Finite Group Databasebeta

← C127×#19785 #44583458

Subgroups — C127×#19785 #44583458

Order 32512.

632 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×#3391C211yesmaximal, characteristic
2C127×#3360C211yesmaximal, characteristic, complemented
3C127×#3333C211yesmaximal, characteristic, complemented
4C127×#3304C211yesmaximal, characteristic, complemented
5C127×#1717C211yesmaximal, characteristic, complemented
6C127×#1701C211yesmaximal, characteristic, complemented
7C127×#1684C211yesmaximal, characteristic, complemented
8C127×#1677C211yesmaximal, characteristic, complemented
9C127×#1668C211yesmaximal, characteristic, complemented
10C127×#1642C211yesmaximal, characteristic, complemented
11C127×#1631C211yesmaximal, characteristic, complemented
12C127×#1628C211yesmaximal, characteristic, complemented
13C127×#1622C211yesmaximal, characteristic, complemented
14C127×#1581C211yesmaximal, characteristic, complemented
15C127×#1579C211yesmaximal, characteristic, complemented
16#556×C127C2211yescharacteristic
17#554×C127C2211yescharacteristic
18#550×C127C2211yescharacteristic
19#550×C127C2211yescharacteristic
20#493×C127—21no—
21#493×C127C2211yescharacteristic
22#492×C127C2211yescharacteristic
23#488×C127—21no—
24#487×C127C2211yescharacteristic
25#486×C127C2211yescharacteristic
26#486×C127C2211yescharacteristic
27#486×C127C2211yescharacteristic
28#482×C127—21no—
29#480×C127—21no—
30#479×C127—21no—
31#477×C127C2211yescharacteristic
32#476×C127C2211yescharacteristic
33#475×C127C2211yescharacteristic
34#468×C127—21no—
35#465×C127—21no—
36#463×C127—21no—
37#461×C127C2211yescharacteristic
38#460×C127C2211yescharacteristic
39#460×C127C2211yescharacteristic
40#459×C127—21no—
41#459×C127—21no—
42#459×C127C2211yescharacteristic
43#459×C127C2211yescharacteristic
44#452×C127—21no—
45#452×C127—21no—
46C8×Q8×C127C2211yescharacteristic
47C8×Q8×C127C2211yescharacteristic
48C4×Q16×C127C2211yescharacteristic
49C4×SD16×C127—21no—
50C4×D8×C127—21no—
51C4×D8×C127C2211yescharacteristic
52#436×C127C2211yescharacteristic
53C8×D4×C127C2211yescharacteristic
54#417×C127—21no—
55#416×C127—21no—
56#335×C127C2211yescharacteristic
57#334×C127C2211yescharacteristic
58#333×C127C2211yescharacteristic
59#332×C127C2211yescharacteristic
60#331×C127C2211yescharacteristic
61#331×C127C2211yescharacteristic
62Q8⋊C8×C127C2211yescharacteristic
63Q8⋊C8×C127C2211yescharacteristic
64D4⋊C8×C127C2211yescharacteristic
65D4⋊C8×C127C2211yescharacteristic
66#322×C127C2211yescharacteristic
67C2×#41×C127—21no—
68C2×#41×C127—21no—
69C2×Q16×C127D411yescharacteristic
70C2×SD16×C127—21no—
71C2×SD16×C127—21no—
72C2×SD16×C127—21no—
73C2×SD16×C127—41no—
74C2×D8×C127—21no—
75C2×D8×C127—21no—
76C2×D8×C127—21no—
77C2×D8×C127—21no—
78C2×D8×C127D411yescharacteristic
79C2×M16×C127—21no—
80C22×C8×C127—21no—
81C4⋊Q8×C127C2311yescharacteristic
82C4⋊Q8×C127C2311yescharacteristic
83#127×C127—21no—
84#127×C127—21no—
85#127×C127C2311yescharacteristic
86#127×C127C2311yescharacteristic
87#126×C127—41no—
88#125×C127—21no—
89#124×C127—21no—
90C22⋊Q8×C127—21no—
91C22⋊Q8×C127—21no—
92C22⋊Q8×C127—41no—
93#121×C127—21no—
94#121×C127—21no—
95#121×C127—41no—
96#121×C127—41no—
97C4×Q8×C127—21no—
98C4×Q8×C127C2311yescharacteristic
99C4×Q8×C127C2311yescharacteristic
100C4×D4×C127—21no—
101C4×D4×C127—21no—
102C4×D4×C127—21no—
103C4×D4×C127C2311yescharacteristic
104C4×D4×C127C2311yescharacteristic
