Finite Group Databasebeta

← C127×#16801 #44580474

Subgroups — C127×#16801 #44580474

Order 32512.

2090 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#399×C127C211yesmaximal, characteristic, complemented
2C2×#396×C127C212yesmaximal, complemented
3C2×#394×C127C212yesmaximal, complemented
4C2×#392×C127C211yesmaximal, characteristic
5C2×#390×C127C211yesmaximal, characteristic, complemented
6C2×#388×C127C211yesmaximal, characteristic, complemented
7C127×#1445C211yesmaximal, characteristic, complemented
8C127×#1439C212yesmaximal, complemented
9C127×#1438C212yesmaximal, complemented
10C127×#1438C211yesmaximal, characteristic, complemented
11C127×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C127C2211yescharacteristic
13C23×D4×C127C2212yes—
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C4⋊C4×C127C2212yes—
17C22×C4⋊C4×C127C2212yes—
18C22×C22⋊C4×C127C2211yescharacteristic
19C22×C22⋊C4×C127C2212yes—
20C22×C22⋊C4×C127C2212yes—
21C22×C22⋊C4×C127C2212yes—
22C22×C22⋊C4×C127C2212yes—
23C22×C22⋊C4×C127C2211yescharacteristic
24C22×C22⋊C4×C127C2212yes—
25C22×C22⋊C4×C127C2211yescharacteristic
26C22×C22⋊C4×C127C2212yes—
27C22×C42×C127C2211yescharacteristic
28#399×C127—24no—
29#396×C127—28no—
30#394×C127—28no—
31#392×C127—24no—
32#390×C127—24no—
33#388×C127—24no—
34C2×#95×C127C2211yescharacteristic
35C2×#95×C127C2212yes—
36C2×#95×C127C2212yes—
37C2×#95×C127C2211yescharacteristic
38C2×#95×C127C2211yescharacteristic
39C2×#95×C127C2211yescharacteristic
40C2×#95×C127C2212yes—
41C25×C127C2311yescharacteristic
42C25×C127C2312yes—
43C22×D4×C127—24no—
44C22×D4×C127—24no—
45C22×D4×C127—24no—
46C22×D4×C127—22no—
47C22×D4×C127—22no—
48C22×D4×C127—24no—
49C22×D4×C127—22no—
50C22×D4×C127—42no—
51C22×D4×C127—42no—
52C22×D4×C127—42no—
53C22×D4×C127—42no—
54C22×D4×C127—42no—
55C23×C4×C127C2312yes—
56C23×C4×C127C2311yescharacteristic
57C23×C4×C127C2311yescharacteristic
58C23×C4×C127C2311yescharacteristic
59C23×C4×C127C2311yescharacteristic
60C23×C4×C127C2312yes—
61C23×C4×C127C2312yes—
62C23×C4×C127C2311yescharacteristic
63C23×C4×C127C2311yescharacteristic
64C2×C4⋊C4×C127—22no—
65C2×C4⋊C4×C127—22no—
66C2×C4⋊C4×C127—24no—
67C2×C4⋊C4×C127—24no—
68C2×C4⋊C4×C127—24no—
69C2×C4⋊C4×C127—22no—
70C2×C4⋊C4×C127—22no—
71C2×C4⋊C4×C127—42no—
72C2×C4⋊C4×C127—42no—
73C2×C4⋊C4×C127—42no—
74C2×C4⋊C4×C127D418yescomplemented
75C2×C22⋊C4×C127—22no—
76C2×C22⋊C4×C127—22no—
77C2×C22⋊C4×C127—24no—
78C2×C22⋊C4×C127—24no—
79C2×C22⋊C4×C127—22no—
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—42no—
92C2×C22⋊C4×C127—42no—
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×C127D414yes—
100C2×C42×C127—42no—
101C2×C42×C127D414yescomplemented
102#95×C127—22no—
103#95×C127—22no—
104#95×C127—22no—
105#95×C127—24no—
106#95×C127—24no—
107#95×C127—22no—
108#95×C127—42no—
109C24×C127—21no—
110C24×C127—22no—
111C24×C127—22no—
112C24×C127—22no—
113C24×C127—22no—
114C24×C127—22no—
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—21no—
