Finite Group Databasebeta

← C127×#14727 #44578400

Subgroups — C127×#14727 #44578400

Order 32512.

3350 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C127C211yesmaximal, characteristic
2C2×#397×C127C212yesmaximal, complemented
3C2×#385×C127C211yesmaximal, characteristic, complemented
4C2×#379×C127C211yesmaximal, characteristic
5C2×#379×C127C211yesmaximal, characteristic
6C127×#1440C212yesmaximal, complemented
7C127×#1440C212yesmaximal, complemented
8C127×#1439C212yesmaximal, complemented
9C127×C22⋊#95C211yesmaximal, characteristic, complemented
10C127×C22⋊#95C211yesmaximal, characteristic, complemented
11C127×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C127C2211yescharacteristic
13C24×C4×C127C2211yescharacteristic
14C24×C4×C127C2211yescharacteristic
15C22×C4⋊C4×C127C2212yescomplemented
16C22×C22⋊C4×C127—24no—
17C22×C22⋊C4×C127—28no—
18C22×C22⋊C4×C127C2211yescharacteristic
19C22×C22⋊C4×C127C2212yes—
20C22×C22⋊C4×C127C2211yescharacteristic
21C22×C22⋊C4×C127C2211yescharacteristic
22C22×C22⋊C4×C127C2211yescharacteristic
23C22×C22⋊C4×C127C2211yescharacteristic
24C22×C22⋊C4×C127C2212yes—
25C22×C22⋊C4×C127C2212yes—
26C22×C22⋊C4×C127C2212yes—
27C22×C22⋊C4×C127C2211yescharacteristic
28C22×C22⋊C4×C127C2211yescharacteristic
29C22×C22⋊C4×C127C2211yescharacteristic
30#397×C127—28no—
31#385×C127—24no—
32#379×C127—24no—
33#379×C127—24no—
34C2×#95×C127C2212yescomplemented
35C2×#95×C127C2212yescomplemented
36C2×#95×C127C2212yescomplemented
37C2×#95×C127C2212yescomplemented
38C2×#95×C127C2212yescomplemented
39C2×#95×C127C2212yescomplemented
40C2×#95×C127C2212yescomplemented
41C25×C127—24no—
42C25×C127—24no—
43C25×C127—22no—
44C25×C127—22no—
45C25×C127—22no—
46C25×C127—22no—
47C25×C127—22no—
48C25×C127—22no—
49C25×C127—42no—
50C25×C127—42no—
51C25×C127D414yes—
52C25×C127C2311yescharacteristic
53C25×C127C2311yescharacteristic
54C25×C127C2311yescharacteristic
55C23×C4×C127—22no—
56C23×C4×C127—22no—
57C23×C4×C127—24no—
58C23×C4×C127—24no—
59C23×C4×C127—22no—
60C23×C4×C127—22no—
61C23×C4×C127—22no—
62C23×C4×C127—22no—
63C23×C4×C127—42no—
64C23×C4×C127—42no—
65C23×C4×C127C2311yescharacteristic
66C23×C4×C127C2311yescharacteristic
67C23×C4×C127C2312yes—
68C23×C4×C127C2311yescharacteristic
69C23×C4×C127C2311yescharacteristic
70C23×C4×C127C2312yes—
71C23×C4×C127C2312yes—
72C23×C4×C127C2312yes—
73C2×C4⋊C4×C127—24no—
74C2×C4⋊C4×C127—24no—
75C2×C4⋊C4×C127—42no—
76C2×C22⋊C4×C127—232no—
77C2×C22⋊C4×C127—24no—
78C2×C22⋊C4×C127—24no—
79C2×C22⋊C4×C127—24no—
80C2×C22⋊C4×C127—22no—
81C2×C22⋊C4×C127—22no—
82C2×C22⋊C4×C127—24no—
83C2×C22⋊C4×C127—24no—
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—22no—
91C2×C22⋊C4×C127—22no—
92C2×C22⋊C4×C127—24no—
93C2×C22⋊C4×C127—24no—
94C2×C22⋊C4×C127—24no—
95C2×C22⋊C4×C127—22no—
96C2×C22⋊C4×C127—24no—
97C2×C22⋊C4×C127—22no—
98C2×C22⋊C4×C127—22no—
99C2×C22⋊C4×C127—22no—
100C2×C22⋊C4×C127—22no—
101C2×C22⋊C4×C127—24no—
102C2×C22⋊C4×C127—24no—
103C2×C22⋊C4×C127—42no—
104C2×C22⋊C4×C127—42no—
105C2×C22⋊C4×C127—42no—
106C2×C22⋊C4×C127—42no—
