Finite Group Databasebeta

← C127×#14571 #44578244

Subgroups — C127×#14571 #44578244

Order 32512.

1966 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
1C2×#394×C127C211yesmaximal, characteristic
2C2×#388×C127C212yesmaximal, complemented
3C2×#386×C127C212yesmaximal
4C127×#1445C211yesmaximal, characteristic, complemented
5C127×#1442C212yesmaximal, complemented
6C127×#1439C212yesmaximal, complemented
7C127×#1436C211yesmaximal, characteristic, complemented
8C127×C22⋊#95C212yesmaximal, complemented
9C127×C22⋊#95C212yesmaximal, complemented
10C23×D4×C127C2211yescharacteristic
11C24×C4×C127C2212yes—
12C22×C4⋊C4×C127C2212yes—
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C22⋊C4×C127C2212yes—
15C22×C22⋊C4×C127C2212yes—
16C22×C22⋊C4×C127C2212yes—
17C22×C22⋊C4×C127C2212yes—
18C22×C22⋊C4×C127C2212yes—
19C22×C42×C127C2211yescharacteristic
20#394×C127C418yescomplemented
21#388×C127—28no—
22#386×C127—28no—
23C2×#95×C127C2212yes—
24C2×#95×C127C2212yes—
25C2×#95×C127C2212yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2212yes—
28C2×#95×C127C2211yescharacteristic
29C2×#95×C127C2212yes—
30C2×#95×C127C2211yescharacteristic
31C2×#95×C127C2212yes—
32C2×#95×C127C2211yescharacteristic
33C2×#95×C127C2211yescharacteristic
34C25×C127C2312yes—
35C22×D4×C127—24no—
36C22×D4×C127—24no—
37C22×D4×C127—41no—
38C22×D4×C127—41no—
39C22×D4×C127C2×C414yes—
40C23×C4×C127—24no—
41C23×C4×C127—24no—
42C23×C4×C127—24no—
43C23×C4×C127—42no—
44C23×C4×C127—42no—
45C23×C4×C127—42no—
46C23×C4×C127—42no—
47C23×C4×C127C2312yes—
48C23×C4×C127C2311yescharacteristic
49C23×C4×C127C2312yes—
50C23×C4×C127C2311yescharacteristic
51C23×C4×C127C2311yescharacteristic
52C23×C4×C127C2312yes—
53C23×C4×C127C2312yes—
54C23×C4×C127C2312yes—
55C2×C4⋊C4×C127—24no—
56C2×C4⋊C4×C127—41no—
57C2×C4⋊C4×C127—41no—
58C2×C4⋊C4×C127—42no—
59C2×C4⋊C4×C127—42no—
60C2×C4⋊C4×C127C2×C414yescomplemented
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—42no—
68C2×C22⋊C4×C127—42no—
69C2×C22⋊C4×C127—42no—
70C2×C22⋊C4×C127—42no—
71C2×C22⋊C4×C127—42no—
72C2×C22⋊C4×C127—42no—
73C2×C22⋊C4×C127C2×C418yescomplemented
74C2×C22⋊C4×C127C2×C418yescomplemented
75C2×C22⋊C4×C127D418yes—
76C2×C42×C127—24no—
77C2×C42×C127—41no—
78#95×C127—24no—
79#95×C127—24no—
80#95×C127—24no—
81#95×C127—24no—
82#95×C127—24no—
83#95×C127—42no—
84#95×C127—41no—
85#95×C127—42no—
86#95×C127—41no—
87#95×C127—41no—
88#95×C127C2×C414yescomplemented
89C24×C127—22no—
90C24×C127—22no—
91C24×C127—22no—
92C24×C127—22no—
93C24×C127—22no—
94C24×C127—22no—
95C24×C127—22no—
96C24×C127—22no—
97C24×C127—22no—
98C24×C127—22no—
99C24×C127—22no—
100C24×C127—22no—
101C24×C127C22×C414yes—
102C24×C127C2×D414yes—
103C24×C127#4114yes—
104C24×C127C2411yescharacteristic
105C2×D4×C127—216no—
106C2×D4×C127—44no—
107C2×D4×C127—44no—
108C2×D4×C127—48no—
109C2×D4×C127—44no—
110C22×C4×C127—22no—
111C22×C4×C127—22no—
112C22×C4×C127—22no—
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—21no—
125C22×C4×C127—21no—
126C22×C4×C127—21no—
