Finite Group Databasebeta

← C127×#15340 #44579013

Subgroups — C127×#15340 #44579013

Order 32512.

2442 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C127C211yesmaximal, characteristic
2C2×#399×C127C211yesmaximal, characteristic, complemented
3C2×#398×C127C211yesmaximal, characteristic, complemented
4C2×#394×C127C212yesmaximal, complemented
5C2×#390×C127C211yesmaximal, characteristic, complemented
6C2×#385×C127C212yesmaximal, complemented
7C127×#1439C212yesmaximal, complemented
8C127×#1438C211yesmaximal, characteristic, complemented
9C127×#1438C212yesmaximal, complemented
10C127×#1437C211yesmaximal, characteristic, complemented
11C127×#1436C211yesmaximal, characteristic, complemented
12C23×D4×C127C2211yescharacteristic
13C23×D4×C127C2211yescharacteristic
14C23×D4×C127C2211yescharacteristic
15C24×C4×C127C2211yescharacteristic
16C2×#121×C127—24no—
17C2×#121×C127—24no—
18C2×#121×C127—24no—
19C22×C4⋊C4×C127C2212yes—
20C22×C4⋊C4×C127C2211yescharacteristic
21C22×C4⋊C4×C127C2212yes—
22C22×C4⋊C4×C127C2211yescharacteristic
23C22×C22⋊C4×C127C2211yescharacteristic
24C22×C22⋊C4×C127C2212yes—
25C22×C22⋊C4×C127C2212yes—
26C22×C22⋊C4×C127C2212yes—
27C22×C22⋊C4×C127C2212yes—
28C22×C22⋊C4×C127C2212yes—
29C22×C22⋊C4×C127C2212yes—
30C22×C22⋊C4×C127C2211yescharacteristic
31C22×C42×C127C2211yescharacteristic
32#399×C127—24no—
33#398×C127—24no—
34#394×C127—28no—
35#390×C127—24no—
36#385×C127—28no—
37C2×#95×C127C2211yescharacteristic
38C2×#95×C127C2212yes—
39C2×#95×C127C2211yescharacteristic
40C2×#95×C127C2212yes—
41C2×#95×C127C2212yes—
42C2×#95×C127C2212yes—
43C25×C127C2311yescharacteristic
44C25×C127C2311yescharacteristic
45C25×C127C2311yescharacteristic
46C22×D4×C127—22no—
47C22×D4×C127—22no—
48C22×D4×C127—22no—
49C22×D4×C127—22no—
50C22×D4×C127—24no—
51C22×D4×C127—24no—
52C22×D4×C127—22no—
53C22×D4×C127—22no—
54C22×D4×C127—22no—
55C22×D4×C127—22no—
56C22×D4×C127—24no—
57C22×D4×C127—42no—
58C22×D4×C127—42no—
59C22×D4×C127—42no—
60C22×D4×C127D414yes—
61C23×C4×C127—22no—
62C23×C4×C127—22no—
63C23×C4×C127—22no—
64C23×C4×C127—24no—
65C23×C4×C127—42no—
66C23×C4×C127C2312yes—
67C23×C4×C127C2312yes—
68C23×C4×C127C2312yes—
69C23×C4×C127C2311yescharacteristic
70C23×C4×C127C2311yescharacteristic
71C23×C4×C127C2312yes—
72C23×C4×C127C2311yescharacteristic
73C23×C4×C127C2311yescharacteristic
74#121×C127—232no—
75C2×C4⋊C4×C127—22no—
76C2×C4⋊C4×C127—22no—
77C2×C4⋊C4×C127—24no—
78C2×C4⋊C4×C127—24no—
79C2×C4⋊C4×C127—22no—
80C2×C4⋊C4×C127—24no—
81C2×C4⋊C4×C127—22no—
82C2×C4⋊C4×C127—24no—
83C2×C4⋊C4×C127—24no—
84C2×C4⋊C4×C127—22no—
85C2×C4⋊C4×C127—42no—
86C2×C4⋊C4×C127D414yes—
87C2×C22⋊C4×C127—22no—
88C2×C22⋊C4×C127—24no—
89C2×C22⋊C4×C127—22no—
90C2×C22⋊C4×C127—22no—
91C2×C22⋊C4×C127—22no—
92C2×C22⋊C4×C127—22no—
93C2×C22⋊C4×C127—24no—
94C2×C22⋊C4×C127—24no—
95C2×C22⋊C4×C127—24no—
96C2×C22⋊C4×C127—24no—
97C2×C22⋊C4×C127—24no—
98C2×C22⋊C4×C127—24no—
99C2×C22⋊C4×C127—24no—
100C2×C22⋊C4×C127—24no—
101C2×C22⋊C4×C127—24no—
102C2×C22⋊C4×C127—24no—
103C2×C22⋊C4×C127—24no—
104C2×C22⋊C4×C127—24no—
105C2×C22⋊C4×C127—42no—
