Finite Group Databasebeta

← C127×#19578 #44583251

Subgroups — C127×#19578 #44583251

Order 32512.

618 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3251C211yesmaximal, characteristic, complemented
2C127×#3212C211yesmaximal, characteristic, complemented
3C127×#3207C211yesmaximal, characteristic, complemented
4C127×#2994C211yesmaximal, characteristic, complemented
5C127×#1701C211yesmaximal, characteristic, complemented
6C127×#1700C211yesmaximal, characteristic, complemented
7C127×#1688C211yesmaximal, characteristic, complemented
8C127×#1685C211yesmaximal, characteristic, complemented
9C127×#1682C211yesmaximal, characteristic, complemented
10C127×#1679C211yesmaximal, characteristic, complemented
11C127×#1667C211yesmaximal, characteristic, complemented
12C127×#1666C211yesmaximal, characteristic, complemented
13C127×#1574C211yesmaximal, characteristic, complemented
14C127×#1547C211yesmaximal, characteristic, complemented
15C127×#1540C211yesmaximal, characteristic, complemented
16#532×C127C2211yescharacteristic
17#532×C127C2211yescharacteristic
18#529×C127C2211yescharacteristic
19#495×C127—21no—
20#493×C127C2211yescharacteristic
21#492×C127C2211yescharacteristic
22#488×C127—21no—
23#487×C127C2211yescharacteristic
24#486×C127C2211yescharacteristic
25#478×C127—21no—
26#475×C127C2211yescharacteristic
27#474×C127C2211yescharacteristic
28#469×C127—21no—
29#468×C127—21no—
30#463×C127—21no—
31#463×C127—21no—
32#463×C127—21no—
33#462×C127C2211yescharacteristic
34#461×C127C2211yescharacteristic
35#460×C127C2211yescharacteristic
36#460×C127C2211yescharacteristic
37#459×C127C2211yescharacteristic
38#459×C127C2211yescharacteristic
39#452×C127—21no—
40#449×C127—21no—
41#449×C127—21no—
42#449×C127—21no—
43#446×C127C2211yescharacteristic
44C8×Q8×C127C2211yescharacteristic
45#436×C127C2211yescharacteristic
46#435×C127—21no—
47C8×D4×C127—21no—
48C8×D4×C127C2211yescharacteristic
49#433×C127—21no—
50#431×C127C2211yescharacteristic
51#431×C127C2211yescharacteristic
52#424×C127—21no—
53#423×C127C2211yescharacteristic
54C2×C4⋊C8×C127C2211yescharacteristic
55#335×C127C2211yescharacteristic
56#335×C127C2211yescharacteristic
57#334×C127C2211yescharacteristic
58#334×C127C2211yescharacteristic
59#332×C127C2211yescharacteristic
60#332×C127C2211yescharacteristic
61#332×C127C2211yescharacteristic
62#332×C127C2211yescharacteristic
63#331×C127C2211yescharacteristic
64#331×C127C2211yescharacteristic
65#331×C127C2211yescharacteristic
66#331×C127C2211yescharacteristic
67C2×#41×C127—21no—
68C2×#41×C127—21no—
69C2×Q16×C127—21no—
70C2×SD16×C127—21no—
71C2×SD16×C127—21no—
72C2×SD16×C127—21no—
73C2×SD16×C127—21no—
74C2×SD16×C127—21no—
75C2×D8×C127—21no—
76C2×D8×C127—21no—
77C2×D8×C127—21no—
78C2×D8×C127—21no—
79C2×M16×C127—21no—
80C2×M16×C127—21no—
81C22×C8×C127—21no—
82C22×C8×C127—21no—
83C4⋊Q8×C127C2311yescharacteristic
84C4⋊Q8×C127C2311yescharacteristic
85#127×C127C2311yescharacteristic
86#127×C127C2311yescharacteristic
