Finite Group Databasebeta

← C127×#19778 #44583451

Subgroups — C127×#19778 #44583451

Order 32512.

606 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3360C211yesmaximal, characteristic, complemented
2C127×#3334C211yesmaximal, characteristic
3C127×#3331C211yesmaximal, characteristic, complemented
4C127×#3302C211yesmaximal, characteristic, complemented
5C127×#1718C211yesmaximal, characteristic, complemented
6C127×#1699C211yesmaximal, characteristic, complemented
7C127×#1683C211yesmaximal, characteristic, complemented
8C127×#1683C211yesmaximal, characteristic, complemented
9C127×#1674C211yesmaximal, characteristic, complemented
10C127×#1654C211yesmaximal, characteristic, complemented
11C127×#1652C211yesmaximal, characteristic, complemented
12C127×#1644C211yesmaximal, characteristic, complemented
13C127×#1635C211yesmaximal, characteristic, complemented
14C127×#1581C211yesmaximal, characteristic, complemented
15C127×SD16⋊C8C211yesmaximal, characteristic, complemented
16#556×C127C2211yescharacteristic
17#554×C127C2211yescharacteristic
18#547×C127C2211yescharacteristic
19#547×C127C2211yescharacteristic
20#500×C127C2211yescharacteristic
21#498×C127C2211yescharacteristic
22#488×C127—21no—
23#487×C127C2211yescharacteristic
24#487×C127C2211yescharacteristic
25#487×C127C2211yescharacteristic
26#487×C127C2211yescharacteristic
27#485×C127—21no—
28#483×C127—21no—
29#480×C127—21no—
30#480×C127—21no—
31#479×C127—21no—
32#476×C127C2211yescharacteristic
33#476×C127C2211yescharacteristic
34#474×C127C2211yescharacteristic
35#474×C127C2211yescharacteristic
36#474×C127C2211yescharacteristic
37#470×C127—21no—
38#467×C127—21no—
39#466×C127—21no—
40#463×C127—21no—
41#462×C127C2211yescharacteristic
42#462×C127C2211yescharacteristic
43#461×C127C2211yescharacteristic
44#452×C127—21no—
45#452×C127—21no—
46C8×Q8×C127C2211yescharacteristic
47C4×SD16×C127—21no—
48C4×SD16×C127C2211yescharacteristic
49C4×D8×C127C2211yescharacteristic
50#436×C127C2211yescharacteristic
51C8×D4×C127C2211yescharacteristic
52C8×D4×C127C2211yescharacteristic
53C2×#107×C127—21no—
54#417×C127—21no—
55#416×C127—21no—
56#335×C127C2211yescharacteristic
57#335×C127C2211yescharacteristic
58#333×C127C2211yescharacteristic
59#332×C127C2211yescharacteristic
60#332×C127C2211yescharacteristic
61#332×C127C2211yescharacteristic
62Q8⋊C8×C127C2211yescharacteristic
63D4⋊C8×C127C2211yescharacteristic
64D4⋊C8×C127C2211yescharacteristic
65D4⋊C8×C127C2211yescharacteristic
66#322×C127C2211yescharacteristic
67C2×#41×C127—21no—
68C2×#41×C127—21no—
69C2×Q16×C127—21no—
70C2×Q16×C127—21no—
71C2×SD16×C127—21no—
72C2×SD16×C127D411yescharacteristic
73C2×D8×C127D411yescharacteristic
74C2×M16×C127—21no—
75C22×C8×C127—21no—
76C22×C8×C127—21no—
77C4⋊Q8×C127C2311yescharacteristic
78C4⋊Q8×C127C2311yescharacteristic
79C4⋊Q8×C127C2311yescharacteristic
80C4⋊Q8×C127C2311yescharacteristic
81#126×C127—41no—
82#125×C127—21no—
83#124×C127—21no—
84#123×C127—41no—
85#123×C127—41no—
86C22⋊Q8×C127—21no—
87C22⋊Q8×C127—21no—
88C22⋊Q8×C127—21no—
89C22⋊Q8×C127—21no—
90C22⋊Q8×C127—41no—
91#121×C127—21no—
92#121×C127—21no—
93C4×Q8×C127—21no—
94C4×Q8×C127C2311yescharacteristic
95C4×D4×C127—21no—
96C4×D4×C127C2311yescharacteristic
97C4×D4×C127C2311yescharacteristic
98C4×D4×C127C2311yescharacteristic
99#117×C127—21no—
100C2×C4⋊C4×C127—21no—
101C2×C4⋊C4×C127—21no—
102C2×C4⋊C4×C127—21no—
103#107×C127—21no—
104#107×C127—21no—
105#107×C127—21no—
106#107×C127—21no—
107#107×C127—21no—
