Finite Group Databasebeta

← #36525767

Subgroups — #36525767

Order 22784.

616 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26030258C211yesmaximal, characteristic
2#26029350C211yesmaximal, characteristic, complemented
3#26029284C211yesmaximal, characteristic
4#26019151C211yesmaximal, characteristic, complemented
5#26019128C211yesmaximal, characteristic, complemented
6#26019107C211yesmaximal, characteristic, complemented
7#26019096C211yesmaximal, characteristic, complemented
8#26019087C211yesmaximal, characteristic, complemented
9#26019067C211yesmaximal, characteristic, complemented
10C8×#13083563C211yesmaximal, characteristic, complemented
11#26019029C211yesmaximal, characteristic, complemented
12#26018723C211yesmaximal, characteristic, complemented
13#26018641C211yesmaximal, characteristic
14#26018551C211yesmaximal, characteristic, complemented
15C89×#1590C211yesmaximal, characteristic, complemented
16#19152152C2211yescharacteristic
17C4×D4×D89C2211yescharacteristic
18#19151930C411yescharacteristic
19#19151927C411yescharacteristic
20#19151887C411yescharacteristic
21#19151886C411yescharacteristic
22#19151802C411yescharacteristic
23#19151801C411yescharacteristic
24#19151750C411yescharacteristic
25#19151747C411yescharacteristic
26#19151726—21no—
27#19151725C2211yescharacteristic, complemented
28Q8×#10623494C2211yescharacteristic, complemented
29C8×Dic178C2211yescharacteristic, complemented
30#19151722—21no—
31C4×#13083563C2211yescharacteristic
32C4×#13083561C2211yescharacteristic
33C4×#13083562C2211yescharacteristic
34#19151676C2211yescharacteristic
35#19151672—21no—
36#19151667—21no—
37C8×D356C2211yescharacteristic
38#19151663C2211yescharacteristic
39#19151660—21no—
40#19151658—21no—
41#19151654C2211yescharacteristic
42#19151650C2211yescharacteristic
43#19151649C2211yescharacteristic
44#19151649C2211yescharacteristic
45#19151649C2211yescharacteristic
46#19151561—21no—
47C22⋊C8×D89—21no—
48#19151350C2211yescharacteristic, complemented
49#19151350C2211yescharacteristic, complemented
50#19151349C2211yescharacteristic, complemented
51#19151330C2211yescharacteristic, complemented
52Q8⋊#10623494C2211yescharacteristic, complemented
53#19151328C2211yescharacteristic, complemented
54#19151327C2211yescharacteristic
55D4⋊#10623494C2211yescharacteristic
56#19151325C2211yescharacteristic
57#19151320C2211yescharacteristic, complemented
58#19151320C2211yescharacteristic, complemented
59#19151320C2211yescharacteristic, complemented
60#446×C89C2211yescharacteristic, complemented
61C4×SD16×C89C2211yescharacteristic
62#436×C89C2211yescharacteristic
63#334×C89C2211yescharacteristic, complemented
64Q8⋊C8×C89C2211yescharacteristic, complemented
65D4⋊C8×C89C2211yescharacteristic
66C82×C89C2211yescharacteristic, complemented
67C2×D4×D89C2×C411yescharacteristic
68C22×C4×D89—21no—
69C2×#13083563C2×C411yescharacteristic
70C2×#13083562C2×C411yescharacteristic
71C2×#13083561C2×C411yescharacteristic
72C2×#13083558—21no—
73C2×C8×D89—21no—
74C2×C8×D89—21no—
75#15668011C2×C411yescharacteristic
76#15668010C2×C411yescharacteristic
77#15668002—21no—
78#15667992C2×C411yescharacteristic
79#15667990—21no—
80#15667988C2×C411yescharacteristic
81C4×Dic178—21no—
82C4×Dic178C2311yescharacteristic
83C4×D356C2311yescharacteristic
84D4×Dic89C2×C411yescharacteristic
85#15667974C2×C411yescharacteristic
86C4×C22⋊D89—21no—
87#15667972—21no—
88#15667969—21no—
89C4⋊C4×D89C2×C411yescharacteristic
90C22⋊C4×D89—21no—
91C42×D89C2311yescharacteristic
92#15667944C2×C411yescharacteristic
93#15667943C2×C411yescharacteristic
