Finite Group Databasebeta

← C127×#18235 #44581908

Subgroups — C127×#18235 #44581908

Order 32512.

938 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3535C211yesmaximal, characteristic
2C127×#3092C211yesmaximal, characteristic, complemented
3C2×#484×C127C211yesmaximal, characteristic, complemented
4C127×#2623C211yesmaximal, characteristic, complemented
5C127×#1618C212yesmaximal, complemented
6C127×#1617C212yesmaximal, complemented
7C127×#1615C212yesmaximal, complemented
8C127×#1614C212yesmaximal, complemented
9C127×#1516C211yesmaximal, characteristic, complemented
10C127×#1511C211yesmaximal, characteristic, complemented
11C127×#1468C211yesmaximal, characteristic, complemented
12#563×C127—21no—
13#562×C127—21no—
14#554×C127—21no—
15#552×C127—21no—
16#551×C127—21no—
17#551×C127—21no—
18#547×C127—21no—
19#546×C127—21no—
20#544×C127C2211yescharacteristic
21#543×C127C2211yescharacteristic
22#542×C127—21no—
23#539×C127—21no—
24#539×C127—21no—
25#539×C127C2211yescharacteristic
26#538×C127C2211yescharacteristic
27#536×C127—21no—
28#525×C127C2211yescharacteristic
29C2×#123×C127C2211yescharacteristic
30C2×C22⋊Q8×C127C2211yescharacteristic
31C22×C4⋊C4×C127C2211yescharacteristic
32#484×C127—21no—
33#484×C127—21no—
34#484×C127C2212yes—
35#484×C127C2212yes—
36#484×C127C2212yes—
37#483×C127—21no—
38#481×C127C2212yes—
39#480×C127—21no—
40#428×C127—21no—
41C2×#107×C127—21no—
42#417×C127—21no—
43C2×#103×C127—21no—
44#407×C127C2211yescharacteristic
45C2×C22⋊C8×C127C2211yescharacteristic
46#400×C127C2212yes—
47#399×C127C2212yes—
48#398×C127—21no—
49#397×C127—21no—
50#386×C127—21no—
51#385×C127—21no—
52#381×C127C2211yescharacteristic
53#328×C127C2212yes—
54#328×C127C2212yes—
55#328×C127C2212yes—
56#327×C127C2212yes—
57#324×C127C2212yes—
58#323×C127C2212yes—
59C2×#41×C127—21no—
60C2×#41×C127D411yescharacteristic
61C22×Q8×C127D411yescharacteristic
62C22×D4×C127D411yescharacteristic
63C23×C4×C127—21no—
64C23×C4×C127C2311yescharacteristic
65C2×M16×C127—21no—
66C22×C8×C127—21no—
67C4⋊Q8×C127—21no—
68C4⋊Q8×C127—21no—
69C4⋊Q8×C127—21no—
70#126×C127—21no—
71#126×C127—21no—
72#126×C127—21no—
73#126×C127—21no—
74#126×C127—21no—
75#126×C127—21no—
76#125×C127—21no—
77#125×C127—21no—
78#125×C127—21no—
79#125×C127—21no—
80#125×C127—21no—
81#124×C127—21no—
82#124×C127—21no—
83#124×C127—21no—
84#124×C127—21no—
85#123×C127—21no—
86#123×C127—21no—
87#123×C127—21no—
88#123×C127—21no—
89#123×C127—21no—
90#123×C127—21no—
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—
99C22⋊Q8×C127—21no—
100C22⋊Q8×C127—21no—
101C22⋊Q8×C127—21no—
102C22⋊Q8×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×C127—21no—
111C22⋊Q8×C127—21no—
112C22⋊Q8×C127—21no—
113C22⋊Q8×C127D411yescharacteristic
114C22⋊Q8×C127D411yescharacteristic
115C22⋊Q8×C127D411yescharacteristic
116C22⋊Q8×C127C2311yescharacteristic
117C22⋊Q8×C127C2311yescharacteristic
118C22⋊Q8×C127C2311yescharacteristic
119#121×C127—21no—
120#121×C127—21no—
121#121×C127—21no—
