Finite Group Databasebeta

← C127×#19876 #44583549

Subgroups — C127×#19876 #44583549

Order 32512.

640 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3392C211yesmaximal, characteristic, complemented
2C127×#3364C211yesmaximal, characteristic, complemented
3C127×#3353C211yesmaximal, characteristic, complemented
4C127×#3284C211yesmaximal, characteristic
5C127×#1714C211yesmaximal, characteristic, complemented
6C127×#1685C211yesmaximal, characteristic, complemented
7C127×#1679C211yesmaximal, characteristic, complemented
8C127×#1674C211yesmaximal, characteristic, complemented
9C127×#1666C211yesmaximal, characteristic, complemented
10C127×#1654C211yesmaximal, characteristic, complemented
11C127×#1653C211yesmaximal, characteristic, complemented
12C127×#1641C211yesmaximal, characteristic, complemented
13C127×#1628C211yesmaximal, characteristic, complemented
14C127×#1583C211yesmaximal, characteristic, complemented
15C127×SD16⋊C8C211yesmaximal, characteristic, complemented
16C2×#135×C127—21no—
17#557×C127C2211yescharacteristic
18#556×C127C2211yescharacteristic
19#550×C127C2211yescharacteristic
20#547×C127C2211yescharacteristic
21#500×C127C2211yescharacteristic
22#498×C127C2211yescharacteristic
23#492×C127—21no—
24#492×C127C2211yescharacteristic
25#492×C127C2211yescharacteristic
26#488×C127—21no—
27#487×C127C2211yescharacteristic
28#486×C127C2211yescharacteristic
29#484×C127—21no—
30#482×C127—21no—
31#479×C127—21no—
32#475×C127C2211yescharacteristic
33#474×C127C2211yescharacteristic
34#474×C127C2211yescharacteristic
35#468×C127—21no—
36#465×C127—21no—
37#464×C127—21no—
38#462×C127C2211yescharacteristic
39#462×C127C2211yescharacteristic
40#461×C127—21no—
41#461×C127C2211yescharacteristic
42#460×C127—21no—
43#460×C127C2211yescharacteristic
44#459×C127C2211yescharacteristic
45#452×C127—21no—
46#449×C127—21no—
47C8×Q8×C127C2211yescharacteristic
48C8×Q8×C127C2211yescharacteristic
49C4×Q16×C127—21no—
50C4×SD16×C127—21no—
51C4×SD16×C127C2211yescharacteristic
52C4×SD16×C127C2211yescharacteristic
53#436×C127C2211yescharacteristic
54C8×D4×C127C2211yescharacteristic
55#428×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—
68C2×#41×C127—21no—
69#135×C127—44no—
70C2×Q16×C127—21no—
71C2×Q16×C127—21no—
72C2×SD16×C127—21no—
73C2×SD16×C127—21no—
74C2×SD16×C127—21no—
75C2×SD16×C127—21no—
76C2×SD16×C127—21no—
77C2×SD16×C127—21no—
78C2×SD16×C127D411yescharacteristic
79C2×SD16×C127D411yescharacteristic
80C2×D8×C127—21no—
81C2×M16×C127—21no—
82C22×C8×C127—21no—
83C4⋊Q8×C127—21no—
84C4⋊Q8×C127C2311yescharacteristic
85C4⋊Q8×C127C2311yescharacteristic
86C4⋊Q8×C127C2311yescharacteristic
87#127×C127—21no—
88#127×C127C2311yescharacteristic
89#126×C127—41no—
90#125×C127—21no—
91#125×C127—41no—
92#124×C127—21no—
93#123×C127—41no—
94C22⋊Q8×C127—21no—
95C22⋊Q8×C127—21no—
96#121×C127—21no—
97#121×C127—21no—
98#121×C127—41no—
99C4×Q8×C127—21no—
100C4×Q8×C127—21no—
101C4×Q8×C127—21no—
