Finite Group Databasebeta

← #29665253

Subgroups — #29665253

Order 15616.

642 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456971C211yesmaximal, characteristic, complemented
2#21455617C211yesmaximal, characteristic
3#476×D61C211yesmaximal, characteristic
4#21454840C211yesmaximal, characteristic
5#21445273C211yesmaximal, characteristic, complemented
6#21445272C211yesmaximal, characteristic, complemented
7#21445271C211yesmaximal, characteristic, complemented
8#21445270C211yesmaximal, characteristic, complemented
9#21445217C211yesmaximal, characteristic, complemented
10#21445216C211yesmaximal, characteristic, complemented
11#21445215C211yesmaximal, characteristic, complemented
12#21444592C211yesmaximal, characteristic, complemented
13#21444498C211yesmaximal, characteristic, complemented
14#21444473C211yesmaximal, characteristic, complemented
15C61×#1675C211yesmaximal, characteristic, complemented
16#16840317C2211yescharacteristic
17C4⋊Q8×D61C2211yescharacteristic
18C4×D4×D61C2211yescharacteristic
19#16840165C2211yescharacteristic, complemented
20#16840114C2211yescharacteristic, complemented
21#16840113C2211yescharacteristic, complemented
22#16840099—21no—
23#16840099—21no—
24#16840061—21no—
25#16840060—21no—
26#16840056—21no—
27#16840056—21no—
28#16840053C2211yescharacteristic
29#16840052C2211yescharacteristic
30#16840051—21no—
31#16840050—21no—
32#16840049C2211yescharacteristic
33#16840049C2211yescharacteristic
34#16840043C2211yescharacteristic
35#16840042C2211yescharacteristic
36C8×D244C2211yescharacteristic
37D4×#92418C2211yescharacteristic
38#16839827C2211yescharacteristic
39C8×C22⋊D61—21no—
40#16839825—21no—
41#16839814C2211yescharacteristic
42#16839813C2211yescharacteristic
43#16839801—21no—
44#106×D61—21no—
45#16839784C2211yescharacteristic
46C4⋊C8×D61C2211yescharacteristic
47#16839765—21no—
48#102×D61—21no—
49C2×#14519689—21no—
50C22⋊C8×D61—21no—
51#16839515C2211yescharacteristic, complemented
52#16839514C2211yescharacteristic, complemented
53#16839514C2211yescharacteristic, complemented
54#16839511C2211yescharacteristic, complemented
55#16839511C2211yescharacteristic, complemented
56#16839510C2211yescharacteristic, complemented
57#16839510C2211yescharacteristic, complemented
58#16839509C2211yescharacteristic, complemented
59#16839507C2211yescharacteristic, complemented
60C61×#500C2211yescharacteristic, complemented
61C61×#476C2211yescharacteristic
62C61×#476C2211yescharacteristic
63C8×D4×C61C2211yescharacteristic
64C61×#335C2211yescharacteristic, complemented
65C61×#333C2211yescharacteristic, complemented
66C61×#333C2211yescharacteristic, complemented
67C2×Q8×D61—21no—
68C2×D4×D61D411yescharacteristic
69C22×C4×D61—21no—
70C2×#11758189—21no—
71C22×#92418—21no—
72C2×C8×D61—21no—
73C2×C8×D61—21no—
74C2×C8×D61—21no—
75#14519777C2311yescharacteristic
76#14519777C2311yescharacteristic
77#14519776—21no—
78#14519776—21no—
79#14519775—21no—
80#14519768—21no—
81#14519757—21no—
82#14519753—21no—
83Q8×Dic61—21no—
84#14519742—21no—
85C4×D244C2311yescharacteristic
86D4×Dic61D411yescharacteristic
87#14519739D411yescharacteristic
88C4×C22⋊D61—21no—
89#14519737—21no—
90#14519735—21no—
91C4⋊C4×D61—21no—
92C4⋊C4×D61—21no—
93C4⋊C4×D61D411yescharacteristic
94C22⋊C4×D61—21no—
95C42×D61C2311yescharacteristic
96#14519711—21no—
97#14519710—21no—
98#14519710—21no—
99#14519710—21no—
100#14519709—21no—
101#14519708—21no—
102#14519708—21no—
103#14519708—21no—
104C4⋊#92418C2311yescharacteristic
105C4⋊#92418C2311yescharacteristic
106C4⋊#92418C2311yescharacteristic
107#14519706—21no—
108#14519706—21no—
109#14519706D411yescharacteristic
110#14519706D411yescharacteristic
111#14519702—21no—
112#14519702—21no—
113#14519700—21no—
114#14519700—21no—
115#14519699—21no—
116#14519699—21no—
117#14519698—21no—
118#14519698—21no—
119#14519697—21no—
120#14519697—21no—
121C22⋊#92418—21no—
122#14519689—21no—
123#14519689—21no—
124#14519689—21no—
125#14519689D411yescharacteristic
126#14519689D411yescharacteristic
127C4×#92418C2311yescharacteristic
128C8×Dic61—21no—
129C22×C8×C61—21no—
130C4⋊Q8×C61C2311yescharacteristic
131C4⋊Q8×C61C2311yescharacteristic
132C4×D4×C61C2311yescharacteristic
133#107×C61—21no—
134#107×C61—21no—
135#106×C61—21no—
136#106×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140#102×C61—21no—
