Finite Group Databasebeta

← C127×#19834 #44583507

Subgroups — C127×#19834 #44583507

Order 32512.

590 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3394C211yesmaximal, characteristic
2C127×#3365C211yesmaximal, characteristic, complemented
3C127×#3359C211yesmaximal, characteristic, complemented
4C127×#3328C211yesmaximal, characteristic, complemented
5C127×#1719C211yesmaximal, characteristic, complemented
6C127×#1701C211yesmaximal, characteristic
7C127×#1680C211yesmaximal, characteristic, complemented
8C127×#1680C211yesmaximal, characteristic, complemented
9C127×#1666C211yesmaximal, characteristic, complemented
10C127×#1650C211yesmaximal, characteristic, complemented
11C127×#1648C211yesmaximal, characteristic, complemented
12C127×#1640C211yesmaximal, characteristic, complemented
13C127×#1627C211yesmaximal, characteristic
14C127×#1583C211yesmaximal, characteristic, complemented
15C127×#1579C211yesmaximal, characteristic, complemented
16#559×C127C2211yescharacteristic
17#557×C127C2211yescharacteristic
18#556×C127C2211yescharacteristic
19D4×Q8×C127C2211yescharacteristic
20#500×C127C2211yescharacteristic
21#495×C127—21no—
22#492×C127C2211yescharacteristic
23#488×C127—21no—
24#487×C127—21no—
25#487×C127C2211yescharacteristic
26#487×C127C2211yescharacteristic
27#486×C127C2211yescharacteristic
28#486×C127C2211yescharacteristic
29#485×C127—21no—
30#478×C127—21no—
31#475×C127—21no—
32#475×C127C2211yescharacteristic
33#475×C127C2211yescharacteristic
34#475×C127C2211yescharacteristic
35#470×C127—21no—
36#464×C127—21no—
37#464×C127—21no—
38#463×C127—21no—
39#462×C127C2211yescharacteristic
40#462×C127C2211yescharacteristic
41#461×C127—21no—
42#461×C127C2211yescharacteristic
43#460×C127C2211yescharacteristic
44#459×C127C2211yescharacteristic
45#451×C127—21no—
46C8×Q8×C127C2211yescharacteristic
47C8×Q8×C127C2211yescharacteristic
48C8×Q8×C127C2211yescharacteristic
49C4×Q16×C127C2211yescharacteristic
50C4×SD16×C127—21no—
51C4×SD16×C127—21no—
52C4×SD16×C127—21no—
53C4×SD16×C127C2211yescharacteristic
54#436×C127C2211yescharacteristic
55#419×C127—21no—
56#334×C127C2211yescharacteristic
57#334×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
67C22×Q8×C127—21no—
68C2×Q16×C127—21no—
69C2×Q16×C127—21no—
70C2×Q16×C127D411yescharacteristic
71C2×SD16×C127—21no—
72C2×SD16×C127—21no—
73C2×SD16×C127—21no—
74C2×SD16×C127—21no—
75C2×SD16×C127D411yescharacteristic
76C2×D8×C127—21no—
77C2×M16×C127—21no—
78C4⋊Q8×C127—21no—
79C4⋊Q8×C127—21no—
80C4⋊Q8×C127C2311yescharacteristic
81C4⋊Q8×C127C2311yescharacteristic
82C4⋊Q8×C127C2311yescharacteristic
83#127×C127C2311yescharacteristic
84#126×C127—41no—
85#125×C127—21no—
86#125×C127—41no—
87#124×C127—21no—
88#124×C127—21no—
89#124×C127—21no—
90#123×C127—41no—
91C22⋊Q8×C127—21no—
92C22⋊Q8×C127—21no—
93C22⋊Q8×C127—41no—
94C4×Q8×C127—21no—
95C4×Q8×C127—21no—
96C4×Q8×C127—21no—
97C4×Q8×C127C2311yescharacteristic
98C4×Q8×C127C2311yescharacteristic
99C4×Q8×C127C2311yescharacteristic
100C4×D4×C127—21no—
101C4×D4×C127—21no—
102C4×D4×C127—21no—
103C4×D4×C127C2311yescharacteristic
104#117×C127—21no—
105#107×C127—41no—
106#107×C127D411yescharacteristic
107#106×C127—21no—
108#106×C127—21no—
109#106×C127—21no—
110#106×C127D411yescharacteristic
111C4⋊C8×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—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—
138C4×C8×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×C127—41no—
148C2×Q8×C127—42no—
149C2×Q8×C127—81no—
150C2×Q8×C127C2×D411yescharacteristic
151C2×Q8×C127C2×D411yescharacteristic
152C2×Q8×C127C2×D411yescharacteristic
153C2×D4×C127—21no—
154C2×D4×C127—21no—
155C2×D4×C127—21no—
156C2×D4×C127C2×D411yescharacteristic
157C22×C4×C127—21no—
158C22×C4×C127—41no—
159C22×C4×C127—41no—
160Q16×C127—22no—
161Q16×C127—81no—
162Q16×C127—81no—
163SD16×C127—41no—
164SD16×C127—42no—
165SD16×C127—42no—
166SD16×C127—42no—
167SD16×C127—81no—
168D8×C127—81no—
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×C127C2×D411yescharacteristic
