Finite Group Databasebeta

← C127×#15313 #44578986

Subgroups — C127×#15313 #44578986

Order 32512.

2830 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#127×C127C211yesmaximal, characteristic
2C2×#394×C127C212yesmaximal, complemented
3C2×#394×C127C212yesmaximal, complemented
4C2×#386×C127C211yesmaximal, characteristic, complemented
5C2×#386×C127C212yesmaximal, complemented
6C127×#1438C211yesmaximal, characteristic, complemented
7C127×#1438C212yesmaximal, complemented
8C127×#1438C212yesmaximal, complemented
9C127×#1436C212yesmaximal, complemented
10C23×D4×C127C2212yes—
11C23×D4×C127C2211yescharacteristic
12C23×D4×C127C2212yes—
13C23×D4×C127C2211yescharacteristic
14C24×C4×C127C2211yescharacteristic
15C2×#127×C127—24no—
16C2×#127×C127—28no—
17C22×C4⋊C4×C127C2212yes—
18C22×C22⋊C4×C127C2211yescharacteristic
19C22×C22⋊C4×C127C2212yes—
20C22×C22⋊C4×C127C2211yescharacteristic
21C22×C22⋊C4×C127C2212yes—
22C22×C22⋊C4×C127C2212yes—
23C22×C22⋊C4×C127C2212yes—
24C22×C22⋊C4×C127C2212yes—
25C22×C22⋊C4×C127C2212yes—
26C22×C22⋊C4×C127C2211yescharacteristic
27C22×C42×C127C2211yescharacteristic
28#394×C127—28no—
29#394×C127—28no—
30#386×C127—24no—
31#386×C127—28no—
32C2×#95×C127C2212yes—
33C2×#95×C127C2212yes—
34C2×#95×C127C2212yes—
35C2×#95×C127C2212yes—
36C2×#95×C127C2212yes—
37C25×C127C2311yescharacteristic
38C25×C127C2312yes—
39C25×C127C2311yescharacteristic
40C22×D4×C127—24no—
41C22×D4×C127—24no—
42C22×D4×C127—24no—
43C22×D4×C127—24no—
44C22×D4×C127—24no—
45C22×D4×C127—24no—
46C22×D4×C127—24no—
47C22×D4×C127—22no—
48C22×D4×C127—24no—
49C22×D4×C127—24no—
50C22×D4×C127—24no—
51C22×D4×C127—24no—
52C22×D4×C127—24no—
53C22×D4×C127—24no—
54C22×D4×C127—42no—
55C22×D4×C127—42no—
56C22×D4×C127—41no—
57C22×D4×C127—41no—
58C22×D4×C127—42no—
59C22×D4×C127—42no—
60C22×D4×C127—41no—
61C22×D4×C127—41no—
62C22×D4×C127D414yes—
63C22×D4×C127D418yes—
64C23×C4×C127—22no—
65C23×C4×C127—24no—
66C23×C4×C127—41no—
67C23×C4×C127—42no—
68C23×C4×C127—41no—
69C23×C4×C127C2312yes—
70C23×C4×C127C2312yes—
71C23×C4×C127C2312yes—
72C23×C4×C127C2312yes—
73C23×C4×C127C2312yes—
74C23×C4×C127C2311yescharacteristic
75#127×C127—232no—
76C2×C4⋊C4×C127—24no—
77C2×C4⋊C4×C127—24no—
78C2×C4⋊C4×C127—24no—
79C2×C22⋊C4×C127—24no—
80C2×C22⋊C4×C127—22no—
81C2×C22⋊C4×C127—24no—
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—41no—
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×C127—42no—
101C2×C22⋊C4×C127—42no—
102C2×C22⋊C4×C127—41no—
103C2×C42×C127—24no—
104C2×C42×C127—22no—
105#95×C127—24no—
106#95×C127—24no—
107#95×C127—24no—
108#95×C127—24no—
109#95×C127D418yescomplemented
110C24×C127—22no—
111C24×C127—22no—
112C24×C127—22no—
113C24×C127—22no—
114C24×C127—21no—
115C24×C127—21no—
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—21no—
132C24×C127—21no—
133C24×C127—22no—
134C24×C127—22no—
135C24×C127—22no—
136C24×C127—22no—
137C24×C127—22no—
138C24×C127—22no—
139C24×C127C2×D414yes—
140C24×C127C2×D412yes—
