Finite Group Databasebeta

← C127×#18629 #44582302

Subgroups — C127×#18629 #44582302

Order 32512.

924 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3522C211yesmaximal, characteristic
2C127×#3248C211yesmaximal, characteristic, complemented
3C127×#3131C211yesmaximal, characteristic, complemented
4C127×#3113C211yesmaximal, characteristic, complemented
5C127×#1645C211yesmaximal, characteristic, complemented
6C127×#1645C211yesmaximal, characteristic, complemented
7C127×#1644C211yesmaximal, characteristic, complemented
8C127×#1643C211yesmaximal, characteristic, complemented
9C127×#1642C211yesmaximal, characteristic, complemented
10C127×#1641C211yesmaximal, characteristic, complemented
11C127×#1640C211yesmaximal, characteristic, complemented
12C127×#1640C211yesmaximal, characteristic, complemented
13C127×#1551C211yesmaximal, characteristic, complemented
14C127×#1494C211yesmaximal, characteristic, complemented
15C2×Q8⋊C8×C127C211yesmaximal, characteristic, complemented
16#559×C127—21no—
17#559×C127C2211yescharacteristic
18Q82×C127C2211yescharacteristic
19#554×C127—21no—
20#554×C127C2211yescharacteristic
21#550×C127C2211yescharacteristic
22#548×C127—21no—
23#547×C127—22no—
24#547×C127—21no—
25#542×C127—22no—
26#542×C127—21no—
27#533×C127C2211yescharacteristic
28#532×C127—21no—
29#532×C127C2211yescharacteristic
30#529×C127—21no—
31#529×C127C2211yescharacteristic
32#520×C127—21no—
33C2×C4×Q8×C127C2211yescharacteristic
34#488×C127—22no—
35#487×C127C2211yescharacteristic
36#487×C127C2211yescharacteristic
37#486×C127C2211yescharacteristic
38#486×C127C2211yescharacteristic
39#483×C127—21no—
40#479×C127—21no—
41#475×C127C2211yescharacteristic
42#475×C127C2211yescharacteristic
43#475×C127C2211yescharacteristic
44#474×C127C2211yescharacteristic
45#467×C127—21no—
46#465×C127—21no—
47#464×C127—21no—
48#462×C127C2211yescharacteristic
49#462×C127C2211yescharacteristic
50#462×C127C2211yescharacteristic
51#461×C127C2211yescharacteristic
52#451×C127—21no—
53#441×C127—21no—
54#441×C127—21no—
55#432×C127C2211yescharacteristic
56C2×C4⋊C8×C127C2211yescharacteristic
57#416×C127—22no—
58C2×C4×C8×C127C2211yescharacteristic
59#333×C127C2211yescharacteristic
60#333×C127C2211yescharacteristic
61#331×C127C2211yescharacteristic
62#331×C127C2211yescharacteristic
63Q8⋊C8×C127C2211yescharacteristic
64Q8⋊C8×C127C2211yescharacteristic
65Q8⋊C8×C127C2211yescharacteristic
66Q8⋊C8×C127C2211yescharacteristic
67Q8⋊C8×C127C2211yescharacteristic
68Q8⋊C8×C127C2211yescharacteristic
69D4⋊C8×C127C2211yescharacteristic
70D4⋊C8×C127C2211yescharacteristic
71C2×#41×C127—22no—
72C2×#41×C127—21no—
73C2×#41×C127D412yes—
74C22×Q8×C127D411yescharacteristic
75C2×Q16×C127—21no—
76C2×Q16×C127—21no—
77C2×Q16×C127—21no—
78C2×SD16×C127—21no—
79C22×C8×C127—21no—
80C22×C8×C127—21no—
81C4⋊Q8×C127—22no—
82C4⋊Q8×C127—21no—
83C4⋊Q8×C127—21no—
84C4⋊Q8×C127C2311yescharacteristic
85C4⋊Q8×C127C2311yescharacteristic
86C4⋊Q8×C127C2311yescharacteristic
87#127×C127—21no—
88#127×C127C2311yescharacteristic
89#126×C127—22no—
90#126×C127—21no—
91#125×C127—21no—
92#125×C127—21no—
93#125×C127D411yescharacteristic
94#124×C127—22no—
95#124×C127—22no—
96#124×C127—21no—
97#124×C127—21no—
98#124×C127D411yescharacteristic
99#124×C127D412yes—
100#123×C127—22no—
101#123×C127—22no—
102#123×C127—22no—
103#123×C127—22no—
104#123×C127—21no—
105C22⋊Q8×C127—22no—
