Finite Group Databasebeta

← C127×#14228 #44577901

Subgroups — C127×#14228 #44577901

Order 32512.

2462 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#392×C127C211yesmaximal, characteristic
2C2×#390×C127C212yesmaximal, complemented
3C2×#390×C127C211yesmaximal, characteristic, complemented
4C2×#388×C127C212yesmaximal, complemented
5C2×#386×C127C212yesmaximal, complemented
6C2×C4×C22⋊C4×C127C211yesmaximal, characteristic, complemented
7C127×#1444C211yesmaximal, characteristic, complemented
8C127×#1439C211yesmaximal, characteristic, complemented
9C127×#1438C211yesmaximal, characteristic, complemented
10C127×#1437C212yesmaximal, complemented
11C4×#95×C127C211yesmaximal, characteristic, complemented
12C23×D4×C127C2212yes—
13C23×D4×C127C2211yescharacteristic
14C24×C4×C127C2211yescharacteristic
15C22×C4⋊C4×C127C2212yes—
16C22×C4⋊C4×C127C2211yescharacteristic
17C22×C22⋊C4×C127C2212yes—
18C22×C22⋊C4×C127C2212yes—
19C22×C22⋊C4×C127C2212yes—
20C22×C22⋊C4×C127C2212yes—
21C22×C22⋊C4×C127C2212yes—
22C22×C22⋊C4×C127C2211yescharacteristic
23C22×C22⋊C4×C127C2212yes—
24C22×C22⋊C4×C127C2211yescharacteristic
25C22×C42×C127C2211yescharacteristic
26C22×C42×C127C2212yes—
27C22×C42×C127C2211yescharacteristic
28#392×C127C418yescomplemented
29#390×C127—28no—
30#390×C127—24no—
31#388×C127—28no—
32#386×C127—28no—
33C4×C22⋊C4×C127—24no—
34C2×#95×C127C2211yescharacteristic
35C2×#95×C127C2211yescharacteristic
36C2×#95×C127C2212yes—
37C2×#95×C127C2212yes—
38C2×#95×C127C2211yescharacteristic
39C2×#95×C127C2211yescharacteristic
40C2×#95×C127C2212yes—
41C25×C127C2312yes—
42C25×C127C2311yescharacteristic
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—42no—
50C22×D4×C127—42no—
51C22×D4×C127—42no—
52C22×D4×C127—42no—
53C22×D4×C127C2×C418yes—
54C22×D4×C127C2×C414yescomplemented
55C23×C4×C127—22no—
56C23×C4×C127—22no—
57C23×C4×C127—22no—
58C23×C4×C127—24no—
59C23×C4×C127—42no—
60C23×C4×C127C2312yes—
61C23×C4×C127C2311yescharacteristic
62C23×C4×C127C2311yescharacteristic
63C23×C4×C127C2312yes—
64C23×C4×C127C2311yescharacteristic
65C23×C4×C127C2312yes—
66C23×C4×C127C2311yescharacteristic
67C23×C4×C127C2311yescharacteristic
68C23×C4×C127C2311yescharacteristic
69C2×C4⋊C4×C127—24no—
70C2×C4⋊C4×C127—24no—
71C2×C4⋊C4×C127—22no—
72C2×C4⋊C4×C127—42no—
73C2×C4⋊C4×C127—42no—
74C2×C22⋊C4×C127—22no—
75C2×C22⋊C4×C127—22no—
76C2×C22⋊C4×C127—24no—
77C2×C22⋊C4×C127—22no—
78C2×C22⋊C4×C127—24no—
79C2×C22⋊C4×C127—22no—
80C2×C22⋊C4×C127—24no—
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—24no—
92C2×C22⋊C4×C127—42no—
93C2×C22⋊C4×C127—42no—
94C2×C22⋊C4×C127—42no—
95C2×C22⋊C4×C127C2×C414yes—
96C2×C22⋊C4×C127C2×C418yescomplemented
97C2×C22⋊C4×C127D414yescomplemented
98C2×C42×C127—22no—
99C2×C42×C127—24no—
100C2×C42×C127—24no—
101C2×C42×C127—24no—
102C2×C42×C127—42no—
103C2×C42×C127—42no—
104C2×C42×C127D414yescomplemented
105#95×C127—22no—
106#95×C127—22no—
107#95×C127—24no—
108#95×C127—24no—
109#95×C127—22no—
110#95×C127C2×C414yescomplemented
111#95×C127D418yescomplemented
112C24×C127—21no—
113C24×C127—22no—
114C24×C127—21no—
115C24×C127—21no—
116C24×C127—21no—
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—22no—
127C24×C127—22no—
128C24×C127—22no—
