Finite Group Databasebeta

← C127×#15909 #44579582

Subgroups — C127×#15909 #44579582

Order 32512.

2150 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#126×C127C211yesmaximal, characteristic, complemented
2C2×#394×C127C211yesmaximal, characteristic, complemented
3C2×#392×C127C211yesmaximal, characteristic
4C2×#390×C127C211yesmaximal, characteristic, complemented
5C127×#1445C211yesmaximal, characteristic, complemented
6C127×#1439C212yesmaximal, complemented
7C127×#1438C212yesmaximal, complemented
8C127×#1438C212yesmaximal, complemented
9C127×#1437C212yesmaximal, complemented
10C127×#1437C211yesmaximal, characteristic, complemented
11C127×#1436C211yesmaximal, characteristic, complemented
12C23×D4×C127C2211yescharacteristic
13C23×D4×C127C2212yes—
14C2×#126×C127—24no—
15C2×#126×C127—24no—
16C2×#126×C127—24no—
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C4⋊C4×C127C2211yescharacteristic
19C22×C4⋊C4×C127C2211yescharacteristic
20C22×C22⋊C4×C127C2211yescharacteristic
21C22×C22⋊C4×C127C2211yescharacteristic
22C22×C22⋊C4×C127C2212yes—
23C22×C22⋊C4×C127C2212yes—
24C22×C22⋊C4×C127C2212yes—
25C22×C22⋊C4×C127C2212yes—
26C22×C22⋊C4×C127C2211yescharacteristic
27C22×C22⋊C4×C127C2212yes—
28C22×C22⋊C4×C127C2212yes—
29C22×C42×C127C2211yescharacteristic
30C22×C42×C127C2211yescharacteristic
31#394×C127—24no—
32#392×C127—24no—
33#390×C127—24no—
34C2×#95×C127C2211yescharacteristic
35C2×#95×C127C2211yescharacteristic
36C2×#95×C127C2212yes—
37C2×#95×C127C2212yes—
38C2×#95×C127C2212yes—
39C2×#95×C127C2212yes—
40C2×#95×C127C2212yes—
41C25×C127C2311yescharacteristic
42C25×C127C2312yes—
43C22×D4×C127—24no—
44C22×D4×C127—24no—
45C22×D4×C127—24no—
46C22×D4×C127—22no—
47C22×D4×C127—22no—
48C22×D4×C127—22no—
49C22×D4×C127—24no—
50C22×D4×C127—42no—
51C22×D4×C127—42no—
52C22×D4×C127—42no—
53C22×D4×C127—42no—
54C22×D4×C127—42no—
55C23×C4×C127C2312yes—
56C23×C4×C127C2311yescharacteristic
57C23×C4×C127C2311yescharacteristic
58C23×C4×C127C2311yescharacteristic
59C23×C4×C127C2311yescharacteristic
60C23×C4×C127C2311yescharacteristic
61C23×C4×C127C2312yes—
62C23×C4×C127C2312yes—
63C23×C4×C127C2311yescharacteristic
64#126×C127—232no—
65C2×C4⋊C4×C127—22no—
66C2×C4⋊C4×C127—22no—
67C2×C4⋊C4×C127—22no—
68C2×C4⋊C4×C127—22no—
69C2×C4⋊C4×C127—22no—
70C2×C4⋊C4×C127—22no—
71C2×C4⋊C4×C127—22no—
72C2×C4⋊C4×C127D414yescomplemented
73C2×C4⋊C4×C127D414yescomplemented
74C2×C22⋊C4×C127—22no—
75C2×C22⋊C4×C127—22no—
76C2×C22⋊C4×C127—22no—
77C2×C22⋊C4×C127—22no—
78C2×C22⋊C4×C127—22no—
79C2×C22⋊C4×C127—22no—
80C2×C22⋊C4×C127—22no—
81C2×C22⋊C4×C127—22no—
82C2×C22⋊C4×C127—24no—
83C2×C22⋊C4×C127—24no—
84C2×C22⋊C4×C127—24no—
85C2×C22⋊C4×C127—24no—
86C2×C22⋊C4×C127—24no—
87C2×C22⋊C4×C127—24no—
88C2×C22⋊C4×C127—24no—
89C2×C22⋊C4×C127—24no—
90C2×C22⋊C4×C127—24no—
91C2×C22⋊C4×C127—24no—
92C2×C22⋊C4×C127—42no—
93C2×C22⋊C4×C127—42no—
94C2×C22⋊C4×C127—42no—
95C2×C22⋊C4×C127—42no—
96C2×C22⋊C4×C127—42no—
97C2×C22⋊C4×C127—42no—
98C2×C22⋊C4×C127—42no—
99C2×C22⋊C4×C127—42no—
100C2×C22⋊C4×C127D414yes—
101C2×C42×C127—22no—
102C2×C42×C127—22no—
103C2×C42×C127—22no—
