Finite Group Databasebeta

← C127×#14249 #44577922

Subgroups — C127×#14249 #44577922

Order 32512.

1470 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#397×C127C211yesmaximal, characteristic
2C2×#388×C127C211yesmaximal, characteristic
3C2×C4×C4⋊C4×C127C211yesmaximal, characteristic, complemented
4C127×#1445C211yesmaximal, characteristic, complemented
5C127×#1442C211yesmaximal, characteristic, complemented
6C127×#1439C211yesmaximal, characteristic
7C127×#1437C212yesmaximal
8C127×#1437C212yesmaximal
9C127×#1436C212yesmaximal, complemented
10C127×#1434C212yesmaximal, complemented
11C4×#95×C127C211yesmaximal, characteristic, complemented
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C22⋊C4×C127C2211yescharacteristic
16C22×C22⋊C4×C127C2211yescharacteristic
17C22×C22⋊C4×C127C2212yes—
18C22×C22⋊C4×C127C2211yescharacteristic
19C22×C22⋊C4×C127C2212yes—
20C22×C42×C127C2212yes—
21C22×C42×C127C2211yescharacteristic
22C22×C42×C127C2212yes—
23#397×C127C418yescomplemented
24#388×C127—24no—
25C4×C4⋊C4×C127—24no—
26C2×#95×C127C2212yes—
27C2×#95×C127C2211yescharacteristic
28C2×#95×C127C2211yescharacteristic
29C2×#95×C127C2212yes—
30C2×#95×C127C2212yes—
31C2×#95×C127C2212yes—
32C2×#95×C127C2211yescharacteristic
33C2×#95×C127C2212yes—
34C2×#95×C127C2212yes—
35C2×#95×C127C2212yes—
36C2×#95×C127C2211yescharacteristic
37C2×#95×C127C2212yes—
38C25×C127C2311yescharacteristic
39C23×C4×C127C2311yescharacteristic
40C23×C4×C127C2311yescharacteristic
41C23×C4×C127C2312yes—
42C23×C4×C127C2312yes—
43C23×C4×C127C2311yescharacteristic
44C23×C4×C127C2312yes—
45C23×C4×C127C2312yes—
46C23×C4×C127C2311yescharacteristic
47C23×C4×C127C2311yescharacteristic
48C23×C4×C127C2311yescharacteristic
49C2×C4⋊C4×C127—22no—
50C2×C4⋊C4×C127—22no—
51C2×C4⋊C4×C127—24no—
52C2×C4⋊C4×C127—22no—
53C2×C4⋊C4×C127—22no—
54C2×C4⋊C4×C127—24no—
55C2×C4⋊C4×C127C2×C414yes—
56C2×C22⋊C4×C127—22no—
57C2×C22⋊C4×C127—22no—
58C2×C22⋊C4×C127—22no—
59C2×C22⋊C4×C127—22no—
60C2×C22⋊C4×C127—24no—
61C2×C22⋊C4×C127—24no—
62C2×C22⋊C4×C127—24no—
63C2×C22⋊C4×C127—24no—
64C2×C22⋊C4×C127—42no—
65C2×C22⋊C4×C127—42no—
66C2×C22⋊C4×C127—42no—
67C2×C22⋊C4×C127C2×C414yes—
68C2×C22⋊C4×C127C2×C418yes—
69C2×C42×C127—24no—
70C2×C42×C127—24no—
71C2×C42×C127—24no—
72C2×C42×C127—24no—
73C2×C42×C127—42no—
74C2×C42×C127—42no—
75C2×C42×C127—42no—
76C2×C42×C127D414yes—
77#95×C127—24no—
78#95×C127—22no—
79#95×C127—22no—
80#95×C127—24no—
81#95×C127—22no—
82#95×C127—24no—
83#95×C127—24no—
84#95×C127—42no—
85#95×C127—42no—
86#95×C127—42no—
87#95×C127C2×C418yes—
88#95×C127C2×C414yes—
89C24×C127—21no—
90C24×C127—21no—
91C24×C127—22no—
92C24×C127—22no—
93C24×C127—22no—
94C24×C127—22no—
95C24×C127—21no—
96C24×C127—21no—
97C24×C127—21no—
98C24×C127—21no—
99C24×C127C22×C412yes—
100C24×C127C2411yescharacteristic
101C22×C4×C127—22no—
102C22×C4×C127—22no—
103C22×C4×C127—22no—
104C22×C4×C127—22no—
105C22×C4×C127—21no—
106C22×C4×C127—21no—
107C22×C4×C127—21no—
108C22×C4×C127—21no—
109C22×C4×C127—22no—
110C22×C4×C127—22no—
111C22×C4×C127—21no—
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—21no—
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—21no—
138C22×C4×C127—21no—
139C22×C4×C127—22no—
140C22×C4×C127—22no—
141C22×C4×C127—22no—
142C22×C4×C127—22no—
143C22×C4×C127—21no—
144C22×C4×C127—21no—
145C22×C4×C127—21no—
146C22×C4×C127—21no—
147C22×C4×C127C22×C412yes—
148C22×C4×C127C22×C414yes—
149C22×C4×C127C22×C414yes—
150C22×C4×C127C22×C412yes—
151C22×C4×C127C2×D412yes—
152C22×C4×C127C2×D412yes—
