Finite Group Databasebeta

← C127×#14926 #44578599

Subgroups — C127×#14926 #44578599

Order 32512.

3030 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C127C212yesmaximal, complemented
2C22×#121×C127C211yesmaximal, characteristic
3C2×#386×C127C212yesmaximal, complemented
4C22×#95×C127C211yesmaximal, characteristic, complemented
5C127×#1444C212yesmaximal, complemented
6C127×#1439C214yesmaximal, complemented
7C127×#1438C212yesmaximal, complemented
8C127×C22⋊#95C211yesmaximal, characteristic, complemented
9C23×D4×C127C2212yes—
10C23×D4×C127C2211yescharacteristic
11C24×C4×C127C2211yescharacteristic
12C24×C4×C127C2211yescharacteristic
13C24×C4×C127C2211yescharacteristic
14C2×#123×C127—28no—
15C2×#123×C127—28no—
16C2×#123×C127—28no—
17C2×#121×C127—28no—
18C2×#121×C127—24no—
19C22×C4⋊C4×C127C2211yescharacteristic
20C22×C4⋊C4×C127C2214yes—
21C22×C22⋊C4×C127C2212yes—
22C22×C22⋊C4×C127C2214yes—
23C22×C22⋊C4×C127C2214yes—
24C22×C22⋊C4×C127C2212yes—
25#386×C127—28no—
26C2×#95×C127—24no—
27C2×#95×C127C2212yes—
28C2×#95×C127C2212yes—
29C2×#95×C127C2212yes—
30C2×#95×C127C2214yes—
31C2×#95×C127C2212yes—
32C25×C127C2312yes—
33C25×C127C2311yescharacteristic
34C22×D4×C127—24no—
35C22×D4×C127—24no—
36C22×D4×C127—24no—
37C22×D4×C127—24no—
38C22×D4×C127—24no—
39C22×D4×C127—24no—
40C22×D4×C127—24no—
41C22×D4×C127—22no—
42C22×D4×C127—24no—
43C22×D4×C127—42no—
44C22×D4×C127D418yes—
45C23×C4×C127—24no—
46C23×C4×C127—24no—
47C23×C4×C127—24no—
48C23×C4×C127—22no—
49C23×C4×C127—22no—
50C23×C4×C127—22no—
51C23×C4×C127—24no—
52C23×C4×C127—24no—
53C23×C4×C127—24no—
54C23×C4×C127—42no—
55C23×C4×C127—42no—
56C23×C4×C127D414yes—
57C23×C4×C127D414yescomplemented
58C23×C4×C127C2314yes—
59C23×C4×C127C2312yes—
60C23×C4×C127C2311yescharacteristic
61C23×C4×C127C2312yes—
62C23×C4×C127C2312yes—
63C23×C4×C127C2311yescharacteristic
64#123×C127—264no—
65#121×C127—232no—
66C2×C4⋊C4×C127—24no—
67C2×C4⋊C4×C127—22no—
68C2×C4⋊C4×C127—28no—
69C2×C4⋊C4×C127—28no—
70C2×C4⋊C4×C127—28no—
71C2×C22⋊C4×C127—24no—
72C2×C22⋊C4×C127—28no—
73C2×C22⋊C4×C127—24no—
74C2×C22⋊C4×C127—24no—
75C2×C22⋊C4×C127—24no—
76C2×C22⋊C4×C127—24no—
77C2×C22⋊C4×C127—28no—
78C2×C22⋊C4×C127—28no—
79C2×C22⋊C4×C127—28no—
80C2×C22⋊C4×C127—28no—
81C2×C22⋊C4×C127—44no—
82C2×C22⋊C4×C127D418yescomplemented
83#95×C127—24no—
84#95×C127—24no—
85#95×C127—28no—
86#95×C127—24no—
87#95×C127—42no—
88C24×C127—22no—
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—24no—
98C24×C127—22no—
99C24×C127—24no—
100C24×C127—24no—
101C24×C127—24no—
102C24×C127C2×D414yes—
103C24×C127C2×D412yes—
104C24×C127C2×D414yes—
105C24×C127C2×D414yes—
106C24×C127C2×D412yes—
107C24×C127#4112yes—
108C24×C127C2411yescharacteristic
109C2×D4×C127—28no—
