Finite Group Databasebeta

← C127×#14969 #44578642

Subgroups — C127×#14969 #44578642

Order 32512.

1686 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C127C211yesmaximal, characteristic, complemented
2C2×#387×C127C212yesmaximal, complemented
3C2×#385×C127C212yesmaximal
4C2×C4×C22⋊C4×C127C211yesmaximal, characteristic
5C127×#1445C212yesmaximal, complemented
6C127×#1444C211yesmaximal, characteristic, complemented
7C127×#1444C211yesmaximal, characteristic, complemented
8C127×#1439C212yesmaximal
9C127×#1439C211yesmaximal, characteristic
10C127×#1439C211yesmaximal, characteristic
11C127×#1434C211yesmaximal, characteristic, complemented
12C24×C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2212yes—
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C4⋊C4×C127C2212yes—
16C22×C4⋊C4×C127C2212yes—
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C22⋊C4×C127C2211yescharacteristic
19C22×C22⋊C4×C127C2212yes—
20C22×C22⋊C4×C127C2212yes—
21C22×C22⋊C4×C127C2211yescharacteristic
22C22×C42×C127C2211yescharacteristic
23C22×C42×C127C2211yescharacteristic
24#389×C127—24no—
25#387×C127—28no—
26#385×C127—28no—
27C4×C22⋊C4×C127—24no—
28C2×#95×C127C2211yescharacteristic
29C2×#95×C127C2211yescharacteristic
30C2×#95×C127C2212yes—
31C2×#95×C127C2212yes—
32C2×#95×C127C2212yes—
33C2×#95×C127C2212yes—
34C2×#95×C127C2211yescharacteristic
35C2×#95×C127C2212yes—
36C2×#95×C127C2211yescharacteristic
37C2×#95×C127C2212yes—
38C2×#95×C127C2212yes—
39C25×C127C2311yescharacteristic
40C23×C4×C127—22no—
41C23×C4×C127—22no—
42C23×C4×C127—22no—
43C23×C4×C127—24no—
44C23×C4×C127—42no—
45C23×C4×C127C2312yes—
46C23×C4×C127C2311yescharacteristic
47C23×C4×C127C2312yes—
48C23×C4×C127C2312yes—
49C23×C4×C127C2311yescharacteristic
50C23×C4×C127C2311yescharacteristic
51C23×C4×C127C2312yes—
52C23×C4×C127C2311yescharacteristic
53C23×C4×C127C2311yescharacteristic
54C23×C4×C127C2311yescharacteristic
55C2×C4⋊C4×C127—24no—
56C2×C4⋊C4×C127—22no—
57C2×C4⋊C4×C127—24no—
58C2×C4⋊C4×C127—24no—
59C2×C4⋊C4×C127—24no—
60C2×C4⋊C4×C127—24no—
61C2×C4⋊C4×C127—24no—
62C2×C4⋊C4×C127—24no—
63C2×C4⋊C4×C127—22no—
64C2×C4⋊C4×C127—24no—
65C2×C4⋊C4×C127—24no—
66C2×C4⋊C4×C127—42no—
67C2×C4⋊C4×C127—42no—
68C2×C22⋊C4×C127—22no—
69C2×C22⋊C4×C127—24no—
70C2×C22⋊C4×C127—22no—
71C2×C22⋊C4×C127—22no—
72C2×C22⋊C4×C127—24no—
73C2×C22⋊C4×C127—22no—
74C2×C22⋊C4×C127—24no—
75C2×C22⋊C4×C127—22no—
76C2×C22⋊C4×C127—24no—
77C2×C22⋊C4×C127—24no—
78C2×C22⋊C4×C127—42no—
79C2×C22⋊C4×C127Q814yes—
80C2×C42×C127—22no—
81C2×C42×C127—24no—
82C2×C42×C127—42no—
83C2×C42×C127D414yes—
84#95×C127—22no—
85#95×C127—22no—
86#95×C127—24no—
87#95×C127—24no—
88#95×C127—24no—
89#95×C127—24no—
90#95×C127—24no—
91#95×C127—22no—
92#95×C127—22no—
93#95×C127—42no—
