Finite Group Databasebeta

← C127×#19840 #44583513

Subgroups — C127×#19840 #44583513

Order 32512.

600 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×#3366C211yesmaximal, characteristic
2C127×#3360C211yesmaximal, characteristic, complemented
3C127×#3338C211yesmaximal, characteristic, complemented
4C127×#3304C211yesmaximal, characteristic, complemented
5C127×#1719C211yesmaximal, characteristic, complemented
6C127×#1704C211yesmaximal, characteristic, complemented
7C127×#1681C211yesmaximal, characteristic, complemented
8C127×#1678C211yesmaximal, characteristic, complemented
9C127×#1675C211yesmaximal, characteristic, complemented
10C127×#1643C211yesmaximal, characteristic, complemented
11C127×#1638C211yesmaximal, characteristic, complemented
12C127×#1631C211yesmaximal, characteristic, complemented
13C127×#1622C211yesmaximal, characteristic, complemented
14C127×#1584C211yesmaximal, characteristic, complemented
15C127×#1580C211yesmaximal, characteristic, complemented
16#556×C127C2211yescharacteristic
17#554×C127C2211yescharacteristic
18#554×C127C2211yescharacteristic
19#550×C127C2211yescharacteristic
20#500×C127C2211yescharacteristic
21#492×C127C2211yescharacteristic
22#490×C127—21no—
23#488×C127—21no—
24#487×C127C2211yescharacteristic
25#487×C127C2211yescharacteristic
26#486×C127C2211yescharacteristic
27#486×C127C2211yescharacteristic
28#484×C127—21no—
29#484×C127—21no—
30#482×C127—21no—
31#479×C127—21no—
32#478×C127—21no—
33#477×C127C2211yescharacteristic
34#477×C127C2211yescharacteristic
35#476×C127C2211yescharacteristic
36#476×C127C2211yescharacteristic
37#475×C127C2211yescharacteristic
38#467×C127—21no—
39#465×C127—21no—
40#463×C127—21no—
41#461×C127C2211yescharacteristic
42#460×C127C2211yescharacteristic
43#459×C127—21no—
44#459×C127C2211yescharacteristic
45#452×C127—21no—
46#446×C127C2211yescharacteristic
47C8×Q8×C127C2211yescharacteristic
48#442×C127—21no—
49C4×Q16×C127C2211yescharacteristic
50C4×SD16×C127—21no—
51C4×D8×C127C2211yescharacteristic
52C8×D4×C127C2211yescharacteristic
53C8×D4×C127C2211yescharacteristic
54C2×#107×C127—21no—
55#416×C127—21no—
56#335×C127C2211yescharacteristic
57#334×C127C2211yescharacteristic
58#333×C127C2211yescharacteristic
59#333×C127C2211yescharacteristic
60#332×C127C2211yescharacteristic
61#331×C127C2211yescharacteristic
62Q8⋊C8×C127C2211yescharacteristic
63Q8⋊C8×C127C2211yescharacteristic
64D4⋊C8×C127C2211yescharacteristic
65D4⋊C8×C127C2211yescharacteristic
66#322×C127C2211yescharacteristic
67C2×#41×C127—21no—
68C2×Q16×C127D411yescharacteristic
69C2×SD16×C127—21no—
70C2×SD16×C127—21no—
71C2×SD16×C127—41no—
72C2×D8×C127—21no—
73C2×D8×C127D411yescharacteristic
74C22×C8×C127—21no—
75C22×C8×C127—21no—
76C4⋊Q8×C127C2311yescharacteristic
77C4⋊Q8×C127C2311yescharacteristic
78C4⋊Q8×C127C2311yescharacteristic
79#127×C127—21no—
80#127×C127C2311yescharacteristic
81#126×C127—41no—
82#125×C127—21no—
83#125×C127—21no—
84#124×C127—21no—
85C22⋊Q8×C127—21no—
86C22⋊Q8×C127—21no—
87C22⋊Q8×C127—21no—
88C22⋊Q8×C127—41no—
89C22⋊Q8×C127—41no—
90#121×C127—21no—
91#121×C127—41no—
92C4×Q8×C127—21no—
93C4×Q8×C127C2311yescharacteristic
94C4×Q8×C127C2311yescharacteristic
95C4×D4×C127—21no—
96C4×D4×C127—21no—
97C4×D4×C127—21no—
98C4×D4×C127C2311yescharacteristic
99C4×D4×C127C2311yescharacteristic
100#117×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×C127D411yescharacteristic
108#107×C127D411yescharacteristic
109#106×C127—21no—
110#106×C127—21no—
111#106×C127—21no—
