Finite Group Databasebeta

← C127×#19221 #44582894

Subgroups — C127×#19221 #44582894

Order 32512.

606 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3248C211yesmaximal, characteristic, complemented
2C127×#3247C211yesmaximal, characteristic
3C127×#3167C211yesmaximal, characteristic, complemented
4C127×#2966C211yesmaximal, characteristic, complemented
5C127×#1704C211yesmaximal, characteristic, complemented
6C127×#1703C211yesmaximal, characteristic, complemented
7C127×#1702C211yesmaximal, characteristic, complemented
8C127×#1701C211yesmaximal, characteristic, complemented
9C127×#1672C211yesmaximal, characteristic, complemented
10C127×#1671C211yesmaximal, characteristic, complemented
11C127×#1666C211yesmaximal, characteristic, complemented
12C127×#1665C211yesmaximal, characteristic, complemented
13C2×#334×C127C211yesmaximal, characteristic, complemented
14C127×#1552C211yesmaximal, characteristic, complemented
15C127×#1551C211yesmaximal, characteristic, complemented
16#533×C127C2211yescharacteristic
17#532×C127C2211yescharacteristic
18#529×C127C2211yescharacteristic
19#498×C127C2211yescharacteristic
20#492×C127C2211yescharacteristic
21#487×C127C2211yescharacteristic
22#486×C127C2211yescharacteristic
23#479×C127—21no—
24#478×C127—21no—
25#477×C127C2211yescharacteristic
26#476×C127C2211yescharacteristic
27#475×C127C2211yescharacteristic
28#474×C127C2211yescharacteristic
29#467×C127—21no—
30#466×C127—21no—
31#465×C127—21no—
32#465×C127—21no—
33#465×C127—21no—
34#465×C127—21no—
35#464×C127—21no—
36#463×C127—21no—
37#462×C127C2211yescharacteristic
38#461×C127C2211yescharacteristic
39#460×C127C2211yescharacteristic
40#459×C127C2211yescharacteristic
41#446×C127C2211yescharacteristic
42C8×Q8×C127C2211yescharacteristic
43C4×SD16×C127—21no—
44C4×SD16×C127—21no—
45#436×C127C2211yescharacteristic
46#435×C127—21no—
47C8×D4×C127—21no—
48C8×D4×C127C2211yescharacteristic
49#433×C127—21no—
50#432×C127C2211yescharacteristic
51C2×C4⋊C8×C127C2211yescharacteristic
52C2×C4⋊C8×C127C2211yescharacteristic
53#405×C127—21no—
54C2×C4×C8×C127C2211yescharacteristic
55#334×C127C2211yescharacteristic
56#334×C127C2211yescharacteristic
57#334×C127C2211yescharacteristic
58#334×C127C2211yescharacteristic
59#333×C127C2211yescharacteristic
60#333×C127C2211yescharacteristic
61#332×C127C2211yescharacteristic
62#332×C127C2211yescharacteristic
63#332×C127C2211yescharacteristic
64#332×C127C2211yescharacteristic
65#331×C127C2211yescharacteristic
66#331×C127C2211yescharacteristic
67C2×#41×C127—21no—
68C2×Q16×C127—21no—
69C2×SD16×C127—21no—
70C2×SD16×C127—21no—
71C2×SD16×C127—21no—
72C2×SD16×C127—21no—
73C2×D8×C127—21no—
74C2×M16×C127—21no—
75C22×C8×C127—21no—
76C22×C8×C127—21no—
77C22×C8×C127—21no—
78C22×C8×C127D411yescharacteristic
79C22×C8×C127D411yescharacteristic
80C4⋊Q8×C127C2311yescharacteristic
81C4⋊Q8×C127C2311yescharacteristic
82C4⋊Q8×C127C2311yescharacteristic
83#127×C127C2311yescharacteristic
84#126×C127—21no—
85#125×C127—21no—
86#125×C127D411yescharacteristic
87#124×C127—21no—
88#124×C127D411yescharacteristic
89#123×C127—21no—
90C22⋊Q8×C127—21no—
91C22⋊Q8×C127—21no—
92C22⋊Q8×C127D411yescharacteristic
93#121×C127—21no—
94#121×C127—21no—
95#121×C127D411yescharacteristic
96C4×Q8×C127—21no—
97C4×Q8×C127—21no—
98C4×Q8×C127C2311yescharacteristic
99C4×D4×C127—21no—
100C4×D4×C127—21no—
101C4×D4×C127—21no—
102C4×D4×C127C2311yescharacteristic
103#117×C127—21no—
104#117×C127—21no—
105C2×C42×C127C2311yescharacteristic
106#107×C127—21no—
107#107×C127—21no—
108#106×C127—21no—
109#106×C127—21no—
110#106×C127—21no—
111#106×C127—21no—
112C4⋊C8×C127—21no—
113C4⋊C8×C127—21no—