105#117×C127—21no—
106C2×C4⋊C4×C127—21no—
107#107×C127—21no—
108#107×C127D411yescharacteristic
109#107×C127D411yescharacteristic
110#106×C127—21no—
111#106×C127—21no—
112C4⋊C8×C127—21no—
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#103×C127D411yescharacteristic
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—21no—
134#102×C127—41no—
135#102×C127D411yescharacteristic
136#102×C127D411yescharacteristic
137C22⋊C8×C127—21no—
138C22⋊C8×C127—21no—
139C4×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—81no—
147#41×C127—81no—
148C2×Q8×C127—21no—
149C2×Q8×C127—21no—
150C2×Q8×C127C2×D411yescharacteristic
151C2×Q8×C127C2×D411yescharacteristic
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×C127—41no—
161C2×D4×C127—41no—
162C2×D4×C127C2×D411yescharacteristic
163C2×D4×C127C2×D411yescharacteristic
164C22×C4×C127—21no—
165C22×C4×C127—21no—
166C22×C4×C127—41no—
167C22×C4×C127—41no—
168C22×C4×C127—41no—
169Q16×C127—22no—
170SD16×C127—42no—
171SD16×C127—81no—
172SD16×C127—81no—
173SD16×C127—82no—
174D8×C127—41no—
175D8×C127—42no—
176D8×C127—81no—
177D8×C127—81no—
178D8×C127—81no—
179M16×C127—81no—
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×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×C127—41no—
198C4⋊C4×C127—41no—
199C4⋊C4×C127C2×D411yescharacteristic
200C4⋊C4×C127C2×D411yescharacteristic
201C4⋊C4×C127C2×D411yescharacteristic
202C4⋊C4×C127C2×D411yescharacteristic
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—
210C42×C127—21no—
211C42×C127—21no—
212C42×C127—41no—
213C42×C127C2411yescharacteristic
214C23×C127—21no—
215C23×C127—21no—
216C23×C127—41no—
217C23×C127—41no—
218Q8×C127—21no—
219Q8×C127—21no—
220Q8×C127—21no—
221Q8×C127—41no—
222Q8×C127—41no—
223Q8×C127—81no—
224Q8×C127#13512yes—
225D4×C127—21no—
226D4×C127—21no—
227D4×C127—21no—
228D4×C127—21no—
229D4×C127—41no—
230D4×C127—41no—
231D4×C127—41no—
232D4×C127—41no—
233D4×C127—41no—
234D4×C127—41no—
235D4×C127—41no—
236D4×C127—41no—
237D4×C127—82no—
238D4×C127—82no—
239D4×C127—81no—
240D4×C127—81no—
241D4×C127—161no—
242D4×C127—161no—
243C2×C4×C127—21no—
244C2×C4×C127—21no—
245C2×C4×C127—21no—
246C2×C4×C127—21no—
247C2×C4×C127—21no—
248C2×C4×C127—21no—
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—161no—
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—41no—
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×C127—81no—
280C22×C127—81no—
281C22×C127—81no—
282C22×C127D4211yescharacteristic
283C4×C127—22no—
284C4×C127—21no—
285C4×C127—41no—
286C4×C127—41no—
287C4×C127—41no—
288C4×C127—41no—
289C4×C127—41no—
290C4×C127—81no—
291C4×C127—81no—
292C4×C127C2×#13511yescharacteristic
293C4×C127#57511yescharacteristic
294C4×C127#57611yescharacteristic
295C4×C127#57711yescharacteristic
296#19785C12711yesmaximal, characteristic, direct product factor, Sylow
297C2×C127—81no—
298C2×C127—81no—
299C2×C127—161no—
300C2×C127—161no—
301C2×C127#327111yescharacteristic
302C2×C127#328011yescharacteristic
303C2×C127#328811yescharacteristic
304#3391C2×C12711yescharacteristic
305#3360C2×C12711yescharacteristic, complemented
306#3333C2×C12711yescharacteristic, complemented
307#3304C2×C12711yescharacteristic, complemented
308#1717C2×C12711yescharacteristic, complemented
309#1701C2×C12711yescharacteristic, complemented
310#1684C2×C12711yescharacteristic, complemented
311#1677C2×C12711yescharacteristic, complemented
