Finite Group Databasebeta

← C127×#19584 #44583257

Subgroups — C127×#19584 #44583257

Order 32512.

584 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3252C211yesmaximal, characteristic, complemented
2C127×#3228C211yesmaximal, characteristic, complemented
3C127×#3212C211yesmaximal, characteristic
4C127×#2994C211yesmaximal, characteristic, complemented
5C127×#1702C211yesmaximal, characteristic, complemented
6C127×#1697C211yesmaximal, characteristic, complemented
7C127×#1693C211yesmaximal, characteristic, complemented
8C127×#1692C211yesmaximal, characteristic, complemented
9C127×#1681C211yesmaximal, characteristic, complemented
10C127×#1678C211yesmaximal, characteristic, complemented
11C127×#1674C211yesmaximal, characteristic, complemented
12C127×#1671C211yesmaximal, characteristic, complemented
13C127×#1574C211yesmaximal, characteristic, complemented
14C127×#1547C211yesmaximal, characteristic, complemented
15C127×#1542C211yesmaximal, characteristic, complemented
16#533×C127C2211yescharacteristic
17#532×C127C2211yescharacteristic
18#529×C127C2211yescharacteristic
19#500×C127C2211yescharacteristic
20#498×C127C2211yescharacteristic
21#495×C127—21no—
22#488×C127—21no—
23#486×C127C2211yescharacteristic
24#486×C127C2211yescharacteristic
25#482×C127—21no—
26#482×C127—21no—
27#479×C127—21no—
28#478×C127—21no—
29#478×C127—21no—
30#477×C127C2211yescharacteristic
31#476×C127C2211yescharacteristic
32#470×C127—21no—
33#468×C127—21no—
34#464×C127—21no—
35#462×C127C2211yescharacteristic
36#462×C127C2211yescharacteristic
37#461×C127C2211yescharacteristic
38#461×C127C2211yescharacteristic
39#460×C127C2211yescharacteristic
40#459×C127C2211yescharacteristic
41#452×C127—21no—
42#449×C127—21no—
43#446×C127C2211yescharacteristic
44C8×Q8×C127C2211yescharacteristic
45#436×C127C2211yescharacteristic
46#435×C127—21no—
47C8×D4×C127—21no—
48C8×D4×C127C2211yescharacteristic
49#433×C127—21no—
50#431×C127C2211yescharacteristic
51#431×C127C2211yescharacteristic
52#424×C127—21no—
53#423×C127C2211yescharacteristic
54C2×C4⋊C8×C127C2211yescharacteristic
55#335×C127C2211yescharacteristic
56#335×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×Q16×C127—21no—
70C2×SD16×C127—21no—
71C2×SD16×C127—21no—
72C2×SD16×C127—21no—
73C2×D8×C127—21no—
74C2×M16×C127—21no—
75C2×M16×C127—21no—
76C22×C8×C127—21no—
77C22×C8×C127—21no—
78C4⋊Q8×C127C2311yescharacteristic
79C4⋊Q8×C127C2311yescharacteristic
80C4⋊Q8×C127C2311yescharacteristic
81#127×C127C2311yescharacteristic
82#126×C127—21no—
83#125×C127—21no—
84#125×C127D411yescharacteristic
85#124×C127—21no—
86#124×C127D411yescharacteristic
87#123×C127—21no—
88C22⋊Q8×C127—21no—
89C22⋊Q8×C127—21no—
90C22⋊Q8×C127D411yescharacteristic
91#121×C127—21no—
92#121×C127—21no—
93#121×C127D411yescharacteristic
94C4×Q8×C127—21no—
95C4×Q8×C127—21no—
96C4×Q8×C127C2311yescharacteristic
97C4×D4×C127—21no—
98C4×D4×C127—21no—
99C4×D4×C127—21no—
100C4×D4×C127C2311yescharacteristic
101#117×C127—21no—
102#117×C127—21no—
103C2×C42×C127C2311yescharacteristic
104#107×C127—21no—
105#107×C127—21no—
106#107×C127—21no—
107#106×C127—21no—
108#106×C127—21no—
109#106×C127—21no—
110C4⋊C8×C127—21no—
111C4⋊C8×C127—21no—
112C4⋊C8×C127—21no—
113C4⋊C8×C127—21no—
114C4⋊C8×C127D411yescharacteristic
115C4⋊C8×C127D411yescharacteristic
