Finite Group Databasebeta

← C127×#14260 #44577933

Subgroups — C127×#14260 #44577933

Order 32512.

1774 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#390×C127C211yesmaximal, characteristic
2C2×#390×C127C211yesmaximal, characteristic
3C2×#390×C127C211yesmaximal, characteristic
4C2×#389×C127C211yesmaximal, characteristic, complemented
5C2×#376×C127C211yesmaximal, characteristic, complemented
6C127×#1440C214yesmaximal, complemented
7C127×#1439C214yesmaximal, complemented
8C127×C4⋊#95C211yesmaximal, characteristic, complemented
9C127×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×D4×C127C2211yescharacteristic
11C22×C4⋊C4×C127C2211yescharacteristic
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2212yes—
15C22×C22⋊C4×C127C2212yes—
16C22×C22⋊C4×C127C2214yes—
17C22×C22⋊C4×C127C2212yes—
18C22×C22⋊C4×C127C2214yes—
19C22×C42×C127C2211yescharacteristic
20C22×C42×C127C2211yescharacteristic
21C22×C42×C127C2211yescharacteristic
22#390×C127—24no—
23#390×C127—24no—
24#390×C127C418yescomplemented
25#389×C127—24no—
26#376×C127—24no—
27C2×#95×C127C2212yes—
28C2×#95×C127C2212yes—
29C2×#95×C127C2212yes—
30C2×#95×C127C2214yes—
31C2×#95×C127C2214yes—
32C25×C127C2312yes—
33C22×D4×C127—22no—
34C22×D4×C127—22no—
35C22×D4×C127—22no—
36C22×D4×C127—22no—
37C22×D4×C127—22no—
38C22×D4×C127—22no—
39C22×D4×C127C2×C414yes—
40C23×C4×C127C2312yes—
41C23×C4×C127C2312yes—
42C23×C4×C127C2312yes—
43C23×C4×C127C2312yes—
44C23×C4×C127C2311yescharacteristic
45C23×C4×C127C2311yescharacteristic
46C23×C4×C127C2312yes—
47C23×C4×C127C2311yescharacteristic
48C2×C4⋊C4×C127—22no—
49C2×C4⋊C4×C127—22no—
50C2×C4⋊C4×C127—24no—
51C2×C4⋊C4×C127—22no—
52C2×C4⋊C4×C127—22no—
53C2×C4⋊C4×C127—22no—
54C2×C4⋊C4×C127—22no—
55C2×C4⋊C4×C127—22no—
56C2×C4⋊C4×C127—22no—
57C2×C4⋊C4×C127—44no—
58C2×C4⋊C4×C127C2×C414yes—
59C2×C22⋊C4×C127—28no—
60C2×C22⋊C4×C127—24no—
61C2×C22⋊C4×C127—24no—
62C2×C22⋊C4×C127—44no—
63C2×C22⋊C4×C127—44no—
64C2×C22⋊C4×C127—44no—
65C2×C22⋊C4×C127—44no—
66C2×C22⋊C4×C127—44no—
67C2×C22⋊C4×C127—44no—
68C2×C22⋊C4×C127C2×C4116yes—
69C2×C42×C127—22no—
70C2×C42×C127—22no—
71C2×C42×C127—22no—
72C2×C42×C127—22no—
73C2×C42×C127—22no—
74C2×C42×C127—22no—
75C2×C42×C127C2×C414yes—
76C2×C42×C127D414yes—
77C2×C42×C127D414yes—
78#95×C127—24no—
79#95×C127—24no—
80#95×C127—24no—
81#95×C127—44no—
82#95×C127—44no—
83C24×C127—22no—
84C24×C127—22no—
85C24×C127—22no—
86C24×C127—22no—
87C24×C127—22no—
88C24×C127—22no—
89C24×C127—24no—
90C24×C127—24no—
91C24×C127—24no—
92C24×C127—24no—
93C24×C127C22×C414yes—
94C24×C127C2411yescharacteristic
95C2×D4×C127—28no—
96C2×D4×C127—28no—
97C2×D4×C127—28no—
98C2×D4×C127—44no—
99C2×D4×C127—44no—
100C2×D4×C127—44no—
101C2×D4×C127—44no—
102C22×C4×C127—22no—
103C22×C4×C127—21no—
104C22×C4×C127—21no—
105C22×C4×C127—22no—
106C22×C4×C127—22no—
107C22×C4×C127—21no—
108C22×C4×C127—21no—
109C22×C4×C127—22no—
110C22×C4×C127—22no—
111C22×C4×C127—22no—
112C22×C4×C127—22no—
113C22×C4×C127—22no—
114C22×C4×C127—24no—
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—24no—
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—24no—
133C22×C4×C127—24no—
134C22×C4×C127—24no—