108#107×C127D411yescharacteristic
109#106×C127—21no—
110#106×C127—21no—
111#106×C127—41no—
112#106×C127D411yescharacteristic
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×C127—21no—
124#103×C127—21no—
125#103×C127—21no—
126#103×C127—21no—
127#103×C127—41no—
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×C127D411yescharacteristic
135#102×C127D411yescharacteristic
136#102×C127D411yescharacteristic
137C22⋊C8×C127—21no—
138C22⋊C8×C127—21no—
139C22⋊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×C127—21no—
151C2×Q8×C127—21no—
152C2×Q8×C127C2×D411yescharacteristic
153C2×D4×C127—41no—
154C2×D4×C127—41no—
155C2×D4×C127C2×D411yescharacteristic
156C2×D4×C127C2×D411yescharacteristic
157C2×D4×C127C2×D411yescharacteristic
158C22×C4×C127—21no—
159C22×C4×C127—21no—
160C22×C4×C127—21no—
161C22×C4×C127—41no—
162C22×C4×C127—41no—
163C22×C4×C127—41no—
164Q16×C127—81no—
165Q16×C127—81no—
166SD16×C127—22no—
167SD16×C127—42no—
168D8×C127—41no—
169M16×C127—81no—
170C2×C8×C127—21no—
171C2×C8×C127—21no—
172C2×C8×C127—21no—
173C2×C8×C127—21no—
174C2×C8×C127—21no—
175C2×C8×C127—42no—
176C2×C8×C127—81no—
177C2×C8×C127C2×D411yescharacteristic
178C2×C8×C127C2×D411yescharacteristic
179C2×C8×C127C2×D411yescharacteristic
180C2×C8×C127C2×D411yescharacteristic
181C4⋊C4×C127—21no—
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—41no—
191C4⋊C4×C127—41no—
192C4⋊C4×C127—41no—
193C4⋊C4×C127—41no—
194C4⋊C4×C127—41no—
195C4⋊C4×C127C2×D411yescharacteristic
196C4⋊C4×C127C2×D411yescharacteristic
197C4⋊C4×C127C2×D411yescharacteristic
198C4⋊C4×C127C2×D411yescharacteristic
199C22⋊C4×C127—21no—
200C22⋊C4×C127—21no—
201C22⋊C4×C127—21no—
202C22⋊C4×C127—41no—
203C22⋊C4×C127—41no—
204C22⋊C4×C127—41no—
205C22⋊C4×C127—41no—
206C22⋊C4×C127—41no—
207C42×C127—21no—
208C42×C127—41no—
209C42×C127C2411yescharacteristic
210C23×C127—21no—
211C23×C127—21no—
212C23×C127—21no—
213Q8×C127—21no—
214Q8×C127—21no—
215Q8×C127—41no—
216Q8×C127—41no—
217Q8×C127—41no—
218Q8×C127—41no—
219Q8×C127—41no—
220Q8×C127—41no—
221Q8×C127—81no—
222D4×C127—21no—
223D4×C127—21no—
224D4×C127—21no—
225D4×C127—21no—
226D4×C127—21no—
227D4×C127—82no—
228D4×C127—82no—
229D4×C127#13512yes—
230C2×C4×C127—21no—
231C2×C4×C127—21no—
232C2×C4×C127—21no—
233C2×C4×C127—21no—
234C2×C4×C127—21no—
235C2×C4×C127—41no—
236C2×C4×C127—41no—
237C2×C4×C127—41no—
238C2×C4×C127—41no—
239C2×C4×C127—41no—
240C2×C4×C127—41no—
241C2×C4×C127—41no—
242C2×C4×C127—41no—
243C2×C4×C127—41no—
244C2×C4×C127—41no—
245C2×C4×C127—82no—
246C2×C4×C127—82no—
247C2×C4×C127—161no—
248C2×C4×C127C22×D411yescharacteristic
249C2×C4×C127C22×D411yescharacteristic
250C2×C4×C127H(5,𝔽2)11yescharacteristic
251C8×C127—21no—
252C8×C127—21no—
253C8×C127—21no—
254C8×C127—21no—
255C8×C127—41no—
256C8×C127—41no—
257C8×C127—41no—
258C8×C127—41no—
259C8×C127—41no—
260C22×C127—22no—
261C22×C127—41no—
262C22×C127—41no—
263C22×C127—41no—
264C22×C127—41no—
265C22×C127—41no—
266C22×C127—41no—
267C22×C127—41no—
268C22×C127—41no—
269C22×C127D4211yescharacteristic
270C4×C127—21no—
271C4×C127—41no—
272C4×C127—41no—
273C4×C127—41no—
274C4×C127—41no—
275C4×C127—41no—
276C4×C127—81no—
277C4×C127—81no—
278C4×C127—81no—
279C4×C127—81no—
280C4×C127C2×#13511yescharacteristic
281C4×C127#57511yescharacteristic
282C4×C127#57611yescharacteristic
283C4×C127#57811yescharacteristic
284#19778C12711yesmaximal, characteristic, direct product factor, Sylow
285C2×C127—42no—
286C2×C127—81no—
287C2×C127—81no—
