Finite Group Databasebeta

← C127×#15465 #44579138

Subgroups — C127×#15465 #44579138

Order 32512.

1738 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊Q8×C127C211yesmaximal, characteristic
2C2×#400×C127C211yesmaximal, characteristic, complemented
3C2×#397×C127C211yesmaximal, characteristic
4C2×#391×C127C211yesmaximal, characteristic, complemented
5C127×#1446C211yesmaximal, characteristic, complemented
6C127×#1442C212yesmaximal, complemented
7C127×#1442C212yesmaximal, complemented
8C127×#1440C212yesmaximal
9C127×#1437C211yesmaximal, characteristic
10C127×#1436C211yesmaximal, characteristic, complemented
11C127×C22⋊#95C212yesmaximal
12C23×Q8×C127C2211yescharacteristic
13C24×C4×C127C2211yescharacteristic
14C2×C22⋊Q8×C127—24no—
15C2×C22⋊Q8×C127—24no—
16C2×C22⋊Q8×C127—24no—
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C4⋊C4×C127C2211yescharacteristic
19C22×C4⋊C4×C127C2211yescharacteristic
20C22×C4⋊C4×C127C2211yescharacteristic
21C22×C22⋊C4×C127C2212yes—
22C22×C22⋊C4×C127C2211yescharacteristic
23C22×C22⋊C4×C127C2212yes—
24C22×C22⋊C4×C127C2211yescharacteristic
25C22×C42×C127C2211yescharacteristic
26#400×C127—24no—
27#397×C127—24no—
28#391×C127—24no—
29C2×#95×C127C2211yescharacteristic
30C2×#95×C127C2212yes—
31C2×#95×C127C2212yes—
32C2×#95×C127C2211yescharacteristic
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
42C22×Q8×C127—22no—
43C22×Q8×C127—22no—
44C22×Q8×C127—24no—
45C22×Q8×C127—42no—
46C22×Q8×C127D414yes—
47C23×C4×C127—22no—
48C23×C4×C127—22no—
49C23×C4×C127—22no—
50C23×C4×C127—24no—
51C23×C4×C127—42no—
52C23×C4×C127C2312yes—
53C23×C4×C127C2312yes—
54C23×C4×C127C2312yes—
55C23×C4×C127C2311yescharacteristic
56C23×C4×C127C2311yescharacteristic
57C23×C4×C127C2311yescharacteristic
58C23×C4×C127C2311yescharacteristic
59C23×C4×C127C2312yes—
60C23×C4×C127C2311yescharacteristic
61C23×C4×C127C2311yescharacteristic
62C22⋊Q8×C127—232no—
63C2×C4⋊C4×C127—22no—
64C2×C4⋊C4×C127—22no—
65C2×C4⋊C4×C127—22no—
66C2×C4⋊C4×C127—22no—
67C2×C4⋊C4×C127—22no—
68C2×C4⋊C4×C127—22no—
69C2×C4⋊C4×C127—22no—
70C2×C4⋊C4×C127—22no—
71C2×C4⋊C4×C127—22no—
72C2×C4⋊C4×C127—22no—
73C2×C4⋊C4×C127—22no—
74C2×C4⋊C4×C127D414yes—
75C2×C22⋊C4×C127—22no—
76C2×C22⋊C4×C127—22no—
77C2×C22⋊C4×C127—22no—
78C2×C22⋊C4×C127—22no—
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—42no—
86C2×C22⋊C4×C127D414yes—
87C2×C42×C127—22no—
88C2×C42×C127—42no—
89#95×C127—24no—
90#95×C127—24no—
91#95×C127—22no—
92#95×C127—24no—
93#95×C127—22no—
94#95×C127—24no—
95#95×C127—24no—
96#95×C127—24no—
97#95×C127—24no—
98#95×C127—24no—
99#95×C127—42no—
100#95×C127—42no—
101C24×C127—21no—
102C24×C127—21no—
103C24×C127—22no—
104C24×C127—22no—
105C24×C127—22no—
106C24×C127—22no—
107C24×C127—22no—
108C24×C127C2×D412yes—
109C24×C127#4114yes—
110C24×C127C2411yescharacteristic
111C2×Q8×C127—28no—
112C2×Q8×C127—28no—
113C2×Q8×C127—44no—
114C2×Q8×C127—48no—
115C2×Q8×C127—48no—
116C22×C4×C127—21no—
117C22×C4×C127—21no—
118C22×C4×C127—22no—
119C22×C4×C127—22no—
120C22×C4×C127—22no—
121C22×C4×C127—28no—
122C22×C4×C127—22no—