110C2×D4×C127—216no—
111C2×D4×C127—216no—
112C2×D4×C127—216no—
113C2×D4×C127—416no—
114C2×D4×C127—44no—
115C2×D4×C127—48no—
116C2×D4×C127—48no—
117C2×D4×C127—48no—
118C2×D4×C127—48no—
119C2×D4×C127—44no—
120C22×C4×C127—22no—
121C22×C4×C127—22no—
122C22×C4×C127—28no—
123C22×C4×C127—28no—
124C22×C4×C127—216no—
125C22×C4×C127—28no—
126C22×C4×C127—22no—
127C22×C4×C127—22no—
128C22×C4×C127—22no—
129C22×C4×C127—24no—
130C22×C4×C127—24no—
131C22×C4×C127—24no—
132C22×C4×C127—22no—
133C22×C4×C127—24no—
134C22×C4×C127—24no—
135C22×C4×C127—22no—
136C22×C4×C127—22no—
137C22×C4×C127—22no—
138C22×C4×C127—22no—
139C22×C4×C127—24no—
140C22×C4×C127—24no—
141C22×C4×C127—22no—
142C22×C4×C127—22no—
143C22×C4×C127—22no—
144C22×C4×C127—22no—
145C22×C4×C127—24no—
146C22×C4×C127—22no—
147C22×C4×C127—24no—
148C22×C4×C127—24no—
149C22×C4×C127—28no—
150C22×C4×C127—44no—
151C22×C4×C127—416no—
152C22×C4×C127—416no—
153C22×C4×C127—44no—
154C22×C4×C127—44no—
155C22×C4×C127—48no—
156C22×C4×C127—44no—
157C22×C4×C127—44no—
158C22×C4×C127C2×D412yes—
159C22×C4×C127C2×D418yes—
160C22×C4×C127C2×D414yes—
161C22×C4×C127C2×D414yes—
162C22×C4×C127C2×D412yes—
163C22×C4×C127#4114yes—
164C22×C4×C127#4114yes—
165C4⋊C4×C127—28no—
166C4⋊C4×C127—232no—
167C22⋊C4×C127—216no—
168C22⋊C4×C127—232no—
169C22⋊C4×C127—216no—
170C22⋊C4×C127—416no—
171C23×C127—22no—
172C23×C127—22no—
173C23×C127—24no—
174C23×C127—24no—
175C23×C127—22no—
176C23×C127—22no—
177C23×C127—24no—
178C23×C127—24no—
179C23×C127—28no—
180C23×C127—28no—
181C23×C127—28no—
182C23×C127—28no—
183C23×C127—24no—
184C23×C127—24no—
185C23×C127—24no—
186C23×C127—28no—
187C23×C127—28no—
188C23×C127—42no—
189C23×C127—42no—
190C23×C127—42no—
191C23×C127—42no—
192C23×C127—42no—
193C23×C127—44no—
194C23×C127—42no—
195C23×C127—44no—
196C23×C127—42no—
197C23×C127—42no—
198C23×C127—44no—
199C23×C127—44no—
200C23×C127—44no—
201C23×C127—44no—
202C23×C127—44no—
203C23×C127—44no—
204C23×C127—44no—
205C23×C127—44no—
206C23×C127#12018yes—
207C23×C127#12014yes—
208C23×C127#12114yes—
209C23×C127#12118yes—
210C23×C127#12714yes—
211C23×C127C22×D411yescharacteristic
212C23×C127C22×D412yes—
213C23×C127C22×D411yescharacteristic
214C23×C127C22×D412yes—
215C23×C127C2×#4111yescharacteristic
216C23×C127C2×#4112yes—
217C23×C127C2×#4112yes—
218C23×C127H(5,𝔽2)12yes—
219C23×C1272−1+412yes—
220D4×C127—416no—
221D4×C127—432no—
222C2×C4×C127—22no—
223C2×C4×C127—22no—
224C2×C4×C127—28no—
225C2×C4×C127—28no—
226C2×C4×C127—22no—
227C2×C4×C127—28no—
228C2×C4×C127—24no—
229C2×C4×C127—24no—
230C2×C4×C127—24no—
231C2×C4×C127—24no—
232C2×C4×C127—22no—
233C2×C4×C127—24no—
234C2×C4×C127—22no—
235C2×C4×C127—28no—
236C2×C4×C127—28no—
237C2×C4×C127—28no—
238C2×C4×C127—416no—
