Finite Group Databasebeta

← #12070255

Subgroups — #12070255

Order 1280.

672 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10611649C211yesmaximal, characteristic, complemented
2#10611382C211yesmaximal, characteristic
3D4×#676C211yesmaximal, characteristic
4C5×SD16⋊C8C211yesmaximal, characteristic, complemented
5#10601729C211yesmaximal, characteristic, complemented
6#10601690C211yesmaximal, characteristic, complemented
7#10601636C211yesmaximal, characteristic, complemented
8#10599365C211yesmaximal, characteristic, complemented
9#10599355C211yesmaximal, characteristic, complemented
10#10599033C211yesmaximal, characteristic, complemented
11#10599019C211yesmaximal, characteristic, complemented
12D5×D4⋊C8C211yesmaximal, characteristic
13#10598943C211yesmaximal, characteristic, complemented
14#10598875C211yesmaximal, characteristic, complemented
15#10598863C211yesmaximal, characteristic, complemented
16C22×#676—21no—
17#65912C2211yescharacteristic
18C4×D4×D5C2211yescharacteristic
19C5×C8×Q8C2211yescharacteristic, complemented
20C4×C5×SD16C2211yescharacteristic
21C5×C8×D4C2211yescharacteristic
22#65458C411yescharacteristic
23#65451C411yescharacteristic
24#65400—21no—
25C4×#688C2211yescharacteristic
26#65313C2211yescharacteristic, complemented
27C4×#687C2211yescharacteristic
28D4×#168C2211yescharacteristic
29#65159C411yescharacteristic
30#65151C411yescharacteristic
31#65128—21no—
32#65127C2211yescharacteristic
33#65126C2211yescharacteristic
34D5×C4⋊C8C2211yescharacteristic
35#65119C2211yescharacteristic, complemented
36#65117—21no—
37#65107C411yescharacteristic
38#65094C411yescharacteristic
39#65065C411yescharacteristic
40#65050C411yescharacteristic
41#65019—21no—
42#65015—21no—
43C4×#677C2211yescharacteristic
44#64978—21no—
45#64977C2211yescharacteristic
46C4×#676C2211yescharacteristic
47#64974C2211yescharacteristic
48C4×C8×D5C2211yescharacteristic
49#64968—21no—
50#64968C2211yescharacteristic, complemented
51C5×#335C2211yescharacteristic, complemented
52C5×Q8⋊C8C2211yescharacteristic, complemented
53C5×D4⋊C8C2211yescharacteristic
54C5×#322C2211yescharacteristic, complemented
55Q8⋊#168C2211yescharacteristic, complemented
56D4⋊#168C2211yescharacteristic
57#64704C2211yescharacteristic, complemented
58#64703C2211yescharacteristic
59#64699C2211yescharacteristic, complemented
60#64699C2211yescharacteristic, complemented
61#64679C2211yescharacteristic
62#64678C2211yescharacteristic, complemented
63#64676C2211yescharacteristic, complemented
64#64674C2211yescharacteristic, complemented
65#64674C2211yescharacteristic, complemented
66#64674C2211yescharacteristic, complemented
67#18000—51nomaximal, Sylow
68C2×D4×D5C2×C411yescharacteristic
69C22×C4×D5—21no—
70C2×C5×SD16C2×C411yescharacteristic
71C22×C5×C8—21no—
72C4×C5×Q8C2311yescharacteristic
73C4×C5×D4C2311yescharacteristic
74#4092C2×C411yescharacteristic
75#4090C2×C411yescharacteristic
76C2×#688C2×C411yescharacteristic
77D4×Dic5C2×C411yescharacteristic
78C2×#687C2×C411yescharacteristic
79C4×C22⋊D5—21no—
80C22×#168—21no—
81C2×#677C2×C411yescharacteristic
82C2×#676—21no—
83C2×#676—21no—
84C2×#676—21no—
85C2×#676—44no—
86C2×#676D411yescharacteristic
87C2×#676D411yescharacteristic
88C2×C8×D5—21no—
89C2×C8×D5—21no—
90#4043C2×C411yescharacteristic
91#4042—21no—
92#4039C2×C411yescharacteristic
93D5×C4⋊C4C2×C411yescharacteristic
94#4035—21no—
