Finite Group Databasebeta

← C127×#19775 #44583448

Subgroups — C127×#19775 #44583448

Order 32512.

656 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3341C211yesmaximal, characteristic, complemented
2C127×#3325C211yesmaximal, characteristic, complemented
3C127×#3303C211yesmaximal, characteristic, complemented
4C127×#3294C211yesmaximal, characteristic, complemented
5C127×#1719C211yesmaximal, characteristic, complemented
6C127×#1703C211yesmaximal, characteristic, complemented
7C127×#1681C211yesmaximal, characteristic, complemented
8C127×#1677C211yesmaximal, characteristic, complemented
9C127×#1675C211yesmaximal, characteristic, complemented
10C127×#1646C211yesmaximal, characteristic, complemented
11C127×#1635C211yesmaximal, characteristic, complemented
12C127×#1629C211yesmaximal, characteristic, complemented
13C127×#1624C211yesmaximal, characteristic, complemented
14C127×#1581C211yesmaximal, characteristic, complemented
15C127×#1580C211yesmaximal, characteristic, complemented
16#555×C127C2211yescharacteristic
17#555×C127C2211yescharacteristic, complemented
18#547×C127C2211yescharacteristic
19D42×C127C2211yescharacteristic
20#500×C127C2211yescharacteristic, complemented
21#492×C127C2211yescharacteristic
22#487×C127C2211yescharacteristic, complemented
23#487×C127C2211yescharacteristic, complemented
24#486×C127C2211yescharacteristic
25#486×C127C2211yescharacteristic
26#485×C127—21no—
27#482×C127—21no—
28#482×C127—21no—
29#482×C127—21no—
30#480×C127—21no—
31#476×C127C2211yescharacteristic
32#476×C127C2211yescharacteristic
33#476×C127C2211yescharacteristic
34#476×C127C2211yescharacteristic, complemented
35#474×C127C2211yescharacteristic
36#469×C127—21no—
37#466×C127—21no—
38#466×C127—21no—
39#465×C127—21no—
40#461×C127C2211yescharacteristic, complemented
41#459×C127C2211yescharacteristic
42#459×C127C2211yescharacteristic
43#449×C127—21no—
44#447×C127—21no—
45#447×C127—21no—
46C4×D8×C127C2211yescharacteristic
47C4×D8×C127C2211yescharacteristic
48#436×C127C2211yescharacteristic
49C8×D4×C127C2211yescharacteristic
50C8×D4×C127C2211yescharacteristic, complemented
51C8×D4×C127C2211yescharacteristic, complemented
52#427×C127—21no—
53#418×C127—21no—
54#416×C127—21no—
55C2×#102×C127—21no—
56#335×C127C2211yescharacteristic, complemented
57#334×C127C2211yescharacteristic, complemented
58#333×C127C2211yescharacteristic, complemented
59#333×C127C2211yescharacteristic, complemented
60#332×C127C2211yescharacteristic, complemented
61#331×C127C2211yescharacteristic
62D4⋊C8×C127C2211yescharacteristic
63D4⋊C8×C127C2211yescharacteristic
64D4⋊C8×C127C2211yescharacteristic, complemented
65D4⋊C8×C127C2211yescharacteristic, complemented
66#322×C127C2211yescharacteristic, complemented
67C2×#41×C127—21no—
68C22×D4×C127—21no—
69C22×D4×C127—21no—
70C2×SD16×C127—21no—
71C2×SD16×C127—41no—
72C2×D8×C127—21no—
73C2×D8×C127—21no—
74C2×D8×C127D411yescharacteristic
75C2×D8×C127D411yescharacteristic
76C2×M16×C127—21no—
77C22×C8×C127—21no—
78C22×C8×C127—21no—
79C22×C8×C127—21no—
80C4⋊Q8×C127C2311yescharacteristic
