Finite Group Databasebeta

← C127×#19071 #44582744

Subgroups — C127×#19071 #44582744

Order 32512.

810 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3553C211yesmaximal, characteristic
2C127×#3240C211yesmaximal, characteristic, complemented
3C127×#3236C211yesmaximal, characteristic, complemented
4C127×#3172C211yesmaximal, characteristic, complemented
5C127×#1664C211yesmaximal, characteristic, complemented
6C127×#1664C211yesmaximal, characteristic, complemented
7C127×#1664C211yesmaximal, characteristic, complemented
8C127×#1663C211yesmaximal, characteristic, complemented
9C127×#1663C211yesmaximal, characteristic, complemented
10C127×#1662C211yesmaximal, characteristic, complemented
11C127×#1661C211yesmaximal, characteristic, complemented
12C127×#1660C211yesmaximal, characteristic, complemented
13C127×#1535C211yesmaximal, characteristic, complemented
14C127×#1529C211yesmaximal, characteristic, complemented
15C127×#1528C211yesmaximal, characteristic, complemented
16#564×C127C2211yescharacteristic
17#563×C127C2211yescharacteristic
18#563×C127C2211yescharacteristic
19#562×C127C2211yescharacteristic
20#554×C127—21no—
21#554×C127—21no—
22#553×C127—21no—
23#553×C127—21no—
24#552×C127—21no—
25#552×C127—21no—
26#541×C127—21no—
27#541×C127—21no—
28#539×C127—21no—
29#539×C127—21no—
30#539×C127—21no—
31#539×C127—21no—
32#533×C127C2211yescharacteristic
33#529×C127C2211yescharacteristic
34#529×C127C2211yescharacteristic
35C2×#125×C127C2211yescharacteristic
36#501×C127C2211yescharacteristic
37#501×C127C2211yescharacteristic
38#501×C127C2211yescharacteristic
39#501×C127C2211yescharacteristic
40#501×C127C2211yescharacteristic
41#497×C127C2211yescharacteristic
42#491×C127C2211yescharacteristic
43#491×C127C2211yescharacteristic
44#491×C127C2211yescharacteristic
45#489×C127C2211yescharacteristic
46#489×C127C2211yescharacteristic
47#489×C127C2211yescharacteristic
48#485×C127—21no—
49#484×C127—21no—
50#483×C127—21no—
51#482×C127—21no—
52#479×C127—21no—
53#479×C127—21no—
54#479×C127—21no—
55#478×C127—21no—
56#470×C127—21no—
57#468×C127—21no—
58C4×Q16×C127—21no—
59C4×SD16×C127—21no—
60#432×C127C2211yescharacteristic
61#432×C127C2211yescharacteristic
62C4×M16×C127C2211yescharacteristic
63#330×C127C2211yescharacteristic
64#330×C127C2211yescharacteristic
65#330×C127C2211yescharacteristic
66#330×C127C2211yescharacteristic
67#330×C127C2211yescharacteristic
68#330×C127C2211yescharacteristic
69#330×C127C2211yescharacteristic
70#330×C127C2211yescharacteristic
71#329×C127C2211yescharacteristic
72#329×C127C2211yescharacteristic
73#329×C127C2211yescharacteristic
74#329×C127C2211yescharacteristic
75C2×Q16×C127—21no—
76C2×SD16×C127—21no—
77C2×M16×C127—21no—
78C4⋊Q8×C127—21no—
79C4⋊Q8×C127—21no—
80C4⋊Q8×C127C2311yescharacteristic
81C4⋊Q8×C127C2311yescharacteristic
82#126×C127—21no—
83#126×C127—21no—
84#126×C127—21no—
85#126×C127—21no—
86#126×C127—21no—
87#126×C127—21no—
88#126×C127—21no—
89#126×C127—21no—
90#126×C127—21no—
91#126×C127—21no—
92#125×C127—21no—
93#125×C127—21no—
94#125×C127—21no—
95#125×C127—21no—