288C2×C127#326911yescharacteristic
289C2×C127#328011yescharacteristic
290C2×C127#328911yescharacteristic
291#3360C2×C12711yescharacteristic, complemented
292#3334C2×C12711yescharacteristic
293#3331C2×C12711yescharacteristic, complemented
294#3302C2×C12711yescharacteristic, complemented
295#1718C2×C12711yescharacteristic, complemented
296#1699C2×C12711yescharacteristic, complemented
297#1683C2×C12711yescharacteristic, complemented
298#1683C2×C12711yescharacteristic, complemented
299#1674C2×C12711yescharacteristic, complemented
300#1654C2×C12711yescharacteristic, complemented
301#1652C2×C12711yescharacteristic, complemented
302#1644C2×C12711yescharacteristic, complemented
303#1635C2×C12711yescharacteristic, complemented
304#1581C2×C12711yescharacteristic, complemented
305SD16⋊C8C2×C12711yescharacteristic, complemented
306C127#1977811yescharacteristic, direct product factor, Sylow
307#556C22×C12711yescharacteristic
308#554C22×C12711yescharacteristic
309#547C22×C12711yescharacteristic
310#547C22×C12711yescharacteristic
311#500C22×C12711yescharacteristic
312#498C22×C12711yescharacteristic
313#488—21no—
314#487C22×C12711yescharacteristic
315#487C22×C12711yescharacteristic
316#487C22×C12711yescharacteristic
317#487C22×C12711yescharacteristic
318#485—21no—
319#483—21no—
320#480—21no—
321#480—21no—
322#479—21no—
323#476C22×C12711yescharacteristic
324#476C22×C12711yescharacteristic
325#474C22×C12711yescharacteristic
326#474C22×C12711yescharacteristic
327#474C22×C12711yescharacteristic
328#470—21no—
329#467—21no—
330#466—21no—
331#463—21no—
332#462C22×C12711yescharacteristic
333#462C22×C12711yescharacteristic
334#461C22×C12711yescharacteristic
335#452—21no—
336#452—21no—
337C8×Q8C22×C12711yescharacteristic
338C4×SD16—21no—
339C4×SD16C22×C12711yescharacteristic
340C4×D8C22×C12711yescharacteristic
341#436C22×C12711yescharacteristic
342C8×D4C22×C12711yescharacteristic
343C8×D4C22×C12711yescharacteristic
344C2×#107—21no—
345#417—21no—
346#416—21no—
347#335C22×C12711yescharacteristic
348#335C22×C12711yescharacteristic
349#333C22×C12711yescharacteristic
350#332C22×C12711yescharacteristic
351#332C22×C12711yescharacteristic
352#332C22×C12711yescharacteristic
353Q8⋊C8C22×C12711yescharacteristic
354D4⋊C8C22×C12711yescharacteristic
355D4⋊C8C22×C12711yescharacteristic
356D4⋊C8C22×C12711yescharacteristic
357#322C22×C12711yescharacteristic
358C2×#41—21no—
359C2×#41—21no—
360C2×Q16—21no—
361C2×Q16—21no—
362C2×SD16—21no—
363C2×SD16D4×C12711yescharacteristic
364C2×D8D4×C12711yescharacteristic
365C2×M16—21no—
366C22×C8—21no—
367C22×C8—21no—
368C4⋊Q8C23×C12711yescharacteristic
369C4⋊Q8C23×C12711yescharacteristic
370C4⋊Q8C23×C12711yescharacteristic
371C4⋊Q8C23×C12711yescharacteristic
372#126—41no—
373#125—21no—
374#124—21no—
375#123—41no—
376#123—41no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—21no—
380C22⋊Q8—21no—
381C22⋊Q8—41no—
382#121—21no—
383#121—21no—
384C4×Q8—21no—
385C4×Q8C23×C12711yescharacteristic
386C4×D4—21no—
387C4×D4C23×C12711yescharacteristic
388C4×D4C23×C12711yescharacteristic
389C4×D4C23×C12711yescharacteristic
390#117—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394#107—21no—
395#107—21no—
396#107—21no—
397#107—21no—
398#107—21no—
399#107D4×C12711yescharacteristic
400#106—21no—
401#106—21no—
402#106—41no—
403#106D4×C12711yescharacteristic
404C4⋊C8—21no—
405C4⋊C8C23×C12711yescharacteristic
406C4⋊C8C23×C12711yescharacteristic
407C4⋊C8C23×C12711yescharacteristic
