Finite Group Databasebeta

← C127×#18494 #44582167

Subgroups — C127×#18494 #44582167

Order 32512.

944 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3482C211yesmaximal, characteristic, complemented
2C127×#3131C211yesmaximal, characteristic, complemented
3C127×#3106C211yesmaximal, characteristic, complemented
4C127×#3106C211yesmaximal, characteristic, complemented
5C127×#1638C211yesmaximal, characteristic, complemented
6C127×#1637C211yesmaximal, characteristic, complemented
7C127×#1636C211yesmaximal, characteristic, complemented
8C127×#1635C211yesmaximal, characteristic, complemented
9C127×#1628C211yesmaximal, characteristic, complemented
10C127×#1627C211yesmaximal, characteristic, complemented
11C127×#1626C211yesmaximal, characteristic, complemented
12C127×#1625C211yesmaximal, characteristic, complemented
13C127×#1544C211yesmaximal, characteristic, complemented
14C127×#1476C211yesmaximal, characteristic, complemented
15C127×#1476C211yesmaximal, characteristic, complemented
16#557×C127C2211yescharacteristic
17#556×C127—21no—
18#556×C127C2211yescharacteristic
19#552×C127—22no—
20#552×C127—21no—
21D4×Q8×C127C2211yescharacteristic
22#548×C127—21no—
23#547×C127—21no—
24#547×C127C2211yescharacteristic
25#533×C127—21no—
26#533×C127C2211yescharacteristic
27#532×C127C2211yescharacteristic
28#529×C127—21no—
29#529×C127—22no—
30C4×#41×C127—21no—
31C4×#41×C127C2211yescharacteristic
32C4×#41×C127C2211yescharacteristic
33C2×C4×Q8×C127—21no—
34#488×C127—22no—
35#487×C127C2211yescharacteristic
36#487×C127C2211yescharacteristic
37#486×C127C2211yescharacteristic
38#486×C127C2211yescharacteristic
39#482×C127—21no—
40#482×C127—21no—
41#477×C127C2211yescharacteristic
42#477×C127C2211yescharacteristic
43#476×C127C2211yescharacteristic
44#476×C127C2211yescharacteristic
45#460×C127C2211yescharacteristic
46#460×C127C2211yescharacteristic
47#459×C127C2211yescharacteristic
48#459×C127C2211yescharacteristic
49#449×C127—21no—
50#449×C127—21no—
51C4×SD16×C127—21no—
52C4×SD16×C127—21no—
53C4×D8×C127—21no—
54C4×D8×C127—21no—
55#431×C127C2211yescharacteristic
56#431×C127C2211yescharacteristic
57#416×C127—22no—
58C2×C4×C8×C127C2211yescharacteristic
59#332×C127C2211yescharacteristic
60#332×C127C2211yescharacteristic
61#332×C127C2211yescharacteristic
62#332×C127C2211yescharacteristic
63Q8⋊C8×C127C2211yescharacteristic
64Q8⋊C8×C127C2211yescharacteristic
65Q8⋊C8×C127C2211yescharacteristic
66Q8⋊C8×C127C2211yescharacteristic
67D4⋊C8×C127C2211yescharacteristic
68D4⋊C8×C127C2211yescharacteristic
69D4⋊C8×C127C2211yescharacteristic
70D4⋊C8×C127C2211yescharacteristic
71C2×#41×C127—21no—
72C2×#41×C127—21no—
73C2×#41×C127D411yescharacteristic
74C2×#41×C127D411yescharacteristic
75C22×Q8×C127—21no—
76C2×SD16×C127—21no—
77C2×SD16×C127—21no—
78C2×D8×C127—21no—
79C2×D8×C127—21no—
80C22×C8×C127—21no—
81C4⋊Q8×C127—21no—
82C4⋊Q8×C127—21no—
83C4⋊Q8×C127C2311yescharacteristic
84C4⋊Q8×C127C2311yescharacteristic
85C4⋊Q8×C127C2311yescharacteristic
