Finite Group Databasebeta

← C127×#19833 #44583506

Subgroups — C127×#19833 #44583506

Order 32512.

608 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3392C211yesmaximal, characteristic, complemented
2C127×#3365C211yesmaximal, characteristic, complemented
3C127×#3361C211yesmaximal, characteristic, complemented
4C127×#3333C211yesmaximal, characteristic, complemented
5C127×#1717C211yesmaximal, characteristic, complemented
6C127×#1701C211yesmaximal, characteristic, complemented
7C127×#1678C211yesmaximal, characteristic, complemented
8C127×#1678C211yesmaximal, characteristic, complemented
9C127×#1666C211yesmaximal, characteristic, complemented
10C127×#1643C211yesmaximal, characteristic, complemented
11C127×#1636C211yesmaximal, characteristic, complemented
12C127×#1621C211yesmaximal, characteristic
13C127×#1620C211yesmaximal, characteristic, complemented
14C127×#1583C211yesmaximal, characteristic, complemented
15C127×#1579C211yesmaximal, characteristic, complemented
16#559×C127C2211yescharacteristic
17#557×C127C2211yescharacteristic
18#554×C127C2211yescharacteristic
19#550×C127C2211yescharacteristic
20#493×C127C2211yescharacteristic
21#492×C127—21no—
22#492×C127C2211yescharacteristic
23#488×C127—21no—
24#488×C127—21no—
25#487×C127C2211yescharacteristic
26#486×C127C2211yescharacteristic
27#486×C127C2211yescharacteristic
28#486×C127C2211yescharacteristic
29#480×C127—21no—
30#478×C127—21no—
31#478×C127—21no—
32#477×C127C2211yescharacteristic
33#477×C127C2211yescharacteristic
34#475×C127C2211yescharacteristic
35#468×C127—21no—
36#464×C127—21no—
37#463×C127—21no—
38#461×C127—21no—
39#461×C127C2211yescharacteristic
40#460×C127—21no—
41#460×C127C2211yescharacteristic
42#460×C127C2211yescharacteristic
43#460×C127C2211yescharacteristic
44#459×C127C2211yescharacteristic
45#452×C127—21no—
46C8×Q8×C127C2211yescharacteristic
47C8×Q8×C127C2211yescharacteristic
48C8×Q8×C127C2211yescharacteristic
49C4×Q16×C127C2211yescharacteristic
50C4×SD16×C127—21no—
51C4×SD16×C127—21no—
52C4×SD16×C127C2211yescharacteristic
53C4×D8×C127—21no—
54#436×C127C2211yescharacteristic
55#417×C127—21no—
56#334×C127C2211yescharacteristic
57#334×C127C2211yescharacteristic
58#333×C127C2211yescharacteristic
59#332×C127C2211yescharacteristic
60#331×C127C2211yescharacteristic
61#331×C127C2211yescharacteristic
62Q8⋊C8×C127C2211yescharacteristic
63Q8⋊C8×C127C2211yescharacteristic
64Q8⋊C8×C127C2211yescharacteristic
65D4⋊C8×C127C2211yescharacteristic
66#322×C127C2211yescharacteristic
67C2×#41×C127—21no—
68C2×Q16×C127D411yescharacteristic
69C2×SD16×C127—21no—
70C2×SD16×C127—21no—
71C2×SD16×C127—21no—
72C2×SD16×C127—21no—
73C2×SD16×C127—21no—
74C2×SD16×C127—21no—
75C2×SD16×C127D411yescharacteristic
76C2×D8×C127—21no—
77C2×D8×C127—41no—
78C2×M16×C127—21no—
79C4⋊Q8×C127—21no—
80C4⋊Q8×C127C2311yescharacteristic
81C4⋊Q8×C127C2311yescharacteristic
82#127×C127—21no—
83#127×C127C2311yescharacteristic
