Finite Group Databasebeta

← C127×#19770 #44583443

Subgroups — C127×#19770 #44583443

Order 32512.

650 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3392C211yesmaximal, characteristic, complemented
2C127×#3387C211yesmaximal, characteristic, complemented
3C127×#3362C211yesmaximal, characteristic, complemented
4C127×#3287C211yesmaximal, characteristic
5C127×#1715C211yesmaximal, characteristic, complemented
6C127×#1688C211yesmaximal, characteristic, complemented
7C127×#1678C211yesmaximal, characteristic, complemented
8C127×#1671C211yesmaximal, characteristic, complemented
9C127×#1666C211yesmaximal, characteristic, complemented
10C127×#1642C211yesmaximal, characteristic, complemented
11C127×#1631C211yesmaximal, characteristic, complemented
12C127×#1626C211yesmaximal, characteristic, complemented
13C127×#1623C211yesmaximal, characteristic, complemented
14C127×#1582C211yesmaximal, characteristic, complemented
15C127×#1579C211yesmaximal, characteristic, complemented
16C2×#135×C127—21no—
17Q82×C127C2211yescharacteristic
18#557×C127C2211yescharacteristic
19#550×C127C2211yescharacteristic
20#550×C127C2211yescharacteristic
21#501×C127—21no—
22#498×C127C2211yescharacteristic
23#493×C127C2211yescharacteristic
24#492×C127—21no—
25#492×C127C2211yescharacteristic
26#492×C127C2211yescharacteristic
27#486×C127—21no—
28#486×C127C2211yescharacteristic
29#486×C127C2211yescharacteristic
30#479×C127—21no—
31#477×C127C2211yescharacteristic
32#476×C127—21no—
33#476×C127C2211yescharacteristic
34#475×C127—21no—
35#475×C127C2211yescharacteristic
36#466×C127—21no—
37#461×C127—21no—
38#461×C127C2211yescharacteristic
39#460×C127—21no—
40#460×C127—21no—
41#460×C127C2211yescharacteristic
42#460×C127C2211yescharacteristic
43#460×C127C2211yescharacteristic
44#460×C127C2211yescharacteristic
45#449×C127—21no—
46#449×C127—21no—
47#446×C127C2211yescharacteristic
48C8×Q8×C127C2211yescharacteristic
49C8×Q8×C127C2211yescharacteristic
50#441×C127—21no—
51C4×Q16×C127C2211yescharacteristic
52C4×SD16×C127—21no—
53C4×SD16×C127—21no—
54C4×SD16×C127C2211yescharacteristic
55C8×D4×C127C2211yescharacteristic
56#334×C127C2211yescharacteristic
57#334×C127C2211yescharacteristic
58#333×C127C2211yescharacteristic
59#332×C127C2211yescharacteristic
60#331×C127C2211yescharacteristic
61#331×C127C2211yescharacteristic
62Q8⋊C8×C127C2211yescharacteristic
63Q8⋊C8×C127C2211yescharacteristic
64Q8⋊C8×C127C2211yescharacteristic
65D4⋊C8×C127C2211yescharacteristic
66#322×C127C2211yescharacteristic
67C2×#41×C127—21no—
68C2×#41×C127—21no—
69#135×C127—44no—
70C2×Q16×C127D411yescharacteristic
71C2×SD16×C127—21no—
72C2×SD16×C127—21no—
73C2×SD16×C127—21no—
74C2×SD16×C127—21no—
75C2×SD16×C127—21no—
76C2×SD16×C127—21no—
77C2×SD16×C127—21no—
78C2×SD16×C127—41no—
79C2×SD16×C127D411yescharacteristic
80C2×D8×C127—21no—
81C2×D8×C127—21no—
82C22×C8×C127—21no—
83C4⋊Q8×C127—21no—
84C4⋊Q8×C127—21no—
85C4⋊Q8×C127—21no—
86C4⋊Q8×C127—41no—
87C4⋊Q8×C127C2311yescharacteristic
88C4⋊Q8×C127C2311yescharacteristic
89#127×C127—21no—
90#127×C127—21no—
91#127×C127C2311yescharacteristic
92#127×C127C2311yescharacteristic
93#125×C127—21no—
94#125×C127—41no—
95#121×C127—21no—
96#121×C127—21no—
97#121×C127—41no—
98#121×C127—41no—
99C4×Q8×C127—21no—
100C4×Q8×C127—21no—
101C4×Q8×C127—21no—
102C4×Q8×C127—21no—
103C4×Q8×C127C2311yescharacteristic
104C4×Q8×C127C2311yescharacteristic
105C4×Q8×C127C2311yescharacteristic
106C4×D4×C127—21no—
107C4×D4×C127—21no—
108C4×D4×C127C2311yescharacteristic
109#107×C127—21no—
110#107×C127D411yescharacteristic
111#106×C127—21no—