96#125×C127—21no—
97#125×C127—21no—
98#125×C127—21no—
99#125×C127—21no—
100#125×C127—21no—
101#125×C127—21no—
102#125×C127—21no—
103#125×C127—21no—
104#125×C127—21no—
105#125×C127D411yescharacteristic
106#125×C127D411yescharacteristic
107#125×C127C2311yescharacteristic
108#125×C127C2311yescharacteristic
109#125×C127C2311yescharacteristic
110#125×C127C2311yescharacteristic
111#124×C127C2311yescharacteristic
112#124×C127C2311yescharacteristic
113#123×C127—21no—
114#123×C127—21no—
115#123×C127—21no—
116#123×C127—21no—
117#123×C127—21no—
118#123×C127—21no—
119#123×C127—21no—
120#123×C127—21no—
121#123×C127—21no—
122#123×C127—21no—
123C22⋊Q8×C127—21no—
124C22⋊Q8×C127—21no—
125C22⋊Q8×C127—21no—
126C22⋊Q8×C127—21no—
127C22⋊Q8×C127—21no—
128C22⋊Q8×C127—21no—
129C22⋊Q8×C127—21no—
130C22⋊Q8×C127—21no—
131C22⋊Q8×C127—21no—
132C22⋊Q8×C127—21no—
133C22⋊Q8×C127—21no—
134C22⋊Q8×C127—21no—
135C22⋊Q8×C127—21no—
136C22⋊Q8×C127—21no—
137C22⋊Q8×C127D411yescharacteristic
138C22⋊Q8×C127D411yescharacteristic
139#121×C127—21no—
140#121×C127—21no—
141#121×C127—21no—
142#121×C127—21no—
143#121×C127D411yescharacteristic
144#121×C127D411yescharacteristic
145C4×Q8×C127—21no—
146C4×Q8×C127—21no—
147C4×Q8×C127—21no—
148C4×Q8×C127—21no—
149C4×Q8×C127D411yescharacteristic
150C4×Q8×C127D411yescharacteristic
151C4×D4×C127—21no—
152C4×D4×C127—21no—
153C4×D4×C127—21no—
154C4×D4×C127—21no—
155C4×D4×C127—21no—
156C4×D4×C127—21no—
157C4×D4×C127—21no—
158C4×D4×C127—21no—
159C4×D4×C127D411yescharacteristic
160C4×D4×C127D411yescharacteristic
161#117×C127—21no—
162#117×C127—21no—
163#117×C127—21no—
164#117×C127—21no—
165#117×C127—21no—
166C2×C4⋊C4×C127—21no—
167C2×C4⋊C4×C127—21no—
168C2×C4⋊C4×C127—21no—
169C2×C4⋊C4×C127—21no—
170C2×C4⋊C4×C127D411yescharacteristic
171C2×C4⋊C4×C127D411yescharacteristic
172C2×C42×C127C2311yescharacteristic
173#107×C127—21no—
174#107×C127—21no—
175#107×C127—21no—
176#107×C127—21no—
177#107×C127—21no—
178#106×C127—21no—
179#106×C127—21no—
180#106×C127—21no—
181#106×C127—21no—
182#106×C127—21no—
183C4⋊C8×C127—21no—
184C4⋊C8×C127—21no—
185#103×C127—21no—
186#103×C127—21no—
187#103×C127—21no—
188#103×C127—21no—
189#103×C127—21no—
190#103×C127—21no—
191#103×C127—21no—
192#103×C127—21no—
193#103×C127—21no—
194#102×C127—21no—
195#102×C127—21no—
196#102×C127—21no—
197C22⋊C8×C127—21no—
198C22⋊C8×C127—21no—
199#97×C127C2311yescharacteristic
200#97×C127C2311yescharacteristic
201#97×C127C2311yescharacteristic
202#97×C127C2311yescharacteristic
203#97×C127C2311yescharacteristic
204#97×C127C2311yescharacteristic
205C4×C8×C127—21no—
206C2×Q8×C127—21no—
207C2×Q8×C127—21no—
208C2×Q8×C127—21no—
209C2×Q8×C127—21no—
210C2×Q8×C127C2×D411yescharacteristic
211C2×Q8×C127C2×D411yescharacteristic
212C2×D4×C127—21no—
213C2×D4×C127—21no—
214C2×D4×C127—21no—
215C2×D4×C127—21no—
216C2×D4×C127C2×D411yescharacteristic
217C2×D4×C127C2×D411yescharacteristic
218C22×C4×C127—21no—
219C22×C4×C127—21no—
220C22×C4×C127—21no—
221C22×C4×C127—21no—
222C22×C4×C127—21no—
223C22×C4×C127—21no—
224C22×C4×C127—21no—
225C22×C4×C127—21no—