112C4⋊C8×C127—21no—
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—41no—
125#103×C127D411yescharacteristic
126#103×C127D411yescharacteristic
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—
134#102×C127—21no—
135#102×C127D411yescharacteristic
136#102×C127D411yescharacteristic
137C22⋊C8×C127—21no—
138C22⋊C8×C127—21no—
139#97×C127—21no—
140C4×C8×C127—21no—
141C4×C8×C127C2311yescharacteristic
142C4×C8×C127C2311yescharacteristic
143C4×C8×C127C2311yescharacteristic
144#41×C127—42no—
145#41×C127—81no—
146C2×Q8×C127—21no—
147C2×Q8×C127—21no—
148C2×Q8×C127—21no—
149C2×Q8×C127C2×D411yescharacteristic
150C2×Q8×C127C2×D411yescharacteristic
151C2×D4×C127—21no—
152C2×D4×C127—21no—
153C2×D4×C127—21no—
154C2×D4×C127—41no—
155C2×D4×C127—41no—
156C2×D4×C127C2×D411yescharacteristic
157C2×D4×C127C2×D411yescharacteristic
158C22×C4×C127—21no—
159C22×C4×C127—21no—
160C22×C4×C127—41no—
161C22×C4×C127—41no—
162C22×C4×C127—41no—
163Q16×C127—41no—
164SD16×C127—42no—
165SD16×C127—81no—
166SD16×C127—82no—
167D8×C127—22no—
168D8×C127—42no—
169C2×C8×C127—21no—
170C2×C8×C127—21no—
171C2×C8×C127—21no—
172C2×C8×C127—21no—
173C2×C8×C127—21no—
174C2×C8×C127—42no—
175C2×C8×C127—81no—
176C2×C8×C127C2×D411yescharacteristic
177C2×C8×C127C2×D411yescharacteristic
178C2×C8×C127C2×D411yescharacteristic
179C2×C8×C127C2×D411yescharacteristic
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—21no—
187C4⋊C4×C127—21no—
188C4⋊C4×C127—41no—
189C4⋊C4×C127—41no—
190C4⋊C4×C127—41no—
191C4⋊C4×C127—41no—
192C4⋊C4×C127—41no—
193C4⋊C4×C127C2×D411yescharacteristic
194C4⋊C4×C127C2×D411yescharacteristic
195C4⋊C4×C127C2×D411yescharacteristic
196C4⋊C4×C127C2×D411yescharacteristic
197C22⋊C4×C127—21no—
198C22⋊C4×C127—21no—
199C22⋊C4×C127—41no—
200C22⋊C4×C127—41no—
201C22⋊C4×C127—41no—
202C22⋊C4×C127—41no—
203C22⋊C4×C127—41no—
204C42×C127—21no—
205C42×C127—21no—
206C42×C127—41no—
207C42×C127C2411yescharacteristic
208C23×C127—21no—
209C23×C127—21no—
210C23×C127—41no—
211Q8×C127—21no—
212Q8×C127—21no—
213Q8×C127—21no—
214Q8×C127—21no—
215Q8×C127—41no—
216Q8×C127—41no—
217Q8×C127—81no—
218Q8×C127—81no—
219D4×C127—21no—
220D4×C127—21no—
221D4×C127—21no—
222D4×C127—41no—
223D4×C127—41no—
224D4×C127—41no—
225D4×C127—41no—
226D4×C127—81no—
227D4×C127—82no—
228D4×C127—161no—
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—21no—
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—82no—
244C2×C4×C127—161no—
245C2×C4×C127—161no—
246C2×C4×C127C22×D411yescharacteristic
247C2×C4×C127C22×D411yescharacteristic
248C2×C4×C127H(5,𝔽2)11yescharacteristic
249C8×C127—21no—
250C8×C127—21no—
251C8×C127—21no—
252C8×C127—21no—
253C8×C127—41no—
254C8×C127—41no—
255C8×C127—41no—
256C8×C127—41no—
257C8×C127—41no—
258C22×C127—22no—
259C22×C127—41no—
260C22×C127—41no—
261C22×C127—41no—
262C22×C127—41no—
263C22×C127—41no—
264C22×C127—81no—
265C22×C127—81no—
266C22×C127—81no—
267C22×C127D4211yescharacteristic
268C4×C127—21no—
269C4×C127—41no—
270C4×C127—41no—
271C4×C127—41no—
272C4×C127—41no—
273C4×C127—41no—
274C4×C127—41no—
275C4×C127—81no—
276C4×C127—81no—
277C4×C127—81no—
278C4×C127C2×#13511yescharacteristic
279C4×C127#57511yescharacteristic
280C4×C127#57711yescharacteristic
281C4×C127#57811yescharacteristic
282#19840C12711yesmaximal, characteristic, direct product factor, Sylow
283C2×C127—42no—
284C2×C127—81no—
285C2×C127—161no—
286C2×C127#326711yescharacteristic
287C2×C127#328511yescharacteristic
288C2×C127#328811yescharacteristic
289#3366C2×C12711yescharacteristic
