Finite Group Databasebeta

← C127×#19872 #44583545

Subgroups — C127×#19872 #44583545

Order 32512.

580 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3398C211yesmaximal, characteristic, complemented
2C127×#3394C211yesmaximal, characteristic
3C127×#3365C211yesmaximal, characteristic, complemented
4C127×#3342C211yesmaximal, characteristic, complemented
5C127×#1722C211yesmaximal, characteristic, complemented
6C127×#1686C211yesmaximal, characteristic, complemented
7C127×#1681C211yesmaximal, characteristic
8C127×#1674C211yesmaximal, characteristic, complemented
9C127×#1670C211yesmaximal, characteristic, complemented
10C127×#1650C211yesmaximal, characteristic, complemented
11C127×#1648C211yesmaximal, characteristic, complemented
12C127×#1640C211yesmaximal, characteristic, complemented
13C127×#1628C211yesmaximal, characteristic
14C127×#1584C211yesmaximal, characteristic, complemented
15C127×SD16⋊C8C211yesmaximal, characteristic, complemented
16#559×C127C2211yescharacteristic
17#557×C127C2211yescharacteristic
18#556×C127C2211yescharacteristic
19#556×C127C2211yescharacteristic
20#500×C127C2211yescharacteristic
21#500×C127C2211yescharacteristic
22#497×C127—21no—
23#495×C127—21no—
24#494×C127C2211yescharacteristic
25#492×C127C2211yescharacteristic
26#488×C127—21no—
27#486×C127C2211yescharacteristic
28#486×C127C2211yescharacteristic
29#485×C127—21no—
30#485×C127—21no—
31#478×C127—21no—
32#475×C127C2211yescharacteristic
33#475×C127C2211yescharacteristic
34#475×C127C2211yescharacteristic
35#467×C127—21no—
36#464×C127—21no—
37#464×C127—21no—
38#464×C127—21no—
39#463×C127—21no—
40#462×C127—21no—
41#462×C127C2211yescharacteristic
42#462×C127C2211yescharacteristic
43#461×C127C2211yescharacteristic
44#460×C127C2211yescharacteristic
45#459×C127C2211yescharacteristic
46#446×C127C2211yescharacteristic
47C8×Q8×C127C2211yescharacteristic
48C8×Q8×C127C2211yescharacteristic
49#441×C127—21no—
50C4×Q16×C127C2211yescharacteristic
51C4×SD16×C127—21no—
52C4×SD16×C127—21no—
53C4×SD16×C127C2211yescharacteristic
54C8×D4×C127C2211yescharacteristic
55#427×C127—21no—
56#335×C127C2211yescharacteristic
57#335×C127C2211yescharacteristic
58#332×C127C2211yescharacteristic
59#332×C127C2211yescharacteristic
60#332×C127C2211yescharacteristic
61#331×C127C2211yescharacteristic
62Q8⋊C8×C127C2211yescharacteristic
63Q8⋊C8×C127C2211yescharacteristic
64Q8⋊C8×C127C2211yescharacteristic
65D4⋊C8×C127C2211yescharacteristic
66#322×C127C2211yescharacteristic
67C2×Q16×C127—21no—
68C2×Q16×C127—21no—
69C2×Q16×C127—21no—
70C2×Q16×C127—21no—
71C2×Q16×C127D411yescharacteristic
72C2×SD16×C127—21no—
73C2×SD16×C127—21no—
74C2×SD16×C127—21no—
75C2×SD16×C127—21no—
76C2×SD16×C127D411yescharacteristic
77C2×D8×C127—21no—
78C22×C8×C127—21no—
79C4⋊Q8×C127—21no—
80C4⋊Q8×C127C2311yescharacteristic
81C4⋊Q8×C127C2311yescharacteristic
82C4⋊Q8×C127C2311yescharacteristic
83#127×C127C2311yescharacteristic
84#126×C127—41no—
85#126×C127—41no—
86#125×C127—21no—
87#125×C127—41no—
88#124×C127—21no—
89#124×C127—21no—
90#124×C127—21no—
91#124×C127—21no—
92#123×C127—41no—
93C22⋊Q8×C127—21no—
94C22⋊Q8×C127—21no—
95C4×Q8×C127—21no—
96C4×Q8×C127—21no—
97C4×Q8×C127—21no—
98C4×Q8×C127—21no—
99C4×Q8×C127C2311yescharacteristic
100C4×Q8×C127C2311yescharacteristic
101C4×Q8×C127C2311yescharacteristic
102C4×D4×C127—21no—
103C4×D4×C127—21no—
104C4×D4×C127C2311yescharacteristic
105#117×C127—21no—
106#117×C127—21no—
107#107×C127—21no—
108#107×C127—21no—
109#107×C127—41no—
110#107×C127D411yescharacteristic
111#106×C127—21no—