104C2×C42×C127—22no—
105C2×C42×C127—42no—
106#95×C127—22no—
107#95×C127—22no—
108#95×C127—24no—
109#95×C127—42no—
110#95×C127—42no—
111#95×C127—42no—
112#95×C127—42no—
113C24×C127—21no—
114C24×C127—21no—
115C24×C127—22no—
116C24×C127—22no—
117C24×C127—22no—
118C24×C127—22no—
119C24×C127—22no—
120C24×C127—22no—
121C24×C127—22no—
122C24×C127—22no—
123C24×C127—22no—
124C24×C127—22no—
125C24×C127—22no—
126C24×C127—22no—
127C24×C127—22no—
128C24×C127—22no—
129C24×C127—22no—
130C24×C127—22no—
131C24×C127—22no—
132C24×C127—22no—
133C24×C127—22no—
134C24×C127—22no—
135C24×C127C2×D412yes—
136C24×C127#4114yes—
137C24×C127C2411yescharacteristic
138C2×D4×C127—28no—
139C2×D4×C127—48no—
140C2×D4×C127—48no—
141C2×D4×C127—48no—
142C2×D4×C127—48no—
143C2×D4×C127—44no—
144C2×D4×C127—48no—
145C2×D4×C127—48no—
146C2×D4×C127—48no—
147C2×D4×C127—48no—
148C2×D4×C127—48no—
149C2×D4×C127—44no—
150C22×C4×C127—22no—
151C22×C4×C127—22no—
152C22×C4×C127—22no—
153C22×C4×C127—22no—
154C22×C4×C127—21no—
155C22×C4×C127—21no—
156C22×C4×C127—21no—
157C22×C4×C127—21no—
158C22×C4×C127—21no—
159C22×C4×C127—21no—
160C22×C4×C127—21no—
161C22×C4×C127—21no—
162C22×C4×C127—21no—
163C22×C4×C127—21no—
164C22×C4×C127—22no—
165C22×C4×C127—22no—
166C22×C4×C127—22no—
167C22×C4×C127—22no—
168C22×C4×C127—22no—
169C22×C4×C127—22no—
170C22×C4×C127—22no—
171C22×C4×C127—22no—
172C22×C4×C127—22no—
173C22×C4×C127—22no—
174C22×C4×C127—22no—
175C22×C4×C127—22no—
176C22×C4×C127—22no—
177C22×C4×C127—22no—
178C22×C4×C127—22no—
179C22×C4×C127—22no—
180C22×C4×C127—22no—
181C22×C4×C127—22no—
182C22×C4×C127—22no—
183C22×C4×C127—22no—
184C22×C4×C127—22no—
185C22×C4×C127—22no—
186C22×C4×C127—22no—
187C22×C4×C127—22no—
188C22×C4×C127—22no—
189C22×C4×C127—22no—
190C22×C4×C127—22no—
191C22×C4×C127C2×D412yes—
192C22×C4×C127C2×D412yes—
193C22×C4×C127C2×D412yes—
194C22×C4×C127C2×D412yes—
195C22×C4×C127C2×D412yes—
196C22×C4×C127C2×D412yes—
197C22×C4×C127C2×D412yes—
198C22×C4×C127C2×D412yes—
199C22×C4×C127#4114yes—
200C22×C4×C127#4114yes—
201C4⋊C4×C127—28no—
202C4⋊C4×C127—28no—
203C4⋊C4×C127—28no—
204C22⋊C4×C127—28no—
205C22⋊C4×C127—28no—
206C22⋊C4×C127—28no—
207C22⋊C4×C127—48no—
208C22⋊C4×C127—48no—
209C22⋊C4×C127—48no—
210C22⋊C4×C127—48no—
211C22⋊C4×C127—48no—
212C22⋊C4×C127—48no—
213C42×C127—28no—
214C42×C127—44no—
215C23×C127—22no—
216C23×C127—24no—
217C23×C127—24no—
218C23×C127—22no—
219C23×C127—22no—
220C23×C127—24no—
221C23×C127—24no—
222C23×C127—24no—
223C23×C127—24no—
224C23×C127—24no—
225C23×C127—24no—
226C23×C127—24no—
227C23×C127—42no—
228C23×C127—41no—
229C23×C127—42no—
230C23×C127—42no—
231C23×C127—41no—
232C23×C127—42no—
233C23×C127—42no—
234C23×C127—42no—
235C23×C127—42no—
236C23×C127—42no—
237C23×C127—41no—
238C23×C127—41no—
239C23×C127—42no—
240C23×C127—42no—
241C23×C127—42no—
242C23×C127—42no—
243C23×C127—42no—
244C23×C127—42no—
245C23×C127—42no—
246C23×C127—42no—
247C23×C127—42no—
248C23×C127—42no—
249C23×C127—42no—
250C23×C127—42no—
251C23×C127—42no—
252C23×C127—42no—
253C23×C127—42no—
254C23×C127—42no—
255C23×C127—42no—
256C23×C127—42no—
257C23×C127—42no—
