Finite Group Databasebeta

← C127×#19769 #44583442

Subgroups — C127×#19769 #44583442

Order 32512.

616 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3387C211yesmaximal, characteristic, complemented
2Q8×SD16×C127C211yesmaximal, characteristic
3C127×#3359C211yesmaximal, characteristic
4D4×Q16×C127C211yesmaximal, characteristic
5C127×#1716C211yesmaximal, characteristic, complemented
6C127×#1690C211yesmaximal, characteristic, complemented
7C127×#1680C211yesmaximal, characteristic, complemented
8C127×#1672C211yesmaximal, characteristic, complemented
9C127×#1671C211yesmaximal, characteristic
10C127×#1653C211yesmaximal, characteristic, complemented
11C127×#1651C211yesmaximal, characteristic
12C127×#1645C211yesmaximal, characteristic, complemented
13C127×#1637C211yesmaximal, characteristic
14C127×#1582C211yesmaximal, characteristic
15C127×#1579C211yesmaximal, characteristic, complemented
16C22×Q16×C127—21no—
17Q82×C127C2211yescharacteristic
18#557×C127C2211yescharacteristic
19D4×Q8×C127C2211yescharacteristic
20D4×Q8×C127C2211yescharacteristic
21#501×C127—21no—
22#498×C127—21no—
23#498×C127C2211yescharacteristic
24#498×C127C2211yescharacteristic
25#498×C127C2211yescharacteristic
26#494×C127C2211yescharacteristic
27#487×C127—21no—
28#487×C127C2211yescharacteristic
29#487×C127C2211yescharacteristic
30#479×C127—21no—
31#477×C127C2211yescharacteristic
32#476×C127—21no—
33#476×C127C2211yescharacteristic
34#475×C127—21no—
35#475×C127—21no—
36#475×C127—21no—
37#475×C127C2211yescharacteristic
38#475×C127C2211yescharacteristic
39#475×C127C2211yescharacteristic
40#467×C127—21no—
41#462×C127C2211yescharacteristic
42#462×C127C2211yescharacteristic
43#461×C127—21no—
44#461×C127C2211yescharacteristic
45#451×C127—21no—
46#451×C127—21no—
47#446×C127C2211yescharacteristic
48C8×Q8×C127C2211yescharacteristic
49C8×Q8×C127C2211yescharacteristic
50#441×C127—21no—
51C4×Q16×C127C2211yescharacteristic
52C4×SD16×C127—21no—
53C4×SD16×C127—21no—
54C4×SD16×C127C2211yescharacteristic
55C8×D4×C127C2211yescharacteristic
56#334×C127C2211yescharacteristic
57#334×C127C2211yescharacteristic
58#333×C127C2211yescharacteristic
59#332×C127C2211yescharacteristic
60#332×C127C2211yescharacteristic
61#332×C127C2211yescharacteristic
62Q8⋊C8×C127C2211yescharacteristic
63Q8⋊C8×C127C2211yescharacteristic
64Q8⋊C8×C127C2211yescharacteristic
65D4⋊C8×C127C2211yescharacteristic
66#322×C127C2211yescharacteristic
67C22×Q8×C127—21no—
68C22×Q8×C127—21no—
69C2×Q16×C127—21no—
70C2×Q16×C127—21no—
71C2×Q16×C127—21no—
72C2×Q16×C127—21no—
73C2×Q16×C127—44no—
74C2×Q16×C127D411yescharacteristic
75C2×SD16×C127—21no—
76C2×SD16×C127D411yescharacteristic
77C22×C8×C127—21no—
78C4⋊Q8×C127—21no—
79C4⋊Q8×C127—21no—
80C4⋊Q8×C127—21no—
81C4⋊Q8×C127—21no—
82C4⋊Q8×C127—21no—
83C4⋊Q8×C127—41no—
84C4⋊Q8×C127C2311yescharacteristic
85C4⋊Q8×C127C2311yescharacteristic
86C4⋊Q8×C127C2311yescharacteristic
87C4⋊Q8×C127C2311yescharacteristic
88#125×C127—21no—
89#125×C127—41no—
90C22⋊Q8×C127—21no—
91C22⋊Q8×C127—21no—
92C22⋊Q8×C127—41no—
93C22⋊Q8×C127—41no—
94C4×Q8×C127—21no—
95C4×Q8×C127—21no—
96C4×Q8×C127—21no—
97C4×Q8×C127—21no—
98C4×Q8×C127C2311yescharacteristic
99C4×Q8×C127C2311yescharacteristic
100C4×Q8×C127C2311yescharacteristic
101C4×D4×C127—21no—
102C4×D4×C127—21no—
103C4×D4×C127C2311yescharacteristic
104#107×C127—21no—
105#107×C127D411yescharacteristic
106#106×C127—21no—