95#4034C2×C411yescharacteristic
96#4027—21no—
97D5×C22⋊C4—21no—
98C4×D20C2311yescharacteristic
99#4018—21no—
100C42×D5C2311yescharacteristic
101C4×Dic10—21no—
102C4×Dic10C2311yescharacteristic
103C5×#106C2×C411yescharacteristic
104C5×C4⋊C8—21no—
105C5×C4⋊C8C2311yescharacteristic
106C5×C4⋊C8C2311yescharacteristic
107C5×#103C2×C411yescharacteristic
108C5×#102C2×C411yescharacteristic
109C5×C22⋊C8—21no—
110C4×C5×C8—21no—
111C4×C5×C8C2311yescharacteristic
112C4×C5×C8C2311yescharacteristic
113C4×C5×C8C2311yescharacteristic
114#3967C2×C411yescharacteristic
115#3964C2×C411yescharacteristic
116C22⋊#168—21no—
117#3953C2×C411yescharacteristic
118#3952—21no—
119#3952—21no—
120#3952C2×C411yescharacteristic
121#3952C2×C411yescharacteristic
122#3949C2×C411yescharacteristic
123#3948C2×C411yescharacteristic
124#3947—21no—
125#3947D411yescharacteristic
126#3947D411yescharacteristic
127#3946—21no—
128#3946—21no—
129#3946—21no—
130#3946—21no—
131#3946C2×C411yescharacteristic
132#3946C2×C411yescharacteristic
133C8×Dic5—21no—
134C8×Dic5—21no—
135#3942C2×C411yescharacteristic
136#3941C2×C411yescharacteristic
137#3940C2×C411yescharacteristic
138#3940C2×C411yescharacteristic
139C4⋊#168—21no—
140C4⋊#168C2311yescharacteristic
141C4⋊#168C2311yescharacteristic
142#3935—21no—
143C4×#168C2311yescharacteristic
144C4×#168C2311yescharacteristic
145C4×#168C2311yescharacteristic
146#3101—51no—
147#2962—51no—
148D4×M16—51no—
149#1592—51no—
150#1592—51no—
151#1588—51no—
152#1588—51no—
153#1585—51no—
154#1585—51no—
155SD16⋊C8—51no—
156SD16⋊C8D511yescharacteristic, complemented
157#1571—51no—
158#1493—51no—
159C2×D4⋊C8—51no—
160#1451—51no—
161C23×D5—21no—
162C2×C5×Q8C22×C411yescharacteristic
163C2×C5×D4C22×C411yescharacteristic
164C22×C4×C5—21no—
165C2×C22⋊D5—21no—
166C22×Dic5—21no—
167D4×D5—22no—
168D4×D5—41no—
169C2×D20C22×C411yescharacteristic
170C2×C4×D5—21no—
171C2×C4×D5—21no—
172C2×C4×D5—21no—
173C2×C4×D5—42no—
174C2×C4×D5—42no—
175C2×C4×D5C22×C411yescharacteristic
176C2×C4×D5C2×D411yescharacteristic
177C2×C4×D5#4111yescharacteristic
178C2×Dic10—21no—
179C2×Dic10C22×C411yescharacteristic
180C5×SD16—22no—
181C2×C5×C8—21no—
182C2×C5×C8—21no—
183C2×C5×C8—21no—
184C2×C5×C8—42no—
185C2×C5×C8C22×C411yescharacteristic
186C2×C5×C8C22×C411yescharacteristic
187C2×C5×C8C2×D411yescharacteristic
188C2×C5×C8C2×D411yescharacteristic
189C5×C4⋊C4—21no—
190C5×C4⋊C4C22×C411yescharacteristic
191C5×C4⋊C4C22×C411yescharacteristic
192C5×C22⋊C4—21no—
193C42×C5—21no—
194C42×C5C2411yescharacteristic
195C22⋊Dic5—21no—
196#688—41no—
197#687—22no—
198#685—21no—
199#685—21no—
200#685—21no—
201#685—21no—
202C4⋊Dic5—21no—
203C4⋊Dic5C22×C411yescharacteristic
204C4⋊Dic5C22×C411yescharacteristic
205#683—21no—
206#683—21no—
207#683—21no—
208#683—21no—
209#683—21no—
210#683—21no—
211C4×Dic5—21no—
212C4×Dic5C22×C411yescharacteristic
213C4×Dic5C2×D411yescharacteristic
214C4×Dic5#4111yescharacteristic
215C2×#168—21no—
216C2×#168—21no—
217C2×#168—21no—
218C2×#168—42no—
219C2×#168C22×C411yescharacteristic
220C2×#168C22×C411yescharacteristic
221C2×#168C2×D411yescharacteristic
222C2×#168C2×D411yescharacteristic
223#677—41no—
224#676—22no—
225#676—22no—
226#676—42no—
227#676—42no—
228#676—42no—
229C8×D5—42no—
230C8×D5—42no—
231C22×M16—101no—
232#533—51no—
233C2×C4×D4—51no—
234#483—51no—
235#483—51no—
236#476—51no—
237#476—51no—
238#461—51no—
239#461—51no—
240#450—51no—
241#450—51no—