86#127×C127C2311yescharacteristic
87#126×C127—22no—
88#126×C127—22no—
89#126×C127—22no—
90#125×C127—22no—
91#125×C127—22no—
92#125×C127—21no—
93#125×C127D412yes—
94#124×C127—22no—
95#124×C127—21no—
96#124×C127—21no—
97#123×C127—22no—
98#123×C127—22no—
99#123×C127—22no—
100C22⋊Q8×C127—22no—
101C22⋊Q8×C127—21no—
102C22⋊Q8×C127—21no—
103C22⋊Q8×C127—21no—
104C22⋊Q8×C127—21no—
105C22⋊Q8×C127—22no—
106C22⋊Q8×C127—21no—
107#121×C127—22no—
108#121×C127—21no—
109#121×C127—21no—
110#121×C127—21no—
111C4×Q8×C127—22no—
112C4×Q8×C127—22no—
113C4×Q8×C127—21no—
114C4×Q8×C127—21no—
115C4×Q8×C127—21no—
116C4×Q8×C127—21no—
117C4×Q8×C127—21no—
118C4×Q8×C127D411yescharacteristic
119C4×Q8×C127D411yescharacteristic
120C4×Q8×C127C2311yescharacteristic
121C4×Q8×C127C2311yescharacteristic
122C4×D4×C127—22no—
123C4×D4×C127—22no—
124C4×D4×C127—21no—
125C4×D4×C127—21no—
126C4×D4×C127—21no—
127C4×D4×C127—21no—
128C4×D4×C127—21no—
129C4×D4×C127—21no—
130C4×D4×C127—21no—
131C4×D4×C127D411yescharacteristic
132C4×D4×C127D411yescharacteristic
133C4×D4×C127C2311yescharacteristic
134C4×D4×C127C2311yescharacteristic
135#117×C127—22no—
136#117×C127—22no—
137#117×C127—21no—
138#117×C127—21no—
139#117×C127—21no—
140#117×C127D411yescharacteristic
141#117×C127D411yescharacteristic
142#117×C127D412yes—
143C2×C4⋊C4×C127—22no—
144C2×C4⋊C4×C127—21no—
145C2×C42×C127—22no—
146C2×C42×C127—21no—
147C2×C42×C127—21no—
148C2×C42×C127C2311yescharacteristic
149#107×C127—21no—
150#107×C127—21no—
151#106×C127—21no—
152#106×C127—21no—
153C4⋊C8×C127C2311yescharacteristic
154C4⋊C8×C127C2311yescharacteristic
155C4⋊C8×C127C2311yescharacteristic
156C4⋊C8×C127C2311yescharacteristic
157#103×C127—21no—
158#103×C127—21no—
159#103×C127—22no—
160#103×C127—22no—
161#102×C127—21no—
162#102×C127—21no—
163#102×C127—22no—
164#102×C127—22no—
165#102×C127—21no—
166#102×C127—21no—
167#102×C127—21no—
168#102×C127—21no—
169C22⋊C8×C127—21no—
170C22⋊C8×C127—21no—
171C4×C8×C127—21no—
172C4×C8×C127—21no—
173C4×C8×C127—21no—
174C4×C8×C127C2311yescharacteristic
175C4×C8×C127C2311yescharacteristic
176#41×C127—22no—
177#41×C127—22no—
178#41×C127—41no—
179#41×C127—41no—
180#41×C127—44no—
181#41×C127—42no—
182#41×C127—42no—
183C2×Q8×C127—22no—
184C2×Q8×C127—21no—
185C2×Q8×C127—21no—
186C2×Q8×C127—21no—
187C2×Q8×C127—42no—
188C2×Q8×C127—42no—
189C2×Q8×C127C2×D411yescharacteristic
190C2×Q8×C127C2×D411yescharacteristic
191C2×D4×C127—22no—
192C2×D4×C127—21no—
193C2×D4×C127—21no—
194C2×D4×C127—21no—
195C2×D4×C127—21no—
196C2×D4×C127—21no—
197C2×D4×C127—41no—
198C2×D4×C127C2×D411yescharacteristic
199C2×D4×C127C2×D411yescharacteristic
200C22×C4×C127—22no—
201C22×C4×C127—22no—
202C22×C4×C127—21no—
203C22×C4×C127—21no—
204C22×C4×C127—21no—
205C22×C4×C127—21no—
206C22×C4×C127—21no—
207C22×C4×C127—21no—
208C22×C4×C127—41no—
209C22×C4×C127C2×D411yescharacteristic
210C22×C4×C127C2×D411yescharacteristic
211C22×C4×C127C2×D411yescharacteristic
212SD16×C127—42no—
213SD16×C127—42no—
214D8×C127—42no—
