Finite Group Databasebeta

← C127×#16024 #44579697

Subgroups — C127×#16024 #44579697

Order 32512.

1690 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#126×C127C211yesmaximal, characteristic
2C2×#385×C127C211yesmaximal, characteristic
3C2×#385×C127C211yesmaximal, characteristic
4C2×#381×C127C211yesmaximal, characteristic
5C127×#1444C212yesmaximal, complemented
6C127×#1442C212yesmaximal, complemented
7C127×#1441C212yesmaximal, complemented
8C127×#1440C211yesmaximal, characteristic
9C127×#1440C211yesmaximal, characteristic
10C127×#1440C211yesmaximal, characteristic
11C127×#1436C212yesmaximal, complemented
12C24×C4×C127C2211yescharacteristic
13C2×#126×C127—24no—
14C2×#126×C127—24no—
15C2×#126×C127—24no—
16C22×C4⋊C4×C127C2211yescharacteristic
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C4⋊C4×C127C2211yescharacteristic
19C22×C4⋊C4×C127C2212yes—
20C22×C4⋊C4×C127C2212yes—
21C22×C22⋊C4×C127C2211yescharacteristic
22C22×C22⋊C4×C127C2211yescharacteristic
23C22×C22⋊C4×C127C2211yescharacteristic
24C22×C22⋊C4×C127C2211yescharacteristic
25C22×C22⋊C4×C127C2211yescharacteristic
26C22×C22⋊C4×C127C2211yescharacteristic
27C22×C42×C127C2211yescharacteristic
28#385×C127—24no—
29#385×C127—24no—
30#381×C127—24no—
31C2×#95×C127C2212yes—
32C2×#95×C127C2212yes—
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
42C23×C4×C127—22no—
43C23×C4×C127—24no—
44C23×C4×C127—22no—
45C23×C4×C127—22no—
46C23×C4×C127—42no—
47C23×C4×C127C2312yes—
48C23×C4×C127C2311yescharacteristic
49C23×C4×C127C2311yescharacteristic
50C23×C4×C127C2311yescharacteristic
51C23×C4×C127C2311yescharacteristic
52C23×C4×C127C2311yescharacteristic
53C23×C4×C127C2311yescharacteristic
54C23×C4×C127C2312yes—
55C23×C4×C127C2312yes—
56C23×C4×C127C2312yes—
57#126×C127—232no—
58C2×C4⋊C4×C127—22no—
59C2×C4⋊C4×C127—22no—
60C2×C4⋊C4×C127—22no—
61C2×C4⋊C4×C127—22no—
62C2×C4⋊C4×C127—22no—
63C2×C4⋊C4×C127—22no—
64C2×C4⋊C4×C127—22no—
65C2×C4⋊C4×C127—22no—
66C2×C4⋊C4×C127—22no—
67C2×C4⋊C4×C127—24no—
68C2×C4⋊C4×C127—24no—
69C2×C4⋊C4×C127—24no—
70C2×C4⋊C4×C127—24no—
71C2×C4⋊C4×C127—42no—
72C2×C4⋊C4×C127—42no—
73C2×C22⋊C4×C127—22no—
74C2×C22⋊C4×C127—22no—
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—22no—
81C2×C22⋊C4×C127—24no—
82C2×C22⋊C4×C127—24no—
83C2×C22⋊C4×C127—22no—
84C2×C22⋊C4×C127—42no—
85C2×C22⋊C4×C127D414yes—
86C2×C22⋊C4×C127D414yes—
87C2×C22⋊C4×C127D414yes—
88C2×C42×C127—22no—
89C2×C42×C127—22no—
90C2×C42×C127—22no—
91#95×C127—24no—
92#95×C127—24no—
93#95×C127—24no—
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—22no—
102C24×C127—22no—
103C24×C127—22no—
104C24×C127—22no—
105C24×C127—22no—
106C24×C127—22no—
107C24×C127C2×D412yes—
108C24×C127C2×D412yes—
109C24×C127C2×D412yes—
110C24×C127C2411yescharacteristic
111C22×C4×C127—28no—
112C22×C4×C127—22no—
113C22×C4×C127—22no—
114C22×C4×C127—22no—
115C22×C4×C127—22no—
116C22×C4×C127—22no—
