Finite Group Databasebeta

← C127×#19786 #44583459

Subgroups — C127×#19786 #44583459

Order 32512.

614 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3393C211yesmaximal, characteristic, complemented
2C127×#3358C211yesmaximal, characteristic
3C127×#3328C211yesmaximal, characteristic, complemented
4C127×#3304C211yesmaximal, characteristic, complemented
5C127×#1720C211yesmaximal, characteristic, complemented
6C127×#1701C211yesmaximal, characteristic, complemented
7C127×#1682C211yesmaximal, characteristic, complemented
8C127×#1679C211yesmaximal, characteristic, complemented
9C127×#1670C211yesmaximal, characteristic, complemented
10C127×#1652C211yesmaximal, characteristic, complemented
11C127×#1651C211yesmaximal, characteristic, complemented
12C127×#1642C211yesmaximal, characteristic, complemented
13C127×#1628C211yesmaximal, characteristic, complemented
14C127×#1581C211yesmaximal, characteristic, complemented
15C127×#1579C211yesmaximal, characteristic, complemented
16#556×C127C2211yescharacteristic
17#556×C127C2211yescharacteristic
18#550×C127C2211yescharacteristic
19D4×Q8×C127C2211yescharacteristic
20#498×C127C2211yescharacteristic
21#495×C127—21no—
22#494×C127C2211yescharacteristic
23#487×C127C2211yescharacteristic
24#486×C127—21no—
25#486×C127C2211yescharacteristic
26#486×C127C2211yescharacteristic
27#486×C127C2211yescharacteristic
28#485×C127—21no—
29#482×C127—21no—
30#475×C127C2211yescharacteristic
31#475×C127C2211yescharacteristic
32#474×C127—21no—
33#474×C127C2211yescharacteristic
34#470×C127—21no—
35#465×C127—21no—
36#464×C127—21no—
37#464×C127—21no—
38#462×C127C2211yescharacteristic
39#461×C127C2211yescharacteristic
40#461×C127C2211yescharacteristic
41#460×C127C2211yescharacteristic
42#459×C127—21no—
43#459×C127C2211yescharacteristic
44#452×C127—21no—
45#451×C127—21no—
46C8×Q8×C127C2211yescharacteristic
47C8×Q8×C127C2211yescharacteristic
48C4×Q16×C127—21no—
49C4×Q16×C127C2211yescharacteristic
50C4×D8×C127—21no—
51C4×D8×C127C2211yescharacteristic
52#436×C127C2211yescharacteristic
53C8×D4×C127C2211yescharacteristic
54#419×C127—21no—
55#416×C127—21no—
56#335×C127C2211yescharacteristic
57#334×C127C2211yescharacteristic
58#332×C127C2211yescharacteristic
59#332×C127C2211yescharacteristic
60#332×C127C2211yescharacteristic
61#331×C127C2211yescharacteristic
62Q8⋊C8×C127C2211yescharacteristic
63Q8⋊C8×C127C2211yescharacteristic
64D4⋊C8×C127C2211yescharacteristic
65D4⋊C8×C127C2211yescharacteristic
66#322×C127C2211yescharacteristic
67C2×#41×C127—21no—
68C22×Q8×C127—21no—
69C2×Q16×C127—21no—
70C2×Q16×C127—21no—
71C2×Q16×C127—21no—
72C2×Q16×C127D411yescharacteristic
73C2×SD16×C127—21no—
74C2×SD16×C127—21no—
75C2×SD16×C127—21no—
76C2×D8×C127—21no—
77C2×D8×C127D411yescharacteristic
78C2×M16×C127—21no—
79C22×C8×C127—21no—
80C4⋊Q8×C127—21no—
81C4⋊Q8×C127C2311yescharacteristic
82C4⋊Q8×C127C2311yescharacteristic
83C4⋊Q8×C127C2311yescharacteristic
84#127×C127—21no—
85#127×C127C2311yescharacteristic
86#126×C127—41no—
87#126×C127—41no—
88#124×C127—21no—
89#124×C127—21no—
90C22⋊Q8×C127—21no—
91C22⋊Q8×C127—21no—
92C22⋊Q8×C127—21no—
93C22⋊Q8×C127—41no—
94#121×C127—21no—
95#121×C127—41no—
96C4×Q8×C127—21no—
97C4×Q8×C127—21no—
98C4×Q8×C127C2311yescharacteristic
99C4×Q8×C127C2311yescharacteristic
100C4×D4×C127—21no—
101C4×D4×C127—21no—
102C4×D4×C127C2311yescharacteristic
103C4×D4×C127C2311yescharacteristic
104#117×C127—21no—
105#117×C127—21no—