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—21no—
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—21no—
143C22×C4×C127—21no—
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—48no—
154C22×C4×C127—48no—
155C22×C4×C127—48no—
156C22×C4×C127—48no—
157C22×C4×C127—48no—
158C22×C4×C127—48no—
159C22×C4×C127—48no—
160C22×C4×C127C22×C414yes—
161C22×C4×C127C22×C412yes—
162C22×C4×C127C22×C412yes—
163C22×C4×C127C22×C412yes—
164C22×C4×C127C2×D414yes—
165C22×C4×C127C2×D414yes—
166C22×C4×C127#4114yes—
167C4⋊C4×C127—44no—
168C4⋊C4×C127—48no—
169C22⋊C4×C127—216no—
170C22⋊C4×C127—48no—
171C22⋊C4×C127—48no—
172C22⋊C4×C127—48no—
173C22⋊C4×C127—48no—
174C42×C127—44no—
175C23×C127—24no—
176C23×C127—24no—
177C23×C127—24no—
178C23×C127—24no—
179C23×C127—24no—
180C23×C127—24no—
181C23×C127—24no—
182C23×C127—24no—
183C23×C127—24no—
184C23×C127—24no—
185C23×C127—24no—
186C23×C127—24no—
187C23×C127—24no—
188C23×C127—24no—
189C23×C127—24no—
190C23×C127—24no—
191C23×C127—24no—
192C23×C127—24no—
193C23×C127—42no—
194C23×C127—42no—
195C23×C127—42no—
196C23×C127—42no—
197C23×C127—42no—
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—42no—
207C23×C127—42no—
208C23×C127—42no—
209C23×C127C4×D418yes—
210C23×C127C23×C411yescharacteristic
211C23×C127C22×D412yes—
212C23×C127C2×#4112yes—
213C23×C127C2×#4112yes—
214C23×C127H(5,𝔽2)12yes—
215C23×C127H(5,𝔽2)11yescharacteristic
216C23×C127H(5,𝔽2)11yescharacteristic
217C23×C127H(5,𝔽2)12yes—
218C23×C1272−1+412yes—
219D4×C127—416no—
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—22no—
228C2×C4×C127—22no—
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—24no—
238C2×C4×C127—24no—
239C2×C4×C127—432no—
240C2×C4×C127—42no—
241C2×C4×C127—42no—
242C2×C4×C127—42no—
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—42no—
250C2×C4×C127—42no—
251C2×C4×C127—42no—
252C2×C4×C127—41no—
253C2×C4×C127—41no—
254C2×C4×C127—42no—
255C2×C4×C127—42no—
256C2×C4×C127—42no—
257C2×C4×C127—42no—
258C2×C4×C127—41no—
259C2×C4×C127—42no—
260C2×C4×C127—41no—
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—
271C22×C127—28no—
272C22×C127—28no—
273C22×C127—28no—
274C22×C127—44no—
275C22×C127—44no—
276C22×C127—44no—
277C22×C127—44no—
278C22×C127—44no—
279C22×C127—44no—
280C22×C127—44no—
281C22×C127—44no—
282C22×C127—44no—
283C22×C127—44no—
284C22×C127—44no—
285C22×C127—44no—
286C22×C127C2×C4×D412yes—
287C22×C127C4×#4111yescharacteristic
288C22×C127#51811yescharacteristic
289C22×C127#51811yescharacteristic
290C22×C127#52012yes—
291C22×C127#53412yes—
292C22×C127#53712yes—
293C22×C127#53812yes—
294C22×C127#53812yes—
295C22×C127#53912yes—
296C22×C127#54012yes—
297C22×C127D4211yescharacteristic
298C22×C127#54612yes—
299C22×C127#54612yes—
300C22×C127#54712yes—
301C22×C127#55111yescharacteristic
302C22×C127#55112yes—
303C22×C127#55212yes—
304C22×C127H(3,𝔽4)11yescharacteristic
305C22×C127#56212yes—
306C22×C127#56311yescharacteristic
307C4×C127—44no—
308C4×C127—42no—
309C4×C127—42no—
310C4×C127—42no—