117C22×C4×C127—21no—
118C22×C4×C127—21no—
119C22×C4×C127—21no—
120C22×C4×C127—21no—
121C22×C4×C127—21no—
122C22×C4×C127—21no—
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—22no—
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—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—48no—
162C22×C4×C127—48no—
163C22×C4×C127—44no—
164C22×C4×C127—44no—
165C22×C4×C127C2×D412yes—
166C22×C4×C127C2×D412yes—
167C22×C4×C127C2×D412yes—
168C22×C4×C127C2×D412yes—
169C22×C4×C127C2×D412yes—
170C22×C4×C127C2×D412yes—
171C22×C4×C127#4114yes—
172C22×C4×C127#4114yes—
173C22×C4×C127#4114yes—
174C4⋊C4×C127—28no—
175C4⋊C4×C127—28no—
176C4⋊C4×C127—28no—
177C4⋊C4×C127—48no—
178C4⋊C4×C127—48no—
179C22⋊C4×C127—28no—
180C22⋊C4×C127—28no—
181C22⋊C4×C127—28no—
182C22⋊C4×C127—28no—
183C22⋊C4×C127—28no—
184C22⋊C4×C127—44no—
185C42×C127—28no—
186C23×C127—22no—
187C23×C127—22no—
188C23×C127—22no—
189C23×C127—22no—
190C23×C127—22no—
191C23×C127—22no—
192C23×C127—24no—
193C23×C127—24no—
194C23×C127—24no—
195C23×C127—24no—
196C23×C127—24no—
197C23×C127—24no—
198C23×C127—42no—
199C23×C127—42no—
200C23×C127—42no—
201C23×C127—42no—
202C23×C127—42no—
203C23×C127—42no—
204C23×C127—42no—
205C23×C127—42no—
206C23×C127#12014yes—
207C23×C127C22×D411yescharacteristic
208C23×C127C22×D411yescharacteristic
209C23×C127C22×D411yescharacteristic
210C23×C127C2×#4112yes—
211C23×C127C2×#4112yes—
212C23×C127C2×#4112yes—
213C23×C127H(5,𝔽2)12yes—
214C23×C1272−1+412yes—
215C23×C1272−1+412yes—
216C2×C4×C127—22no—
217C2×C4×C127—22no—
218C2×C4×C127—22no—
219C2×C4×C127—22no—
220C2×C4×C127—22no—
221C2×C4×C127—22no—
222C2×C4×C127—24no—
223C2×C4×C127—24no—
224C2×C4×C127—24no—
225C2×C4×C127—24no—
226C2×C4×C127—24no—
227C2×C4×C127—24no—
228C2×C4×C127—24no—
229C2×C4×C127—24no—
230C2×C4×C127—24no—
231C2×C4×C127—24no—
232C2×C4×C127—24no—
233C2×C4×C127—24no—
234C2×C4×C127—24no—
235C2×C4×C127—24no—
236C2×C4×C127—24no—
237C2×C4×C127—416no—
238C2×C4×C127—42no—
239C2×C4×C127—41no—
240C2×C4×C127—41no—
241C2×C4×C127—41no—
242C2×C4×C127—41no—
243C2×C4×C127—41no—
244C2×C4×C127—41no—
245C2×C4×C127—42no—
246C2×C4×C127—41no—
247C2×C4×C127—41no—
248C2×C4×C127—42no—
249C2×C4×C127—41no—
250C2×C4×C127—41no—
251C2×C4×C127—41no—
252C2×C4×C127—41no—
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—
275C22×C127—24no—
276C22×C127—24no—
277C22×C127—24no—
278C22×C127—44no—
279C22×C127—44no—
280C22×C127—44no—
281C22×C127—44no—
282C22×C127—44no—
283C22×C127—44no—
284C22×C127C2×#12011yescharacteristic
285C22×C127#52511yescharacteristic
286C22×C127#52511yescharacteristic
287C22×C127#52511yescharacteristic
288C22×C127#52912yes—
289C22×C127#53511yescharacteristic
290C22×C127#53611yescharacteristic
291C22×C127#53611yescharacteristic
292C22×C127#53912yes—
293C22×C127#54112yes—
294C22×C127#54212yes—
295C22×C127#54612yes—
296C22×C127#54612yes—
297C22×C127#54712yes—
298C22×C127#54712yes—