141C24×C127C2×D414yes—
142C24×C127C2×D412yes—
143C24×C127C2411yescharacteristic
144C2×D4×C127—28no—
145C2×D4×C127—216no—
146C2×D4×C127—28no—
147C2×D4×C127—216no—
148C2×D4×C127—216no—
149C2×D4×C127—28no—
150C2×D4×C127—44no—
151C2×D4×C127—48no—
152C2×D4×C127—48no—
153C2×D4×C127—48no—
154C2×D4×C127—48no—
155C2×D4×C127—48no—
156C2×D4×C127—48no—
157C2×D4×C127—48no—
158C2×D4×C127—48no—
159C2×D4×C127—48no—
160C2×D4×C127—48no—
161C2×D4×C127—48no—
162C2×D4×C127—48no—
163C2×D4×C127—48no—
164C2×D4×C127—44no—
165C2×D4×C127—48no—
166C2×D4×C127—48no—
167C2×D4×C127—44no—
168C22×C4×C127—22no—
169C22×C4×C127—22no—
170C22×C4×C127—22no—
171C22×C4×C127—22no—
172C22×C4×C127—22no—
173C22×C4×C127—21no—
174C22×C4×C127—21no—
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×C127—22no—
192C22×C4×C127—22no—
193C22×C4×C127—22no—
194C22×C4×C127—22no—
195C22×C4×C127—22no—
196C22×C4×C127—22no—
197C22×C4×C127—22no—
198C22×C4×C127—22no—
199C22×C4×C127—22no—
200C22×C4×C127—22no—
201C22×C4×C127—44no—
202C22×C4×C127—48no—
203C22×C4×C127—48no—
204C22×C4×C127—44no—
205C22×C4×C127—44no—
206C22×C4×C127C2×D414yes—
207C22×C4×C127C2×D414yes—
208C22×C4×C127C2×D414yes—
209C22×C4×C127C2×D414yes—
210C22×C4×C127C2×D412yes—
211C22×C4×C127#4114yes—
212C22×C4×C127#4114yes—
213C4⋊C4×C127—48no—
214C22⋊C4×C127—44no—
215C22⋊C4×C127—48no—
216C22⋊C4×C127—48no—
217C22⋊C4×C127—48no—
218C22⋊C4×C127—48no—
219C22⋊C4×C127—48no—
220C22⋊C4×C127—48no—
221C22⋊C4×C127—44no—
222C22⋊C4×C127—44no—
223C42×C127—28no—
224C23×C127—24no—
225C23×C127—22no—
226C23×C127—22no—
227C23×C127—24no—
228C23×C127—24no—
229C23×C127—24no—
230C23×C127—24no—
231C23×C127—24no—
232C23×C127—24no—
233C23×C127—24no—
234C23×C127—22no—
235C23×C127—24no—
236C23×C127—24no—
237C23×C127—22no—
238C23×C127—24no—
239C23×C127—22no—
240C23×C127—24no—
241C23×C127—24no—
242C23×C127—24no—
243C23×C127—24no—
244C23×C127—24no—
245C23×C127—24no—
246C23×C127—42no—
247C23×C127—42no—
248C23×C127—42no—
249C23×C127—42no—
250C23×C127—41no—
251C23×C127—42no—
252C23×C127—42no—
253C23×C127—41no—
254C23×C127—41no—
255C23×C127—41no—
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×C127—42no—
272C23×C127—42no—
273C23×C127—42no—
274C23×C127—41no—
275C23×C127—42no—
276C23×C127—42no—
277C23×C127—42no—
278C23×C127—42no—
279C23×C127—42no—
280C23×C127—42no—
281C23×C127—42no—
282C23×C127—42no—
283C23×C127—42no—
284C23×C127—42no—
285C23×C127—42no—
286C23×C127—42no—
287C23×C127—42no—
288C23×C127—42no—
289C23×C127—42no—
290C23×C127—42no—
291C23×C127—42no—
292C23×C127—42no—
293C23×C127—41no—
294C23×C127—42no—
295C23×C127—42no—
296C23×C127—41no—
297C23×C127—41no—
298C23×C127—42no—
299C23×C127—42no—
300C23×C127#12014yes—
301C23×C127C22×D412yes—
302C23×C127C22×D411yescharacteristic
303C23×C127C22×D412yes—
304C23×C127C2×#4112yes—
305C23×C127C2×#4112yes—
306C23×C127H(5,𝔽2)11yescharacteristic
307C23×C127H(5,𝔽2)12yes—
308C23×C127H(5,𝔽2)11yescharacteristic
309C23×C127H(5,𝔽2)12yes—
310D4×C127—416no—
311D4×C127—432no—
