Finite Group Databasebeta

← C127×#16895 #44580568

Subgroups — C127×#16895 #44580568

Order 32512.

1666 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#386×C127C211yesmaximal, characteristic
2C2×#380×C127C211yesmaximal, characteristic, complemented
3C127×#1444C211yesmaximal, characteristic, complemented
4C127×#1443C212yesmaximal, complemented
5C127×#1442C211yesmaximal, characteristic, complemented
6C127×#1439C211yesmaximal, characteristic, complemented
7C127×#1439C211yesmaximal, characteristic, complemented
8C127×#1439C212yesmaximal, complemented
9C127×#1439C212yesmaximal, complemented
10C127×#1438C212yesmaximal
11C127×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C127C2211yescharacteristic
13C24×C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C4⋊C4×C127C2212yes—
17C22×C22⋊C4×C127C2211yescharacteristic
18C22×C22⋊C4×C127C2212yes—
19C22×C22⋊C4×C127C2212yes—
20C22×C22⋊C4×C127C2212yes—
21C22×C22⋊C4×C127C2211yescharacteristic
22C22×C22⋊C4×C127C2211yescharacteristic
23C22×C22⋊C4×C127C2212yes—
24#386×C127—24no—
25#380×C127—24no—
26C2×#95×C127C2211yescharacteristic
27C2×#95×C127C2211yescharacteristic
28C2×#95×C127C2212yes—
29C2×#95×C127C2212yes—
30C2×#95×C127C2211yescharacteristic
31C2×#95×C127C2211yescharacteristic
32C2×#95×C127C2212yes—
33C2×#95×C127C2212yes—
34C2×#95×C127C2212yes—
35C2×#95×C127C2212yes—
36C2×#95×C127C2212yes—
37C25×C127C2311yescharacteristic
38C25×C127C2311yescharacteristic
39C22×D4×C127—22no—
40C22×D4×C127—22no—
41C22×D4×C127—42no—
42C22×D4×C127—42no—
43C22×D4×C127Q814yes—
44C23×C4×C127—22no—
45C23×C4×C127—22no—
46C23×C4×C127—42no—
47C23×C4×C127—42no—
48C23×C4×C127D414yes—
49C23×C4×C127C2311yescharacteristic
50C23×C4×C127C2312yes—
51C23×C4×C127C2312yes—
52C23×C4×C127C2311yescharacteristic
53C23×C4×C127C2312yes—
54C23×C4×C127C2311yescharacteristic
55C23×C4×C127C2311yescharacteristic
56C23×C4×C127C2312yes—
57C23×C4×C127C2311yescharacteristic
58C2×C4⋊C4×C127—22no—
59C2×C4⋊C4×C127—22no—
60C2×C4⋊C4×C127—42no—
61C2×C4⋊C4×C127—42no—
62C2×C4⋊C4×C127—42no—
63C2×C4⋊C4×C127—42no—
64C2×C4⋊C4×C127—42no—
65C2×C22⋊C4×C127—24no—
66C2×C22⋊C4×C127—22no—
67C2×C22⋊C4×C127—24no—
68C2×C22⋊C4×C127—22no—
69C2×C22⋊C4×C127—22no—
70C2×C22⋊C4×C127—24no—
71C2×C22⋊C4×C127—24no—
72C2×C22⋊C4×C127—22no—
73C2×C22⋊C4×C127—22no—
74C2×C22⋊C4×C127—42no—
75C2×C22⋊C4×C127—42no—
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×C127—42no—
84#95×C127—24no—
85#95×C127—22no—
86#95×C127—22no—
87#95×C127—22no—
88#95×C127—24no—
89#95×C127—22no—
90#95×C127—42no—
91#95×C127—42no—
92#95×C127—42no—
93#95×C127—42no—
94#95×C127—42no—
95C24×C127—22no—
96C24×C127—21no—
97C24×C127—21no—
98C24×C127—21no—
99C24×C127—21no—
100C24×C127—22no—
101C24×C127—22no—
102C24×C127—22no—
103C24×C127—21no—
104C24×C127—21no—
105C24×C127—21no—
106C24×C127—22no—
107C24×C127—21no—
108C24×C127—22no—
109C24×C127—21no—
110C24×C127—21no—
111C24×C127—22no—