408C4⋊C8C23×C12711yescharacteristic
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—41no—
419#103D4×C12711yescharacteristic
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102D4×C12711yescharacteristic
426#102D4×C12711yescharacteristic
427#102D4×C12711yescharacteristic
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C4×C8—21no—
432C4×C8C23×C12711yescharacteristic
433C4×C8C23×C12711yescharacteristic
434C4×C8C23×C12711yescharacteristic
435#41—42no—
436#41—42no—
437#41—81no—
438#41—81no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8C2×D4×C12711yescharacteristic
444C2×D4—41no—
445C2×D4—41no—
446C2×D4C2×D4×C12711yescharacteristic
447C2×D4C2×D4×C12711yescharacteristic
448C2×D4C2×D4×C12711yescharacteristic
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455Q16—81no—
456Q16—81no—
457SD16—22no—
458SD16—42no—
459D8—41no—
460M16—81no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—42no—
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—41no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4C2×D4×C12711yescharacteristic
487C4⋊C4C2×D4×C12711yescharacteristic
488C4⋊C4C2×D4×C12711yescharacteristic
489C4⋊C4C2×D4×C12711yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C42—21no—
499C42—41no—
500C42C24×C12711yescharacteristic
501C23—21no—
502C23—21no—
503C23—21no—
504Q8—21no—
505Q8—21no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—81no—
513D4—21no—
514D4—21no—
515D4—21no—
516D4—21no—
517D4—21no—
518D4—82no—
519D4—82no—
520D4#135×C12712yes—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—82no—
537C2×C4—82no—
538C2×C4—161no—
539C2×C4C22×D4×C12711yescharacteristic
540C2×C4C22×D4×C12711yescharacteristic
541C2×C4H(5,𝔽2)×C12711yescharacteristic
542C8—21no—
543C8—21no—
544C8—21no—
545C8—21no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8—41no—
551C22—22no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22D42×C12711yescharacteristic
561C4—21no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—81no—
571C4C2×#135×C12711yescharacteristic
572C4#575×C12711yescharacteristic
573C4#576×C12711yescharacteristic
574C4#578×C12711yescharacteristic
575C2—42no—
576C2—81no—
577C2—81no—
578C2C127×#326911yescharacteristic
579C2C127×#328011yescharacteristic
580C2C127×#328911yescharacteristic
subgroupG/H
center, socleC22×C127D42
commutator, Frattini, cosocleC42C24×C127
prime radicalC127×#3334C2
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×#3360C2semidirect
3. C127×#3331C2semidirect
4. C127×#3302C2semidirect
5. C127×#1718C2semidirect
6. C127×#1699C2semidirect
7. C127×#1683C2semidirect
8. C127×#1683C2semidirect
9. C127×#1674C2semidirect
10. C127×#1654C2semidirect
11. C127×#1652C2semidirect
12. C127×#1644C2semidirect
13. C127×#1635C2semidirect
14. C127×#1581C2semidirect
15. C127×SD16⋊C8C2semidirect
284. #19778C127direct (N × H)
291. #3360C2×C127semidirect
293. #3331C2×C127semidirect
294. #3302C2×C127semidirect
295. #1718C2×C127semidirect
296. #1699C2×C127semidirect
297. #1683C2×C127semidirect
298. #1683C2×C127semidirect
299. #1674C2×C127semidirect
300. #1654C2×C127semidirect
301. #1652C2×C127semidirect
302. #1644C2×C127semidirect
303. #1635C2×C127semidirect
304. #1581C2×C127semidirect
305. SD16⋊C8C2×C127semidirect
306. C127#19778direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#33602
C127×#33342
C127×#33312
C127×#33022
C127×#17182
C127×#16992
C127×#16832
C127×#16742
C127×#16542
C127×#16522
C127×#16442
C127×#16352
C127×#15812
C127×SD16⋊C82
#19778127