215D8×C127—42no—
216C2×C8×C127—21no—
217C2×C8×C127—21no—
218C2×C8×C127—21no—
219C2×C8×C127—21no—
220C2×C8×C127—21no—
221C2×C8×C127—21no—
222C2×C8×C127—42no—
223C4⋊C4×C127—22no—
224C4⋊C4×C127—22no—
225C4⋊C4×C127—22no—
226C4⋊C4×C127—22no—
227C4⋊C4×C127—22no—
228C4⋊C4×C127—22no—
229C4⋊C4×C127—21no—
230C4⋊C4×C127—22no—
231C4⋊C4×C127—22no—
232C4⋊C4×C127—21no—
233C4⋊C4×C127—21no—
234C4⋊C4×C127—21no—
235C4⋊C4×C127—21no—
236C4⋊C4×C127—21no—
237C4⋊C4×C127—21no—
238C4⋊C4×C127—21no—
239C4⋊C4×C127C2×D412yes—
240C4⋊C4×C127C2×D412yes—
241C4⋊C4×C127C2×D411yescharacteristic
242C4⋊C4×C127C2×D411yescharacteristic
243C4⋊C4×C127C2×D411yescharacteristic
244C4⋊C4×C127C2×D411yescharacteristic
245C22⋊C4×C127—22no—
246C22⋊C4×C127—22no—
247C22⋊C4×C127—22no—
248C22⋊C4×C127—22no—
249C22⋊C4×C127—21no—
250C22⋊C4×C127—21no—
251C22⋊C4×C127—22no—
252C22⋊C4×C127—21no—
253C22⋊C4×C127—21no—
254C22⋊C4×C127—21no—
255C22⋊C4×C127—21no—
256C22⋊C4×C127—41no—
257C22⋊C4×C127—41no—
258C42×C127—22no—
259C42×C127—22no—
260C42×C127—21no—
261C42×C127—21no—
262C42×C127—21no—
263C42×C127—21no—
264C42×C127—22no—
265C42×C127—21no—
266C42×C127—21no—
267C42×C127C2×D411yescharacteristic
268C42×C127C2×D411yescharacteristic
269C42×C127C2×D411yescharacteristic
270C42×C127C2411yescharacteristic
271C23×C127—21no—
272C23×C127—21no—
273C23×C127—41no—
274C23×C127#12011yescharacteristic
275Q8×C127—21no—
276Q8×C127—21no—
277Q8×C127—21no—
278Q8×C127—44no—
279Q8×C127—42no—
280Q8×C127—41no—
281Q8×C127—41no—
282Q8×C127—41no—
283Q8×C127—41no—
284Q8×C127#13512yes—
285D4×C127—21no—
286D4×C127—21no—
287D4×C127—21no—
288D4×C127—42no—
289D4×C127—42no—
290D4×C127—42no—
291D4×C127—44no—
292D4×C127—41no—
293D4×C127—41no—
294D4×C127—41no—
295D4×C127—41no—
296D4×C127—82no—
297D4×C127#13512yes—
298C2×C4×C127—21no—
299C2×C4×C127—21no—
300C2×C4×C127—21no—
301C2×C4×C127—21no—
302C2×C4×C127—21no—
303C2×C4×C127—22no—
304C2×C4×C127—21no—
305C2×C4×C127—21no—
306C2×C4×C127—21no—
307C2×C4×C127—22no—
308C2×C4×C127—21no—
309C2×C4×C127—21no—
310C2×C4×C127—22no—
311C2×C4×C127—42no—
312C2×C4×C127—42no—
313C2×C4×C127—44no—
314C2×C4×C127—44no—
315C2×C4×C127—41no—
316C2×C4×C127—41no—
317C2×C4×C127—41no—
318C2×C4×C127—41no—
319C2×C4×C127—42no—
320C2×C4×C127—42no—
321C2×C4×C127—41no—
322C2×C4×C127—82no—
323C2×C4×C127#12011yescharacteristic
324C2×C4×C127#12011yescharacteristic
325C2×C4×C127#12011yescharacteristic
326C2×C4×C127C22×D411yescharacteristic
327C2×C4×C127C22×D411yescharacteristic
328C2×C4×C127C22×D411yescharacteristic
329C8×C127—41no—
330C8×C127—41no—
331C8×C127—41no—
332C8×C127—41no—
333C8×C127—41no—
334C8×C127—41no—
335C22×C127—21no—
336C22×C127—21no—
337C22×C127—22no—
338C22×C127—21no—
339C22×C127—41no—
340C22×C127—41no—
341C22×C127—41no—
342C22×C127—41no—
343C22×C127—41no—
344C22×C127—81no—
345C22×C127—81no—
346C22×C127—81no—
347C22×C127C2×#12011yescharacteristic
348C4×C127—21no—
349C4×C127—21no—
350C4×C127—22no—
351C4×C127—21no—
352C4×C127—41no—
353C4×C127—41no—
354C4×C127—42no—
