Finite Group Databasebeta

← C127×#19866 #44583539

Subgroups — C127×#19866 #44583539

Order 32512.

570 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3393C211yesmaximal, characteristic
2C127×#3360C211yesmaximal, characteristic
3C127×#3356C211yesmaximal, characteristic, complemented
4C127×#3342C211yesmaximal, characteristic, complemented
5C127×#1723C211yesmaximal, characteristic, complemented
6C127×#1693C211yesmaximal, characteristic, complemented
7C127×#1684C211yesmaximal, characteristic, complemented
8C127×#1671C211yesmaximal, characteristic, complemented
9C127×#1670C211yesmaximal, characteristic, complemented
10C127×#1650C211yesmaximal, characteristic, complemented
11C127×#1650C211yesmaximal, characteristic, complemented
12C127×#1643C211yesmaximal, characteristic, complemented
13C127×#1638C211yesmaximal, characteristic, complemented
14C127×#1581C211yesmaximal, characteristic
15C127×#1579C211yesmaximal, characteristic, complemented
16#556×C127C2211yescharacteristic
17#556×C127C2211yescharacteristic
18#556×C127C2211yescharacteristic
19#554×C127C2211yescharacteristic
20#500×C127C2211yescharacteristic
21#500×C127C2211yescharacteristic
22#498×C127C2211yescharacteristic
23#495×C127—21no—
24#494×C127C2211yescharacteristic
25#488×C127—21no—
26#487×C127C2211yescharacteristic
27#487×C127C2211yescharacteristic
28#485×C127—21no—
29#485×C127—21no—
30#485×C127—21no—
31#483×C127—21no—
32#479×C127—21no—
33#477×C127C2211yescharacteristic
34#476×C127C2211yescharacteristic
35#475×C127C2211yescharacteristic
36#475×C127C2211yescharacteristic
37#475×C127C2211yescharacteristic
38#470×C127—21no—
39#467×C127—21no—
40#464×C127—21no—
41#464×C127—21no—
42#463×C127—21no—
43#461×C127C2211yescharacteristic
44#461×C127C2211yescharacteristic
45#461×C127C2211yescharacteristic
46C8×Q8×C127C2211yescharacteristic
47C8×Q8×C127C2211yescharacteristic
48C4×Q16×C127—21no—
49C4×Q16×C127C2211yescharacteristic
50C4×SD16×C127—21no—
51C4×D8×C127C2211yescharacteristic
52#436×C127C2211yescharacteristic
53C8×D4×C127C2211yescharacteristic
54#428×C127—21no—
55#427×C127—21no—
56#335×C127C2211yescharacteristic
57#334×C127C2211yescharacteristic
58#333×C127C2211yescharacteristic
59#332×C127C2211yescharacteristic
60#332×C127C2211yescharacteristic
61#332×C127C2211yescharacteristic
62Q8⋊C8×C127C2211yescharacteristic
63Q8⋊C8×C127C2211yescharacteristic
64D4⋊C8×C127C2211yescharacteristic
65D4⋊C8×C127C2211yescharacteristic
66#322×C127C2211yescharacteristic
67C2×Q16×C127—21no—
68C2×Q16×C127—21no—
69C2×Q16×C127D411yescharacteristic
70C2×SD16×C127—21no—
71C2×SD16×C127—21no—
72C2×SD16×C127—21no—
73C2×D8×C127D411yescharacteristic
74C2×M16×C127—21no—
75C22×C8×C127—21no—
76C4⋊Q8×C127C2311yescharacteristic
77C4⋊Q8×C127C2311yescharacteristic
78C4⋊Q8×C127C2311yescharacteristic
79C4⋊Q8×C127C2311yescharacteristic
80#126×C127—41no—
81#126×C127—41no—
82#126×C127—41no—
83#125×C127—21no—
84#124×C127—21no—
85#124×C127—21no—
86#124×C127—21no—
87C22⋊Q8×C127—21no—
88C22⋊Q8×C127—21no—
89C22⋊Q8×C127—21no—
90C22⋊Q8×C127—21no—
91C22⋊Q8×C127—41no—
92C4×Q8×C127—21no—
93C4×Q8×C127—21no—
94C4×Q8×C127—21no—
95C4×Q8×C127C2311yescharacteristic
96C4×Q8×C127C2311yescharacteristic
97C4×D4×C127—21no—
98C4×D4×C127C2311yescharacteristic
99C4×D4×C127C2311yescharacteristic
100#117×C127—21no—
101#117×C127—21no—
102#117×C127—21no—
103C2×C4⋊C4×C127—21no—
104#107×C127—21no—
105#107×C127—21no—
106#107×C127—21no—
107#107×C127—41no—
108#107×C127D411yescharacteristic