141#102×C61—21no—
142C22⋊C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C23×D61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×D4×C61C2×D411yescharacteristic
148C22×C4×C61—21no—
149C2×C22⋊D61—21no—
150C22×Dic61—21no—
151Q8×D61—82no—
152D4×D61—22no—
153D4×D61Q1614yes—
154C2×D244C2×D411yescharacteristic
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—41no—
159C2×C4×D61—81no—
160C2×C4×D61—81no—
161C2×C4×D61C2×D411yescharacteristic
162C2×C4×D61C2×D411yescharacteristic
163C2×C4×D61#4111yescharacteristic
164C2×Dic122—21no—
165C2×Dic122—21no—
166C2×Dic122—41no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—81no—
171C2×C8×C61C2×D411yescharacteristic
172C2×C8×C61C2×D411yescharacteristic
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61C2×D411yescharacteristic
178C22⋊C4×C61—21no—
179C42×C61C2411yescharacteristic
180C22⋊Dic61—21no—
181#11758198—21no—
182#11758198—21no—
183#11758198—41no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—41no—
189C4⋊Dic61C2×D411yescharacteristic
190#11758196—21no—
191#11758196—41no—
192#11758196—41no—
193#11758196—41no—
194C4×Dic61—41no—
195C4×Dic61C2×D411yescharacteristic
196C4×Dic61C2×D411yescharacteristic
197C4×Dic61#4111yescharacteristic
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—81no—
202C2×#92418C2×D411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204#11758189—42no—
205C8×D61—42no—
206C8×D61—81no—
207C8×D61—81no—
208C23×C61—21no—
209C22×D61—21no—
210C22×D61—24no—
211C22×D61—81no—
212C22×D61—81no—
213C22×D61#12111yescharacteristic
214Q8×C61—81no—
215Q8×C61—81no—
216D4×C61—21no—
217D4×C61C2×Q1612yes—
218C2×C4×C61—21no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61C22×D411yescharacteristic
224C2×C4×C61C22×D411yescharacteristic
225C2×C4×C61C2×#4111yescharacteristic
226C22⋊D61—24no—
227C2×Dic61—21no—
228C2×Dic61—41no—
229C2×Dic61—41no—
230C2×Dic61—81no—
231C2×Dic61#12111yescharacteristic
232C2×Dic61#12111yescharacteristic
233C2×Dic61#12111yescharacteristic
234D244—21no—
235D244C2×Q1612yes—
236C4×D61—21no—
237C4×D61—21no—
238C4×D61—41no—
239C4×D61—41no—
240C4×D61—41no—
241C4×D61—81no—
242C4×D61—81no—
243C4×D61—82no—
244C4×D61C2×Q1612yes—
245C4×D61#13512yes—
246Dic122—41no—
247Dic122—41no—
248Dic122—82no—
249Dic122—81no—
250C8×C61—21no—
251C8×C61—21no—
252C8×C61—41no—
253C8×C61—41no—
254C8×C61—41no—
255#92418—21no—
256#92418—21no—
257#92418—41no—
258#92418—41no—
259#92418—41no—
260#19393—611nomaximal, Sylow
261C22×C61—22no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61C2×#12111yescharacteristic
265C2×D61—21no—
266C2×D61—21no—
267C2×D61—22no—
268C2×D61—41no—
269C2×D61—41no—
270C2×D61—84no—
271C2×D61#46712yes—
272C4×C61—21no—
273C4×C61—41no—
274C4×C61—81no—
275C4×C61—81no—
276C4×C61C22×Q1611yescharacteristic
277C4×C61C2×#13511yescharacteristic
278C4×C61#57711yescharacteristic
279C4×C61#57711yescharacteristic
280Dic61—21no—
281Dic61—21no—
282Dic61—41no—
283Dic61—81no—
284Dic61—81no—
285Dic61#46712yes—
286#3230—611no—
287#3077—611no—
288C2×#476—611no—
289#2972—611no—
290#1683—611no—
291#1683—611no—
292#1683—611no—
293#1683—611no—
294#1675—611no—
295#1675—611no—
296#1675—611no—
297#1675D6111yescharacteristic, complemented
298#1571—611no—
299#1548—611no—
300#1542—611no—
301C2×C61—42no—
302C2×C61#304211yescharacteristic
303C2×C61C2×#46711yescharacteristic
304C2×C61#306811yescharacteristic
305D61—22no—
306D61—42no—
307#533—611no—
308C2×C4⋊Q8—611no—
309C2×C4×D4—611no—
310#500—611no—
311#500C2×D6111yescharacteristic, complemented
312#487—611no—
313#487—611no—
314#484—1221no—
315#484—1221no—
316#478—1221no—
317#478—1221no—
318#477—1221no—
319#477—1221no—
320#476—611no—
321#476—611no—
322#476—611no—
323#476—611no—
324#476—1221no—
325#476—1221no—
326#476C2×D6111yescharacteristic
327#476C2×D6111yescharacteristic
328#474—611no—
329#474—611no—
330C8×D4—611no—
331C8×D4—611no—
332C8×D4—611no—
333C8×D4—1221no—
334C8×D4—1221no—
335C8×D4C2×D6111yescharacteristic
336#431—611no—
337#431—611no—
338#428—1221no—
339C2×#106—1221no—
340#423—611no—
341C2×C4⋊C8—611no—
342#418—1221no—
343C2×#102—1221no—
344C2×C22⋊C8—1221no—
345C2×C22⋊C8—1221no—
346#335—611no—
347#335—611no—
348#335—611no—
349#335C2×D6111yescharacteristic, complemented
350#333—611no—
351#333—611no—
352#333—611no—