107C2×C22⋊C4×C127D418yes—
108C2×C22⋊C4×C127D414yes—
109#95×C127—24no—
110#95×C127—24no—
111#95×C127—24no—
112#95×C127—24no—
113#95×C127—42no—
114#95×C127—42no—
115#95×C127—42no—
116C24×C127—22no—
117C24×C127—22no—
118C24×C127—22no—
119C24×C127—22no—
120C24×C127—216no—
121C24×C127—216no—
122C24×C127—28no—
123C24×C127—28no—
124C24×C127—28no—
125C24×C127—22no—
126C24×C127—21no—
127C24×C127—21no—
128C24×C127—21no—
129C24×C127—21no—
130C24×C127—21no—
131C24×C127—21no—
132C24×C127—22no—
133C24×C127—21no—
134C24×C127—21no—
135C24×C127—21no—
136C24×C127—21no—
137C24×C127—21no—
138C24×C127—21no—
139C24×C127—22no—
140C24×C127—22no—
141C24×C127—22no—
142C24×C127—22no—
143C24×C127—28no—
144C24×C127—28no—
145C24×C127—44no—
146C24×C127—44no—
147C24×C127—48no—
148C24×C127—48no—
149C24×C127—48no—
150C24×C127—48no—
151C24×C127—48no—
152C24×C127—48no—
153C24×C127—48no—
154C24×C127—48no—
155C24×C127—48no—
156C24×C127—48no—
157C24×C127—44no—
158C24×C127—44no—
159C24×C127—44no—
160C24×C127—44no—
161C24×C127C2×D412yes—
162C24×C127C2×D414yes—
163C24×C127C2×D412yes—
164C24×C127C2×D412yes—
165C24×C127C2×D412yes—
166C24×C127#4114yes—
167C24×C127#4112yes—
168C24×C127#4112yes—
169C24×C127#4112yes—
170C24×C127#4112yes—
171C24×C127#4112yes—
172C24×C127C2411yescharacteristic
173C22×C4×C127—28no—
174C22×C4×C127—28no—
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—21no—
195C22×C4×C127—22no—
196C22×C4×C127—22no—
197C22×C4×C127—21no—
198C22×C4×C127—21no—
199C22×C4×C127—21no—
200C22×C4×C127—21no—
201C22×C4×C127—22no—
202C22×C4×C127—21no—
203C22×C4×C127—21no—
204C22×C4×C127—21no—
205C22×C4×C127—21no—
206C22×C4×C127—21no—
207C22×C4×C127—22no—
208C22×C4×C127—21no—
209C22×C4×C127—21no—
210C22×C4×C127—22no—
211C22×C4×C127—22no—
212C22×C4×C127—22no—
213C22×C4×C127—22no—
214C22×C4×C127—22no—
215C22×C4×C127—22no—
216C22×C4×C127—22no—
217C22×C4×C127—22no—
218C22×C4×C127—22no—
219C22×C4×C127—22no—
220C22×C4×C127—48no—
221C22×C4×C127—48no—
222C22×C4×C127—48no—
223C22×C4×C127—48no—
224C22×C4×C127—44no—
225C22×C4×C127—44no—
226C22×C4×C127—44no—
227C22×C4×C127—44no—
228C22×C4×C127C2×D414yes—
229C22×C4×C127C2×D414yes—
230C22×C4×C127C2×D414yes—
231C4⋊C4×C127—48no—
232C22⋊C4×C127—216no—
233C22⋊C4×C127—216no—
234C22⋊C4×C127—28no—
235C22⋊C4×C127—48no—
236C22⋊C4×C127—48no—
237C22⋊C4×C127—44no—
238C22⋊C4×C127—44no—
239C22⋊C4×C127—44no—
240C22⋊C4×C127—44no—
241C22⋊C4×C127—44no—
242C22⋊C4×C127—44no—
243C22⋊C4×C127—44no—
244C23×C127—22no—
245C23×C127—22no—
246C23×C127—24no—
247C23×C127—24no—
248C23×C127—22no—
249C23×C127—22no—
250C23×C127—24no—
251C23×C127—24no—
252C23×C127—24no—
253C23×C127—24no—
254C23×C127—24no—
255C23×C127—24no—
256C23×C127—24no—
257C23×C127—24no—
258C23×C127—24no—
259C23×C127—24no—
260C23×C127—232no—
261C23×C127—22no—
262C23×C127—22no—
263C23×C127—22no—
264C23×C127—22no—
265C23×C127—22no—
266C23×C127—22no—
267C23×C127—22no—
268C23×C127—22no—
269C23×C127—24no—
270C23×C127—24no—
271C23×C127—24no—
272C23×C127—24no—
273C23×C127—22no—
274C23×C127—22no—
275C23×C127—22no—
276C23×C127—22no—
277C23×C127—24no—