226C22×C4×C127C2×D411yescharacteristic
227C22×C4×C127C2×D411yescharacteristic
228C22×C4×C127C2×D411yescharacteristic
229Q16×C127—42no—
230SD16×C127—42no—
231M16×C127—42no—
232C2×C8×C127—21no—
233C2×C8×C127—21no—
234C2×C8×C127—21no—
235C2×C8×C127—21no—
236C2×C8×C127—21no—
237C2×C8×C127—21no—
238C4⋊C4×C127—21no—
239C4⋊C4×C127—21no—
240C4⋊C4×C127—21no—
241C4⋊C4×C127—21no—
242C4⋊C4×C127—21no—
243C4⋊C4×C127—21no—
244C4⋊C4×C127—21no—
245C4⋊C4×C127—21no—
246C4⋊C4×C127—21no—
247C4⋊C4×C127—21no—
248C4⋊C4×C127—21no—
249C4⋊C4×C127—21no—
250C4⋊C4×C127—21no—
251C4⋊C4×C127—21no—
252C4⋊C4×C127—21no—
253C4⋊C4×C127—21no—
254C4⋊C4×C127—21no—
255C4⋊C4×C127—21no—
256C4⋊C4×C127—21no—
257C4⋊C4×C127—21no—
258C4⋊C4×C127—21no—
259C4⋊C4×C127—21no—
260C4⋊C4×C127—21no—
261C4⋊C4×C127—21no—
262C4⋊C4×C127—21no—
263C4⋊C4×C127—21no—
264C4⋊C4×C127—21no—
265C4⋊C4×C127—21no—
266C4⋊C4×C127—21no—
267C4⋊C4×C127—21no—
268C4⋊C4×C127—21no—
269C4⋊C4×C127—21no—
270C4⋊C4×C127—21no—
271C4⋊C4×C127—21no—
272C4⋊C4×C127—41no—
273C4⋊C4×C127—41no—
274C4⋊C4×C127C2×D411yescharacteristic
275C4⋊C4×C127C2×D411yescharacteristic
276C4⋊C4×C127C2×D411yescharacteristic
277C4⋊C4×C127C2×D411yescharacteristic
278C4⋊C4×C127C2×D411yescharacteristic
279C4⋊C4×C127C2×D411yescharacteristic
280C4⋊C4×C127C2×D411yescharacteristic
281C4⋊C4×C127C2×D411yescharacteristic
282C22⋊C4×C127—21no—
283C22⋊C4×C127—21no—
284C22⋊C4×C127—21no—
285C22⋊C4×C127—21no—
286C22⋊C4×C127—21no—
287C22⋊C4×C127—21no—
288C22⋊C4×C127—21no—
289C22⋊C4×C127—21no—
290C22⋊C4×C127—21no—
291C22⋊C4×C127—21no—
292C22⋊C4×C127—21no—
293C22⋊C4×C127—21no—
294C22⋊C4×C127—21no—
295C22⋊C4×C127—21no—
296C22⋊C4×C127—21no—
297C22⋊C4×C127—21no—
298C22⋊C4×C127—21no—
299C22⋊C4×C127—21no—
300C22⋊C4×C127—41no—
301C42×C127—21no—
302C42×C127—21no—
303C42×C127—21no—
304C42×C127—21no—
305C42×C127—21no—
306C42×C127—21no—
307C42×C127—41no—
308C42×C127C2×D411yescharacteristic
309C42×C127C2×D411yescharacteristic
310C42×C127C2×D411yescharacteristic
311C42×C127C2411yescharacteristic
312C23×C127—21no—
313C23×C127—21no—
314C23×C127#12011yescharacteristic
315Q8×C127—41no—
316Q8×C127—41no—
317Q8×C127—41no—
318Q8×C127—41no—
319Q8×C127—42no—
320Q8×C127—81no—
321Q8×C127—81no—
322D4×C127—41no—
323D4×C127—41no—
324D4×C127—42no—
325D4×C127—42no—
326D4×C127—81no—
327D4×C127—81no—
328C2×C4×C127—21no—
329C2×C4×C127—21no—
330C2×C4×C127—21no—
331C2×C4×C127—21no—
332C2×C4×C127—21no—
333C2×C4×C127—21no—
334C2×C4×C127—21no—
335C2×C4×C127—21no—
336C2×C4×C127—21no—
337C2×C4×C127—21no—
338C2×C4×C127—41no—
339C2×C4×C127—41no—
340C2×C4×C127—41no—
341C2×C4×C127—41no—
342C2×C4×C127—41no—
343C2×C4×C127—81no—
344C2×C4×C127—81no—
345C2×C4×C127—81no—
346C2×C4×C127—81no—
347C2×C4×C127—81no—
348C2×C4×C127—81no—
349C2×C4×C127—81no—
350C2×C4×C127—81no—
351C2×C4×C127#12011yescharacteristic
352C2×C4×C127#12011yescharacteristic
353C2×C4×C127#12011yescharacteristic
354C2×C4×C127C22×D411yescharacteristic
355C2×C4×C127C22×D411yescharacteristic
356C2×C4×C127C22×D411yescharacteristic
357C8×C127—22no—
358C8×C127—41no—
359C8×C127—41no—
360C8×C127—41no—