84#127×C127C2311yescharacteristic
85#125×C127—21no—
86#125×C127—21no—
87#125×C127—41no—
88#124×C127—21no—
89#124×C127—21no—
90#123×C127—41no—
91C22⋊Q8×C127—21no—
92C22⋊Q8×C127—41no—
93#121×C127—21no—
94#121×C127—41no—
95C4×Q8×C127—21no—
96C4×Q8×C127—21no—
97C4×Q8×C127C2311yescharacteristic
98C4×Q8×C127C2311yescharacteristic
99C4×Q8×C127C2311yescharacteristic
100C4×D4×C127—21no—
101C4×D4×C127—21no—
102C4×D4×C127—21no—
103C4×D4×C127—21no—
104C4×D4×C127C2311yescharacteristic
105C2×C4⋊C4×C127—21no—
106#107×C127—21no—
107#107×C127—21no—
108#107×C127D411yescharacteristic
109#106×C127—21no—
110#106×C127D411yescharacteristic
111C4⋊C8×C127—21no—
112C4⋊C8×C127—21no—
113C4⋊C8×C127—21no—
114C4⋊C8×C127C2311yescharacteristic
115C4⋊C8×C127C2311yescharacteristic
116C4⋊C8×C127C2311yescharacteristic
117C4⋊C8×C127C2311yescharacteristic
118#103×C127—21no—
119#103×C127—21no—
120#103×C127—21no—
121#103×C127—21no—
122#103×C127—41no—
123#103×C127D411yescharacteristic
124#103×C127D411yescharacteristic
125#103×C127D411yescharacteristic
126#102×C127—21no—
127#102×C127—21no—
128#102×C127—21no—
129#102×C127—21no—
130#102×C127—21no—
131#102×C127—21no—
132#102×C127—21no—
133#102×C127—21no—
134#102×C127—21no—
135#102×C127—21no—
136#102×C127D411yescharacteristic
137C22⋊C8×C127—21no—
138C4×C8×C127—21no—
139C4×C8×C127—21no—
140C4×C8×C127—21no—
141C4×C8×C127C2311yescharacteristic
142C4×C8×C127C2311yescharacteristic
143C4×C8×C127C2311yescharacteristic
144#41×C127—42no—
145#41×C127—81no—
146C2×Q8×C127—21no—
147C2×Q8×C127—21no—
148C2×Q8×C127C2×D411yescharacteristic
149C2×Q8×C127C2×D411yescharacteristic
150C2×Q8×C127C2×D411yescharacteristic
151C2×D4×C127—21no—
152C2×D4×C127—21no—
153C2×D4×C127—21no—
154C2×D4×C127—21no—
155C2×D4×C127—21no—
156C2×D4×C127—21no—
157C2×D4×C127—41no—
158C2×D4×C127—41no—
159C2×D4×C127C2×D411yescharacteristic
160C22×C4×C127—21no—
161C22×C4×C127—41no—
162C22×C4×C127—41no—
163C22×C4×C127—41no—
164Q16×C127—22no—
165SD16×C127—41no—
166SD16×C127—42no—
167SD16×C127—42no—
168SD16×C127—81no—
169SD16×C127—81no—
170SD16×C127—81no—
171SD16×C127—81no—
172D8×C127—42no—
173D8×C127—82no—
174M16×C127—81no—
175C2×C8×C127—21no—
176C2×C8×C127—21no—
177C2×C8×C127—21no—
178C2×C8×C127—21no—
179C2×C8×C127—21no—
180C2×C8×C127C2×D411yescharacteristic
181C2×C8×C127C2×D411yescharacteristic
182C2×C8×C127C2×D411yescharacteristic
183C2×C8×C127C2×D411yescharacteristic
184C4⋊C4×C127—21no—
185C4⋊C4×C127—21no—
186C4⋊C4×C127—21no—
187C4⋊C4×C127—21no—
188C4⋊C4×C127—21no—
189C4⋊C4×C127—21no—
190C4⋊C4×C127—21no—
191C4⋊C4×C127—41no—
192C4⋊C4×C127—41no—
193C4⋊C4×C127—41no—
194C4⋊C4×C127—41no—
195C4⋊C4×C127—41no—
196C4⋊C4×C127C2×D411yescharacteristic
197C4⋊C4×C127C2×D411yescharacteristic
198C4⋊C4×C127C2×D411yescharacteristic
199C4⋊C4×C127C2×D411yescharacteristic
200C22⋊C4×C127—21no—
201C22⋊C4×C127—41no—
202C22⋊C4×C127—41no—
203C22⋊C4×C127—41no—
204C22⋊C4×C127—41no—
205C22⋊C4×C127—41no—
206C42×C127—21no—
207C42×C127—21no—