127C24×C127—21no—
128C24×C127—22no—
129C24×C127—21no—
130C24×C127—21no—
131C24×C127—22no—
132C24×C127—22no—
133C24×C127C2×D412yes—
134C24×C127#4114yes—
135C24×C127C2411yescharacteristic
136C2×D4×C127—28no—
137C2×D4×C127—48no—
138C2×D4×C127—48no—
139C2×D4×C127—48no—
140C2×D4×C127—48no—
141C2×D4×C127—44no—
142C2×D4×C127—48no—
143C2×D4×C127—48no—
144C2×D4×C127—48no—
145C2×D4×C127—48no—
146C2×D4×C127—48no—
147C2×D4×C127—44no—
148C22×C4×C127—22no—
149C22×C4×C127—22no—
150C22×C4×C127—22no—
151C22×C4×C127—21no—
152C22×C4×C127—21no—
153C22×C4×C127—21no—
154C22×C4×C127—22no—
155C22×C4×C127—22no—
156C22×C4×C127—22no—
157C22×C4×C127—21no—
158C22×C4×C127—22no—
159C22×C4×C127—22no—
160C22×C4×C127—21no—
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—21no—
173C22×C4×C127—21no—
174C22×C4×C127—22no—
175C22×C4×C127—22no—
176C22×C4×C127—22no—
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—21no—
184C22×C4×C127—22no—
185C22×C4×C127—22no—
186C22×C4×C127—21no—
187C22×C4×C127—22no—
188C22×C4×C127—21no—
189C22×C4×C127—21no—
190C22×C4×C127C2×D414yes—
191C22×C4×C127C2×D412yes—
192C22×C4×C127C2×D414yes—
193C22×C4×C127C2×D412yes—
194C22×C4×C127C2×D412yes—
195C22×C4×C127C2×D412yes—
196C22×C4×C127C2×D412yes—
197C22×C4×C127C2×D414yes—
198C22×C4×C127#4112yes—
199C4⋊C4×C127—48no—
200C4⋊C4×C127—48no—
201C4⋊C4×C127—44no—
202C4⋊C4×C127—44no—
203C22⋊C4×C127—28no—
204C22⋊C4×C127—48no—
205C22⋊C4×C127—48no—
206C22⋊C4×C127—48no—
207C22⋊C4×C127—44no—
208C22⋊C4×C127—48no—
209C22⋊C4×C127—48no—
210C22⋊C4×C127—44no—
211C22⋊C4×C127—48no—
212C42×C127—44no—
213C23×C127—22no—
214C23×C127—24no—
215C23×C127—22no—
216C23×C127—22no—
217C23×C127—24no—
218C23×C127—24no—
219C23×C127—24no—
220C23×C127—24no—
221C23×C127—24no—
222C23×C127—24no—
223C23×C127—24no—
224C23×C127—24no—
225C23×C127—42no—
226C23×C127—41no—
227C23×C127—42no—
228C23×C127—41no—
229C23×C127—42no—
230C23×C127—41no—
231C23×C127—42no—
232C23×C127—42no—
233C23×C127—42no—
234C23×C127—42no—
235C23×C127—42no—
236C23×C127—41no—
237C23×C127—42no—
238C23×C127—41no—
239C23×C127—41no—
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—41no—
250C23×C127—41no—
251C23×C127—42no—
252C23×C127—42no—
253C23×C127—42no—
254C23×C127—42no—
255C23×C127—42no—
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×C127C22×D411yescharacteristic
272C23×C127C22×D411yescharacteristic
273C23×C127C22×D412yes—
274C23×C127C2×#4111yescharacteristic
275C23×C127C2×#4112yes—
276C23×C127H(5,𝔽2)11yescharacteristic
277C23×C127H(5,𝔽2)12yes—
278C23×C127H(5,𝔽2)11yescharacteristic
279C23×C127H(5,𝔽2)12yes—
280C23×C1272−1+411yescharacteristic
281C23×C1272−1+411yescharacteristic
282D4×C127—416no—
283D4×C127—432no—
284C2×C4×C127—22no—
285C2×C4×C127—22no—
286C2×C4×C127—22no—
287C2×C4×C127—24no—
288C2×C4×C127—22no—
289C2×C4×C127—24no—
290C2×C4×C127—24no—
291C2×C4×C127—24no—
292C2×C4×C127—22no—
293C2×C4×C127—22no—
294C2×C4×C127—24no—
295C2×C4×C127—24no—
296C2×C4×C127—22no—
297C2×C4×C127—22no—
298C2×C4×C127—24no—