239C2×C4×C127—416no—
240C2×C4×C127—42no—
241C2×C4×C127—42no—
242C2×C4×C127—44no—
243C2×C4×C127—42no—
244C2×C4×C127—42no—
245C2×C4×C127—42no—
246C2×C4×C127—42no—
247C2×C4×C127—42no—
248C2×C4×C127—44no—
249C2×C4×C127—42no—
250C2×C4×C127—44no—
251C2×C4×C127—44no—
252C2×C4×C127—44no—
253C2×C4×C127—44no—
254C2×C4×C127—44no—
255C2×C4×C127—416no—
256C2×C4×C127#12314yescomplemented
257C22×C127—24no—
258C22×C127—24no—
259C22×C127—24no—
260C22×C127—24no—
261C22×C127—216no—
262C22×C127—216no—
263C22×C127—24no—
264C22×C127—24no—
265C22×C127—44no—
266C22×C127—44no—
267C22×C127—44no—
268C22×C127—48no—
269C22×C127—48no—
270C22×C127—82no—
271C22×C127—82no—
272C22×C127—84no—
273C22×C127—84no—
274C22×C127—82no—
275C22×C127—82no—
276C22×C127#39218yes—
277C22×C127C2×#12011yescharacteristic
278C22×C127C2×#12012yes—
279C22×C127C2×#12111yescharacteristic
280C22×C127C2×#12112yes—
281C22×C127C2×#12311yescharacteristic
282C22×C127#52511yescharacteristic
283C22×C127#52912yes—
284C22×C127C2×#12711yescharacteristic
285C22×C127#53212yes—
286C22×C127#53411yescharacteristic
287C22×C127#53611yescharacteristic
288C22×C127#53712yes—
289C22×C127#53912yes—
290C22×C127#54614yes—
291C22×C127#54614yes—
292C22×C127#54714yes—
293C22×C127#54714yes—
294C4×C127—24no—
295C4×C127—44no—
296C4×C127—44no—
297C4×C127—42no—
298C4×C127—48no—
299C4×C127—44no—
300#14926C12711yesmaximal, characteristic, direct product factor, Sylow
301C2×C127—28no—
302C2×C127—84no—
303C2×C127C2×#39211yescharacteristic
304C2×C127#240511yescharacteristic
305C2×C127#240611yescharacteristic
306C2×C127#242514yes—
307C2×C127#243014yes—
308C2×C127#250111yescharacteristic
309C2×C127#253911yescharacteristic
310C2×C127#261811yescharacteristic
311C2×C127#285411yescharacteristic
312C22×#123C2×C12712yescomplemented
313C22×#121C2×C12711yescharacteristic
314C2×#386C2×C12712yescomplemented
315C22×#95C2×C12711yescharacteristic, complemented
316#1444C2×C12712yescomplemented
317#1439C2×C12714yescomplemented
318#1438C2×C12712yescomplemented
319C22⋊#95C2×C12711yescharacteristic, complemented
320C127#1492611yescharacteristic, direct product factor, Sylow
321C23×D4C22×C12712yes—
322C23×D4C22×C12711yescharacteristic
323C24×C4C22×C12711yescharacteristic
324C24×C4C22×C12711yescharacteristic
325C24×C4C22×C12711yescharacteristic
326C2×#123—28no—
327C2×#123—28no—
328C2×#123—28no—
329C2×#121—28no—
330C2×#121—24no—
331C22×C4⋊C4C22×C12711yescharacteristic
332C22×C4⋊C4C22×C12714yes—
333C22×C22⋊C4C22×C12712yes—
334C22×C22⋊C4C22×C12714yes—
335C22×C22⋊C4C22×C12714yes—
336C22×C22⋊C4C22×C12712yes—
337#386—28no—
338C2×#95—24no—
339C2×#95C22×C12712yes—
340C2×#95C22×C12712yes—
341C2×#95C22×C12712yes—
342C2×#95C22×C12714yes—
343C2×#95C22×C12712yes—
