Finite Group Databasebeta

← C127×#15384 #44579057

Subgroups — C127×#15384 #44579057

Order 32512.

2118 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C127C211yesmaximal, characteristic
2C2×#399×C127C211yesmaximal, characteristic, complemented
3C2×#397×C127C211yesmaximal, characteristic, complemented
4C2×#394×C127C212yesmaximal
5C2×#385×C127C212yesmaximal, complemented
6C2×#384×C127C211yesmaximal, characteristic, complemented
7C127×#1445C211yesmaximal, characteristic, complemented
8C127×#1444C212yesmaximal, complemented
9C127×#1439C212yesmaximal, complemented
10C127×#1437C211yesmaximal, characteristic, complemented
11C127×#1437C211yesmaximal, characteristic, complemented
12C23×D4×C127C2211yescharacteristic
13C24×C4×C127C2211yescharacteristic
14C2×#123×C127—24no—
15C2×#123×C127—24no—
16C2×#123×C127—24no—
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C4⋊C4×C127C2211yescharacteristic
19C22×C4⋊C4×C127C2212yes—
20C22×C4⋊C4×C127C2212yes—
21C22×C4⋊C4×C127C2212yes—
22C22×C4⋊C4×C127C2211yescharacteristic
23C22×C22⋊C4×C127C2212yes—
24C22×C22⋊C4×C127C2212yes—
25C22×C22⋊C4×C127C2211yescharacteristic
26C22×C22⋊C4×C127C2212yes—
27C22×C22⋊C4×C127C2212yes—
28C22×C22⋊C4×C127C2211yescharacteristic
29C22×C22⋊C4×C127C2211yescharacteristic
30C22×C42×C127C2211yescharacteristic
31#399×C127—24no—
32#397×C127—24no—
33#394×C127—28no—
34#385×C127—28no—
35#384×C127—24no—
36C2×#95×C127C2212yes—
37C2×#95×C127C2211yescharacteristic
38C2×#95×C127C2212yes—
39C2×#95×C127C2211yescharacteristic
40C2×#95×C127C2212yes—
41C2×#95×C127C2212yes—
42C2×#95×C127C2212yes—
43C25×C127C2311yescharacteristic
44C25×C127C2311yescharacteristic
45C22×D4×C127—22no—
46C22×D4×C127—22no—
47C22×D4×C127—24no—
48C22×D4×C127—22no—
49C22×D4×C127—42no—
50C23×C4×C127—22no—
51C23×C4×C127—22no—
52C23×C4×C127—22no—
53C23×C4×C127—24no—
54C23×C4×C127—42no—
55C23×C4×C127C2312yes—
56C23×C4×C127C2312yes—
57C23×C4×C127C2312yes—
58C23×C4×C127C2311yescharacteristic
59C23×C4×C127C2311yescharacteristic
60C23×C4×C127C2311yescharacteristic
61C23×C4×C127C2311yescharacteristic
62C23×C4×C127C2311yescharacteristic
63C23×C4×C127C2312yes—
64#123×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—24no—
71C2×C4⋊C4×C127—24no—
72C2×C4⋊C4×C127—22no—
73C2×C4⋊C4×C127—24no—
74C2×C4⋊C4×C127—24no—
75C2×C4⋊C4×C127—24no—
76C2×C4⋊C4×C127—22no—
77C2×C4⋊C4×C127—24no—
78C2×C4⋊C4×C127—22no—
79C2×C4⋊C4×C127—42no—
80C2×C4⋊C4×C127—42no—
81C2×C4⋊C4×C127—42no—
82C2×C4⋊C4×C127D414yes—
83C2×C22⋊C4×C127—22no—
84C2×C22⋊C4×C127—22no—
85C2×C22⋊C4×C127—22no—
86C2×C22⋊C4×C127—22no—
87C2×C22⋊C4×C127—22no—
88C2×C22⋊C4×C127—22no—
89C2×C22⋊C4×C127—22no—
90C2×C22⋊C4×C127—24no—
91C2×C22⋊C4×C127—24no—
92C2×C22⋊C4×C127—24no—
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—42no—
101C2×C22⋊C4×C127D414yes—
102C2×C22⋊C4×C127D414yes—
103C2×C22⋊C4×C127D418yes—
104C2×C42×C127—22no—
105C2×C42×C127—24no—
106#95×C127—24no—
107#95×C127—24no—
108#95×C127—24no—
109#95×C127—22no—
110#95×C127—24no—
111#95×C127—22no—
112#95×C127—24no—
113C24×C127—21no—
114C24×C127—21no—
115C24×C127—22no—
116C24×C127—22no—
117C24×C127—22no—
118C24×C127—22no—
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×C127C2×D412yes—
129C24×C127C2×D412yes—
130C24×C127C2×D414yes—
131C24×C127C2411yescharacteristic
132C2×D4×C127—28no—
133C2×D4×C127—48no—
134C2×D4×C127—48no—
135C2×D4×C127—44no—
136C2×D4×C127—44no—
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—28no—