107#106×C127—21no—
108#106×C127—21no—
109#106×C127—21no—
110#106×C127—21no—
111#106×C127—21no—
112#106×C127—21no—
113#106×C127—21no—
114#106×C127—41no—
115#106×C127D411yescharacteristic
116C4⋊C8×C127—21no—
117C4⋊C8×C127—21no—
118C4⋊C8×C127—21no—
119C4⋊C8×C127C2311yescharacteristic
120C4⋊C8×C127C2311yescharacteristic
121C4⋊C8×C127C2311yescharacteristic
122C4⋊C8×C127C2311yescharacteristic
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—21no—
132#103×C127—41no—
133#103×C127D411yescharacteristic
134#103×C127D411yescharacteristic
135#103×C127D411yescharacteristic
136#102×C127—21no—
137#102×C127D411yescharacteristic
138C22⋊C8×C127—21no—
139#97×C127—21no—
140C4×C8×C127—21no—
141C4×C8×C127—21no—
142C4×C8×C127C2311yescharacteristic
143C4×C8×C127C2311yescharacteristic
144C4×C8×C127C2311yescharacteristic
145C2×Q8×C127—21no—
146C2×Q8×C127—21no—
147C2×Q8×C127—21no—
148C2×Q8×C127—21no—
149C2×Q8×C127—41no—
150C2×Q8×C127—41no—
151C2×Q8×C127—41no—
152C2×Q8×C127—42no—
153C2×Q8×C127—42no—
154C2×Q8×C127—81no—
155C2×Q8×C127—81no—
156C2×Q8×C127C2×D411yescharacteristic
157C2×Q8×C127C2×D411yescharacteristic
158C2×Q8×C127C2×D411yescharacteristic
159C2×D4×C127C2×D411yescharacteristic
160C22×C4×C127—21no—
161C22×C4×C127—41no—
162C22×C4×C127—41no—
163Q16×C127—42no—
164Q16×C127—42no—
165Q16×C127—42no—
166Q16×C127—81no—
167Q16×C127SD1614yescomplemented
168SD16×C127—22no—
169SD16×C127—42no—
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×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—21no—
189C4⋊C4×C127—21no—
190C4⋊C4×C127—21no—
191C4⋊C4×C127—41no—
192C4⋊C4×C127—41no—
193C4⋊C4×C127—41no—
194C4⋊C4×C127—41no—
195C4⋊C4×C127—41no—
196C4⋊C4×C127—41no—
197C4⋊C4×C127—41no—
198C4⋊C4×C127C2×D411yescharacteristic
199C4⋊C4×C127C2×D411yescharacteristic
200C4⋊C4×C127C2×D411yescharacteristic
201C4⋊C4×C127C2×D411yescharacteristic
202C22⋊C4×C127—21no—
203C22⋊C4×C127—41no—
204C22⋊C4×C127—41no—
205C42×C127—21no—
206C42×C127—21no—
207C42×C127—21no—
208C42×C127—41no—
209C42×C127—41no—
210C42×C127C2411yescharacteristic
211C23×C127—21no—
212Q8×C127—21no—
213Q8×C127—21no—
214Q8×C127—21no—
215Q8×C127—21no—
216Q8×C127—41no—
217Q8×C127—41no—
218Q8×C127—41no—
219Q8×C127—41no—
220Q8×C127—41no—
221Q8×C127—41no—
222Q8×C127—82no—
223Q8×C127—82no—
224Q8×C127—81no—
225Q8×C127—161no—
226Q8×C127C2×SD1612yes—
227Q8×C127C2×SD1612yes—
228D4×C127—21no—
229D4×C127#13712yes—
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—21no—
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—82no—
245C2×C4×C127C22×D411yescharacteristic
246C2×C4×C127C22×D411yescharacteristic
247C2×C4×C127H(5,𝔽2)11yescharacteristic
248C8×C127—21no—
249C8×C127—21no—
250C8×C127—21no—
251C8×C127—41no—
252C8×C127—41no—
253C8×C127—41no—
254C8×C127—41no—
255C8×C127—41no—
256C8×C127C2×SD1612yes—
257C22×C127—22no—
258C22×C127—41no—
259C22×C127—41no—
260C22×C127D4211yescharacteristic
261C4×C127—22no—
262C4×C127—22no—
263C4×C127—21no—
264C4×C127—41no—
265C4×C127—41no—
266C4×C127—41no—
267C4×C127—41no—
268C4×C127—41no—
269C4×C127—81no—
270C4×C127—81no—
271C4×C127—81no—
272C4×C127—81no—
273C4×C127C22×SD1611yescharacteristic
274C4×C127C2×#13711yescharacteristic
275C4×C127#57711yescharacteristic
276C4×C127#57811yescharacteristic
277#19769C12711yesmaximal, characteristic, direct product factor, Sylow
278C2×C127—42no—
279C2×C127#327011yescharacteristic
280C2×C127D4×SD1611yescharacteristic
