Finite Group Databasebeta

← C127×#18463 #44582136

Subgroups — C127×#18463 #44582136

Order 32512.

930 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3560C211yesmaximal, characteristic
2C127×#3218C211yesmaximal, characteristic, complemented
3C127×#3206C211yesmaximal, characteristic, complemented
4C127×#2821C211yesmaximal, characteristic, complemented
5C127×#1606C212yesmaximal, complemented
6C127×#1604C212yesmaximal, complemented
7C127×#1603C212yesmaximal, complemented
8C127×#1601C212yesmaximal, complemented
9C127×#1521C211yesmaximal, characteristic, complemented
10C127×#1514C211yesmaximal, characteristic, complemented
11C127×#1473C211yesmaximal, characteristic, complemented
12#563×C127—21no—
13#560×C127—21no—
14#553×C127—21no—
15#553×C127—21no—
16#551×C127—21no—
17#547×C127—21no—
18#546×C127—21no—
19#546×C127—21no—
20#542×C127—21no—
21#539×C127—21no—
22#539×C127C2211yescharacteristic
23#538×C127—21no—
24#538×C127—21no—
25#538×C127C2211yescharacteristic
26#537×C127C2211yescharacteristic
27#534×C127C2211yescharacteristic
28#532×C127C2211yescharacteristic
29C2×C4⋊Q8×C127C2211yescharacteristic, complemented
30#529×C127C2211yescharacteristic
31C2×#126×C127C2211yescharacteristic
32#497×C127—21no—
33#492×C127—21no—
34#491×C127—21no—
35#487×C127—21no—
36#462×C127—21no—
37#461×C127—21no—
38#461×C127—21no—
39#461×C127—21no—
40#451×C127C2212yescomplemented
41#448×C127C2212yes—
42#448×C127C2212yes—
43#448×C127C2212yescomplemented
44#432×C127C2211yescharacteristic, complemented
45#431×C127C2211yescharacteristic, complemented
46#400×C127—21no—
47#399×C127—21no—
48#398×C127—21no—
49#397×C127—21no—
50#395×C127C2212yescomplemented
51#393×C127C2212yes—
52#383×C127C2211yescharacteristic, complemented
53#328×C127C2212yescomplemented
54#327×C127C2212yes—
55#327×C127C2212yes—
56#327×C127C2212yescomplemented
57#324×C127C2212yescomplemented
58#323×C127C2212yes—
59C2×#41×C127—21no—
60C2×#41×C127—21no—
61C22×Q8×C127C2312yes—
62C22×D4×C127—21no—
63C2×Q16×C127—22no—
64C2×SD16×C127—22no—
65C2×SD16×C127—22no—
66C2×SD16×C127—22no—
67C4⋊Q8×C127—21no—
68C4⋊Q8×C127—21no—
69C4⋊Q8×C127—21no—
70C4⋊Q8×C127—21no—
71C4⋊Q8×C127—21no—
72C4⋊Q8×C127D411yescharacteristic
73#127×C127D411yescharacteristic
74#126×C127—21no—
75#126×C127—21no—
76#126×C127—21no—
77#126×C127—21no—
78#126×C127—21no—
79#126×C127—21no—
80#126×C127—21no—
81#126×C127—21no—
82#126×C127—21no—
83#125×C127—21no—
84#125×C127—21no—
85#125×C127D411yescharacteristic
86#124×C127—21no—
87#124×C127—21no—
88#124×C127—21no—
89#124×C127—21no—
90#124×C127D411yescharacteristic
91#123×C127—21no—
92#123×C127—21no—
93#123×C127—21no—
94#123×C127—21no—
95#123×C127—21no—
96#123×C127—21no—
97#123×C127—21no—
98#123×C127—21no—
99#123×C127—21no—
100#123×C127—21no—
101#123×C127—21no—
102#123×C127—21no—