361C8×C127—41no—
362C8×C127—41no—
363C22×C127—21no—
364C22×C127—21no—
365C22×C127—21no—
366C22×C127—41no—
367C22×C127—41no—
368C22×C127—41no—
369C22×C127—41no—
370C22×C127—41no—
371C22×C127—41no—
372C22×C127C2×#12011yescharacteristic
373C4×C127—21no—
374C4×C127—21no—
375C4×C127—21no—
376C4×C127—21no—
377C4×C127—21no—
378C4×C127—21no—
379C4×C127—41no—
380C4×C127—41no—
381C4×C127—41no—
382C4×C127—41no—
383C4×C127—41no—
384C4×C127—41no—
385C4×C127—41no—
386C4×C127—41no—
387C4×C127—41no—
388C4×C127—41no—
389C4×C127—81no—
390C4×C127—81no—
391#19071C12711yesmaximal, characteristic, direct product factor, Sylow
392C2×C127—41no—
393C2×C127—81no—
394C2×C127—81no—
395C2×C127#301811yescharacteristic
396C2×C127#302011yescharacteristic
397C2×C127#302211yescharacteristic
398#3553C2×C12711yescharacteristic
399#3240C2×C12711yescharacteristic, complemented
400#3236C2×C12711yescharacteristic, complemented
401#3172C2×C12711yescharacteristic, complemented
402#1664C2×C12711yescharacteristic, complemented
403#1664C2×C12711yescharacteristic, complemented
404#1664C2×C12711yescharacteristic, complemented
405#1663C2×C12711yescharacteristic, complemented
406#1663C2×C12711yescharacteristic, complemented
407#1662C2×C12711yescharacteristic, complemented
408#1661C2×C12711yescharacteristic, complemented
409#1660C2×C12711yescharacteristic, complemented
410#1535C2×C12711yescharacteristic, complemented
411#1529C2×C12711yescharacteristic, complemented
412#1528C2×C12711yescharacteristic, complemented
413C127#1907111yescharacteristic, direct product factor, Sylow
414#564C22×C12711yescharacteristic
415#563C22×C12711yescharacteristic
416#563C22×C12711yescharacteristic
417#562C22×C12711yescharacteristic
418#554—21no—
419#554—21no—
420#553—21no—
421#553—21no—
422#552—21no—
423#552—21no—
424#541—21no—
425#541—21no—
426#539—21no—
427#539—21no—
428#539—21no—
429#539—21no—
430#533C22×C12711yescharacteristic
431#529C22×C12711yescharacteristic
432#529C22×C12711yescharacteristic
433C2×#125C22×C12711yescharacteristic
434#501C22×C12711yescharacteristic
435#501C22×C12711yescharacteristic
436#501C22×C12711yescharacteristic
437#501C22×C12711yescharacteristic
438#501C22×C12711yescharacteristic
439#497C22×C12711yescharacteristic
440#491C22×C12711yescharacteristic
441#491C22×C12711yescharacteristic
442#491C22×C12711yescharacteristic
443#489C22×C12711yescharacteristic
444#489C22×C12711yescharacteristic
445#489C22×C12711yescharacteristic
446#485—21no—
447#484—21no—
448#483—21no—
449#482—21no—
450#479—21no—
451#479—21no—
452#479—21no—
453#478—21no—
454#470—21no—
455#468—21no—
456C4×Q16—21no—
457C4×SD16—21no—
458#432C22×C12711yescharacteristic
459#432C22×C12711yescharacteristic
460C4×M16C22×C12711yescharacteristic
461#330C22×C12711yescharacteristic
462#330C22×C12711yescharacteristic
463#330C22×C12711yescharacteristic
464#330C22×C12711yescharacteristic
465#330C22×C12711yescharacteristic
466#330C22×C12711yescharacteristic
467#330C22×C12711yescharacteristic
468#330C22×C12711yescharacteristic
469#329C22×C12711yescharacteristic