344C25C23×C12712yes—
345C25C23×C12711yescharacteristic
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—24no—
351C22×D4—24no—
352C22×D4—24no—
353C22×D4—22no—
354C22×D4—24no—
355C22×D4—42no—
356C22×D4D4×C12718yes—
357C23×C4—24no—
358C23×C4—24no—
359C23×C4—24no—
360C23×C4—22no—
361C23×C4—22no—
362C23×C4—22no—
363C23×C4—24no—
364C23×C4—24no—
365C23×C4—24no—
366C23×C4—42no—
367C23×C4—42no—
368C23×C4D4×C12714yes—
369C23×C4D4×C12714yescomplemented
370C23×C4C23×C12714yes—
371C23×C4C23×C12712yes—
372C23×C4C23×C12711yescharacteristic
373C23×C4C23×C12712yes—
374C23×C4C23×C12712yes—
375C23×C4C23×C12711yescharacteristic
376#123—264no—
377#121—232no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—28no—
381C2×C4⋊C4—28no—
382C2×C4⋊C4—28no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—28no—
390C2×C22⋊C4—28no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4D4×C12718yescomplemented
395#95—24no—
396#95—24no—
397#95—28no—
398#95—24no—
399#95—42no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—24no—
410C24—22no—
411C24—24no—
412C24—24no—
413C24—24no—
414C24C2×D4×C12714yes—
415C24C2×D4×C12712yes—
416C24C2×D4×C12714yes—
417C24C2×D4×C12714yes—
418C24C2×D4×C12712yes—
419C24#41×C12712yes—
420C24C24×C12711yescharacteristic
421C2×D4—28no—
422C2×D4—216no—
423C2×D4—216no—
424C2×D4—216no—
425C2×D4—416no—
426C2×D4—44no—
427C2×D4—48no—
428C2×D4—48no—
429C2×D4—48no—
430C2×D4—48no—
431C2×D4—44no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—28no—
435C22×C4—28no—
436C22×C4—216no—
437C22×C4—28no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—22no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—28no—
462C22×C4—44no—
463C22×C4—416no—
464C22×C4—416no—
465C22×C4—44no—
466C22×C4—44no—
467C22×C4—48no—
468C22×C4—44no—
469C22×C4—44no—
470C22×C4C2×D4×C12712yes—
471C22×C4C2×D4×C12718yes—
472C22×C4C2×D4×C12714yes—
473C22×C4C2×D4×C12714yes—
474C22×C4C2×D4×C12712yes—
475C22×C4#41×C12714yes—
476C22×C4#41×C12714yes—
477C4⋊C4—28no—
478C4⋊C4—232no—
479C22⋊C4—216no—
480C22⋊C4—232no—
481C22⋊C4—216no—
482C22⋊C4—416no—
483C23—22no—
484C23—22no—
485C23—24no—
486C23—24no—
487C23—22no—
488C23—22no—
489C23—24no—
490C23—24no—
491C23—28no—
492C23—28no—
493C23—28no—
494C23—28no—
495C23—24no—
496C23—24no—
497C23—24no—
498C23—28no—
499C23—28no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—44no—
506C23—42no—
507C23—44no—
508C23—42no—
509C23—42no—
510C23—44no—
511C23—44no—
512C23—44no—
513C23—44no—
514C23—44no—
515C23—44no—
516C23—44no—
517C23—44no—
518C23#120×C12718yes—
519C23#120×C12714yes—
520C23#121×C12714yes—
521C23#121×C12718yes—
522C23#127×C12714yes—
523C23C22×D4×C12711yescharacteristic
524C23C22×D4×C12712yes—
525C23C22×D4×C12711yescharacteristic