103C22⋊Q8×C127—21no—
104C22⋊Q8×C127—21no—
105C22⋊Q8×C127—21no—
106C22⋊Q8×C127—21no—
107C22⋊Q8×C127—21no—
108C22⋊Q8×C127—21no—
109C22⋊Q8×C127—21no—
110C22⋊Q8×C127C2311yescharacteristic
111#121×C127—21no—
112#121×C127—21no—
113#121×C127—21no—
114#121×C127—21no—
115#121×C127—21no—
116#121×C127—21no—
117#121×C127—21no—
118#121×C127—21no—
119#121×C127—21no—
120#121×C127—21no—
121#121×C127—21no—
122#121×C127—21no—
123#121×C127C2311yescharacteristic
124#121×C127C2311yescharacteristic
125#121×C127C2311yescharacteristic
126#120×C127—21no—
127#120×C127—21no—
128#120×C127—21no—
129#120×C127—21no—
130#120×C127—21no—
131C4×Q8×C127D411yescharacteristic
132C4×D4×C127—21no—
133C4×D4×C127—21no—
134C4×D4×C127—21no—
135C4×D4×C127—21no—
136C4×D4×C127—21no—
137C4×D4×C127—21no—
138C4×D4×C127—21no—
139C4×D4×C127—21no—
140C4×D4×C127D411yescharacteristic
141C4×D4×C127D411yescharacteristic
142C4×D4×C127D411yescharacteristic
143#117×C127—21no—
144#117×C127—21no—
145C2×C4⋊C4×C127—21no—
146C2×C4⋊C4×C127—21no—
147C2×C4⋊C4×C127—21no—
148C2×C4⋊C4×C127—22no—
149C2×C4⋊C4×C127D411yescharacteristic
150C2×C4⋊C4×C127D411yescharacteristic
151C2×C4⋊C4×C127C2311yescharacteristic
152C2×C22⋊C4×C127—21no—
153C2×C22⋊C4×C127—21no—
154C2×C22⋊C4×C127—22no—
155C2×C22⋊C4×C127D411yescharacteristic
156C2×C22⋊C4×C127D411yescharacteristic
157C2×C22⋊C4×C127C2311yescharacteristic
158C2×C42×C127C2311yescharacteristic
159C4⋊C8×C127—21no—
160C4⋊C8×C127—21no—
161#103×C127—22no—
162#103×C127—22no—
163#103×C127—22no—
164#103×C127—22no—
165C22⋊C8×C127C2312yes—
166C22⋊C8×C127C2312yes—
167#97×C127—21no—
168C4×C8×C127—21no—
169#95×C127—21no—
170#95×C127—21no—
171#95×C127—22no—
172#95×C127—22no—
173#95×C127C2312yes—
174C24×C127—21no—
175C24×C127C2×D411yescharacteristic
176#41×C127—82no—
177#41×C127—82no—
178C2×Q8×C127—21no—
179C2×Q8×C127—21no—
180C2×Q8×C127—22no—
181C2×Q8×C127—22no—
182C2×Q8×C127—82no—
183C2×Q8×C127C2×D411yescharacteristic
184C2×D4×C127—21no—
185C2×D4×C127—21no—
186C2×D4×C127—21no—
187C2×D4×C127—21no—
188C2×D4×C127—21no—
189C2×D4×C127—21no—
190C2×D4×C127—21no—
191C2×D4×C127—21no—
192C2×D4×C127—21no—
193C2×D4×C127—21no—
194C2×D4×C127—21no—
195C2×D4×C127—21no—
196C2×D4×C127—82no—
197C2×D4×C127C2×D411yescharacteristic
198C2×D4×C127C2×D411yescharacteristic
199C2×D4×C127C2×D411yescharacteristic
200C22×C4×C127—21no—
201C22×C4×C127—21no—
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—22no—
209C22×C4×C127—22no—
210C22×C4×C127C2×D411yescharacteristic
211C22×C4×C127C2×D411yescharacteristic
212C22×C4×C127C2×D411yescharacteristic
213C22×C4×C127C2×D411yescharacteristic
214C22×C4×C127C2×D411yescharacteristic
215C22×C4×C127C2411yescharacteristic
216Q16×C127—82no—
217SD16×C127—82no—
218SD16×C127—82no—
219SD16×C127—82no—
220C2×C8×C127—22no—
221C2×C8×C127—22no—