94#15667943C2×C411yescharacteristic
95C4⋊#10623494—21no—
96C4⋊#10623494C2311yescharacteristic
97C4⋊#10623494C2311yescharacteristic
98#15667941—21no—
99#15667941—21no—
100#15667941—21no—
101#15667941C2×C411yescharacteristic
102#15667941C2×C411yescharacteristic
103#15667941D411yescharacteristic
104#15667941D411yescharacteristic
105#15667937C2×C411yescharacteristic
106#15667936C2×C411yescharacteristic
107#15667935C2×C411yescharacteristic
108#15667934C2×C411yescharacteristic
109#15667933C2×C411yescharacteristic
110#15667932C2×C411yescharacteristic
111C22⋊#10623494—21no—
112#15667924—21no—
113#15667924—21no—
114#15667924—21no—
115#15667924—21no—
116#15667924—21no—
117#15667924C2×C411yescharacteristic
118#15667924C2×C411yescharacteristic
119#15667924D411yescharacteristic
120#15667924D411yescharacteristic
121#15667922—21no—
122#15667922—21no—
123C4×#10623494—21no—
124C4×#10623494C2311yescharacteristic
125C4×#10623494C2311yescharacteristic
126C4×#10623494C2311yescharacteristic
127C8×Dic89—21no—
128C8×Dic89—21no—
129C2×SD16×C89C2×C411yescharacteristic
130C2×M16×C89—21no—
131C4×Q8×C89C2311yescharacteristic
132C4×D4×C89C2311yescharacteristic
133#106×C89C2×C411yescharacteristic
134C4⋊C8×C89—21no—
135C4⋊C8×C89C2311yescharacteristic
136C4⋊C8×C89C2311yescharacteristic
137#103×C89C2×C411yescharacteristic
138#102×C89C2×C411yescharacteristic
139C22⋊C8×C89—21no—
140#97×C89—21no—
141C4×C8×C89C2311yescharacteristic
142C4×C8×C89C2311yescharacteristic
143C4×C8×C89C2311yescharacteristic
144C23×D89—21no—
145C2×Dic178—21no—
146C2×Dic178C22×C411yescharacteristic
147C2×D356C22×C411yescharacteristic
148C2×C22⋊D89—21no—
149D4×D89—22no—
150D4×D89—41no—
151C22×Dic89—21no—
152C2×C4×D89—21no—
153C2×C4×D89—21no—
154C2×C4×D89—21no—
155C2×C4×D89—81no—
156C2×C4×D89—81no—
157C2×C4×D89C22×C411yescharacteristic
158C2×C4×D89C2×D411yescharacteristic
159C2×C4×D89#4111yescharacteristic
160#13083563—22no—
161#13083562—41no—
162#13083561—22no—
163#13083558—81no—
164C2×#10623494—21no—
165C2×#10623494—21no—
166C2×#10623494—21no—
167C2×#10623494C22×C411yescharacteristic
168C2×#10623494C22×C411yescharacteristic
169C2×#10623494C2×D411yescharacteristic
170C2×#10623494C2×D411yescharacteristic
171C8×D89—81no—
172C8×D89—81no—
173C4⋊Dic89—21no—
174C4⋊Dic89C22×C411yescharacteristic
175C4⋊Dic89C22×C411yescharacteristic
176#13083553—21no—
177#13083553—21no—
178#13083553—21no—
179#13083553—21no—
180#13083553—21no—
181#13083553—21no—
182C22⋊Dic89—21no—
183#13083551—21no—
184#13083551—21no—
185#13083551—21no—
186#13083551—21no—
187C4×Dic89—21no—
188C4×Dic89C22×C411yescharacteristic
189C4×Dic89C2×D411yescharacteristic
190C4×Dic89#4111yescharacteristic
191C2×Q8×C89C22×C411yescharacteristic
192C2×D4×C89C22×C411yescharacteristic
193C22×C4×C89—21no—
194SD16×C89—41no—
195M16×C89—81no—
196C2×C8×C89—21no—
197C2×C8×C89—21no—
198C2×C8×C89—21no—
199C2×C8×C89C22×C411yescharacteristic
200C2×C8×C89C22×C411yescharacteristic
201C2×C8×C89C2×D411yescharacteristic
202C2×C8×C89C2×D411yescharacteristic
203C4⋊C4×C89—21no—
204C4⋊C4×C89C22×C411yescharacteristic
205C4⋊C4×C89C22×C411yescharacteristic
206C22⋊C4×C89—21no—
207C42×C89—21no—
208C42×C89C2411yescharacteristic
209C23×C89—21no—
210C22×D89—21no—
211C22×D89—42no—
212C22×D89—42no—
213C22×D89—81no—
214C22×D89C4×D411yescharacteristic
215Q8×C89—21no—
216Q8×C89—21no—
217D4×C89—21no—
218D4×C89—21no—
219C2×C4×C89—21no—
220C2×C4×C89—21no—
221C2×C4×C89—21no—
222C2×C4×C89—41no—
223C2×C4×C89—41no—
224C2×C4×C89C23×C411yescharacteristic
225C2×C4×C89C22×D411yescharacteristic
226C2×C4×C89C2×#4111yescharacteristic