312D4×C127—416no—
313D4×C127—432no—
314C2×C4×C127—22no—
315C2×C4×C127—24no—
316C2×C4×C127—22no—
317C2×C4×C127—24no—
318C2×C4×C127—24no—
319C2×C4×C127—24no—
320C2×C4×C127—24no—
321C2×C4×C127—24no—
322C2×C4×C127—24no—
323C2×C4×C127—24no—
324C2×C4×C127—24no—
325C2×C4×C127—24no—
326C2×C4×C127—24no—
327C2×C4×C127—24no—
328C2×C4×C127—24no—
329C2×C4×C127—24no—
330C2×C4×C127—416no—
331C2×C4×C127—42no—
332C2×C4×C127—42no—
333C2×C4×C127—42no—
334C2×C4×C127—42no—
335C2×C4×C127—42no—
336C2×C4×C127—42no—
337C2×C4×C127—42no—
338C2×C4×C127—42no—
339C2×C4×C127—42no—
340C2×C4×C127—42no—
341C2×C4×C127—42no—
342C2×C4×C127—42no—
343C2×C4×C127—42no—
344C2×C4×C127—42no—
345C2×C4×C127—42no—
346C2×C4×C127—42no—
347C2×C4×C127—42no—
348C2×C4×C127—42no—
349C2×C4×C127—42no—
350C2×C4×C127—42no—
351C2×C4×C127—42no—
352C2×C4×C127—42no—
353C2×C4×C127#12118yes—
354C2×C4×C127#12314yes—
355C22×C127—24no—
356C22×C127—28no—
357C22×C127—42no—
358C22×C127—44no—
359C22×C127—44no—
360C22×C127—44no—
361C22×C127—42no—
362C22×C127—44no—
363C22×C127—44no—
364C22×C127—42no—
365C22×C127—44no—
366C22×C127—44no—
367C22×C127—44no—
368C22×C127—44no—
369C22×C127—42no—
370C22×C127—44no—
371C22×C127—44no—
372C22×C127—44no—
373C22×C127—44no—
374C22×C127—42no—
375C22×C127—44no—
376C22×C127—82no—
377C22×C127—82no—
378C22×C127—82no—
379C22×C127—82no—
380C22×C127—82no—
381C22×C127—82no—
382C22×C127—82no—
383C22×C127—82no—
384C22×C127—82no—
385C22×C127—82no—
386C22×C127—82no—
387C22×C127—82no—
388C22×C127C2×#12011yescharacteristic
389C22×C127C2×#12112yes—
390C22×C127C2×#12311yescharacteristic
391C22×C127#53212yes—
392C22×C127#53411yescharacteristic
393C22×C127#53412yes—
394C22×C127#53512yes—
395C22×C127#54012yes—
396C22×C127#54012yes—
397C22×C127D4212yes—
398C22×C127D4212yes—
399C22×C127D4211yescharacteristic
400C22×C127#54612yes—
401C22×C127#54612yes—
402C22×C127#54612yes—
403C22×C127#54612yes—
404C22×C127#55012yes—
405C22×C127#55912yes—
406C22×C127#55911yescharacteristic
407C22×C127#56011yescharacteristic
408C22×C127#56011yescharacteristic
409C4×C127—24no—
410C4×C127—28no—
411C4×C127—44no—
412C4×C127—44no—
413C4×C127—82no—
414C4×C127—82no—
415#15313C12711yesmaximal, characteristic, direct product factor, Sylow
416C2×C127—44no—
417C2×C127—82no—
418C2×C127—84no—
419C2×C127#240511yescharacteristic
420C2×C127#241012yes—
421C2×C127#242812yes—
422C2×C127#244512yes—
423C2×C127#254412yes—
424C2×C127#266911yescharacteristic
425C2×C127#267312yes—
426C2×C127#270911yescharacteristic
427C2×C127#270912yes—
428C22×#127C2×C12711yescharacteristic
429C2×#394C2×C12712yescomplemented
430C2×#394C2×C12712yescomplemented
431C2×#386C2×C12711yescharacteristic, complemented
432C2×#386C2×C12712yescomplemented
433#1438C2×C12711yescharacteristic, complemented
434#1438C2×C12712yescomplemented
435#1438C2×C12712yescomplemented
436#1436C2×C12712yescomplemented
437C127#1531311yescharacteristic, direct product factor, Sylow
438C23×D4C22×C12712yes—
439C23×D4C22×C12711yescharacteristic