312#1668C2×C12711yescharacteristic, complemented
313#1642C2×C12711yescharacteristic, complemented
314#1631C2×C12711yescharacteristic, complemented
315#1628C2×C12711yescharacteristic, complemented
316#1622C2×C12711yescharacteristic, complemented
317#1581C2×C12711yescharacteristic, complemented
318#1579C2×C12711yescharacteristic, complemented
319C127#1978511yescharacteristic, direct product factor, Sylow
320#556C22×C12711yescharacteristic
321#554C22×C12711yescharacteristic
322#550C22×C12711yescharacteristic
323#550C22×C12711yescharacteristic
324#493—21no—
325#493C22×C12711yescharacteristic
326#492C22×C12711yescharacteristic
327#488—21no—
328#487C22×C12711yescharacteristic
329#486C22×C12711yescharacteristic
330#486C22×C12711yescharacteristic
331#486C22×C12711yescharacteristic
332#482—21no—
333#480—21no—
334#479—21no—
335#477C22×C12711yescharacteristic
336#476C22×C12711yescharacteristic
337#475C22×C12711yescharacteristic
338#468—21no—
339#465—21no—
340#463—21no—
341#461C22×C12711yescharacteristic
342#460C22×C12711yescharacteristic
343#460C22×C12711yescharacteristic
344#459—21no—
345#459—21no—
346#459C22×C12711yescharacteristic
347#459C22×C12711yescharacteristic
348#452—21no—
349#452—21no—
350C8×Q8C22×C12711yescharacteristic
351C8×Q8C22×C12711yescharacteristic
352C4×Q16C22×C12711yescharacteristic
353C4×SD16—21no—
354C4×D8—21no—
355C4×D8C22×C12711yescharacteristic
356#436C22×C12711yescharacteristic
357C8×D4C22×C12711yescharacteristic
358#417—21no—
359#416—21no—
360#335C22×C12711yescharacteristic
361#334C22×C12711yescharacteristic
362#333C22×C12711yescharacteristic
363#332C22×C12711yescharacteristic
364#331C22×C12711yescharacteristic
365#331C22×C12711yescharacteristic
366Q8⋊C8C22×C12711yescharacteristic
367Q8⋊C8C22×C12711yescharacteristic
368D4⋊C8C22×C12711yescharacteristic
369D4⋊C8C22×C12711yescharacteristic
370#322C22×C12711yescharacteristic
371C2×#41—21no—
372C2×#41—21no—
373C2×Q16D4×C12711yescharacteristic
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—41no—
378C2×D8—21no—
379C2×D8—21no—
380C2×D8—21no—
381C2×D8—21no—
382C2×D8D4×C12711yescharacteristic
383C2×M16—21no—
384C22×C8—21no—
385C4⋊Q8C23×C12711yescharacteristic
386C4⋊Q8C23×C12711yescharacteristic
387#127—21no—
388#127—21no—
389#127C23×C12711yescharacteristic
390#127C23×C12711yescharacteristic
391#126—41no—
392#125—21no—
393#124—21no—
394C22⋊Q8—21no—
395C22⋊Q8—21no—
396C22⋊Q8—41no—
397#121—21no—
398#121—21no—
399#121—41no—
400#121—41no—
401C4×Q8—21no—
402C4×Q8C23×C12711yescharacteristic
403C4×Q8C23×C12711yescharacteristic
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4C23×C12711yescharacteristic
408C4×D4C23×C12711yescharacteristic
409#117—21no—
410C2×C4⋊C4—21no—
411#107—21no—
412#107D4×C12711yescharacteristic
413#107D4×C12711yescharacteristic
414#106—21no—
415#106—21no—
416C4⋊C8—21no—
417C4⋊C8—21no—
418C4⋊C8C23×C12711yescharacteristic
419C4⋊C8C23×C12711yescharacteristic
420C4⋊C8C23×C12711yescharacteristic
421C4⋊C8C23×C12711yescharacteristic
422#103—21no—
423#103—21no—
424#103—21no—
425#103—21no—
426#103—21no—
427#103D4×C12711yescharacteristic
428#103D4×C12711yescharacteristic
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—41no—
439#102D4×C12711yescharacteristic
440#102D4×C12711yescharacteristic
441C22⋊C8—21no—
442C22⋊C8—21no—
443C4×C8—21no—
444C4×C8—21no—
445C4×C8C23×C12711yescharacteristic