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#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—
134C22⋊C8×C127—21no—
135C22⋊C8×C127—21no—
136C22⋊C8×C127—21no—
137C22⋊C8×C127D411yescharacteristic
138C22⋊C8×C127D411yescharacteristic
139#97×C127—21no—
140C4×C8×C127—21no—
141C4×C8×C127—21no—
142C4×C8×C127C2311yescharacteristic
143C4×C8×C127C2311yescharacteristic
144#41×C127—81no—
145#41×C127—81no—
146C2×Q8×C127—21no—
147C2×Q8×C127—21no—
148C2×Q8×C127—21no—
149C2×Q8×C127C2×D411yescharacteristic
150C2×D4×C127—21no—
151C2×D4×C127—21no—
152C2×D4×C127—21no—
153C2×D4×C127—21no—
154C2×D4×C127—41no—
155C2×D4×C127C2×D411yescharacteristic
156C22×C4×C127—21no—
157C22×C4×C127—41no—
158C22×C4×C127C2×D411yescharacteristic
159C22×C4×C127C2×D411yescharacteristic
160C22×C4×C127#4111yescharacteristic
161Q16×C127—81no—
162Q16×C127—81no—
163SD16×C127—81no—
164SD16×C127—81no—
165SD16×C127—81no—
166D8×C127—81no—
167M16×C127—81no—
168M16×C127—81no—
169C2×C8×C127—21no—
170C2×C8×C127—21no—
171C2×C8×C127—21no—
172C2×C8×C127—21no—
173C2×C8×C127—21no—
174C2×C8×C127—21no—
175C2×C8×C127—81no—
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—21no—
191C4⋊C4×C127—41no—
192C4⋊C4×C127—41no—
193C4⋊C4×C127C2×D411yescharacteristic
194C4⋊C4×C127C2×D411yescharacteristic
195C22⋊C4×C127—21no—
196C22⋊C4×C127—21no—
197C22⋊C4×C127—21no—
198C22⋊C4×C127—21no—
199C22⋊C4×C127—21no—
200C22⋊C4×C127—41no—
201C22⋊C4×C127—41no—
202C22⋊C4×C127—41no—
203C42×C127—21no—
204C42×C127—41no—
205C42×C127C2×D411yescharacteristic
206C42×C127C2×D411yescharacteristic
207C42×C127#4111yescharacteristic
208C42×C127C2411yescharacteristic
209C23×C127—21no—
210C23×C127—41no—
211C23×C127#12111yescharacteristic
212Q8×C127—21no—
213Q8×C127—21no—
214Q8×C127—41no—
215Q8×C127—41no—
216Q8×C127—41no—
217Q8×C127—41no—
218Q8×C127—81no—
219D4×C127—21no—
220D4×C127—21no—
221D4×C127—42no—
222D4×C127—41no—
223D4×C127—41no—
224D4×C127—41no—
225D4×C127—41no—
226D4×C127—81no—
227D4×C127—82no—
228C2×C4×C127—21no—
229C2×C4×C127—21no—
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—82no—
242C2×C4×C127#12111yescharacteristic
243C2×C4×C127#12111yescharacteristic
244C2×C4×C127#12111yescharacteristic
245C2×C4×C127C22×D411yescharacteristic
246C2×C4×C127C22×D411yescharacteristic
247C2×C4×C127C2×#4111yescharacteristic
248C8×C127—21no—
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—
258C22×C127—21no—
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×C127C2×#12111yescharacteristic
268C4×C127—21no—
269C4×C127—21no—
270C4×C127—21no—
271C4×C127—21no—
272C4×C127—41no—
273C4×C127—41no—
274C4×C127—41no—
275C4×C127—81no—
276C4×C127—81no—
277C4×C127—81no—
278C4×C127#57611yescharacteristic
279C4×C127#57711yescharacteristic
280C4×C127#57711yescharacteristic
281C4×C127#57811yescharacteristic
282#19584C12711yesmaximal, characteristic, direct product factor, Sylow
283C2×C127—41no—
284C2×C127—81no—
285C2×C127—161no—
286C2×C127#304611yescharacteristic
287C2×C127#306211yescharacteristic
288C2×C127#306711yescharacteristic
289#3252C2×C12711yescharacteristic, complemented
290#3228C2×C12711yescharacteristic, complemented
291#3212C2×C12711yescharacteristic
292#2994C2×C12711yescharacteristic, complemented
293#1702C2×C12711yescharacteristic, complemented
294#1697C2×C12711yescharacteristic, complemented