440C23×D4C22×C12712yes—
441C23×D4C22×C12711yescharacteristic
442C24×C4C22×C12711yescharacteristic
443C2×#127—24no—
444C2×#127—28no—
445C22×C4⋊C4C22×C12712yes—
446C22×C22⋊C4C22×C12711yescharacteristic
447C22×C22⋊C4C22×C12712yes—
448C22×C22⋊C4C22×C12711yescharacteristic
449C22×C22⋊C4C22×C12712yes—
450C22×C22⋊C4C22×C12712yes—
451C22×C22⋊C4C22×C12712yes—
452C22×C22⋊C4C22×C12712yes—
453C22×C22⋊C4C22×C12712yes—
454C22×C22⋊C4C22×C12711yescharacteristic
455C22×C42C22×C12711yescharacteristic
456#394—28no—
457#394—28no—
458#386—24no—
459#386—28no—
460C2×#95C22×C12712yes—
461C2×#95C22×C12712yes—
462C2×#95C22×C12712yes—
463C2×#95C22×C12712yes—
464C2×#95C22×C12712yes—
465C25C23×C12711yescharacteristic
466C25C23×C12712yes—
467C25C23×C12711yescharacteristic
468C22×D4—24no—
469C22×D4—24no—
470C22×D4—24no—
471C22×D4—24no—
472C22×D4—24no—
473C22×D4—24no—
474C22×D4—24no—
475C22×D4—22no—
476C22×D4—24no—
477C22×D4—24no—
478C22×D4—24no—
479C22×D4—24no—
480C22×D4—24no—
481C22×D4—24no—
482C22×D4—42no—
483C22×D4—42no—
484C22×D4—41no—
485C22×D4—41no—
486C22×D4—42no—
487C22×D4—42no—
488C22×D4—41no—
489C22×D4—41no—
490C22×D4D4×C12714yes—
491C22×D4D4×C12718yes—
492C23×C4—22no—
493C23×C4—24no—
494C23×C4—41no—
495C23×C4—42no—
496C23×C4—41no—
497C23×C4C23×C12712yes—
498C23×C4C23×C12712yes—
499C23×C4C23×C12712yes—
500C23×C4C23×C12712yes—
501C23×C4C23×C12712yes—
502C23×C4C23×C12711yescharacteristic
503#127—232no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—24no—
506C2×C4⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—41no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—41no—
531C2×C42—24no—
532C2×C42—22no—
533#95—24no—
534#95—24no—
535#95—24no—
536#95—24no—
537#95D4×C12718yescomplemented
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—21no—
543C24—21no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—21no—
560C24—21no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24—22no—
566C24—22no—
567C24C2×D4×C12714yes—
568C24C2×D4×C12712yes—
569C24C2×D4×C12714yes—
570C24C2×D4×C12712yes—
571C24C24×C12711yescharacteristic
572C2×D4—28no—
573C2×D4—216no—
574C2×D4—28no—
575C2×D4—216no—
576C2×D4—216no—
577C2×D4—28no—
578C2×D4—44no—
579C2×D4—48no—
580C2×D4—48no—
581C2×D4—48no—
582C2×D4—48no—
583C2×D4—48no—
584C2×D4—48no—
585C2×D4—48no—
586C2×D4—48no—
587C2×D4—48no—
588C2×D4—48no—
589C2×D4—48no—
590C2×D4—48no—
591C2×D4—48no—
592C2×D4—44no—
593C2×D4—48no—
594C2×D4—48no—
595C2×D4—44no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—44no—
630C22×C4—48no—
631C22×C4—48no—
632C22×C4—44no—
633C22×C4—44no—
634C22×C4C2×D4×C12714yes—
635C22×C4C2×D4×C12714yes—
636C22×C4C2×D4×C12714yes—
637C22×C4C2×D4×C12714yes—
638C22×C4C2×D4×C12712yes—
639C22×C4#41×C12714yes—
640C22×C4#41×C12714yes—
641C4⋊C4—48no—
642C22⋊C4—44no—
643C22⋊C4—48no—
644C22⋊C4—48no—
645C22⋊C4—48no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—44no—
650C22⋊C4—44no—
651C42—28no—
652C23—24no—
653C23—22no—