112C24×C127—22no—
113C24×C127C2×D412yes—
114C24×C127C2×Q812yes—
115C24×C127C2×Q812yes—
116C24×C127#4112yes—
117C24×C127C2411yescharacteristic
118C2×D4×C127—28no—
119C2×D4×C127—48no—
120C2×D4×C127—44no—
121C2×D4×C127—44no—
122C2×D4×C127—48no—
123C22×C4×C127—22no—
124C22×C4×C127—22no—
125C22×C4×C127—21no—
126C22×C4×C127—22no—
127C22×C4×C127—22no—
128C22×C4×C127—21no—
129C22×C4×C127—21no—
130C22×C4×C127—21no—
131C22×C4×C127—22no—
132C22×C4×C127—22no—
133C22×C4×C127—22no—
134C22×C4×C127—22no—
135C22×C4×C127—22no—
136C22×C4×C127—22no—
137C22×C4×C127—22no—
138C22×C4×C127—22no—
139C22×C4×C127—28no—
140C22×C4×C127—21no—
141C22×C4×C127—21no—
142C22×C4×C127—22no—
143C22×C4×C127—22no—
144C22×C4×C127—22no—
145C22×C4×C127—22no—
146C22×C4×C127—22no—
147C22×C4×C127—21no—
148C22×C4×C127—21no—
149C22×C4×C127—22no—
150C22×C4×C127—22no—
151C22×C4×C127—22no—
152C22×C4×C127—22no—
153C22×C4×C127—21no—
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—21no—
171C22×C4×C127—44no—
172C22×C4×C127—44no—
173C22×C4×C127—48no—
174C22×C4×C127—48no—
175C22×C4×C127C2×D412yes—
176C22×C4×C127C2×D412yes—
177C22×C4×C127C2×Q812yes—
178C22×C4×C127#4114yes—
179C22×C4×C127#4112yes—
180C22×C4×C127#4112yes—
181C4⋊C4×C127—44no—
182C4⋊C4×C127—44no—
183C4⋊C4×C127—48no—
184C22⋊C4×C127—48no—
185C22⋊C4×C127—44no—
186C22⋊C4×C127—48no—
187C22⋊C4×C127—48no—
188C22⋊C4×C127—44no—
189C22⋊C4×C127—48no—
190C22⋊C4×C127—44no—
191C23×C127—22no—
192C23×C127—22no—
193C23×C127—22no—
194C23×C127—22no—
195C23×C127—22no—
196C23×C127—22no—
197C23×C127—24no—
198C23×C127—24no—
199C23×C127—24no—
200C23×C127—22no—
201C23×C127—22no—
202C23×C127—24no—
203C23×C127—22no—
204C23×C127—22no—
205C23×C127—22no—
206C23×C127—24no—
207C23×C127—24no—
208C23×C127—22no—
209C23×C127—22no—
210C23×C127—42no—
211C23×C127—42no—
212C23×C127—42no—
213C23×C127—42no—
214C23×C127—42no—
215C23×C127—42no—
216C23×C127—42no—
217C23×C127—42no—
218C23×C127—41no—
219C23×C127—41no—
220C23×C127—41no—
221C23×C127—41no—
222C23×C127—41no—
223C23×C127—41no—
224C23×C127—42no—
225C23×C127—42no—
226C23×C127—42no—
227C23×C127—42no—
228C23×C127—42no—
229C23×C127—42no—
230C23×C127—41no—
231C23×C127—41no—
232C23×C127—42no—
233C23×C127—42no—
234C23×C127—42no—
235C23×C127—42no—
236C23×C127C22⋊Q814yes—
237C23×C127C22×D411yescharacteristic
238C23×C127C22×Q811yescharacteristic
239C23×C127C2×#4111yescharacteristic
240C23×C127C2×#4111yescharacteristic
241C23×C127C2×#4111yescharacteristic
242C23×C127C2×#4112yes—
243C23×C127H(5,𝔽2)12yes—
244C23×C127H(5,𝔽2)12yes—
245C23×C127H(5,𝔽2)11yescharacteristic
246C23×C127H(5,𝔽2)12yes—
247C23×C127H(5,𝔽2)11yescharacteristic
248D4×C127—416no—
249C2×C4×C127—22no—
250C2×C4×C127—22no—
251C2×C4×C127—24no—
252C2×C4×C127—24no—
253C2×C4×C127—22no—
254C2×C4×C127—22no—
255C2×C4×C127—22no—
256C2×C4×C127—22no—
257C2×C4×C127—24no—
258C2×C4×C127—24no—
259C2×C4×C127—24no—
260C2×C4×C127—24no—
261C2×C4×C127—416no—