87#126×C127—21no—
88#125×C127D411yescharacteristic
89#124×C127—21no—
90#124×C127—21no—
91#124×C127D411yescharacteristic
92#123×C127—21no—
93C22⋊Q8×C127D411yescharacteristic
94#121×C127—21no—
95#121×C127—21no—
96#121×C127—21no—
97#121×C127—21no—
98#121×C127D411yescharacteristic
99C4×Q8×C127C2311yescharacteristic
100C4×D4×C127—21no—
101C4×D4×C127—21no—
102C4×D4×C127—21no—
103C4×D4×C127—21no—
104C4×D4×C127—21no—
105C4×D4×C127C2311yescharacteristic
106#117×C127—21no—
107C2×C42×C127C2311yescharacteristic
108#107×C127—21no—
109#106×C127—21no—
110C4⋊C8×C127—21no—
111C4⋊C8×C127—21no—
112C4⋊C8×C127—21no—
113C4⋊C8×C127—21no—
114C4⋊C8×C127D411yescharacteristic
115C4⋊C8×C127D411yescharacteristic
116C4⋊C8×C127C2311yescharacteristic
117C4⋊C8×C127C2311yescharacteristic
118C4⋊C8×C127C2311yescharacteristic
119C4⋊C8×C127C2311yescharacteristic
120C4⋊C8×C127C2311yescharacteristic
121C4⋊C8×C127C2311yescharacteristic
122#103×C127—21no—
123#103×C127—21no—
124#103×C127—21no—
125#103×C127—21no—
126#103×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—21no—
134C22⋊C8×C127—21no—
135C22⋊C8×C127—21no—
136C22⋊C8×C127—21no—
137C22⋊C8×C127D411yescharacteristic
138C22⋊C8×C127D411yescharacteristic
139#97×C127—21no—
140C4×C8×C127—21no—
141C4×C8×C127—21no—
142C4×C8×C127C2311yescharacteristic
143C4×C8×C127C2311yescharacteristic
144#41×C127—81no—
145#41×C127—81no—
146#41×C127—81no—
147#41×C127—81no—
148C2×Q8×C127—21no—
149C2×Q8×C127—21no—
150C2×Q8×C127C2×D411yescharacteristic
151C2×D4×C127—21no—
152C2×D4×C127—21no—
153C2×D4×C127—21no—
154C2×D4×C127—21no—
155C2×D4×C127—21no—
156C2×D4×C127—21no—
157C2×D4×C127—21no—
158C2×D4×C127—41no—
159C2×D4×C127—41no—
160C2×D4×C127C2×D411yescharacteristic
161C22×C4×C127—21no—
162C22×C4×C127—41no—
163C22×C4×C127—41no—
164C22×C4×C127C2×D411yescharacteristic
165C22×C4×C127C2×D411yescharacteristic
166C22×C4×C127#4111yescharacteristic
167Q16×C127—81no—
168SD16×C127—81no—
169SD16×C127—81no—
170SD16×C127—81no—
171SD16×C127—81no—
172SD16×C127—81no—
173D8×C127—81no—
174D8×C127—81no—
175D8×C127—81no—
176D8×C127—81no—
177M16×C127—81no—
178M16×C127—81no—
179C2×C8×C127—21no—
180C2×C8×C127—21no—
181C2×C8×C127—21no—
182C2×C8×C127—21no—
183C2×C8×C127—21no—
184C2×C8×C127—21no—
185C2×C8×C127—81no—
186C2×C8×C127—81no—
187C2×C8×C127C2×D411yescharacteristic
188C2×C8×C127C2×D411yescharacteristic
189C2×C8×C127C2×D411yescharacteristic
190C2×C8×C127C2×D411yescharacteristic
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—21no—
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—21no—
206C22⋊C4×C127—41no—
207C22⋊C4×C127—41no—
208C22⋊C4×C127—41no—
209C22⋊C4×C127—41no—
210C42×C127—21no—
211C42×C127C2×D411yescharacteristic
212C42×C127C2×D411yescharacteristic
213C42×C127#4111yescharacteristic
214C42×C127C2411yescharacteristic
215C23×C127—21no—
216C23×C127—41no—
217C23×C127—41no—
218C23×C127#12111yescharacteristic
219Q8×C127—21no—
220Q8×C127—21no—
221Q8×C127—41no—
222Q8×C127—41no—
223Q8×C127—41no—