135C22×C4×C127—24no—
136C22×C4×C127C22×C414yes—
137C22×C4×C127C22×C414yes—
138C22×C4×C127C22×C412yes—
139C22×C4×C127C2×D412yes—
140C22×C4×C127C2×D414yes—
141C22×C4×C127C2×D412yes—
142C22×C4×C127C2×D412yes—
143C22×C4×C127C2×D412yes—
144C22×C4×C127#4112yes—
145C22×C4×C127#4112yes—
146C22×C4×C127#4112yes—
147C22×C4×C127#4112yes—
148C4⋊C4×C127—28no—
149C4⋊C4×C127—48no—
150C4⋊C4×C127—44no—
151C4⋊C4×C127—44no—
152C22⋊C4×C127—416no—
153C22⋊C4×C127—48no—
154C22⋊C4×C127—48no—
155C22⋊C4×C127—416no—
156C42×C127—28no—
157C42×C127—28no—
158C42×C127—28no—
159C23×C127—24no—
160C23×C127—24no—
161C23×C127—24no—
162C23×C127—28no—
163C23×C127—28no—
164C23×C127—42no—
165C23×C127—42no—
166C23×C127—42no—
167C23×C127—42no—
168C23×C127—44no—
169C23×C127—42no—
170C23×C127—42no—
171C23×C127—42no—
172C23×C127—42no—
173C23×C127—44no—
174C23×C127—44no—
175C23×C127—44no—
176C23×C127—44no—
177C23×C127—44no—
178C23×C127—44no—
179C23×C127—44no—
180C23×C127—44no—
181C23×C127—44no—
182C23×C127C23×C411yescharacteristic
183C23×C127C22×D411yescharacteristic
184C23×C127C22×D411yescharacteristic
185C23×C127C2×#4111yescharacteristic
186C23×C127C2×#4111yescharacteristic
187C23×C127C2×#4111yescharacteristic
188C23×C127C2×#4111yescharacteristic
189C23×C127H(5,𝔽2)12yes—
190C23×C127H(5,𝔽2)12yes—
191C23×C127H(5,𝔽2)12yes—
192C23×C1272−1+412yes—
193D4×C127—416no—
194C2×C4×C127—24no—
195C2×C4×C127—24no—
196C2×C4×C127—24no—
197C2×C4×C127—28no—
198C2×C4×C127—24no—
199C2×C4×C127—22no—
200C2×C4×C127—22no—
201C2×C4×C127—24no—
202C2×C4×C127—22no—
203C2×C4×C127—22no—
204C2×C4×C127—24no—
205C2×C4×C127—22no—
206C2×C4×C127—22no—
207C2×C4×C127—24no—
208C2×C4×C127—42no—
209C2×C4×C127—42no—
210C2×C4×C127—42no—
211C2×C4×C127—42no—
212C2×C4×C127—42no—
213C2×C4×C127—42no—
214C2×C4×C127—42no—
215C2×C4×C127—44no—
216C2×C4×C127—42no—
217C2×C4×C127—42no—
218C2×C4×C127—42no—
219C2×C4×C127—42no—
220C2×C4×C127—42no—
221C2×C4×C127—42no—
222C2×C4×C127—42no—
223C2×C4×C127—42no—
224C2×C4×C127—42no—
225C2×C4×C127—44no—
226C2×C4×C127—42no—
227C2×C4×C127—42no—
228C2×C4×C127—42no—
229C2×C4×C127—42no—
230C2×C4×C127—44no—
231C2×C4×C127—44no—
232C2×C4×C127—44no—
233C2×C4×C127#11714yes—
234C2×C4×C127C4×D414yes—
235C2×C4×C127C4×D414yes—
236C2×C4×C127#12114yes—
237C2×C4×C127#12314yes—
238C2×C4×C127#12414yes—
239C2×C4×C127#12614yes—
240C22×C127—48no—
241C22×C127—48no—
242C22×C127—44no—
243C22×C127—44no—
244C22×C127—44no—
245C22×C127—82no—
246C22×C127—82no—
247C22×C127—84no—
248C22×C127—82no—
249C22×C127—82no—
250C22×C127—84no—
251C22×C127C2×#11711yescharacteristic
252C22×C127C2×C4×D411yescharacteristic
253C22×C127C2×C4×D411yescharacteristic
254C22×C127#51812yes—
255C22×C127#52012yes—
256C22×C127C2×#12111yescharacteristic
257C22×C127C2×#12311yescharacteristic
258C22×C127C2×#12411yescharacteristic
259C22×C127C2×#12611yescharacteristic
260C22×C127#53512yes—
261C22×C127#53511yescharacteristic
262C22×C127#53511yescharacteristic
263C22×C127#53511yescharacteristic
264C22×C127#53611yescharacteristic
265C22×C127#53712yes—
266C22×C127#54012yes—
267C22×C127#54012yes—
268C22×C127#54012yes—
269C22×C127#54012yes—
270C22×C127#54212yes—
271C22×C127#54212yes—