112#106×C127—21no—
113#106×C127—21no—
114#106×C127—21no—
115#106×C127D411yescharacteristic
116C4⋊C8×C127—21no—
117C4⋊C8×C127—21no—
118C4⋊C8×C127—21no—
119C4⋊C8×C127C2311yescharacteristic
120C4⋊C8×C127C2311yescharacteristic
121C4⋊C8×C127C2311yescharacteristic
122C4⋊C8×C127C2311yescharacteristic
123#103×C127—21no—
124#103×C127—21no—
125#103×C127—21no—
126#103×C127D411yescharacteristic
127#103×C127D411yescharacteristic
128#103×C127D411yescharacteristic
129#102×C127—21no—
130#102×C127—21no—
131#102×C127—21no—
132#102×C127—21no—
133#102×C127—21no—
134#102×C127—21no—
135#102×C127—21no—
136#102×C127—41no—
137#102×C127D411yescharacteristic
138C22⋊C8×C127—21no—
139#97×C127—21no—
140C4×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—81no—
148#41×C127—81no—
149C2×Q8×C127—21no—
150C2×Q8×C127—21no—
151C2×Q8×C127—41no—
152C2×Q8×C127C2×D411yescharacteristic
153C2×Q8×C127C2×D411yescharacteristic
154C2×Q8×C127C2×D411yescharacteristic
155C2×D4×C127—21no—
156C2×D4×C127—21no—
157C2×D4×C127—21no—
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
166C22×C4×C127—21no—
167C22×C4×C127—41no—
168C22×C4×C127—41no—
169Q16×C127SD1614yescomplemented
170SD16×C127—41no—
171SD16×C127—42no—
172SD16×C127—42no—
173SD16×C127—42no—
174SD16×C127—42no—
175SD16×C127—81no—
176SD16×C127—81no—
177SD16×C127—81no—
178SD16×C127—82no—
179D8×C127—42no—
180D8×C127—81no—
181C2×C8×C127—21no—
182C2×C8×C127—21no—
183C2×C8×C127—21no—
184C2×C8×C127—21no—
185C2×C8×C127—21no—
186C2×C8×C127—42no—
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—41no—
199C4⋊C4×C127—41no—
200C4⋊C4×C127—41no—
201C4⋊C4×C127—41no—
202C4⋊C4×C127—41no—
203C4⋊C4×C127C2×D411yescharacteristic
204C4⋊C4×C127C2×D411yescharacteristic
205C4⋊C4×C127C2×D411yescharacteristic
206C4⋊C4×C127C2×D411yescharacteristic
207C22⋊C4×C127—21no—
208C22⋊C4×C127—41no—
209C22⋊C4×C127—41no—
210C42×C127—21no—
211C42×C127—21no—
212C42×C127—21no—
213C42×C127—41no—
214C42×C127—41no—
215C42×C127C2411yescharacteristic
216C23×C127—21no—
217C23×C127—41no—
218C23×C127—41no—
219Q8×C127—21no—
220Q8×C127—21no—
221Q8×C127—21no—
222Q8×C127—21no—
223Q8×C127—41no—
224Q8×C127—41no—
225Q8×C127—81no—
226Q8×C127—161no—
227Q8×C127C2×SD1612yes—
228Q8×C127C2×SD1612yes—
229D4×C127—21no—
230D4×C127—21no—
231D4×C127—41no—
232D4×C127—41no—
233D4×C127—41no—
234D4×C127—41no—
235D4×C127—41no—
236D4×C127—41no—
237D4×C127—41no—
238D4×C127—41no—
239D4×C127—82no—
240D4×C127—82no—
241D4×C127—81no—
242D4×C127—81no—
243D4×C127—161no—
244D4×C127—161no—
245C2×C4×C127—21no—
246C2×C4×C127—21no—
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—82no—
257C2×C4×C127—82no—
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—41no—
265C8×C127—41no—
266C8×C127—41no—
267C8×C127—41no—
268C8×C127—41no—
269C8×C127C2×SD1612yes—
270C22×C127—41no—
271C22×C127—41no—
272C22×C127—41no—
273C22×C127—81no—
274C22×C127—81no—
275C22×C127—81no—
276C22×C127—81no—
277C22×C127—81no—
278C22×C127—81no—
279C22×C127D4211yescharacteristic
280C4×C127—22no—
281C4×C127—22no—
282C4×C127—21no—
283C4×C127—41no—
284C4×C127—41no—
285C4×C127—41no—
286C4×C127—41no—
287C4×C127—41no—
288C4×C127—81no—
289C4×C127—81no—
290C4×C127C22×SD1611yescharacteristic
291C4×C127#57511yescharacteristic
292C4×C127#57711yescharacteristic
293C4×C127#57711yescharacteristic
294#19770C12711yesmaximal, characteristic, direct product factor, Sylow
295C2×C127—81no—
296C2×C127—161no—
297C2×C127—161no—
298C2×C127#327111yescharacteristic
299C2×C127D4×SD1611yescharacteristic
300C2×C127#328811yescharacteristic
301#3392C2×C12711yescharacteristic, complemented
