Finite Group Databasebeta

← C127×#14621 #44578294

Subgroups — C127×#14621 #44578294

Order 32512.

2018 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#392×C127C211yesmaximal, characteristic
2C2×#386×C127C212yesmaximal, complemented
3C127×#1443C212yesmaximal, complemented
4C127×#1440C212yesmaximal, complemented
5C127×#1439C211yesmaximal, characteristic, complemented
6C127×#1439C212yesmaximal, complemented
7C127×#1438C212yesmaximal, complemented
8C127×#1438C212yesmaximal, complemented
9C127×C22⋊#95C211yesmaximal, characteristic, complemented
10C23×D4×C127C2212yes—
11C23×D4×C127C2211yescharacteristic
12C24×C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C22⋊C4×C127C2211yescharacteristic
15C22×C22⋊C4×C127C2212yes—
16C22×C22⋊C4×C127C2212yes—
17C22×C22⋊C4×C127C2212yes—
18C22×C22⋊C4×C127C2212yes—
19C22×C22⋊C4×C127C2212yes—
20C22×C22⋊C4×C127C2211yescharacteristic
21C22×C22⋊C4×C127C2212yes—
22#392×C127C418yescomplemented
23#386×C127—28no—
24C2×#95×C127C2212yes—
25C2×#95×C127C2212yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2212yes—
28C2×#95×C127C2212yes—
29C2×#95×C127C2212yes—
30C2×#95×C127C2212yes—
31C2×#95×C127C2211yescharacteristic
32C2×#95×C127C2211yescharacteristic
33C25×C127C2312yes—
34C25×C127C2311yescharacteristic
35C22×D4×C127—24no—
36C22×D4×C127—24no—
37C22×D4×C127—42no—
38C22×D4×C127—42no—
39C22×D4×C127—42no—
40C22×D4×C127—42no—
41C22×D4×C127—42no—
42C22×D4×C127—42no—
43C22×D4×C127—41no—
44C22×D4×C127—41no—
45C22×D4×C127C2×C418yes—
46C22×D4×C127C2×C414yescomplemented
47C23×C4×C127—42no—
48C23×C4×C127—42no—
49C23×C4×C127—41no—
50C23×C4×C127—41no—
51C23×C4×C127D414yescomplemented
52C23×C4×C127C2312yes—
53C23×C4×C127C2312yes—
54C23×C4×C127C2312yes—
55C23×C4×C127C2311yescharacteristic
56C23×C4×C127C2312yes—
57C23×C4×C127C2311yescharacteristic
58C23×C4×C127C2312yes—
59C2×C4⋊C4×C127—41no—
60C2×C4⋊C4×C127—42no—
61C2×C22⋊C4×C127—24no—
62C2×C22⋊C4×C127—22no—
63C2×C22⋊C4×C127—24no—
64C2×C22⋊C4×C127—24no—
65C2×C22⋊C4×C127—41no—
66C2×C22⋊C4×C127—41no—
67C2×C22⋊C4×C127—42no—
68C2×C22⋊C4×C127—42no—
69C2×C22⋊C4×C127—42no—
70C2×C22⋊C4×C127—42no—
71C2×C22⋊C4×C127—42no—
72C2×C22⋊C4×C127—42no—
73C2×C22⋊C4×C127—42no—
74C2×C22⋊C4×C127—41no—
75C2×C22⋊C4×C127—41no—
76C2×C22⋊C4×C127—42no—
77C2×C22⋊C4×C127—42no—
78C2×C22⋊C4×C127—42no—
79C2×C22⋊C4×C127—42no—
80C2×C22⋊C4×C127—42no—
81C2×C22⋊C4×C127—42no—
82C2×C22⋊C4×C127—42no—
83C2×C22⋊C4×C127C2×C414yes—
84C2×C22⋊C4×C127C2×C418yescomplemented
85#95×C127—24no—
86#95×C127—24no—
87#95×C127—42no—
88#95×C127—41no—
89#95×C127—42no—
90#95×C127—42no—
91#95×C127—42no—
92#95×C127—42no—
93#95×C127C2×C414yescomplemented
94C24×C127—21no—
95C24×C127—21no—
96C24×C127—21no—
97C24×C127—22no—
98C24×C127—22no—
99C24×C127—22no—
100C24×C127—22no—
101C24×C127—21no—
102C24×C127—22no—
103C24×C127—22no—
104C24×C127—22no—
105C24×C127—22no—
106C24×C127—22no—
107C24×C127—22no—
108C24×C127—22no—
109C24×C127—22no—
110C24×C127—22no—
111C24×C127—22no—
112C24×C127—22no—
113C24×C127—22no—
114C24×C127—22no—
115C24×C127—22no—