281C2×C127#328911yescharacteristic
282#3387C2×C12711yescharacteristic, complemented
283Q8×SD16C2×C12711yescharacteristic
284#3359C2×C12711yescharacteristic
285D4×Q16C2×C12711yescharacteristic
286#1716C2×C12711yescharacteristic, complemented
287#1690C2×C12711yescharacteristic, complemented
288#1680C2×C12711yescharacteristic, complemented
289#1672C2×C12711yescharacteristic, complemented
290#1671C2×C12711yescharacteristic
291#1653C2×C12711yescharacteristic, complemented
292#1651C2×C12711yescharacteristic
293#1645C2×C12711yescharacteristic, complemented
294#1637C2×C12711yescharacteristic
295#1582C2×C12711yescharacteristic
296#1579C2×C12711yescharacteristic, complemented
297C127#1976911yescharacteristic, direct product factor, Sylow
298C22×Q16—21no—
299Q82C22×C12711yescharacteristic
300#557C22×C12711yescharacteristic
301D4×Q8C22×C12711yescharacteristic
302D4×Q8C22×C12711yescharacteristic
303#501—21no—
304#498—21no—
305#498C22×C12711yescharacteristic
306#498C22×C12711yescharacteristic
307#498C22×C12711yescharacteristic
308#494C22×C12711yescharacteristic
309#487—21no—
310#487C22×C12711yescharacteristic
311#487C22×C12711yescharacteristic
312#479—21no—
313#477C22×C12711yescharacteristic
314#476—21no—
315#476C22×C12711yescharacteristic
316#475—21no—
317#475—21no—
318#475—21no—
319#475C22×C12711yescharacteristic
320#475C22×C12711yescharacteristic
321#475C22×C12711yescharacteristic
322#467—21no—
323#462C22×C12711yescharacteristic
324#462C22×C12711yescharacteristic
325#461—21no—
326#461C22×C12711yescharacteristic
327#451—21no—
328#451—21no—
329#446C22×C12711yescharacteristic
330C8×Q8C22×C12711yescharacteristic
331C8×Q8C22×C12711yescharacteristic
332#441—21no—
333C4×Q16C22×C12711yescharacteristic
334C4×SD16—21no—
335C4×SD16—21no—
336C4×SD16C22×C12711yescharacteristic
337C8×D4C22×C12711yescharacteristic
338#334C22×C12711yescharacteristic
339#334C22×C12711yescharacteristic
340#333C22×C12711yescharacteristic
341#332C22×C12711yescharacteristic
342#332C22×C12711yescharacteristic
343#332C22×C12711yescharacteristic
344Q8⋊C8C22×C12711yescharacteristic
345Q8⋊C8C22×C12711yescharacteristic
346Q8⋊C8C22×C12711yescharacteristic
347D4⋊C8C22×C12711yescharacteristic
348#322C22×C12711yescharacteristic
349C22×Q8—21no—
350C22×Q8—21no—
351C2×Q16—21no—
352C2×Q16—21no—
353C2×Q16—21no—
354C2×Q16—21no—
355C2×Q16—44no—
356C2×Q16D4×C12711yescharacteristic
357C2×SD16—21no—
358C2×SD16D4×C12711yescharacteristic
359C22×C8—21no—
360C4⋊Q8—21no—
361C4⋊Q8—21no—
362C4⋊Q8—21no—
363C4⋊Q8—21no—
364C4⋊Q8—21no—
365C4⋊Q8—41no—
366C4⋊Q8C23×C12711yescharacteristic
367C4⋊Q8C23×C12711yescharacteristic
368C4⋊Q8C23×C12711yescharacteristic
369C4⋊Q8C23×C12711yescharacteristic
370#125—21no—
371#125—41no—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374C22⋊Q8—41no—
375C22⋊Q8—41no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8C23×C12711yescharacteristic
381C4×Q8C23×C12711yescharacteristic
382C4×Q8C23×C12711yescharacteristic
383C4×D4—21no—
384C4×D4—21no—
385C4×D4C23×C12711yescharacteristic
386#107—21no—
387#107D4×C12711yescharacteristic
388#106—21no—
389#106—21no—
390#106—21no—
391#106—21no—
392#106—21no—
393#106—21no—
394#106—21no—
395#106—21no—
396#106—41no—
397#106D4×C12711yescharacteristic
398C4⋊C8—21no—
399C4⋊C8—21no—
400C4⋊C8—21no—
401C4⋊C8C23×C12711yescharacteristic
402C4⋊C8C23×C12711yescharacteristic
403C4⋊C8C23×C12711yescharacteristic