262C2×C4×C127—41no—
263C2×C4×C127—41no—
264C2×C4×C127—42no—
265C2×C4×C127—42no—
266C2×C4×C127—42no—
267C2×C4×C127—42no—
268C2×C4×C127—42no—
269C2×C4×C127—42no—
270C2×C4×C127—42no—
271C2×C4×C127—41no—
272C2×C4×C127—42no—
273C2×C4×C127—41no—
274C2×C4×C127—41no—
275C2×C4×C127—42no—
276C2×C4×C127—42no—
277C2×C4×C127—42no—
278C2×C4×C127—41no—
279C2×C4×C127—41no—
280C2×C4×C127—42no—
281C2×C4×C127—42no—
282C2×C4×C127—41no—
283C2×C4×C127—42no—
284C2×C4×C127—42no—
285C2×C4×C127—42no—
286C2×C4×C127—42no—
287C2×C4×C127—42no—
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#12314yes—
303C22×C127—24no—
304C22×C127—24no—
305C22×C127—24no—
306C22×C127—42no—
307C22×C127—42no—
308C22×C127—42no—
309C22×C127—44no—
310C22×C127—44no—
311C22×C127—44no—
312C22×C127—44no—
313C22×C127—42no—
314C22×C127—42no—
315C22×C127—42no—
316C22×C127—42no—
317C22×C127—44no—
318C22×C127—44no—
319C22×C127—81no—
320C22×C127—81no—
321C22×C127—81no—
322C22×C127—82no—
323C22×C127—82no—
324C22×C127—81no—
325C22×C127C2×C22⋊Q811yescharacteristic
326C22×C127C2×#12311yescharacteristic
327C22×C127#53211yescharacteristic
328C22×C127#53411yescharacteristic
329C22×C127#53411yescharacteristic
330C22×C127#53511yescharacteristic
331C22×C127#53511yescharacteristic
332C22×C127#53812yes—
333C22×C127#53812yes—
334C22×C127#53812yes—
335C22×C127#53812yes—
336C22×C127#54012yes—
337C22×C127#54312yes—
338C22×C127#55112yes—
339C22×C127#55311yescharacteristic
340C22×C127#55311yescharacteristic
341C22×C127#55312yes—
342C22×C127#55412yes—
343C22×C127#55411yescharacteristic
344C22×C127#55411yescharacteristic
345C22×C127#55512yes—
346C22×C127#56012yes—
347C22×C127#56012yes—
348C4×C127—24no—
349C4×C127—42no—
350C4×C127—42no—
351C4×C127—44no—
352C4×C127—82no—
353C4×C127—81no—
354C4×C127—82no—
355C4×C127—81no—
356C4×C127—82no—
357#16895C12711yesmaximal, characteristic, direct product factor, Sylow
358C2×C127—44no—
359C2×C127—82no—
360C2×C127#248711yescharacteristic
361C2×C127#250011yescharacteristic
362C2×C127#256411yescharacteristic
363C2×C127#262211yescharacteristic
364C2×C127#262611yescharacteristic
365C2×C127#266111yescharacteristic
366C2×C127#275612yes—
367C2×C127#277812yes—
368C2×C127#278012yes—
369C2×C127#278412yes—
370C2×C127#281511yescharacteristic
371C2×#386C2×C12711yescharacteristic
372C2×#380C2×C12711yescharacteristic, complemented
373#1444C2×C12711yescharacteristic, complemented
374#1443C2×C12712yescomplemented
375#1442C2×C12711yescharacteristic, complemented
376#1439C2×C12711yescharacteristic, complemented
377#1439C2×C12711yescharacteristic, complemented
378#1439C2×C12712yescomplemented
379#1439C2×C12712yescomplemented
380#1438C2×C12712yes—
381C22⋊#95C2×C12711yescharacteristic, complemented
382C127#1689511yescharacteristic, direct product factor, Sylow
383C23×D4C22×C12711yescharacteristic
384C24×C4C22×C12711yescharacteristic
385C22×C4⋊C4C22×C12711yescharacteristic
