Finite Group Databasebeta

← C127×#15984 #44579657

Subgroups — C127×#15984 #44579657

Order 32512.

2382 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C127C211yesmaximal, characteristic
2C2×#386×C127C211yesmaximal, characteristic, complemented
3C2×#386×C127C211yesmaximal, characteristic, complemented
4C2×#381×C127C211yesmaximal, characteristic, complemented
5C127×#1442C212yesmaximal, complemented
6C127×#1440C212yesmaximal, complemented
7C127×#1440C211yesmaximal, characteristic, complemented
8C127×#1438C212yesmaximal, complemented
9C127×#1438C211yesmaximal, characteristic, complemented
10C127×#1438C211yesmaximal, characteristic, complemented
11C127×C22⋊#95C212yesmaximal, complemented
12C23×D4×C127C2211yescharacteristic
13C23×D4×C127C2211yescharacteristic
14C23×D4×C127C2211yescharacteristic
15C24×C4×C127C2211yescharacteristic
16C24×C4×C127C2211yescharacteristic
17C2×#121×C127—24no—
18C2×#121×C127—24no—
19C2×#121×C127—24no—
20C22×C4⋊C4×C127C2211yescharacteristic
21C22×C22⋊C4×C127C2211yescharacteristic
22C22×C22⋊C4×C127C2212yes—
23C22×C22⋊C4×C127C2212yes—
24C22×C22⋊C4×C127C2211yescharacteristic
25C22×C22⋊C4×C127C2212yes—
26C22×C22⋊C4×C127C2211yescharacteristic
27C22×C22⋊C4×C127C2211yescharacteristic
28C22×C22⋊C4×C127C2211yescharacteristic
29C22×C22⋊C4×C127C2212yes—
30#386×C127—24no—
31#386×C127—24no—
32#381×C127—24no—
33C2×#95×C127C2212yes—
34C2×#95×C127C2212yes—
35C2×#95×C127C2212yes—
36C2×#95×C127C2212yes—
37C2×#95×C127C2212yes—
38C2×#95×C127C2212yes—
39C2×#95×C127C2212yes—
40C2×#95×C127C2212yes—
41C25×C127C2311yescharacteristic
42C25×C127C2311yescharacteristic
43C25×C127C2311yescharacteristic
44C22×D4×C127—22no—
45C22×D4×C127—22no—
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—24no—
54C22×D4×C127—42no—
55C22×D4×C127—42no—
56C22×D4×C127—42no—
57C22×D4×C127D414yes—
58C22×D4×C127D414yes—
59C23×C4×C127—22no—
60C23×C4×C127—22no—
61C23×C4×C127—22no—
62C23×C4×C127—22no—
63C23×C4×C127—24no—
64C23×C4×C127—22no—
65C23×C4×C127—22no—
66C23×C4×C127—24no—
67C23×C4×C127—42no—
68C23×C4×C127—42no—
69C23×C4×C127C2312yes—
70C23×C4×C127C2312yes—
71C23×C4×C127C2312yes—
72C23×C4×C127C2311yescharacteristic
73C23×C4×C127C2311yescharacteristic
74C23×C4×C127C2311yescharacteristic
75C23×C4×C127C2312yes—
76C23×C4×C127C2311yescharacteristic
77#121×C127—232no—
78C2×C4⋊C4×C127—22no—
79C2×C4⋊C4×C127—22no—
80C2×C4⋊C4×C127—22no—
81C2×C22⋊C4×C127—22no—
82C2×C22⋊C4×C127—22no—
83C2×C22⋊C4×C127—22no—
84C2×C22⋊C4×C127—22no—
85C2×C22⋊C4×C127—22no—
86C2×C22⋊C4×C127—22no—
87C2×C22⋊C4×C127—24no—
88C2×C22⋊C4×C127—24no—
89C2×C22⋊C4×C127—22no—
90C2×C22⋊C4×C127—22no—
91C2×C22⋊C4×C127—24no—
92C2×C22⋊C4×C127—24no—
93C2×C22⋊C4×C127—24no—
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—42no—
103C2×C22⋊C4×C127—42no—
104C2×C22⋊C4×C127D414yes—
105#95×C127—24no—
106#95×C127—24no—