654C23—22no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—22no—
663C23—24no—
664C23—24no—
665C23—22no—
666C23—24no—
667C23—22no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—41no—
679C23—42no—
680C23—42no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—41no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—41no—
725C23—41no—
726C23—42no—
727C23—42no—
728C23#120×C12714yes—
729C23C22×D4×C12712yes—
730C23C22×D4×C12711yescharacteristic
731C23C22×D4×C12712yes—
732C23C2×#41×C12712yes—
733C23C2×#41×C12712yes—
734C23H(5,𝔽2)×C12711yescharacteristic
735C23H(5,𝔽2)×C12712yes—
736C23H(5,𝔽2)×C12711yescharacteristic
737C23H(5,𝔽2)×C12712yes—
738D4—416no—
739D4—432no—
740D4—416no—
741D4—432no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—416no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4#121×C12718yes—
782C2×C4#123×C12714yes—
783C22—24no—
784C22—28no—
785C22—42no—
786C22—44no—
787C22—44no—
788C22—44no—
789C22—42no—
790C22—44no—
791C22—44no—
792C22—42no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—42no—
798C22—44no—
799C22—44no—
800C22—44no—
801C22—44no—
802C22—42no—
803C22—44no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22—82no—
810C22—82no—
811C22—82no—
812C22—82no—
813C22—82no—
814C22—82no—
815C22—82no—
816C22C2×#120×C12711yescharacteristic
817C22C2×#121×C12712yes—
818C22C2×#123×C12711yescharacteristic
819C22#532×C12712yes—
820C22#534×C12711yescharacteristic
821C22#534×C12712yes—
822C22#535×C12712yes—
823C22#540×C12712yes—
824C22#540×C12712yes—
825C22D42×C12712yes—
826C22D42×C12712yes—
827C22D42×C12711yescharacteristic
828C22#546×C12712yes—
829C22#546×C12712yes—
830C22#546×C12712yes—
831C22#546×C12712yes—
832C22#550×C12712yes—
833C22#559×C12712yes—
834C22#559×C12711yescharacteristic
835C22#560×C12711yescharacteristic
836C22#560×C12711yescharacteristic
837C4—24no—
838C4—28no—
839C4—44no—
840C4—44no—
841C4—82no—
842C4—82no—
843C2—44no—
844C2—82no—
845C2—84no—
846C2C127×#240511yescharacteristic
847C2C127×#241012yes—
848C2C127×#242812yes—
849C2C127×#244512yes—
850C2C127×#254412yes—
851C2C127×#266911yescharacteristic
852C2C127×#267312yes—
853C2C127×#270911yescharacteristic
854C2C127×#270912yes—
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC22×#127×C127C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#394×C127C2semidirect
3. C2×#394×C127C2semidirect
4. C2×#386×C127C2semidirect
5. C2×#386×C127C2semidirect
6. C127×#1438C2semidirect
7. C127×#1438C2semidirect
8. C127×#1438C2semidirect
9. C127×#1436C2semidirect
109. #95×C127D4semidirect
415. #15313C127direct (N × H)
429. C2×#394C2×C127semidirect
430. C2×#394C2×C127semidirect
431. C2×#386C2×C127semidirect
432. C2×#386C2×C127semidirect
433. #1438C2×C127semidirect
434. #1438C2×C127semidirect
435. #1438C2×C127semidirect
436. #1436C2×C127semidirect
437. C127#15313direct (N × H)
537. #95D4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#127×C1272
C2×#394×C1272
C2×#386×C1272
C127×#14382
C127×#14362
#15313127