81C4⋊Q8×C127C2311yescharacteristic
82C4⋊Q8×C127C2311yescharacteristic
83#127×C127C2311yescharacteristic
84#124×C127—41no—
85#124×C127—41no—
86#123×C127—41no—
87C22⋊Q8×C127—21no—
88#121×C127—21no—
89#121×C127—21no—
90#121×C127—21no—
91#121×C127—21no—
92#121×C127—21no—
93#121×C127—21no—
94#121×C127—21no—
95#120×C127—41no—
96C4×D4×C127C2311yescharacteristic
97C4×D4×C127C2311yescharacteristic
98C4×D4×C127C2311yescharacteristic
99C4×D4×C127C2311yescharacteristic
100#117×C127—21no—
101#117×C127—21no—
102#117×C127—21no—
103#117×C127—21no—
104C2×C4⋊C4×C127—21no—
105#107×C127—21no—
106#107×C127—21no—
107#107×C127—21no—
108#107×C127D411yescharacteristic
109#107×C127D411yescharacteristic
110#106×C127—21no—
111#106×C127—21no—
112#106×C127—21no—
113#106×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—41no—
122#102×C127—21no—
123#102×C127—21no—
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×C127D411yescharacteristic
134#102×C127D411yescharacteristic
135#102×C127D411yescharacteristic
136#102×C127D411yescharacteristic
137C22⋊C8×C127—21no—
138C22⋊C8×C127—21no—
139C22⋊C8×C127—21no—
140C22⋊C8×C127—21no—
141C4×C8×C127C2311yescharacteristic
142C4×C8×C127C2311yescharacteristic
143C4×C8×C127C2311yescharacteristic
144C24×C127—41no—
145#41×C127—42no—
146#41×C127—81no—
147C2×Q8×C127—21no—
148C2×Q8×C127—21no—
149C2×Q8×C127—21no—
150C2×D4×C127—21no—
151C2×D4×C127—21no—
152C2×D4×C127—21no—
153C2×D4×C127—41no—
154C2×D4×C127—41no—
155C2×D4×C127—42no—
156C2×D4×C127—42no—
157C2×D4×C127—41no—
158C2×D4×C127—41no—
159C2×D4×C127—41no—
160C2×D4×C127—81no—
161C2×D4×C127—81no—
162C2×D4×C127C2×D411yescharacteristic
163C2×D4×C127C2×D411yescharacteristic
164C2×D4×C127C2×D411yescharacteristic
165C2×D4×C127C2×D411yescharacteristic
166C22×C4×C127—21no—
167C22×C4×C127—21no—
168C22×C4×C127—21no—
169C22×C4×C127—21no—
170C22×C4×C127—41no—
171SD16×C127—81no—
172SD16×C127—82no—
173D8×C127—22no—
174D8×C127—41no—
175D8×C127—81no—
176D8×C127—81no—
177M16×C127—81no—
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×C127—81no—
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—41no—
197C4⋊C4×C127C2×D411yescharacteristic
198C4⋊C4×C127C2×D411yescharacteristic
199C4⋊C4×C127C2×D411yescharacteristic
200C4⋊C4×C127C2×D411yescharacteristic
201C22⋊C4×C127—21no—
202C22⋊C4×C127—21no—
203C22⋊C4×C127—21no—
204C22⋊C4×C127—21no—
205C22⋊C4×C127—41no—
206C22⋊C4×C127—41no—
207C22⋊C4×C127—41no—
208C22⋊C4×C127—41no—
209C22⋊C4×C127—41no—
210C22⋊C4×C127—41no—
211C42×C127—41no—
212C42×C127—41no—
213C42×C127C2411yescharacteristic
214C23×C127—21no—
215C23×C127—21no—
216C23×C127—21no—
217C23×C127—21no—
218C23×C127—41no—
219C23×C127—82no—
220C23×C127—82no—
221C23×C127—161no—
222Q8×C127—41no—
223Q8×C127—41no—
224Q8×C127—81no—
225Q8×C127—81no—
226D4×C127—21no—
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—81no—
238D4×C127—82no—
239D4×C127—82no—
240D4×C127—82no—
241D4×C127—161no—
242D4×C127—161no—
243D4×C127#13512yes—
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—41no—
256C2×C4×C127—41no—
257C2×C4×C127—41no—
258C2×C4×C127—41no—
