Finite Group Databasebeta

← C127×#14145 #44577818

Subgroups — C127×#14145 #44577818

Order 32512.

1962 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#388×C127C212yesmaximal, complemented
2C2×#386×C127C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C127C212yesmaximal, complemented
4C127×#1439C212yesmaximal, complemented
5C127×#1438C211yesmaximal, characteristic
6C127×#1438C211yesmaximal, characteristic
7C127×#1437C212yesmaximal, complemented
8C127×#1436C212yesmaximal, complemented
9C127×#1434C212yesmaximal, complemented
10C23×D4×C127C2211yescharacteristic
11C24×C4×C127C2211yescharacteristic
12C22×C4⋊C4×C127C2212yes—
13C22×C22⋊C4×C127C2212yes—
14C22×C22⋊C4×C127C2212yes—
15C22×C22⋊C4×C127C2211yescharacteristic
16C22×C22⋊C4×C127C2212yes—
17C22×C22⋊C4×C127C2211yescharacteristic
18C22×C22⋊C4×C127C2212yes—
19C22×C22⋊C4×C127C2211yescharacteristic
20C22×C42×C127C2212yes—
21C22×C42×C127C2212yes—
22#388×C127—28no—
23#386×C127C418yescomplemented
24C4×C22⋊C4×C127—28no—
25C2×#95×C127C2212yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2212yes—
28C2×#95×C127C2211yescharacteristic
29C2×#95×C127C2212yes—
30C2×#95×C127C2212yes—
31C2×#95×C127C2211yescharacteristic
32C2×#95×C127C2212yes—
33C2×#95×C127C2212yes—
34C25×C127C2311yescharacteristic
35C25×C127C2311yescharacteristic
36C22×D4×C127—24no—
37C22×D4×C127—42no—
38C22×D4×C127—41no—
39C22×D4×C127—41no—
40C22×D4×C127C2×C414yes—
41C23×C4×C127—24no—
42C23×C4×C127—24no—
43C23×C4×C127—41no—
44C23×C4×C127—41no—
45C23×C4×C127C2×C414yes—
46C23×C4×C127C2312yes—
47C23×C4×C127C2311yescharacteristic
48C23×C4×C127C2312yes—
49C23×C4×C127C2312yes—
50C23×C4×C127C2312yes—
51C23×C4×C127C2312yes—
52C23×C4×C127C2312yes—
53C2×C4⋊C4×C127—24no—
54C2×C4⋊C4×C127—24no—
55C2×C4⋊C4×C127—42no—
56C2×C22⋊C4×C127—24no—
57C2×C22⋊C4×C127—24no—
58C2×C22⋊C4×C127—24no—
59C2×C22⋊C4×C127—24no—
60C2×C22⋊C4×C127—24no—
61C2×C22⋊C4×C127—24no—
62C2×C22⋊C4×C127—24no—
63C2×C22⋊C4×C127—24no—
64C2×C22⋊C4×C127—24no—
65C2×C22⋊C4×C127—24no—
66C2×C22⋊C4×C127—24no—
67C2×C22⋊C4×C127—24no—
68C2×C22⋊C4×C127—42no—
69C2×C22⋊C4×C127—42no—
70C2×C22⋊C4×C127—41no—
71C2×C22⋊C4×C127—41no—
72C2×C22⋊C4×C127C2×C418yes—
73C2×C22⋊C4×C127C2×C414yes—
74C2×C42×C127—24no—
75C2×C42×C127—24no—
76C2×C42×C127—24no—
77C2×C42×C127—24no—
78C2×C42×C127—42no—
79C2×C42×C127—42no—
80#95×C127—24no—
81#95×C127—24no—
82#95×C127—24no—
83#95×C127—42no—
84#95×C127—42no—
85#95×C127—41no—
86#95×C127—41no—
87#95×C127C2×C418yes—
88#95×C127D418yescomplemented
89C24×C127—22no—
90C24×C127—22no—
91C24×C127—22no—
92C24×C127—22no—
93C24×C127—22no—
94C24×C127—21no—
95C24×C127—21no—
96C24×C127—22no—
97C24×C127—22no—
98C24×C127—22no—
99C24×C127—22no—
100C24×C127—22no—
101C24×C127—21no—
102C24×C127—22no—
103C24×C127—21no—
104C24×C127C22×C412yes—
105C24×C127C22×C412yes—
106C24×C127#4114yes—
107C24×C127C2411yescharacteristic
108C2×D4×C127—28no—
109C2×D4×C127—44no—
110C2×D4×C127—44no—
111C2×D4×C127—48no—
112C2×D4×C127—48no—
113C22×C4×C127—22no—
114C22×C4×C127—22no—
115C22×C4×C127—22no—
116C22×C4×C127—22no—
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—22no—
125C22×C4×C127—22no—
126C22×C4×C127—22no—
127C22×C4×C127—22no—