176C2×C8×C127C2×D411yescharacteristic
177C2×C8×C127C2×D411yescharacteristic
178C2×C8×C127C2×D411yescharacteristic
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—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—41no—
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—21no—
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—41no—
218Q8×C127—41no—
219Q8×C127—41no—
220Q8×C127—41no—
221Q8×C127—41no—
222Q8×C127—41no—
223Q8×C127—82no—
224Q8×C127#13512yes—
225D4×C127—21no—
226D4×C127—21no—
227D4×C127—41no—
228D4×C127—41no—
229D4×C127—41no—
230D4×C127—41no—
231D4×C127—81no—
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—21no—
239C2×C4×C127—41no—
240C2×C4×C127—41no—
241C2×C4×C127—41no—
242C2×C4×C127—41no—
243C2×C4×C127—41no—
244C2×C4×C127—82no—
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—41no—
259C22×C127—41no—
260C22×C127—41no—
261C22×C127—81no—
262C22×C127—81no—
263C22×C127—81no—
264C22×C127D4211yescharacteristic
265C4×C127—22no—
266C4×C127—21no—
267C4×C127—41no—
268C4×C127—41no—
269C4×C127—41no—
270C4×C127—41no—
271C4×C127—41no—
272C4×C127—41no—
273C4×C127—81no—
274C4×C127—81no—
275C4×C127—81no—
276C4×C127C2×#13511yescharacteristic
277C4×C127#57511yescharacteristic
278C4×C127#57711yescharacteristic
279C4×C127#57711yescharacteristic
280#19834C12711yesmaximal, characteristic, direct product factor, Sylow
281C2×C127—81no—
282C2×C127—161no—
283C2×C127#327111yescharacteristic
284C2×C127#328211yescharacteristic
285C2×C127#328911yescharacteristic
286#3394C2×C12711yescharacteristic
287#3365C2×C12711yescharacteristic, complemented
288#3359C2×C12711yescharacteristic, complemented
289#3328C2×C12711yescharacteristic, complemented
290#1719C2×C12711yescharacteristic, complemented
291#1701C2×C12711yescharacteristic
292#1680C2×C12711yescharacteristic, complemented
293#1680C2×C12711yescharacteristic, complemented
294#1666C2×C12711yescharacteristic, complemented
295#1650C2×C12711yescharacteristic, complemented
296#1648C2×C12711yescharacteristic, complemented
297#1640C2×C12711yescharacteristic, complemented
298#1627C2×C12711yescharacteristic
299#1583C2×C12711yescharacteristic, complemented
300#1579C2×C12711yescharacteristic, complemented
301C127#1983411yescharacteristic, direct product factor, Sylow
302#559C22×C12711yescharacteristic
303#557C22×C12711yescharacteristic
304#556C22×C12711yescharacteristic
305D4×Q8C22×C12711yescharacteristic
306#500C22×C12711yescharacteristic
307#495—21no—
308#492C22×C12711yescharacteristic
309#488—21no—
310#487—21no—
311#487C22×C12711yescharacteristic
312#487C22×C12711yescharacteristic
313#486C22×C12711yescharacteristic
314#486C22×C12711yescharacteristic
315#485—21no—
316#478—21no—
317#475—21no—
318#475C22×C12711yescharacteristic
319#475C22×C12711yescharacteristic
320#475C22×C12711yescharacteristic
321#470—21no—
322#464—21no—
323#464—21no—
324#463—21no—
325#462C22×C12711yescharacteristic
326#462C22×C12711yescharacteristic
327#461—21no—
328#461C22×C12711yescharacteristic
329#460C22×C12711yescharacteristic
330#459C22×C12711yescharacteristic
331#451—21no—
332C8×Q8C22×C12711yescharacteristic
333C8×Q8C22×C12711yescharacteristic
334C8×Q8C22×C12711yescharacteristic
335C4×Q16C22×C12711yescharacteristic
336C4×SD16—21no—
337C4×SD16—21no—
338C4×SD16—21no—
339C4×SD16C22×C12711yescharacteristic
340#436C22×C12711yescharacteristic
341#419—21no—
342#334C22×C12711yescharacteristic
343#334C22×C12711yescharacteristic
344#332C22×C12711yescharacteristic
345#332C22×C12711yescharacteristic
346#332C22×C12711yescharacteristic
347#331C22×C12711yescharacteristic
348Q8⋊C8C22×C12711yescharacteristic
349Q8⋊C8C22×C12711yescharacteristic
350Q8⋊C8C22×C12711yescharacteristic
351D4⋊C8C22×C12711yescharacteristic
352#322C22×C12711yescharacteristic
353C22×Q8—21no—
354C2×Q16—21no—
355C2×Q16—21no—
356C2×Q16D4×C12711yescharacteristic
357C2×SD16—21no—
358C2×SD16—21no—
359C2×SD16—21no—
360C2×SD16—21no—
361C2×SD16D4×C12711yescharacteristic
362C2×D8—21no—
363C2×M16—21no—
364C4⋊Q8—21no—
365C4⋊Q8—21no—