311C4×C127—44no—
312C4×C127—44no—
313C4×C127—44no—
314C4×C127—82no—
315#14571C12711yesmaximal, characteristic, direct product factor, Sylow
316C2×C127—48no—
317C2×C127#232512yes—
318C2×C127#233311yescharacteristic
319C2×C127#235811yescharacteristic
320C2×C127#235912yes—
321C2×C127#237911yescharacteristic
322C2×C127#267112yes—
323C2×C127#268412yes—
324C2×C127#269512yes—
325C2×C127#274312yes—
326C2×#394C2×C12711yescharacteristic
327C2×#388C2×C12712yescomplemented
328C2×#386C2×C12712yes—
329#1445C2×C12711yescharacteristic, complemented
330#1442C2×C12712yescomplemented
331#1439C2×C12712yescomplemented
332#1436C2×C12711yescharacteristic, complemented
333C22⋊#95C2×C12712yescomplemented
334C22⋊#95C2×C12712yescomplemented
335C127#1457111yescharacteristic, direct product factor, Sylow
336C23×D4C22×C12711yescharacteristic
337C24×C4C22×C12712yes—
338C22×C4⋊C4C22×C12712yes—
339C22×C4⋊C4C22×C12711yescharacteristic
340C22×C22⋊C4C22×C12712yes—
341C22×C22⋊C4C22×C12712yes—
342C22×C22⋊C4C22×C12712yes—
343C22×C22⋊C4C22×C12712yes—
344C22×C22⋊C4C22×C12712yes—
345C22×C42C22×C12711yescharacteristic
346#394C4×C12718yescomplemented
347#388—28no—
348#386—28no—
349C2×#95C22×C12712yes—
350C2×#95C22×C12712yes—
351C2×#95C22×C12712yes—
352C2×#95C22×C12712yes—
353C2×#95C22×C12712yes—
354C2×#95C22×C12711yescharacteristic
355C2×#95C22×C12712yes—
356C2×#95C22×C12711yescharacteristic
357C2×#95C22×C12712yes—
358C2×#95C22×C12711yescharacteristic
359C2×#95C22×C12711yescharacteristic
360C25C23×C12712yes—
361C22×D4—24no—
362C22×D4—24no—
363C22×D4—41no—
364C22×D4—41no—
365C22×D4C2×C4×C12714yes—
366C23×C4—24no—
367C23×C4—24no—
368C23×C4—24no—
369C23×C4—42no—
370C23×C4—42no—
371C23×C4—42no—
372C23×C4—42no—
373C23×C4C23×C12712yes—
374C23×C4C23×C12712yes—
375C23×C4C23×C12711yescharacteristic
376C23×C4C23×C12711yescharacteristic
377C23×C4C23×C12711yescharacteristic
378C23×C4C23×C12712yes—
379C23×C4C23×C12712yes—
380C23×C4C23×C12712yes—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—41no—
383C2×C4⋊C4—41no—
384C2×C4⋊C4—42no—
385C2×C4⋊C4—42no—
386C2×C4⋊C4C2×C4×C12714yescomplemented
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4C2×C4×C12718yescomplemented
400C2×C22⋊C4C2×C4×C12718yescomplemented
401C2×C22⋊C4D4×C12718yes—
402C2×C42—24no—
403C2×C42—41no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—42no—
410#95—41no—
411#95—42no—
412#95—41no—
413#95—41no—
414#95C2×C4×C12714yescomplemented
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24C22×C4×C12714yes—
428C24C2×D4×C12714yes—
429C24#41×C12714yes—
430C24C24×C12711yescharacteristic
431C2×D4—216no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—48no—
435C2×D4—44no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
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—48no—
480C22×C4—48no—
481C22×C4—48no—
482C22×C4—48no—
483C22×C4—48no—
484C22×C4—48no—
485C22×C4—48no—
486C22×C4C22×C4×C12714yes—
487C22×C4C22×C4×C12712yes—
488C22×C4C22×C4×C12712yes—
489C22×C4C22×C4×C12712yes—