299C22×C127#54712yes—
300C22×C127#54712yes—
301C22×C127#55212yes—
302C22×C127#55312yes—
303C22×C127#55612yes—
304C22×C127#56312yes—
305C4×C127—42no—
306C4×C127—42no—
307C4×C127—44no—
308C4×C127—42no—
309C4×C127—42no—
310C4×C127—42no—
311C4×C127—42no—
312C4×C127—44no—
313C4×C127—44no—
314C4×C127—82no—
315#16024C12711yesmaximal, characteristic, direct product factor, Sylow
316C2×C127—44no—
317C2×C127#240411yescharacteristic
318C2×C127#240611yescharacteristic
319C2×C127#240611yescharacteristic
320C2×C127#246612yes—
321C2×C127#246812yes—
322C2×C127#247812yes—
323C2×C127#268912yes—
324C2×C127#269812yes—
325C2×C127#271812yes—
326C22×#126C2×C12711yescharacteristic
327C2×#385C2×C12711yescharacteristic
328C2×#385C2×C12711yescharacteristic
329C2×#381C2×C12711yescharacteristic
330#1444C2×C12712yescomplemented
331#1442C2×C12712yescomplemented
332#1441C2×C12712yescomplemented
333#1440C2×C12711yescharacteristic
334#1440C2×C12711yescharacteristic
335#1440C2×C12711yescharacteristic
336#1436C2×C12712yescomplemented
337C127#1602411yescharacteristic, direct product factor, Sylow
338C24×C4C22×C12711yescharacteristic
339C2×#126—24no—
340C2×#126—24no—
341C2×#126—24no—
342C22×C4⋊C4C22×C12711yescharacteristic
343C22×C4⋊C4C22×C12711yescharacteristic
344C22×C4⋊C4C22×C12711yescharacteristic
345C22×C4⋊C4C22×C12712yes—
346C22×C4⋊C4C22×C12712yes—
347C22×C22⋊C4C22×C12711yescharacteristic
348C22×C22⋊C4C22×C12711yescharacteristic
349C22×C22⋊C4C22×C12711yescharacteristic
350C22×C22⋊C4C22×C12711yescharacteristic
351C22×C22⋊C4C22×C12711yescharacteristic
352C22×C22⋊C4C22×C12711yescharacteristic
353C22×C42C22×C12711yescharacteristic
354#385—24no—
355#385—24no—
356#381—24no—
357C2×#95C22×C12712yes—
358C2×#95C22×C12712yes—
359C2×#95C22×C12712yes—
360C2×#95C22×C12712yes—
361C2×#95C22×C12712yes—
362C2×#95C22×C12712yes—
363C2×#95C22×C12712yes—
364C2×#95C22×C12712yes—
365C2×#95C22×C12712yes—
366C2×#95C22×C12712yes—
367C25C23×C12711yescharacteristic
368C23×C4—22no—
369C23×C4—24no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—42no—
373C23×C4C23×C12712yes—
374C23×C4C23×C12711yescharacteristic
375C23×C4C23×C12711yescharacteristic
376C23×C4C23×C12711yescharacteristic
377C23×C4C23×C12711yescharacteristic
378C23×C4C23×C12711yescharacteristic
379C23×C4C23×C12711yescharacteristic
380C23×C4C23×C12712yes—
381C23×C4C23×C12712yes—
382C23×C4C23×C12712yes—
383#126—232no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—24no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—42no—
398C2×C4⋊C4—42no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—24no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—42no—
411C2×C22⋊C4D4×C12714yes—
412C2×C22⋊C4D4×C12714yes—
413C2×C22⋊C4D4×C12714yes—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—42no—
426#95—42no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24C2×D4×C12712yes—