224Q8×C127—41no—
225D4×C127—21no—
226D4×C127—21no—
227D4×C127—42no—
228D4×C127—41no—
229D4×C127—41no—
230D4×C127—41no—
231D4×C127—41no—
232D4×C127—41no—
233D4×C127—41no—
234D4×C127—41no—
235D4×C127—41no—
236D4×C127—81no—
237D4×C127—81no—
238D4×C127—82no—
239D4×C127—82no—
240C2×C4×C127—21no—
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—82no—
253C2×C4×C127—82no—
254C2×C4×C127#12111yescharacteristic
255C2×C4×C127#12111yescharacteristic
256C2×C4×C127#12111yescharacteristic
257C2×C4×C127C22×D411yescharacteristic
258C2×C4×C127C22×D411yescharacteristic
259C2×C4×C127C2×#4111yescharacteristic
260C8×C127—21no—
261C8×C127—21no—
262C8×C127—21no—
263C8×C127—21no—
264C8×C127—41no—
265C8×C127—41no—
266C8×C127—41no—
267C8×C127—41no—
268C8×C127—41no—
269C8×C127—41no—
270C22×C127—21no—
271C22×C127—21no—
272C22×C127—21no—
273C22×C127—41no—
274C22×C127—41no—
275C22×C127—41no—
276C22×C127—81no—
277C22×C127—81no—
278C22×C127—81no—
279C22×C127—81no—
280C22×C127—81no—
281C22×C127—81no—
282C22×C127C2×#12111yescharacteristic
283C4×C127—21no—
284C4×C127—21no—
285C4×C127—21no—
286C4×C127—21no—
287C4×C127—41no—
288C4×C127—41no—
289C4×C127—41no—
290C4×C127—81no—
291C4×C127—81no—
292C4×C127#57611yescharacteristic
293C4×C127#57611yescharacteristic
294C4×C127#57711yescharacteristic
295C4×C127#57711yescharacteristic
296#19578C12711yesmaximal, characteristic, direct product factor, Sylow
297C2×C127—41no—
298C2×C127—81no—
299C2×C127—161no—
300C2×C127—161no—
301C2×C127#304511yescharacteristic
302C2×C127#306211yescharacteristic
303C2×C127#306711yescharacteristic
304#3251C2×C12711yescharacteristic, complemented
305#3212C2×C12711yescharacteristic, complemented
306#3207C2×C12711yescharacteristic, complemented
307#2994C2×C12711yescharacteristic, complemented
308#1701C2×C12711yescharacteristic, complemented
309#1700C2×C12711yescharacteristic, complemented
310#1688C2×C12711yescharacteristic, complemented
311#1685C2×C12711yescharacteristic, complemented
312#1682C2×C12711yescharacteristic, complemented
313#1679C2×C12711yescharacteristic, complemented
314#1667C2×C12711yescharacteristic, complemented
315#1666C2×C12711yescharacteristic, complemented
316#1574C2×C12711yescharacteristic, complemented
317#1547C2×C12711yescharacteristic, complemented
318#1540C2×C12711yescharacteristic, complemented
319C127#1957811yescharacteristic, direct product factor, Sylow
320#532C22×C12711yescharacteristic
321#532C22×C12711yescharacteristic
322#529C22×C12711yescharacteristic
323#495—21no—
324#493C22×C12711yescharacteristic
325#492C22×C12711yescharacteristic
326#488—21no—
327#487C22×C12711yescharacteristic
328#486C22×C12711yescharacteristic
329#478—21no—
330#475C22×C12711yescharacteristic
331#474C22×C12711yescharacteristic
332#469—21no—
333#468—21no—
334#463—21no—
335#463—21no—
336#463—21no—
337#462C22×C12711yescharacteristic
338#461C22×C12711yescharacteristic
339#460C22×C12711yescharacteristic
340#460C22×C12711yescharacteristic