106#107×C127—21no—
107#107×C127D411yescharacteristic
108#107×C127D411yescharacteristic
109#106×C127—21no—
110#106×C127—21no—
111#106×C127—41no—
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—21no—
123#103×C127—21no—
124#103×C127—21no—
125#103×C127D411yescharacteristic
126#103×C127D411yescharacteristic
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—41no—
135#102×C127D411yescharacteristic
136#102×C127D411yescharacteristic
137C22⋊C8×C127—21no—
138C22⋊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×C127—21no—
149C2×Q8×C127—41no—
150C2×Q8×C127—42no—
151C2×Q8×C127—81no—
152C2×Q8×C127C2×D411yescharacteristic
153C2×Q8×C127C2×D411yescharacteristic
154C2×D4×C127—21no—
155C2×D4×C127—21no—
156C2×D4×C127—21no—
157C2×D4×C127—41no—
158C2×D4×C127—41no—
159C2×D4×C127C2×D411yescharacteristic
160C2×D4×C127C2×D411yescharacteristic
161C22×C4×C127—21no—
162C22×C4×C127—21no—
163C22×C4×C127—41no—
164C22×C4×C127—41no—
165Q16×C127—22no—
166Q16×C127—42no—
167Q16×C127—81no—
168Q16×C127—81no—
169SD16×C127—81no—
170SD16×C127—81no—
171SD16×C127—81no—
172D8×C127—41no—
173D8×C127—42no—
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×C127—81no—
181C2×C8×C127C2×D411yescharacteristic
182C2×C8×C127C2×D411yescharacteristic
183C2×C8×C127C2×D411yescharacteristic
184C2×C8×C127C2×D411yescharacteristic
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—21no—
192C4⋊C4×C127—21no—
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—21no—
202C22⋊C4×C127—41no—
203C22⋊C4×C127—41no—
204C22⋊C4×C127—41no—
205C22⋊C4×C127—41no—
206C22⋊C4×C127—41no—
207C22⋊C4×C127—41no—
208C42×C127—21no—
209C42×C127—21no—
210C42×C127—41no—
211C42×C127—41no—
212C42×C127C2411yescharacteristic
213C23×C127—21no—
214C23×C127—21no—
215C23×C127—41no—
216Q8×C127—21no—
217Q8×C127—21no—
218Q8×C127—21no—
219Q8×C127—41no—
220Q8×C127—41no—
221Q8×C127—41no—
222Q8×C127—41no—
223Q8×C127—41no—
224Q8×C127—41no—
225Q8×C127—82no—
226Q8×C127#13512yes—
227D4×C127—21no—
228D4×C127—21no—
229D4×C127—21no—
230D4×C127—21no—
231D4×C127—41no—
232D4×C127—41no—
233D4×C127—41no—
234D4×C127—41no—
235D4×C127—82no—
236D4×C127—81no—
237D4×C127—161no—
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—41no—
249C2×C4×C127—41no—
250C2×C4×C127—41no—
251C2×C4×C127—82no—
252C2×C4×C127—82no—
253C2×C4×C127C22×D411yescharacteristic
254C2×C4×C127C22×D411yescharacteristic
255C2×C4×C127H(5,𝔽2)11yescharacteristic
256C8×C127—21no—
257C8×C127—21no—
258C8×C127—21no—
259C8×C127—21no—
260C8×C127—41no—
261C8×C127—41no—
262C8×C127—41no—
263C8×C127—41no—
264C8×C127—41no—
265C22×C127—41no—
266C22×C127—41no—
267C22×C127—41no—
268C22×C127—41no—
269C22×C127—41no—
270C22×C127—41no—
271C22×C127—81no—
272C22×C127—81no—
273C22×C127—81no—
274C22×C127D4211yescharacteristic
275C4×C127—22no—
276C4×C127—21no—
277C4×C127—41no—
278C4×C127—41no—
279C4×C127—41no—
280C4×C127—41no—
281C4×C127—41no—
282C4×C127—81no—
283C4×C127—81no—
284C4×C127—81no—
285C4×C127C2×#13511yescharacteristic
286C4×C127#57511yescharacteristic
287C4×C127#57611yescharacteristic
288C4×C127#57711yescharacteristic
289#19786C12711yesmaximal, characteristic, direct product factor, Sylow
290C2×C127—81no—
291C2×C127—81no—
292C2×C127—161no—
293C2×C127#327111yescharacteristic
294C2×C127#328011yescharacteristic
295C2×C127#328911yescharacteristic
296#3393C2×C12711yescharacteristic, complemented
297#3358C2×C12711yescharacteristic
298#3328C2×C12711yescharacteristic, complemented