278C23×C127—24no—
279C23×C127—24no—
280C23×C127—24no—
281C23×C127—24no—
282C23×C127—24no—
283C23×C127—24no—
284C23×C127—24no—
285C23×C127—416no—
286C23×C127—416no—
287C23×C127—416no—
288C23×C127—416no—
289C23×C127—416no—
290C23×C127—432no—
291C23×C127—432no—
292C23×C127—432no—
293C23×C127—432no—
294C23×C127—41no—
295C23×C127—41no—
296C23×C127—41no—
297C23×C127—41no—
298C23×C127—41no—
299C23×C127—41no—
300C23×C127—41no—
301C23×C127—41no—
302C23×C127—42no—
303C23×C127—42no—
304C23×C127—42no—
305C23×C127—42no—
306C23×C127—42no—
307C23×C127—42no—
308C23×C127—42no—
309C23×C127—42no—
310C23×C127—42no—
311C23×C127—42no—
312C23×C127—42no—
313C23×C127—42no—
314C23×C127—416no—
315C23×C127#12014yes—
316C23×C127#12114yes—
317C23×C127#12314yes—
318C23×C127#12314yes—
319C23×C127#12314yes—
320C23×C127#12314yes—
321C23×C127#12414yes—
322C23×C127#12614yes—
323C23×C127#12614yes—
324C23×C127C22×D411yescharacteristic
325C23×C127C22×D412yes—
326C23×C127C22×D411yescharacteristic
327C23×C127C2×#4111yescharacteristic
328C23×C127C2×#4111yescharacteristic
329C23×C127C2×#4111yescharacteristic
330C23×C127C2×#4111yescharacteristic
331C23×C127C2×#4112yes—
332C23×C127C2×#4111yescharacteristic
333C23×C127H(5,𝔽2)12yes—
334C23×C127H(5,𝔽2)12yes—
335C2×C4×C127—24no—
336C2×C4×C127—24no—
337C2×C4×C127—24no—
338C2×C4×C127—24no—
339C2×C4×C127—24no—
340C2×C4×C127—24no—
341C2×C4×C127—24no—
342C2×C4×C127—24no—
343C2×C4×C127—24no—
344C2×C4×C127—416no—
345C2×C4×C127—416no—
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—42no—
354C2×C4×C127—42no—
355C2×C4×C127—42no—
356C2×C4×C127—42no—
357C2×C4×C127—42no—
358C2×C4×C127—41no—
359C2×C4×C127—41no—
360C2×C4×C127—41no—
361C2×C4×C127—41no—
362C2×C4×C127—41no—
363C2×C4×C127—41no—
364C2×C4×C127—41no—
365C2×C4×C127—41no—
366C2×C4×C127—42no—
367C2×C4×C127—42no—
368C2×C4×C127—42no—
369C2×C4×C127—42no—
370C2×C4×C127—41no—
371C2×C4×C127—41no—
372C2×C4×C127—41no—
373C2×C4×C127—41no—
374C2×C4×C127—42no—
375C2×C4×C127—42no—
376C2×C4×C127—42no—
377C2×C4×C127—42no—
378C2×C4×C127—42no—
379C2×C4×C127—42no—
380C2×C4×C127—42no—
381C2×C4×C127—42no—
382C2×C4×C127—42no—
383C2×C4×C127—42no—
384C2×C4×C127—42no—
385C22×C127—24no—
386C22×C127—24no—
387C22×C127—24no—
388C22×C127—24no—
389C22×C127—24no—
390C22×C127—28no—
391C22×C127—28no—
392C22×C127—28no—
393C22×C127—28no—
394C22×C127—24no—
395C22×C127—24no—
396C22×C127—24no—
397C22×C127—24no—
398C22×C127—24no—
399C22×C127—24no—
400C22×C127—24no—
401C22×C127—464no—
402C22×C127—42no—
403C22×C127—42no—
404C22×C127—42no—
405C22×C127—42no—
406C22×C127—42no—
407C22×C127—42no—
408C22×C127—42no—
409C22×C127—44no—
410C22×C127—44no—
411C22×C127—44no—
412C22×C127—44no—
413C22×C127—44no—
414C22×C127—44no—
415C22×C127—44no—
416C22×C127—44no—
417C22×C127—42no—
418C22×C127#39718yescomplemented
419C22×C127C2×#12011yescharacteristic
420C22×C127C2×#12111yescharacteristic
421C22×C127C2×#12311yescharacteristic
422C22×C127C2×#12311yescharacteristic
423C22×C127C2×#12311yescharacteristic
424C22×C127C2×#12311yescharacteristic
425C22×C127#52512yes—
426C22×C127#52512yes—
