Finite Group Databasebeta

← C127×#19779 #44583452

Subgroups — C127×#19779 #44583452

Order 32512.

676 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3358C211yesmaximal, characteristic, complemented
2C127×#3332C211yesmaximal, characteristic, complemented
3C127×#3298C211yesmaximal, characteristic, complemented
4C127×#3283C211yesmaximal, characteristic, complemented
5C127×#1720C211yesmaximal, characteristic, complemented
6C127×#1699C211yesmaximal, characteristic, complemented
7C127×#1681C211yesmaximal, characteristic, complemented
8C127×#1681C211yesmaximal, characteristic, complemented
9C127×#1670C211yesmaximal, characteristic, complemented
10C127×#1654C211yesmaximal, characteristic, complemented
11C127×#1651C211yesmaximal, characteristic, complemented
12C127×#1642C211yesmaximal, characteristic, complemented
13C127×#1625C211yesmaximal, characteristic, complemented
14C127×#1581C211yesmaximal, characteristic, complemented
15C127×SD16⋊C8C211yesmaximal, characteristic, complemented
16C2×#135×C127—21no—
17#550×C127C2211yescharacteristic
18D4×Q8×C127C2211yescharacteristic
19#547×C127C2211yescharacteristic
20#547×C127C2211yescharacteristic
21#498×C127C2211yescharacteristic
22#494×C127C2211yescharacteristic
23#487×C127C2211yescharacteristic
24#486×C127—21no—
25#486×C127C2211yescharacteristic
26#486×C127C2211yescharacteristic
27#486×C127C2211yescharacteristic
28#483×C127—21no—
29#481×C127—21no—
30#475×C127C2211yescharacteristic
31#475×C127C2211yescharacteristic
32#474×C127—21no—
33#474×C127C2211yescharacteristic
34#469×C127—21no—
35#467×C127—21no—
36#465×C127—21no—
37#461×C127C2211yescharacteristic
38#461×C127C2211yescharacteristic
39#461×C127C2211yescharacteristic
40#459×C127—21no—
41#459×C127C2211yescharacteristic
42#459×C127C2211yescharacteristic
43#452×C127—21no—
44#452×C127—21no—
45#449×C127—21no—
46#448×C127—21no—
47C8×Q8×C127C2211yescharacteristic
48C4×SD16×C127C2211yescharacteristic
49C4×D8×C127—21no—
50C4×D8×C127C2211yescharacteristic
51#436×C127C2211yescharacteristic
52C8×D4×C127C2211yescharacteristic
53C8×D4×C127C2211yescharacteristic
54#417×C127—21no—
55C2×#103×C127—21no—
56#335×C127C2211yescharacteristic
57#335×C127C2211yescharacteristic
58#332×C127C2211yescharacteristic
59#332×C127C2211yescharacteristic
60#332×C127C2211yescharacteristic
61#331×C127C2211yescharacteristic
62Q8⋊C8×C127C2211yescharacteristic
63D4⋊C8×C127C2211yescharacteristic
64D4⋊C8×C127C2211yescharacteristic
65D4⋊C8×C127C2211yescharacteristic
66#322×C127C2211yescharacteristic
67C2×#41×C127—21no—
68C2×#41×C127—21no—
69C2×#41×C127—21no—
70C22×Q8×C127—21no—
71#135×C127—44no—
72C2×Q16×C127—21no—
73C2×Q16×C127—21no—
74C2×SD16×C127—21no—
75C2×SD16×C127—21no—
76C2×SD16×C127—21no—
77C2×SD16×C127D411yescharacteristic
78C2×D8×C127—21no—
79C2×D8×C127—21no—
80C2×D8×C127D411yescharacteristic
81C2×M16×C127—21no—
82C22×C8×C127—21no—
83C22×C8×C127—21no—
84C4⋊Q8×C127—21no—
85C4⋊Q8×C127C2311yescharacteristic
86C4⋊Q8×C127C2311yescharacteristic