353#333—611no—
354#333C2×D6111yescharacteristic, complemented
355#333C2×D6111yescharacteristic, complemented
356#332—611no—
357#332—611no—
358C61#1939311yescharacteristic, complemented, Sylow
359C22×Q8—1221no—
360C22×D4—611no—
361C23×C4—1221no—
362C2×M16—1221no—
363C22×C8—21no—
364C22×C8—1221no—
365C22×C8—1221no—
366C22×C8—1221no—
367C22×C8—1221no—
368C4⋊Q8—611no—
369C4⋊Q8—611no—
370C4⋊Q8—1221no—
371C4⋊Q8—1221no—
372C4⋊Q8—1221no—
373C4⋊Q8C22×D6111yescharacteristic
374C4⋊Q8C22×D6111yescharacteristic
375#125—1221no—
376C22⋊Q8—1221no—
377C22⋊Q8—1221no—
378C4×Q8—1221no—
379C4×Q8—1221no—
380C4×D4—611no—
381C4×D4—611no—
382C4×D4—611no—
383C4×D4—1221no—
384C4×D4—1221no—
385C4×D4C22×D6111yescharacteristic
386#117—1221no—
387C2×C4⋊C4—611no—
388C2×C4⋊C4—1221no—
389C2×C4⋊C4—1221no—
390C2×C22⋊C4—1221no—
391C2×C42—611no—
392#107—21no—
393#107—21no—
394#107—1221no—
395#107—1221no—
396#107—1221no—
397#107—1221no—
398#106—21no—
399#106—21no—
400#106—1221no—
401#106—1221no—
402#106—1221no—
403#106—1221no—
404C4⋊C8—611no—
405C4⋊C8—611no—
406C4⋊C8—611no—
407C4⋊C8—611no—
408C4⋊C8—611no—
409C4⋊C8—1221no—
410C4⋊C8—1221no—
411C4⋊C8C22×D6111yescharacteristic
412C4⋊C8C22×D6111yescharacteristic
413C4⋊C8C22×D6111yescharacteristic
414#103—1221no—
415#103—1221no—
416#103—1221no—
417#103—1221no—
418#102—21no—
419#102—21no—
420#102—1221no—
421#102—1221no—
422#102—1221no—
423#102—1221no—
424#102—1221no—
425#102—1221no—
426C22⋊C8—21no—
427C22⋊C8—611no—
428C22⋊C8—611no—
429C22⋊C8—1221no—
430C22⋊C8—1221no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433C4×C8—611no—
434C4×C8—1221no—
435C4×C8C22×D6111yescharacteristic
436C24—1221no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—1221no—
440C2×Q8—1221no—
441C2×Q8—4882no—
442C2×Q8—2441no—
443C2×D4—614no—
444C2×D4—611no—
445C2×D4—1222no—
446C2×D4—1221no—
447C2×D4D4×D6111yescharacteristic
448C22×C4—21no—
449C22×C4—611no—
450C22×C4—611no—
451C22×C4—611no—
452C22×C4—1221no—
453C22×C4—1221no—
454C22×C4—1221no—
455C22×C4—1221no—
456C22×C4—4881no—
457C22×C4—4881no—
458C22×C4—2441no—
459M16—2442no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—81no—
464C2×C8—611no—
465C2×C8—611no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—4881no—
470C2×C8—4881no—
471C2×C8—4881no—
472C2×C8—2442no—
473C2×C8D4×D6111yescharacteristic
474C2×C8D4×D6111yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—611no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4—2441no—
486C4⋊C4—2441no—
487C4⋊C4—2441no—
488C4⋊C4—2441no—
489C4⋊C4D4×D6111yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—1221no—
492C22⋊C4—1221no—
493C22⋊C4—1221no—
494C22⋊C4—2441no—
495C42—611no—
496C42—611no—
497C42—611no—
498C42—2441no—
499C42C23×D6111yescharacteristic
500C23—21no—
501C23—611no—
502C23—1224no—
503C23—1221no—
504C23—4881no—
505C23—4881no—
506Q8—81no—
507Q8—81no—
508Q8—4881no—
509Q8—4882no—
510Q8—2441no—
511Q8—2441no—
512D4—21no—
513D4—612no—
514D4—1224no—
515D4—1221no—
516D4Q16×D6112yes—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—611no—
523C2×C4—612no—
524C2×C4—612no—
525C2×C4—611no—
526C2×C4—611no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—4881no—
531C2×C4—4881no—
532C2×C4—4882no—
533C2×C4—4881no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4C2×D4×D6111yescharacteristic
540C2×C4C2×D4×D6111yescharacteristic
541C2×C4#41×D6111yescharacteristic
542C8—21no—
543C8—21no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8—1221no—
548C8—1221no—
549C8—2441no—
550C8—2441no—
551C8—2441no—
552C22—22no—
553C22—41no—
554C22—41no—
555C22—612no—
556C22—1221no—
557C22—1221no—
558C22—1222no—
559C22—4884no—
560C22—2441no—
561C22—2441no—
562C22#121×D6111yescharacteristic
563C4—21no—
564C4—41no—
565C4—81no—
566C4—81no—
567C4—612no—
568C4—1221no—
569C4—1221no—
570C4—4881no—
571C4—4881no—
572C4—2441no—
573C4C2×Q16×D6111yescharacteristic
574C4#135×D6111yescharacteristic
575C4#1684056811yescharacteristic
576C4#1684057111yescharacteristic
577C2—42no—
578C2—1222no—
579C2—2442no—
580C2#2145532611yescharacteristic
581C2#467×D6111yescharacteristic
582C2#2145554511yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1675C2
socleC22×C61C2×#121
prime radicalC2×D4×D61D4
hypercenter#1675D61
hypocenterC61#19393
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1675