427C22×C127C2×#12411yescharacteristic
428C22×C127C2×#12611yescharacteristic
429C22×C127C2×#12611yescharacteristic
430C22×C127#53411yescharacteristic
431C22×C127#53411yescharacteristic
432C22×C127#53812yes—
433C22×C127#53812yes—
434C22×C127D4212yes—
435C22×C127#54612yes—
436C22×C127#54612yes—
437C22×C127#54612yes—
438C22×C127#54612yes—
439C22×C127#55112yes—
440C22×C127#55112yes—
441C22×C127#55112yes—
442C4×C127—44no—
443C4×C127—44no—
444C4×C127—44no—
445C4×C127—81no—
446C4×C127—81no—
447C4×C127—81no—
448C4×C127—81no—
449C4×C127—82no—
450#14727C12711yesmaximal, characteristic, direct product factor, Sylow
451C2×C127—28no—
452C2×C127—44no—
453C2×C127—44no—
454C2×C127C2×#39711yescharacteristic
455C2×C127#240511yescharacteristic
456C2×C127#241011yescharacteristic
457C2×C127#241211yescharacteristic
458C2×C127#241812yes—
459C2×C127#247212yes—
460C2×C127#248012yes—
461C2×C127#248012yes—
462C2×C127#248311yescharacteristic
463C2×C127#262211yescharacteristic
464C2×C127#284911yescharacteristic
465C23×C22⋊C4C2×C12711yescharacteristic
466C2×#397C2×C12712yescomplemented
467C2×#385C2×C12711yescharacteristic, complemented
468C2×#379C2×C12711yescharacteristic
469C2×#379C2×C12711yescharacteristic
470#1440C2×C12712yescomplemented
471#1440C2×C12712yescomplemented
472#1439C2×C12712yescomplemented
473C22⋊#95C2×C12711yescharacteristic, complemented
474C22⋊#95C2×C12711yescharacteristic, complemented
475C22⋊#95C2×C12711yescharacteristic, complemented
476C127#1472711yescharacteristic, direct product factor, Sylow
477C26C22×C12711yescharacteristic
478C24×C4C22×C12711yescharacteristic
479C24×C4C22×C12711yescharacteristic
480C22×C4⋊C4C22×C12712yescomplemented
481C22×C22⋊C4—24no—
482C22×C22⋊C4—28no—
483C22×C22⋊C4C22×C12711yescharacteristic
484C22×C22⋊C4C22×C12712yes—
485C22×C22⋊C4C22×C12711yescharacteristic
486C22×C22⋊C4C22×C12711yescharacteristic
487C22×C22⋊C4C22×C12711yescharacteristic
488C22×C22⋊C4C22×C12711yescharacteristic
489C22×C22⋊C4C22×C12712yes—
490C22×C22⋊C4C22×C12712yes—
491C22×C22⋊C4C22×C12712yes—
492C22×C22⋊C4C22×C12711yescharacteristic
493C22×C22⋊C4C22×C12711yescharacteristic
494C22×C22⋊C4C22×C12711yescharacteristic
495#397—28no—
496#385—24no—
497#379—24no—
498#379—24no—
499C2×#95C22×C12712yescomplemented
500C2×#95C22×C12712yescomplemented
501C2×#95C22×C12712yescomplemented
502C2×#95C22×C12712yescomplemented
503C2×#95C22×C12712yescomplemented
504C2×#95C22×C12712yescomplemented
505C2×#95C22×C12712yescomplemented
506C25—24no—
507C25—24no—
508C25—22no—
509C25—22no—
510C25—22no—
511C25—22no—
512C25—22no—
513C25—22no—
514C25—42no—
515C25—42no—
516C25D4×C12714yes—
517C25C23×C12711yescharacteristic
518C25C23×C12711yescharacteristic
519C25C23×C12711yescharacteristic
520C23×C4—22no—
521C23×C4—22no—
522C23×C4—24no—
523C23×C4—24no—
524C23×C4—22no—
525C23×C4—22no—
526C23×C4—22no—
527C23×C4—22no—
528C23×C4—42no—
529C23×C4—42no—
530C23×C4C23×C12711yescharacteristic
531C23×C4C23×C12711yescharacteristic
532C23×C4C23×C12712yes—
533C23×C4C23×C12711yescharacteristic
534C23×C4C23×C12711yescharacteristic