109#107×C127D411yescharacteristic
110#106×C127—21no—
111#106×C127—21no—
112#106×C127—21no—
113#106×C127—21no—
114#106×C127—21no—
115#106×C127—21no—
116C4⋊C8×C127—21no—
117C4⋊C8×C127—21no—
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#103×C127—21no—
129#103×C127—21no—
130#103×C127—21no—
131#103×C127—41no—
132#103×C127D411yescharacteristic
133#103×C127D411yescharacteristic
134#102×C127—21no—
135#102×C127D411yescharacteristic
136#102×C127D411yescharacteristic
137C22⋊C8×C127—21no—
138C22⋊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—21no—
148C2×Q8×C127C2×D411yescharacteristic
149C2×Q8×C127C2×D411yescharacteristic
150C2×D4×C127C2×D411yescharacteristic
151C2×D4×C127C2×D411yescharacteristic
152C22×C4×C127—21no—
153C22×C4×C127—21no—
154C22×C4×C127—41no—
155Q16×C127—22no—
156Q16×C127—42no—
157Q16×C127—81no—
158SD16×C127—42no—
159SD16×C127—81no—
160SD16×C127—81no—
161D8×C127—41no—
162M16×C127—42no—
163C2×C8×C127—21no—
164C2×C8×C127—21no—
165C2×C8×C127—21no—
166C2×C8×C127—21no—
167C2×C8×C127—21no—
168C2×C8×C127—42no—
169C2×C8×C127C2×D411yescharacteristic
170C2×C8×C127C2×D411yescharacteristic
171C2×C8×C127C2×D411yescharacteristic
172C2×C8×C127C2×D411yescharacteristic
173C4⋊C4×C127—21no—
174C4⋊C4×C127—21no—
175C4⋊C4×C127—21no—
176C4⋊C4×C127—21no—
177C4⋊C4×C127—21no—
178C4⋊C4×C127—21no—
179C4⋊C4×C127—21no—
180C4⋊C4×C127—21no—
181C4⋊C4×C127—21no—
182C4⋊C4×C127—21no—
183C4⋊C4×C127—41no—
184C4⋊C4×C127—41no—
185C4⋊C4×C127—41no—
186C4⋊C4×C127—41no—
187C4⋊C4×C127—41no—
188C4⋊C4×C127C2×D411yescharacteristic
189C4⋊C4×C127C2×D411yescharacteristic
190C4⋊C4×C127C2×D411yescharacteristic
191C4⋊C4×C127C2×D411yescharacteristic
192C22⋊C4×C127—21no—
193C22⋊C4×C127—21no—
194C22⋊C4×C127—41no—
195C22⋊C4×C127—41no—
196C22⋊C4×C127—41no—
197C22⋊C4×C127—41no—
198C22⋊C4×C127—41no—
199C22⋊C4×C127—41no—
200C22⋊C4×C127—41no—
201C42×C127—21no—
202C42×C127—21no—
203C42×C127—41no—
204C42×C127—41no—
205C42×C127—41no—
206C42×C127C2411yescharacteristic
207C23×C127—21no—
208C23×C127—21no—
209Q8×C127—21no—
210Q8×C127—21no—
211Q8×C127—21no—
212Q8×C127—21no—
213Q8×C127—41no—
214Q8×C127—41no—
215Q8×C127—41no—
216Q8×C127—41no—
217Q8×C127—41no—
218Q8×C127—41no—
219Q8×C127—81no—
220D4×C127—21no—
221D4×C127—21no—
222D4×C127—21no—
223D4×C127—21no—
224C2×C4×C127—21no—
225C2×C4×C127—21no—
226C2×C4×C127—21no—
227C2×C4×C127—21no—
228C2×C4×C127—21no—
229C2×C4×C127—21no—
230C2×C4×C127—41no—
231C2×C4×C127—41no—
232C2×C4×C127—41no—
233C2×C4×C127—41no—
234C2×C4×C127—41no—
235C2×C4×C127—41no—
236C2×C4×C127—41no—
237C2×C4×C127—41no—
238C2×C4×C127—161no—
239C2×C4×C127C22×D411yescharacteristic
240C2×C4×C127C22×D411yescharacteristic
241C2×C4×C127H(5,𝔽2)11yescharacteristic
242C8×C127—21no—
243C8×C127—21no—
244C8×C127—21no—
245C8×C127—41no—
246C8×C127—41no—
247C8×C127—41no—
248C8×C127—41no—
249C8×C127—41no—
250C8×C127#13512yes—
251C22×C127—41no—
252C22×C127—41no—
253C22×C127—41no—
254C22×C127—41no—
255C22×C127—41no—
256C22×C127—41no—
257C22×C127D4211yescharacteristic
258C4×C127—21no—
259C4×C127—41no—
260C4×C127—41no—
261C4×C127—41no—
262C4×C127—41no—
263C4×C127—41no—
264C4×C127—41no—
265C4×C127—81no—
266C4×C127—81no—
267C4×C127—81no—
268C4×C127—81no—
269C4×C127C2×#13511yescharacteristic
270C4×C127#57511yescharacteristic
271C4×C127#57711yescharacteristic
272C4×C127#57811yescharacteristic
273#19866C12711yesmaximal, characteristic, direct product factor, Sylow
274C2×C127—81no—
275C2×C127—81no—