128C22×C4×C127—22no—
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—21no—
145C22×C4×C127—21no—
146C22×C4×C127—22no—
147C22×C4×C127—22no—
148C22×C4×C127—22no—
149C22×C4×C127—22no—
150C22×C4×C127—22no—
151C22×C4×C127—216no—
152C22×C4×C127—44no—
153C22×C4×C127—44no—
154C22×C4×C127—48no—
155C22×C4×C127—44no—
156C22×C4×C127C22×C412yes—
157C22×C4×C127C22×C414yes—
158C22×C4×C127C22×C414yes—
159C22×C4×C127C2×D414yes—
160C22×C4×C127C2×D414yes—
161C22×C4×C127C2×D414yes—
162C22×C4×C127#4114yes—
163C22×C4×C127#4114yes—
164C22×C4×C127#4114yes—
165C4⋊C4×C127—48no—
166C22⋊C4×C127—216no—
167C22⋊C4×C127—216no—
168C22⋊C4×C127—216no—
169C22⋊C4×C127—44no—
170C22⋊C4×C127—44no—
171C22⋊C4×C127—48no—
172C22⋊C4×C127—44no—
173C42×C127—48no—
174C42×C127—48no—
175C23×C127—24no—
176C23×C127—24no—
177C23×C127—22no—
178C23×C127—22no—
179C23×C127—24no—
180C23×C127—24no—
181C23×C127—24no—
182C23×C127—24no—
183C23×C127—24no—
184C23×C127—24no—
185C23×C127—22no—
186C23×C127—24no—
187C23×C127—24no—
188C23×C127—22no—
189C23×C127—22no—
190C23×C127—41no—
191C23×C127—42no—
192C23×C127—42no—
193C23×C127—42no—
194C23×C127—41no—
195C23×C127—41no—
196C23×C127—42no—
197C23×C127—42no—
198C23×C127—42no—
199C23×C127—41no—
200C23×C127—42no—
201C23×C127—42no—
202C23×C127—42no—
203C23×C127—42no—
204C23×C127—42no—
205C23×C127—42no—
206C23×C127—41no—
207C23×C127—42no—
208C23×C127—42no—
209C23×C127—42no—
210C23×C127—41no—
211C23×C127—41no—
212C23×C127—42no—
213C23×C127—42no—
214C23×C127—42no—
215C23×C127—41no—
216C23×C127#11714yes—
217C23×C127C23×C411yescharacteristic
218C23×C127C22×D412yes—
219C23×C127C2×#4112yes—
220C23×C127C2×#4112yes—
221C23×C127C2×#4112yes—
222C23×C127C2×#4112yes—
223C23×C127H(5,𝔽2)11yescharacteristic
224C23×C127H(5,𝔽2)11yescharacteristic
225C23×C127H(5,𝔽2)12yes—
226D4×C127—416no—
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—22no—
234C2×C4×C127—24no—
235C2×C4×C127—24no—
236C2×C4×C127—24no—
237C2×C4×C127—22no—
238C2×C4×C127—22no—
239C2×C4×C127—24no—
240C2×C4×C127—24no—
241C2×C4×C127—24no—
242C2×C4×C127—24no—
243C2×C4×C127—24no—
244C2×C4×C127—24no—
245C2×C4×C127—24no—
246C2×C4×C127—24no—
247C2×C4×C127—24no—
248C2×C4×C127—24no—
249C2×C4×C127—24no—
250C2×C4×C127—24no—
251C2×C4×C127—416no—
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×C127C4×D418yes—
275C22×C127—24no—
276C22×C127—28no—
277C22×C127—42no—
278C22×C127—44no—
279C22×C127—42no—
280C22×C127—44no—
281C22×C127—44no—
282C22×C127—44no—
283C22×C127—44no—
284C22×C127—42no—
285C22×C127—42no—
286C22×C127—44no—
287C22×C127—42no—
288C22×C127—44no—
289C22×C127—82no—
290C22×C127—82no—
291C22×C127—82no—
292C22×C127—82no—
293C22×C127C2×#11711yescharacteristic
294C22×C127C2×C4×D412yes—
295C22×C127C4×#4112yes—
296C22×C127#51811yescharacteristic
297C22×C127#51811yescharacteristic
298C22×C127#52512yes—
299C22×C127#52512yes—
300C22×C127#52912yes—
301C22×C127#52912yes—
302C22×C127#53812yes—
303C22×C127#53812yes—
304C22×C127D4211yescharacteristic
305C22×C127#54612yes—
306C22×C127#54612yes—
307C22×C127#55012yes—
308C22×C127#55111yescharacteristic
309C22×C127#55111yescharacteristic
310C22×C127#55312yes—
311C22×C127#55312yes—
312C22×C127#55512yes—