144C22×C4×C127—22no—
145C22×C4×C127—22no—
146C22×C4×C127—22no—
147C22×C4×C127—22no—
148C22×C4×C127—21no—
149C22×C4×C127—21no—
150C22×C4×C127—21no—
151C22×C4×C127—21no—
152C22×C4×C127—21no—
153C22×C4×C127—21no—
154C22×C4×C127—21no—
155C22×C4×C127—21no—
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—22no—
175C22×C4×C127—22no—
176C22×C4×C127—22no—
177C22×C4×C127—22no—
178C22×C4×C127—22no—
179C22×C4×C127—22no—
180C22×C4×C127—48no—
181C22×C4×C127—48no—
182C22×C4×C127—44no—
183C22×C4×C127—44no—
184C22×C4×C127C2×D412yes—
185C22×C4×C127C2×D414yes—
186C22×C4×C127C2×D412yes—
187C22×C4×C127C2×D412yes—
188C22×C4×C127C2×D412yes—
189C22×C4×C127C2×D412yes—
190C22×C4×C127C2×D412yes—
191C22×C4×C127C2×D412yes—
192C22×C4×C127C2×D414yes—
193C22×C4×C127#4114yes—
194C22×C4×C127#4114yes—
195C4⋊C4×C127—28no—
196C4⋊C4×C127—28no—
197C4⋊C4×C127—48no—
198C4⋊C4×C127—48no—
199C4⋊C4×C127—48no—
200C4⋊C4×C127—44no—
201C22⋊C4×C127—28no—
202C22⋊C4×C127—28no—
203C22⋊C4×C127—28no—
204C22⋊C4×C127—216no—
205C22⋊C4×C127—48no—
206C22⋊C4×C127—48no—
207C22⋊C4×C127—48no—
208C42×C127—28no—
209C23×C127—22no—
210C23×C127—24no—
211C23×C127—22no—
212C23×C127—24no—
213C23×C127—24no—
214C23×C127—24no—
215C23×C127—24no—
216C23×C127—24no—
217C23×C127—24no—
218C23×C127—24no—
219C23×C127—22no—
220C23×C127—22no—
221C23×C127—22no—
222C23×C127—24no—
223C23×C127—24no—
224C23×C127—41no—
225C23×C127—41no—
226C23×C127—41no—
227C23×C127—41no—
228C23×C127—42no—
229C23×C127—42no—
230C23×C127—42no—
231C23×C127—42no—
232C23×C127—42no—
233C23×C127—42no—
234C23×C127—42no—
235C23×C127—41no—
236C23×C127—41no—
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#12714yes—
251C23×C127C22×D411yescharacteristic
252C23×C127C22×D411yescharacteristic
253C23×C127C22×D411yescharacteristic
254C23×C127C22×D412yes—
255C23×C127C2×#4112yes—
256C23×C127C2×#4112yes—
257C23×C127H(5,𝔽2)12yes—
258C23×C1272−1+412yes—
259C23×C1272−1+412yes—
260D4×C127—416no—
261C2×C4×C127—22no—
262C2×C4×C127—24no—
263C2×C4×C127—22no—
264C2×C4×C127—24no—
265C2×C4×C127—24no—
266C2×C4×C127—24no—
267C2×C4×C127—24no—
268C2×C4×C127—24no—
269C2×C4×C127—24no—
270C2×C4×C127—24no—
271C2×C4×C127—22no—
272C2×C4×C127—22no—
273C2×C4×C127—22no—
274C2×C4×C127—22no—
275C2×C4×C127—24no—
276C2×C4×C127—24no—
277C2×C4×C127—24no—
278C2×C4×C127—24no—
279C2×C4×C127—24no—
280C2×C4×C127—24no—
281C2×C4×C127—24no—
282C2×C4×C127—416no—
283C2×C4×C127—41no—
284C2×C4×C127—41no—
285C2×C4×C127—41no—
286C2×C4×C127—42no—
287C2×C4×C127—41no—
288C2×C4×C127—41no—
289C2×C4×C127—41no—
290C2×C4×C127—41no—
291C2×C4×C127—41no—
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—
309C2×C4×C127—42no—
310C2×C4×C127—42no—
311C2×C4×C127—42no—
312C2×C4×C127—42no—
313C2×C4×C127#12014yes—
314C2×C4×C127#12318yescomplemented
315C22×C127—24no—
316C22×C127—28no—
317C22×C127—42no—
318C22×C127—44no—
319C22×C127—44no—
320C22×C127—44no—
321C22×C127—42no—
322C22×C127—44no—
323C22×C127—44no—
324C22×C127—42no—
325C22×C127—44no—
326C22×C127—44no—
327C22×C127—42no—
328C22×C127—42no—
329C22×C127—82no—
330C22×C127—82no—
331C22×C127—82no—
332C22×C127—82no—
333C22×C127C2×#12011yescharacteristic
334C22×C127C2×#12312yes—
335C22×C127#52511yescharacteristic
336C22×C127C2×#12711yescharacteristic
337C22×C127#53211yescharacteristic
338C22×C127#53511yescharacteristic
339C22×C127#53611yescharacteristic
340C22×C127#53612yes—
341C22×C127#53611yescharacteristic
342C22×C127#53912yes—
343C22×C127#54212yes—