434C24C2×D4×C12712yes—
435C24C2×D4×C12712yes—
436C24C24×C12711yescharacteristic
437C22×C4—28no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
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—48no—
488C22×C4—48no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4C2×D4×C12712yes—
492C22×C4C2×D4×C12712yes—
493C22×C4C2×D4×C12712yes—
494C22×C4C2×D4×C12712yes—
495C22×C4C2×D4×C12712yes—
496C22×C4C2×D4×C12712yes—
497C22×C4#41×C12714yes—
498C22×C4#41×C12714yes—
499C22×C4#41×C12714yes—
500C4⋊C4—28no—
501C4⋊C4—28no—
502C4⋊C4—28no—
503C4⋊C4—48no—
504C4⋊C4—48no—
505C22⋊C4—28no—
506C22⋊C4—28no—
507C22⋊C4—28no—
508C22⋊C4—28no—
509C22⋊C4—28no—
510C22⋊C4—44no—
511C42—28no—
512C23—22no—
513C23—22no—
514C23—22no—
515C23—22no—
516C23—22no—
517C23—22no—
518C23—24no—
519C23—24no—
520C23—24no—
521C23—24no—
522C23—24no—
523C23—24no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23#120×C12714yes—
533C23C22×D4×C12711yescharacteristic
534C23C22×D4×C12711yescharacteristic
535C23C22×D4×C12711yescharacteristic
536C23C2×#41×C12712yes—
537C23C2×#41×C12712yes—
538C23C2×#41×C12712yes—
539C23H(5,𝔽2)×C12712yes—
540C232−1+4×C12712yes—
541C232−1+4×C12712yes—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—416no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
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—
601C22—24no—
602C22—24no—
603C22—24no—
604C22—44no—
605C22—44no—
606C22—44no—
607C22—44no—
608C22—44no—
609C22—44no—
610C22C2×#120×C12711yescharacteristic
611C22#525×C12711yescharacteristic
612C22#525×C12711yescharacteristic
613C22#525×C12711yescharacteristic
614C22#529×C12712yes—
615C22#535×C12711yescharacteristic
616C22#536×C12711yescharacteristic
617C22#536×C12711yescharacteristic
618C22#539×C12712yes—
619C22#541×C12712yes—
620C22#542×C12712yes—
621C22#546×C12712yes—
622C22#546×C12712yes—
623C22#547×C12712yes—
624C22#547×C12712yes—
625C22#547×C12712yes—
626C22#547×C12712yes—
627C22#552×C12712yes—
628C22#553×C12712yes—
629C22#556×C12712yes—
630C22#563×C12712yes—
631C4—44no—
632C4—42no—
633C4—42no—
634C4—42no—
635C4—42no—
636C4—42no—
637C4—42no—
638C4—44no—
639C4—44no—
640C4—82no—
641C2—44no—
642C2C127×#240411yescharacteristic
643C2C127×#240611yescharacteristic
644C2C127×#240611yescharacteristic
645C2C127×#246612yes—
646C2C127×#246812yes—
647C2C127×#247812yes—
648C2C127×#268912yes—
649C2C127×#269812yes—
650C2C127×#271812yes—
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
5. C127×#1444C2semidirect
6. C127×#1442C2semidirect
7. C127×#1441C2semidirect
11. C127×#1436C2semidirect
315. #16024C127direct (N × H)
330. #1444C2×C127semidirect
331. #1442C2×C127semidirect
332. #1441C2×C127semidirect
336. #1436C2×C127semidirect
337. C127#16024direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#126×C1272
C2×#385×C1272
C2×#381×C1272
C127×#14442
C127×#14422
C127×#14412
C127×#14402
C127×#14362
#16024127