258C23×C127—42no—
259C23×C127—42no—
260C23×C127—42no—
261C23×C127—42no—
262C23×C127—42no—
263C23×C127—42no—
264C23×C127—42no—
265C23×C127—42no—
266C23×C127—42no—
267C23×C127—42no—
268C23×C127—42no—
269C23×C127—42no—
270C23×C127—42no—
271C23×C127C22×D411yescharacteristic
272C23×C127C22×D411yescharacteristic
273C23×C127C22×D411yescharacteristic
274C23×C127C2×#4112yes—
275C23×C127C2×#4112yes—
276C23×C127C2×#4112yes—
277C23×C127H(5,𝔽2)12yes—
278C23×C127H(5,𝔽2)12yes—
279C23×C127H(5,𝔽2)12yes—
280D4×C127—416no—
281D4×C127—432no—
282C2×C4×C127—22no—
283C2×C4×C127—22no—
284C2×C4×C127—24no—
285C2×C4×C127—24no—
286C2×C4×C127—22no—
287C2×C4×C127—22no—
288C2×C4×C127—22no—
289C2×C4×C127—22no—
290C2×C4×C127—22no—
291C2×C4×C127—22no—
292C2×C4×C127—22no—
293C2×C4×C127—24no—
294C2×C4×C127—24no—
295C2×C4×C127—24no—
296C2×C4×C127—24no—
297C2×C4×C127—24no—
298C2×C4×C127—24no—
299C2×C4×C127—24no—
300C2×C4×C127—24no—
301C2×C4×C127—24no—
302C2×C4×C127—24no—
303C2×C4×C127—41no—
304C2×C4×C127—41no—
305C2×C4×C127—41no—
306C2×C4×C127—41no—
307C2×C4×C127—42no—
308C2×C4×C127—41no—
309C2×C4×C127—41no—
310C2×C4×C127—41no—
311C2×C4×C127—41no—
312C2×C4×C127—42no—
313C2×C4×C127—42no—
314C2×C4×C127—42no—
315C2×C4×C127—42no—
316C2×C4×C127—42no—
317C2×C4×C127—42no—
318C2×C4×C127—42no—
319C2×C4×C127—42no—
320C2×C4×C127—42no—
321C2×C4×C127—42no—
322C2×C4×C127—42no—
323C2×C4×C127—42no—
324C2×C4×C127—42no—
325C2×C4×C127—42no—
326C2×C4×C127—42no—
327C2×C4×C127—42no—
328C2×C4×C127—42no—
329C2×C4×C127—42no—
330C2×C4×C127—42no—
331C2×C4×C127—42no—
332C2×C4×C127#12014yes—
333C22×C127—44no—
334C22×C127—42no—
335C22×C127—44no—
336C22×C127—44no—
337C22×C127—42no—
338C22×C127—42no—
339C22×C127—44no—
340C22×C127—44no—
341C22×C127—44no—
342C22×C127—44no—
343C22×C127—44no—
344C22×C127—44no—
345C22×C127—82no—
346C22×C127—82no—
347C22×C127—82no—
348C22×C127—82no—
349C22×C127—82no—
350C22×C127—82no—
351C22×C127—82no—
352C22×C127—82no—
353C22×C127—82no—
354C22×C127—82no—
355C22×C127—82no—
356C22×C127—82no—
357C22×C127C2×#12011yescharacteristic
358C22×C127#52511yescharacteristic
359C22×C127#52912yes—
360C22×C127#53211yescharacteristic
361C22×C127#53211yescharacteristic
362C22×C127#53511yescharacteristic
363C22×C127#53511yescharacteristic
364C22×C127#53511yescharacteristic
365C22×C127#53812yes—
366C22×C127#53812yes—
367C22×C127#53812yes—
368C22×C127#54612yes—
369C22×C127#54612yes—
370C22×C127#54612yes—
371C22×C127#54612yes—
372C22×C127#55012yes—
373C22×C127#55012yes—
374C22×C127#55112yes—
375C22×C127#55312yes—
376C22×C127#55312yes—
377C22×C127#56012yes—
378C4×C127—24no—
379C4×C127—42no—
380C4×C127—44no—
381C4×C127—42no—
382C4×C127—42no—
383C4×C127—42no—
384C4×C127—42no—
385C4×C127—44no—
386C4×C127—82no—
387#15909C12711yesmaximal, characteristic, direct product factor, Sylow
388C2×C127—84no—
389C2×C127—82no—
390C2×C127#240411yescharacteristic
391C2×C127#243111yescharacteristic
392C2×C127#243111yescharacteristic
393C2×C127#246712yes—
394C2×C127#255412yes—
395C2×C127#255912yes—
396C2×C127#268512yes—
397C2×C127#271412yes—
398C2×C127#271412yes—