129C24×C127—22no—
130C24×C127—22no—
131C24×C127—22no—
132C24×C127—22no—
133C24×C127—22no—
134C24×C127C22×C414yes—
135C24×C127C22×C412yes—
136C24×C127C2×D412yes—
137C24×C127#4112yes—
138C24×C127C2411yescharacteristic
139C2×D4×C127—216no—
140C2×D4×C127—216no—
141C2×D4×C127—28no—
142C2×D4×C127—48no—
143C2×D4×C127—48no—
144C2×D4×C127—48no—
145C2×D4×C127—48no—
146C2×D4×C127—48no—
147C2×D4×C127—48no—
148C2×D4×C127—44no—
149C2×D4×C127—44no—
150C2×D4×C127—48no—
151C22×C4×C127—22no—
152C22×C4×C127—22no—
153C22×C4×C127—21no—
154C22×C4×C127—21no—
155C22×C4×C127—22no—
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—28no—
163C22×C4×C127—21no—
164C22×C4×C127—21no—
165C22×C4×C127—22no—
166C22×C4×C127—21no—
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—22no—
174C22×C4×C127—21no—
175C22×C4×C127—22no—
176C22×C4×C127—21no—
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—48no—
189C22×C4×C127—48no—
190C22×C4×C127—44no—
191C22×C4×C127—44no—
192C22×C4×C127C22×C412yes—
193C22×C4×C127C22×C412yes—
194C22×C4×C127C22×C414yes—
195C22×C4×C127C2×D414yes—
196C22×C4×C127C2×D412yes—
197C22×C4×C127C2×D414yes—
198C22×C4×C127C2×D412yes—
199C22×C4×C127C2×D412yes—
200C22×C4×C127C2×D412yes—
201C22×C4×C127C2×D414yes—
202C22×C4×C127C2×D412yes—
203C22×C4×C127#4112yes—
204C22×C4×C127#4112yes—
205C22×C4×C127#4114yes—
206C22×C4×C127#4112yes—
207C4⋊C4×C127—48no—
208C4⋊C4×C127—44no—
209C22⋊C4×C127—28no—
210C22⋊C4×C127—216no—
211C22⋊C4×C127—28no—
212C22⋊C4×C127—48no—
213C22⋊C4×C127—48no—
214C22⋊C4×C127—48no—
215C22⋊C4×C127—48no—
216C22⋊C4×C127—48no—
217C42×C127—44no—
218C42×C127—48no—
219C42×C127—44no—
220C23×C127—22no—
221C23×C127—24no—
222C23×C127—22no—
223C23×C127—24no—
224C23×C127—22no—
225C23×C127—22no—
226C23×C127—22no—
227C23×C127—22no—
228C23×C127—24no—
229C23×C127—24no—
230C23×C127—24no—
231C23×C127—24no—
232C23×C127—24no—
233C23×C127—24no—
234C23×C127—24no—
235C23×C127—24no—
236C23×C127—24no—
237C23×C127—24no—
238C23×C127—24no—
239C23×C127—41no—
240C23×C127—41no—
241C23×C127—42no—
242C23×C127—41no—
243C23×C127—41no—
244C23×C127—42no—
245C23×C127—42no—
246C23×C127—42no—
247C23×C127—42no—
248C23×C127—42no—
249C23×C127—42no—
250C23×C127—42no—
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×C127—42no—
272C23×C127—42no—
273C23×C127—42no—
274C23×C127—42no—
275C23×C127—42no—
276C23×C127—42no—
277C23×C127C4×D414yes—
278C23×C127C23×C411yescharacteristic
279C23×C127C22×D411yescharacteristic
280C23×C127C22×D411yescharacteristic
281C23×C127C22×D412yes—
282C23×C127C2×#4111yescharacteristic
283C23×C127C2×#4111yescharacteristic
284C23×C127C2×#4112yes—
285C23×C127C2×#4111yescharacteristic
286C23×C127C2×#4111yescharacteristic
287C23×C127H(5,𝔽2)12yes—
288C23×C127H(5,𝔽2)12yes—
289D4×C127—432no—
290D4×C127—416no—
291C2×C4×C127—24no—
292C2×C4×C127—24no—
293C2×C4×C127—24no—
294C2×C4×C127—22no—
295C2×C4×C127—22no—
296C2×C4×C127—22no—
297C2×C4×C127—22no—
298C2×C4×C127—22no—
299C2×C4×C127—22no—
300C2×C4×C127—24no—
301C2×C4×C127—24no—
302C2×C4×C127—24no—
303C2×C4×C127—24no—
304C2×C4×C127—24no—
305C2×C4×C127—24no—
306C2×C4×C127—24no—
307C2×C4×C127—24no—
308C2×C4×C127—24no—
309C2×C4×C127—22no—
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—416no—