106C2×C22⋊C4×C127—42no—
107C2×C22⋊C4×C127—42no—
108C2×C22⋊C4×C127—42no—
109C2×C22⋊C4×C127—42no—
110C2×C22⋊C4×C127D414yes—
111C2×C42×C127—22no—
112C2×C42×C127—42no—
113#95×C127—24no—
114#95×C127—22no—
115#95×C127—24no—
116#95×C127—22no—
117#95×C127—42no—
118#95×C127D418yescomplemented
119C24×C127—22no—
120C24×C127—21no—
121C24×C127—21no—
122C24×C127—22no—
123C24×C127—22no—
124C24×C127—22no—
125C24×C127—22no—
126C24×C127—22no—
127C24×C127—22no—
128C24×C127—21no—
129C24×C127—21no—
130C24×C127—21no—
131C24×C127—21no—
132C24×C127—22no—
133C24×C127—22no—
134C24×C127—22no—
135C24×C127—22no—
136C24×C127—22no—
137C24×C127—22no—
138C24×C127—22no—
139C24×C127—22no—
140C24×C127—22no—
141C24×C127—22no—
142C24×C127C2×D412yes—
143C24×C127C2×D412yes—
144C24×C127C2×D412yes—
145C24×C127#4114yes—
146C24×C127C2411yescharacteristic
147C2×D4×C127—28no—
148C2×D4×C127—28no—
149C2×D4×C127—28no—
150C2×D4×C127—28no—
151C2×D4×C127—44no—
152C2×D4×C127—48no—
153C2×D4×C127—48no—
154C2×D4×C127—48no—
155C2×D4×C127—48no—
156C2×D4×C127—48no—
157C2×D4×C127—44no—
158C2×D4×C127—48no—
159C2×D4×C127—44no—
160C2×D4×C127—44no—
161C2×D4×C127—44no—
162C22×C4×C127—21no—
163C22×C4×C127—21no—
164C22×C4×C127—22no—
165C22×C4×C127—22no—
166C22×C4×C127—22no—
167C22×C4×C127—28no—
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—21no—
175C22×C4×C127—21no—
176C22×C4×C127—21no—
177C22×C4×C127—21no—
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—48no—
202C22×C4×C127—48no—
203C22×C4×C127—44no—
204C22×C4×C127—44no—
205C22×C4×C127C2×D412yes—
206C22×C4×C127C2×D414yes—
207C22×C4×C127C2×D414yes—
208C22×C4×C127C2×D412yes—
209C22×C4×C127C2×D412yes—
210C22×C4×C127C2×D412yes—
211C22×C4×C127C2×D412yes—
212C22×C4×C127C2×D414yes—
213C22×C4×C127C2×D412yes—
214C22×C4×C127#4114yes—
215C4⋊C4×C127—28no—
216C4⋊C4×C127—48no—
217C4⋊C4×C127—44no—
218C4⋊C4×C127—48no—
219C22⋊C4×C127—216no—
220C22⋊C4×C127—28no—
221C22⋊C4×C127—28no—
222C22⋊C4×C127—48no—
223C22⋊C4×C127—48no—
224C22⋊C4×C127—48no—
225C22⋊C4×C127—48no—
226C22⋊C4×C127—48no—
227C42×C127—44no—
228C23×C127—22no—
229C23×C127—24no—
230C23×C127—22no—
231C23×C127—24no—
232C23×C127—24no—
233C23×C127—24no—
234C23×C127—24no—
235C23×C127—24no—
236C23×C127—24no—
237C23×C127—24no—
238C23×C127—22no—
239C23×C127—22no—
240C23×C127—22no—
241C23×C127—22no—
242C23×C127—22no—
243C23×C127—22no—
244C23×C127—24no—
245C23×C127—24no—
246C23×C127—24no—
247C23×C127—24no—
248C23×C127—41no—
249C23×C127—41no—
250C23×C127—41no—
251C23×C127—41no—
252C23×C127—42no—
253C23×C127—42no—
254C23×C127—42no—
255C23×C127—42no—
256C23×C127—42no—
257C23×C127—42no—
258C23×C127—41no—
259C23×C127—42no—
260C23×C127—42no—
261C23×C127—41no—
262C23×C127—41no—
263C23×C127—41no—
264C23×C127—41no—
265C23×C127—41no—
266C23×C127—41no—
267C23×C127—41no—
268C23×C127—42no—
269C23×C127—42no—
270C23×C127—42no—
271C23×C127—42no—
272C23×C127—42no—
273C23×C127—42no—
274C23×C127—42no—
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#12314yes—
291C23×C127C22×D411yescharacteristic
292C23×C127C22×D411yescharacteristic
293C23×C127C22×D411yescharacteristic
294C23×C127C22×D412yes—