123C22×C4×C127—21no—
124C22×C4×C127—21no—
125C22×C4×C127—21no—
126C22×C4×C127—21no—
127C22×C4×C127—21no—
128C22×C4×C127—21no—
129C22×C4×C127—21no—
130C22×C4×C127—21no—
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—22no—
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—22no—
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—22no—
163C22×C4×C127—22no—
164C22×C4×C127—22no—
165C22×C4×C127—48no—
166C22×C4×C127—48no—
167C22×C4×C127—44no—
168C22×C4×C127—44no—
169C22×C4×C127C2×D412yes—
170C22×C4×C127C2×D412yes—
171C22×C4×C127C2×D412yes—
172C22×C4×C127C2×D412yes—
173C22×C4×C127C2×D412yes—
174C22×C4×C127C2×D412yes—
175C22×C4×C127C2×D412yes—
176C22×C4×C127C2×D412yes—
177C22×C4×C127#4114yes—
178C22×C4×C127#4114yes—
179C4⋊C4×C127—28no—
180C4⋊C4×C127—28no—
181C4⋊C4×C127—28no—
182C4⋊C4×C127—44no—
183C22⋊C4×C127—28no—
184C22⋊C4×C127—28no—
185C22⋊C4×C127—48no—
186C22⋊C4×C127—48no—
187C42×C127—44no—
188C23×C127—22no—
189C23×C127—24no—
190C23×C127—22no—
191C23×C127—24no—
192C23×C127—24no—
193C23×C127—24no—
194C23×C127—24no—
195C23×C127—24no—
196C23×C127—24no—
197C23×C127—24no—
198C23×C127—41no—
199C23×C127—41no—
200C23×C127—41no—
201C23×C127—41no—
202C23×C127—42no—
203C23×C127—42no—
204C23×C127—42no—
205C23×C127—42no—
206C23×C127—42no—
207C23×C127—42no—
208C23×C127#12414yes—
209C23×C127C22×D411yescharacteristic
210C23×C127C22×D411yescharacteristic
211C23×C127C22×D411yescharacteristic
212C23×C127C2×#4112yes—
213C23×C127C2×#4112yes—
214C23×C127C2×#4112yes—
215C23×C127H(5,𝔽2)12yes—
216C23×C1272−1+412yes—
217C23×C1272−1+412yes—
218Q8×C127—416no—
219C2×C4×C127—22no—
220C2×C4×C127—22no—
221C2×C4×C127—22no—
222C2×C4×C127—22no—
223C2×C4×C127—24no—
224C2×C4×C127—24no—
225C2×C4×C127—24no—
226C2×C4×C127—24no—
227C2×C4×C127—22no—
228C2×C4×C127—22no—
229C2×C4×C127—22no—
230C2×C4×C127—22no—
231C2×C4×C127—22no—
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—416no—
241C2×C4×C127—41no—
242C2×C4×C127—41no—
243C2×C4×C127—42no—
244C2×C4×C127—41no—
245C2×C4×C127—41no—
246C2×C4×C127—42no—
247C2×C4×C127—42no—
248C2×C4×C127—42no—
249C2×C4×C127—42no—
250C2×C4×C127—42no—
251C2×C4×C127—42no—
252C2×C4×C127—42no—
253C2×C4×C127—42no—
254C2×C4×C127—42no—
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×C127—42no—
273C2×C4×C127—42no—
274C2×C4×C127—42no—
275C2×C4×C127—42no—
276C2×C4×C127#12014yes—
277C2×C4×C127#12314yes—
278C22×C127—24no—
279C22×C127—28no—
280C22×C127—44no—
281C22×C127—42no—
282C22×C127—44no—
283C22×C127—42no—
284C22×C127—44no—
285C22×C127—44no—
286C22×C127—44no—
287C22×C127C2×#12011yescharacteristic
288C22×C127C2×#12311yescharacteristic
289C22×C127C2×#12411yescharacteristic
290C22×C127#52912yes—
291C22×C127#53211yescharacteristic
292C22×C127#53411yescharacteristic
293C22×C127#53611yescharacteristic
294C22×C127#53611yescharacteristic
295C22×C127#53912yes—
296C22×C127#53912yes—
297C22×C127#54112yes—
298C22×C127#54612yes—
299C22×C127#54612yes—
300C22×C127#54712yes—
301C22×C127#54812yes—
302C22×C127#54812yes—
303C22×C127#54812yes—
304C22×C127#55112yes—
305C22×C127#55212yes—