290#3360C2×C12711yescharacteristic, complemented
291#3338C2×C12711yescharacteristic, complemented
292#3304C2×C12711yescharacteristic, complemented
293#1719C2×C12711yescharacteristic, complemented
294#1704C2×C12711yescharacteristic, complemented
295#1681C2×C12711yescharacteristic, complemented
296#1678C2×C12711yescharacteristic, complemented
297#1675C2×C12711yescharacteristic, complemented
298#1643C2×C12711yescharacteristic, complemented
299#1638C2×C12711yescharacteristic, complemented
300#1631C2×C12711yescharacteristic, complemented
301#1622C2×C12711yescharacteristic, complemented
302#1584C2×C12711yescharacteristic, complemented
303#1580C2×C12711yescharacteristic, complemented
304C127#1984011yescharacteristic, direct product factor, Sylow
305#556C22×C12711yescharacteristic
306#554C22×C12711yescharacteristic
307#554C22×C12711yescharacteristic
308#550C22×C12711yescharacteristic
309#500C22×C12711yescharacteristic
310#492C22×C12711yescharacteristic
311#490—21no—
312#488—21no—
313#487C22×C12711yescharacteristic
314#487C22×C12711yescharacteristic
315#486C22×C12711yescharacteristic
316#486C22×C12711yescharacteristic
317#484—21no—
318#484—21no—
319#482—21no—
320#479—21no—
321#478—21no—
322#477C22×C12711yescharacteristic
323#477C22×C12711yescharacteristic
324#476C22×C12711yescharacteristic
325#476C22×C12711yescharacteristic
326#475C22×C12711yescharacteristic
327#467—21no—
328#465—21no—
329#463—21no—
330#461C22×C12711yescharacteristic
331#460C22×C12711yescharacteristic
332#459—21no—
333#459C22×C12711yescharacteristic
334#452—21no—
335#446C22×C12711yescharacteristic
336C8×Q8C22×C12711yescharacteristic
337#442—21no—
338C4×Q16C22×C12711yescharacteristic
339C4×SD16—21no—
340C4×D8C22×C12711yescharacteristic
341C8×D4C22×C12711yescharacteristic
342C8×D4C22×C12711yescharacteristic
343C2×#107—21no—
344#416—21no—
345#335C22×C12711yescharacteristic
346#334C22×C12711yescharacteristic
347#333C22×C12711yescharacteristic
348#333C22×C12711yescharacteristic
349#332C22×C12711yescharacteristic
350#331C22×C12711yescharacteristic
351Q8⋊C8C22×C12711yescharacteristic
352Q8⋊C8C22×C12711yescharacteristic
353D4⋊C8C22×C12711yescharacteristic
354D4⋊C8C22×C12711yescharacteristic
355#322C22×C12711yescharacteristic
356C2×#41—21no—
357C2×Q16D4×C12711yescharacteristic
358C2×SD16—21no—
359C2×SD16—21no—
360C2×SD16—41no—
361C2×D8—21no—
362C2×D8D4×C12711yescharacteristic
363C22×C8—21no—
364C22×C8—21no—
365C4⋊Q8C23×C12711yescharacteristic
366C4⋊Q8C23×C12711yescharacteristic
367C4⋊Q8C23×C12711yescharacteristic
368#127—21no—
369#127C23×C12711yescharacteristic
370#126—41no—
371#125—21no—
372#125—21no—
373#124—21no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376C22⋊Q8—21no—
377C22⋊Q8—41no—
378C22⋊Q8—41no—
379#121—21no—
380#121—41no—
381C4×Q8—21no—
382C4×Q8C23×C12711yescharacteristic
383C4×Q8C23×C12711yescharacteristic
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4C23×C12711yescharacteristic
388C4×D4C23×C12711yescharacteristic
389#117—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392#107—21no—
393#107—21no—
394#107—21no—
395#107—21no—
396#107D4×C12711yescharacteristic
397#107D4×C12711yescharacteristic
398#106—21no—
399#106—21no—
400#106—21no—
401C4⋊C8—21no—
402C4⋊C8—21no—
403C4⋊C8C23×C12711yescharacteristic
404C4⋊C8C23×C12711yescharacteristic
405C4⋊C8C23×C12711yescharacteristic
406C4⋊C8C23×C12711yescharacteristic
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—41no—
414#103D4×C12711yescharacteristic