276C2×C127#327111yescharacteristic
277C2×C127#328311yescharacteristic
278C2×C127#328911yescharacteristic
279#3393C2×C12711yescharacteristic
280#3360C2×C12711yescharacteristic
281#3356C2×C12711yescharacteristic, complemented
282#3342C2×C12711yescharacteristic, complemented
283#1723C2×C12711yescharacteristic, complemented
284#1693C2×C12711yescharacteristic, complemented
285#1684C2×C12711yescharacteristic, complemented
286#1671C2×C12711yescharacteristic, complemented
287#1670C2×C12711yescharacteristic, complemented
288#1650C2×C12711yescharacteristic, complemented
289#1650C2×C12711yescharacteristic, complemented
290#1643C2×C12711yescharacteristic, complemented
291#1638C2×C12711yescharacteristic, complemented
292#1581C2×C12711yescharacteristic
293#1579C2×C12711yescharacteristic, complemented
294C127#1986611yescharacteristic, direct product factor, Sylow
295#556C22×C12711yescharacteristic
296#556C22×C12711yescharacteristic
297#556C22×C12711yescharacteristic
298#554C22×C12711yescharacteristic
299#500C22×C12711yescharacteristic
300#500C22×C12711yescharacteristic
301#498C22×C12711yescharacteristic
302#495—21no—
303#494C22×C12711yescharacteristic
304#488—21no—
305#487C22×C12711yescharacteristic
306#487C22×C12711yescharacteristic
307#485—21no—
308#485—21no—
309#485—21no—
310#483—21no—
311#479—21no—
312#477C22×C12711yescharacteristic
313#476C22×C12711yescharacteristic
314#475C22×C12711yescharacteristic
315#475C22×C12711yescharacteristic
316#475C22×C12711yescharacteristic
317#470—21no—
318#467—21no—
319#464—21no—
320#464—21no—
321#463—21no—
322#461C22×C12711yescharacteristic
323#461C22×C12711yescharacteristic
324#461C22×C12711yescharacteristic
325C8×Q8C22×C12711yescharacteristic
326C8×Q8C22×C12711yescharacteristic
327C4×Q16—21no—
328C4×Q16C22×C12711yescharacteristic
329C4×SD16—21no—
330C4×D8C22×C12711yescharacteristic
331#436C22×C12711yescharacteristic
332C8×D4C22×C12711yescharacteristic
333#428—21no—
334#427—21no—
335#335C22×C12711yescharacteristic
336#334C22×C12711yescharacteristic
337#333C22×C12711yescharacteristic
338#332C22×C12711yescharacteristic
339#332C22×C12711yescharacteristic
340#332C22×C12711yescharacteristic
341Q8⋊C8C22×C12711yescharacteristic
342Q8⋊C8C22×C12711yescharacteristic
343D4⋊C8C22×C12711yescharacteristic
344D4⋊C8C22×C12711yescharacteristic
345#322C22×C12711yescharacteristic
346C2×Q16—21no—
347C2×Q16—21no—
348C2×Q16D4×C12711yescharacteristic
349C2×SD16—21no—
350C2×SD16—21no—
351C2×SD16—21no—
352C2×D8D4×C12711yescharacteristic
353C2×M16—21no—
354C22×C8—21no—
355C4⋊Q8C23×C12711yescharacteristic
356C4⋊Q8C23×C12711yescharacteristic
357C4⋊Q8C23×C12711yescharacteristic
358C4⋊Q8C23×C12711yescharacteristic
359#126—41no—
360#126—41no—
361#126—41no—
362#125—21no—
363#124—21no—
364#124—21no—
365#124—21no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8—21no—
370C22⋊Q8—41no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8C23×C12711yescharacteristic
375C4×Q8C23×C12711yescharacteristic
376C4×D4—21no—
377C4×D4C23×C12711yescharacteristic
378C4×D4C23×C12711yescharacteristic
379#117—21no—
380#117—21no—
381#117—21no—
382C2×C4⋊C4—21no—
383#107—21no—
384#107—21no—
385#107—21no—
386#107—41no—
387#107D4×C12711yescharacteristic
388#107D4×C12711yescharacteristic
389#106—21no—
390#106—21no—
391#106—21no—
392#106—21no—
393#106—21no—
394#106—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8C23×C12711yescharacteristic
398C4⋊C8C23×C12711yescharacteristic