94#95×C127D418yes—
95C24×C127—21no—
96C24×C127—22no—
97C24×C127—21no—
98C24×C127—21no—
99C24×C127—22no—
100C24×C127—21no—
101C24×C127—22no—
102C24×C127—22no—
103C24×C127C2×Q812yes—
104C24×C127#4112yes—
105C24×C127#4112yes—
106C24×C127C2411yescharacteristic
107C22×C4×C127—22no—
108C22×C4×C127—21no—
109C22×C4×C127—21no—
110C22×C4×C127—22no—
111C22×C4×C127—22no—
112C22×C4×C127—28no—
113C22×C4×C127—22no—
114C22×C4×C127—21no—
115C22×C4×C127—21no—
116C22×C4×C127—21no—
117C22×C4×C127—22no—
118C22×C4×C127—22no—
119C22×C4×C127—22no—
120C22×C4×C127—22no—
121C22×C4×C127—22no—
122C22×C4×C127—22no—
123C22×C4×C127—22no—
124C22×C4×C127—21no—
125C22×C4×C127—22no—
126C22×C4×C127—21no—
127C22×C4×C127—21no—
128C22×C4×C127—22no—
129C22×C4×C127—21no—
130C22×C4×C127—22no—
131C22×C4×C127—22no—
132C22×C4×C127—22no—
133C22×C4×C127—22no—
134C22×C4×C127—22no—
135C22×C4×C127—22no—
136C22×C4×C127—22no—
137C22×C4×C127—22no—
138C22×C4×C127—21no—
139C22×C4×C127—22no—
140C22×C4×C127—22no—
141C22×C4×C127—22no—
142C22×C4×C127—22no—
143C22×C4×C127—22no—
144C22×C4×C127—22no—
145C22×C4×C127—22no—
146C22×C4×C127—22no—
147C22×C4×C127—22no—
148C22×C4×C127—22no—
149C22×C4×C127—22no—
150C22×C4×C127—22no—
151C22×C4×C127—22no—
152C22×C4×C127—22no—
153C22×C4×C127—22no—
154C22×C4×C127—48no—
155C22×C4×C127—48no—
156C22×C4×C127—44no—
157C22×C4×C127—44no—
158C22×C4×C127C2×D412yes—
159C22×C4×C127C2×D414yes—
160C22×C4×C127C2×D414yes—
161C22×C4×C127C2×D412yes—
162C22×C4×C127C2×D414yes—
163C22×C4×C127C2×D412yes—
164C22×C4×C127C2×Q812yes—
165C22×C4×C127C2×Q812yes—
166C22×C4×C127#4112yes—
167C22×C4×C127#4114yes—
168C22×C4×C127#4112yes—
169C22×C4×C127#4112yes—
170C4⋊C4×C127—28no—
171C4⋊C4×C127—216no—
172C4⋊C4×C127—48no—
173C4⋊C4×C127—44no—
174C4⋊C4×C127—48no—
175C22⋊C4×C127—28no—
176C22⋊C4×C127—216no—
177C22⋊C4×C127—28no—
178C22⋊C4×C127—48no—
179C42×C127—44no—
180C42×C127—44no—
181C23×C127—22no—
182C23×C127—22no—
183C23×C127—24no—
184C23×C127—22no—
185C23×C127—22no—
186C23×C127—22no—
187C23×C127—22no—
188C23×C127—24no—
189C23×C127—24no—
190C23×C127—24no—
191C23×C127—24no—
192C23×C127—24no—
193C23×C127—41no—
194C23×C127—42no—
195C23×C127—41no—
196C23×C127—41no—
197C23×C127—41no—
198C23×C127—42no—
199C23×C127—42no—
200C23×C127—42no—
201C23×C127—42no—
202C23×C127—42no—
203C23×C127#12514yes—
204C23×C127C22×D411yescharacteristic
205C23×C127C22×D412yes—
206C23×C127C22×Q811yescharacteristic
207C23×C127C2×#4111yescharacteristic
208C23×C127C2×#4111yescharacteristic
209C23×C127C2×#4111yescharacteristic
210C23×C127C2×#4112yes—
211C23×C127C2×#4111yescharacteristic
212C23×C127C2×#4111yescharacteristic
213C23×C127H(5,𝔽2)12yes—
214C23×C1272−1+412yes—
215C2×C4×C127—22no—
216C2×C4×C127—22no—
217C2×C4×C127—22no—
218C2×C4×C127—22no—
219C2×C4×C127—24no—