295C23×C127C2×#4112yes—
296C23×C127C2×#4112yes—
297C23×C127H(5,𝔽2)12yes—
298C23×C127H(5,𝔽2)12yes—
299C23×C1272−1+412yes—
300D4×C127—416no—
301D4×C127—416no—
302D4×C127—416no—
303C2×C4×C127—22no—
304C2×C4×C127—22no—
305C2×C4×C127—22no—
306C2×C4×C127—22no—
307C2×C4×C127—24no—
308C2×C4×C127—24no—
309C2×C4×C127—24no—
310C2×C4×C127—24no—
311C2×C4×C127—22no—
312C2×C4×C127—22no—
313C2×C4×C127—24no—
314C2×C4×C127—24no—
315C2×C4×C127—24no—
316C2×C4×C127—24no—
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—416no—
325C2×C4×C127—41no—
326C2×C4×C127—42no—
327C2×C4×C127—41no—
328C2×C4×C127—42no—
329C2×C4×C127—42no—
330C2×C4×C127—41no—
331C2×C4×C127—41no—
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#12014yes—
351C2×C4×C127#12714yes—
352C22×C127—24no—
353C22×C127—28no—
354C22×C127—44no—
355C22×C127—44no—
356C22×C127—42no—
357C22×C127—42no—
358C22×C127—44no—
359C22×C127—44no—
360C22×C127—44no—
361C22×C127—42no—
362C22×C127—42no—
363C22×C127—44no—
364C22×C127—44no—
365C22×C127—42no—
366C22×C127—42no—
367C22×C127—42no—
368C22×C127—42no—
369C22×C127—44no—
370C22×C127—44no—
371C22×C127—82no—
372C22×C127—82no—
373C22×C127—82no—
374C22×C127—82no—
375C22×C127—82no—
376C22×C127—82no—
377C22×C127—82no—
378C22×C127—82no—
379C22×C127C2×#12011yescharacteristic
380C22×C127C2×#12311yescharacteristic
381C22×C127#52512yes—
382C22×C127C2×#12711yescharacteristic
383C22×C127#53211yescharacteristic
384C22×C127#53411yescharacteristic
385C22×C127#53511yescharacteristic
386C22×C127#53611yescharacteristic
387C22×C127#53712yes—
388C22×C127#53912yes—
389C22×C127#54012yes—
390C22×C127D4212yes—
391C22×C127D4212yes—
392C22×C127#54612yes—
393C22×C127#54612yes—
394C22×C127#54612yes—
395C22×C127#54712yes—
396C22×C127#54812yes—
397C22×C127#54812yes—
398C22×C127#55312yes—
399C22×C127#56212yes—
400C4×C127—24no—
401C4×C127—24no—
402C4×C127—42no—
403C4×C127—44no—
404C4×C127—42no—
405C4×C127—44no—
406C4×C127—44no—
407C4×C127—82no—
408#15340C12711yesmaximal, characteristic, direct product factor, Sylow
409C2×C127—44no—
410C2×C127—82no—
411C2×C127—82no—
412C2×C127#240511yescharacteristic
413C2×C127#243211yescharacteristic
414C2×C127#243311yescharacteristic
415C2×C127#244312yes—
416C2×C127#246412yes—
417C2×C127#254012yes—
418C2×C127#267112yes—
419C2×C127#268112yes—
420C2×C127#271112yes—
421C22×#121C2×C12711yescharacteristic
422C2×#399C2×C12711yescharacteristic, complemented
423C2×#398C2×C12711yescharacteristic, complemented
424C2×#394C2×C12712yescomplemented
425C2×#390C2×C12711yescharacteristic, complemented
426C2×#385C2×C12712yescomplemented
427#1439C2×C12712yescomplemented
428#1438C2×C12711yescharacteristic, complemented
429#1438C2×C12712yescomplemented
430#1437C2×C12711yescharacteristic, complemented
431#1436C2×C12711yescharacteristic, complemented
432C127#1534011yescharacteristic, direct product factor, Sylow
433C23×D4C22×C12711yescharacteristic
434C23×D4C22×C12711yescharacteristic
435C23×D4C22×C12711yescharacteristic
436C24×C4C22×C12711yescharacteristic
437C2×#121—24no—
438C2×#121—24no—
439C2×#121—24no—
440C22×C4⋊C4C22×C12712yes—