272C22×C127#54212yes—
273C22×C127#54212yes—
274C4×C127—44no—
275C4×C127—44no—
276C4×C127—42no—
277C4×C127—42no—
278C4×C127—44no—
279C4×C127—82no—
280C4×C127—82no—
281C4×C127#38818yes—
282#14260C12711yesmaximal, characteristic, direct product factor, Sylow
283C2×C127—84no—
284C2×C127C2×#38811yescharacteristic
285C2×C127#231912yes—
286C2×C127#232412yes—
287C2×C127#232611yescharacteristic
288C2×C127#232811yescharacteristic
289C2×C127#261911yescharacteristic
290C2×C127#262011yescharacteristic
291C2×C127#262412yes—
292C2×C127#264011yescharacteristic
293C2×C127#264111yescharacteristic
294C2×C127#264412yes—
295C2×#390C2×C12711yescharacteristic
296C2×#390C2×C12711yescharacteristic
297C2×#390C2×C12711yescharacteristic
298C2×#389C2×C12711yescharacteristic, complemented
299C2×#376C2×C12711yescharacteristic, complemented
300#1440C2×C12714yescomplemented
301#1439C2×C12714yescomplemented
302C4⋊#95C2×C12711yescharacteristic, complemented
303C4⋊#95C2×C12711yescharacteristic, complemented
304C127#1426011yescharacteristic, direct product factor, Sylow
305C23×D4C22×C12711yescharacteristic
306C22×C4⋊C4C22×C12711yescharacteristic
307C22×C4⋊C4C22×C12711yescharacteristic
308C22×C4⋊C4C22×C12711yescharacteristic
309C22×C4⋊C4C22×C12712yes—
310C22×C22⋊C4C22×C12712yes—
311C22×C22⋊C4C22×C12714yes—
312C22×C22⋊C4C22×C12712yes—
313C22×C22⋊C4C22×C12714yes—
314C22×C42C22×C12711yescharacteristic
315C22×C42C22×C12711yescharacteristic
316C22×C42C22×C12711yescharacteristic
317#390—24no—
318#390—24no—
319#390C4×C12718yescomplemented
320#389—24no—
321#376—24no—
322C2×#95C22×C12712yes—
323C2×#95C22×C12712yes—
324C2×#95C22×C12712yes—
325C2×#95C22×C12714yes—
326C2×#95C22×C12714yes—
327C25C23×C12712yes—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4C2×C4×C12714yes—
335C23×C4C23×C12712yes—
336C23×C4C23×C12712yes—
337C23×C4C23×C12712yes—
338C23×C4C23×C12712yes—
339C23×C4C23×C12711yescharacteristic
340C23×C4C23×C12711yescharacteristic
341C23×C4C23×C12712yes—
342C23×C4C23×C12711yescharacteristic
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4C2×C4×C12714yes—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4C2×C4×C127116yes—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42C2×C4×C12714yes—
371C2×C42D4×C12714yes—
372C2×C42D4×C12714yes—
373#95—24no—
374#95—24no—
375#95—24no—
376#95—44no—
377#95—44no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—24no—
385C24—24no—
386C24—24no—
387C24—24no—
388C24C22×C4×C12714yes—
389C24C24×C12711yescharacteristic
390C2×D4—28no—
391C2×D4—28no—
392C2×D4—28no—
393C2×D4—44no—
394C2×D4—44no—
395C2×D4—44no—
396C2×D4—44no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—24no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4C22×C4×C12714yes—
432C22×C4C22×C4×C12714yes—
433C22×C4C22×C4×C12712yes—
434C22×C4C2×D4×C12712yes—
435C22×C4C2×D4×C12714yes—
436C22×C4C2×D4×C12712yes—
437C22×C4C2×D4×C12712yes—
438C22×C4C2×D4×C12712yes—
439C22×C4#41×C12712yes—
440C22×C4#41×C12712yes—
441C22×C4#41×C12712yes—
442C22×C4#41×C12712yes—
443C4⋊C4—28no—
444C4⋊C4—48no—
445C4⋊C4—44no—
446C4⋊C4—44no—
447C22⋊C4—416no—
448C22⋊C4—48no—
449C22⋊C4—48no—
