Finite Group Databasebeta

← C127×#18464 #44582137

Subgroups — C127×#18464 #44582137

Order 32512.

970 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3564C211yesmaximal, characteristic, complemented
2C127×#3217C211yesmaximal, characteristic, complemented
3C127×#3208C211yesmaximal, characteristic, complemented
4C127×#2818C211yesmaximal, characteristic, complemented
5C127×#1600C212yesmaximal, complemented
6C127×#1599C212yesmaximal, complemented
7C127×#1597C212yesmaximal, complemented
8C127×#1596C212yesmaximal, complemented
9C127×#1521C211yesmaximal, characteristic, complemented
10C127×#1515C211yesmaximal, characteristic, complemented
11C127×#1473C211yesmaximal, characteristic, complemented
12#563×C127—21no—
13#563×C127—21no—
14#556×C127—21no—
15#554×C127—21no—
16#552×C127—21no—
17#552×C127—21no—
18#551×C127—21no—
19#551×C127—21no—
20#544×C127C2211yescharacteristic
21#543×C127C2211yescharacteristic
22#542×C127—21no—
23#541×C127—21no—
24#541×C127—21no—
25#539×C127—21no—
26#539×C127C2211yescharacteristic
27#538×C127C2211yescharacteristic
28#533×C127C2211yescharacteristic
29C2×#127×C127C2211yescharacteristic
30#529×C127C2211yescharacteristic
31C2×#126×C127C2211yescharacteristic
32#496×C127—21no—
33#492×C127—21no—
34#490×C127—21no—
35#486×C127—21no—
36#460×C127—21no—
37#460×C127—21no—
38#460×C127—21no—
39#459×C127—21no—
40#450×C127C2212yes—
41#450×C127C2212yes—
42#450×C127C2212yes—
43#447×C127C2212yes—
44#432×C127C2211yescharacteristic
45#431×C127C2211yescharacteristic
46#394×C127—21no—
47#394×C127—21no—
48#394×C127C2212yes—
49#392×C127—21no—
50#392×C127—21no—
51#392×C127C2212yes—
52#383×C127C2211yescharacteristic
53#328×C127C2212yes—
54#328×C127C2212yes—
55#328×C127C2212yes—
56#327×C127C2212yes—
57#324×C127C2212yes—
58#323×C127C2212yes—
59C22×D4×C127—22no—
60C22×D4×C127—21no—
61C22×D4×C127—21no—
62C22×D4×C127C2312yes—
63C2×SD16×C127—22no—
64C2×SD16×C127—22no—
65C2×SD16×C127—22no—
66C2×D8×C127—22no—
67C4⋊Q8×C127—21no—
68C4⋊Q8×C127—21no—
69C4⋊Q8×C127—21no—
70C4⋊Q8×C127D411yescharacteristic, complemented
71C4⋊Q8×C127D411yescharacteristic, complemented
72#127×C127—21no—
73#127×C127—21no—
74#127×C127—21no—
75#127×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#126×C127—21no—
84#126×C127—21no—
85#126×C127—21no—
86#126×C127—21no—
87#126×C127—21no—
88#126×C127—21no—
89#125×C127—21no—
90#125×C127—21no—
91#125×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×C127D411yescharacteristic, complemented
99#124×C127—21no—
100#124×C127—21no—
101#124×C127—21no—
102#124×C127D411yescharacteristic, complemented
103#123×C127—21no—
104#123×C127—21no—
105#123×C127—21no—
106#123×C127—21no—
107#123×C127—21no—
108#123×C127—21no—
109#123×C127—21no—
110#123×C127—21no—
111C22⋊Q8×C127—21no—
112C22⋊Q8×C127—21no—
113C22⋊Q8×C127—21no—
114C22⋊Q8×C127—21no—
115C22⋊Q8×C127—21no—
116C22⋊Q8×C127—21no—
117C22⋊Q8×C127—21no—
118C22⋊Q8×C127—21no—
119C22⋊Q8×C127—21no—
120C22⋊Q8×C127—21no—
121C22⋊Q8×C127—21no—
122C22⋊Q8×C127—21no—
123C22⋊Q8×C127—21no—
124C22⋊Q8×C127—21no—
125C22⋊Q8×C127C2311yescharacteristic
126C22⋊Q8×C127C2311yescharacteristic
127C22⋊Q8×C127C2311yescharacteristic
128#121×C127—21no—
129#121×C127C2311yescharacteristic