399C22×#126C2×C12711yescharacteristic, complemented
400C2×#394C2×C12711yescharacteristic, complemented
401C2×#392C2×C12711yescharacteristic
402C2×#390C2×C12711yescharacteristic, complemented
403#1445C2×C12711yescharacteristic, complemented
404#1439C2×C12712yescomplemented
405#1438C2×C12712yescomplemented
406#1438C2×C12712yescomplemented
407#1437C2×C12712yescomplemented
408#1437C2×C12711yescharacteristic, complemented
409#1436C2×C12711yescharacteristic, complemented
410C127#1590911yescharacteristic, direct product factor, Sylow
411C23×D4C22×C12711yescharacteristic
412C23×D4C22×C12712yes—
413C2×#126—24no—
414C2×#126—24no—
415C2×#126—24no—
416C22×C4⋊C4C22×C12711yescharacteristic
417C22×C4⋊C4C22×C12711yescharacteristic
418C22×C4⋊C4C22×C12711yescharacteristic
419C22×C22⋊C4C22×C12711yescharacteristic
420C22×C22⋊C4C22×C12711yescharacteristic
421C22×C22⋊C4C22×C12712yes—
422C22×C22⋊C4C22×C12712yes—
423C22×C22⋊C4C22×C12712yes—
424C22×C22⋊C4C22×C12712yes—
425C22×C22⋊C4C22×C12711yescharacteristic
426C22×C22⋊C4C22×C12712yes—
427C22×C22⋊C4C22×C12712yes—
428C22×C42C22×C12711yescharacteristic
429C22×C42C22×C12711yescharacteristic
430#394—24no—
431#392—24no—
432#390—24no—
433C2×#95C22×C12711yescharacteristic
434C2×#95C22×C12711yescharacteristic
435C2×#95C22×C12712yes—
436C2×#95C22×C12712yes—
437C2×#95C22×C12712yes—
438C2×#95C22×C12712yes—
439C2×#95C22×C12712yes—
440C25C23×C12711yescharacteristic
441C25C23×C12712yes—
442C22×D4—24no—
443C22×D4—24no—
444C22×D4—24no—
445C22×D4—22no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—24no—
449C22×D4—42no—
450C22×D4—42no—
451C22×D4—42no—
452C22×D4—42no—
453C22×D4—42no—
454C23×C4C23×C12712yes—
455C23×C4C23×C12711yescharacteristic
456C23×C4C23×C12711yescharacteristic
457C23×C4C23×C12711yescharacteristic
458C23×C4C23×C12711yescharacteristic
459C23×C4C23×C12711yescharacteristic
460C23×C4C23×C12712yes—
461C23×C4C23×C12712yes—
462C23×C4C23×C12711yescharacteristic
463#126—232no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4D4×C12714yescomplemented
472C2×C4⋊C4D4×C12714yescomplemented
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4—42no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—42no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4D4×C12714yes—
500C2×C42—22no—
501C2×C42—22no—
502C2×C42—22no—
503C2×C42—22no—
504C2×C42—42no—
505#95—22no—
506#95—22no—
507#95—24no—
508#95—42no—
509#95—42no—
510#95—42no—
511#95—42no—
512C24—21no—
513C24—21no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24C2×D4×C12712yes—
535C24#41×C12714yes—
536C24C24×C12711yescharacteristic
537C2×D4—28no—
538C2×D4—48no—
539C2×D4—48no—
540C2×D4—48no—
541C2×D4—48no—
542C2×D4—44no—
543C2×D4—48no—
544C2×D4—48no—
545C2×D4—48no—
546C2×D4—48no—
547C2×D4—48no—
548C2×D4—44no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4C2×D4×C12712yes—
591C22×C4C2×D4×C12712yes—
592C22×C4C2×D4×C12712yes—
593C22×C4C2×D4×C12712yes—
594C22×C4C2×D4×C12712yes—
595C22×C4C2×D4×C12712yes—
596C22×C4C2×D4×C12712yes—
597C22×C4C2×D4×C12712yes—
598C22×C4#41×C12714yes—
599C22×C4#41×C12714yes—
600C4⋊C4—28no—
601C4⋊C4—28no—
602C4⋊C4—28no—