106C22⋊Q8×C127—22no—
107C22⋊Q8×C127—22no—
108C22⋊Q8×C127—22no—
109C22⋊Q8×C127—21no—
110C22⋊Q8×C127—21no—
111C22⋊Q8×C127—21no—
112C22⋊Q8×C127D411yescharacteristic
113#121×C127—22no—
114#121×C127—22no—
115#121×C127—21no—
116#121×C127—21no—
117#121×C127—21no—
118#121×C127D411yescharacteristic
119C4×Q8×C127—21no—
120C4×Q8×C127—21no—
121C4×Q8×C127—21no—
122C4×Q8×C127—21no—
123C4×Q8×C127—21no—
124C4×Q8×C127—21no—
125C4×Q8×C127D411yescharacteristic
126C4×Q8×C127D411yescharacteristic
127C4×Q8×C127C2311yescharacteristic
128C4×Q8×C127C2311yescharacteristic
129C4×Q8×C127C2311yescharacteristic
130C4×D4×C127—22no—
131C4×D4×C127—22no—
132C4×D4×C127—22no—
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×C127C2311yescharacteristic
141#117×C127—22no—
142#117×C127—21no—
143#117×C127—21no—
144C2×C4⋊C4×C127—22no—
145C2×C4⋊C4×C127—21no—
146C2×C4⋊C4×C127—21no—
147C2×C4⋊C4×C127D411yescharacteristic
148C2×C42×C127—21no—
149C2×C42×C127C2311yescharacteristic
150#107×C127—21no—
151#106×C127—21no—
152#106×C127—21no—
153#106×C127—21no—
154C4⋊C8×C127—21no—
155C4⋊C8×C127C2311yescharacteristic
156C4⋊C8×C127C2311yescharacteristic
157C4⋊C8×C127C2311yescharacteristic
158C4⋊C8×C127C2311yescharacteristic
159#103×C127—22no—
160#103×C127—22no—
161#103×C127—21no—
162#103×C127—21no—
163#103×C127—21no—
164#103×C127—21no—
165#103×C127—21no—
166#103×C127—21no—
167#103×C127—21no—
168#102×C127—22no—
169#102×C127—22no—
170#102×C127—21no—
171C22⋊C8×C127—21no—
172#97×C127—21no—
173C4×C8×C127—21no—
174C4×C8×C127C2311yescharacteristic
175C4×C8×C127C2311yescharacteristic
176#41×C127—44no—
177#41×C127—42no—
178#41×C127—42no—
179#41×C127—84no—
180C2×Q8×C127—22no—
181C2×Q8×C127—21no—
182C2×Q8×C127—22no—
183C2×Q8×C127—21no—
184C2×Q8×C127—21no—
185C2×Q8×C127—41no—
186C2×Q8×C127C2×D411yescharacteristic
187C2×Q8×C127C2×D411yescharacteristic
188C2×Q8×C127C2×D411yescharacteristic
189C2×Q8×C127C2×D412yes—
190C2×D4×C127—22no—
191C2×D4×C127—22no—
192C2×D4×C127—21no—
193C2×D4×C127—22no—
194C2×D4×C127—21no—
195C2×D4×C127—21no—
196C2×D4×C127C2×D411yescharacteristic
197C2×D4×C127C2×D412yes—
198C22×C4×C127—22no—
199C22×C4×C127—21no—
200C22×C4×C127—21no—
201C22×C4×C127—22no—
202C22×C4×C127—22no—
203C22×C4×C127—21no—
204C22×C4×C127—22no—
205C22×C4×C127C2×D411yescharacteristic
206C22×C4×C127C2×D411yescharacteristic
207C22×C4×C127C2×D411yescharacteristic
208Q16×C127—42no—
209Q16×C127—42no—
210Q16×C127—81no—
211SD16×C127—81no—
212C2×C8×C127—21no—
213C2×C8×C127—21no—
214C2×C8×C127—21no—
215C2×C8×C127—21no—
216C2×C8×C127—21no—
217C2×C8×C127—21no—
218C2×C8×C127—42no—
219C2×C8×C127—81no—
220C4⋊C4×C127—22no—
221C4⋊C4×C127—22no—
222C4⋊C4×C127—22no—
223C4⋊C4×C127—22no—
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×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—22no—
250C22⋊C4×C127—21no—
251C22⋊C4×C127—22no—
252C22⋊C4×C127—21no—
253C22⋊C4×C127—21no—
254C22⋊C4×C127—22no—
255C22⋊C4×C127—21no—
256C22⋊C4×C127—21no—
257C22⋊C4×C127—41no—
258C42×C127—22no—
259C42×C127—21no—
260C42×C127—21no—
261C42×C127—21no—
262C42×C127—21no—
263C42×C127—21no—
264C42×C127—41no—
265C42×C127C2×D411yescharacteristic
266C42×C127C2×D411yescharacteristic
267C42×C127C2×D411yescharacteristic
268C42×C127C2411yescharacteristic
269C23×C127—21no—
270C23×C127—22no—
271C23×C127#12011yescharacteristic
272Q8×C127—21no—
273Q8×C127—21no—
274Q8×C127—21no—
275Q8×C127—21no—