299#3304C2×C12711yescharacteristic, complemented
300#1720C2×C12711yescharacteristic, complemented
301#1701C2×C12711yescharacteristic, complemented
302#1682C2×C12711yescharacteristic, complemented
303#1679C2×C12711yescharacteristic, complemented
304#1670C2×C12711yescharacteristic, complemented
305#1652C2×C12711yescharacteristic, complemented
306#1651C2×C12711yescharacteristic, complemented
307#1642C2×C12711yescharacteristic, complemented
308#1628C2×C12711yescharacteristic, complemented
309#1581C2×C12711yescharacteristic, complemented
310#1579C2×C12711yescharacteristic, complemented
311C127#1978611yescharacteristic, direct product factor, Sylow
312#556C22×C12711yescharacteristic
313#556C22×C12711yescharacteristic
314#550C22×C12711yescharacteristic
315D4×Q8C22×C12711yescharacteristic
316#498C22×C12711yescharacteristic
317#495—21no—
318#494C22×C12711yescharacteristic
319#487C22×C12711yescharacteristic
320#486—21no—
321#486C22×C12711yescharacteristic
322#486C22×C12711yescharacteristic
323#486C22×C12711yescharacteristic
324#485—21no—
325#482—21no—
326#475C22×C12711yescharacteristic
327#475C22×C12711yescharacteristic
328#474—21no—
329#474C22×C12711yescharacteristic
330#470—21no—
331#465—21no—
332#464—21no—
333#464—21no—
334#462C22×C12711yescharacteristic
335#461C22×C12711yescharacteristic
336#461C22×C12711yescharacteristic
337#460C22×C12711yescharacteristic
338#459—21no—
339#459C22×C12711yescharacteristic
340#452—21no—
341#451—21no—
342C8×Q8C22×C12711yescharacteristic
343C8×Q8C22×C12711yescharacteristic
344C4×Q16—21no—
345C4×Q16C22×C12711yescharacteristic
346C4×D8—21no—
347C4×D8C22×C12711yescharacteristic
348#436C22×C12711yescharacteristic
349C8×D4C22×C12711yescharacteristic
350#419—21no—
351#416—21no—
352#335C22×C12711yescharacteristic
353#334C22×C12711yescharacteristic
354#332C22×C12711yescharacteristic
355#332C22×C12711yescharacteristic
356#332C22×C12711yescharacteristic
357#331C22×C12711yescharacteristic
358Q8⋊C8C22×C12711yescharacteristic
359Q8⋊C8C22×C12711yescharacteristic
360D4⋊C8C22×C12711yescharacteristic
361D4⋊C8C22×C12711yescharacteristic
362#322C22×C12711yescharacteristic
363C2×#41—21no—
364C22×Q8—21no—
365C2×Q16—21no—
366C2×Q16—21no—
367C2×Q16—21no—
368C2×Q16D4×C12711yescharacteristic
369C2×SD16—21no—
370C2×SD16—21no—
371C2×SD16—21no—
372C2×D8—21no—
373C2×D8D4×C12711yescharacteristic
374C2×M16—21no—
375C22×C8—21no—
376C4⋊Q8—21no—
377C4⋊Q8C23×C12711yescharacteristic
378C4⋊Q8C23×C12711yescharacteristic
379C4⋊Q8C23×C12711yescharacteristic
380#127—21no—
381#127C23×C12711yescharacteristic
382#126—41no—
383#126—41no—
384#124—21no—
385#124—21no—
386C22⋊Q8—21no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389C22⋊Q8—41no—
390#121—21no—
391#121—41no—
392C4×Q8—21no—
393C4×Q8—21no—
394C4×Q8C23×C12711yescharacteristic
395C4×Q8C23×C12711yescharacteristic
396C4×D4—21no—
397C4×D4—21no—
398C4×D4C23×C12711yescharacteristic
399C4×D4C23×C12711yescharacteristic
400#117—21no—
401#117—21no—
402#107—21no—
403#107D4×C12711yescharacteristic
404#107D4×C12711yescharacteristic
405#106—21no—
406#106—21no—
407#106—41no—
408C4⋊C8—21no—
409C4⋊C8—21no—
410C4⋊C8C23×C12711yescharacteristic
411C4⋊C8C23×C12711yescharacteristic
412C4⋊C8C23×C12711yescharacteristic
413C4⋊C8C23×C12711yescharacteristic
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#103D4×C12711yescharacteristic
422#103D4×C12711yescharacteristic
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—41no—