102C4×Q8×C127C2311yescharacteristic
103C4×Q8×C127C2311yescharacteristic
104C4×D4×C127—21no—
105C4×D4×C127C2311yescharacteristic
106C4×D4×C127C2311yescharacteristic
107#117×C127—21no—
108C2×C4⋊C4×C127—21no—
109#107×C127—21no—
110#107×C127—21no—
111#107×C127—21no—
112#107×C127—21no—
113#106×C127—21no—
114#106×C127—41no—
115#106×C127D411yescharacteristic
116#106×C127D411yescharacteristic
117C4⋊C8×C127—21no—
118C4⋊C8×C127—21no—
119C4⋊C8×C127C2311yescharacteristic
120C4⋊C8×C127C2311yescharacteristic
121C4⋊C8×C127C2311yescharacteristic
122C4⋊C8×C127C2311yescharacteristic
123#103×C127—21no—
124#103×C127—21no—
125#103×C127—21no—
126#103×C127—21no—
127#103×C127—21no—
128#103×C127—21no—
129#103×C127D411yescharacteristic
130#103×C127D411yescharacteristic
131#102×C127—21no—
132#102×C127—21no—
133#102×C127—21no—
134#102×C127—21no—
135#102×C127—41no—
136#102×C127D411yescharacteristic
137#102×C127D411yescharacteristic
138C22⋊C8×C127—21no—
139C22⋊C8×C127—21no—
140C4×C8×C127—21no—
141C4×C8×C127—21no—
142C4×C8×C127C2311yescharacteristic
143C4×C8×C127C2311yescharacteristic
144C4×C8×C127C2311yescharacteristic
145#41×C127—42no—
146#41×C127—42no—
147#41×C127—81no—
148#41×C127—81no—
149C2×Q8×C127—21no—
150C2×Q8×C127—21no—
151C2×Q8×C127—21no—
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×C127—41no—
160C2×D4×C127C2×D411yescharacteristic
161C2×D4×C127C2×D411yescharacteristic
162C22×C4×C127—21no—
163C22×C4×C127—21no—
164C22×C4×C127—41no—
165C22×C4×C127—41no—
166Q16×C127—42no—
167Q16×C127—42no—
168SD16×C127—22no—
169SD16×C127—22no—
170SD16×C127—42no—
171SD16×C127—42no—
172SD16×C127—81no—
173SD16×C127—81no—
174SD16×C127—81no—
175SD16×C127—81no—
176D8×C127—42no—
177M16×C127—42no—
178C2×C8×C127—21no—
179C2×C8×C127—21no—
180C2×C8×C127—21no—
181C2×C8×C127—21no—
182C2×C8×C127—21no—
183C2×C8×C127—42no—
184C2×C8×C127C2×D411yescharacteristic
185C2×C8×C127C2×D411yescharacteristic
186C2×C8×C127C2×D411yescharacteristic
187C2×C8×C127C2×D411yescharacteristic
188C4⋊C4×C127—21no—
189C4⋊C4×C127—21no—
190C4⋊C4×C127—21no—
191C4⋊C4×C127—21no—
192C4⋊C4×C127—21no—
193C4⋊C4×C127—21no—
194C4⋊C4×C127—21no—
195C4⋊C4×C127—21no—
196C4⋊C4×C127—41no—
197C4⋊C4×C127—41no—
198C4⋊C4×C127—41no—
199C4⋊C4×C127—41no—
200C4⋊C4×C127—41no—
201C4⋊C4×C127C2×D411yescharacteristic
202C4⋊C4×C127C2×D411yescharacteristic
203C4⋊C4×C127C2×D411yescharacteristic
204C4⋊C4×C127C2×D411yescharacteristic
205C22⋊C4×C127—21no—
206C22⋊C4×C127—21no—
207C22⋊C4×C127—41no—
208C22⋊C4×C127—41no—
209C22⋊C4×C127—41no—
210C22⋊C4×C127—41no—
211C42×C127—21no—
212C42×C127—21no—
213C42×C127—41no—
214C42×C127—41no—
215C42×C127C2411yescharacteristic
216C23×C127—21no—
217C23×C127—21no—
218C23×C127—41no—
219Q8×C127—21no—
220Q8×C127—21no—
221Q8×C127—21no—
222Q8×C127—41no—
223Q8×C127—41no—
224Q8×C127—41no—
225Q8×C127—41no—
226Q8×C127—41no—
227Q8×C127—41no—
228Q8×C127AGL(1,ℤ/8)12yes—
229D4×C127—21no—
230D4×C127—21no—
231D4×C127—21no—
232D4×C127—21no—