276Q8×C127—21no—
277Q8×C127—42no—
278Q8×C127—42no—
279Q8×C127—41no—
280Q8×C127—41no—
281Q8×C127—41no—
282Q8×C127—41no—
283Q8×C127—82no—
284Q8×C127#13512yes—
285D4×C127—21no—
286D4×C127—21no—
287D4×C127—42no—
288D4×C127—44no—
289D4×C127—44no—
290D4×C127—42no—
291D4×C127—41no—
292D4×C127—41no—
293D4×C127—41no—
294D4×C127—41no—
295D4×C127—82no—
296C2×C4×C127—21no—
297C2×C4×C127—22no—
298C2×C4×C127—21no—
299C2×C4×C127—21no—
300C2×C4×C127—21no—
301C2×C4×C127—21no—
302C2×C4×C127—21no—
303C2×C4×C127—21no—
304C2×C4×C127—21no—
305C2×C4×C127—21no—
306C2×C4×C127—22no—
307C2×C4×C127—21no—
308C2×C4×C127—21no—
309C2×C4×C127—42no—
310C2×C4×C127—44no—
311C2×C4×C127—42no—
312C2×C4×C127—41no—
313C2×C4×C127—41no—
314C2×C4×C127—41no—
315C2×C4×C127—41no—
316C2×C4×C127—82no—
317C2×C4×C127—82no—
318C2×C4×C127—82no—
319C2×C4×C127#12011yescharacteristic
320C2×C4×C127#12011yescharacteristic
321C2×C4×C127#12011yescharacteristic
322C2×C4×C127C22×D411yescharacteristic
323C2×C4×C127C22×D411yescharacteristic
324C2×C4×C127C22×D411yescharacteristic
325C8×C127—41no—
326C8×C127—41no—
327C8×C127—41no—
328C8×C127—41no—
329C8×C127—41no—
330C8×C127—41no—
331C22×C127—21no—
332C22×C127—21no—
333C22×C127—42no—
334C22×C127—41no—
335C22×C127—41no—
336C22×C127—42no—
337C22×C127—42no—
338C22×C127—41no—
339C22×C127#45512yes—
340C22×C127C2×#12011yescharacteristic
341C4×C127—21no—
342C4×C127—22no—
343C4×C127—21no—
344C4×C127—21no—
345C4×C127—21no—
346C4×C127—41no—
347C4×C127—41no—
348C4×C127—41no—
349C4×C127—41no—
350C4×C127—41no—
351C4×C127—42no—
352C4×C127—41no—
353C4×C127—81no—
354C4×C127—81no—
355C4×C127C2×#13511yescharacteristic
356C4×C127#57511yescharacteristic
357C4×C127#57711yescharacteristic
358C4×C127#57811yescharacteristic
359#18629C12711yesmaximal, characteristic, direct product factor, Sylow
360C2×C127—22no—
361C2×C127—81no—
362C2×C127—82no—
363C2×C127#300211yescharacteristic
364C2×C127#301311yescharacteristic
365C2×C127C2×#45511yescharacteristic
366#3522C2×C12711yescharacteristic
367#3248C2×C12711yescharacteristic, complemented
368#3131C2×C12711yescharacteristic, complemented
369#3113C2×C12711yescharacteristic, complemented
370#1645C2×C12711yescharacteristic, complemented
371#1645C2×C12711yescharacteristic, complemented
372#1644C2×C12711yescharacteristic, complemented
373#1643C2×C12711yescharacteristic, complemented
374#1642C2×C12711yescharacteristic, complemented
375#1641C2×C12711yescharacteristic, complemented
376#1640C2×C12711yescharacteristic, complemented
377#1640C2×C12711yescharacteristic, complemented
378#1551C2×C12711yescharacteristic, complemented
379#1494C2×C12711yescharacteristic, complemented
380C2×Q8⋊C8C2×C12711yescharacteristic, complemented
381C127#1862911yescharacteristic, direct product factor, Sylow
382#559—21no—
383#559C22×C12711yescharacteristic
384Q82C22×C12711yescharacteristic
385#554—21no—
386#554C22×C12711yescharacteristic
387#550C22×C12711yescharacteristic
388#548—21no—
389#547—22no—
390#547—21no—
391#542—22no—
392#542—21no—
393#533C22×C12711yescharacteristic
394#532—21no—
395#532C22×C12711yescharacteristic
396#529—21no—
397#529C22×C12711yescharacteristic
398#520—21no—
399C2×C4×Q8C22×C12711yescharacteristic
400#488—22no—
401#487C22×C12711yescharacteristic
402#487C22×C12711yescharacteristic
403#486C22×C12711yescharacteristic
404#486C22×C12711yescharacteristic
405#483—21no—
406#479—21no—