116C24×C127C22×C414yes—
117C24×C127C22×C412yes—
118C24×C127C2×D412yes—
119C24×C127#4112yes—
120C24×C127C2411yescharacteristic
121C2×D4×C127—216no—
122C2×D4×C127—48no—
123C2×D4×C127—48no—
124C2×D4×C127—44no—
125C2×D4×C127—48no—
126C2×D4×C127—48no—
127C2×D4×C127—48no—
128C2×D4×C127—48no—
129C2×D4×C127—48no—
130C2×D4×C127—48no—
131C2×D4×C127—44no—
132C2×D4×C127—44no—
133C22×C4×C127—22no—
134C22×C4×C127—22no—
135C22×C4×C127—22no—
136C22×C4×C127—21no—
137C22×C4×C127—22no—
138C22×C4×C127—22no—
139C22×C4×C127—22no—
140C22×C4×C127—22no—
141C22×C4×C127—22no—
142C22×C4×C127—22no—
143C22×C4×C127—21no—
144C22×C4×C127—22no—
145C22×C4×C127—22no—
146C22×C4×C127—22no—
147C22×C4×C127—22no—
148C22×C4×C127—22no—
149C22×C4×C127—22no—
150C22×C4×C127—22no—
151C22×C4×C127—21no—
152C22×C4×C127—21no—
153C22×C4×C127—22no—
154C22×C4×C127—22no—
155C22×C4×C127—22no—
156C22×C4×C127—22no—
157C22×C4×C127—22no—
158C22×C4×C127—22no—
159C22×C4×C127—22no—
160C22×C4×C127—22no—
161C22×C4×C127—22no—
162C22×C4×C127—22no—
163C22×C4×C127—22no—
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—44no—
175C22×C4×C127—48no—
176C22×C4×C127—48no—
177C22×C4×C127—44no—
178C22×C4×C127—44no—
179C22×C4×C127C22×C412yes—
180C22×C4×C127C22×C414yes—
181C22×C4×C127C22×C412yes—
182C22×C4×C127C2×D414yes—
183C4⋊C4×C127—44no—
184C22⋊C4×C127—44no—
185C22⋊C4×C127—48no—
186C22⋊C4×C127—48no—
187C22⋊C4×C127—48no—
188C22⋊C4×C127—48no—
189C22⋊C4×C127—44no—
190C22⋊C4×C127—48no—
191C22⋊C4×C127—48no—
192C23×C127—22no—
193C23×C127—24no—
194C23×C127—24no—
195C23×C127—22no—
196C23×C127—24no—
197C23×C127—22no—
198C23×C127—24no—
199C23×C127—22no—
200C23×C127—22no—
201C23×C127—24no—
202C23×C127—24no—
203C23×C127—22no—
204C23×C127—24no—
205C23×C127—24no—
206C23×C127—24no—
207C23×C127—24no—
208C23×C127—24no—
209C23×C127—24no—
210C23×C127—24no—
211C23×C127—42no—
212C23×C127—41no—
213C23×C127—41no—
214C23×C127—42no—
215C23×C127—42no—
216C23×C127—42no—
217C23×C127—41no—
218C23×C127—41no—
219C23×C127—42no—
220C23×C127—42no—
221C23×C127—42no—
222C23×C127—42no—
223C23×C127—42no—
224C23×C127—42no—
225C23×C127—42no—
226C23×C127—42no—
227C23×C127—42no—
228C23×C127—42no—
229C23×C127—42no—
230C23×C127—42no—
231C23×C127—42no—
232C23×C127—42no—
233C23×C127—42no—
234C23×C127—42no—
235C23×C127—42no—
236C23×C127—42no—
237C23×C127—42no—
238C23×C127—42no—
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×C127C4×D414yes—
250C23×C127C23×C411yescharacteristic
251C23×C127C22×D411yescharacteristic
252C23×C127C2×#4111yescharacteristic
253C23×C127H(5,𝔽2)12yes—
254C23×C127H(5,𝔽2)12yes—
255C23×C127H(5,𝔽2)11yescharacteristic
256C23×C127H(5,𝔽2)12yes—
257C23×C127H(5,𝔽2)12yes—
258C23×C127H(5,𝔽2)11yescharacteristic
259C23×C127H(5,𝔽2)11yescharacteristic
260C23×C1272−1+411yescharacteristic
261D4×C127—432no—
262D4×C127—416no—
263C2×C4×C127—24no—
264C2×C4×C127—24no—
265C2×C4×C127—22no—
266C2×C4×C127—24no—
267C2×C4×C127—22no—
268C2×C4×C127—24no—
269C2×C4×C127—24no—
270C2×C4×C127—24no—
271C2×C4×C127—24no—
272C2×C4×C127—24no—
273C2×C4×C127—416no—
274C2×C4×C127—42no—