220C2×C4×C127—24no—
221C2×C4×C127—24no—
222C2×C4×C127—24no—
223C2×C4×C127—22no—
224C2×C4×C127—22no—
225C2×C4×C127—24no—
226C2×C4×C127—22no—
227C2×C4×C127—24no—
228C2×C4×C127—24no—
229C2×C4×C127—24no—
230C2×C4×C127—24no—
231C2×C4×C127—24no—
232C2×C4×C127—22no—
233C2×C4×C127—22no—
234C2×C4×C127—22no—
235C2×C4×C127—24no—
236C2×C4×C127—24no—
237C2×C4×C127—24no—
238C2×C4×C127—24no—
239C2×C4×C127—24no—
240C2×C4×C127—24no—
241C2×C4×C127—416no—
242C2×C4×C127—41no—
243C2×C4×C127—42no—
244C2×C4×C127—42no—
245C2×C4×C127—42no—
246C2×C4×C127—42no—
247C2×C4×C127—42no—
248C2×C4×C127—42no—
249C2×C4×C127—41no—
250C2×C4×C127—41no—
251C2×C4×C127—42no—
252C2×C4×C127—41no—
253C2×C4×C127—41no—
254C2×C4×C127—41no—
255C2×C4×C127—42no—
256C2×C4×C127—42no—
257C2×C4×C127—42no—
258C2×C4×C127—42no—
259C2×C4×C127—42no—
260C2×C4×C127—42no—
261C2×C4×C127—42no—
262C2×C4×C127—42no—
263C2×C4×C127—42no—
264C2×C4×C127—42no—
265C2×C4×C127—42no—
266C2×C4×C127—42no—
267C2×C4×C127—42no—
268C2×C4×C127—42no—
269C2×C4×C127—42no—
270C2×C4×C127—42no—
271C2×C4×C127—42no—
272C2×C4×C127C22⋊Q814yes—
273C2×C4×C127#12714yes—
274C22×C127—24no—
275C22×C127—28no—
276C22×C127—42no—
277C22×C127—42no—
278C22×C127—42no—
279C22×C127—42no—
280C22×C127—44no—
281C22×C127—44no—
282C22×C127—44no—
283C22×C127—42no—
284C22×C127—42no—
285C22×C127C2×C22⋊Q811yescharacteristic
286C22×C127#52511yescharacteristic
287C22×C127#52511yescharacteristic
288C22×C127#52511yescharacteristic
289C22×C127#52512yes—
290C22×C127#52512yes—
291C22×C127C2×#12511yescharacteristic
292C22×C127#52911yescharacteristic
293C22×C127#52911yescharacteristic
294C22×C127C2×#12711yescharacteristic
295C22×C127#53311yescharacteristic
296C22×C127#53411yescharacteristic
297C22×C127#53611yescharacteristic
298C22×C127#53912yes—
299C22×C127#54212yes—
300C22×C127#54612yes—
301C22×C127#54612yes—
302C22×C127#54712yes—
303C22×C127D4×Q812yes—
304C22×C127#55212yes—
305C22×C127#55312yes—
306C22×C127#55412yes—
307C22×C127#55612yes—
308C4×C127—24no—
309C4×C127—24no—
310C4×C127—42no—
311C4×C127—42no—
312C4×C127—44no—
313C4×C127—44no—
314C4×C127—44no—
315C4×C127—42no—
316C4×C127—42no—
317C4×C127—82no—
318#14969C12711yesmaximal, characteristic, direct product factor, Sylow
319C2×C127—44no—
320C2×C127#239711yescharacteristic
321C2×C127#246512yes—
322C2×C127#246612yes—
323C2×C127#247012yes—
324C2×C127#247312yes—
325C2×C127#253911yescharacteristic
326C2×C127#254211yescharacteristic
327C2×C127#257911yescharacteristic
328C2×C127#259911yescharacteristic
329C2×C127#263811yescharacteristic
330C2×C127#285111yescharacteristic
331C2×#389C2×C12711yescharacteristic, complemented
332C2×#387C2×C12712yescomplemented
333C2×#385C2×C12712yes—
334C2×C4×C22⋊C4C2×C12711yescharacteristic
