Finite Group Databasebeta

← C127×#19783 #44583456

Subgroups — C127×#19783 #44583456

Order 32512.

656 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3391C211yesmaximal, characteristic, complemented
2C127×#3332C211yesmaximal, characteristic, complemented
3C127×#3305C211yesmaximal, characteristic, complemented
4C127×#3303C211yesmaximal, characteristic, complemented
5C127×#1717C211yesmaximal, characteristic, complemented
6C127×#1697C211yesmaximal, characteristic, complemented
7C127×#1684C211yesmaximal, characteristic, complemented
8C127×#1681C211yesmaximal, characteristic, complemented
9C127×#1667C211yesmaximal, characteristic, complemented
10C127×#1642C211yesmaximal, characteristic, complemented
11C127×#1631C211yesmaximal, characteristic, complemented
12C127×#1625C211yesmaximal, characteristic, complemented
13C127×#1624C211yesmaximal, characteristic, complemented
14C127×#1581C211yesmaximal, characteristic, complemented
15C127×SD16⋊C8C211yesmaximal, characteristic, complemented
16#555×C127C2211yescharacteristic
17#550×C127C2211yescharacteristic
18#550×C127C2211yescharacteristic
19#547×C127C2211yescharacteristic
20#493×C127—21no—
21#493×C127C2211yescharacteristic
22#492×C127C2211yescharacteristic
23#487×C127C2211yescharacteristic
24#486×C127C2211yescharacteristic
25#486×C127C2211yescharacteristic
26#486×C127C2211yescharacteristic
27#485×C127—21no—
28#482×C127—21no—
29#481×C127—21no—
30#477×C127C2211yescharacteristic
31#476×C127C2211yescharacteristic
32#475×C127C2211yescharacteristic
33#469×C127—21no—
34#466×C127—21no—
35#465×C127—21no—
36#461×C127C2211yescharacteristic
37#459×C127—21no—
38#459×C127—21no—
39#459×C127C2211yescharacteristic
40#459×C127C2211yescharacteristic
41#459×C127C2211yescharacteristic
42#459×C127C2211yescharacteristic
43#449×C127—21no—
44#449×C127—21no—
45#449×C127—21no—
46C8×Q8×C127C2211yescharacteristic
47C4×SD16×C127C2211yescharacteristic
48C4×D8×C127—21no—
49C4×D8×C127C2211yescharacteristic
50#436×C127C2211yescharacteristic
51C8×D4×C127C2211yescharacteristic
52C8×D4×C127C2211yescharacteristic
53#417×C127—21no—
54#416×C127—21no—
55#416×C127—21no—
56#335×C127C2211yescharacteristic
57#335×C127C2211yescharacteristic
58#333×C127C2211yescharacteristic
59#332×C127C2211yescharacteristic
60#331×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—
70C2×SD16×C127—21no—
71C2×SD16×C127—41no—
72C2×SD16×C127D411yescharacteristic
73C2×D8×C127—21no—
74C2×D8×C127—21no—
75C2×D8×C127—21no—
76C2×D8×C127—21no—
77C2×D8×C127—21no—
78C2×D8×C127—21no—
79C2×D8×C127D411yescharacteristic
80C2×M16×C127—21no—
81C22×C8×C127—21no—
82C22×C8×C127—21no—
83C4⋊Q8×C127C2311yescharacteristic
84C4⋊Q8×C127C2311yescharacteristic
85#127×C127—21no—
86#127×C127—21no—
87#127×C127C2311yescharacteristic
88#127×C127C2311yescharacteristic
89#124×C127—41no—
90#123×C127—41no—
91C22⋊Q8×C127—21no—
92#121×C127—21no—
93#121×C127—21no—
94#121×C127—21no—
95#121×C127—21no—
96#121×C127—21no—
97#121×C127—41no—
98#121×C127—41no—
99C4×Q8×C127C2311yescharacteristic
100C4×D4×C127—21no—
101C4×D4×C127—21no—
102C4×D4×C127C2311yescharacteristic
103C4×D4×C127C2311yescharacteristic
104C4×D4×C127C2311yescharacteristic
105#117×C127—21no—
106#117×C127—21no—
107C2×C4⋊C4×C127—21no—
108#107×C127—21no—
109#107×C127D411yescharacteristic
110#106×C127—21no—
111#106×C127—21no—