319C2×C4×C127—41no—
320C2×C4×C127—41no—
321C2×C4×C127—41no—
322C2×C4×C127—41no—
323C2×C4×C127—42no—
324C2×C4×C127—42no—
325C2×C4×C127—41no—
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—42no—
334C2×C4×C127—42no—
335C2×C4×C127—42no—
336C2×C4×C127—42no—
337C2×C4×C127—42no—
338C2×C4×C127—42no—
339C2×C4×C127C4×D414yes—
340C2×C4×C127C4×D418yes—
341C2×C4×C127#12114yes—
342C2×C4×C127#12714yes—
343C22×C127—28no—
344C22×C127—24no—
345C22×C127—42no—
346C22×C127—42no—
347C22×C127—42no—
348C22×C127—44no—
349C22×C127—42no—
350C22×C127—42no—
351C22×C127—42no—
352C22×C127—44no—
353C22×C127—44no—
354C22×C127—44no—
355C22×C127—44no—
356C22×C127—44no—
357C22×C127—44no—
358C22×C127—44no—
359C22×C127—44no—
360C22×C127—44no—
361C22×C127—82no—
362C22×C127—82no—
363C22×C127—82no—
364C22×C127—82no—
365C22×C127—82no—
366C22×C127—82no—
367C22×C127—82no—
368C22×C127—82no—
369C22×C127C2×C4×D411yescharacteristic
370C22×C127C2×C4×D412yes—
371C22×C127C2×C4×D411yescharacteristic
372C22×C127C4×#4111yescharacteristic
373C22×C127#51812yes—
374C22×C127C2×#12111yescharacteristic
375C22×C127#52511yescharacteristic
376C22×C127#52911yescharacteristic
377C22×C127C2×#12711yescharacteristic
378C22×C127#53211yescharacteristic
379C22×C127#53212yes—
380C22×C127#53211yescharacteristic
381C22×C127#53411yescharacteristic
382C22×C127#53511yescharacteristic
383C22×C127#53812yes—
384C22×C127D4212yes—
385C22×C127#54612yes—
386C22×C127#54612yes—
387C22×C127#54612yes—
388C22×C127#55012yes—
389C22×C127#55112yes—
390C22×C127#55312yes—
391C22×C127#55512yes—
392C4×C127—24no—
393C4×C127—28no—
394C4×C127—24no—
395C4×C127—24no—
396C4×C127—42no—
397C4×C127—42no—
398C4×C127—42no—
399C4×C127—44no—
400C4×C127—82no—
401#14228C12711yesmaximal, characteristic, direct product factor, Sylow
402C2×C127—44no—
403C2×C127—84no—
404C2×C127C4×#12111yescharacteristic
405C2×C127C4×#12711yescharacteristic
406C2×C127#232111yescharacteristic
407C2×C127#235812yes—
408C2×C127#236312yes—
409C2×C127#253911yescharacteristic
410C2×C127#254111yescharacteristic
411C2×C127#254311yescharacteristic
412C2×C127#255412yes—
413C2×C127#255512yes—
414C2×C127#261011yescharacteristic
415C2×#392C2×C12711yescharacteristic
416C2×#390C2×C12711yescharacteristic, complemented
417C2×#390C2×C12712yescomplemented
418C2×#388C2×C12712yescomplemented
419C2×#386C2×C12712yescomplemented
420C2×C4×C22⋊C4C2×C12711yescharacteristic, complemented
421#1444C2×C12711yescharacteristic, complemented
422#1439C2×C12711yescharacteristic, complemented
423#1438C2×C12711yescharacteristic, complemented
424#1437C2×C12712yescomplemented
425C4×#95C2×C12711yescharacteristic, complemented
426C127#1422811yescharacteristic, direct product factor, Sylow
427C23×D4C22×C12712yes—
428C23×D4C22×C12711yescharacteristic
429C24×C4C22×C12711yescharacteristic
430C22×C4⋊C4C22×C12712yes—
431C22×C4⋊C4C22×C12711yescharacteristic
432C22×C22⋊C4C22×C12712yes—
433C22×C22⋊C4C22×C12712yes—
434C22×C22⋊C4C22×C12712yes—
435C22×C22⋊C4C22×C12712yes—
436C22×C22⋊C4C22×C12712yes—
437C22×C22⋊C4C22×C12711yescharacteristic
438C22×C22⋊C4C22×C12712yes—
439C22×C22⋊C4C22×C12711yescharacteristic
440C22×C42C22×C12711yescharacteristic
441C22×C42C22×C12712yes—