87C4⋊Q8×C127C2311yescharacteristic
88#127×C127—21no—
89#127×C127C2311yescharacteristic
90#123×C127—41no—
91#123×C127—41no—
92C22⋊Q8×C127—21no—
93C22⋊Q8×C127—21no—
94C22⋊Q8×C127—21no—
95C22⋊Q8×C127—41no—
96#121×C127—21no—
97#121×C127—21no—
98#121×C127—21no—
99#121×C127—41no—
100C4×Q8×C127C2311yescharacteristic
101C4×D4×C127—21no—
102C4×D4×C127—21no—
103C4×D4×C127C2311yescharacteristic
104C4×D4×C127C2311yescharacteristic
105C4×D4×C127C2311yescharacteristic
106C2×C4⋊C4×C127—21no—
107C2×C4⋊C4×C127—21no—
108#107×C127—21no—
109#107×C127D411yescharacteristic
110#106×C127—21no—
111#106×C127—21no—
112#106×C127—41no—
113#106×C127D411yescharacteristic
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×C127—21no—
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
137#102×C127D411yescharacteristic
138C22⋊C8×C127—21no—
139C22⋊C8×C127—21no—
140C22⋊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—42no—
148#41×C127—81no—
149#41×C127—81no—
150#41×C127—81no—
151C2×Q8×C127—21no—
152C2×Q8×C127—21no—
153C2×Q8×C127—21no—
154C2×Q8×C127—41no—
155C2×Q8×C127—42no—
156C2×Q8×C127—81no—
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×C127—41no—
164C2×D4×C127—41no—
165C2×D4×C127C2×D411yescharacteristic
166C2×D4×C127C2×D411yescharacteristic
167C2×D4×C127C2×D411yescharacteristic
168C22×C4×C127—21no—
169C22×C4×C127—21no—
170C22×C4×C127—21no—
171C22×C4×C127—41no—
172C22×C4×C127—41no—
173C22×C4×C127—41no—
174C22×C4×C127—41no—
175Q16×C127—42no—
176Q16×C127—81no—
177SD16×C127—22no—
178SD16×C127—42no—
179SD16×C127—42no—
180SD16×C127—81no—
181D8×C127—22no—
182D8×C127—42no—
183D8×C127—81no—
184M16×C127—81no—
185C2×C8×C127—21no—
186C2×C8×C127—21no—
187C2×C8×C127—21no—
188C2×C8×C127—21no—
189C2×C8×C127—21no—
190C2×C8×C127—42no—
191C2×C8×C127—81no—
192C2×C8×C127C2×D411yescharacteristic
193C2×C8×C127C2×D411yescharacteristic
194C2×C8×C127C2×D411yescharacteristic
195C2×C8×C127C2×D411yescharacteristic
196C4⋊C4×C127—21no—
197C4⋊C4×C127—21no—
198C4⋊C4×C127—21no—
199C4⋊C4×C127—21no—
200C4⋊C4×C127—21no—
201C4⋊C4×C127—21no—
202C4⋊C4×C127—21no—
203C4⋊C4×C127—41no—
204C4⋊C4×C127—41no—
205C4⋊C4×C127—41no—
206C4⋊C4×C127C2×D411yescharacteristic
207C4⋊C4×C127C2×D411yescharacteristic
208C4⋊C4×C127C2×D411yescharacteristic
209C4⋊C4×C127C2×D411yescharacteristic
210C22⋊C4×C127—21no—
211C22⋊C4×C127—21no—
212C22⋊C4×C127—21no—
213C22⋊C4×C127—41no—
214C22⋊C4×C127—41no—
215C22⋊C4×C127—41no—
216C22⋊C4×C127—41no—
217C42×C127—21no—
218C42×C127C2411yescharacteristic
219C23×C127—21no—
220C23×C127—21no—
221C23×C127—21no—
222C23×C127—41no—
223Q8×C127—21no—
224Q8×C127—41no—
225Q8×C127—41no—
226Q8×C127—41no—
227Q8×C127—41no—
228Q8×C127—41no—
229Q8×C127—41no—
230Q8×C127—82no—
231Q8×C127#13512yescomplemented
232D4×C127—21no—
233D4×C127—21no—
234D4×C127—21no—
235D4×C127—21no—
236D4×C127—21no—
237D4×C127—41no—
238D4×C127—41no—
239D4×C127—41no—
240D4×C127—41no—
241D4×C127—82no—
242D4×C127—81no—
243D4×C127—82no—
244D4×C127—82no—
245D4×C127—161no—
246D4×C127AGL(1,ℤ/8)12yes—
247C2×C4×C127—21no—