355C4×C127—42no—
356C4×C127—41no—
357C4×C127—41no—
358C4×C127—41no—
359C4×C127—81no—
360C4×C127#45412yes—
361C4×C127C2×#13511yescharacteristic
362C4×C127C2×#13511yescharacteristic
363C4×C127#57511yescharacteristic
364C4×C127#57511yescharacteristic
365#18494C12711yesmaximal, characteristic, direct product factor, Sylow
366C2×C127—41no—
367C2×C127—42no—
368C2×C127—81no—
369C2×C127—161no—
370C2×C127#300211yescharacteristic
371C2×C127#300211yescharacteristic
372C2×C127C2×#45411yescharacteristic
373#3482C2×C12711yescharacteristic, complemented
374#3131C2×C12711yescharacteristic, complemented
375#3106C2×C12711yescharacteristic, complemented
376#3106C2×C12711yescharacteristic, complemented
377#1638C2×C12711yescharacteristic, complemented
378#1637C2×C12711yescharacteristic, complemented
379#1636C2×C12711yescharacteristic, complemented
380#1635C2×C12711yescharacteristic, complemented
381#1628C2×C12711yescharacteristic, complemented
382#1627C2×C12711yescharacteristic, complemented
383#1626C2×C12711yescharacteristic, complemented
384#1625C2×C12711yescharacteristic, complemented
385#1544C2×C12711yescharacteristic, complemented
386#1476C2×C12711yescharacteristic, complemented
387#1476C2×C12711yescharacteristic, complemented
388C127#1849411yescharacteristic, direct product factor, Sylow
389#557C22×C12711yescharacteristic
390#556—21no—
391#556C22×C12711yescharacteristic
392#552—22no—
393#552—21no—
394D4×Q8C22×C12711yescharacteristic
395#548—21no—
396#547—21no—
397#547C22×C12711yescharacteristic
398#533—21no—
399#533C22×C12711yescharacteristic
400#532C22×C12711yescharacteristic
401#529—21no—
402#529—22no—
403C4×#41—21no—
404C4×#41C22×C12711yescharacteristic
405C4×#41C22×C12711yescharacteristic
406C2×C4×Q8—21no—
407#488—22no—
408#487C22×C12711yescharacteristic
409#487C22×C12711yescharacteristic
410#486C22×C12711yescharacteristic
411#486C22×C12711yescharacteristic
412#482—21no—
413#482—21no—
414#477C22×C12711yescharacteristic
415#477C22×C12711yescharacteristic
416#476C22×C12711yescharacteristic
417#476C22×C12711yescharacteristic
418#460C22×C12711yescharacteristic
419#460C22×C12711yescharacteristic
420#459C22×C12711yescharacteristic
421#459C22×C12711yescharacteristic
422#449—21no—
423#449—21no—
424C4×SD16—21no—
425C4×SD16—21no—
426C4×D8—21no—
427C4×D8—21no—
428#431C22×C12711yescharacteristic
429#431C22×C12711yescharacteristic
430#416—22no—
431C2×C4×C8C22×C12711yescharacteristic
432#332C22×C12711yescharacteristic
433#332C22×C12711yescharacteristic
434#332C22×C12711yescharacteristic
435#332C22×C12711yescharacteristic
436Q8⋊C8C22×C12711yescharacteristic
437Q8⋊C8C22×C12711yescharacteristic
438Q8⋊C8C22×C12711yescharacteristic
439Q8⋊C8C22×C12711yescharacteristic
440D4⋊C8C22×C12711yescharacteristic
441D4⋊C8C22×C12711yescharacteristic
442D4⋊C8C22×C12711yescharacteristic
443D4⋊C8C22×C12711yescharacteristic
444C2×#41—21no—
445C2×#41—21no—
446C2×#41D4×C12711yescharacteristic
447C2×#41D4×C12711yescharacteristic
448C22×Q8—21no—
