Finite Group Databasebeta

← #29665282

Subgroups — #29665282

Order 15616.

628 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456979C211yesmaximal, characteristic, complemented
2#21455917C211yesmaximal, characteristic
3#21455826C211yesmaximal, characteristic
4#21454840C211yesmaximal, characteristic
5#21445271C211yesmaximal, characteristic, complemented
6#21445270C211yesmaximal, characteristic, complemented
7#21445245C211yesmaximal, characteristic, complemented
8#21445244C211yesmaximal, characteristic, complemented
9#21445205C211yesmaximal, characteristic, complemented
10#21445193C211yesmaximal, characteristic, complemented
11#21445192C211yesmaximal, characteristic, complemented
12#21444598C211yesmaximal, characteristic, complemented
13#21444526C211yesmaximal, characteristic, complemented
14#21444482C211yesmaximal, characteristic, complemented
15C61×#1673C211yesmaximal, characteristic, complemented
16#16840317C2211yescharacteristic
17#16840317C2211yescharacteristic
18C4×D4×D61C2211yescharacteristic
19#16840158C2211yescharacteristic, complemented
20#16840114C2211yescharacteristic, complemented
21#16840113C2211yescharacteristic, complemented
22#16840105—21no—
23#16840105—21no—
24#16840096—21no—
25#16840091—21no—
26#16840068—21no—
27#16840068—21no—
28#16840053C2211yescharacteristic
29#16840052C2211yescharacteristic
30#16840043C2211yescharacteristic
31#16840042C2211yescharacteristic
32#16839964C2211yescharacteristic
33#16839964C2211yescharacteristic
34#16839911—21no—
35#16839911—21no—
36#16839865—21no—
37#16839863—21no—
38SD16×Dic61—21no—
39#16839847—21no—
40C8×D244C2211yescharacteristic
41D4×#92418C2211yescharacteristic
42#16839827C2211yescharacteristic
43C8×C22⋊D61—21no—
44#16839825—21no—
45#16839818C2211yescharacteristic
46#16839814C2211yescharacteristic
47#16839814C2211yescharacteristic
48#16839813C2211yescharacteristic
49C2×#14519689—21no—
50C22⋊C8×D61—21no—
51#16839515C2211yescharacteristic, 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×#500C2211yescharacteristic, complemented
61C61×#461C2211yescharacteristic
62C61×#461C2211yescharacteristic
63C8×D4×C61C2211yescharacteristic
64C61×#335C2211yescharacteristic, complemented
65C61×#332C2211yescharacteristic, complemented
66C61×#332C2211yescharacteristic, complemented
67C2×D4×D61D411yescharacteristic
68C22×C4×D61—21no—
69C2×#11758201—21no—
70C2×#11758201—21no—
71C22×#92418—21no—
72C2×C8×D61—21no—
73C2×C8×D61—21no—
74#14519777C2311yescharacteristic
75#14519777C2311yescharacteristic
76#14519768—21no—
77#14519768—21no—
78#14519757—21no—
79#14519757—21no—
80#14519753—21no—
81#14519753—21no—
82Q8×Dic61—21no—
83Q8×Dic61—21no—
84#14519742—21no—
85#14519742—21no—
86C4×D244C2311yescharacteristic
87D4×Dic61D411yescharacteristic
88#14519739D411yescharacteristic
89C4×C22⋊D61—21no—
90#14519737—21no—
91#14519735—21no—
92#14519735—21no—
93C4⋊C4×D61D411yescharacteristic
94C22⋊C4×D61—21no—
95C42×D61C2311yescharacteristic
96#14519711—21no—
97#14519710—21no—
98#14519709—21no—
99#14519708—21no—
100#14519708—21no—
101#14519708—21no—
102C4⋊#92418C2311yescharacteristic
103C4⋊#92418C2311yescharacteristic
104C4⋊#92418C2311yescharacteristic
105#14519706D411yescharacteristic
106#14519706D411yescharacteristic
107#14519702—21no—
108#14519702—21no—
109#14519701—21no—
110#14519701—21no—
111#14519700—21no—
112#14519700—21no—
113#14519699—21no—
114#14519699—21no—
115#14519698—21no—
116#14519698—21no—
117C22⋊#92418—21no—
118#14519689—21no—
119#14519689—21no—
120#14519689—21no—
121#14519689—21no—
122#14519689—21no—
123#14519689D411yescharacteristic
124#14519689D411yescharacteristic
125#14519687—21no—
126C4×#92418C2311yescharacteristic
127C8×Dic61—21no—
128C8×Dic61—21no—
129C2×SD16×C61—21no—
130C2×SD16×C61—21no—
131C22×C8×C61—21no—
132C4⋊Q8×C61C2311yescharacteristic
133C4⋊Q8×C61C2311yescharacteristic
134C4×D4×C61C2311yescharacteristic
135#107×C61—21no—
136#107×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140#103×C61—21no—