208C42×C127—21no—
209C42×C127—41no—
210C42×C127C2411yescharacteristic
211C23×C127—21no—
212C23×C127—41no—
213C23×C127—41no—
214Q8×C127—21no—
215Q8×C127—21no—
216Q8×C127—21no—
217Q8×C127—21no—
218Q8×C127—21no—
219Q8×C127—41no—
220Q8×C127—41no—
221Q8×C127—81no—
222Q8×C127#13512yes—
223D4×C127—21no—
224D4×C127—21no—
225D4×C127—41no—
226D4×C127—41no—
227D4×C127—41no—
228D4×C127—41no—
229D4×C127—41no—
230D4×C127—41no—
231D4×C127—41no—
232D4×C127—41no—
233D4×C127—82no—
234D4×C127—81no—
235D4×C127—81no—
236D4×C127—161no—
237C2×C4×C127—21no—
238C2×C4×C127—21no—
239C2×C4×C127—21no—
240C2×C4×C127—21no—
241C2×C4×C127—21no—
242C2×C4×C127—21no—
243C2×C4×C127—21no—
244C2×C4×C127—41no—
245C2×C4×C127—41no—
246C2×C4×C127—41no—
247C2×C4×C127—41no—
248C2×C4×C127—82no—
249C2×C4×C127—161no—
250C2×C4×C127—161no—
251C2×C4×C127C22×D411yescharacteristic
252C2×C4×C127C22×D411yescharacteristic
253C2×C4×C127H(5,𝔽2)11yescharacteristic
254C8×C127—21no—
255C8×C127—21no—
256C8×C127—21no—
257C8×C127—21no—
258C8×C127—41no—
259C8×C127—41no—
260C8×C127—41no—
261C8×C127—41no—
262C8×C127—41no—
263C22×C127—41no—
264C22×C127—41no—
265C22×C127—41no—
266C22×C127—81no—
267C22×C127—81no—
268C22×C127—81no—
269C22×C127—81no—
270C22×C127—81no—
271C22×C127—81no—
272C22×C127D4211yescharacteristic
273C4×C127—22no—
274C4×C127—21no—
275C4×C127—41no—
276C4×C127—41no—
277C4×C127—41no—
278C4×C127—41no—
279C4×C127—41no—
280C4×C127—41no—
281C4×C127—81no—
282C4×C127—81no—
283C4×C127C2×#13511yescharacteristic
284C4×C127#57511yescharacteristic
285C4×C127#57711yescharacteristic
286C4×C127#57711yescharacteristic
287#19833C12711yesmaximal, characteristic, direct product factor, Sylow
288C2×C127—81no—
289C2×C127—161no—
290C2×C127—161no—
291C2×C127#327111yescharacteristic
292C2×C127#328211yescharacteristic
293C2×C127#328811yescharacteristic
294#3392C2×C12711yescharacteristic, complemented
295#3365C2×C12711yescharacteristic, complemented
296#3361C2×C12711yescharacteristic, complemented
297#3333C2×C12711yescharacteristic, complemented
298#1717C2×C12711yescharacteristic, complemented
299#1701C2×C12711yescharacteristic, complemented
300#1678C2×C12711yescharacteristic, complemented
301#1678C2×C12711yescharacteristic, complemented
302#1666C2×C12711yescharacteristic, complemented
303#1643C2×C12711yescharacteristic, complemented
304#1636C2×C12711yescharacteristic, complemented
305#1621C2×C12711yescharacteristic
306#1620C2×C12711yescharacteristic, complemented
307#1583C2×C12711yescharacteristic, complemented
308#1579C2×C12711yescharacteristic, complemented
309C127#1983311yescharacteristic, direct product factor, Sylow
310#559C22×C12711yescharacteristic
311#557C22×C12711yescharacteristic
312#554C22×C12711yescharacteristic
313#550C22×C12711yescharacteristic
314#493C22×C12711yescharacteristic
315#492—21no—
316#492C22×C12711yescharacteristic
317#488—21no—
318#488—21no—
319#487C22×C12711yescharacteristic
320#486C22×C12711yescharacteristic