335#1445C2×C12712yescomplemented
336#1444C2×C12711yescharacteristic, complemented
337#1444C2×C12711yescharacteristic, complemented
338#1439C2×C12712yes—
339#1439C2×C12711yescharacteristic
340#1439C2×C12711yescharacteristic
341#1434C2×C12711yescharacteristic, complemented
342C127#1496911yescharacteristic, direct product factor, Sylow
343C24×C4C22×C12711yescharacteristic
344C22×C4⋊C4C22×C12712yes—
345C22×C4⋊C4C22×C12711yescharacteristic
346C22×C4⋊C4C22×C12712yes—
347C22×C4⋊C4C22×C12712yes—
348C22×C4⋊C4C22×C12711yescharacteristic
349C22×C22⋊C4C22×C12711yescharacteristic
350C22×C22⋊C4C22×C12712yes—
351C22×C22⋊C4C22×C12712yes—
352C22×C22⋊C4C22×C12711yescharacteristic
353C22×C42C22×C12711yescharacteristic
354C22×C42C22×C12711yescharacteristic
355#389—24no—
356#387—28no—
357#385—28no—
358C4×C22⋊C4—24no—
359C2×#95C22×C12711yescharacteristic
360C2×#95C22×C12711yescharacteristic
361C2×#95C22×C12712yes—
362C2×#95C22×C12712yes—
363C2×#95C22×C12712yes—
364C2×#95C22×C12712yes—
365C2×#95C22×C12711yescharacteristic
366C2×#95C22×C12712yes—
367C2×#95C22×C12711yescharacteristic
368C2×#95C22×C12712yes—
369C2×#95C22×C12712yes—
370C25C23×C12711yescharacteristic
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—24no—
375C23×C4—42no—
376C23×C4C23×C12712yes—
377C23×C4C23×C12712yes—
378C23×C4C23×C12712yes—
379C23×C4C23×C12711yescharacteristic
380C23×C4C23×C12711yescharacteristic
381C23×C4C23×C12712yes—
382C23×C4C23×C12711yescharacteristic
383C23×C4C23×C12711yescharacteristic
384C23×C4C23×C12711yescharacteristic
385C23×C4C23×C12711yescharacteristic
386C2×C4⋊C4—24no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—42no—
398C2×C4⋊C4—42no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—24no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—42no—
410C2×C22⋊C4Q8×C12714yes—
411C2×C42—22no—
412C2×C42—24no—
413C2×C42—42no—
414C2×C42D4×C12714yes—
415#95—22no—
416#95—22no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—22no—
423#95—22no—
424#95—42no—
425#95D4×C12718yes—
426C24—21no—
427C24—22no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—21no—
432C24—22no—
433C24—22no—
434C24C2×Q8×C12712yes—
435C24#41×C12712yes—
436C24#41×C12712yes—
437C24C24×C12711yescharacteristic
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—28no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—48no—
486C22×C4—48no—
487C22×C4—44no—
488C22×C4—44no—
489C22×C4C2×D4×C12712yes—
490C22×C4C2×D4×C12714yes—
491C22×C4C2×D4×C12714yes—
492C22×C4C2×D4×C12712yes—
493C22×C4C2×D4×C12714yes—
494C22×C4C2×D4×C12712yes—
495C22×C4C2×Q8×C12712yes—
496C22×C4C2×Q8×C12712yes—
497C22×C4#41×C12712yes—
498C22×C4#41×C12714yes—
499C22×C4#41×C12712yes—
500C22×C4#41×C12712yes—
501C4⋊C4—28no—
502C4⋊C4—216no—
503C4⋊C4—48no—
504C4⋊C4—44no—