112#106×C127D411yescharacteristic
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×C127D411yescharacteristic
124#102×C127—21no—
125#102×C127—21no—
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—41no—
134#102×C127D411yescharacteristic
135#102×C127D411yescharacteristic
136#102×C127D411yescharacteristic
137C22⋊C8×C127—21no—
138C22⋊C8×C127—21no—
139C22⋊C8×C127—21no—
140C4×C8×C127—21no—
141C4×C8×C127C2311yescharacteristic
142C4×C8×C127C2311yescharacteristic
143C4×C8×C127C2311yescharacteristic
144#41×C127—42no—
145#41×C127—42no—
146#41×C127—42no—
147#41×C127—81no—
148#41×C127—81no—
149#41×C127—81no—
150C2×Q8×C127—21no—
151C2×Q8×C127—21no—
152C2×Q8×C127C2×D411yescharacteristic
153C2×D4×C127—21no—
154C2×D4×C127—21no—
155C2×D4×C127—21no—
156C2×D4×C127—21no—
157C2×D4×C127—21no—
158C2×D4×C127—21no—
159C2×D4×C127—41no—
160C2×D4×C127—41no—
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—
174SD16×C127—22no—
175SD16×C127—81no—
176SD16×C127—82no—
177D8×C127—41no—
178D8×C127—42no—
179D8×C127—81no—
180D8×C127—81no—
181D8×C127—81no—
182D8×C127—81no—
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—81no—
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—41no—
202C4⋊C4×C127C2×D411yescharacteristic
203C4⋊C4×C127C2×D411yescharacteristic
204C4⋊C4×C127C2×D411yescharacteristic
205C4⋊C4×C127C2×D411yescharacteristic
206C22⋊C4×C127—21no—
207C22⋊C4×C127—21no—
208C22⋊C4×C127—21no—
209C22⋊C4×C127—41no—
210C22⋊C4×C127—41no—
211C22⋊C4×C127—41no—
212C22⋊C4×C127—41no—
213C22⋊C4×C127—41no—
214C42×C127—21no—
215C42×C127—41no—
216C42×C127C2411yescharacteristic
217C23×C127—21no—
218C23×C127—21no—
219C23×C127—21no—
220C23×C127—41no—
221C23×C127—41no—
222Q8×C127—21no—
223Q8×C127—41no—
224Q8×C127—41no—
225Q8×C127—81no—
226Q8×C127#13512yes—
227D4×C127—21no—
228D4×C127—21no—
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—41no—
238D4×C127—41no—
239D4×C127—41no—
240D4×C127—41no—
241D4×C127—82no—
242D4×C127—82no—
243D4×C127—81no—
244D4×C127—81no—
245D4×C127—82no—
246D4×C127—161no—
247D4×C127—161no—
248D4×C127—161no—
249C2×C4×C127—21no—
250C2×C4×C127—21no—
251C2×C4×C127—21no—
252C2×C4×C127—21no—
253C2×C4×C127—21no—
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—41no—
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—41no—
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×C127—81no—
290C22×C127—81no—
291C22×C127—81no—
292C22×C127D4211yescharacteristic
293C4×C127—22no—
294C4×C127—21no—
295C4×C127—41no—
296C4×C127—41no—
297C4×C127—41no—
298C4×C127—41no—
299C4×C127—81no—
300C4×C127—81no—
301C4×C127C2×#13511yescharacteristic
302C4×C127#57511yescharacteristic
303C4×C127#57611yescharacteristic
304C4×C127#57611yescharacteristic
305#19783C12711yesmaximal, characteristic, direct product factor, Sylow
306C2×C127—81no—
307C2×C127—81no—
308C2×C127—81no—
309C2×C127—161no—
310C2×C127—161no—
311C2×C127#326811yescharacteristic
312C2×C127#328011yescharacteristic
313C2×C127#328811yescharacteristic
314#3391C2×C12711yescharacteristic, complemented
315#3332C2×C12711yescharacteristic, complemented
316#3305C2×C12711yescharacteristic, complemented
317#3303C2×C12711yescharacteristic, complemented
318#1717C2×C12711yescharacteristic, complemented
319#1697C2×C12711yescharacteristic, complemented
320#1684C2×C12711yescharacteristic, complemented
321#1681C2×C12711yescharacteristic, complemented