404C4⋊C8C23×C12711yescharacteristic
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#103—41no—
415#103D4×C12711yescharacteristic
416#103D4×C12711yescharacteristic
417#103D4×C12711yescharacteristic
418#102—21no—
419#102D4×C12711yescharacteristic
420C22⋊C8—21no—
421#97—21no—
422C4×C8—21no—
423C4×C8—21no—
424C4×C8C23×C12711yescharacteristic
425C4×C8C23×C12711yescharacteristic
426C4×C8C23×C12711yescharacteristic
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—41no—
432C2×Q8—41no—
433C2×Q8—41no—
434C2×Q8—42no—
435C2×Q8—42no—
436C2×Q8—81no—
437C2×Q8—81no—
438C2×Q8C2×D4×C12711yescharacteristic
439C2×Q8C2×D4×C12711yescharacteristic
440C2×Q8C2×D4×C12711yescharacteristic
441C2×D4C2×D4×C12711yescharacteristic
442C22×C4—21no—
443C22×C4—41no—
444C22×C4—41no—
445Q16—42no—
446Q16—42no—
447Q16—42no—
448Q16—81no—
449Q16SD16×C12714yescomplemented
450SD16—22no—
451SD16—42no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—42no—
458C2×C8C2×D4×C12711yescharacteristic
459C2×C8C2×D4×C12711yescharacteristic
460C2×C8C2×D4×C12711yescharacteristic
461C2×C8C2×D4×C12711yescharacteristic
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
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—41no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4C2×D4×C12711yescharacteristic
481C4⋊C4C2×D4×C12711yescharacteristic
482C4⋊C4C2×D4×C12711yescharacteristic
483C4⋊C4C2×D4×C12711yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—41no—
491C42—41no—
492C42C24×C12711yescharacteristic
493C23—21no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502Q8—41no—
503Q8—41no—
504Q8—82no—
505Q8—82no—
506Q8—81no—
507Q8—161no—
508Q8C2×SD16×C12712yes—
509Q8C2×SD16×C12712yes—
510D4—21no—
511D4#137×C12712yes—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—82no—
526C2×C4—82no—
527C2×C4C22×D4×C12711yescharacteristic
528C2×C4C22×D4×C12711yescharacteristic
529C2×C4H(5,𝔽2)×C12711yescharacteristic
530C8—21no—
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8C2×SD16×C12712yes—
539C22—22no—
540C22—41no—
541C22—41no—
542C22D42×C12711yescharacteristic
543C4—22no—
544C4—22no—
545C4—21no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—81no—
552C4—81no—
553C4—81no—
554C4—81no—
555C4C22×SD16×C12711yescharacteristic
556C4C2×#137×C12711yescharacteristic
557C4#577×C12711yescharacteristic
558C4#578×C12711yescharacteristic
559C2—42no—
560C2C127×#327011yescharacteristic
561C2D4×SD16×C12711yescharacteristic
562C2C127×#328911yescharacteristic
subgroupG/H
center, socleC22×C127D42
commutator, Frattini, cosocleC42C24×C127
prime radicalC2×D4×C127C2×D4
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×#3387C2semidirect
5. C127×#1716C2semidirect
6. C127×#1690C2semidirect
7. C127×#1680C2semidirect
8. C127×#1672C2semidirect
10. C127×#1653C2semidirect
12. C127×#1645C2semidirect
15. C127×#1579C2semidirect
167. Q16×C127SD16semidirect
277. #19769C127direct (N × H)
282. #3387C2×C127semidirect
286. #1716C2×C127semidirect
287. #1690C2×C127semidirect
288. #1680C2×C127semidirect
289. #1672C2×C127semidirect
291. #1653C2×C127semidirect
293. #1645C2×C127semidirect
296. #1579C2×C127semidirect
297. C127#19769direct (N × H)
449. Q16SD16×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#33872
Q8×SD16×C1272
C127×#33592
D4×Q16×C1272
C127×#17162
C127×#16902
C127×#16802
C127×#16722
C127×#16712
C127×#16532
C127×#16512
C127×#16452
C127×#16372
C127×#15822
C127×#15792
#19769127