306C22×C127#55612yes—
307C22×C127#56312yes—
308C4×C127—24no—
309C4×C127—24no—
310C4×C127—42no—
311C4×C127—42no—
312C4×C127—42no—
313C4×C127—42no—
314C4×C127—44no—
315C4×C127—82no—
316C4×C127—82no—
317C4×C127—82no—
318#15465C12711yesmaximal, characteristic, direct product factor, Sylow
319C2×C127—44no—
320C2×C127#240511yescharacteristic
321C2×C127#242112yes—
322C2×C127#243211yescharacteristic
323C2×C127#243611yescharacteristic
324C2×C127#248812yes—
325C2×C127#256012yes—
326C2×C127#268912yes—
327C2×C127#269012yes—
328C2×C127#272812yes—
329C22×C22⋊Q8C2×C12711yescharacteristic
330C2×#400C2×C12711yescharacteristic, complemented
331C2×#397C2×C12711yescharacteristic
332C2×#391C2×C12711yescharacteristic, complemented
333#1446C2×C12711yescharacteristic, complemented
334#1442C2×C12712yescomplemented
335#1442C2×C12712yescomplemented
336#1440C2×C12712yes—
337#1437C2×C12711yescharacteristic
338#1436C2×C12711yescharacteristic, complemented
339C22⋊#95C2×C12712yes—
340C127#1546511yescharacteristic, direct product factor, Sylow
341C23×Q8C22×C12711yescharacteristic
342C24×C4C22×C12711yescharacteristic
343C2×C22⋊Q8—24no—
344C2×C22⋊Q8—24no—
345C2×C22⋊Q8—24no—
346C22×C4⋊C4C22×C12711yescharacteristic
347C22×C4⋊C4C22×C12711yescharacteristic
348C22×C4⋊C4C22×C12711yescharacteristic
349C22×C4⋊C4C22×C12711yescharacteristic
350C22×C22⋊C4C22×C12712yes—
351C22×C22⋊C4C22×C12711yescharacteristic
352C22×C22⋊C4C22×C12712yes—
353C22×C22⋊C4C22×C12711yescharacteristic
354C22×C42C22×C12711yescharacteristic
355#400—24no—
356#397—24no—
357#391—24no—
358C2×#95C22×C12711yescharacteristic
359C2×#95C22×C12712yes—
360C2×#95C22×C12712yes—
361C2×#95C22×C12711yescharacteristic
362C2×#95C22×C12712yes—
363C2×#95C22×C12712yes—
364C2×#95C22×C12712yes—
365C2×#95C22×C12712yes—
366C2×#95C22×C12712yes—
367C2×#95C22×C12712yes—
368C2×#95C22×C12712yes—
369C2×#95C22×C12712yes—
370C25C23×C12711yescharacteristic
371C22×Q8—22no—
372C22×Q8—22no—
373C22×Q8—24no—
374C22×Q8—42no—
375C22×Q8D4×C12714yes—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—24no—
380C23×C4—42no—
381C23×C4C23×C12712yes—
382C23×C4C23×C12712yes—
383C23×C4C23×C12712yes—
384C23×C4C23×C12711yescharacteristic
385C23×C4C23×C12711yescharacteristic
386C23×C4C23×C12711yescharacteristic
387C23×C4C23×C12711yescharacteristic
388C23×C4C23×C12712yes—
389C23×C4C23×C12711yescharacteristic
390C23×C4C23×C12711yescharacteristic
391C22⋊Q8—232no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4D4×C12714yes—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—24no—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—42no—
415C2×C22⋊C4D4×C12714yes—
416C2×C42—22no—
417C2×C42—42no—
418#95—24no—
419#95—24no—
420#95—22no—
421#95—24no—
422#95—22no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—42no—
429#95—42no—
430C24—21no—
431C24—21no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24C2×D4×C12712yes—
438C24#41×C12714yes—
439C24C24×C12711yescharacteristic
440C2×Q8—28no—
441C2×Q8—28no—
442C2×Q8—44no—
443C2×Q8—48no—