341#459C22×C12711yescharacteristic
342#459C22×C12711yescharacteristic
343#452—21no—
344#449—21no—
345#449—21no—
346#449—21no—
347#446C22×C12711yescharacteristic
348C8×Q8C22×C12711yescharacteristic
349#436C22×C12711yescharacteristic
350#435—21no—
351C8×D4—21no—
352C8×D4C22×C12711yescharacteristic
353#433—21no—
354#431C22×C12711yescharacteristic
355#431C22×C12711yescharacteristic
356#424—21no—
357#423C22×C12711yescharacteristic
358C2×C4⋊C8C22×C12711yescharacteristic
359#335C22×C12711yescharacteristic
360#335C22×C12711yescharacteristic
361#334C22×C12711yescharacteristic
362#334C22×C12711yescharacteristic
363#332C22×C12711yescharacteristic
364#332C22×C12711yescharacteristic
365#332C22×C12711yescharacteristic
366#332C22×C12711yescharacteristic
367#331C22×C12711yescharacteristic
368#331C22×C12711yescharacteristic
369#331C22×C12711yescharacteristic
370#331C22×C12711yescharacteristic
371C2×#41—21no—
372C2×#41—21no—
373C2×Q16—21no—
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×D8—21no—
380C2×D8—21no—
381C2×D8—21no—
382C2×D8—21no—
383C2×M16—21no—
384C2×M16—21no—
385C22×C8—21no—
386C22×C8—21no—
387C4⋊Q8C23×C12711yescharacteristic
388C4⋊Q8C23×C12711yescharacteristic
389#127C23×C12711yescharacteristic
390#127C23×C12711yescharacteristic
391#126—21no—
392#125D4×C12711yescharacteristic
393#124—21no—
394#124—21no—
395#124D4×C12711yescharacteristic
396#123—21no—
397C22⋊Q8D4×C12711yescharacteristic
398#121—21no—
399#121—21no—
400#121—21no—
401#121—21no—
402#121D4×C12711yescharacteristic
403C4×Q8C23×C12711yescharacteristic
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4—21no—
409C4×D4C23×C12711yescharacteristic
410#117—21no—
411C2×C42C23×C12711yescharacteristic
412#107—21no—
413#106—21no—
414C4⋊C8—21no—
415C4⋊C8—21no—
416C4⋊C8—21no—
417C4⋊C8—21no—
418C4⋊C8D4×C12711yescharacteristic
419C4⋊C8D4×C12711yescharacteristic
420C4⋊C8C23×C12711yescharacteristic
421C4⋊C8C23×C12711yescharacteristic
422C4⋊C8C23×C12711yescharacteristic
423C4⋊C8C23×C12711yescharacteristic
424C4⋊C8C23×C12711yescharacteristic
425C4⋊C8C23×C12711yescharacteristic
426#103—21no—
427#103—21no—
428#103—21no—
429#103—21no—
430#103—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438C22⋊C8—21no—
439C22⋊C8—21no—
440C22⋊C8—21no—
441C22⋊C8D4×C12711yescharacteristic
442C22⋊C8D4×C12711yescharacteristic
443#97—21no—
444C4×C8—21no—
445C4×C8—21no—
446C4×C8C23×C12711yescharacteristic
447C4×C8C23×C12711yescharacteristic
448#41—81no—
449#41—81no—
450#41—81no—
451#41—81no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8C2×D4×C12711yescharacteristic
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4C2×D4×C12711yescharacteristic
465C22×C4—21no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4C2×D4×C12711yescharacteristic
469C22×C4C2×D4×C12711yescharacteristic
470C22×C4#41×C12711yescharacteristic
471Q16—81no—
472SD16—81no—
473SD16—81no—
474SD16—81no—
475SD16—81no—
476SD16—81no—
477D8—81no—
478D8—81no—
479D8—81no—
480D8—81no—
481M16—81no—