490C22×C4C2×D4×C12714yes—
491C22×C4C2×D4×C12714yes—
492C22×C4#41×C12714yes—
493C4⋊C4—44no—
494C4⋊C4—48no—
495C22⋊C4—216no—
496C22⋊C4—48no—
497C22⋊C4—48no—
498C22⋊C4—48no—
499C22⋊C4—48no—
500C42—44no—
501C23—24no—
502C23—24no—
503C23—24no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—24no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23C4×D4×C12718yes—
536C23C23×C4×C12711yescharacteristic
537C23C22×D4×C12712yes—
538C23C2×#41×C12712yes—
539C23C2×#41×C12712yes—
540C23H(5,𝔽2)×C12712yes—
541C23H(5,𝔽2)×C12711yescharacteristic
542C23H(5,𝔽2)×C12711yescharacteristic
543C23H(5,𝔽2)×C12712yes—
544C232−1+4×C12712yes—
545D4—416no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
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—24no—
564C2×C4—24no—
565C2×C4—432no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—41no—
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—
597C22—28no—
598C22—28no—
599C22—28no—
600C22—44no—
601C22—44no—
602C22—44no—
603C22—44no—
604C22—44no—
605C22—44no—
606C22—44no—
607C22—44no—
608C22—44no—
609C22—44no—
610C22—44no—
611C22—44no—
612C22C2×C4×D4×C12712yes—
613C22C4×#41×C12711yescharacteristic
614C22#518×C12711yescharacteristic
615C22#518×C12711yescharacteristic
616C22#520×C12712yes—
617C22#534×C12712yes—
618C22#537×C12712yes—
619C22#538×C12712yes—
620C22#538×C12712yes—
621C22#539×C12712yes—
622C22#540×C12712yes—
623C22D42×C12711yescharacteristic
624C22#546×C12712yes—
625C22#546×C12712yes—
626C22#547×C12712yes—
627C22#551×C12711yescharacteristic
628C22#551×C12712yes—
629C22#552×C12712yes—
630C22H(3,𝔽4)×C12711yescharacteristic
631C22#562×C12712yes—
632C22#563×C12711yescharacteristic
633C4—44no—
634C4—42no—
635C4—42no—
636C4—42no—
637C4—44no—
638C4—44no—
639C4—44no—
640C4—82no—
641C2—48no—
642C2C127×#232512yes—
643C2C127×#233311yescharacteristic
644C2C127×#235811yescharacteristic
645C2C127×#235912yes—
646C2C127×#237911yescharacteristic
647C2C127×#267112yes—
648C2C127×#268412yes—
649C2C127×#269512yes—
650C2C127×#274312yes—
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
2. C2×#388×C127C2semidirect
4. C127×#1445C2semidirect
5. C127×#1442C2semidirect
6. C127×#1439C2semidirect
7. C127×#1436C2semidirect
8. C127×C22⋊#95C2semidirect
9. C127×C22⋊#95C2semidirect
20. #394×C127C4semidirect
60. C2×C4⋊C4×C127C2×C4semidirect
73. C2×C22⋊C4×C127C2×C4semidirect
74. C2×C22⋊C4×C127C2×C4semidirect
88. #95×C127C2×C4semidirect
315. #14571C127direct (N × H)
327. C2×#388C2×C127semidirect
329. #1445C2×C127semidirect
330. #1442C2×C127semidirect
331. #1439C2×C127semidirect
332. #1436C2×C127semidirect
333. C22⋊#95C2×C127semidirect
334. C22⋊#95C2×C127semidirect
335. C127#14571direct (N × H)
346. #394C4×C127semidirect
386. C2×C4⋊C4C2×C4×C127semidirect
399. C2×C22⋊C4C2×C4×C127semidirect
400. C2×C22⋊C4C2×C4×C127semidirect
414. #95C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#394×C1272
C2×#388×C1272
C2×#386×C1272
C127×#14452
C127×#14422
C127×#14392
C127×#14362
C127×C22⋊#952
#14571127