248C2×C4×C127—21no—
249C2×C4×C127—21no—
250C2×C4×C127—21no—
251C2×C4×C127—21no—
252C2×C4×C127—41no—
253C2×C4×C127—41no—
254C2×C4×C127—41no—
255C2×C4×C127—41no—
256C2×C4×C127—41no—
257C2×C4×C127—41no—
258C2×C4×C127—41no—
259C2×C4×C127—41no—
260C2×C4×C127—41no—
261C2×C4×C127—82no—
262C2×C4×C127—82no—
263C2×C4×C127—82no—
264C2×C4×C127—82no—
265C2×C4×C127C22×D411yescharacteristic
266C2×C4×C127C22×D411yescharacteristic
267C2×C4×C127H(5,𝔽2)11yescharacteristic
268C8×C127—21no—
269C8×C127—21no—
270C8×C127—21no—
271C8×C127—21no—
272C8×C127—41no—
273C8×C127—41no—
274C8×C127—41no—
275C8×C127—41no—
276C8×C127—41no—
277C22×C127—22no—
278C22×C127—41no—
279C22×C127—41no—
280C22×C127—41no—
281C22×C127—41no—
282C22×C127—41no—
283C22×C127—41no—
284C22×C127—41no—
285C22×C127—41no—
286C22×C127—81no—
287C22×C127—81no—
288C22×C127—81no—
289C22×C127D4211yescharacteristic
290C4×C127—22no—
291C4×C127—21no—
292C4×C127—41no—
293C4×C127—41no—
294C4×C127—41no—
295C4×C127—41no—
296C4×C127—81no—
297C4×C127—81no—
298C4×C127—81no—
299C4×C127C2×#13511yescharacteristic
300C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
301C4×C127#57611yescharacteristic
302C4×C127#57711yescharacteristic
303#19779C12711yesmaximal, characteristic, direct product factor, Sylow
304C2×C127—42no—
305C2×C127—81no—
306C2×C127—81no—
307C2×C127—161no—
308C2×C127#326511yescharacteristic
309C2×C127#328011yescharacteristic
310C2×C127#328911yescharacteristic
311#3358C2×C12711yescharacteristic, complemented
312#3332C2×C12711yescharacteristic, complemented
313#3298C2×C12711yescharacteristic, complemented
314#3283C2×C12711yescharacteristic, complemented
315#1720C2×C12711yescharacteristic, complemented
316#1699C2×C12711yescharacteristic, complemented
317#1681C2×C12711yescharacteristic, complemented
318#1681C2×C12711yescharacteristic, complemented
319#1670C2×C12711yescharacteristic, complemented
320#1654C2×C12711yescharacteristic, complemented
321#1651C2×C12711yescharacteristic, complemented
322#1642C2×C12711yescharacteristic, complemented
323#1625C2×C12711yescharacteristic, complemented
324#1581C2×C12711yescharacteristic, complemented
325SD16⋊C8C2×C12711yescharacteristic, complemented
326C127#1977911yescharacteristic, direct product factor, Sylow
327C2×#135—21no—
328#550C22×C12711yescharacteristic
329D4×Q8C22×C12711yescharacteristic
330#547C22×C12711yescharacteristic
331#547C22×C12711yescharacteristic
332#498C22×C12711yescharacteristic
333#494C22×C12711yescharacteristic
334#487C22×C12711yescharacteristic
335#486—21no—
336#486C22×C12711yescharacteristic
337#486C22×C12711yescharacteristic
338#486C22×C12711yescharacteristic
339#483—21no—
340#481—21no—
341#475C22×C12711yescharacteristic
342#475C22×C12711yescharacteristic
343#474—21no—
344#474C22×C12711yescharacteristic
345#469—21no—
346#467—21no—
347#465—21no—
348#461C22×C12711yescharacteristic
349#461C22×C12711yescharacteristic
350#461C22×C12711yescharacteristic
351#459—21no—
352#459C22×C12711yescharacteristic
353#459C22×C12711yescharacteristic