141#103×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—
151D4×D61—22no—
152D4×D61—22no—
153C2×D244C2×D411yescharacteristic
154C2×C4×D61—21no—
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61—81no—
158C2×C4×D61—81no—
159C2×C4×D61C2×D411yescharacteristic
160C2×C4×D61C2×D411yescharacteristic
161C2×C4×D61#4111yescharacteristic
162C2×Dic122—21no—
163C2×Dic122—21no—
164SD16×C61—42no—
165SD16×C61—42no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—81no—
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#11758201—42no—
181#11758201—42no—
182#11758198—21no—
183#11758198—21no—
184#11758198—41no—
185#11758198—41no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—41no—
191C4⋊Dic61—41no—
192C4⋊Dic61C2×D411yescharacteristic
193#11758196—21no—
194#11758196—41no—
195#11758196—41no—
196C4×Dic61—41no—
197C4×Dic61—41no—
198C4×Dic61C2×D411yescharacteristic
199C4×Dic61C2×D411yescharacteristic
200C4×Dic61#4111yescharacteristic
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—81no—
205C2×#92418C2×D411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207C8×D61—81no—
208C8×D61—81no—
209C23×C61—21no—
210C22×D61—21no—
211C22×D61—24no—
212C22×D61—81no—
213C22×D61—81no—
214C22×D61#12111yescharacteristic
215Q8×C61—41no—
216Q8×C61—41no—
217Q8×C61—41no—
218Q8×C61—41no—
219D4×C61—21no—
220D4×C61#13512yes—
221C2×C4×C61—21no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61C22×D411yescharacteristic
227C2×C4×C61C22×D411yescharacteristic
228C2×C4×C61C2×#4111yescharacteristic
229C22⋊D61—24no—
230C2×Dic61—21no—
231C2×Dic61—41no—
232C2×Dic61—41no—
233C2×Dic61—81no—
234C2×Dic61#12111yescharacteristic
235C2×Dic61#12111yescharacteristic
236C2×Dic61#12111yescharacteristic
237D244—21no—
238D244#13512yes—
239C4×D61—21no—
240C4×D61—21no—
241C4×D61—21no—
242C4×D61—21no—
243C4×D61—41no—
244C4×D61—41no—
245C4×D61—41no—
246C4×D61—81no—
247C4×D61—81no—
248Dic122—41no—
249Dic122—41no—
250Dic122—81no—
251C8×C61—21no—
252C8×C61—21no—
253C8×C61—41no—
254C8×C61—41no—
255C8×C61—41no—
256#92418—21no—
257#92418—21no—
258#92418—41no—
259#92418—41no—
260#92418—41no—
261#19395—611nomaximal, Sylow
262C22×C61—22no—
263C22×C61—41no—
264C22×C61—41no—
265C22×C61C2×#12111yescharacteristic
266C2×D61—21no—
267C2×D61—21no—
268C2×D61—22no—
269C2×D61—21no—
270C2×D61—41no—
271C2×D61—41no—
272C2×D61—84no—
273C4×C61—21no—
274C4×C61—41no—
275C4×C61—81no—
276C4×C61—81no—
277C4×C61C2×#13511yescharacteristic
278C4×C61C2×#13511yescharacteristic
279C4×C61#57711yescharacteristic
280C4×C61#57711yescharacteristic
281Dic61—21no—
282Dic61—21no—
283Dic61—21no—
284Dic61—41no—
285Dic61—81no—
286Dic61—81no—
287#3231—611no—
288#3110—611no—
289#3101—611no—
290#2972—611no—
291#1683—611no—
292#1683—611no—
293#1679—611no—
294#1679—611no—
295#1673—611no—
296#1673D6111yescharacteristic, complemented
297#1671—611no—
298#1671—611no—
299#1572—611no—
300#1554—611no—
301#1544—611no—
302C2×C61—42no—
303C2×C61#304211yescharacteristic
304C2×C61#305011yescharacteristic
305C2×C61#306911yescharacteristic
306D61—41no—
307D61—42no—
308#533—611no—
309#533—611no—
310C2×C4×D4—611no—
311#500C2×D6111yescharacteristic, complemented
312#498—611no—
313#487—611no—
314#487—611no—
315#485—1221no—
316#485—1221no—
317#484—1221no—
318#483—1221no—
319#479—1221no—
320#479—1221no—
321#476—611no—
322#476—611no—
323#474—611no—
324#474—611no—
325#461—611no—
326#461—611no—
327#461C2×D6111yescharacteristic
328#461C2×D6111yescharacteristic
329#450—1221no—
330#450—1221no—
331#440—1221no—
332#440—1221no—
333C4×SD16—1221no—
334C4×SD16—1221no—
335C8×D4—611no—
336C8×D4—611no—
337C8×D4—611no—
338C8×D4—1221no—
339C8×D4—1221no—
340C8×D4C2×D6111yescharacteristic
341#432—611no—
342#431—611no—
343#431—611no—
344#431—611no—
345C2×C22⋊C8—1221no—
346C2×C22⋊C8—1221no—
347#335—611no—
348#335C2×D6111yescharacteristic, complemented
349#334—611no—
350#334—611no—
351#333—611no—
352#333—611no—
353#332—611no—
354#332—611no—