112#106×C127—21no—
113#106×C127—21no—
114#106×C127D411yescharacteristic
115C4⋊C8×C127—21no—
116C4⋊C8×C127—21no—
117C4⋊C8×C127—21no—
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#103×C127—21no—
128#103×C127D411yescharacteristic
129#103×C127D411yescharacteristic
130#103×C127D411yescharacteristic
131#102×C127—21no—
132#102×C127—21no—
133#102×C127—21no—
134#102×C127—21no—
135#102×C127—41no—
136#102×C127D411yescharacteristic
137C22⋊C8×C127—21no—
138#97×C127—21no—
139C4×C8×C127—21no—
140C4×C8×C127—21no—
141C4×C8×C127C2311yescharacteristic
142C4×C8×C127C2311yescharacteristic
143C4×C8×C127C2311yescharacteristic
144C2×Q8×C127—21no—
145C2×Q8×C127—21no—
146C2×Q8×C127—21no—
147C2×Q8×C127C2×D411yescharacteristic
148C2×Q8×C127C2×D411yescharacteristic
149C2×Q8×C127C2×D411yescharacteristic
150C2×D4×C127—21no—
151C2×D4×C127—21no—
152C2×D4×C127—21no—
153C2×D4×C127C2×D411yescharacteristic
154C22×C4×C127—21no—
155C22×C4×C127—41no—
156Q16×C127—41no—
157Q16×C127—42no—
158Q16×C127—81no—
159Q16×C127—81no—
160Q16×C127—81no—
161SD16×C127—22no—
162SD16×C127—42no—
163SD16×C127—42no—
164SD16×C127—81no—
165SD16×C127—81no—
166D8×C127—81no—
167C2×C8×C127—21no—
168C2×C8×C127—21no—
169C2×C8×C127—21no—
170C2×C8×C127—21no—
171C2×C8×C127—21no—
172C2×C8×C127—42no—
173C2×C8×C127C2×D411yescharacteristic
174C2×C8×C127C2×D411yescharacteristic
175C2×C8×C127C2×D411yescharacteristic
176C2×C8×C127C2×D411yescharacteristic
177C4⋊C4×C127—21no—
178C4⋊C4×C127—21no—
179C4⋊C4×C127—21no—
180C4⋊C4×C127—21no—
181C4⋊C4×C127—21no—
182C4⋊C4×C127—21no—
183C4⋊C4×C127—21no—
184C4⋊C4×C127—21no—
185C4⋊C4×C127—21no—
186C4⋊C4×C127—41no—
187C4⋊C4×C127—41no—
188C4⋊C4×C127—41no—
189C4⋊C4×C127—41no—
190C4⋊C4×C127—41no—
191C4⋊C4×C127C2×D411yescharacteristic
192C4⋊C4×C127C2×D411yescharacteristic
193C4⋊C4×C127C2×D411yescharacteristic
194C4⋊C4×C127C2×D411yescharacteristic
195C22⋊C4×C127—21no—
196C22⋊C4×C127—41no—
197C22⋊C4×C127—41no—
198C22⋊C4×C127—41no—
199C22⋊C4×C127—41no—
200C22⋊C4×C127—41no—
201C22⋊C4×C127—41no—
202C22⋊C4×C127—41no—
203C42×C127—21no—
204C42×C127—21no—
205C42×C127—21no—
206C42×C127—41no—
207C42×C127—41no—
208C42×C127—41no—
209C42×C127C2411yescharacteristic
210C23×C127—21no—
211C23×C127—41no—
212Q8×C127—21no—
213Q8×C127—21no—
214Q8×C127—21no—
215Q8×C127—21no—
216Q8×C127—21no—
217Q8×C127—21no—
218Q8×C127—41no—
219Q8×C127—41no—
220Q8×C127—41no—
221Q8×C127—41no—
222Q8×C127—41no—
223Q8×C127—41no—
224D4×C127—21no—
225D4×C127—21no—
226D4×C127—41no—
227D4×C127—41no—
228D4×C127—41no—
229D4×C127—41no—
230D4×C127—81no—
231C2×C4×C127—21no—
232C2×C4×C127—21no—
233C2×C4×C127—21no—
234C2×C4×C127—21no—
235C2×C4×C127—21no—
236C2×C4×C127—21no—
237C2×C4×C127—21no—
238C2×C4×C127—41no—
239C2×C4×C127—41no—
240C2×C4×C127—41no—
241C2×C4×C127—41no—
242C2×C4×C127—41no—
243C2×C4×C127—161no—
244C2×C4×C127C22×D411yescharacteristic
245C2×C4×C127C22×D411yescharacteristic
246C2×C4×C127H(5,𝔽2)11yescharacteristic
247C8×C127—21no—
248C8×C127—21no—
249C8×C127—21no—
250C8×C127—41no—
251C8×C127—41no—
252C8×C127—41no—
253C8×C127—41no—
254C8×C127—41no—
255C8×C127#13512yes—
256C22×C127—41no—
257C22×C127—41no—
258C22×C127—41no—
259C22×C127—81no—
260C22×C127—81no—
261C22×C127—81no—
262C22×C127D4211yescharacteristic
263C4×C127—21no—
264C4×C127—41no—
265C4×C127—41no—
266C4×C127—41no—
267C4×C127—41no—
268C4×C127—41no—
269C4×C127—41no—
270C4×C127—41no—
271C4×C127—81no—
272C4×C127—81no—
273C4×C127—81no—
274C4×C127C2×#13511yescharacteristic
275C4×C127#57511yescharacteristic
276C4×C127#57611yescharacteristic
277C4×C127#57811yescharacteristic