407#475C22×C12711yescharacteristic
408#475C22×C12711yescharacteristic
409#475C22×C12711yescharacteristic
410#474C22×C12711yescharacteristic
411#467—21no—
412#465—21no—
413#464—21no—
414#462C22×C12711yescharacteristic
415#462C22×C12711yescharacteristic
416#462C22×C12711yescharacteristic
417#461C22×C12711yescharacteristic
418#451—21no—
419#441—21no—
420#441—21no—
421#432C22×C12711yescharacteristic
422C2×C4⋊C8C22×C12711yescharacteristic
423#416—22no—
424C2×C4×C8C22×C12711yescharacteristic
425#333C22×C12711yescharacteristic
426#333C22×C12711yescharacteristic
427#331C22×C12711yescharacteristic
428#331C22×C12711yescharacteristic
429Q8⋊C8C22×C12711yescharacteristic
430Q8⋊C8C22×C12711yescharacteristic
431Q8⋊C8C22×C12711yescharacteristic
432Q8⋊C8C22×C12711yescharacteristic
433Q8⋊C8C22×C12711yescharacteristic
434Q8⋊C8C22×C12711yescharacteristic
435D4⋊C8C22×C12711yescharacteristic
436D4⋊C8C22×C12711yescharacteristic
437C2×#41—22no—
438C2×#41—21no—
439C2×#41D4×C12712yes—
440C22×Q8D4×C12711yescharacteristic
441C2×Q16—21no—
442C2×Q16—21no—
443C2×Q16—21no—
444C2×SD16—21no—
445C22×C8—21no—
446C22×C8—21no—
447C4⋊Q8—22no—
448C4⋊Q8—21no—
449C4⋊Q8—21no—
450C4⋊Q8C23×C12711yescharacteristic
451C4⋊Q8C23×C12711yescharacteristic
452C4⋊Q8C23×C12711yescharacteristic
453#127—21no—
454#127C23×C12711yescharacteristic
455#126—22no—
456#126—21no—
457#125—21no—
458#125—21no—
459#125D4×C12711yescharacteristic
460#124—22no—
461#124—22no—
462#124—21no—
463#124—21no—
464#124D4×C12711yescharacteristic
465#124D4×C12712yes—
466#123—22no—
467#123—22no—
468#123—22no—
469#123—22no—
470#123—21no—
471C22⋊Q8—22no—
472C22⋊Q8—22no—
473C22⋊Q8—22no—
474C22⋊Q8—22no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477C22⋊Q8—21no—
478C22⋊Q8D4×C12711yescharacteristic
479#121—22no—
480#121—22no—
481#121—21no—
482#121—21no—
483#121—21no—
484#121D4×C12711yescharacteristic
485C4×Q8—21no—
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×Q8C23×C12711yescharacteristic
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—21no—
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4C23×C12711yescharacteristic
507#117—22no—
508#117—21no—
509#117—21no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4D4×C12711yescharacteristic
514C2×C42—21no—
515C2×C42C23×C12711yescharacteristic
516#107—21no—
517#106—21no—
518#106—21no—
519#106—21no—
520C4⋊C8—21no—
521C4⋊C8C23×C12711yescharacteristic
522C4⋊C8C23×C12711yescharacteristic
523C4⋊C8C23×C12711yescharacteristic
524C4⋊C8C23×C12711yescharacteristic
525#103—22no—
526#103—22no—
527#103—21no—
528#103—21no—
529#103—21no—
530#103—21no—
531#103—21no—
532#103—21no—
533#103—21no—
534#102—22no—
535#102—22no—
536#102—21no—
537C22⋊C8—21no—
538#97—21no—
539C4×C8—21no—
540C4×C8C23×C12711yescharacteristic
541C4×C8C23×C12711yescharacteristic
542#41—44no—
543#41—42no—
544#41—42no—
545#41—84no—
546C2×Q8—22no—
547C2×Q8—21no—
548C2×Q8—22no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—41no—
552C2×Q8C2×D4×C12711yescharacteristic
553C2×Q8C2×D4×C12711yescharacteristic
554C2×Q8C2×D4×C12711yescharacteristic
555C2×Q8C2×D4×C12712yes—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—22no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4C2×D4×C12711yescharacteristic
563C2×D4C2×D4×C12712yes—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4C2×D4×C12711yescharacteristic
572C22×C4C2×D4×C12711yescharacteristic