295#1693C2×C12711yescharacteristic, complemented
296#1692C2×C12711yescharacteristic, complemented
297#1681C2×C12711yescharacteristic, complemented
298#1678C2×C12711yescharacteristic, complemented
299#1674C2×C12711yescharacteristic, complemented
300#1671C2×C12711yescharacteristic, complemented
301#1574C2×C12711yescharacteristic, complemented
302#1547C2×C12711yescharacteristic, complemented
303#1542C2×C12711yescharacteristic, complemented
304C127#1958411yescharacteristic, direct product factor, Sylow
305#533C22×C12711yescharacteristic
306#532C22×C12711yescharacteristic
307#529C22×C12711yescharacteristic
308#500C22×C12711yescharacteristic
309#498C22×C12711yescharacteristic
310#495—21no—
311#488—21no—
312#486C22×C12711yescharacteristic
313#486C22×C12711yescharacteristic
314#482—21no—
315#482—21no—
316#479—21no—
317#478—21no—
318#478—21no—
319#477C22×C12711yescharacteristic
320#476C22×C12711yescharacteristic
321#470—21no—
322#468—21no—
323#464—21no—
324#462C22×C12711yescharacteristic
325#462C22×C12711yescharacteristic
326#461C22×C12711yescharacteristic
327#461C22×C12711yescharacteristic
328#460C22×C12711yescharacteristic
329#459C22×C12711yescharacteristic
330#452—21no—
331#449—21no—
332#446C22×C12711yescharacteristic
333C8×Q8C22×C12711yescharacteristic
334#436C22×C12711yescharacteristic
335#435—21no—
336C8×D4—21no—
337C8×D4C22×C12711yescharacteristic
338#433—21no—
339#431C22×C12711yescharacteristic
340#431C22×C12711yescharacteristic
341#424—21no—
342#423C22×C12711yescharacteristic
343C2×C4⋊C8C22×C12711yescharacteristic
344#335C22×C12711yescharacteristic
345#335C22×C12711yescharacteristic
346#334C22×C12711yescharacteristic
347#334C22×C12711yescharacteristic
348#333C22×C12711yescharacteristic
349#333C22×C12711yescharacteristic
350#332C22×C12711yescharacteristic
351#332C22×C12711yescharacteristic
352#332C22×C12711yescharacteristic
353#332C22×C12711yescharacteristic
354#331C22×C12711yescharacteristic
355#331C22×C12711yescharacteristic
356C2×#41—21no—
357C2×Q16—21no—
358C2×Q16—21no—
359C2×SD16—21no—
360C2×SD16—21no—
361C2×SD16—21no—
362C2×D8—21no—
363C2×M16—21no—
364C2×M16—21no—
365C22×C8—21no—
366C22×C8—21no—
367C4⋊Q8C23×C12711yescharacteristic
368C4⋊Q8C23×C12711yescharacteristic
369C4⋊Q8C23×C12711yescharacteristic
370#127C23×C12711yescharacteristic
371#126—21no—
372#125—21no—
373#125D4×C12711yescharacteristic
374#124—21no—
375#124D4×C12711yescharacteristic
376#123—21no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8D4×C12711yescharacteristic
380#121—21no—
381#121—21no—
382#121D4×C12711yescharacteristic
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8C23×C12711yescharacteristic
386C4×D4—21no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4C23×C12711yescharacteristic
390#117—21no—
391#117—21no—
392C2×C42C23×C12711yescharacteristic
393#107—21no—
394#107—21no—
395#107—21no—
396#106—21no—
397#106—21no—
398#106—21no—
399C4⋊C8—21no—
400C4⋊C8—21no—
401C4⋊C8—21no—
402C4⋊C8—21no—
403C4⋊C8D4×C12711yescharacteristic
404C4⋊C8D4×C12711yescharacteristic
405C4⋊C8C23×C12711yescharacteristic
406C4⋊C8C23×C12711yescharacteristic
407C4⋊C8C23×C12711yescharacteristic
408C4⋊C8C23×C12711yescharacteristic
409C4⋊C8C23×C12711yescharacteristic
410C4⋊C8C23×C12711yescharacteristic