259C2×C4×C127—82no—
260C2×C4×C127C22×D411yescharacteristic
261C2×C4×C127C22×D411yescharacteristic
262C2×C4×C127H(5,𝔽2)11yescharacteristic
263C8×C127—21no—
264C8×C127—21no—
265C8×C127—21no—
266C8×C127—21no—
267C8×C127—41no—
268C8×C127—41no—
269C8×C127—41no—
270C8×C127—41no—
271C8×C127—41no—
272C22×C127—22no—
273C22×C127—41no—
274C22×C127—41no—
275C22×C127—41no—
276C22×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—81no—
285C22×C127—81no—
286C22×C127—81no—
287C22×C127—164no—
288C22×C127D4211yescharacteristic
289C4×C127—21no—
290C4×C127—41no—
291C4×C127—41no—
292C4×C127—41no—
293C4×C127—41no—
294C4×C127—81no—
295C4×C127—81no—
296C4×C127—81no—
297C4×C127C2×#13511yescharacteristic
298C4×C127#57511yescharacteristic
299C4×C127#57611yescharacteristic
300C4×C127#57711yescharacteristic
301#19775C12711yesmaximal, characteristic, direct product factor, Sylow
302C2×C127—42no—
303C2×C127—81no—
304C2×C127—81no—
305C2×C127—81no—
306C2×C127—161no—
307C2×C127#326711yescharacteristic
308C2×C127#328011yescharacteristic
309C2×C127#328811yescharacteristic
310#3341C2×C12711yescharacteristic, complemented
311#3325C2×C12711yescharacteristic, complemented
312#3303C2×C12711yescharacteristic, complemented
313#3294C2×C12711yescharacteristic, complemented
314#1719C2×C12711yescharacteristic, complemented
315#1703C2×C12711yescharacteristic, complemented
316#1681C2×C12711yescharacteristic, complemented
317#1677C2×C12711yescharacteristic, complemented
318#1675C2×C12711yescharacteristic, complemented
319#1646C2×C12711yescharacteristic, complemented
320#1635C2×C12711yescharacteristic, complemented
321#1629C2×C12711yescharacteristic, complemented
322#1624C2×C12711yescharacteristic, complemented
323#1581C2×C12711yescharacteristic, complemented
324#1580C2×C12711yescharacteristic, complemented
325C127#1977511yescharacteristic, direct product factor, Sylow
326#555C22×C12711yescharacteristic
327#555C22×C12711yescharacteristic, complemented
328#547C22×C12711yescharacteristic
329D42C22×C12711yescharacteristic
330#500C22×C12711yescharacteristic, complemented
331#492C22×C12711yescharacteristic
332#487C22×C12711yescharacteristic, complemented
333#487C22×C12711yescharacteristic, complemented
334#486C22×C12711yescharacteristic
335#486C22×C12711yescharacteristic
336#485—21no—
337#482—21no—
338#482—21no—
339#482—21no—
340#480—21no—
341#476C22×C12711yescharacteristic
342#476C22×C12711yescharacteristic
343#476C22×C12711yescharacteristic
344#476C22×C12711yescharacteristic, complemented
345#474C22×C12711yescharacteristic
346#469—21no—
347#466—21no—
348#466—21no—
349#465—21no—
350#461C22×C12711yescharacteristic, complemented
351#459C22×C12711yescharacteristic
352#459C22×C12711yescharacteristic
353#449—21no—
354#447—21no—
355#447—21no—
356C4×D8C22×C12711yescharacteristic
357C4×D8C22×C12711yescharacteristic
358#436C22×C12711yescharacteristic
359C8×D4C22×C12711yescharacteristic
360C8×D4C22×C12711yescharacteristic, complemented
361C8×D4C22×C12711yescharacteristic, complemented
362#427—21no—
363#418—21no—
364#416—21no—