227C22⋊D89—42no—
228C2×Dic89—21no—
229C2×Dic89—21no—
230C2×Dic89—21no—
231C2×Dic89—81no—
232C2×Dic89C4×D411yescharacteristic
233C2×Dic89C4×D411yescharacteristic
234C2×Dic89C4×D411yescharacteristic
235D356—21no—
236D356#13112yes—
237C4×D89—21no—
238C4×D89—21no—
239C4×D89—21no—
240C4×D89—21no—
241C4×D89—41no—
242C4×D89—41no—
243C4×D89—41no—
244C4×D89—81no—
245C4×D89—81no—
246Dic178—21no—
247Dic178—21no—
248Dic178—42no—
249C8×C89—21no—
250C8×C89—21no—
251C8×C89—21no—
252C8×C89—21no—
253C8×C89—41no—
254C8×C89—41no—
255C8×C89—41no—
256#10623494—21no—
257#10623494—21no—
258#10623494—21no—
259#10623494—21no—
260#10623494—41no—
261#10623494—41no—
262#10623494—41no—
263C22×C89—41no—
264C22×C89—41no—
265C22×C89—41no—
266C22×C89C2×C4×D411yescharacteristic
267C2×D89—21no—
268C2×D89—22no—
269C2×D89—21no—
270C2×D89—21no—
271C2×D89—41no—
272C2×D89—41no—
273C2×D89—84no—
274C4×C89—21no—
275C4×C89—41no—
276C4×C89—41no—
277C4×C89—41no—
278C4×C89C2×#13111yescharacteristic
279C4×C89#56811yescharacteristic
280C4×C89#57711yescharacteristic
281C4×C89#57711yescharacteristic
282Dic89—21no—
283Dic89—21no—
284Dic89—21no—
285Dic89—41no—
286Dic89—41no—
287Dic89—41no—
288#18028—891nomaximal, Sylow
289C2×C89—81no—
290C2×C89#293311yescharacteristic
291C2×C89#294911yescharacteristic
292C2×C89#295511yescharacteristic
293D89—41no—
294D89—42no—
295#3101—891no—
296#2986—891no—
297#2974—891no—
298#1592—891no—
299#1590D8911yescharacteristic, complemented
300#1588—891no—
301#1585—891no—
302#1583—891no—
303#1582—891no—
304SD16⋊C8—891no—
305C8×SD16—891no—
306#1572—891no—
307#1497—891no—
308#1478—891no—
309#1454—891no—
310C89#1802811yescharacteristic, complemented, Sylow
311#533—891no—
312C2×C4×D4—891no—
313#483—891no—
314#483—891no—
315#476—891no—
316#476—891no—
317#461—891no—
318#461—891no—
319#450—891no—
320#450—891no—
321#446—891no—
322#446—1781no—
323#446C2×D8911yescharacteristic, complemented
324C8×Q8—891no—
325C8×Q8—891no—
326C8×Q8—1781no—
327C4×SD16—891no—
328C4×SD16—891no—
329C4×SD16—891no—
330C4×SD16C2×D8911yescharacteristic
331#436—891no—
332#436C2×D8911yescharacteristic
333#435—1781no—
334#435—1781no—
335C8×D4—891no—
336C8×D4—891no—
337#433—1781no—
338#433—1781no—
339#432—891no—
340#431—891no—
341#431—891no—
342#431—891no—
343#431—891no—
344#407—1781no—
345C2×C22⋊C8—1781no—
346#335—891no—
347#335—891no—
348#334—891no—
349#334C2×D8911yescharacteristic, complemented
350Q8⋊C8—891no—
351Q8⋊C8—891no—
352Q8⋊C8—891no—
353Q8⋊C8C2×D8911yescharacteristic, complemented
354D4⋊C8—891no—
355D4⋊C8—891no—
356D4⋊C8—891no—
357D4⋊C8C2×D8911yescharacteristic
358#322—891no—
359#322—891no—
360#322—891no—
361C82C2×D8911yescharacteristic, complemented
362C22×D4—891no—
363C23×C4—1781no—
364C2×SD16—891no—
365C2×SD16—891no—
366C2×SD16—891no—
367C2×SD16C4×D8911yescharacteristic
368C2×M16—21no—
369C2×M16—1781no—
370C22×C8—1781no—
371C22×C8—1781no—
372C4⋊Q8—891no—
373C4⋊Q8—891no—
374#125—1781no—
375C22⋊Q8—891no—
376C22⋊Q8—891no—
377C22⋊Q8—1781no—
378C4×Q8—891no—
379C4×Q8—1781no—
380C4×Q8C22×D8911yescharacteristic
381C4×D4—891no—
382C4×D4—891no—
383C4×D4—891no—
384C4×D4—1781no—
385C4×D4—1781no—
386C4×D4C22×D8911yescharacteristic
387#117—1781no—
388C2×C4⋊C4—891no—
389C2×C22⋊C4—1781no—
390C2×C42—891no—
391#106—891no—
392#106—891no—
393#106—891no—
394#106C4×D8911yescharacteristic
395C4⋊C8—21no—
396C4⋊C8—891no—
397C4⋊C8—891no—
398C4⋊C8—891no—
399C4⋊C8—891no—
400C4⋊C8—891no—
401C4⋊C8—891no—
402C4⋊C8—1781no—
403C4⋊C8—1781no—
404C4⋊C8—1781no—
405C4⋊C8—1781no—
406C4⋊C8C22×D8911yescharacteristic
407C4⋊C8C22×D8911yescharacteristic