278#19872C12711yesmaximal, characteristic, direct product factor, Sylow
279C2×C127—81no—
280C2×C127—161no—
281C2×C127#326911yescharacteristic
282C2×C127#328711yescharacteristic
283C2×C127#328911yescharacteristic
284#3398C2×C12711yescharacteristic, complemented
285#3394C2×C12711yescharacteristic
286#3365C2×C12711yescharacteristic, complemented
287#3342C2×C12711yescharacteristic, complemented
288#1722C2×C12711yescharacteristic, complemented
289#1686C2×C12711yescharacteristic, complemented
290#1681C2×C12711yescharacteristic
291#1674C2×C12711yescharacteristic, complemented
292#1670C2×C12711yescharacteristic, complemented
293#1650C2×C12711yescharacteristic, complemented
294#1648C2×C12711yescharacteristic, complemented
295#1640C2×C12711yescharacteristic, complemented
296#1628C2×C12711yescharacteristic
297#1584C2×C12711yescharacteristic, complemented
298SD16⋊C8C2×C12711yescharacteristic, complemented
299C127#1987211yescharacteristic, direct product factor, Sylow
300#559C22×C12711yescharacteristic
301#557C22×C12711yescharacteristic
302#556C22×C12711yescharacteristic
303#556C22×C12711yescharacteristic
304#500C22×C12711yescharacteristic
305#500C22×C12711yescharacteristic
306#497—21no—
307#495—21no—
308#494C22×C12711yescharacteristic
309#492C22×C12711yescharacteristic
310#488—21no—
311#486C22×C12711yescharacteristic
312#486C22×C12711yescharacteristic
313#485—21no—
314#485—21no—
315#478—21no—
316#475C22×C12711yescharacteristic
317#475C22×C12711yescharacteristic
318#475C22×C12711yescharacteristic
319#467—21no—
320#464—21no—
321#464—21no—
322#464—21no—
323#463—21no—
324#462—21no—
325#462C22×C12711yescharacteristic
326#462C22×C12711yescharacteristic
327#461C22×C12711yescharacteristic
328#460C22×C12711yescharacteristic
329#459C22×C12711yescharacteristic
330#446C22×C12711yescharacteristic
331C8×Q8C22×C12711yescharacteristic
332C8×Q8C22×C12711yescharacteristic
333#441—21no—
334C4×Q16C22×C12711yescharacteristic
335C4×SD16—21no—
336C4×SD16—21no—
337C4×SD16C22×C12711yescharacteristic
338C8×D4C22×C12711yescharacteristic
339#427—21no—
340#335C22×C12711yescharacteristic
341#335C22×C12711yescharacteristic
342#332C22×C12711yescharacteristic
343#332C22×C12711yescharacteristic
344#332C22×C12711yescharacteristic
345#331C22×C12711yescharacteristic
346Q8⋊C8C22×C12711yescharacteristic
347Q8⋊C8C22×C12711yescharacteristic
348Q8⋊C8C22×C12711yescharacteristic
349D4⋊C8C22×C12711yescharacteristic
350#322C22×C12711yescharacteristic
351C2×Q16—21no—
352C2×Q16—21no—
353C2×Q16—21no—
354C2×Q16—21no—
355C2×Q16D4×C12711yescharacteristic
356C2×SD16—21no—
357C2×SD16—21no—
358C2×SD16—21no—
359C2×SD16—21no—
360C2×SD16D4×C12711yescharacteristic
361C2×D8—21no—
362C22×C8—21no—
363C4⋊Q8—21no—
364C4⋊Q8C23×C12711yescharacteristic
365C4⋊Q8C23×C12711yescharacteristic
366C4⋊Q8C23×C12711yescharacteristic
367#127C23×C12711yescharacteristic
368#126—41no—
369#126—41no—
370#125—21no—
371#125—41no—
372#124—21no—
373#124—21no—
374#124—21no—
375#124—21no—
376#123—41no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C4×Q8—21no—
380C4×Q8—21no—
381C4×Q8—21no—
382C4×Q8—21no—
383C4×Q8C23×C12711yescharacteristic
384C4×Q8C23×C12711yescharacteristic
385C4×Q8C23×C12711yescharacteristic
386C4×D4—21no—
387C4×D4—21no—
388C4×D4C23×C12711yescharacteristic
389#117—21no—
390#117—21no—
391#107—21no—
392#107—21no—
393#107—41no—
394#107D4×C12711yescharacteristic
395#106—21no—
396#106—21no—
397#106—21no—
398#106D4×C12711yescharacteristic
399C4⋊C8—21no—
400C4⋊C8—21no—
401C4⋊C8—21no—
402C4⋊C8C23×C12711yescharacteristic