470#329C22×C12711yescharacteristic
471#329C22×C12711yescharacteristic
472#329C22×C12711yescharacteristic
473C2×Q16—21no—
474C2×SD16—21no—
475C2×M16—21no—
476C4⋊Q8—21no—
477C4⋊Q8—21no—
478C4⋊Q8C23×C12711yescharacteristic
479C4⋊Q8C23×C12711yescharacteristic
480#126—21no—
481#126—21no—
482#126—21no—
483#126—21no—
484#126—21no—
485#126—21no—
486#126—21no—
487#126—21no—
488#126—21no—
489#126—21no—
490#125—21no—
491#125—21no—
492#125—21no—
493#125—21no—
494#125—21no—
495#125—21no—
496#125—21no—
497#125—21no—
498#125—21no—
499#125—21no—
500#125—21no—
501#125—21no—
502#125—21no—
503#125D4×C12711yescharacteristic
504#125D4×C12711yescharacteristic
505#125C23×C12711yescharacteristic
506#125C23×C12711yescharacteristic
507#125C23×C12711yescharacteristic
508#125C23×C12711yescharacteristic
509#124C23×C12711yescharacteristic
510#124C23×C12711yescharacteristic
511#123—21no—
512#123—21no—
513#123—21no—
514#123—21no—
515#123—21no—
516#123—21no—
517#123—21no—
518#123—21no—
519#123—21no—
520#123—21no—
521C22⋊Q8—21no—
522C22⋊Q8—21no—
523C22⋊Q8—21no—
524C22⋊Q8—21no—
525C22⋊Q8—21no—
526C22⋊Q8—21no—
527C22⋊Q8—21no—
528C22⋊Q8—21no—
529C22⋊Q8—21no—
530C22⋊Q8—21no—
531C22⋊Q8—21no—
532C22⋊Q8—21no—
533C22⋊Q8—21no—
534C22⋊Q8—21no—
535C22⋊Q8D4×C12711yescharacteristic
536C22⋊Q8D4×C12711yescharacteristic
537#121—21no—
538#121—21no—
539#121—21no—
540#121—21no—
541#121D4×C12711yescharacteristic
542#121D4×C12711yescharacteristic
543C4×Q8—21no—
544C4×Q8—21no—
545C4×Q8—21no—
546C4×Q8—21no—
547C4×Q8D4×C12711yescharacteristic
548C4×Q8D4×C12711yescharacteristic
549C4×D4—21no—
550C4×D4—21no—
551C4×D4—21no—
552C4×D4—21no—
553C4×D4—21no—
554C4×D4—21no—
555C4×D4—21no—
556C4×D4—21no—
557C4×D4D4×C12711yescharacteristic
558C4×D4D4×C12711yescharacteristic
559#117—21no—
560#117—21no—
561#117—21no—
562#117—21no—
563#117—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4D4×C12711yescharacteristic
569C2×C4⋊C4D4×C12711yescharacteristic
570C2×C42C23×C12711yescharacteristic
571#107—21no—
572#107—21no—
573#107—21no—
574#107—21no—
575#107—21no—
576#106—21no—
577#106—21no—
578#106—21no—
579#106—21no—
580#106—21no—
581C4⋊C8—21no—
582C4⋊C8—21no—
583#103—21no—
584#103—21no—
585#103—21no—
586#103—21no—
587#103—21no—
588#103—21no—
589#103—21no—
590#103—21no—
591#103—21no—
592#102—21no—
593#102—21no—
594#102—21no—
595C22⋊C8—21no—
596C22⋊C8—21no—
597#97C23×C12711yescharacteristic
598#97C23×C12711yescharacteristic
599#97C23×C12711yescharacteristic
600#97C23×C12711yescharacteristic
601#97C23×C12711yescharacteristic
602#97C23×C12711yescharacteristic
603C4×C8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8C2×D4×C12711yescharacteristic
609C2×Q8C2×D4×C12711yescharacteristic
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4C2×D4×C12711yescharacteristic
615C2×D4C2×D4×C12711yescharacteristic
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4C2×D4×C12711yescharacteristic
625C22×C4C2×D4×C12711yescharacteristic
626C22×C4C2×D4×C12711yescharacteristic
627Q16—42no—
628SD16—42no—
629M16—42no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—41no—