535C23×C4C23×C12712yes—
536C23×C4C23×C12712yes—
537C23×C4C23×C12712yes—
538C2×C4⋊C4—24no—
539C2×C4⋊C4—24no—
540C2×C4⋊C4—42no—
541C2×C22⋊C4—232no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—22no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—24no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—22no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4D4×C12718yes—
573C2×C22⋊C4D4×C12714yes—
574#95—24no—
575#95—24no—
576#95—24no—
577#95—24no—
578#95—42no—
579#95—42no—
580#95—42no—
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—216no—
586C24—216no—
587C24—28no—
588C24—28no—
589C24—28no—
590C24—22no—
591C24—21no—
592C24—21no—
593C24—21no—
594C24—21no—
595C24—21no—
596C24—21no—
597C24—22no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—28no—
609C24—28no—
610C24—44no—
611C24—44no—
612C24—48no—
613C24—48no—
614C24—48no—
615C24—48no—
616C24—48no—
617C24—48no—
618C24—48no—
619C24—48no—
620C24—48no—
621C24—48no—
622C24—44no—
623C24—44no—
624C24—44no—
625C24—44no—
626C24C2×D4×C12712yes—
627C24C2×D4×C12714yes—
628C24C2×D4×C12712yes—
629C24C2×D4×C12712yes—
630C24C2×D4×C12712yes—
631C24#41×C12714yes—
632C24#41×C12712yes—
633C24#41×C12712yes—
634C24#41×C12712yes—
635C24#41×C12712yes—
636C24#41×C12712yes—
637C24C24×C12711yescharacteristic
638C22×C4—28no—
639C22×C4—28no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—21no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—22no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—22no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—48no—
686C22×C4—48no—
687C22×C4—48no—
688C22×C4—48no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—44no—
692C22×C4—44no—
693C22×C4C2×D4×C12714yes—
694C22×C4C2×D4×C12714yes—
695C22×C4C2×D4×C12714yes—
696C4⋊C4—48no—
697C22⋊C4—216no—
698C22⋊C4—216no—
699C22⋊C4—28no—
700C22⋊C4—48no—
701C22⋊C4—48no—
702C22⋊C4—44no—
703C22⋊C4—44no—
704C22⋊C4—44no—
705C22⋊C4—44no—
706C22⋊C4—44no—
707C22⋊C4—44no—
708C22⋊C4—44no—
709C23—22no—
710C23—22no—
711C23—24no—
712C23—24no—
713C23—22no—
714C23—22no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—232no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—24no—
735C23—24no—
736C23—24no—
737C23—24no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—24no—
743C23—24no—
744C23—24no—
745C23—24no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—416no—
751C23—416no—
752C23—416no—
753C23—416no—
754C23—416no—
755C23—432no—
756C23—432no—
757C23—432no—
758C23—432no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—416no—
780C23#120×C12714yes—
781C23#121×C12714yes—
782C23#123×C12714yes—
783C23#123×C12714yes—
784C23#123×C12714yes—
785C23#123×C12714yes—
786C23#124×C12714yes—
787C23#126×C12714yes—
788C23#126×C12714yes—
789C23C22×D4×C12711yescharacteristic
790C23C22×D4×C12712yes—
791C23C22×D4×C12711yescharacteristic
792C23C2×#41×C12711yescharacteristic
793C23C2×#41×C12711yescharacteristic
794C23C2×#41×C12711yescharacteristic
795C23C2×#41×C12711yescharacteristic
796C23C2×#41×C12712yes—
797C23C2×#41×C12711yescharacteristic