365C2×#102—21no—
366#335C22×C12711yescharacteristic, complemented
367#334C22×C12711yescharacteristic, complemented
368#333C22×C12711yescharacteristic, complemented
369#333C22×C12711yescharacteristic, complemented
370#332C22×C12711yescharacteristic, complemented
371#331C22×C12711yescharacteristic
372D4⋊C8C22×C12711yescharacteristic
373D4⋊C8C22×C12711yescharacteristic
374D4⋊C8C22×C12711yescharacteristic, complemented
375D4⋊C8C22×C12711yescharacteristic, complemented
376#322C22×C12711yescharacteristic, complemented
377C2×#41—21no—
378C22×D4—21no—
379C22×D4—21no—
380C2×SD16—21no—
381C2×SD16—41no—
382C2×D8—21no—
383C2×D8—21no—
384C2×D8D4×C12711yescharacteristic
385C2×D8D4×C12711yescharacteristic
386C2×M16—21no—
387C22×C8—21no—
388C22×C8—21no—
389C22×C8—21no—
390C4⋊Q8C23×C12711yescharacteristic
391C4⋊Q8C23×C12711yescharacteristic
392C4⋊Q8C23×C12711yescharacteristic
393#127C23×C12711yescharacteristic
394#124—41no—
395#124—41no—
396#123—41no—
397C22⋊Q8—21no—
398#121—21no—
399#121—21no—
400#121—21no—
401#121—21no—
402#121—21no—
403#121—21no—
404#121—21no—
405#120—41no—
406C4×D4C23×C12711yescharacteristic
407C4×D4C23×C12711yescharacteristic
408C4×D4C23×C12711yescharacteristic
409C4×D4C23×C12711yescharacteristic
410#117—21no—
411#117—21no—
412#117—21no—
413#117—21no—
414C2×C4⋊C4—21no—
415#107—21no—
416#107—21no—
417#107—21no—
418#107D4×C12711yescharacteristic
419#107D4×C12711yescharacteristic
420#106—21no—
421#106—21no—
422#106—21no—
423#106—21no—
424C4⋊C8C23×C12711yescharacteristic
425C4⋊C8C23×C12711yescharacteristic
426C4⋊C8C23×C12711yescharacteristic
427C4⋊C8C23×C12711yescharacteristic
428#103—21no—
429#103—21no—
430#103—21no—
431#103—41no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102D4×C12711yescharacteristic
444#102D4×C12711yescharacteristic
445#102D4×C12711yescharacteristic
446#102D4×C12711yescharacteristic
447C22⋊C8—21no—
448C22⋊C8—21no—
449C22⋊C8—21no—
450C22⋊C8—21no—
451C4×C8C23×C12711yescharacteristic
452C4×C8C23×C12711yescharacteristic
453C4×C8C23×C12711yescharacteristic
454C24—41no—
455#41—42no—
456#41—81no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—81no—
471C2×D4—81no—
472C2×D4C2×D4×C12711yescharacteristic
473C2×D4C2×D4×C12711yescharacteristic
474C2×D4C2×D4×C12711yescharacteristic
475C2×D4C2×D4×C12711yescharacteristic
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—41no—
481SD16—81no—
482SD16—82no—
483D8—22no—
484D8—41no—
485D8—81no—
486D8—81no—
487M16—81no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—42no—
494C2×C8—81no—
495C2×C8—81no—
496C2×C8C2×D4×C12711yescharacteristic
497C2×C8C2×D4×C12711yescharacteristic
498C2×C8C2×D4×C12711yescharacteristic
499C2×C8C2×D4×C12711yescharacteristic
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—41no—
507C4⋊C4C2×D4×C12711yescharacteristic
508C4⋊C4C2×D4×C12711yescharacteristic
509C4⋊C4C2×D4×C12711yescharacteristic
510C4⋊C4C2×D4×C12711yescharacteristic
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C42—41no—
522C42—41no—
523C42C24×C12711yescharacteristic
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—41no—