354#452—21no—
355#452—21no—
356#449—21no—
357#448—21no—
358C8×Q8C22×C12711yescharacteristic
359C4×SD16C22×C12711yescharacteristic
360C4×D8—21no—
361C4×D8C22×C12711yescharacteristic
362#436C22×C12711yescharacteristic
363C8×D4C22×C12711yescharacteristic
364C8×D4C22×C12711yescharacteristic
365#417—21no—
366C2×#103—21no—
367#335C22×C12711yescharacteristic
368#335C22×C12711yescharacteristic
369#332C22×C12711yescharacteristic
370#332C22×C12711yescharacteristic
371#332C22×C12711yescharacteristic
372#331C22×C12711yescharacteristic
373Q8⋊C8C22×C12711yescharacteristic
374D4⋊C8C22×C12711yescharacteristic
375D4⋊C8C22×C12711yescharacteristic
376D4⋊C8C22×C12711yescharacteristic
377#322C22×C12711yescharacteristic
378C2×#41—21no—
379C2×#41—21no—
380C2×#41—21no—
381C22×Q8—21no—
382#135—44no—
383C2×Q16—21no—
384C2×Q16—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×SD16—21no—
388C2×SD16D4×C12711yescharacteristic
389C2×D8—21no—
390C2×D8—21no—
391C2×D8D4×C12711yescharacteristic
392C2×M16—21no—
393C22×C8—21no—
394C22×C8—21no—
395C4⋊Q8—21no—
396C4⋊Q8C23×C12711yescharacteristic
397C4⋊Q8C23×C12711yescharacteristic
398C4⋊Q8C23×C12711yescharacteristic
399#127—21no—
400#127C23×C12711yescharacteristic
401#123—41no—
402#123—41no—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405C22⋊Q8—21no—
406C22⋊Q8—41no—
407#121—21no—
408#121—21no—
409#121—21no—
410#121—41no—
411C4×Q8C23×C12711yescharacteristic
412C4×D4—21no—
413C4×D4—21no—
414C4×D4C23×C12711yescharacteristic
415C4×D4C23×C12711yescharacteristic
416C4×D4C23×C12711yescharacteristic
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419#107—21no—
420#107D4×C12711yescharacteristic
421#106—21no—
422#106—21no—
423#106—41no—
424#106D4×C12711yescharacteristic
425C4⋊C8—21no—
426C4⋊C8C23×C12711yescharacteristic
427C4⋊C8C23×C12711yescharacteristic
428C4⋊C8C23×C12711yescharacteristic
429C4⋊C8C23×C12711yescharacteristic
430#103—21no—
431#103—21no—
432#103—21no—
433#103—21no—
434#103—21no—
435#103—21no—
436#103—21no—
437#103D4×C12711yescharacteristic
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—21no—
444#102—21no—
445#102—41no—
446#102D4×C12711yescharacteristic
447#102D4×C12711yescharacteristic
448#102D4×C12711yescharacteristic
449C22⋊C8—21no—
450C22⋊C8—21no—
451C22⋊C8—21no—
452C4×C8—21no—
453C4×C8C23×C12711yescharacteristic
454C4×C8C23×C12711yescharacteristic
455C4×C8C23×C12711yescharacteristic
456#41—42no—
457#41—42no—
458#41—42no—
459#41—81no—
460#41—81no—
461#41—81no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—41no—
466C2×Q8—42no—
467C2×Q8—81no—
468C2×Q8C2×D4×C12711yescharacteristic
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—41no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4C2×D4×C12711yescharacteristic
477C2×D4C2×D4×C12711yescharacteristic
478C2×D4C2×D4×C12711yescharacteristic
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486Q16—42no—
487Q16—81no—
488SD16—22no—
489SD16—42no—
490SD16—42no—
491SD16—81no—
492D8—22no—
493D8—42no—
494D8—81no—