603C22⋊C4—28no—
604C22⋊C4—28no—
605C22⋊C4—28no—
606C22⋊C4—48no—
607C22⋊C4—48no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C22⋊C4—48no—
611C22⋊C4—48no—
612C42—28no—
613C42—44no—
614C23—22no—
615C23—24no—
616C23—24no—
617C23—22no—
618C23—22no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—42no—
627C23—41no—
628C23—42no—
629C23—42no—
630C23—41no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—41no—
637C23—41no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23C22×D4×C12711yescharacteristic
671C23C22×D4×C12711yescharacteristic
672C23C22×D4×C12711yescharacteristic
673C23C2×#41×C12712yes—
674C23C2×#41×C12712yes—
675C23C2×#41×C12712yes—
676C23H(5,𝔽2)×C12712yes—
677C23H(5,𝔽2)×C12712yes—
678C23H(5,𝔽2)×C12712yes—
679D4—416no—
680D4—432no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4#120×C12714yes—
732C22—44no—
733C22—42no—
734C22—44no—
735C22—44no—
736C22—42no—
737C22—42no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—82no—
745C22—82no—
746C22—82no—
747C22—82no—
748C22—82no—
749C22—82no—
750C22—82no—
751C22—82no—
752C22—82no—
753C22—82no—
754C22—82no—
755C22—82no—
756C22C2×#120×C12711yescharacteristic
757C22#525×C12711yescharacteristic
758C22#529×C12712yes—
759C22#532×C12711yescharacteristic
760C22#532×C12711yescharacteristic
761C22#535×C12711yescharacteristic
762C22#535×C12711yescharacteristic
763C22#535×C12711yescharacteristic
764C22#538×C12712yes—
765C22#538×C12712yes—
766C22#538×C12712yes—
767C22#546×C12712yes—
768C22#546×C12712yes—
769C22#546×C12712yes—
770C22#546×C12712yes—
771C22#550×C12712yes—
772C22#550×C12712yes—
773C22#551×C12712yes—
774C22#553×C12712yes—
775C22#553×C12712yes—
776C22#560×C12712yes—
777C4—24no—
778C4—42no—
779C4—44no—
780C4—42no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—44no—
785C4—82no—
786C2—84no—
787C2—82no—
788C2C127×#240411yescharacteristic
789C2C127×#243111yescharacteristic
790C2C127×#243111yescharacteristic
791C2C127×#246712yes—
792C2C127×#255412yes—
793C2C127×#255912yes—
794C2C127×#268512yes—
795C2C127×#271412yes—
796C2C127×#271412yes—
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC2×#392×C127C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#126×C127C2semidirect
2. C2×#394×C127C2semidirect
4. C2×#390×C127C2semidirect
5. C127×#1445C2semidirect
6. C127×#1439C2semidirect
7. C127×#1438C2semidirect
8. C127×#1438C2semidirect
9. C127×#1437C2semidirect
10. C127×#1437C2semidirect
11. C127×#1436C2semidirect
72. C2×C4⋊C4×C127D4semidirect
73. C2×C4⋊C4×C127D4semidirect
387. #15909C127direct (N × H)
399. C22×#126C2×C127semidirect
400. C2×#394C2×C127semidirect
402. C2×#390C2×C127semidirect
403. #1445C2×C127semidirect
404. #1439C2×C127semidirect
405. #1438C2×C127semidirect
406. #1438C2×C127semidirect
407. #1437C2×C127semidirect
408. #1437C2×C127semidirect
409. #1436C2×C127semidirect
410. C127#15909direct (N × H)
471. C2×C4⋊C4D4×C127semidirect
472. C2×C4⋊C4D4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#126×C1272
C2×#394×C1272
C2×#392×C1272
C2×#390×C1272
C127×#14452
C127×#14392
C127×#14382
C127×#14372
C127×#14362
#15909127