302#3387C2×C12711yescharacteristic, complemented
303#3362C2×C12711yescharacteristic, complemented
304#3287C2×C12711yescharacteristic
305#1715C2×C12711yescharacteristic, complemented
306#1688C2×C12711yescharacteristic, complemented
307#1678C2×C12711yescharacteristic, complemented
308#1671C2×C12711yescharacteristic, complemented
309#1666C2×C12711yescharacteristic, complemented
310#1642C2×C12711yescharacteristic, complemented
311#1631C2×C12711yescharacteristic, complemented
312#1626C2×C12711yescharacteristic, complemented
313#1623C2×C12711yescharacteristic, complemented
314#1582C2×C12711yescharacteristic, complemented
315#1579C2×C12711yescharacteristic, complemented
316C127#1977011yescharacteristic, direct product factor, Sylow
317C2×#135—21no—
318Q82C22×C12711yescharacteristic
319#557C22×C12711yescharacteristic
320#550C22×C12711yescharacteristic
321#550C22×C12711yescharacteristic
322#501—21no—
323#498C22×C12711yescharacteristic
324#493C22×C12711yescharacteristic
325#492—21no—
326#492C22×C12711yescharacteristic
327#492C22×C12711yescharacteristic
328#486—21no—
329#486C22×C12711yescharacteristic
330#486C22×C12711yescharacteristic
331#479—21no—
332#477C22×C12711yescharacteristic
333#476—21no—
334#476C22×C12711yescharacteristic
335#475—21no—
336#475C22×C12711yescharacteristic
337#466—21no—
338#461—21no—
339#461C22×C12711yescharacteristic
340#460—21no—
341#460—21no—
342#460C22×C12711yescharacteristic
343#460C22×C12711yescharacteristic
344#460C22×C12711yescharacteristic
345#460C22×C12711yescharacteristic
346#449—21no—
347#449—21no—
348#446C22×C12711yescharacteristic
349C8×Q8C22×C12711yescharacteristic
350C8×Q8C22×C12711yescharacteristic
351#441—21no—
352C4×Q16C22×C12711yescharacteristic
353C4×SD16—21no—
354C4×SD16—21no—
355C4×SD16C22×C12711yescharacteristic
356C8×D4C22×C12711yescharacteristic
357#334C22×C12711yescharacteristic
358#334C22×C12711yescharacteristic
359#333C22×C12711yescharacteristic
360#332C22×C12711yescharacteristic
361#331C22×C12711yescharacteristic
362#331C22×C12711yescharacteristic
363Q8⋊C8C22×C12711yescharacteristic
364Q8⋊C8C22×C12711yescharacteristic
365Q8⋊C8C22×C12711yescharacteristic
366D4⋊C8C22×C12711yescharacteristic
367#322C22×C12711yescharacteristic
368C2×#41—21no—
369C2×#41—21no—
370#135—44no—
371C2×Q16D4×C12711yescharacteristic
372C2×SD16—21no—
373C2×SD16—21no—
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—41no—
380C2×SD16D4×C12711yescharacteristic
381C2×D8—21no—
382C2×D8—21no—
383C22×C8—21no—
384C4⋊Q8—21no—
385C4⋊Q8—21no—
386C4⋊Q8—21no—
387C4⋊Q8—41no—
388C4⋊Q8C23×C12711yescharacteristic
389C4⋊Q8C23×C12711yescharacteristic
390#127—21no—
391#127—21no—
392#127C23×C12711yescharacteristic
393#127C23×C12711yescharacteristic
394#125—21no—
395#125—41no—
396#121—21no—
397#121—21no—
398#121—41no—
399#121—41no—
400C4×Q8—21no—
401C4×Q8—21no—
402C4×Q8—21no—
403C4×Q8—21no—
404C4×Q8C23×C12711yescharacteristic
405C4×Q8C23×C12711yescharacteristic
406C4×Q8C23×C12711yescharacteristic
407C4×D4—21no—
408C4×D4—21no—
409C4×D4C23×C12711yescharacteristic
410#107—21no—
411#107D4×C12711yescharacteristic
412#106—21no—
413#106—21no—
414#106—21no—
415#106—21no—
416#106D4×C12711yescharacteristic
417C4⋊C8—21no—
418C4⋊C8—21no—
419C4⋊C8—21no—
420C4⋊C8C23×C12711yescharacteristic
421C4⋊C8C23×C12711yescharacteristic
422C4⋊C8C23×C12711yescharacteristic
423C4⋊C8C23×C12711yescharacteristic
424#103—21no—
425#103—21no—
426#103—21no—
427#103D4×C12711yescharacteristic
428#103D4×C12711yescharacteristic
429#103D4×C12711yescharacteristic
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—41no—