107#95×C127—24no—
108#95×C127—24no—
109#95×C127—24no—
110#95×C127—42no—
111#95×C127—42no—
112#95×C127—42no—
113C24×C127—21no—
114C24×C127—21no—
115C24×C127—22no—
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—22no—
130C24×C127—22no—
131C24×C127—22no—
132C24×C127—22no—
133C24×C127—22no—
134C24×C127C2×D412yes—
135C24×C127C2×D412yes—
136C24×C127C2×D412yes—
137C24×C127C2×D412yes—
138C24×C127C2×D412yes—
139C24×C127#4114yes—
140C24×C127C2411yescharacteristic
141C2×D4×C127—28no—
142C2×D4×C127—28no—
143C2×D4×C127—28no—
144C2×D4×C127—28no—
145C2×D4×C127—28no—
146C2×D4×C127—44no—
147C2×D4×C127—44no—
148C2×D4×C127—48no—
149C2×D4×C127—48no—
150C2×D4×C127—48no—
151C2×D4×C127—48no—
152C2×D4×C127—48no—
153C2×D4×C127—48no—
154C2×D4×C127—44no—
155C2×D4×C127—44no—
156C22×C4×C127—21no—
157C22×C4×C127—21no—
158C22×C4×C127—22no—
159C22×C4×C127—28no—
160C22×C4×C127—28no—
161C22×C4×C127—22no—
162C22×C4×C127—22no—
163C22×C4×C127—22no—
164C22×C4×C127—21no—
165C22×C4×C127—21no—
166C22×C4×C127—21no—
167C22×C4×C127—21no—
168C22×C4×C127—21no—
169C22×C4×C127—21no—
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—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—48no—
201C22×C4×C127—48no—
202C22×C4×C127—48no—
203C22×C4×C127—48no—
204C22×C4×C127—44no—
205C22×C4×C127—44no—
206C22×C4×C127—44no—
207C22×C4×C127—44no—
208C22×C4×C127C2×D412yes—
209C22×C4×C127C2×D412yes—
210C22×C4×C127C2×D412yes—
211C22×C4×C127C2×D412yes—
212C22×C4×C127#4114yes—
213C22×C4×C127#4114yes—
214C4⋊C4×C127—28no—
215C22⋊C4×C127—28no—
216C22⋊C4×C127—28no—
217C22⋊C4×C127—48no—
218C22⋊C4×C127—48no—
219C22⋊C4×C127—44no—
220C22⋊C4×C127—44no—
221C22⋊C4×C127—44no—
222C22⋊C4×C127—48no—
223C22⋊C4×C127—48no—
224C23×C127—22no—
225C23×C127—22no—
226C23×C127—22no—
227C23×C127—22no—
228C23×C127—24no—
229C23×C127—22no—
230C23×C127—22no—
231C23×C127—22no—
232C23×C127—22no—
233C23×C127—24no—
234C23×C127—24no—
235C23×C127—24no—
236C23×C127—24no—
237C23×C127—24no—
238C23×C127—24no—
239C23×C127—24no—
240C23×C127—24no—
241C23×C127—24no—
242C23×C127—24no—
243C23×C127—24no—
244C23×C127—24no—
245C23×C127—24no—
246C23×C127—22no—
247C23×C127—22no—
248C23×C127—22no—
249C23×C127—24no—
250C23×C127—24no—
251C23×C127—41no—
252C23×C127—41no—
253C23×C127—42no—
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—41no—
270C23×C127—41no—
271C23×C127—42no—
272C23×C127—41no—
273C23×C127—41no—
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#12014yes—
286C23×C127#12314yes—
287C23×C127C22×D411yescharacteristic
288C23×C127C22×D411yescharacteristic
289C23×C127C22×D411yescharacteristic
290C23×C127C2×#4112yes—
291C23×C127C2×#4112yes—
292C23×C127C2×#4112yes—
293C23×C127H(5,𝔽2)12yes—
294C23×C127H(5,𝔽2)12yes—
295C23×C127H(5,𝔽2)12yes—
296D4×C127—416no—
297D4×C127—416no—
298D4×C127—416no—
299C2×C4×C127—22no—
300C2×C4×C127—22no—