449C2×SD16—21no—
450C2×SD16—21no—
451C2×D8—21no—
452C2×D8—21no—
453C22×C8—21no—
454C4⋊Q8—21no—
455C4⋊Q8—21no—
456C4⋊Q8C23×C12711yescharacteristic
457C4⋊Q8C23×C12711yescharacteristic
458C4⋊Q8C23×C12711yescharacteristic
459#127C23×C12711yescharacteristic
460#126—22no—
461#126—22no—
462#126—22no—
463#125—22no—
464#125—22no—
465#125—21no—
466#125D4×C12712yes—
467#124—22no—
468#124—21no—
469#124—21no—
470#123—22no—
471#123—22no—
472#123—22no—
473C22⋊Q8—22no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477C22⋊Q8—21no—
478C22⋊Q8—22no—
479C22⋊Q8—21no—
480#121—22no—
481#121—21no—
482#121—21no—
483#121—21no—
484C4×Q8—22no—
485C4×Q8—22no—
486C4×Q8—21no—
487C4×Q8—21no—
488C4×Q8—21no—
489C4×Q8—21no—
490C4×Q8—21no—
491C4×Q8D4×C12711yescharacteristic
492C4×Q8D4×C12711yescharacteristic
493C4×Q8C23×C12711yescharacteristic
494C4×Q8C23×C12711yescharacteristic
495C4×D4—22no—
496C4×D4—22no—
497C4×D4—21no—
498C4×D4—21no—
499C4×D4—21no—
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4D4×C12711yescharacteristic
505C4×D4D4×C12711yescharacteristic
506C4×D4C23×C12711yescharacteristic
507C4×D4C23×C12711yescharacteristic
508#117—22no—
509#117—22no—
510#117—21no—
511#117—21no—
512#117—21no—
513#117D4×C12711yescharacteristic
514#117D4×C12711yescharacteristic
515#117D4×C12712yes—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—21no—
518C2×C42—22no—
519C2×C42—21no—
520C2×C42—21no—
521C2×C42C23×C12711yescharacteristic
522#107—21no—
523#107—21no—
524#106—21no—
525#106—21no—
526C4⋊C8C23×C12711yescharacteristic
527C4⋊C8C23×C12711yescharacteristic
528C4⋊C8C23×C12711yescharacteristic
529C4⋊C8C23×C12711yescharacteristic
530#103—21no—
531#103—21no—
532#103—22no—
533#103—22no—
534#102—21no—
535#102—21no—
536#102—22no—
537#102—22no—
538#102—21no—
539#102—21no—
540#102—21no—
541#102—21no—
542C22⋊C8—21no—
543C22⋊C8—21no—
544C4×C8—21no—
545C4×C8—21no—
546C4×C8—21no—
547C4×C8C23×C12711yescharacteristic
548C4×C8C23×C12711yescharacteristic
549#41—22no—
550#41—22no—
551#41—41no—
552#41—41no—
553#41—44no—
554#41—42no—
555#41—42no—
556C2×Q8—22no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—42no—
561C2×Q8—42no—
562C2×Q8C2×D4×C12711yescharacteristic
563C2×Q8C2×D4×C12711yescharacteristic
564C2×D4—22no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—41no—
571C2×D4C2×D4×C12711yescharacteristic
572C2×D4C2×D4×C12711yescharacteristic
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—41no—
582C22×C4C2×D4×C12711yescharacteristic
583C22×C4C2×D4×C12711yescharacteristic
584C22×C4C2×D4×C12711yescharacteristic
585SD16—42no—
586SD16—42no—
587D8—42no—
588D8—42no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—42no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—21no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4C2×D4×C12712yes—
613C4⋊C4C2×D4×C12712yes—
614C4⋊C4C2×D4×C12711yescharacteristic
615C4⋊C4C2×D4×C12711yescharacteristic
616C4⋊C4C2×D4×C12711yescharacteristic
617C4⋊C4C2×D4×C12711yescharacteristic