798C23H(5,𝔽2)×C12712yes—
799C23H(5,𝔽2)×C12712yes—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—416no—
810C2×C4—416no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C22—24no—
851C22—24no—
852C22—24no—
853C22—24no—
854C22—24no—
855C22—28no—
856C22—28no—
857C22—28no—
858C22—28no—
859C22—24no—
860C22—24no—
861C22—24no—
862C22—24no—
863C22—24no—
864C22—24no—
865C22—24no—
866C22—464no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—44no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—44no—
879C22—44no—
880C22—44no—
881C22—44no—
882C22—42no—
883C22#397×C12718yescomplemented
884C22C2×#120×C12711yescharacteristic
885C22C2×#121×C12711yescharacteristic
886C22C2×#123×C12711yescharacteristic
887C22C2×#123×C12711yescharacteristic
888C22C2×#123×C12711yescharacteristic
889C22C2×#123×C12711yescharacteristic
890C22#525×C12712yes—
891C22#525×C12712yes—
892C22C2×#124×C12711yescharacteristic
893C22C2×#126×C12711yescharacteristic
894C22C2×#126×C12711yescharacteristic
895C22#534×C12711yescharacteristic
896C22#534×C12711yescharacteristic
897C22#538×C12712yes—
898C22#538×C12712yes—
899C22D42×C12712yes—
900C22#546×C12712yes—
901C22#546×C12712yes—
902C22#546×C12712yes—
903C22#546×C12712yes—
904C22#551×C12712yes—
905C22#551×C12712yes—
906C22#551×C12712yes—
907C4—44no—
908C4—44no—
909C4—44no—
910C4—81no—
911C4—81no—
912C4—81no—
913C4—81no—
914C4—82no—
915C2—28no—
916C2—44no—
917C2—44no—
918C2C2×#397×C12711yescharacteristic
919C2C127×#240511yescharacteristic
920C2C127×#241011yescharacteristic
921C2C127×#241211yescharacteristic
922C2C127×#241812yes—
923C2C127×#247212yes—
924C2C127×#248012yes—
925C2C127×#248012yes—
926C2C127×#248311yescharacteristic
927C2C127×#262211yescharacteristic
928C2C127×#284911yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC26×C127C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#397×C127C2semidirect
3. C2×#385×C127C2semidirect
6. C127×#1440C2semidirect
7. C127×#1440C2semidirect
8. C127×#1439C2semidirect
9. C127×C22⋊#95C2semidirect
10. C127×C22⋊#95C2semidirect
11. C127×C22⋊#95C2semidirect
15. C22×C4⋊C4×C127C22semidirect
34. C2×#95×C127C22semidirect
35. C2×#95×C127C22semidirect
36. C2×#95×C127C22semidirect
37. C2×#95×C127C22semidirect
38. C2×#95×C127C22semidirect
39. C2×#95×C127C22semidirect
40. C2×#95×C127C22semidirect
418. C22×C127#397semidirect
450. #14727C127direct (N × H)
466. C2×#397C2×C127semidirect
467. C2×#385C2×C127semidirect
470. #1440C2×C127semidirect
471. #1440C2×C127semidirect
472. #1439C2×C127semidirect
473. C22⋊#95C2×C127semidirect
474. C22⋊#95C2×C127semidirect
475. C22⋊#95C2×C127semidirect
476. C127#14727direct (N × H)
480. C22×C4⋊C4C22×C127semidirect
499. C2×#95C22×C127semidirect
500. C2×#95C22×C127semidirect
501. C2×#95C22×C127semidirect
502. C2×#95C22×C127semidirect
503. C2×#95C22×C127semidirect
504. C2×#95C22×C127semidirect
505. C2×#95C22×C127semidirect
883. C22#397×C127semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C1272
C2×#397×C1272
C2×#385×C1272
C2×#379×C1272
C127×#14402
C127×#14392
C127×C22⋊#952
#14727127