529C23—82no—
530C23—82no—
531C23—161no—
532Q8—41no—
533Q8—41no—
534Q8—81no—
535Q8—81no—
536D4—21no—
537D4—21no—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—81no—
548D4—82no—
549D4—82no—
550D4—82no—
551D4—161no—
552D4—161no—
553D4#135×C12712yes—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—82no—
570C2×C4C22×D4×C12711yescharacteristic
571C2×C4C22×D4×C12711yescharacteristic
572C2×C4H(5,𝔽2)×C12711yescharacteristic
573C8—21no—
574C8—21no—
575C8—21no—
576C8—21no—
577C8—41no—
578C8—41no—
579C8—41no—
580C8—41no—
581C8—41no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—164no—
598C22D42×C12711yescharacteristic
599C4—21no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4—81no—
607C4C2×#135×C12711yescharacteristic
608C4#575×C12711yescharacteristic
609C4#576×C12711yescharacteristic
610C4#577×C12711yescharacteristic
611C2—42no—
612C2—81no—
613C2—81no—
614C2—81no—
615C2—161no—
616C2C127×#326711yescharacteristic
617C2C127×#328011yescharacteristic
618C2C127×#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×#3341C2semidirect
2. C127×#3325C2semidirect
3. C127×#3303C2semidirect
4. C127×#3294C2semidirect
5. C127×#1719C2semidirect
6. C127×#1703C2semidirect
7. C127×#1681C2semidirect
8. C127×#1677C2semidirect
9. C127×#1675C2semidirect
10. C127×#1646C2semidirect
11. C127×#1635C2semidirect
12. C127×#1629C2semidirect
13. C127×#1624C2semidirect
14. C127×#1581C2semidirect
15. C127×#1580C2semidirect
17. #555×C127C22semidirect
20. #500×C127C22semidirect
22. #487×C127C22semidirect
23. #487×C127C22semidirect
34. #476×C127C22semidirect
40. #461×C127C22semidirect
50. C8×D4×C127C22semidirect
51. C8×D4×C127C22semidirect
56. #335×C127C22semidirect
57. #334×C127C22semidirect
58. #333×C127C22semidirect
59. #333×C127C22semidirect
60. #332×C127C22semidirect
64. D4⋊C8×C127C22semidirect
65. D4⋊C8×C127C22semidirect
66. #322×C127C22semidirect
301. #19775C127direct (N × H)
310. #3341C2×C127semidirect
311. #3325C2×C127semidirect
312. #3303C2×C127semidirect
313. #3294C2×C127semidirect
314. #1719C2×C127semidirect
315. #1703C2×C127semidirect
316. #1681C2×C127semidirect
317. #1677C2×C127semidirect
318. #1675C2×C127semidirect
319. #1646C2×C127semidirect
320. #1635C2×C127semidirect
321. #1629C2×C127semidirect
322. #1624C2×C127semidirect
323. #1581C2×C127semidirect
324. #1580C2×C127semidirect
325. C127#19775direct (N × H)
327. #555C22×C127semidirect
330. #500C22×C127semidirect
332. #487C22×C127semidirect
333. #487C22×C127semidirect
344. #476C22×C127semidirect
350. #461C22×C127semidirect
360. C8×D4C22×C127semidirect
361. C8×D4C22×C127semidirect
366. #335C22×C127semidirect
367. #334C22×C127semidirect
368. #333C22×C127semidirect
369. #333C22×C127semidirect
370. #332C22×C127semidirect
374. D4⋊C8C22×C127semidirect
375. D4⋊C8C22×C127semidirect
376. #322C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#33412
C127×#33252
C127×#33032
C127×#32942
C127×#17192
C127×#17032
C127×#16812
C127×#16772
C127×#16752
C127×#16462
C127×#16352
C127×#16292
C127×#16242
C127×#15812
C127×#15802
#19775127