122#121×C127—21no—
123#121×C127D411yescharacteristic
124#121×C127C2311yescharacteristic
125#120×C127—21no—
126#120×C127—21no—
127C4×Q8×C127—21no—
128C4×D4×C127—21no—
129C4×D4×C127—21no—
130C4×D4×C127—21no—
131C4×D4×C127—21no—
132C4×D4×C127—21no—
133C4×D4×C127—21no—
134C4×D4×C127—21no—
135#117×C127—21no—
136#117×C127—21no—
137#117×C127—21no—
138#117×C127D411yescharacteristic
139C2×C4⋊C4×C127—21no—
140C2×C4⋊C4×C127—21no—
141C2×C4⋊C4×C127—21no—
142C2×C4⋊C4×C127—21no—
143C2×C4⋊C4×C127—21no—
144C2×C4⋊C4×C127—21no—
145C2×C4⋊C4×C127—21no—
146C2×C4⋊C4×C127—22no—
147C2×C4⋊C4×C127D411yescharacteristic
148C2×C4⋊C4×C127D411yescharacteristic
149C2×C4⋊C4×C127C2312yes—
150C2×C4⋊C4×C127C2311yescharacteristic
151C2×C22⋊C4×C127—21no—
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
158#107×C127—22no—
159#107×C127—22no—
160#107×C127—22no—
161#106×C127—22no—
162#103×C127—22no—
163#103×C127—22no—
164#103×C127—22no—
165#102×C127—22no—
166C22⋊C8×C127—21no—
167C22⋊C8×C127—21no—
168C22⋊C8×C127C2312yes—
169C22⋊C8×C127C2312yes—
170#95×C127—21no—
171#95×C127—22no—
172#95×C127—22no—
173#95×C127C2312yes—
174C24×C127C2×D411yescharacteristic
175C24×C127C2×D411yescharacteristic
176#41×C127—42no—
177#41×C127—82no—
178C2×Q8×C127—21no—
179C2×Q8×C127—21no—
180C2×Q8×C127—21no—
181C2×Q8×C127—42no—
182C2×Q8×C127C2×D411yescharacteristic
183C2×Q8×C127C2×D411yescharacteristic
184C2×Q8×C127C2×D411yescharacteristic
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—42no—
193C2×D4×C127C2×D411yescharacteristic
194C22×C4×C127—21no—
195C22×C4×C127—21no—
196C22×C4×C127—21no—
197C22×C4×C127—21no—
198C22×C4×C127—21no—
199C22×C4×C127—21no—
200C22×C4×C127—21no—
201C22×C4×C127—22no—
202C22×C4×C127—22no—
203C22×C4×C127—42no—
204C22×C4×C127—41no—
205C22×C4×C127—41no—
206C22×C4×C127—82no—
207C22×C4×C127C2×D411yescharacteristic
208C22×C4×C127C2×D411yescharacteristic
209C22×C4×C127C2×D411yescharacteristic
210C22×C4×C127C2×D411yescharacteristic
211C22×C4×C127C2×D411yescharacteristic
212C22×C4×C127C2×D411yescharacteristic
213C22×C4×C127C2×D411yescharacteristic
214C22×C4×C127C2×D411yescharacteristic
215C22×C4×C127C2411yescharacteristic
216M16×C127—42no—
217C2×C8×C127—22no—
218C2×C8×C127—22no—
219C2×C8×C127—42no—
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—22no—
244C4⋊C4×C127—22no—
245C4⋊C4×C127—41no—
246C4⋊C4×C127—41no—
247C4⋊C4×C127—82no—
248C4⋊C4×C127C2×D411yescharacteristic
249C4⋊C4×C127C2×D411yescharacteristic
250C4⋊C4×C127C2×D411yescharacteristic
251C4⋊C4×C127C2×D411yescharacteristic
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—21no—
274C22⋊C4×C127—21no—
275C22⋊C4×C127—42no—
276C22⋊C4×C127—82no—
277C42×C127—21no—
278C42×C127—21no—
279C42×C127—21no—
280C42×C127—21no—
281C42×C127—21no—
282C23×C127—22no—
283C23×C127—22no—
284C23×C127—21no—
285C23×C127—21no—
286C23×C127—22no—
287C23×C127—41no—
288C23×C127—41no—
289C23×C127—41no—
290C23×C127#12011yescharacteristic
291C23×C127#12011yescharacteristic
292C23×C127C22×D411yescharacteristic