242#446—51no—
243#446—51no—
244#446—101no—
245#446—101no—
246C8×Q8—51no—
247C8×Q8C2×D511yescharacteristic, complemented
248C4×SD16—51no—
249C4×SD16—51no—
250C4×SD16—51no—
251C4×SD16C2×D511yescharacteristic
252#436—51no—
253#436—51no—
254#435—101no—
255#435—101no—
256C8×D4—51no—
257C8×D4C2×D511yescharacteristic
258#431—51no—
259#424—101no—
260#423—51no—
261C2×C4⋊C8—51no—
262#407—101no—
263#405—101no—
264C4×M16—51no—
265C2×C4×C8—51no—
266#335—51no—
267#335—51no—
268#335—51no—
269#335C2×D511yescharacteristic, complemented
270Q8⋊C8—51no—
271Q8⋊C8—51no—
272Q8⋊C8—51no—
273Q8⋊C8C2×D511yescharacteristic, complemented
274D4⋊C8—51no—
275D4⋊C8—51no—
276D4⋊C8—51no—
277D4⋊C8C2×D511yescharacteristic
278#322—51no—
279#322—51no—
280#322—51no—
281#322C2×D511yescharacteristic, complemented
282C23×C5—21no—
283C22×D5—21no—
284C22×D5—42no—
285C22×D5—42no—
286C22×D5—81no—
287C22×D5C4×D411yescharacteristic
288C5×Q8—21no—
289C5×Q8—21no—
290C5×D4—21no—
291C5×D4#13112yes—
292C2×C4×C5—21no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—41no—
296C2×C4×C5—41no—
297C2×C4×C5C23×C411yescharacteristic
298C2×C4×C5C22×D411yescharacteristic
299C2×C4×C5C2×#4111yescharacteristic
300C22⋊D5—42no—
301C2×Dic5—21no—
302C2×Dic5—21no—
303C2×Dic5—21no—
304C2×Dic5—42no—
305C2×Dic5C4×D411yescharacteristic
306C2×Dic5C4×D411yescharacteristic
307C2×Dic5C4×D411yescharacteristic
308D20—21no—
309D20—21no—
310C4×D5—21no—
311C4×D5—21no—
312C4×D5—41no—
313C4×D5—42no—
314C4×D5—41no—
315C4×D5—41no—
316C4×D5—42no—
317C4×D5AGL(1,ℤ/8)12yes—
318C4×D5#13712yes—
319Dic10—21no—
320Dic10—21no—
321Dic10—81no—
322C5×C8—21no—
323C5×C8—21no—
324C5×C8—21no—
325C5×C8—21no—
326C5×C8—41no—
327C5×C8—41no—
328C5×C8—41no—
329#168—22no—
330#168—21no—
331#168—21no—
332#168—21no—
333#168—21no—
334#168—41no—
335#168—41no—
336C22×D4—51no—
337C23×C4—101no—
338C2×SD16—51no—
339C2×SD16—51no—
340C2×SD16—51no—
341C2×SD16C4×D511yescharacteristic
342C2×M16—51no—
343C2×M16—51no—
344C2×M16—101no—
345C2×M16—101no—
346C2×M16—101no—
347C2×M16—204no—
348C22×C8—21no—
349C22×C8—101no—
350C22×C8—101no—
351C22×C8—101no—
352C4⋊Q8—51no—
353C4⋊Q8—51no—
354#125—101no—
355C22⋊Q8—51no—
356C22⋊Q8—51no—
357C22⋊Q8—101no—
358C4×Q8—51no—
359C4×Q8—101no—
360C4×Q8C22×D511yescharacteristic
361C4×D4—51no—
362C4×D4—51no—
363C4×D4—51no—
364C4×D4—101no—
365C4×D4—101no—
366C4×D4C22×D511yescharacteristic
367#117—101no—
368C2×C4⋊C4—51no—
369C2×C22⋊C4—101no—
370C2×C42—51no—
371#106—51no—
372#106—51no—
373#106—51no—
374#106C4×D511yescharacteristic
375C4⋊C8—21no—
376C4⋊C8—51no—
377C4⋊C8—51no—
378C4⋊C8—51no—
379C4⋊C8—51no—
380C4⋊C8—101no—
381C4⋊C8—101no—
382C4⋊C8—101no—
383C4⋊C8—101no—
384C4⋊C8—101no—
385C4⋊C8C22×D511yescharacteristic
386C4⋊C8C22×D511yescharacteristic
387#103—51no—
388#103—51no—
389#103—51no—
390#103C4×D511yescharacteristic
391#102—51no—
392#102—51no—
393#102—51no—
394#102C4×D511yescharacteristic
395C22⋊C8—21no—
396C22⋊C8—51no—
397C22⋊C8—51no—
398C22⋊C8—101no—
399C22⋊C8—101no—
400C22⋊C8—101no—
401#97—51no—
402#97—51no—
403#97—101no—
404#97—101no—
405C4×C8—21no—
406C4×C8—51no—
407C4×C8—51no—
408C4×C8—51no—
409C4×C8—101no—
410C4×C8—101no—
411C4×C8C22×D511yescharacteristic
412C4×C8C22×D511yescharacteristic
413C4×C8C22×D511yescharacteristic
414C22×C5—22no—
415C22×C5—41no—
416C22×C5—41no—
417C22×C5C2×C4×D411yescharacteristic
418C2×D5—21no—
419C2×D5—21no—
420C2×D5—41no—
421C2×D5—41no—
422C2×D5—41no—