233D4×C127—41no—
234D4×C127—41no—
235D4×C127—41no—
236D4×C127—41no—
237D4×C127—82no—
238D4×C127—81no—
239D4×C127—82no—
240D4×C127—161no—
241C2×C4×C127—21no—
242C2×C4×C127—21no—
243C2×C4×C127—21no—
244C2×C4×C127—21no—
245C2×C4×C127—21no—
246C2×C4×C127—21no—
247C2×C4×C127—41no—
248C2×C4×C127—41no—
249C2×C4×C127—41no—
250C2×C4×C127—41no—
251C2×C4×C127—41no—
252C2×C4×C127—41no—
253C2×C4×C127—41no—
254C2×C4×C127—82no—
255C2×C4×C127—82no—
256C2×C4×C127C22×D411yescharacteristic
257C2×C4×C127C22×D411yescharacteristic
258C2×C4×C127H(5,𝔽2)11yescharacteristic
259C8×C127—21no—
260C8×C127—21no—
261C8×C127—21no—
262C8×C127—41no—
263C8×C127—41no—
264C8×C127—41no—
265C8×C127—41no—
266C8×C127—41no—
267C8×C127#13512yescomplemented
268C22×C127—41no—
269C22×C127—41no—
270C22×C127—41no—
271C22×C127—41no—
272C22×C127—41no—
273C22×C127—41no—
274C22×C127—81no—
275C22×C127—81no—
276C22×C127—81no—
277C22×C127D4211yescharacteristic
278C4×C127—22no—
279C4×C127—21no—
280C4×C127—41no—
281C4×C127—41no—
282C4×C127—41no—
283C4×C127—41no—
284C4×C127—41no—
285C4×C127—81no—
286C4×C127—81no—
287C4×C127—81no—
288C4×C127C2×#13511yescharacteristic
289C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
290C4×C127#57711yescharacteristic
291C4×C127#57711yescharacteristic
292#19876C12711yesmaximal, characteristic, direct product factor, Sylow
293C2×C127—81no—
294C2×C127—81no—
295C2×C127—161no—
296C2×C127#326511yescharacteristic
297C2×C127#328411yescharacteristic
298C2×C127#328911yescharacteristic
299#3392C2×C12711yescharacteristic, complemented
300#3364C2×C12711yescharacteristic, complemented
301#3353C2×C12711yescharacteristic, complemented
302#3284C2×C12711yescharacteristic
303#1714C2×C12711yescharacteristic, complemented
304#1685C2×C12711yescharacteristic, complemented
305#1679C2×C12711yescharacteristic, complemented
306#1674C2×C12711yescharacteristic, complemented
307#1666C2×C12711yescharacteristic, complemented
308#1654C2×C12711yescharacteristic, complemented
309#1653C2×C12711yescharacteristic, complemented
310#1641C2×C12711yescharacteristic, complemented
311#1628C2×C12711yescharacteristic, complemented
312#1583C2×C12711yescharacteristic, complemented
313SD16⋊C8C2×C12711yescharacteristic, complemented
314C127#1987611yescharacteristic, direct product factor, Sylow
315C2×#135—21no—
316#557C22×C12711yescharacteristic
317#556C22×C12711yescharacteristic
318#550C22×C12711yescharacteristic
319#547C22×C12711yescharacteristic
320#500C22×C12711yescharacteristic
321#498C22×C12711yescharacteristic
322#492—21no—
323#492C22×C12711yescharacteristic
324#492C22×C12711yescharacteristic
325#488—21no—
326#487C22×C12711yescharacteristic
327#486C22×C12711yescharacteristic
328#484—21no—
329#482—21no—
330#479—21no—
331#475C22×C12711yescharacteristic
332#474C22×C12711yescharacteristic
333#474C22×C12711yescharacteristic
334#468—21no—
335#465—21no—
336#464—21no—
337#462C22×C12711yescharacteristic
338#462C22×C12711yescharacteristic