293Q8×C127—41no—
294Q8×C127—41no—
295Q8×C127—41no—
296Q8×C127—81no—
297Q8×C127—81no—
298Q8×C127—81no—
299D4×C127—41no—
300D4×C127—42no—
301D4×C127—42no—
302D4×C127—42no—
303D4×C127—81no—
304D4×C127—81no—
305D4×C127—81no—
306D4×C127—81no—
307C2×C4×C127—22no—
308C2×C4×C127—22no—
309C2×C4×C127—21no—
310C2×C4×C127—21no—
311C2×C4×C127—21no—
312C2×C4×C127—21no—
313C2×C4×C127—21no—
314C2×C4×C127—21no—
315C2×C4×C127—21no—
316C2×C4×C127—21no—
317C2×C4×C127—21no—
318C2×C4×C127—21no—
319C2×C4×C127—22no—
320C2×C4×C127—41no—
321C2×C4×C127—41no—
322C2×C4×C127—41no—
323C2×C4×C127—41no—
324C2×C4×C127—42no—
325C2×C4×C127—41no—
326C2×C4×C127—41no—
327C2×C4×C127—42no—
328C2×C4×C127—42no—
329C2×C4×C127—42no—
330C2×C4×C127—42no—
331C2×C4×C127—42no—
332C2×C4×C127—42no—
333C2×C4×C127—81no—
334C2×C4×C127—81no—
335C2×C4×C127—81no—
336C2×C4×C127—81no—
337C2×C4×C127—81no—
338C2×C4×C127—81no—
339C2×C4×C127—82no—
340C2×C4×C127—82no—
341C2×C4×C127#12011yescharacteristic
342C2×C4×C127#12011yescharacteristic
343C2×C4×C127C22×D411yescharacteristic
344C2×C4×C127C22×D411yescharacteristic
345C8×C127—42no—
346C8×C127—42no—
347C22×C127—21no—
348C22×C127—21no—
349C22×C127—21no—
350C22×C127—21no—
351C22×C127—21no—
352C22×C127—21no—
353C22×C127—21no—
354C22×C127—44no—
355C22×C127—41no—
356C22×C127—41no—
357C22×C127—41no—
358C22×C127—41no—
359C22×C127—41no—
360C22×C127—41no—
361C22×C127—82no—
362C22×C127#45812yes—
363C22×C127C2×#12011yescharacteristic
364C22×C127#57812yes—
365C4×C127—21no—
366C4×C127—21no—
367C4×C127—21no—
368C4×C127—21no—
369C4×C127—41no—
370C4×C127—41no—
371C4×C127—41no—
372C4×C127—41no—
373C4×C127—41no—
374C4×C127—41no—
375C4×C127—41no—
376C4×C127—41no—
377C4×C127—41no—
378C4×C127—41no—
379C4×C127—82no—
380C4×C127—82no—
381#18235C12711yesmaximal, characteristic, direct product factor, Sylow
382C2×C127—22no—
383C2×C127—22no—
384C2×C127—41no—
385C2×C127—81no—
386C2×C127—81no—
387C2×C127#301111yescharacteristic
388C2×C127#302111yescharacteristic
389C2×C127C2×#45811yescharacteristic
390#3535C2×C12711yescharacteristic
391#3092C2×C12711yescharacteristic, complemented
392C2×#484C2×C12711yescharacteristic, complemented
393#2623C2×C12711yescharacteristic, complemented
394#1618C2×C12712yescomplemented
395#1617C2×C12712yescomplemented
396#1615C2×C12712yescomplemented
397#1614C2×C12712yescomplemented
398#1516C2×C12711yescharacteristic, complemented
399#1511C2×C12711yescharacteristic, complemented
400#1468C2×C12711yescharacteristic, complemented
401C127#1823511yescharacteristic, direct product factor, Sylow
402#563—21no—
403#562—21no—
404#554—21no—
405#552—21no—
406#551—21no—
407#551—21no—
408#547—21no—
409#546—21no—
410#544C22×C12711yescharacteristic
411#543C22×C12711yescharacteristic
412#542—21no—
413#539—21no—
414#539—21no—
415#539C22×C12711yescharacteristic
416#538C22×C12711yescharacteristic
417#536—21no—
418#525C22×C12711yescharacteristic
419C2×#123C22×C12711yescharacteristic
420C2×C22⋊Q8C22×C12711yescharacteristic
