Finite Group Databasebeta

← C127×#19835 #44583508

Subgroups — C127×#19835 #44583508

Order 32512.

652 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
1C127×#3367C211yesmaximal, characteristic, complemented
2C127×#3358C211yesmaximal, characteristic
3C127×#3304C211yesmaximal, characteristic, complemented
4D4×Q16×C127C211yesmaximal, characteristic, complemented
5C127×#1720C211yesmaximal, characteristic, complemented
6C127×#1702C211yesmaximal, characteristic, complemented
7C127×#1681C211yesmaximal, characteristic, complemented
8C127×#1680C211yesmaximal, characteristic, complemented
9C127×#1669C211yesmaximal, characteristic, complemented
10C127×#1652C211yesmaximal, characteristic, complemented
11C127×#1651C211yesmaximal, characteristic, complemented
12C127×#1641C211yesmaximal, characteristic, complemented
13C127×#1627C211yesmaximal, characteristic, complemented
14C127×#1584C211yesmaximal, characteristic, complemented
15C127×#1580C211yesmaximal, characteristic, complemented
16C22×Q16×C127—21no—
17#556×C127C2211yescharacteristic
18#550×C127C2211yescharacteristic
19D4×Q8×C127C2211yescharacteristic
20D4×Q8×C127C2211yescharacteristic
21#498×C127C2211yescharacteristic
22#494×C127C2211yescharacteristic
23#489×C127—21no—
24#487×C127C2211yescharacteristic
25#486×C127—21no—
26#486×C127C2211yescharacteristic
27#486×C127C2211yescharacteristic
28#486×C127C2211yescharacteristic
29#482×C127—21no—
30#477×C127—21no—
31#475×C127C2211yescharacteristic
32#474×C127—21no—
33#474×C127C2211yescharacteristic
34#474×C127C2211yescharacteristic
35#467×C127—21no—
36#465×C127—21no—
37#463×C127—21no—
38#462×C127C2211yescharacteristic
39#462×C127C2211yescharacteristic
40#461×C127C2211yescharacteristic
41#460×C127C2211yescharacteristic
42#459×C127—21no—
43#459×C127C2211yescharacteristic
44#452×C127—21no—
45#451×C127—21no—
46#451×C127—21no—
47#446×C127C2211yescharacteristic
48C8×Q8×C127C2211yescharacteristic
49#440×C127—21no—
50C4×Q16×C127C2211yescharacteristic
51C4×D8×C127—21no—
52C4×D8×C127C2211yescharacteristic
53C8×D4×C127C2211yescharacteristic
54C8×D4×C127C2211yescharacteristic
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—
69C22×Q8×C127—21no—
70C2×Q16×C127—21no—
71C2×Q16×C127—21no—
72C2×Q16×C127—21no—
73C2×Q16×C127—21no—
74C2×Q16×C127—44no—
75C2×Q16×C127D411yescharacteristic
76C2×SD16×C127—21no—
77C2×SD16×C127—21no—
78C2×D8×C127—21no—
79C2×D8×C127D411yescharacteristic
80C22×C8×C127—21no—
81C22×C8×C127—21no—
82C4⋊Q8×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#124×C127—21no—
91C22⋊Q8×C127—21no—
92C22⋊Q8×C127—21no—
93C22⋊Q8×C127—21no—
94C22⋊Q8×C127—41no—
95C22⋊Q8×C127—41no—
96#121×C127—21no—
97#121×C127—41no—
98C4×Q8×C127—21no—
99C4×Q8×C127C2311yescharacteristic
100C4×Q8×C127C2311yescharacteristic
101C4×D4×C127—21no—
102C4×D4×C127—21no—
103C4×D4×C127—21no—
104C4×D4×C127C2311yescharacteristic
105C4×D4×C127C2311yescharacteristic
106#117×C127—21no—
107#107×C127—21no—
108#107×C127—21no—
109#107×C127D411yescharacteristic
110#107×C127D411yescharacteristic
111#106×C127—21no—
112#106×C127—41no—
113C4⋊C8×C127—21no—
114C4⋊C8×C127—21no—
115C4⋊C8×C127C2311yescharacteristic
116C4⋊C8×C127C2311yescharacteristic
117C4⋊C8×C127C2311yescharacteristic
118C4⋊C8×C127C2311yescharacteristic
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—21no—
135#102×C127—41no—
136#102×C127D411yescharacteristic
137#102×C127D411yescharacteristic