321#486C22×C12711yescharacteristic
322#486C22×C12711yescharacteristic
323#480—21no—
324#478—21no—
325#478—21no—
326#477C22×C12711yescharacteristic
327#477C22×C12711yescharacteristic
328#475C22×C12711yescharacteristic
329#468—21no—
330#464—21no—
331#463—21no—
332#461—21no—
333#461C22×C12711yescharacteristic
334#460—21no—
335#460C22×C12711yescharacteristic
336#460C22×C12711yescharacteristic
337#460C22×C12711yescharacteristic
338#459C22×C12711yescharacteristic
339#452—21no—
340C8×Q8C22×C12711yescharacteristic
341C8×Q8C22×C12711yescharacteristic
342C8×Q8C22×C12711yescharacteristic
343C4×Q16C22×C12711yescharacteristic
344C4×SD16—21no—
345C4×SD16—21no—
346C4×SD16C22×C12711yescharacteristic
347C4×D8—21no—
348#436C22×C12711yescharacteristic
349#417—21no—
350#334C22×C12711yescharacteristic
351#334C22×C12711yescharacteristic
352#333C22×C12711yescharacteristic
353#332C22×C12711yescharacteristic
354#331C22×C12711yescharacteristic
355#331C22×C12711yescharacteristic
356Q8⋊C8C22×C12711yescharacteristic
357Q8⋊C8C22×C12711yescharacteristic
358Q8⋊C8C22×C12711yescharacteristic
359D4⋊C8C22×C12711yescharacteristic
360#322C22×C12711yescharacteristic
361C2×#41—21no—
362C2×Q16D4×C12711yescharacteristic
363C2×SD16—21no—
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16D4×C12711yescharacteristic
370C2×D8—21no—
371C2×D8—41no—
372C2×M16—21no—
373C4⋊Q8—21no—
374C4⋊Q8C23×C12711yescharacteristic
375C4⋊Q8C23×C12711yescharacteristic
376#127—21no—
377#127C23×C12711yescharacteristic
378#127C23×C12711yescharacteristic
379#125—21no—
380#125—21no—
381#125—41no—
382#124—21no—
383#124—21no—
384#123—41no—
385C22⋊Q8—21no—
386C22⋊Q8—41no—
387#121—21no—
388#121—41no—
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8C23×C12711yescharacteristic
392C4×Q8C23×C12711yescharacteristic
393C4×Q8C23×C12711yescharacteristic
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4C23×C12711yescharacteristic
399C2×C4⋊C4—21no—
400#107—21no—
401#107—21no—
402#107D4×C12711yescharacteristic
403#106—21no—
404#106D4×C12711yescharacteristic
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8—21no—
408C4⋊C8C23×C12711yescharacteristic
409C4⋊C8C23×C12711yescharacteristic
410C4⋊C8C23×C12711yescharacteristic
411C4⋊C8C23×C12711yescharacteristic
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—41no—
417#103D4×C12711yescharacteristic
418#103D4×C12711yescharacteristic
419#103D4×C12711yescharacteristic
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102D4×C12711yescharacteristic
431C22⋊C8—21no—
432C4×C8—21no—
433C4×C8—21no—
434C4×C8—21no—
435C4×C8C23×C12711yescharacteristic
436C4×C8C23×C12711yescharacteristic
437C4×C8C23×C12711yescharacteristic
438#41—42no—
439#41—81no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8C2×D4×C12711yescharacteristic
443C2×Q8C2×D4×C12711yescharacteristic
444C2×Q8C2×D4×C12711yescharacteristic
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4C2×D4×C12711yescharacteristic