442C22×C42C22×C12711yescharacteristic
443#392C4×C12718yescomplemented
444#390—28no—
445#390—24no—
446#388—28no—
447#386—28no—
448C4×C22⋊C4—24no—
449C2×#95C22×C12711yescharacteristic
450C2×#95C22×C12711yescharacteristic
451C2×#95C22×C12712yes—
452C2×#95C22×C12712yes—
453C2×#95C22×C12711yescharacteristic
454C2×#95C22×C12711yescharacteristic
455C2×#95C22×C12712yes—
456C25C23×C12712yes—
457C25C23×C12711yescharacteristic
458C22×D4—24no—
459C22×D4—24no—
460C22×D4—24no—
461C22×D4—22no—
462C22×D4—22no—
463C22×D4—24no—
464C22×D4—42no—
465C22×D4—42no—
466C22×D4—42no—
467C22×D4—42no—
468C22×D4C2×C4×C12718yes—
469C22×D4C2×C4×C12714yescomplemented
470C23×C4—22no—
471C23×C4—22no—
472C23×C4—22no—
473C23×C4—24no—
474C23×C4—42no—
475C23×C4C23×C12712yes—
476C23×C4C23×C12711yescharacteristic
477C23×C4C23×C12711yescharacteristic
478C23×C4C23×C12712yes—
479C23×C4C23×C12711yescharacteristic
480C23×C4C23×C12712yes—
481C23×C4C23×C12711yescharacteristic
482C23×C4C23×C12711yescharacteristic
483C23×C4C23×C12711yescharacteristic
484C2×C4⋊C4—24no—
485C2×C4⋊C4—24no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—42no—
488C2×C4⋊C4—42no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4C2×C4×C12714yes—
511C2×C22⋊C4C2×C4×C12718yescomplemented
512C2×C22⋊C4D4×C12714yescomplemented
513C2×C42—22no—
514C2×C42—24no—
515C2×C42—24no—
516C2×C42—24no—
517C2×C42—42no—
518C2×C42—42no—
519C2×C42D4×C12714yescomplemented
520#95—22no—
521#95—22no—
522#95—24no—
523#95—24no—
524#95—22no—
525#95C2×C4×C12714yescomplemented
526#95D4×C12718yescomplemented
527C24—21no—
528C24—22no—
529C24—21no—
530C24—21no—
531C24—21no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24C22×C4×C12714yes—
550C24C22×C4×C12712yes—
551C24C2×D4×C12712yes—
552C24#41×C12712yes—
553C24C24×C12711yescharacteristic
554C2×D4—216no—
555C2×D4—216no—
556C2×D4—28no—
557C2×D4—48no—
558C2×D4—48no—
559C2×D4—48no—
560C2×D4—48no—
561C2×D4—48no—
562C2×D4—48no—
563C2×D4—44no—
564C2×D4—44no—
565C2×D4—48no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—28no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—21no—
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—48no—
604C22×C4—48no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4C22×C4×C12712yes—
608C22×C4C22×C4×C12712yes—
609C22×C4C22×C4×C12714yes—
610C22×C4C2×D4×C12714yes—
611C22×C4C2×D4×C12712yes—
612C22×C4C2×D4×C12714yes—
613C22×C4C2×D4×C12712yes—
614C22×C4C2×D4×C12712yes—
615C22×C4C2×D4×C12712yes—
616C22×C4C2×D4×C12714yes—
617C22×C4C2×D4×C12712yes—
618C22×C4#41×C12712yes—
619C22×C4#41×C12712yes—
620C22×C4#41×C12714yes—
621C22×C4#41×C12712yes—
622C4⋊C4—48no—
623C4⋊C4—44no—
624C22⋊C4—28no—
625C22⋊C4—216no—
626C22⋊C4—28no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C42—44no—
633C42—48no—
634C42—44no—
635C23—22no—
636C23—24no—
637C23—22no—
638C23—24no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—41no—
655C23—41no—
656C23—42no—
657C23—41no—
658C23—41no—
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—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23C4×D4×C12714yes—
693C23C23×C4×C12711yescharacteristic
694C23C22×D4×C12711yescharacteristic
695C23C22×D4×C12711yescharacteristic
696C23C22×D4×C12712yes—
697C23C2×#41×C12711yescharacteristic