114C4⋊C8×C127—21no—
115C4⋊C8×C127—21no—
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#103×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—
137#97×C127—21no—
138#97×C127—21no—
139C4×C8×C127—21no—
140C4×C8×C127D411yescharacteristic
141C4×C8×C127D411yescharacteristic
142C4×C8×C127C2311yescharacteristic
143C4×C8×C127C2311yescharacteristic
144#41×C127—82no—
145C2×Q8×C127—21no—
146C2×Q8×C127—21no—
147C2×Q8×C127—21no—
148C2×Q8×C127C2×D411yescharacteristic
149C2×D4×C127—21no—
150C2×D4×C127—21no—
151C2×D4×C127—21no—
152C2×D4×C127—21no—
153C2×D4×C127—41no—
154C2×D4×C127C2×D411yescharacteristic
155C22×C4×C127—21no—
156C22×C4×C127—41no—
157C22×C4×C127C2×D411yescharacteristic
158C22×C4×C127C2×D411yescharacteristic
159C22×C4×C127#4111yescharacteristic
160Q16×C127—81no—
161SD16×C127—42no—
162SD16×C127—42no—
163SD16×C127—81no—
164SD16×C127—81no—
165D8×C127—81no—
166M16×C127—42no—
167C2×C8×C127—22no—
168C2×C8×C127—21no—
169C2×C8×C127—21no—
170C2×C8×C127—21no—
171C2×C8×C127—21no—
172C2×C8×C127—21no—
173C2×C8×C127—21no—
174C2×C8×C127—41no—
175C2×C8×C127—42no—
176C2×C8×C127—81no—
177C2×C8×C127—81no—
178C2×C8×C127C2×D411yescharacteristic
179C2×C8×C127C2×D411yescharacteristic
180C2×C8×C127C2×D411yescharacteristic
181C2×C8×C127C2×D411yescharacteristic
182C4⋊C4×C127—21no—
183C4⋊C4×C127—21no—
184C4⋊C4×C127—21no—
185C4⋊C4×C127—21no—
186C4⋊C4×C127—21no—
187C4⋊C4×C127—21no—
188C4⋊C4×C127—21no—
189C4⋊C4×C127—21no—
190C4⋊C4×C127—21no—
191C4⋊C4×C127—21no—
192C4⋊C4×C127—41no—
193C4⋊C4×C127—41no—
194C4⋊C4×C127C2×D411yescharacteristic
195C4⋊C4×C127C2×D411yescharacteristic
196C22⋊C4×C127—21no—
197C22⋊C4×C127—21no—
198C22⋊C4×C127—21no—
199C22⋊C4×C127—21no—
200C22⋊C4×C127—21no—
201C22⋊C4×C127—41no—
202C22⋊C4×C127—41no—
203C22⋊C4×C127—41no—
204C42×C127—21no—
205C42×C127—41no—
206C42×C127C2×D411yescharacteristic
207C42×C127C2×D411yescharacteristic
208C42×C127#4111yescharacteristic
209C42×C127C2411yescharacteristic
210C23×C127—21no—
211C23×C127—41no—
212C23×C127#12111yescharacteristic
213Q8×C127—21no—
214Q8×C127—21no—
215Q8×C127—41no—
216Q8×C127—41no—
217Q8×C127—41no—
218Q8×C127—41no—
219Q8×C127—81no—
220D4×C127—21no—
221D4×C127—21no—
222D4×C127—42no—
223D4×C127—41no—
224D4×C127—41no—
225D4×C127—41no—
226D4×C127—41no—
227D4×C127—81no—
228D4×C127—82no—
229C2×C4×C127—22no—
230C2×C4×C127—21no—
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—41no—
238C2×C4×C127—41no—
239C2×C4×C127—41no—
240C2×C4×C127—41no—
241C2×C4×C127—41no—
242C2×C4×C127—82no—
243C2×C4×C127#12111yescharacteristic
244C2×C4×C127#12111yescharacteristic
245C2×C4×C127#12111yescharacteristic
246C2×C4×C127C22×D411yescharacteristic
247C2×C4×C127C22×D411yescharacteristic
248C2×C4×C127C2×#4111yescharacteristic
249C8×C127—21no—
250C8×C127—21no—
251C8×C127—21no—
252C8×C127—41no—
253C8×C127—41no—
254C8×C127—41no—
255C8×C127—41no—
256C8×C127—41no—
257C8×C127—41no—
258C8×C127#13512yes—
259C22×C127—21no—
260C22×C127—21no—
261C22×C127—41no—
262C22×C127—41no—
263C22×C127—41no—
264C22×C127—81no—
265C22×C127—81no—
266C22×C127—81no—
267C22×C127#47112yes—
268C22×C127C2×#12111yescharacteristic
269C4×C127—21no—
270C4×C127—21no—
271C4×C127—21no—
272C4×C127—21no—
273C4×C127—41no—
274C4×C127—41no—
275C4×C127—41no—
276C4×C127—81no—
277C4×C127—81no—
278C4×C127—81no—
279C4×C127C2×#13511yescharacteristic
280C4×C127#57511yescharacteristic
281C4×C127#57711yescharacteristic
282C4×C127#57711yescharacteristic
283#19221C12711yesmaximal, characteristic, direct product factor, Sylow
284C2×C127—22no—
285C2×C127—81no—
286C2×C127—161no—
287C2×C127#303511yescharacteristic
288C2×C127#306011yescharacteristic