671C4⋊C4—41no—
672C4⋊C4C2×D4×C12711yescharacteristic
673C4⋊C4C2×D4×C12711yescharacteristic
674C4⋊C4C2×D4×C12711yescharacteristic
675C4⋊C4C2×D4×C12711yescharacteristic
676C4⋊C4C2×D4×C12711yescharacteristic
677C4⋊C4C2×D4×C12711yescharacteristic
678C4⋊C4C2×D4×C12711yescharacteristic
679C4⋊C4C2×D4×C12711yescharacteristic
680C22⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4—21no—
683C22⋊C4—21no—
684C22⋊C4—21no—
685C22⋊C4—21no—
686C22⋊C4—21no—
687C22⋊C4—21no—
688C22⋊C4—21no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—21no—
693C22⋊C4—21no—
694C22⋊C4—21no—
695C22⋊C4—21no—
696C22⋊C4—21no—
697C22⋊C4—21no—
698C22⋊C4—41no—
699C42—21no—
700C42—21no—
701C42—21no—
702C42—21no—
703C42—21no—
704C42—21no—
705C42—41no—
706C42C2×D4×C12711yescharacteristic
707C42C2×D4×C12711yescharacteristic
708C42C2×D4×C12711yescharacteristic
709C42C24×C12711yescharacteristic
710C23—21no—
711C23—21no—
712C23#120×C12711yescharacteristic
713Q8—41no—
714Q8—41no—
715Q8—41no—
716Q8—41no—
717Q8—42no—
718Q8—81no—
719Q8—81no—
720D4—41no—
721D4—41no—
722D4—42no—
723D4—42no—
724D4—81no—
725D4—81no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—81no—
742C2×C4—81no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—81no—
748C2×C4—81no—
749C2×C4#120×C12711yescharacteristic
750C2×C4#120×C12711yescharacteristic
751C2×C4#120×C12711yescharacteristic
752C2×C4C22×D4×C12711yescharacteristic
753C2×C4C22×D4×C12711yescharacteristic
754C2×C4C22×D4×C12711yescharacteristic
755C8—22no—
756C8—41no—
757C8—41no—
758C8—41no—
759C8—41no—
760C8—41no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22C2×#120×C12711yescharacteristic
771C4—21no—
772C4—21no—
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4—41no—
786C4—41no—
787C4—81no—
788C4—81no—
789C2—41no—
790C2—81no—
791C2—81no—
792C2C127×#301811yescharacteristic
793C2C127×#302011yescharacteristic
794C2C127×#302211yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC42C24×C127
prime radicalC127×#3553C2
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
2. C127×#3240C2semidirect
3. C127×#3236C2semidirect
4. C127×#3172C2semidirect
5. C127×#1664C2semidirect
6. C127×#1664C2semidirect
7. C127×#1664C2semidirect
8. C127×#1663C2semidirect
9. C127×#1663C2semidirect
10. C127×#1662C2semidirect
11. C127×#1661C2semidirect
12. C127×#1660C2semidirect
13. C127×#1535C2semidirect
14. C127×#1529C2semidirect
15. C127×#1528C2semidirect
391. #19071C127direct (N × H)
399. #3240C2×C127semidirect
400. #3236C2×C127semidirect
401. #3172C2×C127semidirect
402. #1664C2×C127semidirect
403. #1664C2×C127semidirect
404. #1664C2×C127semidirect
405. #1663C2×C127semidirect
406. #1663C2×C127semidirect
407. #1662C2×C127semidirect
408. #1661C2×C127semidirect
409. #1660C2×C127semidirect
410. #1535C2×C127semidirect
411. #1529C2×C127semidirect
412. #1528C2×C127semidirect
413. C127#19071direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#35532
C127×#32402
C127×#32362
C127×#31722
C127×#16642
C127×#16632
C127×#16622
C127×#16612
C127×#16602
C127×#15352
C127×#15292
C127×#15282
#19071127