130#120×C127—21no—
131C4×Q8×C127—21no—
132C4×Q8×C127—21no—
133C4×Q8×C127—21no—
134C4×Q8×C127D411yescharacteristic, complemented
135C4×Q8×C127D411yescharacteristic, complemented
136C4×Q8×C127D411yescharacteristic, complemented
137C4×D4×C127—21no—
138C4×D4×C127—21no—
139C4×D4×C127—21no—
140C4×D4×C127—21no—
141C4×D4×C127—21no—
142C4×D4×C127D411yescharacteristic, complemented
143#117×C127—21no—
144#117×C127—21no—
145#117×C127—21no—
146#117×C127—21no—
147#117×C127—21no—
148#117×C127—21no—
149C2×C4⋊C4×C127—21no—
150C2×C4⋊C4×C127D411yescharacteristic
151C2×C4⋊C4×C127D411yescharacteristic
152C2×C4⋊C4×C127C2311yescharacteristic
153C2×C22⋊C4×C127—21no—
154C2×C22⋊C4×C127—22no—
155C2×C22⋊C4×C127—22no—
156C2×C22⋊C4×C127—22no—
157C2×C22⋊C4×C127D411yescharacteristic
158C2×C22⋊C4×C127D411yescharacteristic
159C2×C22⋊C4×C127C2311yescharacteristic
160C2×C42×C127C2311yescharacteristic
161C4⋊C8×C127—21no—
162C4⋊C8×C127—21no—
163#102×C127—22no—
164#102×C127—22no—
165#102×C127—22no—
166#102×C127—22no—
167C22⋊C8×C127C2312yes—
168C22⋊C8×C127C2312yes—
169#97×C127—21no—
170C4×C8×C127—21no—
171#95×C127—21no—
172#95×C127—21no—
173#95×C127C2312yes—
174C24×C127—22no—
175C24×C127C2×D411yescharacteristic
176C2×Q8×C127—21no—
177C2×Q8×C127—21no—
178C2×Q8×C127—21no—
179C2×Q8×C127C2×D411yescharacteristic
180C2×Q8×C127C2×D411yescharacteristic
181C2×Q8×C127C2×D411yescharacteristic
182C2×D4×C127—21no—
183C2×D4×C127—21no—
184C2×D4×C127—21no—
185C2×D4×C127—22no—
186C2×D4×C127—22no—
187C2×D4×C127—41no—
188C2×D4×C127—41no—
189C2×D4×C127—41no—
190C2×D4×C127—41no—
191C2×D4×C127—82no—
192C2×D4×C127—82no—
193C2×D4×C127—82no—
194C2×D4×C127—82no—
195C2×D4×C127—82no—
196C2×D4×C127—82no—
197C2×D4×C127C2×D411yescharacteristic
198C22×C4×C127—21no—
199C22×C4×C127—21no—
200C22×C4×C127—21no—
201C22×C4×C127—21no—
202C22×C4×C127—21no—
203C22×C4×C127—22no—
204C22×C4×C127C2×D411yescharacteristic
205C22×C4×C127C2×D411yescharacteristic
206C22×C4×C127C2×D411yescharacteristic
207C22×C4×C127C2×D411yescharacteristic
208C22×C4×C127C2×D411yescharacteristic
209C22×C4×C127C2411yescharacteristic
210SD16×C127—82no—
211SD16×C127—82no—
212SD16×C127—82no—
213D8×C127—82no—
214C2×C8×C127—22no—
215C2×C8×C127—22no—
216C4⋊C4×C127—21no—
217C4⋊C4×C127—21no—
218C4⋊C4×C127—21no—
219C4⋊C4×C127—21no—
220C4⋊C4×C127—21no—
221C4⋊C4×C127—21no—
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—21no—
240C4⋊C4×C127—21no—
241C4⋊C4×C127—21no—
242C4⋊C4×C127—21no—
243C4⋊C4×C127—21no—
244C4⋊C4×C127—21no—
245C4⋊C4×C127C2×D411yescharacteristic
246C4⋊C4×C127C2×D411yescharacteristic
247C4⋊C4×C127C2×D411yescharacteristic
248C4⋊C4×C127C2×D411yescharacteristic
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—82no—
271C22⋊C4×C127—82no—
272C22⋊C4×C127—82no—
273C42×C127—21no—
274C42×C127—21no—
275C42×C127—21no—
276C42×C127—21no—
277C42×C127—21no—
278C42×C127—21no—
279C42×C127—21no—
280C42×C127C2×D411yescharacteristic
281C42×C127C2×D411yescharacteristic
282C42×C127C2×D411yescharacteristic
283C42×C127C2×D411yescharacteristic
284C23×C127—21no—
285C23×C127—21no—
286C23×C127—22no—
287C23×C127—41no—
288C23×C127—41no—
289C23×C127—42no—
290C23×C127—42no—
291C23×C127—42no—
292C23×C127—42no—