355#332—611no—
356#332—611no—
357#332C2×D6111yescharacteristic, complemented
358#332C2×D6111yescharacteristic, complemented
359C61#1939511yescharacteristic, complemented, Sylow
360C22×D4—611no—
361C23×C4—1221no—
362C2×SD16—21no—
363C2×SD16—21no—
364C2×SD16—1221no—
365C2×SD16—1221no—
366C22×C8—21no—
367C22×C8—1221no—
368C22×C8—1221no—
369C22×C8—1221no—
370C4⋊Q8—611no—
371C4⋊Q8—611no—
372C4⋊Q8C22×D6111yescharacteristic
373C4⋊Q8C22×D6111yescharacteristic
374#125—1221no—
375#125—1221no—
376C22⋊Q8—1221no—
377C22⋊Q8—1221no—
378C22⋊Q8—1221no—
379C22⋊Q8—1221no—
380C4×Q8—1221no—
381C4×Q8—1221no—
382C4×Q8—1221no—
383C4×Q8—1221no—
384C4×D4—611no—
385C4×D4—611no—
386C4×D4—611no—
387C4×D4—1221no—
388C4×D4—1221no—
389C4×D4C22×D6111yescharacteristic
390#117—1221no—
391#117—1221no—
392C2×C4⋊C4—611no—
393C2×C22⋊C4—1221no—
394C2×C42—611no—
395#107—21no—
396#107—21no—
397#107—1221no—
398#107—1221no—
399#106—1221no—
400#106—1221no—
401#106—1221no—
402#106—1221no—
403C4⋊C8—611no—
404C4⋊C8—611no—
405C4⋊C8—611no—
406C4⋊C8—611no—
407C4⋊C8—611no—
408C4⋊C8C22×D6111yescharacteristic
409C4⋊C8C22×D6111yescharacteristic
410C4⋊C8C22×D6111yescharacteristic
411#103—21no—
412#103—21no—
413#103—1221no—
414#103—1221no—
415#103—1221no—
416#103—1221no—
417#103—1221no—
418#103—1221no—
419#102—1221no—
420#102—1221no—
421#102—1221no—
422#102—1221no—
423C22⋊C8—21no—
424C22⋊C8—611no—
425C22⋊C8—611no—
426C22⋊C8—1221no—
427C22⋊C8—1221no—
428C22⋊C8—1221no—
429C22⋊C8—1221no—
430C22⋊C8—1221no—
431C22⋊C8—1221no—
432#97—1221no—
433C4×C8—611no—
434C4×C8—1221no—
435C4×C8—1221no—
436C4×C8C22×D6111yescharacteristic
437C24—1221no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—1221no—
441C2×Q8—1221no—
442C2×D4—611no—
443C2×D4—1221no—
444C2×D4—1222no—
445C2×D4—1222no—
446C2×D4D4×D6111yescharacteristic
447C22×C4—21no—
448C22×C4—611no—
449C22×C4—611no—
450C22×C4—611no—
451C22×C4—1221no—
452C22×C4—1221no—
453C22×C4—1221no—
454C22×C4—1221no—
455C22×C4—4881no—
456C22×C4—4881no—
457SD16—42no—
458SD16—42no—
459SD16—2442no—
460SD16—2442no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—81no—
465C2×C8—611no—
466C2×C8—611no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8—4881no—
471C2×C8—4881no—
472C2×C8—4881no—
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—
495C22⋊C4—2441no—
496C42—611no—
497C42—611no—
498C42—611no—
499C42—2441no—
500C42—2441no—
501C42C23×D6111yescharacteristic
502C23—21no—
503C23—611no—
504C23—1224no—
505C23—1221no—
506C23—4881no—
507C23—4881no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—4881no—
513Q8—2441no—
514Q8—2441no—
515D4—21no—
516D4—612no—
517D4—1224no—
518D4—1221no—
519D4#1451979612yes—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—611no—
526C2×C4—611no—
527C2×C4—611no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—1221no—
533C2×C4—4881no—
534C2×C4—4881no—
535C2×C4—4881no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4C2×D4×D6111yescharacteristic
542C2×C4C2×D4×D6111yescharacteristic
543C2×C4#41×D6111yescharacteristic
544C8—21no—
545C8—21no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8—1221no—
550C8—1221no—
551C8—2441no—
552C8—2441no—
553C8—2441no—
554C22—22no—
555C22—41no—
556C22—41no—
557C22—1221no—
558C22—1222no—
559C22—1221no—
560C22—1221no—
561C22—4884no—
562C22—2441no—
563C22—2441no—
564C22#121×D6111yescharacteristic
565C4—21no—
566C4—41no—
567C4—81no—
568C4—81no—
569C4—1221no—
570C4—1221no—
571C4—1221no—
572C4—4881no—
573C4—4881no—
574C4—2441no—
575C4#135×D6111yescharacteristic
576C4C2×#1451979611yescharacteristic
577C4#1684056811yescharacteristic
578C4#1684057111yescharacteristic
579C2—42no—
580C2—2441no—
581C2—2442no—
582C2#2145532611yescharacteristic
583C2#2145539811yescharacteristic
584C2#2145555411yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1673C2
socleC22×C61C2×#121
prime radicalC2×D4×D61D4
hypercenter#1673D61
hypocenterC61#19395
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1673