222C4⋊C4×C127—21no—
223C4⋊C4×C127—21no—
224C4⋊C4×C127—21no—
225C4⋊C4×C127—21no—
226C4⋊C4×C127—21no—
227C4⋊C4×C127—21no—
228C4⋊C4×C127—21no—
229C4⋊C4×C127—21no—
230C4⋊C4×C127—21no—
231C4⋊C4×C127—21no—
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×C127—41no—
240C4⋊C4×C127—41no—
241C4⋊C4×C127—41no—
242C4⋊C4×C127—41no—
243C4⋊C4×C127—82no—
244C4⋊C4×C127C2×D411yescharacteristic
245C4⋊C4×C127C2×D411yescharacteristic
246C4⋊C4×C127C2×D411yescharacteristic
247C4⋊C4×C127C2×D411yescharacteristic
248C22⋊C4×C127—21no—
249C22⋊C4×C127—21no—
250C22⋊C4×C127—21no—
251C22⋊C4×C127—21no—
252C22⋊C4×C127—21no—
253C22⋊C4×C127—21no—
254C22⋊C4×C127—21no—
255C22⋊C4×C127—21no—
256C22⋊C4×C127—21no—
257C22⋊C4×C127—21no—
258C22⋊C4×C127—21no—
259C22⋊C4×C127—21no—
260C22⋊C4×C127—21no—
261C22⋊C4×C127—21no—
262C22⋊C4×C127—21no—
263C22⋊C4×C127—21no—
264C22⋊C4×C127—21no—
265C22⋊C4×C127—21no—
266C22⋊C4×C127—21no—
267C22⋊C4×C127—21no—
268C22⋊C4×C127—21no—
269C22⋊C4×C127—21no—
270C22⋊C4×C127—21no—
271C22⋊C4×C127—21no—
272C22⋊C4×C127—21no—
273C22⋊C4×C127—82no—
274C42×C127—21no—
275C42×C127—21no—
276C42×C127—21no—
277C42×C127C2×D411yescharacteristic
278C42×C127C2×D411yescharacteristic
279C42×C127C2×D411yescharacteristic
280C42×C127C2×D411yescharacteristic
281C23×C127—21no—
282C23×C127—21no—
283C23×C127—21no—
284C23×C127—21no—
285C23×C127—22no—
286C23×C127—41no—
287C23×C127—41no—
288C23×C127—81no—
289C23×C127—81no—
290C23×C127—81no—
291C23×C127C22×D411yescharacteristic
292Q8×C127—41no—
293Q8×C127—42no—
294Q8×C127—42no—
295Q8×C127—42no—
296Q8×C127—42no—
297Q8×C127—81no—
298Q8×C127—81no—
299D4×C127—41no—
300D4×C127—41no—
301D4×C127—41no—
302D4×C127—42no—
303D4×C127—42no—
304D4×C127—42no—
305D4×C127—81no—
306D4×C127—81no—
307D4×C127—81no—
308D4×C127—81no—
309D4×C127—81no—
310D4×C127—81no—
311D4×C127—81no—
312D4×C127—81no—
313D4×C127—81no—
314C2×C4×C127—22no—
315C2×C4×C127—21no—
316C2×C4×C127—21no—
317C2×C4×C127—21no—
318C2×C4×C127—21no—
319C2×C4×C127—21no—
320C2×C4×C127—21no—
321C2×C4×C127—21no—
322C2×C4×C127—21no—
323C2×C4×C127—22no—
324C2×C4×C127—41no—
325C2×C4×C127—41no—
326C2×C4×C127—41no—
327C2×C4×C127—41no—
328C2×C4×C127—42no—
329C2×C4×C127—42no—
330C2×C4×C127—42no—
331C2×C4×C127—42no—
332C2×C4×C127—42no—
333C2×C4×C127—42no—
334C2×C4×C127—81no—
335C2×C4×C127—81no—
336C2×C4×C127—81no—
337C2×C4×C127—81no—
338C2×C4×C127—81no—
339C2×C4×C127—81no—
340C2×C4×C127—81no—
341C2×C4×C127—81no—
342C2×C4×C127#12011yescharacteristic
343C2×C4×C127#12011yescharacteristic
344C2×C4×C127#12011yescharacteristic
345C2×C4×C127#12011yescharacteristic
346C2×C4×C127C22×D411yescharacteristic
347C2×C4×C127C22×D411yescharacteristic
348C8×C127—42no—
349C8×C127—42no—
350C22×C127—21no—
351C22×C127—21no—
352C22×C127—41no—
353C22×C127—41no—
354C22×C127—41no—
355C22×C127—41no—