293C23×C127—42no—
294C23×C127—42no—
295C23×C127—42no—
296C23×C127C22×D411yescharacteristic
297Q8×C127—41no—
298Q8×C127—41no—
299Q8×C127—41no—
300Q8×C127—81no—
301Q8×C127—81no—
302Q8×C127—81no—
303D4×C127—41no—
304D4×C127—42no—
305D4×C127—42no—
306D4×C127—42no—
307D4×C127—42no—
308D4×C127—42no—
309D4×C127—82no—
310D4×C127—82no—
311D4×C127—82no—
312D4×C127—82no—
313D4×C127—81no—
314D4×C127—81no—
315D4×C127—88no—
316C2×C4×C127—22no—
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—21no—
324C2×C4×C127—21no—
325C2×C4×C127—21no—
326C2×C4×C127—21no—
327C2×C4×C127—22no—
328C2×C4×C127—41no—
329C2×C4×C127—41no—
330C2×C4×C127—41no—
331C2×C4×C127—41no—
332C2×C4×C127—42no—
333C2×C4×C127—42no—
334C2×C4×C127—42no—
335C2×C4×C127—81no—
336C2×C4×C127—81no—
337C2×C4×C127—81no—
338C2×C4×C127—81no—
339C2×C4×C127—81no—
340C2×C4×C127#12011yescharacteristic
341C2×C4×C127#12011yescharacteristic
342C2×C4×C127#12011yescharacteristic
343C2×C4×C127#12011yescharacteristic
344C2×C4×C127C22×D411yescharacteristic
345C2×C4×C127C22×D411yescharacteristic
346C8×C127—42no—
347C8×C127—42no—
348C22×C127—21no—
349C22×C127—21no—
350C22×C127—41no—
351C22×C127—41no—
352C22×C127—41no—
353C22×C127—41no—
354C22×C127—41no—
355C22×C127—41no—
356C22×C127—82no—
357C22×C127—82no—
358C22×C127—82no—
359C22×C127—82no—
360C22×C127—82no—
361C22×C127—82no—
362C22×C127—82no—
363C22×C127—82no—
364C22×C127C2×#12011yescharacteristic
365C22×C127#57712yes—
366C4×C127—21no—
367C4×C127—21no—
368C4×C127—21no—
369C4×C127—21no—
370C4×C127—21no—
371C4×C127—21no—
372C4×C127—41no—
373C4×C127—41no—
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—
383#18464C12711yesmaximal, characteristic, direct product factor, Sylow
384C2×C127—22no—
385C2×C127—81no—
386C2×C127—81no—
387C2×C127—162no—
388C2×C127#301011yescharacteristic
389C2×C127#302111yescharacteristic
390C2×C127#302711yescharacteristic
391#3564C2×C12711yescharacteristic, complemented
392#3217C2×C12711yescharacteristic, complemented
393#3208C2×C12711yescharacteristic, complemented
394#2818C2×C12711yescharacteristic, complemented
395#1600C2×C12712yescomplemented
396#1599C2×C12712yescomplemented
397#1597C2×C12712yescomplemented
398#1596C2×C12712yescomplemented
399#1521C2×C12711yescharacteristic, complemented
400#1515C2×C12711yescharacteristic, complemented
401#1473C2×C12711yescharacteristic, complemented
402C127#1846411yescharacteristic, direct product factor, Sylow
403#563—21no—
404#563—21no—
405#556—21no—
406#554—21no—
407#552—21no—
408#552—21no—
409#551—21no—
410#551—21no—
411#544C22×C12711yescharacteristic
412#543C22×C12711yescharacteristic
413#542—21no—
414#541—21no—
415#541—21no—
416#539—21no—
417#539C22×C12711yescharacteristic
418#538C22×C12711yescharacteristic
419#533C22×C12711yescharacteristic
420C2×#127C22×C12711yescharacteristic
421#529C22×C12711yescharacteristic
422C2×#126C22×C12711yescharacteristic
423#496—21no—
424#492—21no—
425#490—21no—
426#486—21no—
427#460—21no—
428#460—21no—
429#460—21no—
430#459—21no—
431#450C22×C12712yes—
432#450C22×C12712yes—
433#450C22×C12712yes—
434#447C22×C12712yes—
435#432C22×C12711yescharacteristic
436#431C22×C12711yescharacteristic
437#394—21no—
438#394—21no—