403C4⋊C8C23×C12711yescharacteristic
404C4⋊C8C23×C12711yescharacteristic
405C4⋊C8C23×C12711yescharacteristic
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103D4×C12711yescharacteristic
413#103D4×C12711yescharacteristic
414#103D4×C12711yescharacteristic
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—41no—
420#102D4×C12711yescharacteristic
421C22⋊C8—21no—
422#97—21no—
423C4×C8—21no—
424C4×C8—21no—
425C4×C8C23×C12711yescharacteristic
426C4×C8C23×C12711yescharacteristic
427C4×C8C23×C12711yescharacteristic
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8C2×D4×C12711yescharacteristic
432C2×Q8C2×D4×C12711yescharacteristic
433C2×Q8C2×D4×C12711yescharacteristic
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4C2×D4×C12711yescharacteristic
438C22×C4—21no—
439C22×C4—41no—
440Q16—41no—
441Q16—42no—
442Q16—81no—
443Q16—81no—
444Q16—81no—
445SD16—22no—
446SD16—42no—
447SD16—42no—
448SD16—81no—
449SD16—81no—
450D8—81no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—42no—
457C2×C8C2×D4×C12711yescharacteristic
458C2×C8C2×D4×C12711yescharacteristic
459C2×C8C2×D4×C12711yescharacteristic
460C2×C8C2×D4×C12711yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4C2×D4×C12711yescharacteristic
476C4⋊C4C2×D4×C12711yescharacteristic
477C4⋊C4C2×D4×C12711yescharacteristic
478C4⋊C4C2×D4×C12711yescharacteristic
479C22⋊C4—21no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—41no—
491C42—41no—
492C42—41no—
493C42C24×C12711yescharacteristic
494C23—21no—
495C23—41no—
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—21no—
500Q8—21no—
501Q8—21no—
502Q8—41no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508D4—21no—
509D4—21no—
510D4—41no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—81no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—161no—
528C2×C4C22×D4×C12711yescharacteristic
529C2×C4C22×D4×C12711yescharacteristic
530C2×C4H(5,𝔽2)×C12711yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8#135×C12712yes—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22D42×C12711yescharacteristic
547C4—21no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—81no—
556C4—81no—
557C4—81no—
558C4C2×#135×C12711yescharacteristic
559C4#575×C12711yescharacteristic
560C4#576×C12711yescharacteristic
561C4#578×C12711yescharacteristic
562C2—81no—
563C2—161no—
564C2C127×#326911yescharacteristic
565C2C127×#328711yescharacteristic
566C2C127×#328911yescharacteristic
subgroupG/H
center, socleC22×C127D42
commutator, Frattini, cosocleC42C24×C127
prime radical#459×C127C22
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×#3398C2semidirect
3. C127×#3365C2semidirect
4. C127×#3342C2semidirect
5. C127×#1722C2semidirect
6. C127×#1686C2semidirect
8. C127×#1674C2semidirect
9. C127×#1670C2semidirect
10. C127×#1650C2semidirect
11. C127×#1648C2semidirect
12. C127×#1640C2semidirect
14. C127×#1584C2semidirect
15. C127×SD16⋊C8C2semidirect
278. #19872C127direct (N × H)
284. #3398C2×C127semidirect
286. #3365C2×C127semidirect
287. #3342C2×C127semidirect
288. #1722C2×C127semidirect
289. #1686C2×C127semidirect
291. #1674C2×C127semidirect
292. #1670C2×C127semidirect
293. #1650C2×C127semidirect
294. #1648C2×C127semidirect
295. #1640C2×C127semidirect
297. #1584C2×C127semidirect
298. SD16⋊C8C2×C127semidirect
299. C127#19872direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#33982
C127×#33942
C127×#33652
C127×#33422
C127×#17222
C127×#16862
C127×#16812
C127×#16742
C127×#16702
C127×#16502
C127×#16482
C127×#16402
C127×#16282
C127×#15842
C127×SD16⋊C82
#19872127