698C23C2×#41×C12711yescharacteristic
699C23C2×#41×C12712yes—
700C23C2×#41×C12711yescharacteristic
701C23C2×#41×C12711yescharacteristic
702C23H(5,𝔽2)×C12712yes—
703C23H(5,𝔽2)×C12712yes—
704D4—432no—
705D4—416no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—416no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—41no—
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×C4C4×D4×C12714yes—
755C2×C4C4×D4×C12718yes—
756C2×C4#121×C12714yes—
757C2×C4#127×C12714yes—
758C22—28no—
759C22—24no—
760C22—42no—
761C22—42no—
762C22—44no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—44no—
767C22—44no—
768C22—42no—
769C22—44no—
770C22—44no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22C2×C4×D4×C12711yescharacteristic
785C22C2×C4×D4×C12711yescharacteristic
786C22C2×C4×D4×C12712yes—
787C22C4×#41×C12711yescharacteristic
788C22#518×C12712yes—
789C22C2×#121×C12711yescharacteristic
790C22#525×C12711yescharacteristic
791C22#529×C12711yescharacteristic
792C22C2×#127×C12711yescharacteristic
793C22#532×C12711yescharacteristic
794C22#532×C12712yes—
795C22#532×C12711yescharacteristic
796C22#534×C12711yescharacteristic
797C22#535×C12711yescharacteristic
798C22#538×C12712yes—
799C22D42×C12712yes—
800C22#546×C12712yes—
801C22#546×C12712yes—
802C22#546×C12712yes—
803C22#550×C12712yes—
804C22#551×C12712yes—
805C22#553×C12712yes—
806C22#555×C12712yes—
807C4—24no—
808C4—28no—
809C4—24no—
810C4—24no—
811C4—42no—
812C4—42no—
813C4—44no—
814C4—42no—
815C4—82no—
816C2—44no—
817C2—84no—
818C2C4×#121×C12711yescharacteristic
819C2C4×#127×C12711yescharacteristic
820C2C127×#232111yescharacteristic
821C2C127×#235812yes—
822C2C127×#236312yes—
823C2C127×#253911yescharacteristic
824C2C127×#254111yescharacteristic
825C2C127×#254311yescharacteristic
826C2C127×#255412yes—
827C2C127×#255512yes—
828C2C127×#261011yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC2×#392×C127C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#390×C127C2semidirect
3. C2×#390×C127C2semidirect
4. C2×#388×C127C2semidirect
5. C2×#386×C127C2semidirect
6. C2×C4×C22⋊C4×C127C2semidirect
7. C127×#1444C2semidirect
8. C127×#1439C2semidirect
9. C127×#1438C2semidirect
10. C127×#1437C2semidirect
11. C4×#95×C127C2semidirect
28. #392×C127C4semidirect
54. C22×D4×C127C2×C4semidirect
96. C2×C22⋊C4×C127C2×C4semidirect
97. C2×C22⋊C4×C127D4semidirect
104. C2×C42×C127D4semidirect
110. #95×C127C2×C4semidirect
111. #95×C127D4semidirect
401. #14228C127direct (N × H)
416. C2×#390C2×C127semidirect
417. C2×#390C2×C127semidirect
418. C2×#388C2×C127semidirect
419. C2×#386C2×C127semidirect
420. C2×C4×C22⋊C4C2×C127semidirect
421. #1444C2×C127semidirect
422. #1439C2×C127semidirect
423. #1438C2×C127semidirect
424. #1437C2×C127semidirect
425. C4×#95C2×C127semidirect
426. C127#14228direct (N × H)
443. #392C4×C127semidirect
469. C22×D4C2×C4×C127semidirect
511. C2×C22⋊C4C2×C4×C127semidirect
512. C2×C22⋊C4D4×C127semidirect
519. C2×C42D4×C127semidirect
525. #95C2×C4×C127semidirect
526. #95D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#392×C1272
C2×#390×C1272
C2×#388×C1272
C2×#386×C1272
C2×C4×C22⋊C4×C1272
C127×#14442
C127×#14392
C127×#14382
C127×#14372
C4×#95×C1272
#14228127