275C2×C4×C127—42no—
276C2×C4×C127—42no—
277C2×C4×C127—42no—
278C2×C4×C127—41no—
279C2×C4×C127—42no—
280C2×C4×C127—41no—
281C2×C4×C127—42no—
282C2×C4×C127—42no—
283C2×C4×C127—42no—
284C2×C4×C127—42no—
285C2×C4×C127—41no—
286C2×C4×C127—42no—
287C2×C4×C127—41no—
288C2×C4×C127—42no—
289C2×C4×C127—42no—
290C2×C4×C127—42no—
291C2×C4×C127—42no—
292C2×C4×C127—42no—
293C2×C4×C127—42no—
294C2×C4×C127—42no—
295C2×C4×C127—42no—
296C2×C4×C127—42no—
297C2×C4×C127—42no—
298C2×C4×C127—42no—
299C2×C4×C127—42no—
300C2×C4×C127—42no—
301C2×C4×C127—42no—
302C2×C4×C127—42no—
303C2×C4×C127—42no—
304C2×C4×C127—42no—
305C2×C4×C127—42no—
306C2×C4×C127—42no—
307C2×C4×C127—42no—
308C2×C4×C127—42no—
309C22×C127—28no—
310C22×C127—24no—
311C22×C127—42no—
312C22×C127—44no—
313C22×C127—42no—
314C22×C127—42no—
315C22×C127—44no—
316C22×C127—42no—
317C22×C127—42no—
318C22×C127—44no—
319C22×C127—42no—
320C22×C127—44no—
321C22×C127—44no—
322C22×C127—44no—
323C22×C127—44no—
324C22×C127—44no—
325C22×C127—44no—
326C22×C127—44no—
327C22×C127—82no—
328C22×C127—82no—
329C22×C127—82no—
330C22×C127—82no—
331C22×C127—82no—
332C22×C127—82no—
333C22×C127—82no—
334C22×C127—82no—
335C22×C127C2×C4×D411yescharacteristic
336C22×C127#51812yes—
337C22×C127#51812yes—
338C22×C127#51811yescharacteristic
339C22×C127#52011yescharacteristic
340C22×C127#53412yes—
341C22×C127#53411yescharacteristic
342C22×C127#53512yes—
343C22×C127#53711yescharacteristic
344C22×C127#53812yes—
345C22×C127#53811yescharacteristic
346C22×C127#53812yes—
347C22×C127#53911yescharacteristic
348C22×C127#56011yescharacteristic
349C22×C127#56012yes—
350C22×C127#56012yes—
351C22×C127#56012yes—
352C22×C127#56012yes—
353C22×C127#56011yescharacteristic
354C22×C127#56011yescharacteristic
355C22×C127H(3,𝔽4)11yescharacteristic
356C22×C127#56212yes—
357C22×C127#56212yes—
358C4×C127—44no—
359C4×C127—42no—
360C4×C127—42no—
361C4×C127—44no—
362C4×C127—82no—
363C4×C127—82no—
364C4×C127—82no—
365#14621C12711yesmaximal, characteristic, direct product factor, Sylow
366C2×C127—44no—
367C2×C127—84no—
368C2×C127#232112yes—
369C2×C127#232511yescharacteristic
370C2×C127#237511yescharacteristic
371C2×C127#237712yes—
372C2×C127#238011yescharacteristic
373C2×C127#281211yescharacteristic
374C2×C127#281312yes—
375C2×C127#281511yescharacteristic
376C2×C127#282411yescharacteristic
377C2×C127#282512yes—
378C2×C127#282611yescharacteristic
379C2×#392C2×C12711yescharacteristic
380C2×#386C2×C12712yescomplemented
381#1443C2×C12712yescomplemented
382#1440C2×C12712yescomplemented
383#1439C2×C12711yescharacteristic, complemented
384#1439C2×C12712yescomplemented
385#1438C2×C12712yescomplemented
386#1438C2×C12712yescomplemented
387C22⋊#95C2×C12711yescharacteristic, complemented
388C127#1462111yescharacteristic, direct product factor, Sylow
389C23×D4C22×C12712yes—
390C23×D4C22×C12711yescharacteristic
391C24×C4C22×C12711yescharacteristic
392C22×C4⋊C4C22×C12711yescharacteristic
393C22×C22⋊C4C22×C12711yescharacteristic
394C22×C22⋊C4C22×C12712yes—
395C22×C22⋊C4C22×C12712yes—