289C2×C127C2×#47111yescharacteristic
290#3248C2×C12711yescharacteristic, complemented
291#3247C2×C12711yescharacteristic
292#3167C2×C12711yescharacteristic, complemented
293#2966C2×C12711yescharacteristic, complemented
294#1704C2×C12711yescharacteristic, complemented
295#1703C2×C12711yescharacteristic, complemented
296#1702C2×C12711yescharacteristic, complemented
297#1701C2×C12711yescharacteristic, complemented
298#1672C2×C12711yescharacteristic, complemented
299#1671C2×C12711yescharacteristic, complemented
300#1666C2×C12711yescharacteristic, complemented
301#1665C2×C12711yescharacteristic, complemented
302C2×#334C2×C12711yescharacteristic, complemented
303#1552C2×C12711yescharacteristic, complemented
304#1551C2×C12711yescharacteristic, complemented
305C127#1922111yescharacteristic, direct product factor, Sylow
306#533C22×C12711yescharacteristic
307#532C22×C12711yescharacteristic
308#529C22×C12711yescharacteristic
309#498C22×C12711yescharacteristic
310#492C22×C12711yescharacteristic
311#487C22×C12711yescharacteristic
312#486C22×C12711yescharacteristic
313#479—21no—
314#478—21no—
315#477C22×C12711yescharacteristic
316#476C22×C12711yescharacteristic
317#475C22×C12711yescharacteristic
318#474C22×C12711yescharacteristic
319#467—21no—
320#466—21no—
321#465—21no—
322#465—21no—
323#465—21no—
324#465—21no—
325#464—21no—
326#463—21no—
327#462C22×C12711yescharacteristic
328#461C22×C12711yescharacteristic
329#460C22×C12711yescharacteristic
330#459C22×C12711yescharacteristic
331#446C22×C12711yescharacteristic
332C8×Q8C22×C12711yescharacteristic
333C4×SD16—21no—
334C4×SD16—21no—
335#436C22×C12711yescharacteristic
336#435—21no—
337C8×D4—21no—
338C8×D4C22×C12711yescharacteristic
339#433—21no—
340#432C22×C12711yescharacteristic
341C2×C4⋊C8C22×C12711yescharacteristic
342C2×C4⋊C8C22×C12711yescharacteristic
343#405—21no—
344C2×C4×C8C22×C12711yescharacteristic
345#334C22×C12711yescharacteristic
346#334C22×C12711yescharacteristic
347#334C22×C12711yescharacteristic
348#334C22×C12711yescharacteristic
349#333C22×C12711yescharacteristic
350#333C22×C12711yescharacteristic
351#332C22×C12711yescharacteristic
352#332C22×C12711yescharacteristic
353#332C22×C12711yescharacteristic
354#332C22×C12711yescharacteristic
355#331C22×C12711yescharacteristic
356#331C22×C12711yescharacteristic
357C2×#41—21no—
358C2×Q16—21no—
359C2×SD16—21no—
360C2×SD16—21no—
361C2×SD16—21no—
362C2×SD16—21no—
363C2×D8—21no—
364C2×M16—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8D4×C12711yescharacteristic
369C22×C8D4×C12711yescharacteristic
370C4⋊Q8C23×C12711yescharacteristic
371C4⋊Q8C23×C12711yescharacteristic
372C4⋊Q8C23×C12711yescharacteristic
373#127C23×C12711yescharacteristic
374#126—21no—
375#125—21no—
376#125D4×C12711yescharacteristic
377#124—21no—
378#124D4×C12711yescharacteristic
379#123—21no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382C22⋊Q8D4×C12711yescharacteristic
383#121—21no—
384#121—21no—
385#121D4×C12711yescharacteristic
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8C23×C12711yescharacteristic
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4C23×C12711yescharacteristic
393#117—21no—
394#117—21no—
395C2×C42C23×C12711yescharacteristic
396#107—21no—
397#107—21no—
398#106—21no—
399#106—21no—
400#106—21no—
401#106—21no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8C23×C12711yescharacteristic
407C4⋊C8C23×C12711yescharacteristic
408C4⋊C8C23×C12711yescharacteristic
409C4⋊C8C23×C12711yescharacteristic
410C4⋊C8C23×C12711yescharacteristic
411C4⋊C8C23×C12711yescharacteristic
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424C22⋊C8—21no—