313C22×C127#55911yescharacteristic
314C4×C127—28no—
315C4×C127—42no—
316C4×C127—44no—
317C4×C127—44no—
318C4×C127—44no—
319C4×C127—44no—
320C4×C127—44no—
321#14145C12711yesmaximal, characteristic, direct product factor, Sylow
322C2×C127—44no—
323C2×C127—82no—
324C2×C127#229012yes—
325C2×C127#231211yescharacteristic
326C2×C127#235811yescharacteristic
327C2×C127#236312yes—
328C2×C127#237411yescharacteristic
329C2×C127#245612yes—
330C2×C127#245912yes—
331C2×C127#246712yes—
332C2×C127#251812yes—
333C2×#388C2×C12712yescomplemented
334C2×#386C2×C12711yescharacteristic
335C2×C4×C22⋊C4C2×C12712yescomplemented
336#1439C2×C12712yescomplemented
337#1438C2×C12711yescharacteristic
338#1438C2×C12711yescharacteristic
339#1437C2×C12712yescomplemented
340#1436C2×C12712yescomplemented
341#1434C2×C12712yescomplemented
342C127#1414511yescharacteristic, direct product factor, Sylow
343C23×D4C22×C12711yescharacteristic
344C24×C4C22×C12711yescharacteristic
345C22×C4⋊C4C22×C12712yes—
346C22×C22⋊C4C22×C12712yes—
347C22×C22⋊C4C22×C12712yes—
348C22×C22⋊C4C22×C12711yescharacteristic
349C22×C22⋊C4C22×C12712yes—
350C22×C22⋊C4C22×C12711yescharacteristic
351C22×C22⋊C4C22×C12712yes—
352C22×C22⋊C4C22×C12711yescharacteristic
353C22×C42C22×C12712yes—
354C22×C42C22×C12712yes—
355#388—28no—
356#386C4×C12718yescomplemented
357C4×C22⋊C4—28no—
358C2×#95C22×C12712yes—
359C2×#95C22×C12712yes—
360C2×#95C22×C12712yes—
361C2×#95C22×C12711yescharacteristic
362C2×#95C22×C12712yes—
363C2×#95C22×C12712yes—
364C2×#95C22×C12711yescharacteristic
365C2×#95C22×C12712yes—
366C2×#95C22×C12712yes—
367C25C23×C12711yescharacteristic
368C25C23×C12711yescharacteristic
369C22×D4—24no—
370C22×D4—42no—
371C22×D4—41no—
372C22×D4—41no—
373C22×D4C2×C4×C12714yes—
374C23×C4—24no—
375C23×C4—24no—
376C23×C4—41no—
377C23×C4—41no—
378C23×C4C2×C4×C12714yes—
379C23×C4C23×C12712yes—
380C23×C4C23×C12711yescharacteristic
381C23×C4C23×C12712yes—
382C23×C4C23×C12712yes—
383C23×C4C23×C12712yes—
384C23×C4C23×C12712yes—
385C23×C4C23×C12712yes—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—42no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—41no—
404C2×C22⋊C4—41no—
405C2×C22⋊C4C2×C4×C12718yes—
406C2×C22⋊C4C2×C4×C12714yes—
407C2×C42—24no—
408C2×C42—24no—
409C2×C42—24no—
410C2×C42—24no—
411C2×C42—42no—
412C2×C42—42no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—42no—
417#95—42no—
418#95—41no—
419#95—41no—
420#95C2×C4×C12718yes—
421#95D4×C12718yescomplemented
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—21no—
428C24—21no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—21no—
435C24—22no—
436C24—21no—
437C24C22×C4×C12712yes—
438C24C22×C4×C12712yes—
439C24#41×C12714yes—
440C24C24×C12711yescharacteristic
441C2×D4—28no—
442C2×D4—44no—
443C2×D4—44no—
444C2×D4—48no—
445C2×D4—48no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
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—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—216no—
485C22×C4—44no—
486C22×C4—44no—
487C22×C4—48no—
488C22×C4—44no—
489C22×C4C22×C4×C12712yes—
490C22×C4C22×C4×C12714yes—
491C22×C4C22×C4×C12714yes—
492C22×C4C2×D4×C12714yes—