423C2×D5—84no—
424C2×D5#44012yes—
425C4×C5—21no—
426C4×C5—41no—
427C4×C5—41no—
428C4×C5—41no—
429C4×C5C2×#13111yescharacteristic
430C4×C5#56811yescharacteristic
431C4×C5C2×AGL(1,ℤ/8)11yescharacteristic
432C4×C5C2×#13711yescharacteristic
433Dic5—21no—
434Dic5—21no—
435Dic5—41no—
436Dic5—41no—
437Dic5—41no—
438Dic5#44012yes—
439C24—101no—
440C2×Q8—51no—
441C2×Q8—101no—
442C2×Q8C2×C4×D511yescharacteristic
443C2×D4—51no—
444C2×D4—101no—
445C2×D4—102no—
446C2×D4—201no—
447C2×D4C2×C4×D511yescharacteristic
448C22×C4—21no—
449C22×C4—51no—
450C22×C4—51no—
451C22×C4—51no—
452C22×C4—101no—
453C22×C4—101no—
454C22×C4—101no—
455C22×C4—101no—
456C22×C4—202no—
457C22×C4—202no—
458SD16—22no—
459SD16—102no—
460SD16—201no—
461SD16—201no—
462M16—102no—
463M16—102no—
464M16—202no—
465M16—202no—
466M16—202no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—42no—
471C2×C8—51no—
472C2×C8—51no—
473C2×C8—51no—
474C2×C8—51no—
475C2×C8—101no—
476C2×C8—101no—
477C2×C8—101no—
478C2×C8—202no—
479C2×C8—202no—
480C2×C8—202no—
481C2×C8C2×C4×D511yescharacteristic
482C2×C8C2×C4×D511yescharacteristic
483C2×C8D4×D511yescharacteristic
484C2×C8D4×D511yescharacteristic
485C4⋊C4—21no—
486C4⋊C4—51no—
487C4⋊C4—51no—
488C4⋊C4—101no—
489C4⋊C4—101no—
490C4⋊C4—101no—
491C4⋊C4—101no—
492C4⋊C4—101no—
493C4⋊C4—101no—
494C4⋊C4—101no—
495C4⋊C4C2×C4×D511yescharacteristic
496C4⋊C4C2×C4×D511yescharacteristic
497C22⋊C4—21no—
498C22⋊C4—101no—
499C22⋊C4—101no—
500C22⋊C4—101no—
501C22⋊C4—101no—
502C22⋊C4—101no—
503C42—21no—
504C42—51no—
505C42—51no—
506C42—51no—
507C42—101no—
508C42C23×D511yescharacteristic
509C2×C5—42no—
510C2×C5#293311yescharacteristic
511C2×C5C2×#44011yescharacteristic
512C2×C5#295611yescharacteristic
513D5—22no—
514D5—81no—
515C23—21no—
516C23—51no—
517C23—101no—
518C23—202no—
519C23—202no—
520C23—401no—
521Q8—21no—
522Q8—21no—
523Q8—101no—
524Q8—101no—
525Q8—401no—
526D4—21no—
527D4—101no—
528D4—101no—
529D4—202no—
530D4#404712yes—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—51no—
537C2×C4—52no—
538C2×C4—52no—
539C2×C4—51no—
540C2×C4—51no—
541C2×C4—101no—
542C2×C4—101no—
543C2×C4—101no—
544C2×C4—101no—
545C2×C4—101no—
546C2×C4—201no—
547C2×C4—202no—
548C2×C4—202no—
549C2×C4—202no—
550C2×C4—201no—
551C2×C4—201no—
552C2×C4C22×C4×D511yescharacteristic
553C2×C4C2×D4×D511yescharacteristic
554C2×C4D5×#4111yescharacteristic
555C8—21no—
556C8—21no—
557C8—21no—
558C8—21no—
559C8—41no—
560C8—41no—
561C8—41no—
562C8—102no—
563C8—101no—
564C8—101no—
565C8—101no—
566C8—101no—
567C8—201no—
568C8—201no—
569C5#1800011yescharacteristic, complemented, Sylow
570C22—22no—
571C22—41no—
572C22—41no—
573C22—52no—
574C22—101no—
575C22—101no—
576C22—201no—
577C22—201no—
578C22—201no—
579C22—404no—
580C22C4×D4×D511yescharacteristic
581C4—21no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—52no—
586C4—101no—
587C4—101no—
588C4—201no—
589C4—201no—
590C4—201no—
591C4C2×#404711yescharacteristic
592C4#6608411yescharacteristic
593C4D5×AGL(1,ℤ/8)11yescharacteristic
594C4D5×#13711yescharacteristic
595C2—42no—
596C2—102no—
597C2—401no—
598C2#1061115411yescharacteristic
599C2D5×#44011yescharacteristic
600C2#1061162911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×SD16⋊C8C2
socleC22×C5C2×C4×D4
prime radicalC2×D4×D5C2×C4
cosocleC42×C5C24
hypercenterSD16⋊C8D5
hypocenterC5#18000
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ SD16⋊C8

