—42no—
468SD16—2442no—
469SD16—2442no—
470SD16—2442no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—42no—
475C2×C8—611no—
476C2×C8—611no—
477C2×C8—1222no—
478C2×C8—1221no—
479C2×C8—1221no—
480C2×C8—1221no—
481C2×C8—2441no—
482C2×C8—2442no—
483C2×C8—2442no—
484C2×C8—2442no—
485C2×C8—2442no—
486C2×C8D4×D6111yescharacteristic
487C2×C8D4×D6111yescharacteristic
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—611no—
493C4⋊C4—1221no—
494C4⋊C4—1221no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4—2441no—
499C4⋊C4—2441no—
500C4⋊C4—2441no—
501C4⋊C4—2441no—
502C4⋊C4D4×D6111yescharacteristic
503C22⋊C4—21no—
504C22⋊C4—1221no—
505C22⋊C4—1221no—
506C22⋊C4—1221no—
507C22⋊C4—2441no—
508C22⋊C4—2441no—
509C42—611no—
510C42—611no—
511C42—611no—
512C42—2441no—
513C42—2441no—
514C42C23×D6111yescharacteristic
515C23—21no—
516C23—611no—
517C23—1224no—
518C23—1221no—
519C23—2442no—
520C23—2442no—
521Q8—41no—
522Q8—41no—
523Q8—41no—
524Q8—41no—
525Q8—2441no—
526Q8—2441no—
527Q8—2441no—
528Q8—2441no—
529D4—21no—
530D4—612no—
531D4—1224no—
532D4—1221no—
533D4#1451979812yes—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—611no—
540C2×C4—611no—
541C2×C4—611no—
542C2×C4—1222no—
543C2×C4—1221no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—1221no—
547C2×C4—1221no—
548C2×C4—2442no—
549C2×C4—2442no—
550C2×C4—2442no—
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—612no—
564C8—1221no—
565C8—2441no—
566C8—2441no—
567C8—2441no—
568C22—22no—
569C22—41no—
570C22—41no—
571C22—612no—
572C22—1221no—
573C22—1221no—
574C22—1222no—
575C22—2448no—
576C22—2441no—
577C22—2441no—
578C22#121×D6111yescharacteristic
579C4—21no—
580C4—41no—
581C4—81no—
582C4—81no—
583C4—1221no—
584C4—1221no—
585C4—1221no—
586C4—4881no—
587C4—4881no—
588C4—2441no—
589C4#135×D6111yescharacteristic
590C4C2×#1451979811yescharacteristic
591C4AGL(1,ℤ/8)×D6111yescharacteristic
592C4#1684055911yescharacteristic
593C2—42no—
594C2—1222no—
595C2—2442no—
596C2#2145528111yescharacteristic
597C2#2145539511yescharacteristic
598C2#473×D6111yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1679C2
socleC22×C61C2×#121
prime radicalC2×D4×D61D4
hypercenter#1679D61
hypocenterC61#19259
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. #21456404C2semidirect
5. #21445243C2semidirect
6. #21445242C2semidirect
7. #21445239C2semidirect
8. #21445207C2semidirect
9. #21445206C2semidirect
10. #21445183C2semidirect
11. #21445182C2semidirect
12. #21444579C2semidirect
13. #21444518C2semidirect
14. #21444516C2semidirect
15. C61×#1679C2semidirect
20. #16840165C22semidirect
21. #16840141C22semidirect
22. #16840113C22semidirect
51. #16839514C22semidirect
52. #16839514C22semidirect
53. #16839513C22semidirect
54. #16839509C22semidirect
55. #16839509C22semidirect
56. #16839508C22semidirect
57. #16839508C22semidirect
58. #16839507C22semidirect
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#19259semidirect

Maximal subgroups

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

subgroupindex
#214564042
#214559202
#214559172
C8×D4×D612
#214452432
#214452422
#214452392
#214452072
#214452062
#214451832
#214451822
#214445792
#214445182
#214445162
C61×#16792
#1925961