431#102D4×C12711yescharacteristic
432#102D4×C12711yescharacteristic
433C22⋊C8—21no—
434C22⋊C8—21no—
435C4×C8—21no—
436C4×C8—21no—
437C4×C8C23×C12711yescharacteristic
438C4×C8C23×C12711yescharacteristic
439C4×C8C23×C12711yescharacteristic
440#41—42no—
441#41—81no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—41no—
446C2×Q8—42no—
447C2×Q8—81no—
448C2×Q8C2×D4×C12711yescharacteristic
449C2×Q8C2×D4×C12711yescharacteristic
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4C2×D4×C12711yescharacteristic
456C2×D4C2×D4×C12711yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—41no—
460C22×C4—41no—
461Q16—22no—
462Q16—42no—
463Q16—81no—
464Q16—81no—
465SD16—81no—
466SD16—81no—
467SD16—81no—
468D8—41no—
469D8—42no—
470M16—81no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—81no—
477C2×C8C2×D4×C12711yescharacteristic
478C2×C8C2×D4×C12711yescharacteristic
479C2×C8C2×D4×C12711yescharacteristic
480C2×C8C2×D4×C12711yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4C2×D4×C12711yescharacteristic
493C4⋊C4C2×D4×C12711yescharacteristic
494C4⋊C4C2×D4×C12711yescharacteristic
495C4⋊C4C2×D4×C12711yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C42—21no—
505C42—21no—
506C42—41no—
507C42—41no—
508C42C24×C12711yescharacteristic
509C23—21no—
510C23—21no—
511C23—41no—
512Q8—21no—
513Q8—21no—
514Q8—21no—
515Q8—41no—
516Q8—41no—
517Q8—41no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—82no—
522Q8#135×C12712yes—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—82no—
532D4—81no—
533D4—161no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—82no—
548C2×C4—82no—
549C2×C4C22×D4×C12711yescharacteristic
550C2×C4C22×D4×C12711yescharacteristic
551C2×C4H(5,𝔽2)×C12711yescharacteristic
552C8—21no—
553C8—21no—
554C8—21no—
555C8—21no—
556C8—41no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22D42×C12711yescharacteristic
571C4—22no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4C2×#135×C12711yescharacteristic
582C4#575×C12711yescharacteristic
583C4#576×C12711yescharacteristic
584C4#577×C12711yescharacteristic
585C2—81no—
586C2—81no—
587C2—161no—
588C2C127×#327111yescharacteristic
589C2C127×#328011yescharacteristic
590C2C127×#328911yescharacteristic
subgroupG/H
center, socleC22×C127D42
commutator, Frattini, cosocleC42C24×C127
prime radicalC127×#3358C2
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×#3393C2semidirect
3. C127×#3328C2semidirect
4. C127×#3304C2semidirect
5. C127×#1720C2semidirect
6. C127×#1701C2semidirect
7. C127×#1682C2semidirect
8. C127×#1679C2semidirect
9. C127×#1670C2semidirect
10. C127×#1652C2semidirect
11. C127×#1651C2semidirect
12. C127×#1642C2semidirect
13. C127×#1628C2semidirect
14. C127×#1581C2semidirect
15. C127×#1579C2semidirect
289. #19786C127direct (N × H)
296. #3393C2×C127semidirect
298. #3328C2×C127semidirect
299. #3304C2×C127semidirect
300. #1720C2×C127semidirect
301. #1701C2×C127semidirect
302. #1682C2×C127semidirect
303. #1679C2×C127semidirect
304. #1670C2×C127semidirect
305. #1652C2×C127semidirect
306. #1651C2×C127semidirect
307. #1642C2×C127semidirect
308. #1628C2×C127semidirect
309. #1581C2×C127semidirect
310. #1579C2×C127semidirect
311. C127#19786direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#33932
C127×#33582
C127×#33282
C127×#33042
C127×#17202
C127×#17012
C127×#16822
C127×#16792
C127×#16702
C127×#16522
C127×#16512
C127×#16422
C127×#16282
C127×#15812
C127×#15792
#19786127