444C2×Q8—48no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—28no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
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—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—48no—
495C22×C4—48no—
496C22×C4—44no—
497C22×C4—44no—
498C22×C4C2×D4×C12712yes—
499C22×C4C2×D4×C12712yes—
500C22×C4C2×D4×C12712yes—
501C22×C4C2×D4×C12712yes—
502C22×C4C2×D4×C12712yes—
503C22×C4C2×D4×C12712yes—
504C22×C4C2×D4×C12712yes—
505C22×C4C2×D4×C12712yes—
506C22×C4#41×C12714yes—
507C22×C4#41×C12714yes—
508C4⋊C4—28no—
509C4⋊C4—28no—
510C4⋊C4—28no—
511C4⋊C4—44no—
512C22⋊C4—28no—
513C22⋊C4—28no—
514C22⋊C4—48no—
515C22⋊C4—48no—
516C42—44no—
517C23—22no—
518C23—24no—
519C23—22no—
520C23—24no—
521C23—24no—
522C23—24no—
523C23—24no—
524C23—24no—
525C23—24no—
526C23—24no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23#124×C12714yes—
538C23C22×D4×C12711yescharacteristic
539C23C22×D4×C12711yescharacteristic
540C23C22×D4×C12711yescharacteristic
541C23C2×#41×C12712yes—
542C23C2×#41×C12712yes—
543C23C2×#41×C12712yes—
544C23H(5,𝔽2)×C12712yes—
545C232−1+4×C12712yes—
546C232−1+4×C12712yes—
547Q8—416no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—416no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
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×C4—42no—
604C2×C4—42no—
605C2×C4#120×C12714yes—
606C2×C4#123×C12714yes—
607C22—24no—
608C22—28no—
609C22—42no—
610C22—44no—
611C22—42no—
612C22—44no—
613C22—44no—
614C22—44no—
615C22—44no—
616C22C2×#120×C12711yescharacteristic
617C22C2×#123×C12711yescharacteristic
618C22C2×#124×C12711yescharacteristic
619C22#529×C12712yes—
620C22#532×C12711yescharacteristic
621C22#534×C12711yescharacteristic
622C22#536×C12711yescharacteristic
623C22#536×C12711yescharacteristic
624C22#539×C12712yes—
625C22#539×C12712yes—
626C22#541×C12712yes—
627C22#546×C12712yes—
628C22#546×C12712yes—
629C22#547×C12712yes—
630C22#548×C12712yes—
631C22#548×C12712yes—
632C22#548×C12712yes—
633C22#551×C12712yes—
634C22#552×C12712yes—
635C22#556×C12712yes—
636C22#563×C12712yes—
637C4—24no—
638C4—24no—
639C4—42no—
640C4—42no—
641C4—42no—
642C4—42no—
643C4—44no—
644C4—82no—
645C4—82no—
646C4—82no—
647C2—44no—
648C2C127×#240511yescharacteristic
649C2C127×#242112yes—
650C2C127×#243211yescharacteristic
651C2C127×#243611yescharacteristic
652C2C127×#248812yes—
653C2C127×#256012yes—
654C2C127×#268912yes—
655C2C127×#269012yes—
656C2C127×#272812yes—
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
2. C2×#400×C127C2semidirect
4. C2×#391×C127C2semidirect
5. C127×#1446C2semidirect
6. C127×#1442C2semidirect
7. C127×#1442C2semidirect
10. C127×#1436C2semidirect
318. #15465C127direct (N × H)
330. C2×#400C2×C127semidirect
332. C2×#391C2×C127semidirect
333. #1446C2×C127semidirect
334. #1442C2×C127semidirect
335. #1442C2×C127semidirect
338. #1436C2×C127semidirect
340. C127#15465direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C22⋊Q8×C1272
C2×#400×C1272
C2×#397×C1272
C2×#391×C1272
C127×#14462
C127×#14422
C127×#14402
C127×#14372
C127×#14362
C127×C22⋊#952
#15465127