Complements

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

NH ≅ G/Ntype
1. #21456979C2semidirect
5. #21445271C2semidirect
6. #21445270C2semidirect
7. #21445245C2semidirect
8. #21445244C2semidirect
9. #21445205C2semidirect
10. #21445193C2semidirect
11. #21445192C2semidirect
12. #21444598C2semidirect
13. #21444526C2semidirect
14. #21444482C2semidirect
15. C61×#1673C2semidirect
19. #16840158C22semidirect
20. #16840114C22semidirect
21. #16840113C22semidirect
51. #16839515C22semidirect
52. #16839512C22semidirect
53. #16839512C22semidirect
54. #16839510C22semidirect
55. #16839510C22semidirect
56. #16839509C22semidirect
57. #16839508C22semidirect
58. #16839508C22semidirect
59. #16839507C22semidirect
60. C61×#500C22semidirect
64. C61×#335C22semidirect
65. C61×#332C22semidirect
66. C61×#332C22semidirect
296. #1673D61semidirect
311. #500C2×D61semidirect
348. #335C2×D61semidirect
357. #332C2×D61semidirect
358. #332C2×D61semidirect
359. C61#19395semidirect

Maximal subgroups

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

subgroupindex
#214569792
#214559172
#214558262
#214548402
#214452712
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