396C22×C22⋊C4C22×C12712yes—
397C22×C22⋊C4C22×C12712yes—
398C22×C22⋊C4C22×C12712yes—
399C22×C22⋊C4C22×C12711yescharacteristic
400C22×C22⋊C4C22×C12712yes—
401#392C4×C12718yescomplemented
402#386—28no—
403C2×#95C22×C12712yes—
404C2×#95C22×C12712yes—
405C2×#95C22×C12712yes—
406C2×#95C22×C12712yes—
407C2×#95C22×C12712yes—
408C2×#95C22×C12712yes—
409C2×#95C22×C12712yes—
410C2×#95C22×C12711yescharacteristic
411C2×#95C22×C12711yescharacteristic
412C25C23×C12712yes—
413C25C23×C12711yescharacteristic
414C22×D4—24no—
415C22×D4—24no—
416C22×D4—42no—
417C22×D4—42no—
418C22×D4—42no—
419C22×D4—42no—
420C22×D4—42no—
421C22×D4—42no—
422C22×D4—41no—
423C22×D4—41no—
424C22×D4C2×C4×C12718yes—
425C22×D4C2×C4×C12714yescomplemented
426C23×C4—42no—
427C23×C4—42no—
428C23×C4—41no—
429C23×C4—41no—
430C23×C4D4×C12714yescomplemented
431C23×C4C23×C12712yes—
432C23×C4C23×C12712yes—
433C23×C4C23×C12712yes—
434C23×C4C23×C12711yescharacteristic
435C23×C4C23×C12712yes—
436C23×C4C23×C12711yescharacteristic
437C23×C4C23×C12712yes—
438C2×C4⋊C4—41no—
439C2×C4⋊C4—42no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—41no—
445C2×C22⋊C4—41no—
446C2×C22⋊C4—42no—
447C2×C22⋊C4—42no—
448C2×C22⋊C4—42no—
449C2×C22⋊C4—42no—
450C2×C22⋊C4—42no—
451C2×C22⋊C4—42no—
452C2×C22⋊C4—42no—
453C2×C22⋊C4—41no—
454C2×C22⋊C4—41no—
455C2×C22⋊C4—42no—
456C2×C22⋊C4—42no—
457C2×C22⋊C4—42no—
458C2×C22⋊C4—42no—
459C2×C22⋊C4—42no—
460C2×C22⋊C4—42no—
461C2×C22⋊C4—42no—
462C2×C22⋊C4C2×C4×C12714yes—
463C2×C22⋊C4C2×C4×C12718yescomplemented
464#95—24no—
465#95—24no—
466#95—42no—
467#95—41no—
468#95—42no—
469#95—42no—
470#95—42no—
471#95—42no—
472#95C2×C4×C12714yescomplemented
473C24—21no—
474C24—21no—
475C24—21no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—21no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24C22×C4×C12714yes—
496C24C22×C4×C12712yes—
497C24C2×D4×C12712yes—
498C24#41×C12712yes—
499C24C24×C12711yescharacteristic
500C2×D4—216no—
501C2×D4—48no—
502C2×D4—48no—
503C2×D4—44no—
504C2×D4—48no—
505C2×D4—48no—
506C2×D4—48no—
507C2×D4—48no—
508C2×D4—48no—
509C2×D4—48no—
510C2×D4—44no—
511C2×D4—44no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—44no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4C22×C4×C12712yes—
559C22×C4C22×C4×C12714yes—
560C22×C4C22×C4×C12712yes—
561C22×C4C2×D4×C12714yes—
562C4⋊C4—44no—
563C22⋊C4—44no—
564C22⋊C4—48no—
565C22⋊C4—48no—
566C22⋊C4—48no—
567C22⋊C4—48no—
568C22⋊C4—44no—
569C22⋊C4—48no—
570C22⋊C4—48no—
571C23—22no—
572C23—24no—
573C23—24no—
574C23—22no—
575C23—24no—
576C23—22no—
577C23—24no—
578C23—22no—
579C23—22no—
580C23—24no—
581C23—24no—
582C23—22no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—42no—
591C23—41no—
592C23—41no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—41no—
597C23—41no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23C4×D4×C12714yes—
629C23C23×C4×C12711yescharacteristic
630C23C22×D4×C12711yescharacteristic
631C23C2×#41×C12711yescharacteristic
632C23H(5,𝔽2)×C12712yes—
633C23H(5,𝔽2)×C12712yes—