482M16—81no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—81no—
490C2×C8—81no—
491C2×C8C2×D4×C12711yescharacteristic
492C2×C8C2×D4×C12711yescharacteristic
493C2×C8C2×D4×C12711yescharacteristic
494C2×C8C2×D4×C12711yescharacteristic
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4C2×D4×C12711yescharacteristic
504C4⋊C4C2×D4×C12711yescharacteristic
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C42—21no—
515C42C2×D4×C12711yescharacteristic
516C42C2×D4×C12711yescharacteristic
517C42#41×C12711yescharacteristic
518C42C24×C12711yescharacteristic
519C23—21no—
520C23—41no—
521C23—41no—
522C23#121×C12711yescharacteristic
523Q8—21no—
524Q8—21no—
525Q8—41no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529D4—21no—
530D4—21no—
531D4—42no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—81no—
541D4—81no—
542D4—82no—
543D4—82no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—82no—
557C2×C4—82no—
558C2×C4#121×C12711yescharacteristic
559C2×C4#121×C12711yescharacteristic
560C2×C4#121×C12711yescharacteristic
561C2×C4C22×D4×C12711yescharacteristic
562C2×C4C22×D4×C12711yescharacteristic
563C2×C4C2×#41×C12711yescharacteristic
564C8—21no—
565C8—21no—
566C8—21no—
567C8—21no—
568C8—41no—
569C8—41no—
570C8—41no—
571C8—41no—
572C8—41no—
573C8—41no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22C2×#121×C12711yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—81no—
595C4—81no—
596C4#576×C12711yescharacteristic
597C4#576×C12711yescharacteristic
598C4#577×C12711yescharacteristic
599C4#577×C12711yescharacteristic
600C2—41no—
601C2—81no—
602C2—161no—
603C2—161no—
604C2C127×#304511yescharacteristic
605C2C127×#306211yescharacteristic
606C2C127×#306711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#121
commutator, Frattini, cosocleC42C24×C127
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C127×#3251C2semidirect
2. C127×#3212C2semidirect
3. C127×#3207C2semidirect
4. C127×#2994C2semidirect
5. C127×#1701C2semidirect
6. C127×#1700C2semidirect
7. C127×#1688C2semidirect
8. C127×#1685C2semidirect
9. C127×#1682C2semidirect
10. C127×#1679C2semidirect
11. C127×#1667C2semidirect
12. C127×#1666C2semidirect
13. C127×#1574C2semidirect
14. C127×#1547C2semidirect
15. C127×#1540C2semidirect
296. #19578C127direct (N × H)
304. #3251C2×C127semidirect
305. #3212C2×C127semidirect
306. #3207C2×C127semidirect
307. #2994C2×C127semidirect
308. #1701C2×C127semidirect
309. #1700C2×C127semidirect
310. #1688C2×C127semidirect
311. #1685C2×C127semidirect
312. #1682C2×C127semidirect
313. #1679C2×C127semidirect
314. #1667C2×C127semidirect
315. #1666C2×C127semidirect
316. #1574C2×C127semidirect
317. #1547C2×C127semidirect
318. #1540C2×C127semidirect
319. C127#19578direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32512
C127×#32122
C127×#32072
C127×#29942
C127×#17012
C127×#17002
C127×#16882
C127×#16852
C127×#16822
C127×#16792
C127×#16672
C127×#16662
C127×#15742
C127×#15472
C127×#15402
#19578127