495M16—81no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—42no—
502C2×C8—81no—
503C2×C8C2×D4×C12711yescharacteristic
504C2×C8C2×D4×C12711yescharacteristic
505C2×C8C2×D4×C12711yescharacteristic
506C2×C8C2×D4×C12711yescharacteristic
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4C2×D4×C12711yescharacteristic
518C4⋊C4C2×D4×C12711yescharacteristic
519C4⋊C4C2×D4×C12711yescharacteristic
520C4⋊C4C2×D4×C12711yescharacteristic
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C22⋊C4—41no—
528C42—21no—
529C42C24×C12711yescharacteristic
530C23—21no—
531C23—21no—
532C23—21no—
533C23—41no—
534Q8—21no—
535Q8—41no—
536Q8—41no—
537Q8—41no—
538Q8—41no—
539Q8—41no—
540Q8—41no—
541Q8—82no—
542Q8#135×C12712yescomplemented
543D4—21no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—82no—
553D4—81no—
554D4—82no—
555D4—82no—
556D4—161no—
557D4AGL(1,ℤ/8)×C12712yes—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4—82no—
575C2×C4—82no—
576C2×C4C22×D4×C12711yescharacteristic
577C2×C4C22×D4×C12711yescharacteristic
578C2×C4H(5,𝔽2)×C12711yescharacteristic
579C8—21no—
580C8—21no—
581C8—21no—
582C8—21no—
583C8—41no—
584C8—41no—
585C8—41no—
586C8—41no—
587C8—41no—
588C22—22no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22D42×C12711yescharacteristic
601C4—22no—
602C4—21no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—81no—
608C4—81no—
609C4—81no—
610C4C2×#135×C12711yescharacteristic
611C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
612C4#576×C12711yescharacteristic
613C4#577×C12711yescharacteristic
614C2—42no—
615C2—81no—
616C2—81no—
617C2—161no—
618C2C127×#326511yescharacteristic
619C2C127×#328011yescharacteristic
620C2C127×#328911yescharacteristic
subgroupG/H
center, socleC22×C127D42
commutator, Frattini, cosocleC42C24×C127
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×#3358C2semidirect
2. C127×#3332C2semidirect
3. C127×#3298C2semidirect
4. C127×#3283C2semidirect
5. C127×#1720C2semidirect
6. C127×#1699C2semidirect
7. C127×#1681C2semidirect
8. C127×#1681C2semidirect
9. C127×#1670C2semidirect
10. C127×#1654C2semidirect
11. C127×#1651C2semidirect
12. C127×#1642C2semidirect
13. C127×#1625C2semidirect
14. C127×#1581C2semidirect
15. C127×SD16⋊C8C2semidirect
231. Q8×C127#135semidirect
303. #19779C127direct (N × H)
311. #3358C2×C127semidirect
312. #3332C2×C127semidirect
313. #3298C2×C127semidirect
314. #3283C2×C127semidirect
315. #1720C2×C127semidirect
316. #1699C2×C127semidirect
317. #1681C2×C127semidirect
318. #1681C2×C127semidirect
319. #1670C2×C127semidirect
320. #1654C2×C127semidirect
321. #1651C2×C127semidirect
322. #1642C2×C127semidirect
323. #1625C2×C127semidirect
324. #1581C2×C127semidirect
325. SD16⋊C8C2×C127semidirect
326. C127#19779direct (N × H)
542. Q8#135×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#33582
C127×#33322
C127×#32982
C127×#32832
C127×#17202
C127×#16992
C127×#16812
C127×#16702
C127×#16542
C127×#16512
C127×#16422
C127×#16252
C127×#15812
C127×SD16⋊C82
#19779127