339#461—21no—
340#461C22×C12711yescharacteristic
341#460—21no—
342#460C22×C12711yescharacteristic
343#459C22×C12711yescharacteristic
344#452—21no—
345#449—21no—
346C8×Q8C22×C12711yescharacteristic
347C8×Q8C22×C12711yescharacteristic
348C4×Q16—21no—
349C4×SD16—21no—
350C4×SD16C22×C12711yescharacteristic
351C4×SD16C22×C12711yescharacteristic
352#436C22×C12711yescharacteristic
353C8×D4C22×C12711yescharacteristic
354#428—21no—
355#335C22×C12711yescharacteristic
356#334C22×C12711yescharacteristic
357#332C22×C12711yescharacteristic
358#332C22×C12711yescharacteristic
359#332C22×C12711yescharacteristic
360#331C22×C12711yescharacteristic
361Q8⋊C8C22×C12711yescharacteristic
362Q8⋊C8C22×C12711yescharacteristic
363D4⋊C8C22×C12711yescharacteristic
364D4⋊C8C22×C12711yescharacteristic
365#322C22×C12711yescharacteristic
366C2×#41—21no—
367C2×#41—21no—
368#135—44no—
369C2×Q16—21no—
370C2×Q16—21no—
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16—21no—
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16D4×C12711yescharacteristic
378C2×SD16D4×C12711yescharacteristic
379C2×D8—21no—
380C2×M16—21no—
381C22×C8—21no—
382C4⋊Q8—21no—
383C4⋊Q8C23×C12711yescharacteristic
384C4⋊Q8C23×C12711yescharacteristic
385C4⋊Q8C23×C12711yescharacteristic
386#127—21no—
387#127C23×C12711yescharacteristic
388#126—41no—
389#125—21no—
390#125—41no—
391#124—21no—
392#123—41no—
393C22⋊Q8—21no—
394C22⋊Q8—21no—
395#121—21no—
396#121—21no—
397#121—41no—
398C4×Q8—21no—
399C4×Q8—21no—
400C4×Q8—21no—
401C4×Q8C23×C12711yescharacteristic
402C4×Q8C23×C12711yescharacteristic
403C4×D4—21no—
404C4×D4C23×C12711yescharacteristic
405C4×D4C23×C12711yescharacteristic
406#117—21no—
407C2×C4⋊C4—21no—
408#107—21no—
409#107—21no—
410#107—21no—
411#107—21no—
412#106—21no—
413#106—41no—
414#106D4×C12711yescharacteristic
415#106D4×C12711yescharacteristic
416C4⋊C8—21no—
417C4⋊C8—21no—
418C4⋊C8C23×C12711yescharacteristic
419C4⋊C8C23×C12711yescharacteristic
420C4⋊C8C23×C12711yescharacteristic
421C4⋊C8C23×C12711yescharacteristic
422#103—21no—
423#103—21no—
424#103—21no—
425#103—21no—
426#103—21no—
427#103—21no—
428#103D4×C12711yescharacteristic
429#103D4×C12711yescharacteristic
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—41no—
435#102D4×C12711yescharacteristic
436#102D4×C12711yescharacteristic
437C22⋊C8—21no—
438C22⋊C8—21no—
439C4×C8—21no—
440C4×C8—21no—
441C4×C8C23×C12711yescharacteristic
442C4×C8C23×C12711yescharacteristic
443C4×C8C23×C12711yescharacteristic
444#41—42no—
445#41—42no—
446#41—81no—
447#41—81no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8C2×D4×C12711yescharacteristic
452C2×Q8C2×D4×C12711yescharacteristic
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4C2×D4×C12711yescharacteristic
460C2×D4C2×D4×C12711yescharacteristic
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—41no—
464C22×C4—41no—
465Q16—42no—
466Q16—42no—
467SD16—22no—
468SD16—22no—
469SD16—42no—