526C23C22×D4×C12712yes—
527C23C2×#41×C12711yescharacteristic
528C23C2×#41×C12712yes—
529C23C2×#41×C12712yes—
530C23H(5,𝔽2)×C12712yes—
531C232−1+4×C12712yes—
532D4—416no—
533D4—432no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—28no—
537C2×C4—28no—
538C2×C4—22no—
539C2×C4—28no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—22no—
547C2×C4—28no—
548C2×C4—28no—
549C2×C4—28no—
550C2×C4—416no—
551C2×C4—416no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—44no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—44no—
561C2×C4—42no—
562C2×C4—44no—
563C2×C4—44no—
564C2×C4—44no—
565C2×C4—44no—
566C2×C4—44no—
567C2×C4—416no—
568C2×C4#123×C12714yescomplemented
569C22—24no—
570C22—24no—
571C22—24no—
572C22—24no—
573C22—216no—
574C22—216no—
575C22—24no—
576C22—24no—
577C22—44no—
578C22—44no—
579C22—44no—
580C22—48no—
581C22—48no—
582C22—82no—
583C22—82no—
584C22—84no—
585C22—84no—
586C22—82no—
587C22—82no—
588C22#392×C12718yes—
589C22C2×#120×C12711yescharacteristic
590C22C2×#120×C12712yes—
591C22C2×#121×C12711yescharacteristic
592C22C2×#121×C12712yes—
593C22C2×#123×C12711yescharacteristic
594C22#525×C12711yescharacteristic
595C22#529×C12712yes—
596C22C2×#127×C12711yescharacteristic
597C22#532×C12712yes—
598C22#534×C12711yescharacteristic
599C22#536×C12711yescharacteristic
600C22#537×C12712yes—
601C22#539×C12712yes—
602C22#546×C12714yes—
603C22#546×C12714yes—
604C22#547×C12714yes—
605C22#547×C12714yes—
606C4—24no—
607C4—44no—
608C4—44no—
609C4—42no—
610C4—48no—
611C4—44no—
612C2—28no—
613C2—84no—
614C2C2×#392×C12711yescharacteristic
615C2C127×#240511yescharacteristic
616C2C127×#240611yescharacteristic
617C2C127×#242514yes—
618C2C127×#243014yes—
619C2C127×#250111yescharacteristic
620C2C127×#253911yescharacteristic
621C2C127×#261811yescharacteristic
622C2C127×#285411yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC22×#121×C127C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#123×C127C2semidirect
3. C2×#386×C127C2semidirect
4. C22×#95×C127C2semidirect
5. C127×#1444C2semidirect
6. C127×#1439C2semidirect
7. C127×#1438C2semidirect
8. C127×C22⋊#95C2semidirect
57. C23×C4×C127D4semidirect
82. C2×C22⋊C4×C127D4semidirect
256. C2×C4×C127#123semidirect
300. #14926C127direct (N × H)
312. C22×#123C2×C127semidirect
314. C2×#386C2×C127semidirect
315. C22×#95C2×C127semidirect
316. #1444C2×C127semidirect
317. #1439C2×C127semidirect
318. #1438C2×C127semidirect
319. C22⋊#95C2×C127semidirect
320. C127#14926direct (N × H)
369. C23×C4D4×C127semidirect
394. C2×C22⋊C4D4×C127semidirect
568. C2×C4#123×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C1272
C22×#121×C1272
C2×#386×C1272
C22×#95×C1272
C127×#14442
C127×#14392
C127×#14382
C127×C22⋊#952
#14926127