454C22×C4—21no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458Q16—22no—
459SD16—41no—
460SD16—42no—
461SD16—42no—
462SD16—81no—
463SD16—81no—
464SD16—81no—
465SD16—81no—
466D8—42no—
467D8—82no—
468M16—81no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8C2×D4×C12711yescharacteristic
475C2×C8C2×D4×C12711yescharacteristic
476C2×C8C2×D4×C12711yescharacteristic
477C2×C8C2×D4×C12711yescharacteristic
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4C2×D4×C12711yescharacteristic
491C4⋊C4C2×D4×C12711yescharacteristic
492C4⋊C4C2×D4×C12711yescharacteristic
493C4⋊C4C2×D4×C12711yescharacteristic
494C22⋊C4—21no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—41no—
504C42C24×C12711yescharacteristic
505C23—21no—
506C23—41no—
507C23—41no—
508Q8—21no—
509Q8—21no—
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—41no—
514Q8—41no—
515Q8—81no—
516Q8#135×C12712yes—
517D4—21no—
518D4—21no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—82no—
528D4—81no—
529D4—81no—
530D4—161no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—82no—
543C2×C4—161no—
544C2×C4—161no—
545C2×C4C22×D4×C12711yescharacteristic
546C2×C4C22×D4×C12711yescharacteristic
547C2×C4H(5,𝔽2)×C12711yescharacteristic
548C8—21no—
549C8—21no—
550C8—21no—
551C8—21no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22D42×C12711yescharacteristic
567C4—22no—
568C4—21no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—81no—
576C4—81no—
577C4C2×#135×C12711yescharacteristic
578C4#575×C12711yescharacteristic
579C4#577×C12711yescharacteristic
580C4#577×C12711yescharacteristic
581C2—81no—
582C2—161no—
583C2—161no—
584C2C127×#327111yescharacteristic
585C2C127×#328211yescharacteristic
586C2C127×#328811yescharacteristic
subgroupG/H
center, socleC22×C127D42
commutator, Frattini, cosocleC42C24×C127
prime radicalC127×#1621C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#3392C2semidirect
2. C127×#3365C2semidirect
3. C127×#3361C2semidirect
4. C127×#3333C2semidirect
5. C127×#1717C2semidirect
6. C127×#1701C2semidirect
7. C127×#1678C2semidirect
8. C127×#1678C2semidirect
9. C127×#1666C2semidirect
10. C127×#1643C2semidirect
11. C127×#1636C2semidirect
13. C127×#1620C2semidirect
14. C127×#1583C2semidirect
15. C127×#1579C2semidirect
287. #19833C127direct (N × H)
294. #3392C2×C127semidirect
295. #3365C2×C127semidirect
296. #3361C2×C127semidirect
297. #3333C2×C127semidirect
298. #1717C2×C127semidirect
299. #1701C2×C127semidirect
300. #1678C2×C127semidirect
301. #1678C2×C127semidirect
302. #1666C2×C127semidirect
303. #1643C2×C127semidirect
304. #1636C2×C127semidirect
306. #1620C2×C127semidirect
307. #1583C2×C127semidirect
308. #1579C2×C127semidirect
309. C127#19833direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#33922
C127×#33652
C127×#33612
C127×#33332
C127×#17172
C127×#17012
C127×#16782
C127×#16662
C127×#16432
C127×#16362
C127×#16212
C127×#16202
C127×#15832
C127×#15792
#19833127