138C22⋊C8×C127—21no—
139C22⋊C8×C127—21no—
140#97×C127—21no—
141C4×C8×C127—21no—
142C4×C8×C127C2311yescharacteristic
143C4×C8×C127C2311yescharacteristic
144C4×C8×C127C2311yescharacteristic
145#41×C127—42no—
146#41×C127—81no—
147C2×Q8×C127—21no—
148C2×Q8×C127—21no—
149C2×Q8×C127—21no—
150C2×Q8×C127—41no—
151C2×Q8×C127—41no—
152C2×Q8×C127—42no—
153C2×Q8×C127—42no—
154C2×Q8×C127—81no—
155C2×Q8×C127—81no—
156C2×Q8×C127C2×D411yescharacteristic
157C2×Q8×C127C2×D411yescharacteristic
158C2×D4×C127—21no—
159C2×D4×C127—21no—
160C2×D4×C127—21no—
161C2×D4×C127—41no—
162C2×D4×C127—41no—
163C2×D4×C127C2×D411yescharacteristic
164C2×D4×C127C2×D411yescharacteristic
165C22×C4×C127—21no—
166C22×C4×C127—21no—
167C22×C4×C127—41no—
168C22×C4×C127—41no—
169C22×C4×C127—41no—
170Q16×C127—22no—
171Q16×C127—42no—
172Q16×C127—42no—
173Q16×C127—42no—
174Q16×C127—81no—
175SD16×C127—42no—
176SD16×C127—81no—
177D8×C127—22no—
178D8×C127—42no—
179C2×C8×C127—21no—
180C2×C8×C127—21no—
181C2×C8×C127—21no—
182C2×C8×C127—21no—
183C2×C8×C127—21no—
184C2×C8×C127—42no—
185C2×C8×C127—81no—
186C2×C8×C127C2×D411yescharacteristic
187C2×C8×C127C2×D411yescharacteristic
188C2×C8×C127C2×D411yescharacteristic
189C2×C8×C127C2×D411yescharacteristic
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—21no—
197C4⋊C4×C127—21no—
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—
211C22⋊C4×C127—41no—
212C42×C127—21no—
213C42×C127—21no—
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×C127—82no—
229Q8×C127—82no—
230Q8×C127AGL(1,ℤ/8)12yes—
231D4×C127—21no—
232D4×C127—21no—
233D4×C127—21no—
234D4×C127—41no—
235D4×C127—41no—
236D4×C127—41no—
237D4×C127—41no—
238D4×C127—82no—
239D4×C127—81no—
240D4×C127—161no—
241D4×C127#13512yes—
242C2×C4×C127—21no—
243C2×C4×C127—21no—
244C2×C4×C127—21no—
245C2×C4×C127—21no—
246C2×C4×C127—21no—
247C2×C4×C127—21no—
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—41no—
255C2×C4×C127—82no—
256C2×C4×C127—82no—
257C2×C4×C127—82no—
258C2×C4×C127C22×D411yescharacteristic
259C2×C4×C127C22×D411yescharacteristic
260C2×C4×C127H(5,𝔽2)11yescharacteristic
261C8×C127—21no—
262C8×C127—21no—
263C8×C127—21no—
264C8×C127—21no—
265C8×C127—41no—
266C8×C127—41no—
267C8×C127—41no—
268C8×C127—41no—
269C8×C127—41no—
270C22×C127—22no—
271C22×C127—41no—
272C22×C127—41no—
273C22×C127—41no—
274C22×C127—41no—
275C22×C127—41no—
276C22×C127—81no—
277C22×C127—81no—
278C22×C127—81no—
279C22×C127D4211yescharacteristic
280C4×C127—22no—
281C4×C127—21no—
282C4×C127—41no—
283C4×C127—41no—
284C4×C127—41no—
285C4×C127—41no—
286C4×C127—41no—
287C4×C127—81no—
288C4×C127—81no—
289C4×C127—81no—
290C4×C127C2×#13511yescharacteristic
291C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
292C4×C127#57611yescharacteristic
293C4×C127#57811yescharacteristic
294#19835C12711yesmaximal, characteristic, direct product factor, Sylow
295C2×C127—42no—
296C2×C127—81no—
297C2×C127—161no—
298C2×C127#326411yescharacteristic
299C2×C127#328511yescharacteristic
300C2×C127#328911yescharacteristic
301#3367C2×C12711yescharacteristic, complemented
302#3358C2×C12711yescharacteristic
303#3304C2×C12711yescharacteristic, complemented
304D4×Q16C2×C12711yescharacteristic, complemented
305#1720C2×C12711yescharacteristic, complemented
306#1702C2×C12711yescharacteristic, complemented
307#1681C2×C12711yescharacteristic, complemented
308#1680C2×C12711yescharacteristic, complemented