425C22⋊C8—21no—
426C22⋊C8—21no—
427#97—21no—
428#97—21no—
429C4×C8—21no—
430C4×C8D4×C12711yescharacteristic
431C4×C8D4×C12711yescharacteristic
432C4×C8C23×C12711yescharacteristic
433C4×C8C23×C12711yescharacteristic
434#41—82no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8C2×D4×C12711yescharacteristic
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—41no—
444C2×D4C2×D4×C12711yescharacteristic
445C22×C4—21no—
446C22×C4—41no—
447C22×C4C2×D4×C12711yescharacteristic
448C22×C4C2×D4×C12711yescharacteristic
449C22×C4#41×C12711yescharacteristic
450Q16—81no—
451SD16—42no—
452SD16—42no—
453SD16—81no—
454SD16—81no—
455D8—81no—
456M16—42no—
457C2×C8—22no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—41no—
465C2×C8—42no—
466C2×C8—81no—
467C2×C8—81no—
468C2×C8C2×D4×C12711yescharacteristic
469C2×C8C2×D4×C12711yescharacteristic
470C2×C8C2×D4×C12711yescharacteristic
471C2×C8C2×D4×C12711yescharacteristic
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4C2×D4×C12711yescharacteristic
485C4⋊C4C2×D4×C12711yescharacteristic
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C42—21no—
495C42—41no—
496C42C2×D4×C12711yescharacteristic
497C42C2×D4×C12711yescharacteristic
498C42#41×C12711yescharacteristic
499C42C24×C12711yescharacteristic
500C23—21no—
501C23—41no—
502C23#121×C12711yescharacteristic
503Q8—21no—
504Q8—21no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—81no—
510D4—21no—
511D4—21no—
512D4—42no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—41no—
517D4—81no—
518D4—82no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—82no—
533C2×C4#121×C12711yescharacteristic
534C2×C4#121×C12711yescharacteristic
535C2×C4#121×C12711yescharacteristic
536C2×C4C22×D4×C12711yescharacteristic
537C2×C4C22×D4×C12711yescharacteristic
538C2×C4C2×#41×C12711yescharacteristic
539C8—21no—
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8—41no—
548C8#135×C12712yes—
549C22—21no—
550C22—21no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22#471×C12712yes—
558C22C2×#121×C12711yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—81no—
567C4—81no—
568C4—81no—
569C4C2×#135×C12711yescharacteristic
570C4#575×C12711yescharacteristic
571C4#577×C12711yescharacteristic
572C4#577×C12711yescharacteristic
573C2—22no—
574C2—81no—
575C2—161no—
576C2C127×#303511yescharacteristic
577C2C127×#306011yescharacteristic
578C2C2×#471×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#121
commutator, Frattini, cosocleC42C24×C127
prime radicalC127×#3247C2
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×#3248C2semidirect
3. C127×#3167C2semidirect
4. C127×#2966C2semidirect
5. C127×#1704C2semidirect
6. C127×#1703C2semidirect
7. C127×#1702C2semidirect
8. C127×#1701C2semidirect
9. C127×#1672C2semidirect
10. C127×#1671C2semidirect
11. C127×#1666C2semidirect
12. C127×#1665C2semidirect
13. C2×#334×C127C2semidirect
14. C127×#1552C2semidirect
15. C127×#1551C2semidirect
283. #19221C127direct (N × H)
290. #3248C2×C127semidirect
292. #3167C2×C127semidirect
293. #2966C2×C127semidirect
294. #1704C2×C127semidirect
295. #1703C2×C127semidirect
296. #1702C2×C127semidirect
297. #1701C2×C127semidirect
298. #1672C2×C127semidirect
299. #1671C2×C127semidirect
300. #1666C2×C127semidirect
301. #1665C2×C127semidirect
302. C2×#334C2×C127semidirect
303. #1552C2×C127semidirect
304. #1551C2×C127semidirect
305. C127#19221direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32482
C127×#32472
C127×#31672
C127×#29662
C127×#17042
C127×#17032
C127×#17022
C127×#17012
C127×#16722
C127×#16712
C127×#16662
C127×#16652
C2×#334×C1272
C127×#15522
C127×#15512
#19221127