344C22×C127D4212yes—
345C22×C127D4212yes—
346C22×C127#54712yes—
347C22×C127#54712yes—
348C22×C127#54712yes—
349C22×C127#54712yes—
350C22×C127#54712yes—
351C22×C127#54812yes—
352C22×C127#55312yes—
353C22×C127#56312yes—
354C4×C127—24no—
355C4×C127—28no—
356C4×C127—44no—
357C4×C127—42no—
358C4×C127—42no—
359C4×C127—42no—
360C4×C127—42no—
361C4×C127—82no—
362C4×C127—82no—
363#15384C12711yesmaximal, characteristic, direct product factor, Sylow
364C2×C127—44no—
365C2×C127—82no—
366C2×C127#240611yescharacteristic
367C2×C127#242212yes—
368C2×C127#243211yescharacteristic
369C2×C127#243311yescharacteristic
370C2×C127#244312yes—
371C2×C127#250112yes—
372C2×C127#267412yes—
373C2×C127#268012yes—
374C2×C127#271812yes—
375C22×#123C2×C12711yescharacteristic
376C2×#399C2×C12711yescharacteristic, complemented
377C2×#397C2×C12711yescharacteristic, complemented
378C2×#394C2×C12712yes—
379C2×#385C2×C12712yescomplemented
380C2×#384C2×C12711yescharacteristic, complemented
381#1445C2×C12711yescharacteristic, complemented
382#1444C2×C12712yescomplemented
383#1439C2×C12712yescomplemented
384#1437C2×C12711yescharacteristic, complemented
385#1437C2×C12711yescharacteristic, complemented
386C127#1538411yescharacteristic, direct product factor, Sylow
387C23×D4C22×C12711yescharacteristic
388C24×C4C22×C12711yescharacteristic
389C2×#123—24no—
390C2×#123—24no—
391C2×#123—24no—
392C22×C4⋊C4C22×C12711yescharacteristic
393C22×C4⋊C4C22×C12711yescharacteristic
394C22×C4⋊C4C22×C12712yes—
395C22×C4⋊C4C22×C12712yes—
396C22×C4⋊C4C22×C12712yes—
397C22×C4⋊C4C22×C12711yescharacteristic
398C22×C22⋊C4C22×C12712yes—
399C22×C22⋊C4C22×C12712yes—
400C22×C22⋊C4C22×C12711yescharacteristic
401C22×C22⋊C4C22×C12712yes—
402C22×C22⋊C4C22×C12712yes—
403C22×C22⋊C4C22×C12711yescharacteristic
404C22×C22⋊C4C22×C12711yescharacteristic
405C22×C42C22×C12711yescharacteristic
406#399—24no—
407#397—24no—
408#394—28no—
409#385—28no—
410#384—24no—
411C2×#95C22×C12712yes—
412C2×#95C22×C12711yescharacteristic
413C2×#95C22×C12712yes—
414C2×#95C22×C12711yescharacteristic
415C2×#95C22×C12712yes—
416C2×#95C22×C12712yes—
417C2×#95C22×C12712yes—
418C25C23×C12711yescharacteristic
419C25C23×C12711yescharacteristic
420C22×D4—22no—
421C22×D4—22no—
422C22×D4—24no—
423C22×D4—22no—
424C22×D4—42no—
425C23×C4—22no—
426C23×C4—22no—
427C23×C4—22no—
428C23×C4—24no—
429C23×C4—42no—
430C23×C4C23×C12712yes—
431C23×C4C23×C12712yes—
432C23×C4C23×C12712yes—
433C23×C4C23×C12711yescharacteristic
434C23×C4C23×C12711yescharacteristic
435C23×C4C23×C12711yescharacteristic
436C23×C4C23×C12711yescharacteristic
437C23×C4C23×C12711yescharacteristic
438C23×C4C23×C12712yes—
439#123—232no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4D4×C12714yes—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—42no—
476C2×C22⋊C4D4×C12714yes—
477C2×C22⋊C4D4×C12714yes—
478C2×C22⋊C4D4×C12718yes—
479C2×C42—22no—
480C2×C42—24no—
481#95—24no—
482#95—24no—
483#95—24no—
484#95—22no—
485#95—24no—
486#95—22no—
487#95—24no—
488C24—21no—
489C24—21no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—21no—
496C24—21no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24C2×D4×C12712yes—
504C24C2×D4×C12712yes—
505C24C2×D4×C12714yes—
506C24C24×C12711yescharacteristic
507C2×D4—28no—
508C2×D4—48no—
509C2×D4—48no—
510C2×D4—44no—
511C2×D4—44no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—28no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