634C23H(5,𝔽2)×C12711yescharacteristic
635C23H(5,𝔽2)×C12712yes—
636C23H(5,𝔽2)×C12712yes—
637C23H(5,𝔽2)×C12711yescharacteristic
638C23H(5,𝔽2)×C12711yescharacteristic
639C232−1+4×C12711yescharacteristic
640D4—432no—
641D4—416no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—22no—
645C2×C4—24no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—416no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—41no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—41no—
665C2×C4—42no—
666C2×C4—41no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C22—28no—
689C22—24no—
690C22—42no—
691C22—44no—
692C22—42no—
693C22—42no—
694C22—44no—
695C22—42no—
696C22—42no—
697C22—44no—
698C22—42no—
699C22—44no—
700C22—44no—
701C22—44no—
702C22—44no—
703C22—44no—
704C22—44no—
705C22—44no—
706C22—82no—
707C22—82no—
708C22—82no—
709C22—82no—
710C22—82no—
711C22—82no—
712C22—82no—
713C22—82no—
714C22C2×C4×D4×C12711yescharacteristic
715C22#518×C12712yes—
716C22#518×C12712yes—
717C22#518×C12711yescharacteristic
718C22#520×C12711yescharacteristic
719C22#534×C12712yes—
720C22#534×C12711yescharacteristic
721C22#535×C12712yes—
722C22#537×C12711yescharacteristic
723C22#538×C12712yes—
724C22#538×C12711yescharacteristic
725C22#538×C12712yes—
726C22#539×C12711yescharacteristic
727C22#560×C12711yescharacteristic
728C22#560×C12712yes—
729C22#560×C12712yes—
730C22#560×C12712yes—
731C22#560×C12712yes—
732C22#560×C12711yescharacteristic
733C22#560×C12711yescharacteristic
734C22H(3,𝔽4)×C12711yescharacteristic
735C22#562×C12712yes—
736C22#562×C12712yes—
737C4—44no—
738C4—42no—
739C4—42no—
740C4—44no—
741C4—82no—
742C4—82no—
743C4—82no—
744C2—44no—
745C2—84no—
746C2C127×#232112yes—
747C2C127×#232511yescharacteristic
748C2C127×#237511yescharacteristic
749C2C127×#237712yes—
750C2C127×#238011yescharacteristic
751C2C127×#281211yescharacteristic
752C2C127×#281312yes—
753C2C127×#281511yescharacteristic
754C2C127×#282411yescharacteristic
755C2C127×#282512yes—
756C2C127×#282611yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC2×#392×C127C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#386×C127C2semidirect
3. C127×#1443C2semidirect
4. C127×#1440C2semidirect
5. C127×#1439C2semidirect
6. C127×#1439C2semidirect
7. C127×#1438C2semidirect
8. C127×#1438C2semidirect
9. C127×C22⋊#95C2semidirect
22. #392×C127C4semidirect
46. C22×D4×C127C2×C4semidirect
51. C23×C4×C127D4semidirect
84. C2×C22⋊C4×C127C2×C4semidirect
93. #95×C127C2×C4semidirect
365. #14621C127direct (N × H)
380. C2×#386C2×C127semidirect
381. #1443C2×C127semidirect
382. #1440C2×C127semidirect
383. #1439C2×C127semidirect
384. #1439C2×C127semidirect
385. #1438C2×C127semidirect
386. #1438C2×C127semidirect
387. C22⋊#95C2×C127semidirect
388. C127#14621direct (N × H)
401. #392C4×C127semidirect
425. C22×D4C2×C4×C127semidirect
430. C23×C4D4×C127semidirect
463. C2×C22⋊C4C2×C4×C127semidirect
472. #95C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#392×C1272
C2×#386×C1272
C127×#14432
C127×#14402
C127×#14392
C127×#14382
C127×C22⋊#952
#14621127