301C2×C4×C127—24no—
302C2×C4×C127—24no—
303C2×C4×C127—22no—
304C2×C4×C127—22no—
305C2×C4×C127—22no—
306C2×C4×C127—22no—
307C2×C4×C127—24no—
308C2×C4×C127—22no—
309C2×C4×C127—24no—
310C2×C4×C127—24no—
311C2×C4×C127—24no—
312C2×C4×C127—24no—
313C2×C4×C127—416no—
314C2×C4×C127—416no—
315C2×C4×C127—42no—
316C2×C4×C127—41no—
317C2×C4×C127—41no—
318C2×C4×C127—41no—
319C2×C4×C127—41no—
320C2×C4×C127—42no—
321C2×C4×C127—42no—
322C2×C4×C127—42no—
323C2×C4×C127—42no—
324C2×C4×C127—42no—
325C2×C4×C127—42no—
326C2×C4×C127—42no—
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—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#12314yes—
349C22×C127—24no—
350C22×C127—24no—
351C22×C127—24no—
352C22×C127—24no—
353C22×C127—28no—
354C22×C127—42no—
355C22×C127—42no—
356C22×C127—44no—
357C22×C127—44no—
358C22×C127—44no—
359C22×C127—44no—
360C22×C127—44no—
361C22×C127—44no—
362C22×C127—44no—
363C22×C127—44no—
364C22×C127—44no—
365C22×C127—44no—
366C22×C127—44no—
367C22×C127—42no—
368C22×C127—42no—
369C22×C127—42no—
370C22×C127—44no—
371C22×C127—44no—
372C22×C127—82no—
373C22×C127—82no—
374C22×C127—82no—
375C22×C127—82no—
376C22×C127C2×#12011yescharacteristic
377C22×C127C2×#12311yescharacteristic
378C22×C127C2×#12311yescharacteristic
379C22×C127#52511yescharacteristic
380C22×C127#52912yes—
381C22×C127#53411yescharacteristic
382C22×C127#53411yescharacteristic
383C22×C127#53511yescharacteristic
384C22×C127#53812yes—
385C22×C127#54012yes—
386C22×C127#54012yes—
387C22×C127#54612yes—
388C22×C127#54612yes—
389C22×C127#54612yes—
390C22×C127#54612yes—
391C22×C127#54612yes—
392C22×C127#54612yes—
393C22×C127#55312yes—
394C22×C127#55312yes—
395C22×C127#55512yes—
396C22×C127#56012yes—
397C4×C127—24no—
398C4×C127—44no—
399C4×C127—42no—
400C4×C127—42no—
401C4×C127—42no—
402C4×C127—82no—
403C4×C127—82no—
404C4×C127—82no—
405#15984C12711yesmaximal, characteristic, direct product factor, Sylow
406C2×C127—44no—
407C2×C127—44no—
408C2×C127—82no—
409C2×C127#240411yescharacteristic
410C2×C127#240511yescharacteristic
411C2×C127#240511yescharacteristic
412C2×C127#242012yes—
413C2×C127#244412yes—
414C2×C127#247612yes—
415C2×C127#268812yes—
416C2×C127#269912yes—
417C2×C127#270312yes—
418C22×#121C2×C12711yescharacteristic
419C2×#386C2×C12711yescharacteristic, complemented
420C2×#386C2×C12711yescharacteristic, complemented
421C2×#381C2×C12711yescharacteristic, complemented
422#1442C2×C12712yescomplemented
423#1440C2×C12712yescomplemented
424#1440C2×C12711yescharacteristic, complemented
425#1438C2×C12712yescomplemented
426#1438C2×C12711yescharacteristic, complemented
427#1438C2×C12711yescharacteristic, complemented
428C22⋊#95C2×C12712yescomplemented
429C127#1598411yescharacteristic, direct product factor, Sylow
430C23×D4C22×C12711yescharacteristic
431C23×D4C22×C12711yescharacteristic