439#394C22×C12712yes—
440#392—21no—
441#392—21no—
442#392C22×C12712yes—
443#383C22×C12711yescharacteristic
444#328C22×C12712yes—
445#328C22×C12712yes—
446#328C22×C12712yes—
447#327C22×C12712yes—
448#324C22×C12712yes—
449#323C22×C12712yes—
450C22×D4—22no—
451C22×D4—21no—
452C22×D4—21no—
453C22×D4C23×C12712yes—
454C2×SD16—22no—
455C2×SD16—22no—
456C2×SD16—22no—
457C2×D8—22no—
458C4⋊Q8—21no—
459C4⋊Q8—21no—
460C4⋊Q8—21no—
461C4⋊Q8D4×C12711yescharacteristic, complemented
462C4⋊Q8D4×C12711yescharacteristic, complemented
463#127—21no—
464#127—21no—
465#127—21no—
466#127—21no—
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#126—21no—
477#126—21no—
478#126—21no—
479#126—21no—
480#125—21no—
481#125—21no—
482#125—21no—
483#125—21no—
484#125—21no—
485#125—21no—
486#125—21no—
487#125—21no—
488#125—21no—
489#125D4×C12711yescharacteristic, complemented
490#124—21no—
491#124—21no—
492#124—21no—
493#124D4×C12711yescharacteristic, complemented
494#123—21no—
495#123—21no—
496#123—21no—
497#123—21no—
498#123—21no—
499#123—21no—
500#123—21no—
501#123—21no—
502C22⋊Q8—21no—
503C22⋊Q8—21no—
504C22⋊Q8—21no—
505C22⋊Q8—21no—
506C22⋊Q8—21no—
507C22⋊Q8—21no—
508C22⋊Q8—21no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8—21no—
512C22⋊Q8—21no—
513C22⋊Q8—21no—
514C22⋊Q8—21no—
515C22⋊Q8—21no—
516C22⋊Q8C23×C12711yescharacteristic
517C22⋊Q8C23×C12711yescharacteristic
518C22⋊Q8C23×C12711yescharacteristic
519#121—21no—
520#121C23×C12711yescharacteristic
521#120—21no—
522C4×Q8—21no—
523C4×Q8—21no—
524C4×Q8—21no—
525C4×Q8D4×C12711yescharacteristic, complemented
526C4×Q8D4×C12711yescharacteristic, complemented
527C4×Q8D4×C12711yescharacteristic, complemented
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—21no—
533C4×D4D4×C12711yescharacteristic, complemented
534#117—21no—
535#117—21no—
536#117—21no—
537#117—21no—
538#117—21no—
539#117—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4D4×C12711yescharacteristic
542C2×C4⋊C4D4×C12711yescharacteristic
543C2×C4⋊C4C23×C12711yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—22no—
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#102—22no—
555#102—22no—
556#102—22no—
557#102—22no—
558C22⋊C8C23×C12712yes—
559C22⋊C8C23×C12712yes—
560#97—21no—
561C4×C8—21no—
562#95—21no—
563#95—21no—
564#95C23×C12712yes—
565C24—22no—
566C24C2×D4×C12711yescharacteristic
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8C2×D4×C12711yescharacteristic
571C2×Q8C2×D4×C12711yescharacteristic
572C2×Q8C2×D4×C12711yescharacteristic
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—41no—
579C2×D4—41no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—82no—
583C2×D4—82no—
584C2×D4—82no—
585C2×D4—82no—
586C2×D4—82no—
587C2×D4—82no—
588C2×D4C2×D4×C12711yescharacteristic
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4C2×D4×C12711yescharacteristic
596C22×C4C2×D4×C12711yescharacteristic
597C22×C4C2×D4×C12711yescharacteristic
598C22×C4C2×D4×C12711yescharacteristic
599C22×C4C2×D4×C12711yescharacteristic
600C22×C4C24×C12711yescharacteristic
601SD16—82no—
602SD16—82no—
603SD16—82no—
604D8—82no—
605C2×C8—22no—
606C2×C8—22no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