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—22no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—41no—
630C22⋊C4—41no—
631C42—22no—
632C42—22no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—22no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42C2×D4×C12711yescharacteristic
641C42C2×D4×C12711yescharacteristic
642C42C2×D4×C12711yescharacteristic
643C42C24×C12711yescharacteristic
644C23—21no—
645C23—21no—
646C23—41no—
647C23#120×C12711yescharacteristic
648Q8—21no—
649Q8—21no—
650Q8—21no—
651Q8—44no—
652Q8—42no—
653Q8—41no—
654Q8—41no—
655Q8—41no—
656Q8—41no—
657Q8#135×C12712yes—
658D4—21no—
659D4—21no—
660D4—21no—
661D4—42no—
662D4—42no—
663D4—42no—
664D4—44no—
665D4—41no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—82no—
670D4#135×C12712yes—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—82no—
696C2×C4#120×C12711yescharacteristic
697C2×C4#120×C12711yescharacteristic
698C2×C4#120×C12711yescharacteristic
699C2×C4C22×D4×C12711yescharacteristic
700C2×C4C22×D4×C12711yescharacteristic
701C2×C4C22×D4×C12711yescharacteristic
702C8—41no—
703C8—41no—
704C8—41no—
705C8—41no—
706C8—41no—
707C8—41no—
708C22—21no—
709C22—21no—
710C22—22no—
711C22—21no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22C2×#120×C12711yescharacteristic
721C4—21no—
722C4—21no—
723C4—22no—
724C4—21no—
725C4—41no—
726C4—41no—
727C4—42no—
728C4—42no—
729C4—41no—
730C4—41no—
731C4—41no—
732C4—81no—
733C4#454×C12712yes—
734C4C2×#135×C12711yescharacteristic
735C4C2×#135×C12711yescharacteristic
736C4#575×C12711yescharacteristic
737C4#575×C12711yescharacteristic
738C2—41no—
739C2—42no—
740C2—81no—
741C2—161no—
742C2C127×#300211yescharacteristic
743C2C127×#300211yescharacteristic
744C2C2×#454×C12711yescharacteristic
subgroupG/H
centerC2×C4×C127#120
commutator, Frattini, cosocleC42C24×C127
socleC22×C127C2×#120
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#3482C2semidirect
2. C127×#3131C2semidirect
3. C127×#3106C2semidirect
4. C127×#3106C2semidirect
5. C127×#1638C2semidirect
6. C127×#1637C2semidirect
7. C127×#1636C2semidirect
8. C127×#1635C2semidirect
9. C127×#1628C2semidirect
10. C127×#1627C2semidirect
11. C127×#1626C2semidirect
12. C127×#1625C2semidirect
13. C127×#1544C2semidirect
14. C127×#1476C2semidirect
15. C127×#1476C2semidirect
365. #18494C127direct (N × H)
373. #3482C2×C127semidirect
374. #3131C2×C127semidirect
375. #3106C2×C127semidirect
376. #3106C2×C127semidirect
377. #1638C2×C127semidirect
378. #1637C2×C127semidirect
379. #1636C2×C127semidirect
380. #1635C2×C127semidirect
381. #1628C2×C127semidirect
382. #1627C2×C127semidirect
383. #1626C2×C127semidirect
384. #1625C2×C127semidirect
385. #1544C2×C127semidirect
386. #1476C2×C127semidirect
387. #1476C2×C127semidirect
388. C127#18494direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#34822
C127×#31312
C127×#31062
C127×#16382
C127×#16372
C127×#16362
C127×#16352
C127×#16282
C127×#16272
C127×#16262
C127×#16252
C127×#15442
C127×#14762
#18494127