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423C22⋊C8—21no—
424C22⋊C8—21no—
425C22⋊C8—21no—
426C22⋊C8D4×C12711yescharacteristic
427C22⋊C8D4×C12711yescharacteristic
428#97—21no—
429C4×C8—21no—
430C4×C8—21no—
431C4×C8C23×C12711yescharacteristic
432C4×C8C23×C12711yescharacteristic
433#41—81no—
434#41—81no—
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—
451Q16—81no—
452SD16—81no—
453SD16—81no—
454SD16—81no—
455D8—81no—
456M16—81no—
457M16—81no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—81no—
465C2×C8—81no—
466C2×C8C2×D4×C12711yescharacteristic
467C2×C8C2×D4×C12711yescharacteristic
468C2×C8C2×D4×C12711yescharacteristic
469C2×C8C2×D4×C12711yescharacteristic
470C4⋊C4—21no—
471C4⋊C4—21no—
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—41no—
481C4⋊C4—41no—
482C4⋊C4C2×D4×C12711yescharacteristic
483C4⋊C4C2×D4×C12711yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C42—21no—
493C42—41no—
494C42C2×D4×C12711yescharacteristic
495C42C2×D4×C12711yescharacteristic
496C42#41×C12711yescharacteristic
497C42C24×C12711yescharacteristic
498C23—21no—
499C23—41no—
500C23#121×C12711yescharacteristic
501Q8—21no—
502Q8—21no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—81no—
508D4—21no—
509D4—21no—
510D4—42no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—81no—
516D4—82no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—82no—
531C2×C4#121×C12711yescharacteristic
532C2×C4#121×C12711yescharacteristic
533C2×C4#121×C12711yescharacteristic
534C2×C4C22×D4×C12711yescharacteristic
535C2×C4C22×D4×C12711yescharacteristic
536C2×C4C2×#41×C12711yescharacteristic
537C8—21no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—41no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22C2×#121×C12711yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4#576×C12711yescharacteristic
568C4#577×C12711yescharacteristic
569C4#577×C12711yescharacteristic
570C4#578×C12711yescharacteristic
571C2—41no—
572C2—81no—
573C2—161no—
574C2C127×#304611yescharacteristic
575C2C127×#306211yescharacteristic
576C2C127×#306711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#121
commutator, Frattini, cosocleC42C24×C127
prime radicalC127×#3212C2
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×#3252C2semidirect
2. C127×#3228C2semidirect
4. C127×#2994C2semidirect
5. C127×#1702C2semidirect
6. C127×#1697C2semidirect
7. C127×#1693C2semidirect
8. C127×#1692C2semidirect
9. C127×#1681C2semidirect
10. C127×#1678C2semidirect
11. C127×#1674C2semidirect
12. C127×#1671C2semidirect
13. C127×#1574C2semidirect
14. C127×#1547C2semidirect
15. C127×#1542C2semidirect
282. #19584C127direct (N × H)
289. #3252C2×C127semidirect
290. #3228C2×C127semidirect
292. #2994C2×C127semidirect
293. #1702C2×C127semidirect
294. #1697C2×C127semidirect
295. #1693C2×C127semidirect
296. #1692C2×C127semidirect
297. #1681C2×C127semidirect
298. #1678C2×C127semidirect
299. #1674C2×C127semidirect
300. #1671C2×C127semidirect
301. #1574C2×C127semidirect
302. #1547C2×C127semidirect
303. #1542C2×C127semidirect
304. C127#19584direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32522
C127×#32282
C127×#32122
C127×#29942
C127×#17022
C127×#16972
C127×#16932
C127×#16922
C127×#16812
C127×#16782
C127×#16742
C127×#16712
C127×#15742
C127×#15472
C127×#15422
#19584127