493C22×C4C2×D4×C12714yes—
494C22×C4C2×D4×C12714yes—
495C22×C4#41×C12714yes—
496C22×C4#41×C12714yes—
497C22×C4#41×C12714yes—
498C4⋊C4—48no—
499C22⋊C4—216no—
500C22⋊C4—216no—
501C22⋊C4—216no—
502C22⋊C4—44no—
503C22⋊C4—44no—
504C22⋊C4—48no—
505C22⋊C4—44no—
506C42—48no—
507C42—48no—
508C23—24no—
509C23—24no—
510C23—22no—
511C23—22no—
512C23—24no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—22no—
519C23—24no—
520C23—24no—
521C23—22no—
522C23—22no—
523C23—41no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—41no—
528C23—41no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—41no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—41no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—41no—
544C23—41no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—41no—
549C23#117×C12714yes—
550C23C23×C4×C12711yescharacteristic
551C23C22×D4×C12712yes—
552C23C2×#41×C12712yes—
553C23C2×#41×C12712yes—
554C23C2×#41×C12712yes—
555C23C2×#41×C12712yes—
556C23H(5,𝔽2)×C12711yescharacteristic
557C23H(5,𝔽2)×C12711yescharacteristic
558C23H(5,𝔽2)×C12712yes—
559D4—416no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—22no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—416no—
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—42no—
606C2×C4—42no—
607C2×C4C4×D4×C12718yes—
608C22—24no—
609C22—28no—
610C22—42no—
611C22—44no—
612C22—42no—
613C22—44no—
614C22—44no—
615C22—44no—
616C22—44no—
617C22—42no—
618C22—42no—
619C22—44no—
620C22—42no—
621C22—44no—
622C22—82no—
623C22—82no—
624C22—82no—
625C22—82no—
626C22C2×#117×C12711yescharacteristic
627C22C2×C4×D4×C12712yes—
628C22C4×#41×C12712yes—
629C22#518×C12711yescharacteristic
630C22#518×C12711yescharacteristic
631C22#525×C12712yes—
632C22#525×C12712yes—
633C22#529×C12712yes—
634C22#529×C12712yes—
635C22#538×C12712yes—
636C22#538×C12712yes—
637C22D42×C12711yescharacteristic
638C22#546×C12712yes—
639C22#546×C12712yes—
640C22#550×C12712yes—
641C22#551×C12711yescharacteristic
642C22#551×C12711yescharacteristic
643C22#553×C12712yes—
644C22#553×C12712yes—
645C22#555×C12712yes—
646C22#559×C12711yescharacteristic
647C4—28no—
648C4—42no—
649C4—44no—
650C4—44no—
651C4—44no—
652C4—44no—
653C4—44no—
654C2—44no—
655C2—82no—
656C2C127×#229012yes—
657C2C127×#231211yescharacteristic
658C2C127×#235811yescharacteristic
659C2C127×#236312yes—
660C2C127×#237411yescharacteristic
661C2C127×#245612yes—
662C2C127×#245912yes—
663C2C127×#246712yes—
664C2C127×#251812yes—
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#388×C127C2semidirect
3. C2×C4×C22⋊C4×C127C2semidirect
4. C127×#1439C2semidirect
7. C127×#1437C2semidirect
8. C127×#1436C2semidirect
9. C127×#1434C2semidirect
23. #386×C127C4semidirect
88. #95×C127D4semidirect
321. #14145C127direct (N × H)
333. C2×#388C2×C127semidirect
335. C2×C4×C22⋊C4C2×C127semidirect
336. #1439C2×C127semidirect
339. #1437C2×C127semidirect
340. #1436C2×C127semidirect
341. #1434C2×C127semidirect
342. C127#14145direct (N × H)
356. #386C4×C127semidirect
421. #95D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#388×C1272
C2×#386×C1272
C2×C4×C22⋊C4×C1272
C127×#14392
C127×#14382
C127×#14372
C127×#14362
C127×#14342
#14145127