299C2×C4×C127—24no—
300C2×C4×C127—24no—
301C2×C4×C127—24no—
302C2×C4×C127—24no—
303C2×C4×C127—41no—
304C2×C4×C127—42no—
305C2×C4×C127—41no—
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—42no—
314C2×C4×C127—42no—
315C2×C4×C127—42no—
316C2×C4×C127—42no—
317C2×C4×C127—41no—
318C2×C4×C127—41no—
319C2×C4×C127—42no—
320C2×C4×C127—41no—
321C2×C4×C127—42no—
322C2×C4×C127—41no—
323C2×C4×C127—42no—
324C2×C4×C127—41no—
325C2×C4×C127—42no—
326C2×C4×C127—41no—
327C2×C4×C127—42no—
328C2×C4×C127—42no—
329C2×C4×C127—42no—
330C2×C4×C127—42no—
331C2×C4×C127—42no—
332C2×C4×C127—42no—
333C2×C4×C127#12114yes—
334C2×C4×C127#12714yes—
335C22×C127—42no—
336C22×C127—44no—
337C22×C127—44no—
338C22×C127—44no—
339C22×C127—44no—
340C22×C127—44no—
341C22×C127—44no—
342C22×C127—44no—
343C22×C127—44no—
344C22×C127—42no—
345C22×C127—44no—
346C22×C127—42no—
347C22×C127—82no—
348C22×C127—81no—
349C22×C127—81no—
350C22×C127—82no—
351C22×C127—82no—
352C22×C127—82no—
353C22×C127—82no—
354C22×C127—82no—
355C22×C127—82no—
356C22×C127—82no—
357C22×C127—81no—
358C22×C127—82no—
359C22×C127—81no—
360C22×C127—82no—
361C22×C127C2×#12111yescharacteristic
362C22×C127#52511yescharacteristic
363C22×C127C2×#12711yescharacteristic
364C22×C127#53412yes—
365C22×C127#53411yescharacteristic
366C22×C127#53511yescharacteristic
367C22×C127#53511yescharacteristic
368C22×C127#53611yescharacteristic
369C22×C127#53711yescharacteristic
370C22×C127#53711yescharacteristic
371C22×C127#53712yes—
372C22×C127#53812yes—
373C22×C127#53912yes—
374C22×C127#54211yescharacteristic
375C22×C127#54211yescharacteristic
376C22×C127D4212yes—
377C22×C127#54612yes—
378C22×C127#54612yes—
379C22×C127#54812yes—
380C22×C127#55012yes—
381C22×C127#55112yes—
382C22×C127#56012yes—
383C22×C127#56212yes—
384C4×C127—24no—
385C4×C127—24no—
386C4×C127—44no—
387C4×C127—44no—
388C4×C127—42no—
389C4×C127—42no—
390C4×C127—81no—
391C4×C127—81no—
392C4×C127—82no—
393#16801C12711yesmaximal, characteristic, direct product factor, Sylow
394C2×C127—82no—
395C2×C127—84no—
396C2×C127#253411yescharacteristic
397C2×C127#254011yescharacteristic
398C2×C127#254111yescharacteristic
399C2×C127#262011yescharacteristic
400C2×C127#263611yescharacteristic
401C2×C127#265611yescharacteristic
402C2×C127#267812yes—
403C2×C127#268112yes—
404C2×C127#270512yes—
405C2×C127#273012yes—
406C2×C127#281311yescharacteristic
407C2×#399C2×C12711yescharacteristic, complemented
408C2×#396C2×C12712yescomplemented
409C2×#394C2×C12712yescomplemented
410C2×#392C2×C12711yescharacteristic
411C2×#390C2×C12711yescharacteristic, complemented
412C2×#388C2×C12711yescharacteristic, complemented
413#1445C2×C12711yescharacteristic, complemented
414#1439C2×C12712yescomplemented
415#1438C2×C12712yescomplemented
416#1438C2×C12711yescharacteristic, complemented
417C4⋊#95C2×C12711yescharacteristic, complemented
418C127#1680111yescharacteristic, direct product factor, Sylow
419C23×D4C22×C12711yescharacteristic
420C23×D4C22×C12712yes—