432C23×D4C22×C12711yescharacteristic
433C24×C4C22×C12711yescharacteristic
434C24×C4C22×C12711yescharacteristic
435C2×#121—24no—
436C2×#121—24no—
437C2×#121—24no—
438C22×C4⋊C4C22×C12711yescharacteristic
439C22×C22⋊C4C22×C12711yescharacteristic
440C22×C22⋊C4C22×C12712yes—
441C22×C22⋊C4C22×C12712yes—
442C22×C22⋊C4C22×C12711yescharacteristic
443C22×C22⋊C4C22×C12712yes—
444C22×C22⋊C4C22×C12711yescharacteristic
445C22×C22⋊C4C22×C12711yescharacteristic
446C22×C22⋊C4C22×C12711yescharacteristic
447C22×C22⋊C4C22×C12712yes—
448#386—24no—
449#386—24no—
450#381—24no—
451C2×#95C22×C12712yes—
452C2×#95C22×C12712yes—
453C2×#95C22×C12712yes—
454C2×#95C22×C12712yes—
455C2×#95C22×C12712yes—
456C2×#95C22×C12712yes—
457C2×#95C22×C12712yes—
458C2×#95C22×C12712yes—
459C25C23×C12711yescharacteristic
460C25C23×C12711yescharacteristic
461C25C23×C12711yescharacteristic
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4—22no—
466C22×D4—22no—
467C22×D4—22no—
468C22×D4—24no—
469C22×D4—24no—
470C22×D4—22no—
471C22×D4—24no—
472C22×D4—42no—
473C22×D4—42no—
474C22×D4—42no—
475C22×D4D4×C12714yes—
476C22×D4D4×C12714yes—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—22no—
480C23×C4—22no—
481C23×C4—24no—
482C23×C4—22no—
483C23×C4—22no—
484C23×C4—24no—
485C23×C4—42no—
486C23×C4—42no—
487C23×C4C23×C12712yes—
488C23×C4C23×C12712yes—
489C23×C4C23×C12712yes—
490C23×C4C23×C12711yescharacteristic
491C23×C4C23×C12711yescharacteristic
492C23×C4C23×C12711yescharacteristic
493C23×C4C23×C12712yes—
494C23×C4C23×C12711yescharacteristic
495#121—232no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4D4×C12714yes—
523#95—24no—
524#95—24no—
525#95—24no—
526#95—24no—
527#95—24no—
528#95—42no—
529#95—42no—
530#95—42no—
531C24—21no—
532C24—21no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—21no—
545C24—21no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24C2×D4×C12712yes—
553C24C2×D4×C12712yes—
554C24C2×D4×C12712yes—
555C24C2×D4×C12712yes—
556C24C2×D4×C12712yes—
557C24#41×C12714yes—
558C24C24×C12711yescharacteristic
559C2×D4—28no—
560C2×D4—28no—
561C2×D4—28no—
562C2×D4—28no—
563C2×D4—28no—
564C2×D4—44no—
565C2×D4—44no—
566C2×D4—48no—
567C2×D4—48no—
568C2×D4—48no—
569C2×D4—48no—
570C2×D4—48no—
571C2×D4—48no—
572C2×D4—44no—
573C2×D4—44no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—28no—
578C22×C4—28no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
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—48no—
619C22×C4—48no—
620C22×C4—48no—
621C22×C4—48no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4C2×D4×C12712yes—
627C22×C4C2×D4×C12712yes—
628C22×C4C2×D4×C12712yes—
629C22×C4C2×D4×C12712yes—
630C22×C4#41×C12714yes—
631C22×C4#41×C12714yes—
632C4⋊C4—28no—
633C22⋊C4—28no—
634C22⋊C4—28no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—24no—