438#102D4×C12711yescharacteristic
439C22⋊C8—21no—
440#97—21no—
441C4×C8—21no—
442C4×C8—21no—
443C4×C8C23×C12711yescharacteristic
444C4×C8C23×C12711yescharacteristic
445C4×C8C23×C12711yescharacteristic
446#41—42no—
447#41—42no—
448#41—81no—
449#41—81no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—41no—
453C2×Q8C2×D4×C12711yescharacteristic
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
467C22×C4—21no—
468C22×C4—41no—
469C22×C4—41no—
470Q16SD16×C12714yescomplemented
471SD16—41no—
472SD16—42no—
473SD16—42no—
474SD16—42no—
475SD16—42no—
476SD16—81no—
477SD16—81no—
478SD16—81no—
479SD16—82no—
480D8—42no—
481D8—81no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—42no—
488C2×C8C2×D4×C12711yescharacteristic
489C2×C8C2×D4×C12711yescharacteristic
490C2×C8C2×D4×C12711yescharacteristic
491C2×C8C2×D4×C12711yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4C2×D4×C12711yescharacteristic
505C4⋊C4C2×D4×C12711yescharacteristic
506C4⋊C4C2×D4×C12711yescharacteristic
507C4⋊C4C2×D4×C12711yescharacteristic
508C22⋊C4—21no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—41no—
515C42—41no—
516C42C24×C12711yescharacteristic
517C23—21no—
518C23—41no—
519C23—41no—
520Q8—21no—
521Q8—21no—
522Q8—21no—
523Q8—21no—
524Q8—41no—
525Q8—41no—
526Q8—81no—
527Q8—161no—
528Q8C2×SD16×C12712yes—
529Q8C2×SD16×C12712yes—
530D4—21no—
531D4—21no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—82no—
541D4—82no—
542D4—81no—
543D4—81no—
544D4—161no—
545D4—161no—
546C2×C4—21no—
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—82no—
558C2×C4—82no—
559C2×C4C22×D4×C12711yescharacteristic
560C2×C4C22×D4×C12711yescharacteristic
561C2×C4H(5,𝔽2)×C12711yescharacteristic
562C8—21no—
563C8—21no—
564C8—21no—
565C8—41no—
566C8—41no—
567C8—41no—
568C8—41no—
569C8—41no—
570C8C2×SD16×C12712yes—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22D42×C12711yescharacteristic
581C4—22no—
582C4—22no—
583C4—21no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—81no—
590C4—81no—
591C4C22×SD16×C12711yescharacteristic
592C4#575×C12711yescharacteristic
593C4#577×C12711yescharacteristic
594C4#577×C12711yescharacteristic
595C2—81no—
596C2—161no—
597C2—161no—
598C2C127×#327111yescharacteristic
599C2D4×SD16×C12711yescharacteristic
600C2C127×#328811yescharacteristic
subgroupG/H
center, socleC22×C127D42
commutator, Frattini, cosocleC42C24×C127
prime radicalC127×#3287C2
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×#3392C2semidirect
2. C127×#3387C2semidirect
3. C127×#3362C2semidirect
5. C127×#1715C2semidirect
6. C127×#1688C2semidirect
7. C127×#1678C2semidirect
8. C127×#1671C2semidirect
9. C127×#1666C2semidirect
10. C127×#1642C2semidirect
11. C127×#1631C2semidirect
12. C127×#1626C2semidirect
13. C127×#1623C2semidirect
14. C127×#1582C2semidirect
15. C127×#1579C2semidirect
169. Q16×C127SD16semidirect
294. #19770C127direct (N × H)
301. #3392C2×C127semidirect
302. #3387C2×C127semidirect
303. #3362C2×C127semidirect
305. #1715C2×C127semidirect
306. #1688C2×C127semidirect
307. #1678C2×C127semidirect
308. #1671C2×C127semidirect
309. #1666C2×C127semidirect
310. #1642C2×C127semidirect
311. #1631C2×C127semidirect
312. #1626C2×C127semidirect
313. #1623C2×C127semidirect
314. #1582C2×C127semidirect
315. #1579C2×C127semidirect
316. C127#19770direct (N × H)
470. Q16SD16×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#33922
C127×#33872
C127×#33622
C127×#32872
C127×#17152
C127×#16882
C127×#16782
C127×#16712
C127×#16662
C127×#16422
C127×#16312
C127×#16262
C127×#16232
C127×#15822
C127×#15792
#19770127