470SD16—42no—
471SD16—81no—
472SD16—81no—
473SD16—81no—
474SD16—81no—
475D8—42no—
476M16—42no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—42no—
483C2×C8C2×D4×C12711yescharacteristic
484C2×C8C2×D4×C12711yescharacteristic
485C2×C8C2×D4×C12711yescharacteristic
486C2×C8C2×D4×C12711yescharacteristic
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4C2×D4×C12711yescharacteristic
501C4⋊C4C2×D4×C12711yescharacteristic
502C4⋊C4C2×D4×C12711yescharacteristic
503C4⋊C4C2×D4×C12711yescharacteristic
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C42—21no—
511C42—21no—
512C42—41no—
513C42—41no—
514C42C24×C12711yescharacteristic
515C23—21no—
516C23—21no—
517C23—41no—
518Q8—21no—
519Q8—21no—
520Q8—21no—
521Q8—41no—
522Q8—41no—
523Q8—41no—
524Q8—41no—
525Q8—41no—
526Q8—41no—
527Q8AGL(1,ℤ/8)×C12712yes—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—21no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—82no—
537D4—81no—
538D4—82no—
539D4—161no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—82no—
554C2×C4—82no—
555C2×C4C22×D4×C12711yescharacteristic
556C2×C4C22×D4×C12711yescharacteristic
557C2×C4H(5,𝔽2)×C12711yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8#135×C12712yescomplemented
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22D42×C12711yescharacteristic
577C4—22no—
578C4—21no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4C2×#135×C12711yescharacteristic
588C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
589C4#577×C12711yescharacteristic
590C4#577×C12711yescharacteristic
591C2—81no—
592C2—81no—
593C2—161no—
594C2C127×#326511yescharacteristic
595C2C127×#328411yescharacteristic
596C2C127×#328911yescharacteristic
subgroupG/H
center, socleC22×C127D42
commutator, Frattini, cosocleC42C24×C127
prime radicalC127×#3284C2
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×#3364C2semidirect
3. C127×#3353C2semidirect
5. C127×#1714C2semidirect
6. C127×#1685C2semidirect
7. C127×#1679C2semidirect
8. C127×#1674C2semidirect
9. C127×#1666C2semidirect
10. C127×#1654C2semidirect
11. C127×#1653C2semidirect
12. C127×#1641C2semidirect
13. C127×#1628C2semidirect
14. C127×#1583C2semidirect
15. C127×SD16⋊C8C2semidirect
267. C8×C127#135semidirect
292. #19876C127direct (N × H)
299. #3392C2×C127semidirect
300. #3364C2×C127semidirect
301. #3353C2×C127semidirect
303. #1714C2×C127semidirect
304. #1685C2×C127semidirect
305. #1679C2×C127semidirect
306. #1674C2×C127semidirect
307. #1666C2×C127semidirect
308. #1654C2×C127semidirect
309. #1653C2×C127semidirect
310. #1641C2×C127semidirect
311. #1628C2×C127semidirect
312. #1583C2×C127semidirect
313. SD16⋊C8C2×C127semidirect
314. C127#19876direct (N × H)
566. C8#135×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#33922
C127×#33642
C127×#33532
C127×#32842
C127×#17142
C127×#16852
C127×#16792
C127×#16742
C127×#16662
C127×#16542
C127×#16532
C127×#16412
C127×#16282
C127×#15832
C127×SD16⋊C82
#19876127