Complements

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

NH ≅ G/Ntype
1. #21456971C2semidirect
5. #21445273C2semidirect
6. #21445272C2semidirect
7. #21445271C2semidirect
8. #21445270C2semidirect
9. #21445217C2semidirect
10. #21445216C2semidirect
11. #21445215C2semidirect
12. #21444592C2semidirect
13. #21444498C2semidirect
14. #21444473C2semidirect
15. C61×#1675C2semidirect
19. #16840165C22semidirect
20. #16840114C22semidirect
21. #16840113C22semidirect
51. #16839515C22semidirect
52. #16839514C22semidirect
53. #16839514C22semidirect
54. #16839511C22semidirect
55. #16839511C22semidirect
56. #16839510C22semidirect
57. #16839510C22semidirect
58. #16839509C22semidirect
59. #16839507C22semidirect
60. C61×#500C22semidirect
64. C61×#335C22semidirect
65. C61×#333C22semidirect
66. C61×#333C22semidirect
297. #1675D61semidirect
311. #500C2×D61semidirect
349. #335C2×D61semidirect
354. #333C2×D61semidirect
355. #333C2×D61semidirect
358. C61#19393semidirect

Maximal subgroups

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

subgroupindex
#214569712
#214556172
#476×D612
#214548402
#214452732
#214452722
#214452712
#214452702
#214452172
#214452162
#214452152
#214445922
#214444982
#214444732
C61×#16752
#1939361