505C4⋊C4—48no—
506C22⋊C4—28no—
507C22⋊C4—216no—
508C22⋊C4—28no—
509C22⋊C4—48no—
510C42—44no—
511C42—44no—
512C23—22no—
513C23—22no—
514C23—24no—
515C23—22no—
516C23—22no—
517C23—22no—
518C23—22no—
519C23—24no—
520C23—24no—
521C23—24no—
522C23—24no—
523C23—24no—
524C23—41no—
525C23—42no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23#125×C12714yes—
535C23C22×D4×C12711yescharacteristic
536C23C22×D4×C12712yes—
537C23C22×Q8×C12711yescharacteristic
538C23C2×#41×C12711yescharacteristic
539C23C2×#41×C12711yescharacteristic
540C23C2×#41×C12711yescharacteristic
541C23C2×#41×C12712yes—
542C23C2×#41×C12711yescharacteristic
543C23C2×#41×C12711yescharacteristic
544C23H(5,𝔽2)×C12712yes—
545C232−1+4×C12712yes—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—416no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4C22⋊Q8×C12714yes—
604C2×C4#127×C12714yes—
605C22—24no—
606C22—28no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—44no—
612C22—44no—
613C22—44no—
614C22—42no—
615C22—42no—
616C22C2×C22⋊Q8×C12711yescharacteristic
617C22#525×C12711yescharacteristic
618C22#525×C12711yescharacteristic
619C22#525×C12711yescharacteristic
620C22#525×C12712yes—
621C22#525×C12712yes—
622C22C2×#125×C12711yescharacteristic
623C22#529×C12711yescharacteristic
624C22#529×C12711yescharacteristic
625C22C2×#127×C12711yescharacteristic
626C22#533×C12711yescharacteristic
627C22#534×C12711yescharacteristic
628C22#536×C12711yescharacteristic
629C22#539×C12712yes—
630C22#542×C12712yes—
631C22#546×C12712yes—
632C22#546×C12712yes—
633C22#547×C12712yes—
634C22D4×Q8×C12712yes—
635C22#552×C12712yes—
636C22#553×C12712yes—
637C22#554×C12712yes—
638C22#556×C12712yes—
639C4—24no—
640C4—24no—
641C4—42no—
642C4—42no—
643C4—44no—
644C4—44no—
645C4—44no—
646C4—42no—
647C4—42no—
648C4—82no—
649C2—44no—
650C2C127×#239711yescharacteristic
651C2C127×#246512yes—
652C2C127×#246612yes—
653C2C127×#247012yes—
654C2C127×#247312yes—
655C2C127×#253911yescharacteristic
656C2C127×#254211yescharacteristic
657C2C127×#257911yescharacteristic
658C2C127×#259911yescharacteristic
659C2C127×#263811yescharacteristic
660C2C127×#285111yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#389×C127C2semidirect
2. C2×#387×C127C2semidirect
5. C127×#1445C2semidirect
6. C127×#1444C2semidirect
7. C127×#1444C2semidirect
11. C127×#1434C2semidirect
318. #14969C127direct (N × H)
331. C2×#389C2×C127semidirect
332. C2×#387C2×C127semidirect
335. #1445C2×C127semidirect
336. #1444C2×C127semidirect
337. #1444C2×C127semidirect
341. #1434C2×C127semidirect
342. C127#14969direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#389×C1272
C2×#387×C1272
C2×#385×C1272
C2×C4×C22⋊C4×C1272
C127×#14452
C127×#14442
C127×#14392
C127×#14342
#14969127