421C22×C4⋊C4C22×C12711yescharacteristic
422#484—21no—
423#484—21no—
424#484C22×C12712yes—
425#484C22×C12712yes—
426#484C22×C12712yes—
427#483—21no—
428#481C22×C12712yes—
429#480—21no—
430#428—21no—
431C2×#107—21no—
432#417—21no—
433C2×#103—21no—
434#407C22×C12711yescharacteristic
435C2×C22⋊C8C22×C12711yescharacteristic
436#400C22×C12712yes—
437#399C22×C12712yes—
438#398—21no—
439#397—21no—
440#386—21no—
441#385—21no—
442#381C22×C12711yescharacteristic
443#328C22×C12712yes—
444#328C22×C12712yes—
445#328C22×C12712yes—
446#327C22×C12712yes—
447#324C22×C12712yes—
448#323C22×C12712yes—
449C2×#41—21no—
450C2×#41D4×C12711yescharacteristic
451C22×Q8D4×C12711yescharacteristic
452C22×D4D4×C12711yescharacteristic
453C23×C4—21no—
454C23×C4C23×C12711yescharacteristic
455C2×M16—21no—
456C22×C8—21no—
457C4⋊Q8—21no—
458C4⋊Q8—21no—
459C4⋊Q8—21no—
460#126—21no—
461#126—21no—
462#126—21no—
463#126—21no—
464#126—21no—
465#126—21no—
466#125—21no—
467#125—21no—
468#125—21no—
469#125—21no—
470#125—21no—
471#124—21no—
472#124—21no—
473#124—21no—
474#124—21no—
475#123—21no—
476#123—21no—
477#123—21no—
478#123—21no—
479#123—21no—
480#123—21no—
481#123—21no—
482#123—21no—
483#123—21no—
484#123—21no—
485#123—21no—
486#123—21no—
487#123—21no—
488#123—21no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—21no—
500C22⋊Q8—21no—
501C22⋊Q8—21no—
502C22⋊Q8—21no—
503C22⋊Q8D4×C12711yescharacteristic
504C22⋊Q8D4×C12711yescharacteristic
505C22⋊Q8D4×C12711yescharacteristic
506C22⋊Q8C23×C12711yescharacteristic
507C22⋊Q8C23×C12711yescharacteristic
508C22⋊Q8C23×C12711yescharacteristic
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121D4×C12711yescharacteristic
514#121C23×C12711yescharacteristic
515#120—21no—
516#120—21no—
517C4×Q8—21no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525#117—21no—
526#117—21no—
527#117—21no—
528#117D4×C12711yescharacteristic
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—22no—
537C2×C4⋊C4D4×C12711yescharacteristic
538C2×C4⋊C4D4×C12711yescharacteristic
539C2×C4⋊C4C23×C12712yes—
540C2×C4⋊C4C23×C12711yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4D4×C12711yescharacteristic
546C2×C22⋊C4D4×C12711yescharacteristic
547C2×C22⋊C4C23×C12711yescharacteristic
548#107—22no—
549#107—22no—
550#107—22no—
551#106—22no—
552#103—22no—
553#103—22no—
554#103—22no—
555#102—22no—
556C22⋊C8—21no—
557C22⋊C8—21no—
558C22⋊C8C23×C12712yes—
559C22⋊C8C23×C12712yes—
560#95—21no—
561#95—22no—
562#95—22no—
563#95C23×C12712yes—
564C24C2×D4×C12711yescharacteristic
565C24C2×D4×C12711yescharacteristic
566#41—42no—
567#41—82no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—42no—
572C2×Q8C2×D4×C12711yescharacteristic
573C2×Q8C2×D4×C12711yescharacteristic
574C2×Q8C2×D4×C12711yescharacteristic
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—42no—
583C2×D4C2×D4×C12711yescharacteristic
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—42no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—82no—