322#1667C2×C12711yescharacteristic, complemented
323#1642C2×C12711yescharacteristic, complemented
324#1631C2×C12711yescharacteristic, complemented
325#1625C2×C12711yescharacteristic, complemented
326#1624C2×C12711yescharacteristic, complemented
327#1581C2×C12711yescharacteristic, complemented
328SD16⋊C8C2×C12711yescharacteristic, complemented
329C127#1978311yescharacteristic, direct product factor, Sylow
330#555C22×C12711yescharacteristic
331#550C22×C12711yescharacteristic
332#550C22×C12711yescharacteristic
333#547C22×C12711yescharacteristic
334#493—21no—
335#493C22×C12711yescharacteristic
336#492C22×C12711yescharacteristic
337#487C22×C12711yescharacteristic
338#486C22×C12711yescharacteristic
339#486C22×C12711yescharacteristic
340#486C22×C12711yescharacteristic
341#485—21no—
342#482—21no—
343#481—21no—
344#477C22×C12711yescharacteristic
345#476C22×C12711yescharacteristic
346#475C22×C12711yescharacteristic
347#469—21no—
348#466—21no—
349#465—21no—
350#461C22×C12711yescharacteristic
351#459—21no—
352#459—21no—
353#459C22×C12711yescharacteristic
354#459C22×C12711yescharacteristic
355#459C22×C12711yescharacteristic
356#459C22×C12711yescharacteristic
357#449—21no—
358#449—21no—
359#449—21no—
360C8×Q8C22×C12711yescharacteristic
361C4×SD16C22×C12711yescharacteristic
362C4×D8—21no—
363C4×D8C22×C12711yescharacteristic
364#436C22×C12711yescharacteristic
365C8×D4C22×C12711yescharacteristic
366C8×D4C22×C12711yescharacteristic
367#417—21no—
368#416—21no—
369#416—21no—
370#335C22×C12711yescharacteristic
371#335C22×C12711yescharacteristic
372#333C22×C12711yescharacteristic
373#332C22×C12711yescharacteristic
374#331C22×C12711yescharacteristic
375#331C22×C12711yescharacteristic
376Q8⋊C8C22×C12711yescharacteristic
377D4⋊C8C22×C12711yescharacteristic
378D4⋊C8C22×C12711yescharacteristic
379D4⋊C8C22×C12711yescharacteristic
380#322C22×C12711yescharacteristic
381C2×#41—21no—
382C2×#41—21no—
383C2×#41—21no—
384C2×SD16—21no—
385C2×SD16—41no—
386C2×SD16D4×C12711yescharacteristic
387C2×D8—21no—
388C2×D8—21no—
389C2×D8—21no—
390C2×D8—21no—
391C2×D8—21no—
392C2×D8—21no—
393C2×D8D4×C12711yescharacteristic
394C2×M16—21no—
395C22×C8—21no—
396C22×C8—21no—
397C4⋊Q8C23×C12711yescharacteristic
398C4⋊Q8C23×C12711yescharacteristic
399#127—21no—
400#127—21no—
401#127C23×C12711yescharacteristic
402#127C23×C12711yescharacteristic
403#124—41no—
404#123—41no—
405C22⋊Q8—21no—
406#121—21no—
407#121—21no—
408#121—21no—
409#121—21no—
410#121—21no—
411#121—41no—
412#121—41no—
413C4×Q8C23×C12711yescharacteristic
414C4×D4—21no—
415C4×D4—21no—
416C4×D4C23×C12711yescharacteristic
417C4×D4C23×C12711yescharacteristic
418C4×D4C23×C12711yescharacteristic
419#117—21no—
420#117—21no—
421C2×C4⋊C4—21no—
422#107—21no—
423#107D4×C12711yescharacteristic
424#106—21no—
425#106—21no—
426#106D4×C12711yescharacteristic
427C4⋊C8—21no—
428C4⋊C8C23×C12711yescharacteristic
429C4⋊C8C23×C12711yescharacteristic
430C4⋊C8C23×C12711yescharacteristic
431C4⋊C8C23×C12711yescharacteristic
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—21no—
446#102—21no—
447#102—41no—
448#102D4×C12711yescharacteristic
449#102D4×C12711yescharacteristic
450#102D4×C12711yescharacteristic
451C22⋊C8—21no—
452C22⋊C8—21no—
453C22⋊C8—21no—
454C4×C8—21no—
455C4×C8C23×C12711yescharacteristic
456C4×C8C23×C12711yescharacteristic