356C22×C127—41no—
357C22×C127—41no—
358C22×C127—41no—
359C22×C127—41no—
360C22×C127—41no—
361C22×C127—41no—
362C22×C127—41no—
363C22×C127—41no—
364C22×C127—82no—
365C22×C127—162no—
366C22×C127C2×#12011yescharacteristic
367C22×C127#57712yes—
368C4×C127—21no—
369C4×C127—21no—
370C4×C127—21no—
371C4×C127—21no—
372C4×C127—21no—
373C4×C127—21no—
374C4×C127—41no—
375C4×C127—41no—
376C4×C127—41no—
377C4×C127—41no—
378C4×C127—41no—
379C4×C127—41no—
380C4×C127—41no—
381C4×C127—41no—
382C4×C127—82no—
383C4×C127—82no—
384#18463C12711yesmaximal, characteristic, direct product factor, Sylow
385C2×C127—22no—
386C2×C127—81no—
387C2×C127—81no—
388C2×C127—81no—
389C2×C127—81no—
390C2×C127#300911yescharacteristic
391C2×C127#302211yescharacteristic
392C2×C127#302711yescharacteristic
393#3560C2×C12711yescharacteristic
394#3218C2×C12711yescharacteristic, complemented
395#3206C2×C12711yescharacteristic, complemented
396#2821C2×C12711yescharacteristic, complemented
397#1606C2×C12712yescomplemented
398#1604C2×C12712yescomplemented
399#1603C2×C12712yescomplemented
400#1601C2×C12712yescomplemented
401#1521C2×C12711yescharacteristic, complemented
402#1514C2×C12711yescharacteristic, complemented
403#1473C2×C12711yescharacteristic, complemented
404C127#1846311yescharacteristic, direct product factor, Sylow
405#563—21no—
406#560—21no—
407#553—21no—
408#553—21no—
409#551—21no—
410#547—21no—
411#546—21no—
412#546—21no—
413#542—21no—
414#539—21no—
415#539C22×C12711yescharacteristic
416#538—21no—
417#538—21no—
418#538C22×C12711yescharacteristic
419#537C22×C12711yescharacteristic
420#534C22×C12711yescharacteristic
421#532C22×C12711yescharacteristic
422C2×C4⋊Q8C22×C12711yescharacteristic, complemented
423#529C22×C12711yescharacteristic
424C2×#126C22×C12711yescharacteristic
425#497—21no—
426#492—21no—
427#491—21no—
428#487—21no—
429#462—21no—
430#461—21no—
431#461—21no—
432#461—21no—
433#451C22×C12712yescomplemented
434#448C22×C12712yes—
435#448C22×C12712yes—
436#448C22×C12712yescomplemented
437#432C22×C12711yescharacteristic, complemented
438#431C22×C12711yescharacteristic, complemented
439#400—21no—
440#399—21no—
441#398—21no—
442#397—21no—
443#395C22×C12712yescomplemented
444#393C22×C12712yes—
445#383C22×C12711yescharacteristic, complemented
446#328C22×C12712yescomplemented
447#327C22×C12712yes—
448#327C22×C12712yes—
449#327C22×C12712yescomplemented
450#324C22×C12712yescomplemented
451#323C22×C12712yes—
452C2×#41—21no—
453C2×#41—21no—
454C22×Q8C23×C12712yes—
455C22×D4—21no—
456C2×Q16—22no—
457C2×SD16—22no—
458C2×SD16—22no—
459C2×SD16—22no—
460C4⋊Q8—21no—
461C4⋊Q8—21no—
462C4⋊Q8—21no—
463C4⋊Q8—21no—
464C4⋊Q8—21no—
465C4⋊Q8D4×C12711yescharacteristic
466#127D4×C12711yescharacteristic
467#126—21no—
468#126—21no—
469#126—21no—
470#126—21no—
471#126—21no—