386C22×C4⋊C4C22×C12711yescharacteristic
387C22×C4⋊C4C22×C12712yes—
388C22×C22⋊C4C22×C12711yescharacteristic
389C22×C22⋊C4C22×C12712yes—
390C22×C22⋊C4C22×C12712yes—
391C22×C22⋊C4C22×C12712yes—
392C22×C22⋊C4C22×C12711yescharacteristic
393C22×C22⋊C4C22×C12711yescharacteristic
394C22×C22⋊C4C22×C12712yes—
395#386—24no—
396#380—24no—
397C2×#95C22×C12711yescharacteristic
398C2×#95C22×C12711yescharacteristic
399C2×#95C22×C12712yes—
400C2×#95C22×C12712yes—
401C2×#95C22×C12711yescharacteristic
402C2×#95C22×C12711yescharacteristic
403C2×#95C22×C12712yes—
404C2×#95C22×C12712yes—
405C2×#95C22×C12712yes—
406C2×#95C22×C12712yes—
407C2×#95C22×C12712yes—
408C25C23×C12711yescharacteristic
409C25C23×C12711yescharacteristic
410C22×D4—22no—
411C22×D4—22no—
412C22×D4—42no—
413C22×D4—42no—
414C22×D4Q8×C12714yes—
415C23×C4—22no—
416C23×C4—22no—
417C23×C4—42no—
418C23×C4—42no—
419C23×C4D4×C12714yes—
420C23×C4C23×C12711yescharacteristic
421C23×C4C23×C12712yes—
422C23×C4C23×C12712yes—
423C23×C4C23×C12711yescharacteristic
424C23×C4C23×C12712yes—
425C23×C4C23×C12711yescharacteristic
426C23×C4C23×C12711yescharacteristic
427C23×C4C23×C12712yes—
428C23×C4C23×C12711yescharacteristic
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—42no—
432C2×C4⋊C4—42no—
433C2×C4⋊C4—42no—
434C2×C4⋊C4—42no—
435C2×C4⋊C4—42no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—42no—
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—42no—
454C2×C22⋊C4—42no—
455#95—24no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—24no—
460#95—22no—
461#95—42no—
462#95—42no—
463#95—42no—
464#95—42no—
465#95—42no—
466C24—22no—
467C24—21no—
468C24—21no—
469C24—21no—
470C24—21no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—21no—
475C24—21no—
476C24—21no—
477C24—22no—
478C24—21no—
479C24—22no—
480C24—21no—
481C24—21no—
482C24—22no—
483C24—22no—
484C24C2×D4×C12712yes—
485C24C2×Q8×C12712yes—
486C24C2×Q8×C12712yes—
487C24#41×C12712yes—
488C24C24×C12711yescharacteristic
489C2×D4—28no—
490C2×D4—48no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—48no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—28no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
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—21no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4C2×D4×C12712yes—
547C22×C4C2×D4×C12712yes—
548C22×C4C2×Q8×C12712yes—
549C22×C4#41×C12714yes—
550C22×C4#41×C12712yes—
551C22×C4#41×C12712yes—
552C4⋊C4—44no—
553C4⋊C4—44no—
554C4⋊C4—48no—
555C22⋊C4—48no—
556C22⋊C4—44no—
557C22⋊C4—48no—
558C22⋊C4—48no—
559C22⋊C4—44no—
560C22⋊C4—48no—
561C22⋊C4—44no—
562C23—22no—
563C23—22no—
564C23—22no—
565C23—22no—
566C23—22no—
567C23—22no—
568C23—24no—
569C23—24no—
570C23—24no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—24no—
576C23—22no—
577C23—24no—
578C23—22no—
579C23—22no—
580C23—24no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—41no—