457C4×C8C23×C12711yescharacteristic
458#41—42no—
459#41—42no—
460#41—42no—
461#41—81no—
462#41—81no—
463#41—81no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8C2×D4×C12711yescharacteristic
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4C2×D4×C12711yescharacteristic
480C2×D4C2×D4×C12711yescharacteristic
481C2×D4C2×D4×C12711yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488SD16—22no—
489SD16—81no—
490SD16—82no—
491D8—41no—
492D8—42no—
493D8—81no—
494D8—81no—
495D8—81no—
496D8—81no—
497D8—81no—
498M16—81no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—81no—
505C2×C8—81no—
506C2×C8C2×D4×C12711yescharacteristic
507C2×C8C2×D4×C12711yescharacteristic
508C2×C8C2×D4×C12711yescharacteristic
509C2×C8C2×D4×C12711yescharacteristic
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—41no—
516C4⋊C4C2×D4×C12711yescharacteristic
517C4⋊C4C2×D4×C12711yescharacteristic
518C4⋊C4C2×D4×C12711yescharacteristic
519C4⋊C4C2×D4×C12711yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C22⋊C4—41no—
528C42—21no—
529C42—41no—
530C42C24×C12711yescharacteristic
531C23—21no—
532C23—21no—
533C23—21no—
534C23—41no—
535C23—41no—
536Q8—21no—
537Q8—41no—
538Q8—41no—
539Q8—81no—
540Q8#135×C12712yes—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—41no—
555D4—82no—
556D4—82no—
557D4—81no—
558D4—81no—
559D4—82no—
560D4—161no—
561D4—161no—
562D4—161no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—82no—
577C2×C4—82no—
578C2×C4—82no—
579C2×C4C22×D4×C12711yescharacteristic
580C2×C4C22×D4×C12711yescharacteristic
581C2×C4H(5,𝔽2)×C12711yescharacteristic
582C8—21no—
583C8—21no—
584C8—21no—
585C8—21no—
586C8—41no—
587C8—41no—
588C8—41no—
589C8—41no—
590C8—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22D42×C12711yescharacteristic
607C4—22no—
608C4—21no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—81no—
614C4—81no—
615C4C2×#135×C12711yescharacteristic
616C4#575×C12711yescharacteristic
617C4#576×C12711yescharacteristic
618C4#576×C12711yescharacteristic
619C2—81no—
620C2—81no—
621C2—81no—
622C2—161no—
623C2—161no—
624C2C127×#326811yescharacteristic
625C2C127×#328011yescharacteristic
626C2C127×#328811yescharacteristic
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×#3391C2semidirect
2. C127×#3332C2semidirect
3. C127×#3305C2semidirect
4. C127×#3303C2semidirect
5. C127×#1717C2semidirect
6. C127×#1697C2semidirect
7. C127×#1684C2semidirect
8. C127×#1681C2semidirect
9. C127×#1667C2semidirect
10. C127×#1642C2semidirect
11. C127×#1631C2semidirect
12. C127×#1625C2semidirect
13. C127×#1624C2semidirect
14. C127×#1581C2semidirect
15. C127×SD16⋊C8C2semidirect
305. #19783C127direct (N × H)
314. #3391C2×C127semidirect
315. #3332C2×C127semidirect
316. #3305C2×C127semidirect
317. #3303C2×C127semidirect
318. #1717C2×C127semidirect
319. #1697C2×C127semidirect
320. #1684C2×C127semidirect
321. #1681C2×C127semidirect
322. #1667C2×C127semidirect
323. #1642C2×C127semidirect
324. #1631C2×C127semidirect
325. #1625C2×C127semidirect
326. #1624C2×C127semidirect
327. #1581C2×C127semidirect
328. SD16⋊C8C2×C127semidirect
329. C127#19783direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#33912
C127×#33322
C127×#33052
C127×#33032
C127×#17172
C127×#16972
C127×#16842
C127×#16812
C127×#16672
C127×#16422
C127×#16312
C127×#16252
C127×#16242
C127×#15812
C127×SD16⋊C82
#19783127