450C22⋊C4—416no—
451C42—28no—
452C42—28no—
453C42—28no—
454C23—24no—
455C23—24no—
456C23—24no—
457C23—28no—
458C23—28no—
459C23—42no—
460C23—42no—
461C23—42no—
462C23—42no—
463C23—44no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—42no—
468C23—44no—
469C23—44no—
470C23—44no—
471C23—44no—
472C23—44no—
473C23—44no—
474C23—44no—
475C23—44no—
476C23—44no—
477C23C23×C4×C12711yescharacteristic
478C23C22×D4×C12711yescharacteristic
479C23C22×D4×C12711yescharacteristic
480C23C2×#41×C12711yescharacteristic
481C23C2×#41×C12711yescharacteristic
482C23C2×#41×C12711yescharacteristic
483C23C2×#41×C12711yescharacteristic
484C23H(5,𝔽2)×C12712yes—
485C23H(5,𝔽2)×C12712yes—
486C23H(5,𝔽2)×C12712yes—
487C232−1+4×C12712yes—
488D4—416no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—28no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—24no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—44no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—44no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—44no—
526C2×C4—44no—
527C2×C4—44no—
528C2×C4#117×C12714yes—
529C2×C4C4×D4×C12714yes—
530C2×C4C4×D4×C12714yes—
531C2×C4#121×C12714yes—
532C2×C4#123×C12714yes—
533C2×C4#124×C12714yes—
534C2×C4#126×C12714yes—
535C22—48no—
536C22—48no—
537C22—44no—
538C22—44no—
539C22—44no—
540C22—82no—
541C22—82no—
542C22—84no—
543C22—82no—
544C22—82no—
545C22—84no—
546C22C2×#117×C12711yescharacteristic
547C22C2×C4×D4×C12711yescharacteristic
548C22C2×C4×D4×C12711yescharacteristic
549C22#518×C12712yes—
550C22#520×C12712yes—
551C22C2×#121×C12711yescharacteristic
552C22C2×#123×C12711yescharacteristic
553C22C2×#124×C12711yescharacteristic
554C22C2×#126×C12711yescharacteristic
555C22#535×C12712yes—
556C22#535×C12711yescharacteristic
557C22#535×C12711yescharacteristic
558C22#535×C12711yescharacteristic
559C22#536×C12711yescharacteristic
560C22#537×C12712yes—
561C22#540×C12712yes—
562C22#540×C12712yes—
563C22#540×C12712yes—
564C22#540×C12712yes—
565C22#542×C12712yes—
566C22#542×C12712yes—
567C22#542×C12712yes—
568C22#542×C12712yes—
569C4—44no—
570C4—44no—
571C4—42no—
572C4—42no—
573C4—44no—
574C4—82no—
575C4—82no—
576C4#388×C12718yes—
577C2—84no—
578C2C2×#388×C12711yescharacteristic
579C2C127×#231912yes—
580C2C127×#232412yes—
581C2C127×#232611yescharacteristic
582C2C127×#232811yescharacteristic
583C2C127×#261911yescharacteristic
584C2C127×#262011yescharacteristic
585C2C127×#262412yes—
586C2C127×#264011yescharacteristic
587C2C127×#264111yescharacteristic
588C2C127×#264412yes—
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
4. C2×#389×C127C2semidirect
5. C2×#376×C127C2semidirect
6. C127×#1440C2semidirect
7. C127×#1439C2semidirect
8. C127×C4⋊#95C2semidirect
9. C127×C4⋊#95C2semidirect
24. #390×C127C4semidirect
282. #14260C127direct (N × H)
298. C2×#389C2×C127semidirect
299. C2×#376C2×C127semidirect
300. #1440C2×C127semidirect
301. #1439C2×C127semidirect
302. C4⋊#95C2×C127semidirect
303. C4⋊#95C2×C127semidirect
304. C127#14260direct (N × H)
319. #390C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#390×C1272
C2×#389×C1272
C2×#376×C1272
C127×#14402
C127×#14392
C127×C4⋊#952
#14260127