408#103—891no—
409#103—891no—
410#103—891no—
411#103C4×D8911yescharacteristic
412#102—891no—
413#102—891no—
414#102—891no—
415#102C4×D8911yescharacteristic
416C22⋊C8—21no—
417C22⋊C8—891no—
418C22⋊C8—891no—
419C22⋊C8—891no—
420C22⋊C8—891no—
421C22⋊C8—1781no—
422C22⋊C8—1781no—
423C22⋊C8—1781no—
424C22⋊C8—1781no—
425C22⋊C8—1781no—
426C22⋊C8—1781no—
427#97—21no—
428#97—1781no—
429#97—1781no—
430C4×C8—891no—
431C4×C8—891no—
432C4×C8—891no—
433C4×C8—1781no—
434C4×C8—1781no—
435C4×C8—1781no—
436C4×C8C22×D8911yescharacteristic
437C4×C8C22×D8911yescharacteristic
438C4×C8C22×D8911yescharacteristic
439C24—1781no—
440C2×Q8—891no—
441C2×Q8—1781no—
442C2×Q8C2×C4×D8911yescharacteristic
443C2×D4—891no—
444C2×D4—3561no—
445C2×D4—1781no—
446C2×D4—1782no—
447C2×D4C2×C4×D8911yescharacteristic
448C22×C4—21no—
449C22×C4—891no—
450C22×C4—891no—
451C22×C4—891no—
452C22×C4—1781no—
453C22×C4—1781no—
454C22×C4—1781no—
455C22×C4—1781no—
456C22×C4—7121no—
457C22×C4—7121no—
458SD16—41no—
459SD16—3561no—
460SD16—1782no—
461SD16—1782no—
462M16—81no—
463M16—7121no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—891no—
468C2×C8—891no—
469C2×C8—891no—
470C2×C8—891no—
471C2×C8—1781no—
472C2×C8—1781no—
473C2×C8—1781no—
474C2×C8—7121no—
475C2×C8—7121no—
476C2×C8C2×C4×D8911yescharacteristic
477C2×C8C2×C4×D8911yescharacteristic
478C2×C8D4×D8911yescharacteristic
479C2×C8D4×D8911yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—891no—
482C4⋊C4—891no—
483C4⋊C4—1781no—
484C4⋊C4—1781no—
485C4⋊C4—1781no—
486C4⋊C4—1781no—
487C4⋊C4—1781no—
488C4⋊C4—1781no—
489C4⋊C4—1781no—
490C4⋊C4C2×C4×D8911yescharacteristic
491C4⋊C4C2×C4×D8911yescharacteristic
492C22⋊C4—21no—
493C22⋊C4—1781no—
494C22⋊C4—1781no—
495C22⋊C4—1781no—
496C22⋊C4—1781no—
497C22⋊C4—1781no—
498C42—21no—
499C42—891no—
500C42—891no—
501C42—891no—
502C42—1781no—
503C42C23×D8911yescharacteristic
504C23—21no—
505C23—891no—
506C23—3562no—
507C23—3562no—
508C23—1781no—
509C23—7121no—
510Q8—21no—
511Q8—21no—
512Q8—3562no—
513Q8—1781no—
514Q8—1781no—
515D4—21no—
516D4—21no—
517D4—892no—
518D4—3562no—
519D4—1781no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—891no—
526C2×C4—891no—
527C2×C4—891no—
528C2×C4—3561no—
529C2×C4—3561no—
530C2×C4—3561no—
531C2×C4—1781no—
532C2×C4—1781no—
533C2×C4—1781no—
534C2×C4—1781no—
535C2×C4—1781no—
536C2×C4—1781no—
537C2×C4—1781no—
538C2×C4—7121no—
539C2×C4—7121no—
540C2×C4—7121no—
541C2×C4C22×C4×D8911yescharacteristic
542C2×C4C2×D4×D8911yescharacteristic
543C2×C4#41×D8911yescharacteristic
544C8—21no—
545C8—21no—
546C8—21no—
547C8—21no—
548C8—41no—
549C8—41no—
550C8—41no—
551C8—3561no—
552C8—3561no—
553C8—3561no—
554C8—1781no—
555C8—1781no—
556C8—1781no—
557C8—1781no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—3561no—
562C22—3561no—
563C22—1781no—
564C22—1781no—
565C22—1781no—
566C22—1782no—
567C22—7124no—
568C22C4×D4×D8911yescharacteristic
569C4—21no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—3561no—
574C4—3561no—
575C4—3561no—
576C4—1781no—
577C4—1781no—
578C4—1781no—
579C4#131×D8911yescharacteristic
580C4#1915236411yescharacteristic
581C4#1915240411yescharacteristic
582C4#1915240511yescharacteristic
583C2—81no—
584C2—3562no—
585C2—3561no—
586C2#2602898111yescharacteristic
587C2#2602910611yescharacteristic
588C2#2602915011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D89
commutatorC2×C4×C89C23×C4
FrattiniC42C23×D89
FittingC89×#1590C2
socleC22×C89C2×C4×D4
prime radicalC2×D4×D89C2×C4
cosocleC42×C89C24
hypercenter#1590D89
hypocenterC89#18028
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1590