472#126—21no—
473#126—21no—
474#126—21no—
475#126—21no—
476#125—21no—
477#125—21no—
478#125D4×C12711yescharacteristic
479#124—21no—
480#124—21no—
481#124—21no—
482#124—21no—
483#124D4×C12711yescharacteristic
484#123—21no—
485#123—21no—
486#123—21no—
487#123—21no—
488#123—21no—
489#123—21no—
490#123—21no—
491#123—21no—
492#123—21no—
493#123—21no—
494#123—21no—
495#123—21no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—21no—
500C22⋊Q8—21no—
501C22⋊Q8—21no—
502C22⋊Q8—21no—
503C22⋊Q8C23×C12711yescharacteristic
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121—21no—
514#121—21no—
515#121—21no—
516#121C23×C12711yescharacteristic
517#121C23×C12711yescharacteristic
518#121C23×C12711yescharacteristic
519#120—21no—
520#120—21no—
521#120—21no—
522#120—21no—
523#120—21no—
524C4×Q8D4×C12711yescharacteristic
525C4×D4—21no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—21no—
533C4×D4D4×C12711yescharacteristic
534C4×D4D4×C12711yescharacteristic
535C4×D4D4×C12711yescharacteristic
536#117—21no—
537#117—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4D4×C12711yescharacteristic
543C2×C4⋊C4D4×C12711yescharacteristic
544C2×C4⋊C4C23×C12711yescharacteristic
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4D4×C12711yescharacteristic
549C2×C22⋊C4D4×C12711yescharacteristic
550C2×C22⋊C4C23×C12711yescharacteristic
551C2×C42C23×C12711yescharacteristic
552C4⋊C8—21no—
553C4⋊C8—21no—
554#103—22no—
555#103—22no—
556#103—22no—
557#103—22no—
558C22⋊C8C23×C12712yes—
559C22⋊C8C23×C12712yes—
560#97—21no—
561C4×C8—21no—
562#95—21no—
563#95—21no—
564#95—22no—
565#95—22no—
566#95C23×C12712yes—
567C24—21no—
568C24C2×D4×C12711yescharacteristic
569#41—82no—
570#41—82no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—82no—
576C2×Q8C2×D4×C12711yescharacteristic
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—82no—
590C2×D4C2×D4×C12711yescharacteristic
591C2×D4C2×D4×C12711yescharacteristic
592C2×D4C2×D4×C12711yescharacteristic
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4C2×D4×C12711yescharacteristic
604C22×C4C2×D4×C12711yescharacteristic
605C22×C4C2×D4×C12711yescharacteristic
606C22×C4C2×D4×C12711yescharacteristic
607C22×C4C2×D4×C12711yescharacteristic
608C22×C4C24×C12711yescharacteristic
609Q16—82no—
610SD16—82no—
611SD16—82no—
612SD16—82no—
613C2×C8—22no—
614C2×C8—22no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—41no—
633C4⋊C4—41no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4—82no—
637C4⋊C4C2×D4×C12711yescharacteristic
638C4⋊C4C2×D4×C12711yescharacteristic
639C4⋊C4C2×D4×C12711yescharacteristic
640C4⋊C4C2×D4×C12711yescharacteristic
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—82no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42C2×D4×C12711yescharacteristic