366C4⋊Q8C23×C12711yescharacteristic
367C4⋊Q8C23×C12711yescharacteristic
368C4⋊Q8C23×C12711yescharacteristic
369#127C23×C12711yescharacteristic
370#126—41no—
371#125—21no—
372#125—41no—
373#124—21no—
374#124—21no—
375#124—21no—
376#123—41no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—41no—
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×D4—21no—
389C4×D4C23×C12711yescharacteristic
390#117—21no—
391#107—41no—
392#107D4×C12711yescharacteristic
393#106—21no—
394#106—21no—
395#106—21no—
396#106D4×C12711yescharacteristic
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8—21no—
400C4⋊C8C23×C12711yescharacteristic
401C4⋊C8C23×C12711yescharacteristic
402C4⋊C8C23×C12711yescharacteristic
403C4⋊C8C23×C12711yescharacteristic
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103D4×C12711yescharacteristic
415#103D4×C12711yescharacteristic
416#103D4×C12711yescharacteristic
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—41no—
422#102D4×C12711yescharacteristic
423C22⋊C8—21no—
424C4×C8—21no—
425C4×C8—21no—
426C4×C8—21no—
427C4×C8C23×C12711yescharacteristic
428C4×C8C23×C12711yescharacteristic
429C4×C8C23×C12711yescharacteristic
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—41no—
434C2×Q8—42no—
435C2×Q8—81no—
436C2×Q8C2×D4×C12711yescharacteristic
437C2×Q8C2×D4×C12711yescharacteristic
438C2×Q8C2×D4×C12711yescharacteristic
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4C2×D4×C12711yescharacteristic
443C22×C4—21no—
444C22×C4—41no—
445C22×C4—41no—
446Q16—22no—
447Q16—81no—
448Q16—81no—
449SD16—41no—
450SD16—42no—
451SD16—42no—
452SD16—42no—
453SD16—81no—
454D8—81no—
455M16—81no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8C2×D4×C12711yescharacteristic
462C2×C8C2×D4×C12711yescharacteristic
463C2×C8C2×D4×C12711yescharacteristic
464C2×C8C2×D4×C12711yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4C2×D4×C12711yescharacteristic
480C4⋊C4C2×D4×C12711yescharacteristic
481C4⋊C4C2×D4×C12711yescharacteristic
482C4⋊C4C2×D4×C12711yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—41no—
494C42—41no—
495C42C24×C12711yescharacteristic
496C23—21no—
497C23—41no—
498Q8—21no—
499Q8—21no—
500Q8—21no—
501Q8—21no—
502Q8—21no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—82no—
510Q8#135×C12712yes—
511D4—21no—
512D4—21no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—41no—
517D4—81no—
518C2×C4—21no—
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—82no—
531C2×C4—161no—
532C2×C4C22×D4×C12711yescharacteristic
533C2×C4C22×D4×C12711yescharacteristic
534C2×C4H(5,𝔽2)×C12711yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22D42×C12711yescharacteristic
551C4—22no—
552C4—21no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—81no—
560C4—81no—
561C4—81no—
562C4C2×#135×C12711yescharacteristic
563C4#575×C12711yescharacteristic
564C4#577×C12711yescharacteristic
565C4#577×C12711yescharacteristic
566C2—81no—
567C2—161no—
568C2C127×#327111yescharacteristic
569C2C127×#328211yescharacteristic
570C2C127×#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
2. C127×#3365C2semidirect
3. C127×#3359C2semidirect
4. C127×#3328C2semidirect
5. C127×#1719C2semidirect
7. C127×#1680C2semidirect
8. C127×#1680C2semidirect
9. C127×#1666C2semidirect
10. C127×#1650C2semidirect
11. C127×#1648C2semidirect
12. C127×#1640C2semidirect
14. C127×#1583C2semidirect
15. C127×#1579C2semidirect
280. #19834C127direct (N × H)
287. #3365C2×C127semidirect
288. #3359C2×C127semidirect
289. #3328C2×C127semidirect
290. #1719C2×C127semidirect
292. #1680C2×C127semidirect
293. #1680C2×C127semidirect
294. #1666C2×C127semidirect
295. #1650C2×C127semidirect
296. #1648C2×C127semidirect
297. #1640C2×C127semidirect
299. #1583C2×C127semidirect
300. #1579C2×C127semidirect
301. C127#19834direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#33942
C127×#33652
C127×#33592
C127×#33282
C127×#17192
C127×#17012
C127×#16802
C127×#16662
C127×#16502
C127×#16482
C127×#16402
C127×#16272
C127×#15832
C127×#15792
#19834127