309#1669C2×C12711yescharacteristic, complemented
310#1652C2×C12711yescharacteristic, complemented
311#1651C2×C12711yescharacteristic, complemented
312#1641C2×C12711yescharacteristic, complemented
313#1627C2×C12711yescharacteristic, complemented
314#1584C2×C12711yescharacteristic, complemented
315#1580C2×C12711yescharacteristic, complemented
316C127#1983511yescharacteristic, direct product factor, Sylow
317C22×Q16—21no—
318#556C22×C12711yescharacteristic
319#550C22×C12711yescharacteristic
320D4×Q8C22×C12711yescharacteristic
321D4×Q8C22×C12711yescharacteristic
322#498C22×C12711yescharacteristic
323#494C22×C12711yescharacteristic
324#489—21no—
325#487C22×C12711yescharacteristic
326#486—21no—
327#486C22×C12711yescharacteristic
328#486C22×C12711yescharacteristic
329#486C22×C12711yescharacteristic
330#482—21no—
331#477—21no—
332#475C22×C12711yescharacteristic
333#474—21no—
334#474C22×C12711yescharacteristic
335#474C22×C12711yescharacteristic
336#467—21no—
337#465—21no—
338#463—21no—
339#462C22×C12711yescharacteristic
340#462C22×C12711yescharacteristic
341#461C22×C12711yescharacteristic
342#460C22×C12711yescharacteristic
343#459—21no—
344#459C22×C12711yescharacteristic
345#452—21no—
346#451—21no—
347#451—21no—
348#446C22×C12711yescharacteristic
349C8×Q8C22×C12711yescharacteristic
350#440—21no—
351C4×Q16C22×C12711yescharacteristic
352C4×D8—21no—
353C4×D8C22×C12711yescharacteristic
354C8×D4C22×C12711yescharacteristic
355C8×D4C22×C12711yescharacteristic
356#416—21no—
357#335C22×C12711yescharacteristic
358#334C22×C12711yescharacteristic
359#332C22×C12711yescharacteristic
360#332C22×C12711yescharacteristic
361#332C22×C12711yescharacteristic
362#331C22×C12711yescharacteristic
363Q8⋊C8C22×C12711yescharacteristic
364Q8⋊C8C22×C12711yescharacteristic
365D4⋊C8C22×C12711yescharacteristic
366D4⋊C8C22×C12711yescharacteristic
367#322C22×C12711yescharacteristic
368C2×#41—21no—
369C22×Q8—21no—
370C22×Q8—21no—
371C2×Q16—21no—
372C2×Q16—21no—
373C2×Q16—21no—
374C2×Q16—21no—
375C2×Q16—44no—
376C2×Q16D4×C12711yescharacteristic
377C2×SD16—21no—
378C2×SD16—21no—
379C2×D8—21no—
380C2×D8D4×C12711yescharacteristic
381C22×C8—21no—
382C22×C8—21no—
383C4⋊Q8—21no—
384C4⋊Q8—21no—
385C4⋊Q8C23×C12711yescharacteristic
386C4⋊Q8C23×C12711yescharacteristic
387C4⋊Q8C23×C12711yescharacteristic
388#127—21no—
389#127C23×C12711yescharacteristic
390#126—41no—
391#124—21no—
392C22⋊Q8—21no—
393C22⋊Q8—21no—
394C22⋊Q8—21no—
395C22⋊Q8—41no—
396C22⋊Q8—41no—
397#121—21no—
398#121—41no—
399C4×Q8—21no—
400C4×Q8C23×C12711yescharacteristic
401C4×Q8C23×C12711yescharacteristic
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4C23×C12711yescharacteristic
406C4×D4C23×C12711yescharacteristic
407#117—21no—
408#107—21no—
409#107—21no—
410#107D4×C12711yescharacteristic
411#107D4×C12711yescharacteristic
412#106—21no—
413#106—41no—
414C4⋊C8—21no—
415C4⋊C8—21no—
416C4⋊C8C23×C12711yescharacteristic
417C4⋊C8C23×C12711yescharacteristic
418C4⋊C8C23×C12711yescharacteristic
419C4⋊C8C23×C12711yescharacteristic
420#103—21no—
421#103—21no—
422#103—21no—
423#103—21no—
424#103—21no—
425#103—21no—
426#103D4×C12711yescharacteristic
427#103D4×C12711yescharacteristic
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—41no—
437#102D4×C12711yescharacteristic
438#102D4×C12711yescharacteristic
439C22⋊C8—21no—
440C22⋊C8—21no—
441#97—21no—
442C4×C8—21no—
443C4×C8C23×C12711yescharacteristic