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—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4C2×D4×C12711yescharacteristic
637C4⋊C4C2×D4×C12711yescharacteristic
638C4⋊C4C2×D4×C12711yescharacteristic
639C4⋊C4C2×D4×C12711yescharacteristic
640C22⋊C4—21no—
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—82no—
662C22⋊C4—82no—
663C22⋊C4—82no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42C2×D4×C12711yescharacteristic
672C42C2×D4×C12711yescharacteristic
673C42C2×D4×C12711yescharacteristic
674C42C2×D4×C12711yescharacteristic
675C23—21no—
676C23—21no—
677C23—22no—
678C23—41no—
679C23—41no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23C22×D4×C12711yescharacteristic
688Q8—41no—
689Q8—41no—
690Q8—41no—
691Q8—81no—
692Q8—81no—
693Q8—81no—
694D4—41no—
695D4—42no—
696D4—42no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4—82no—
704D4—81no—
705D4—81no—
706D4—88no—
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—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4#120×C12711yescharacteristic
732C2×C4#120×C12711yescharacteristic
733C2×C4#120×C12711yescharacteristic
734C2×C4#120×C12711yescharacteristic
735C2×C4C22×D4×C12711yescharacteristic
736C2×C4C22×D4×C12711yescharacteristic
737C8—42no—
738C8—42no—
739C22—21no—
740C22—21no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—82no—
748C22—82no—
749C22—82no—
750C22—82no—
751C22—82no—
752C22—82no—
753C22—82no—
754C22—82no—
755C22C2×#120×C12711yescharacteristic
756C22#577×C12712yes—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—21no—
762C4—21no—
763C4—41no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—82no—
774C2—22no—
775C2—81no—
776C2—81no—
777C2—162no—
778C2C127×#301011yescharacteristic
779C2C127×#302111yescharacteristic
780C2C127×#302711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC22×C4C24×C127
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
1. C127×#3564C2semidirect
2. C127×#3217C2semidirect
3. C127×#3208C2semidirect
4. C127×#2818C2semidirect
5. C127×#1600C2semidirect
6. C127×#1599C2semidirect
7. C127×#1597C2semidirect
8. C127×#1596C2semidirect
9. C127×#1521C2semidirect
10. C127×#1515C2semidirect
11. C127×#1473C2semidirect
70. C4⋊Q8×C127D4semidirect
71. C4⋊Q8×C127D4semidirect
98. #125×C127D4semidirect
102. #124×C127D4semidirect
134. C4×Q8×C127D4semidirect
135. C4×Q8×C127D4semidirect
136. C4×Q8×C127D4semidirect
142. C4×D4×C127D4semidirect
383. #18464C127direct (N × H)
391. #3564C2×C127semidirect
392. #3217C2×C127semidirect
393. #3208C2×C127semidirect
394. #2818C2×C127semidirect
395. #1600C2×C127semidirect
396. #1599C2×C127semidirect
397. #1597C2×C127semidirect
398. #1596C2×C127semidirect
399. #1521C2×C127semidirect
400. #1515C2×C127semidirect
401. #1473C2×C127semidirect
402. C127#18464direct (N × H)
461. C4⋊Q8D4×C127semidirect
462. C4⋊Q8D4×C127semidirect
489. #125D4×C127semidirect
493. #124D4×C127semidirect
525. C4×Q8D4×C127semidirect
526. C4×Q8D4×C127semidirect
527. C4×Q8D4×C127semidirect
533. C4×D4D4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35642
C127×#32172
C127×#32082
C127×#28182
C127×#16002
C127×#15992
C127×#15972
C127×#15962
C127×#15212
C127×#15152
C127×#14732
#18464127