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—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—22no—
554C22×C4—22no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4C2×D4×C12712yes—
560C22×C4C2×D4×C12714yes—
561C22×C4C2×D4×C12712yes—
562C22×C4C2×D4×C12712yes—
563C22×C4C2×D4×C12712yes—
564C22×C4C2×D4×C12712yes—
565C22×C4C2×D4×C12712yes—
566C22×C4C2×D4×C12712yes—
567C22×C4C2×D4×C12714yes—
568C22×C4#41×C12714yes—
569C22×C4#41×C12714yes—
570C4⋊C4—28no—
571C4⋊C4—28no—
572C4⋊C4—48no—
573C4⋊C4—48no—
574C4⋊C4—48no—
575C4⋊C4—44no—
576C22⋊C4—28no—
577C22⋊C4—28no—
578C22⋊C4—28no—
579C22⋊C4—216no—
580C22⋊C4—48no—
581C22⋊C4—48no—
582C22⋊C4—48no—
583C42—28no—
584C23—22no—
585C23—24no—
586C23—22no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—24no—
598C23—24no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23#127×C12714yes—
626C23C22×D4×C12711yescharacteristic
627C23C22×D4×C12711yescharacteristic
628C23C22×D4×C12711yescharacteristic
629C23C22×D4×C12712yes—
630C23C2×#41×C12712yes—
631C23C2×#41×C12712yes—
632C23H(5,𝔽2)×C12712yes—
633C232−1+4×C12712yes—
634C232−1+4×C12712yes—
635D4—416no—
636C2×C4—22no—
637C2×C4—24no—
638C2×C4—22no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—416no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
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—
688C2×C4#120×C12714yes—
689C2×C4#123×C12718yescomplemented
690C22—24no—
691C22—28no—
692C22—42no—
693C22—44no—
694C22—44no—
695C22—44no—
696C22—42no—
697C22—44no—
698C22—44no—
699C22—42no—
700C22—44no—
701C22—44no—
702C22—42no—
703C22—42no—
704C22—82no—
705C22—82no—
706C22—82no—
707C22—82no—
708C22C2×#120×C12711yescharacteristic
709C22C2×#123×C12712yes—
710C22#525×C12711yescharacteristic
711C22C2×#127×C12711yescharacteristic
712C22#532×C12711yescharacteristic
713C22#535×C12711yescharacteristic
714C22#536×C12711yescharacteristic
715C22#536×C12712yes—
716C22#536×C12711yescharacteristic
717C22#539×C12712yes—
718C22#542×C12712yes—
719C22D42×C12712yes—
720C22D42×C12712yes—
721C22#547×C12712yes—
722C22#547×C12712yes—
723C22#547×C12712yes—
724C22#547×C12712yes—
725C22#547×C12712yes—
726C22#548×C12712yes—
727C22#553×C12712yes—
728C22#563×C12712yes—
729C4—24no—
730C4—28no—
731C4—44no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—42no—
736C4—82no—
737C4—82no—
738C2—44no—
739C2—82no—
740C2C127×#240611yescharacteristic
741C2C127×#242212yes—
742C2C127×#243211yescharacteristic
743C2C127×#243311yescharacteristic
744C2C127×#244312yes—
745C2C127×#250112yes—
746C2C127×#267412yes—
747C2C127×#268012yes—
748C2C127×#271812yes—
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×#399×C127C2semidirect
3. C2×#397×C127C2semidirect
5. C2×#385×C127C2semidirect
6. C2×#384×C127C2semidirect
7. C127×#1445C2semidirect
8. C127×#1444C2semidirect
9. C127×#1439C2semidirect
10. C127×#1437C2semidirect
11. C127×#1437C2semidirect
314. C2×C4×C127#123semidirect
363. #15384C127direct (N × H)
376. C2×#399C2×C127semidirect
377. C2×#397C2×C127semidirect
379. C2×#385C2×C127semidirect
380. C2×#384C2×C127semidirect
381. #1445C2×C127semidirect
382. #1444C2×C127semidirect
383. #1439C2×C127semidirect
384. #1437C2×C127semidirect
385. #1437C2×C127semidirect
386. C127#15384direct (N × H)
689. C2×C4#123×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C1272
C2×#399×C1272
C2×#397×C1272
C2×#394×C1272
C2×#385×C1272
C2×#384×C1272
C127×#14452
C127×#14442
C127×#14392
C127×#14372
#15384127