399C4⋊C8C23×C12711yescharacteristic
400C4⋊C8C23×C12711yescharacteristic
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—41no—
411#103D4×C12711yescharacteristic
412#103D4×C12711yescharacteristic
413#102—21no—
414#102D4×C12711yescharacteristic
415#102D4×C12711yescharacteristic
416C22⋊C8—21no—
417C22⋊C8—21no—
418C4×C8—21no—
419C4×C8—21no—
420C4×C8C23×C12711yescharacteristic
421C4×C8C23×C12711yescharacteristic
422C4×C8C23×C12711yescharacteristic
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8C2×D4×C12711yescharacteristic
428C2×Q8C2×D4×C12711yescharacteristic
429C2×D4C2×D4×C12711yescharacteristic
430C2×D4C2×D4×C12711yescharacteristic
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—41no—
434Q16—22no—
435Q16—42no—
436Q16—81no—
437SD16—42no—
438SD16—81no—
439SD16—81no—
440D8—41no—
441M16—42no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—42no—
448C2×C8C2×D4×C12711yescharacteristic
449C2×C8C2×D4×C12711yescharacteristic
450C2×C8C2×D4×C12711yescharacteristic
451C2×C8C2×D4×C12711yescharacteristic
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4C2×D4×C12711yescharacteristic
468C4⋊C4C2×D4×C12711yescharacteristic
469C4⋊C4C2×D4×C12711yescharacteristic
470C4⋊C4C2×D4×C12711yescharacteristic
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—41no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C42—21no—
481C42—21no—
482C42—41no—
483C42—41no—
484C42—41no—
485C42C24×C12711yescharacteristic
486C23—21no—
487C23—21no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—81no—
499D4—21no—
500D4—21no—
501D4—21no—
502D4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—161no—
518C2×C4C22×D4×C12711yescharacteristic
519C2×C4C22×D4×C12711yescharacteristic
520C2×C4H(5,𝔽2)×C12711yescharacteristic
521C8—21no—
522C8—21no—
523C8—21no—
524C8—41no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8#135×C12712yes—
530C22—41no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22—41no—
535C22—41no—
536C22D42×C12711yescharacteristic
537C4—21no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—41no—
544C4—81no—
545C4—81no—
546C4—81no—
547C4—81no—
548C4C2×#135×C12711yescharacteristic
549C4#575×C12711yescharacteristic
550C4#577×C12711yescharacteristic
551C4#578×C12711yescharacteristic
552C2—81no—
553C2—81no—
554C2C127×#327111yescharacteristic
555C2C127×#328311yescharacteristic
556C2C127×#328911yescharacteristic
subgroupG/H
center, socleC22×C127D42
commutator, Frattini, cosocleC42C24×C127
prime radicalC2×D8×C127D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#3356C2semidirect
4. C127×#3342C2semidirect
5. C127×#1723C2semidirect
6. C127×#1693C2semidirect
7. C127×#1684C2semidirect
8. C127×#1671C2semidirect
9. C127×#1670C2semidirect
10. C127×#1650C2semidirect
11. C127×#1650C2semidirect
12. C127×#1643C2semidirect
13. C127×#1638C2semidirect
15. C127×#1579C2semidirect
273. #19866C127direct (N × H)
281. #3356C2×C127semidirect
282. #3342C2×C127semidirect
283. #1723C2×C127semidirect
284. #1693C2×C127semidirect
285. #1684C2×C127semidirect
286. #1671C2×C127semidirect
287. #1670C2×C127semidirect
288. #1650C2×C127semidirect
289. #1650C2×C127semidirect
290. #1643C2×C127semidirect
291. #1638C2×C127semidirect
293. #1579C2×C127semidirect
294. C127#19866direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#33932
C127×#33602
C127×#33562
C127×#33422
C127×#17232
C127×#16932
C127×#16842
C127×#16712
C127×#16702
C127×#16502
C127×#16432
C127×#16382
C127×#15812
C127×#15792
#19866127