441C22×C4⋊C4C22×C12711yescharacteristic
442C22×C4⋊C4C22×C12712yes—
443C22×C4⋊C4C22×C12711yescharacteristic
444C22×C22⋊C4C22×C12711yescharacteristic
445C22×C22⋊C4C22×C12712yes—
446C22×C22⋊C4C22×C12712yes—
447C22×C22⋊C4C22×C12712yes—
448C22×C22⋊C4C22×C12712yes—
449C22×C22⋊C4C22×C12712yes—
450C22×C22⋊C4C22×C12712yes—
451C22×C22⋊C4C22×C12711yescharacteristic
452C22×C42C22×C12711yescharacteristic
453#399—24no—
454#398—24no—
455#394—28no—
456#390—24no—
457#385—28no—
458C2×#95C22×C12711yescharacteristic
459C2×#95C22×C12712yes—
460C2×#95C22×C12711yescharacteristic
461C2×#95C22×C12712yes—
462C2×#95C22×C12712yes—
463C2×#95C22×C12712yes—
464C25C23×C12711yescharacteristic
465C25C23×C12711yescharacteristic
466C25C23×C12711yescharacteristic
467C22×D4—22no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—22no—
471C22×D4—24no—
472C22×D4—24no—
473C22×D4—22no—
474C22×D4—22no—
475C22×D4—22no—
476C22×D4—22no—
477C22×D4—24no—
478C22×D4—42no—
479C22×D4—42no—
480C22×D4—42no—
481C22×D4D4×C12714yes—
482C23×C4—22no—
483C23×C4—22no—
484C23×C4—22no—
485C23×C4—24no—
486C23×C4—42no—
487C23×C4C23×C12712yes—
488C23×C4C23×C12712yes—
489C23×C4C23×C12712yes—
490C23×C4C23×C12711yescharacteristic
491C23×C4C23×C12711yescharacteristic
492C23×C4C23×C12712yes—
493C23×C4C23×C12711yescharacteristic
494C23×C4C23×C12711yescharacteristic
495#121—232no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—24no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—24no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—24no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—42no—
507C2×C4⋊C4D4×C12714yes—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
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—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4D4×C12714yes—
532C2×C42—22no—
533C2×C42—42no—
534#95—24no—
535#95—22no—
536#95—24no—
537#95—22no—
538#95—42no—
539#95D4×C12718yescomplemented
540C24—22no—
541C24—21no—
542C24—21no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—21no—
550C24—21no—
551C24—21no—
552C24—21no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24C2×D4×C12712yes—
564C24C2×D4×C12712yes—
565C24C2×D4×C12712yes—
566C24#41×C12714yes—
567C24C24×C12711yescharacteristic
568C2×D4—28no—
569C2×D4—28no—
570C2×D4—28no—
571C2×D4—28no—
572C2×D4—44no—
573C2×D4—48no—
574C2×D4—48no—
575C2×D4—48no—
576C2×D4—48no—
577C2×D4—48no—
578C2×D4—44no—
579C2×D4—48no—
580C2×D4—44no—
581C2×D4—44no—
582C2×D4—44no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—28no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
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—48no—
623C22×C4—48no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4C2×D4×C12712yes—
627C22×C4C2×D4×C12714yes—
628C22×C4C2×D4×C12714yes—
629C22×C4C2×D4×C12712yes—
630C22×C4C2×D4×C12712yes—
631C22×C4C2×D4×C12712yes—
632C22×C4C2×D4×C12712yes—
633C22×C4C2×D4×C12714yes—
634C22×C4C2×D4×C12712yes—
635C22×C4#41×C12714yes—
636C4⋊C4—28no—
637C4⋊C4—48no—
638C4⋊C4—44no—
639C4⋊C4—48no—
640C22⋊C4—216no—
641C22⋊C4—28no—
642C22⋊C4—28no—
643C22⋊C4—48no—