Complements

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

NH ≅ G/Ntype
2. #26029350C2semidirect
4. #26019151C2semidirect
5. #26019128C2semidirect
6. #26019107C2semidirect
7. #26019096C2semidirect
8. #26019087C2semidirect
9. #26019067C2semidirect
10. C8×#13083563C2semidirect
11. #26019029C2semidirect
12. #26018723C2semidirect
14. #26018551C2semidirect
15. C89×#1590C2semidirect
27. #19151725C22semidirect
28. Q8×#10623494C22semidirect
29. C8×Dic178C22semidirect
48. #19151350C22semidirect
49. #19151350C22semidirect
50. #19151349C22semidirect
51. #19151330C22semidirect
52. Q8⋊#10623494C22semidirect
53. #19151328C22semidirect
57. #19151320C22semidirect
58. #19151320C22semidirect
59. #19151320C22semidirect
60. #446×C89C22semidirect
63. #334×C89C22semidirect
64. Q8⋊C8×C89C22semidirect
66. C82×C89C22semidirect
299. #1590D89semidirect
310. C89#18028semidirect
323. #446C2×D89semidirect
349. #334C2×D89semidirect
353. Q8⋊C8C2×D89semidirect
361. C82C2×D89semidirect

Maximal subgroups

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

subgroupindex
#260302582
#260293502
#260292842
#260191512
#260191282
#260191072
#260190962
#260190872
#260190672
C8×#130835632
#260190292
#260187232
#260186412
#260185512
C89×#15902
#1802889