421C22×C4⋊C4C22×C12711yescharacteristic
422C22×C4⋊C4C22×C12711yescharacteristic
423C22×C4⋊C4C22×C12712yes—
424C22×C4⋊C4C22×C12712yes—
425C22×C22⋊C4C22×C12711yescharacteristic
426C22×C22⋊C4C22×C12712yes—
427C22×C22⋊C4C22×C12712yes—
428C22×C22⋊C4C22×C12712yes—
429C22×C22⋊C4C22×C12712yes—
430C22×C22⋊C4C22×C12711yescharacteristic
431C22×C22⋊C4C22×C12712yes—
432C22×C22⋊C4C22×C12711yescharacteristic
433C22×C22⋊C4C22×C12712yes—
434C22×C42C22×C12711yescharacteristic
435#399—24no—
436#396—28no—
437#394—28no—
438#392—24no—
439#390—24no—
440#388—24no—
441C2×#95C22×C12711yescharacteristic
442C2×#95C22×C12712yes—
443C2×#95C22×C12712yes—
444C2×#95C22×C12711yescharacteristic
445C2×#95C22×C12711yescharacteristic
446C2×#95C22×C12711yescharacteristic
447C2×#95C22×C12712yes—
448C25C23×C12711yescharacteristic
449C25C23×C12712yes—
450C22×D4—24no—
451C22×D4—24no—
452C22×D4—24no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—24no—
456C22×D4—22no—
457C22×D4—42no—
458C22×D4—42no—
459C22×D4—42no—
460C22×D4—42no—
461C22×D4—42no—
462C23×C4C23×C12712yes—
463C23×C4C23×C12711yescharacteristic
464C23×C4C23×C12711yescharacteristic
465C23×C4C23×C12711yescharacteristic
466C23×C4C23×C12712yes—
467C23×C4C23×C12711yescharacteristic
468C23×C4C23×C12712yes—
469C23×C4C23×C12711yescharacteristic
470C23×C4C23×C12711yescharacteristic
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4—42no—
481C2×C4⋊C4D4×C12718yescomplemented
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4D4×C12714yes—
507C2×C42—42no—
508C2×C42D4×C12714yescomplemented
509#95—22no—
510#95—22no—
511#95—22no—
512#95—24no—
513#95—24no—
514#95—22no—
515#95—42no—
516C24—21no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—21no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—21no—
534C24—21no—
535C24—22no—
536C24—21no—
537C24—21no—
538C24—22no—
539C24—22no—
540C24C2×D4×C12712yes—
541C24#41×C12714yes—
542C24C24×C12711yescharacteristic
543C2×D4—28no—
544C2×D4—48no—
545C2×D4—48no—
546C2×D4—48no—
547C2×D4—48no—
548C2×D4—44no—
549C2×D4—48no—
550C2×D4—48no—
551C2×D4—48no—
552C2×D4—48no—
553C2×D4—48no—
554C2×D4—44no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4C2×D4×C12714yes—
598C22×C4C2×D4×C12712yes—
599C22×C4C2×D4×C12714yes—
600C22×C4C2×D4×C12712yes—
601C22×C4C2×D4×C12712yes—
602C22×C4C2×D4×C12712yes—
603C22×C4C2×D4×C12712yes—
604C22×C4C2×D4×C12714yes—
605C22×C4#41×C12712yes—
606C4⋊C4—48no—
607C4⋊C4—48no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C22⋊C4—28no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—44no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—44no—
618C22⋊C4—48no—
619C42—44no—
620C23—22no—
621C23—24no—
622C23—22no—
623C23—22no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—42no—
633C23—41no—
634C23—42no—
635C23—41no—
636C23—42no—
637C23—41no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—41no—
644C23—42no—
645C23—41no—
646C23—41no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—41no—