602C23—41no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23C22⋊Q8×C12714yes—
608C23C22×D4×C12711yescharacteristic
609C23C22×Q8×C12711yescharacteristic
610C23C2×#41×C12711yescharacteristic
611C23C2×#41×C12711yescharacteristic
612C23C2×#41×C12711yescharacteristic
613C23C2×#41×C12712yes—
614C23H(5,𝔽2)×C12712yes—
615C23H(5,𝔽2)×C12712yes—
616C23H(5,𝔽2)×C12711yescharacteristic
617C23H(5,𝔽2)×C12712yes—
618C23H(5,𝔽2)×C12711yescharacteristic
619D4—416no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—416no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—41no—
643C2×C4—42no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—41no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4#123×C12714yes—
674C22—24no—
675C22—24no—
676C22—24no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—44no—
681C22—44no—
682C22—44no—
683C22—44no—
684C22—42no—
685C22—42no—
686C22—42no—
687C22—44no—
688C22—44no—
689C22—42no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22—82no—
694C22—82no—
695C22—81no—
696C22C2×C22⋊Q8×C12711yescharacteristic
697C22C2×#123×C12711yescharacteristic
698C22#532×C12711yescharacteristic
699C22#534×C12711yescharacteristic
700C22#534×C12711yescharacteristic
701C22#535×C12711yescharacteristic
702C22#535×C12711yescharacteristic
703C22#538×C12712yes—
704C22#538×C12712yes—
705C22#538×C12712yes—
706C22#538×C12712yes—
707C22#540×C12712yes—
708C22#543×C12712yes—
709C22#551×C12712yes—
710C22#553×C12711yescharacteristic
711C22#553×C12711yescharacteristic
712C22#553×C12712yes—
713C22#554×C12711yescharacteristic
714C22#554×C12711yescharacteristic
715C22#554×C12712yes—
716C22#555×C12712yes—
717C22#560×C12712yes—
718C22#560×C12712yes—
719C4—24no—
720C4—42no—
721C4—42no—
722C4—44no—
723C4—82no—
724C4—81no—
725C4—82no—
726C4—81no—
727C4—82no—
728C2—44no—
729C2—82no—
730C2C127×#248711yescharacteristic
731C2C127×#250011yescharacteristic
732C2C127×#256411yescharacteristic
733C2C127×#262211yescharacteristic
734C2C127×#262611yescharacteristic
735C2C127×#266111yescharacteristic
736C2C127×#275612yes—
737C2C127×#277812yes—
738C2C127×#278012yes—
739C2C127×#278412yes—
740C2C127×#281511yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#380×C127C2semidirect
3. C127×#1444C2semidirect
4. C127×#1443C2semidirect
5. C127×#1442C2semidirect
6. C127×#1439C2semidirect
7. C127×#1439C2semidirect
8. C127×#1439C2semidirect
9. C127×#1439C2semidirect
11. C127×C22⋊#95C2semidirect
357. #16895C127direct (N × H)
372. C2×#380C2×C127semidirect
373. #1444C2×C127semidirect
374. #1443C2×C127semidirect
375. #1442C2×C127semidirect
376. #1439C2×C127semidirect
377. #1439C2×C127semidirect
378. #1439C2×C127semidirect
379. #1439C2×C127semidirect
381. C22⋊#95C2×C127semidirect
382. C127#16895direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#386×C1272
C2×#380×C1272
C127×#14442
C127×#14432
C127×#14422
C127×#14392
C127×#14382
C127×C22⋊#952
#16895127