444C4×C8C23×C12711yescharacteristic
445C4×C8C23×C12711yescharacteristic
446#41—42no—
447#41—81no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—41no—
452C2×Q8—41no—
453C2×Q8—42no—
454C2×Q8—42no—
455C2×Q8—81no—
456C2×Q8—81no—
457C2×Q8C2×D4×C12711yescharacteristic
458C2×Q8C2×D4×C12711yescharacteristic
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4C2×D4×C12711yescharacteristic
465C2×D4C2×D4×C12711yescharacteristic
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471Q16—22no—
472Q16—42no—
473Q16—42no—
474Q16—42no—
475Q16—81no—
476SD16—42no—
477SD16—81no—
478D8—22no—
479D8—42no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—42no—
486C2×C8—81no—
487C2×C8C2×D4×C12711yescharacteristic
488C2×C8C2×D4×C12711yescharacteristic
489C2×C8C2×D4×C12711yescharacteristic
490C2×C8C2×D4×C12711yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4C2×D4×C12711yescharacteristic
503C4⋊C4C2×D4×C12711yescharacteristic
504C4⋊C4C2×D4×C12711yescharacteristic
505C4⋊C4C2×D4×C12711yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C42—21no—
514C42—21no—
515C42—41no—
516C42C24×C12711yescharacteristic
517C23—21no—
518C23—21no—
519C23—41no—
520Q8—21no—
521Q8—21no—
522Q8—21no—
523Q8—41no—
524Q8—41no—
525Q8—41no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—82no—
530Q8—82no—
531Q8AGL(1,ℤ/8)×C12712yes—
532D4—21no—
533D4—21no—
534D4—21no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—82no—
540D4—81no—
541D4—161no—
542D4#135×C12712yes—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—82no—
557C2×C4—82no—
558C2×C4—82no—
559C2×C4C22×D4×C12711yescharacteristic
560C2×C4C22×D4×C12711yescharacteristic
561C2×C4H(5,𝔽2)×C12711yescharacteristic
562C8—21no—
563C8—21no—
564C8—21no—
565C8—21no—
566C8—41no—
567C8—41no—
568C8—41no—
569C8—41no—
570C8—41no—
571C22—22no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22D42×C12711yescharacteristic
581C4—22no—
582C4—21no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—81no—
589C4—81no—
590C4—81no—
591C4C2×#135×C12711yescharacteristic
592C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
593C4#576×C12711yescharacteristic
594C4#578×C12711yescharacteristic
595C2—42no—
596C2—81no—
597C2—161no—
598C2C127×#326411yescharacteristic
599C2C127×#328511yescharacteristic
600C2C127×#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×#3367C2semidirect
3. C127×#3304C2semidirect
4. D4×Q16×C127C2semidirect
5. C127×#1720C2semidirect
6. C127×#1702C2semidirect
7. C127×#1681C2semidirect
8. C127×#1680C2semidirect
9. C127×#1669C2semidirect
10. C127×#1652C2semidirect
11. C127×#1651C2semidirect
12. C127×#1641C2semidirect
13. C127×#1627C2semidirect
14. C127×#1584C2semidirect
15. C127×#1580C2semidirect
294. #19835C127direct (N × H)
301. #3367C2×C127semidirect
303. #3304C2×C127semidirect
304. D4×Q16C2×C127semidirect
305. #1720C2×C127semidirect
306. #1702C2×C127semidirect
307. #1681C2×C127semidirect
308. #1680C2×C127semidirect
309. #1669C2×C127semidirect
310. #1652C2×C127semidirect
311. #1651C2×C127semidirect
312. #1641C2×C127semidirect
313. #1627C2×C127semidirect
314. #1584C2×C127semidirect
315. #1580C2×C127semidirect
316. C127#19835direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#33672
C127×#33582
C127×#33042
D4×Q16×C1272
C127×#17202
C127×#17022
C127×#16812
C127×#16802
C127×#16692
C127×#16522
C127×#16512
C127×#16412
C127×#16272
C127×#15842
C127×#15802
#19835127