415#103D4×C12711yescharacteristic
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102D4×C12711yescharacteristic
425#102D4×C12711yescharacteristic
426C22⋊C8—21no—
427C22⋊C8—21no—
428#97—21no—
429C4×C8—21no—
430C4×C8C23×C12711yescharacteristic
431C4×C8C23×C12711yescharacteristic
432C4×C8C23×C12711yescharacteristic
433#41—42no—
434#41—81no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8C2×D4×C12711yescharacteristic
439C2×Q8C2×D4×C12711yescharacteristic
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4C2×D4×C12711yescharacteristic
446C2×D4C2×D4×C12711yescharacteristic
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452Q16—41no—
453SD16—42no—
454SD16—81no—
455SD16—82no—
456D8—22no—
457D8—42no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—42no—
464C2×C8—81no—
465C2×C8C2×D4×C12711yescharacteristic
466C2×C8C2×D4×C12711yescharacteristic
467C2×C8C2×D4×C12711yescharacteristic
468C2×C8C2×D4×C12711yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4C2×D4×C12711yescharacteristic
483C4⋊C4C2×D4×C12711yescharacteristic
484C4⋊C4C2×D4×C12711yescharacteristic
485C4⋊C4C2×D4×C12711yescharacteristic
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C42—21no—
494C42—21no—
495C42—41no—
496C42C24×C12711yescharacteristic
497C23—21no—
498C23—21no—
499C23—41no—
500Q8—21no—
501Q8—21no—
502Q8—21no—
503Q8—21no—
504Q8—41no—
505Q8—41no—
506Q8—81no—
507Q8—81no—
508D4—21no—
509D4—21no—
510D4—21no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—81no—
516D4—82no—
517D4—161no—
518D4#135×C12712yes—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—82no—
533C2×C4—161no—
534C2×C4—161no—
535C2×C4C22×D4×C12711yescharacteristic
536C2×C4C22×D4×C12711yescharacteristic
537C2×C4H(5,𝔽2)×C12711yescharacteristic
538C8—21no—
539C8—21no—
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—41no—
547C22—22no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22D42×C12711yescharacteristic
557C4—21no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4C2×#135×C12711yescharacteristic
568C4#575×C12711yescharacteristic
569C4#577×C12711yescharacteristic
570C4#578×C12711yescharacteristic
571C2—42no—
572C2—81no—
573C2—161no—
574C2C127×#326711yescharacteristic
575C2C127×#328511yescharacteristic
576C2C127×#328811yescharacteristic
subgroupG/H
center, socleC22×C127D42
commutator, Frattini, cosocleC42C24×C127
prime radicalC127×#3366C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C127×#3360C2semidirect
3. C127×#3338C2semidirect
4. C127×#3304C2semidirect
5. C127×#1719C2semidirect
6. C127×#1704C2semidirect
7. C127×#1681C2semidirect
8. C127×#1678C2semidirect
9. C127×#1675C2semidirect
10. C127×#1643C2semidirect
11. C127×#1638C2semidirect
12. C127×#1631C2semidirect
13. C127×#1622C2semidirect
14. C127×#1584C2semidirect
15. C127×#1580C2semidirect
282. #19840C127direct (N × H)
290. #3360C2×C127semidirect
291. #3338C2×C127semidirect
292. #3304C2×C127semidirect
293. #1719C2×C127semidirect
294. #1704C2×C127semidirect
295. #1681C2×C127semidirect
296. #1678C2×C127semidirect
297. #1675C2×C127semidirect
298. #1643C2×C127semidirect
299. #1638C2×C127semidirect
300. #1631C2×C127semidirect
301. #1622C2×C127semidirect
302. #1584C2×C127semidirect
303. #1580C2×C127semidirect
304. C127#19840direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#33662
C127×#33602
C127×#33382
C127×#33042
C127×#17192
C127×#17042
C127×#16812
C127×#16782
C127×#16752
C127×#16432
C127×#16382
C127×#16312
C127×#16222
C127×#15842
C127×#15802
#19840127