644C22⋊C4—48no—
645C22⋊C4—48no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C42—44no—
649C23—22no—
650C23—24no—
651C23—22no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—41no—
680C23—42no—
681C23—42no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
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—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23#123×C12714yes—
712C23C22×D4×C12711yescharacteristic
713C23C22×D4×C12711yescharacteristic
714C23C22×D4×C12711yescharacteristic
715C23C22×D4×C12712yes—
716C23C2×#41×C12712yes—
717C23C2×#41×C12712yes—
718C23H(5,𝔽2)×C12712yes—
719C23H(5,𝔽2)×C12712yes—
720C232−1+4×C12712yes—
721D4—416no—
722D4—416no—
723D4—416no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—416no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
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#120×C12714yes—
772C2×C4#127×C12714yes—
773C22—24no—
774C22—28no—
775C22—44no—
776C22—44no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—42no—
783C22—42no—
784C22—44no—
785C22—44no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—44no—
791C22—44no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22C2×#120×C12711yescharacteristic
801C22C2×#123×C12711yescharacteristic
802C22#525×C12712yes—
803C22C2×#127×C12711yescharacteristic
804C22#532×C12711yescharacteristic
805C22#534×C12711yescharacteristic
806C22#535×C12711yescharacteristic
807C22#536×C12711yescharacteristic
808C22#537×C12712yes—
809C22#539×C12712yes—
810C22#540×C12712yes—
811C22D42×C12712yes—
812C22D42×C12712yes—
813C22#546×C12712yes—
814C22#546×C12712yes—
815C22#546×C12712yes—
816C22#547×C12712yes—
817C22#548×C12712yes—
818C22#548×C12712yes—
819C22#553×C12712yes—
820C22#562×C12712yes—
821C4—24no—
822C4—24no—
823C4—42no—
824C4—44no—
825C4—42no—
826C4—44no—
827C4—44no—
828C4—82no—
829C2—44no—
830C2—82no—
831C2—82no—
832C2C127×#240511yescharacteristic
833C2C127×#243211yescharacteristic
834C2C127×#243311yescharacteristic
835C2C127×#244312yes—
836C2C127×#246412yes—
837C2C127×#254012yes—
838C2C127×#267112yes—
839C2C127×#268112yes—
840C2C127×#271112yes—
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC22×#121×C127C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#399×C127C2semidirect
3. C2×#398×C127C2semidirect
4. C2×#394×C127C2semidirect
5. C2×#390×C127C2semidirect
6. C2×#385×C127C2semidirect
7. C127×#1439C2semidirect
8. C127×#1438C2semidirect
9. C127×#1438C2semidirect
10. C127×#1437C2semidirect
11. C127×#1436C2semidirect
118. #95×C127D4semidirect
408. #15340C127direct (N × H)
422. C2×#399C2×C127semidirect
423. C2×#398C2×C127semidirect
424. C2×#394C2×C127semidirect
425. C2×#390C2×C127semidirect
426. C2×#385C2×C127semidirect
427. #1439C2×C127semidirect
428. #1438C2×C127semidirect
429. #1438C2×C127semidirect
430. #1437C2×C127semidirect
431. #1436C2×C127semidirect
432. C127#15340direct (N × H)
539. #95D4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C1272
C2×#399×C1272
C2×#398×C1272
C2×#394×C1272
C2×#390×C1272
C2×#385×C1272
C127×#14392
C127×#14382
C127×#14372
C127×#14362
#15340127