Complements

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

NH ≅ G/Ntype
1. #10611649C2semidirect
4. C5×SD16⋊C8C2semidirect
5. #10601729C2semidirect
6. #10601690C2semidirect
7. #10601636C2semidirect
8. #10599365C2semidirect
9. #10599355C2semidirect
10. #10599033C2semidirect
11. #10599019C2semidirect
13. #10598943C2semidirect
14. #10598875C2semidirect
15. #10598863C2semidirect
19. C5×C8×Q8C22semidirect
26. #65313C22semidirect
35. #65119C22semidirect
50. #64968C22semidirect
51. C5×#335C22semidirect
52. C5×Q8⋊C8C22semidirect
54. C5×#322C22semidirect
55. Q8⋊#168C22semidirect
57. #64704C22semidirect
59. #64699C22semidirect
60. #64699C22semidirect
62. #64678C22semidirect
63. #64676C22semidirect
64. #64674C22semidirect
65. #64674C22semidirect
66. #64674C22semidirect
156. SD16⋊C8D5semidirect
247. C8×Q8C2×D5semidirect
269. #335C2×D5semidirect
273. Q8⋊C8C2×D5semidirect
281. #322C2×D5semidirect
569. C5#18000semidirect

Maximal subgroups

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

subgroupindex
#106116492
#106113822
D4×#6762
C5×SD16⋊C82
#106017292
#106016902
#106016362
#105993652
#105993552
#105990332
#105990192
D5×D4⋊C82
#105989432
#105988752
#105988632
#180005