671C42C2×D4×C12711yescharacteristic
672C42C2×D4×C12711yescharacteristic
673C42C2×D4×C12711yescharacteristic
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—22no—
679C23—41no—
680C23—41no—
681C23—81no—
682C23—81no—
683C23—81no—
684C23C22×D4×C12711yescharacteristic
685Q8—41no—
686Q8—42no—
687Q8—42no—
688Q8—42no—
689Q8—42no—
690Q8—81no—
691Q8—81no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—42no—
696D4—42no—
697D4—42no—
698D4—81no—
699D4—81no—
700D4—81no—
701D4—81no—
702D4—81no—
703D4—81no—
704D4—81no—
705D4—81no—
706D4—81no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4#120×C12711yescharacteristic
736C2×C4#120×C12711yescharacteristic
737C2×C4#120×C12711yescharacteristic
738C2×C4#120×C12711yescharacteristic
739C2×C4C22×D4×C12711yescharacteristic
740C2×C4C22×D4×C12711yescharacteristic
741C8—42no—
742C8—42no—
743C22—21no—
744C22—21no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—82no—
758C22—162no—
759C22C2×#120×C12711yescharacteristic
760C22#577×C12712yes—
761C4—21no—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—21no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—82no—
776C4—82no—
777C2—22no—
778C2—81no—
779C2—81no—
780C2—81no—
781C2—81no—
782C2C127×#300911yescharacteristic
783C2C127×#302211yescharacteristic
784C2C127×#302711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC22×C4C24×C127
prime radicalC127×#3560C2
LCSG ▷ C22×C4 ▷ 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×#3218C2semidirect
3. C127×#3206C2semidirect
4. C127×#2821C2semidirect
5. C127×#1606C2semidirect
6. C127×#1604C2semidirect
7. C127×#1603C2semidirect
8. C127×#1601C2semidirect
9. C127×#1521C2semidirect
10. C127×#1514C2semidirect
11. C127×#1473C2semidirect
29. C2×C4⋊Q8×C127C22semidirect
40. #451×C127C22semidirect
43. #448×C127C22semidirect
44. #432×C127C22semidirect
45. #431×C127C22semidirect
50. #395×C127C22semidirect
52. #383×C127C22semidirect
53. #328×C127C22semidirect
56. #327×C127C22semidirect
57. #324×C127C22semidirect
384. #18463C127direct (N × H)
394. #3218C2×C127semidirect
395. #3206C2×C127semidirect
396. #2821C2×C127semidirect
397. #1606C2×C127semidirect
398. #1604C2×C127semidirect
399. #1603C2×C127semidirect
400. #1601C2×C127semidirect
401. #1521C2×C127semidirect
402. #1514C2×C127semidirect
403. #1473C2×C127semidirect
404. C127#18463direct (N × H)
422. C2×C4⋊Q8C22×C127semidirect
433. #451C22×C127semidirect
436. #448C22×C127semidirect
437. #432C22×C127semidirect
438. #431C22×C127semidirect
443. #395C22×C127semidirect
445. #383C22×C127semidirect
446. #328C22×C127semidirect
449. #327C22×C127semidirect
450. #324C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35602
C127×#32182
C127×#32062
C127×#28212
C127×#16062
C127×#16042
C127×#16032
C127×#16012
C127×#15212
C127×#15142
C127×#14732
#18463127