668C23—24no—
669C23—41no—
670C23—41no—
671C23—42no—
672C23—41no—
673C23—41no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—41no—
688C23—41no—
689C23—42no—
690C23—41no—
691C23—41no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23#120×C12714yes—
704C23#123×C12714yes—
705C23C22×D4×C12711yescharacteristic
706C23C22×D4×C12711yescharacteristic
707C23C22×D4×C12711yescharacteristic
708C23C2×#41×C12712yes—
709C23C2×#41×C12712yes—
710C23C2×#41×C12712yes—
711C23H(5,𝔽2)×C12712yes—
712C23H(5,𝔽2)×C12712yes—
713C23H(5,𝔽2)×C12712yes—
714D4—416no—
715D4—416no—
716D4—416no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—416no—
732C2×C4—416no—
733C2×C4—42no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
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#123×C12714yes—
767C22—24no—
768C22—24no—
769C22—24no—
770C22—24no—
771C22—28no—
772C22—42no—
773C22—42no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—44no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—44no—
789C22—44no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22C2×#120×C12711yescharacteristic
795C22C2×#123×C12711yescharacteristic
796C22C2×#123×C12711yescharacteristic
797C22#525×C12711yescharacteristic
798C22#529×C12712yes—
799C22#534×C12711yescharacteristic
800C22#534×C12711yescharacteristic
801C22#535×C12711yescharacteristic
802C22#538×C12712yes—
803C22#540×C12712yes—
804C22#540×C12712yes—
805C22#546×C12712yes—
806C22#546×C12712yes—
807C22#546×C12712yes—
808C22#546×C12712yes—
809C22#546×C12712yes—
810C22#546×C12712yes—
811C22#553×C12712yes—
812C22#553×C12712yes—
813C22#555×C12712yes—
814C22#560×C12712yes—
815C4—24no—
816C4—44no—
817C4—42no—
818C4—42no—
819C4—42no—
820C4—82no—
821C4—82no—
822C4—82no—
823C2—44no—
824C2—44no—
825C2—82no—
826C2C127×#240411yescharacteristic
827C2C127×#240511yescharacteristic
828C2C127×#240511yescharacteristic
829C2C127×#242012yes—
830C2C127×#244412yes—
831C2C127×#247612yes—
832C2C127×#268812yes—
833C2C127×#269912yes—
834C2C127×#270312yes—
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×#386×C127C2semidirect
3. C2×#386×C127C2semidirect
4. C2×#381×C127C2semidirect
5. C127×#1442C2semidirect
6. C127×#1440C2semidirect
7. C127×#1440C2semidirect
8. C127×#1438C2semidirect
9. C127×#1438C2semidirect
10. C127×#1438C2semidirect
11. C127×C22⋊#95C2semidirect
405. #15984C127direct (N × H)
419. C2×#386C2×C127semidirect
420. C2×#386C2×C127semidirect
421. C2×#381C2×C127semidirect
422. #1442C2×C127semidirect
423. #1440C2×C127semidirect
424. #1440C2×C127semidirect
425. #1438C2×C127semidirect
426. #1438C2×C127semidirect
427. #1438C2×C127semidirect
428. C22⋊#95C2×C127semidirect
429. C127#15984direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#121×C1272
C2×#386×C1272
C2×#381×C1272
C127×#14422
C127×#14402
C127×#14382
C127×C22⋊#952
#15984127