657C23—41no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23C22×D4×C12711yescharacteristic
679C23C22×D4×C12711yescharacteristic
680C23C22×D4×C12712yes—
681C23C2×#41×C12711yescharacteristic
682C23C2×#41×C12712yes—
683C23H(5,𝔽2)×C12711yescharacteristic
684C23H(5,𝔽2)×C12712yes—
685C23H(5,𝔽2)×C12711yescharacteristic
686C23H(5,𝔽2)×C12712yes—
687C232−1+4×C12711yescharacteristic
688C232−1+4×C12711yescharacteristic
689D4—416no—
690D4—432no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4#121×C12714yes—
741C2×C4#127×C12714yes—
742C22—42no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—44no—
750C22—44no—
751C22—42no—
752C22—44no—
753C22—42no—
754C22—82no—
755C22—81no—
756C22—81no—
757C22—82no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—81no—
765C22—82no—
766C22—81no—
767C22—82no—
768C22C2×#121×C12711yescharacteristic
769C22#525×C12711yescharacteristic
770C22C2×#127×C12711yescharacteristic
771C22#534×C12712yes—
772C22#534×C12711yescharacteristic
773C22#535×C12711yescharacteristic
774C22#535×C12711yescharacteristic
775C22#536×C12711yescharacteristic
776C22#537×C12711yescharacteristic
777C22#537×C12711yescharacteristic
778C22#537×C12712yes—
779C22#538×C12712yes—
780C22#539×C12712yes—
781C22#542×C12711yescharacteristic
782C22#542×C12711yescharacteristic
783C22D42×C12712yes—
784C22#546×C12712yes—
785C22#546×C12712yes—
786C22#548×C12712yes—
787C22#550×C12712yes—
788C22#551×C12712yes—
789C22#560×C12712yes—
790C22#562×C12712yes—
791C4—24no—
792C4—24no—
793C4—44no—
794C4—44no—
795C4—42no—
796C4—42no—
797C4—81no—
798C4—81no—
799C4—82no—
800C2—82no—
801C2—84no—
802C2C127×#253411yescharacteristic
803C2C127×#254011yescharacteristic
804C2C127×#254111yescharacteristic
805C2C127×#262011yescharacteristic
806C2C127×#263611yescharacteristic
807C2C127×#265611yescharacteristic
808C2C127×#267812yes—
809C2C127×#268112yes—
810C2C127×#270512yes—
811C2C127×#273012yes—
812C2C127×#281311yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC2×#392×C127C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#399×C127C2semidirect
2. C2×#396×C127C2semidirect
3. C2×#394×C127C2semidirect
5. C2×#390×C127C2semidirect
6. C2×#388×C127C2semidirect
7. C127×#1445C2semidirect
8. C127×#1439C2semidirect
9. C127×#1438C2semidirect
10. C127×#1438C2semidirect
11. C127×C4⋊#95C2semidirect
74. C2×C4⋊C4×C127D4semidirect
101. C2×C42×C127D4semidirect
393. #16801C127direct (N × H)
407. C2×#399C2×C127semidirect
408. C2×#396C2×C127semidirect
409. C2×#394C2×C127semidirect
411. C2×#390C2×C127semidirect
412. C2×#388C2×C127semidirect
413. #1445C2×C127semidirect
414. #1439C2×C127semidirect
415. #1438C2×C127semidirect
416. #1438C2×C127semidirect
417. C4⋊#95C2×C127semidirect
418. C127#16801direct (N × H)
481. C2×C4⋊C4D4×C127semidirect
508. C2×C42D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#399×C1272
C2×#396×C1272
C2×#394×C1272
C2×#392×C1272
C2×#390×C1272
C2×#388×C1272
C127×#14452
C127×#14392
C127×#14382
C127×C4⋊#952
#16801127