597C22×C4C2×D4×C12711yescharacteristic
598C22×C4C2×D4×C12711yescharacteristic
599C22×C4C2×D4×C12711yescharacteristic
600C22×C4C2×D4×C12711yescharacteristic
601C22×C4C2×D4×C12711yescharacteristic
602C22×C4C2×D4×C12711yescharacteristic
603C22×C4C2×D4×C12711yescharacteristic
604C22×C4C2×D4×C12711yescharacteristic
605C22×C4C24×C12711yescharacteristic
606M16—42no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—42no—
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—22no—
634C4⋊C4—22no—
635C4⋊C4—41no—
636C4⋊C4—41no—
637C4⋊C4—82no—
638C4⋊C4C2×D4×C12711yescharacteristic
639C4⋊C4C2×D4×C12711yescharacteristic
640C4⋊C4C2×D4×C12711yescharacteristic
641C4⋊C4C2×D4×C12711yescharacteristic
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—42no—
666C22⋊C4—82no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42—21no—
672C23—22no—
673C23—22no—
674C23—21no—
675C23—21no—
676C23—22no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23#120×C12711yescharacteristic
681C23#120×C12711yescharacteristic
682C23C22×D4×C12711yescharacteristic
683Q8—41no—
684Q8—41no—
685Q8—41no—
686Q8—81no—
687Q8—81no—
688Q8—81no—
689D4—41no—
690D4—42no—
691D4—42no—
692D4—42no—
693D4—81no—
694D4—81no—
695D4—81no—
696D4—81no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—81no—
724C2×C4—81no—
725C2×C4—81no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—82no—
730C2×C4—82no—
731C2×C4#120×C12711yescharacteristic
732C2×C4#120×C12711yescharacteristic
733C2×C4C22×D4×C12711yescharacteristic
734C2×C4C22×D4×C12711yescharacteristic
735C8—42no—
736C8—42no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—44no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—82no—
752C22#458×C12712yes—
753C22C2×#120×C12711yescharacteristic
754C22#578×C12712yes—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—41no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—82no—
770C4—82no—
771C2—22no—
772C2—22no—
773C2—41no—
774C2—81no—
775C2—81no—
776C2C127×#301111yescharacteristic
777C2C127×#302111yescharacteristic
778C2C2×#458×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC22×C4C24×C127
prime radicalC127×#3535C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#3092C2semidirect
3. C2×#484×C127C2semidirect
4. C127×#2623C2semidirect
5. C127×#1618C2semidirect
6. C127×#1617C2semidirect
7. C127×#1615C2semidirect
8. C127×#1614C2semidirect
9. C127×#1516C2semidirect
10. C127×#1511C2semidirect
11. C127×#1468C2semidirect
381. #18235C127direct (N × H)
391. #3092C2×C127semidirect
392. C2×#484C2×C127semidirect
393. #2623C2×C127semidirect
394. #1618C2×C127semidirect
395. #1617C2×C127semidirect
396. #1615C2×C127semidirect
397. #1614C2×C127semidirect
398. #1516C2×C127semidirect
399. #1511C2×C127semidirect
400. #1468C2×C127semidirect
401. C127#18235direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#35352
C127×#30922
C2×#484×C1272
C127×#26232
C127×#16182
C127×#16172
C127×#16152
C127×#16142
C127×#15162
C127×#15112
C127×#14682
#18235127