446C4×C8C23×C12711yescharacteristic
447C4×C8C23×C12711yescharacteristic
448#41—42no—
449#41—42no—
450#41—81no—
451#41—81no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8C2×D4×C12711yescharacteristic
455C2×Q8C2×D4×C12711yescharacteristic
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×D4—41no—
465C2×D4—41no—
466C2×D4C2×D4×C12711yescharacteristic
467C2×D4C2×D4×C12711yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473Q16—22no—
474SD16—42no—
475SD16—81no—
476SD16—81no—
477SD16—82no—
478D8—41no—
479D8—42no—
480D8—81no—
481D8—81no—
482D8—81no—
483M16—81no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—81no—
490C2×C8C2×D4×C12711yescharacteristic
491C2×C8C2×D4×C12711yescharacteristic
492C2×C8C2×D4×C12711yescharacteristic
493C2×C8C2×D4×C12711yescharacteristic
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4C2×D4×C12711yescharacteristic
504C4⋊C4C2×D4×C12711yescharacteristic
505C4⋊C4C2×D4×C12711yescharacteristic
506C4⋊C4C2×D4×C12711yescharacteristic
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C42—21no—
515C42—21no—
516C42—41no—
517C42C24×C12711yescharacteristic
518C23—21no—
519C23—21no—
520C23—41no—
521C23—41no—
522Q8—21no—
523Q8—21no—
524Q8—21no—
525Q8—41no—
526Q8—41no—
527Q8—81no—
528Q8#135×C12712yes—
529D4—21no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—82no—
542D4—82no—
543D4—81no—
544D4—81no—
545D4—161no—
546D4—161no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—82no—
560C2×C4—82no—
561C2×C4—161no—
562C2×C4C22×D4×C12711yescharacteristic
563C2×C4C22×D4×C12711yescharacteristic
564C2×C4H(5,𝔽2)×C12711yescharacteristic
565C8—21no—
566C8—21no—
567C8—21no—
568C8—21no—
569C8—41no—
570C8—41no—
571C8—41no—
572C8—41no—
573C8—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22D42×C12711yescharacteristic
587C4—22no—
588C4—21no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—81no—
595C4—81no—
596C4C2×#135×C12711yescharacteristic
597C4#575×C12711yescharacteristic
598C4#576×C12711yescharacteristic
599C4#577×C12711yescharacteristic
600C2—81no—
601C2—81no—
602C2—161no—
603C2—161no—
604C2C127×#327111yescharacteristic
605C2C127×#328011yescharacteristic
606C2C127×#328811yescharacteristic
subgroupG/H
center, socleC22×C127D42
commutator, Frattini, cosocleC42C24×C127
prime radicalC127×#3391C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#3360C2semidirect
3. C127×#3333C2semidirect
4. C127×#3304C2semidirect
5. C127×#1717C2semidirect
6. C127×#1701C2semidirect
7. C127×#1684C2semidirect
8. C127×#1677C2semidirect
9. C127×#1668C2semidirect
10. C127×#1642C2semidirect
11. C127×#1631C2semidirect
12. C127×#1628C2semidirect
13. C127×#1622C2semidirect
14. C127×#1581C2semidirect
15. C127×#1579C2semidirect
296. #19785C127direct (N × H)
305. #3360C2×C127semidirect
306. #3333C2×C127semidirect
307. #3304C2×C127semidirect
308. #1717C2×C127semidirect
309. #1701C2×C127semidirect
310. #1684C2×C127semidirect
311. #1677C2×C127semidirect
312. #1668C2×C127semidirect
313. #1642C2×C127semidirect
314. #1631C2×C127semidirect
315. #1628C2×C127semidirect
316. #1622C2×C127semidirect
317. #1581C2×C127semidirect
318. #1579C2×C127semidirect
319. C127#19785direct (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×#33602
C127×#33332
C127×#33042
C127×#17172
C127×#17012
C127×#16842
C127×#16772
C127×#16682
C127×#16422
C127×#16312
C127×#16282
C127×#16222
C127×#15812
C127×#15792
#19785127