573C22×C4C2×D4×C12711yescharacteristic
574Q16—42no—
575Q16—42no—
576Q16—81no—
577SD16—81no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—42no—
585C2×C8—81no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—41no—
606C4⋊C4—41no—
607C4⋊C4C2×D4×C12711yescharacteristic
608C4⋊C4C2×D4×C12711yescharacteristic
609C4⋊C4C2×D4×C12711yescharacteristic
610C4⋊C4C2×D4×C12711yescharacteristic
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—21no—
617C22⋊C4—22no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—41no—
624C42—22no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42—41no—
631C42C2×D4×C12711yescharacteristic
632C42C2×D4×C12711yescharacteristic
633C42C2×D4×C12711yescharacteristic
634C42C24×C12711yescharacteristic
635C23—21no—
636C23—22no—
637C23#120×C12711yescharacteristic
638Q8—21no—
639Q8—21no—
640Q8—21no—
641Q8—21no—
642Q8—21no—
643Q8—42no—
644Q8—42no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649Q8—82no—
650Q8#135×C12712yes—
651D4—21no—
652D4—21no—
653D4—42no—
654D4—44no—
655D4—44no—
656D4—42no—
657D4—41no—
658D4—41no—
659D4—41no—
660D4—41no—
661D4—82no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—42no—
676C2×C4—44no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—82no—
683C2×C4—82no—
684C2×C4—82no—
685C2×C4#120×C12711yescharacteristic
686C2×C4#120×C12711yescharacteristic
687C2×C4#120×C12711yescharacteristic
688C2×C4C22×D4×C12711yescharacteristic
689C2×C4C22×D4×C12711yescharacteristic
690C2×C4C22×D4×C12711yescharacteristic
691C8—41no—
692C8—41no—
693C8—41no—
694C8—41no—
695C8—41no—
696C8—41no—
697C22—21no—
698C22—21no—
699C22—42no—
700C22—41no—
701C22—41no—
702C22—42no—
703C22—42no—
704C22—41no—
705C22#455×C12712yes—
706C22C2×#120×C12711yescharacteristic
707C4—21no—
708C4—22no—
709C4—21no—
710C4—21no—
711C4—21no—
712C4—41no—
713C4—41no—
714C4—41no—
715C4—41no—
716C4—41no—
717C4—42no—
718C4—41no—
719C4—81no—
720C4—81no—
721C4C2×#135×C12711yescharacteristic
722C4#575×C12711yescharacteristic
723C4#577×C12711yescharacteristic
724C4#578×C12711yescharacteristic
725C2—22no—
726C2—81no—
727C2—82no—
728C2C127×#300211yescharacteristic
729C2C127×#301311yescharacteristic
730C2C2×#455×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC42C24×C127
prime radicalC127×#3522C2
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×#3248C2semidirect
3. C127×#3131C2semidirect
4. C127×#3113C2semidirect
5. C127×#1645C2semidirect
6. C127×#1645C2semidirect
7. C127×#1644C2semidirect
8. C127×#1643C2semidirect
9. C127×#1642C2semidirect
10. C127×#1641C2semidirect
11. C127×#1640C2semidirect
12. C127×#1640C2semidirect
13. C127×#1551C2semidirect
14. C127×#1494C2semidirect
15. C2×Q8⋊C8×C127C2semidirect
359. #18629C127direct (N × H)
367. #3248C2×C127semidirect
368. #3131C2×C127semidirect
369. #3113C2×C127semidirect
370. #1645C2×C127semidirect
371. #1645C2×C127semidirect
372. #1644C2×C127semidirect
373. #1643C2×C127semidirect
374. #1642C2×C127semidirect
375. #1641C2×C127semidirect
376. #1640C2×C127semidirect
377. #1640C2×C127semidirect
378. #1551C2×C127semidirect
379. #1494C2×C127semidirect
380. C2×Q8⋊C8C2×C127semidirect
381. C127#18629direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#35222
C127×#32482
C127×#31312
C127×#31132
C127×#16452
C127×#16442
C127×#16432
C127×#16422
C127×#16412
C127×#16402
C127×#15512
C127×#14942
C2×Q8⋊C8×C1272
#18629127