153C22×C4×C127C2×D412yes—
154C22×C4×C127#4114yes—
155C22×C4×C127#4114yes—
156C22×C4×C127#4112yes—
157C22×C4×C127#4114yes—
158C22×C4×C127#4114yes—
159C4⋊C4×C127—28no—
160C4⋊C4×C127—28no—
161C4⋊C4×C127—44no—
162C22⋊C4×C127—28no—
163C22⋊C4×C127—48no—
164C22⋊C4×C127—48no—
165C22⋊C4×C127—44no—
166C22⋊C4×C127—44no—
167C42×C127—28no—
168C42×C127—48no—
169C42×C127—48no—
170C23×C127—22no—
171C23×C127—24no—
172C23×C127—24no—
173C23×C127—22no—
174C23×C127—22no—
175C23×C127—41no—
176C23×C127—41no—
177C23×C127—41no—
178C23×C127—42no—
179C23×C127—42no—
180C23×C127—41no—
181C23×C127—41no—
182C23×C127—41no—
183C23×C127—41no—
184C23×C127—41no—
185C23×C127—42no—
186C23×C127—42no—
187C23×C127—42no—
188C23×C127—42no—
189C23×C127—42no—
190C23×C127—42no—
191C23×C127—42no—
192C23×C127—42no—
193C23×C127C23×C411yescharacteristic
194C23×C127C22×D411yescharacteristic
195C23×C127C2×#4111yescharacteristic
196C23×C127C2×#4112yes—
197C23×C127C2×#4112yes—
198C23×C127C2×#4112yes—
199C23×C127C2×#4112yes—
200C23×C127H(5,𝔽2)11yescharacteristic
201C23×C127H(5,𝔽2)11yescharacteristic
202C23×C127H(5,𝔽2)11yescharacteristic
203C23×C1272−1+411yescharacteristic
204C2×C4×C127—24no—
205C2×C4×C127—22no—
206C2×C4×C127—22no—
207C2×C4×C127—22no—
208C2×C4×C127—24no—
209C2×C4×C127—22no—
210C2×C4×C127—22no—
211C2×C4×C127—22no—
212C2×C4×C127—24no—
213C2×C4×C127—24no—
214C2×C4×C127—24no—
215C2×C4×C127—24no—
216C2×C4×C127—22no—
217C2×C4×C127—24no—
218C2×C4×C127—24no—
219C2×C4×C127—24no—
220C2×C4×C127—24no—
221C2×C4×C127—24no—
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—41no—
231C2×C4×C127—42no—
232C2×C4×C127—42no—
233C2×C4×C127—42no—
234C2×C4×C127—41no—
235C2×C4×C127—42no—
236C2×C4×C127—42no—
237C2×C4×C127—42no—
238C2×C4×C127—42no—
239C2×C4×C127—42no—
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—41no—
250C2×C4×C127—41no—
251C2×C4×C127—41no—
252C2×C4×C127—41no—
253C2×C4×C127—41no—
254C2×C4×C127—41no—
255C2×C4×C127—42no—
256C2×C4×C127—42no—
257C2×C4×C127—42no—
258C2×C4×C127—42no—
259C2×C4×C127C4×D414yes—
260C2×C4×C127#12314yes—
261C2×C4×C127#12414yes—
262C22×C127—42no—
263C22×C127—44no—
264C22×C127—44no—
265C22×C127—42no—
266C22×C127—42no—
267C22×C127—81no—
268C22×C127—81no—
269C22×C127—81no—
270C22×C127—81no—
271C22×C127—82no—
272C22×C127—82no—
273C22×C127C2×C4×D411yescharacteristic
274C22×C127C4×#4112yes—
275C22×C127C4×#4112yes—
276C22×C127#51811yescharacteristic
277C22×C127#52011yescharacteristic
278C22×C127C2×#12311yescharacteristic
279C22×C127#52511yescharacteristic
280C22×C127C2×#12411yescharacteristic
281C22×C127#52912yes—
282C22×C127#52912yes—
283C22×C127#53211yescharacteristic
284C22×C127#53511yescharacteristic
285C22×C127#53711yescharacteristic
286C22×C127#54011yescharacteristic
287C22×C127#54211yescharacteristic
288C22×C127#55112yes—
289C22×C127#55112yes—
290C22×C127#55212yes—
291C22×C127#55312yes—
292C22×C127#55312yes—
293C22×C127#55312yes—
294C22×C127#55612yes—
295C22×C127#55912yes—
296C4×C127—24no—
297C4×C127—24no—
298C4×C127—24no—
299C4×C127—44no—
300C4×C127—44no—
301C4×C127—44no—
302C4×C127—44no—
303C4×C127—42no—
304C4×C127—81no—
305C4×C127—81no—
306#14249C12711yesmaximal, characteristic, direct product factor, Sylow
307C2×C127—82no—
308C2×C127C4×#12311yescharacteristic
309C2×C127C4×#12411yescharacteristic
310C2×C127#232411yescharacteristic
311C2×C127#237312yes—
312C2×C127#237412yes—
313C2×C127#249811yescharacteristic
314C2×C127#250411yescharacteristic
315C2×C127#251612yes—
316C2×C127#252512yes—
317C2×C127#259211yescharacteristic
318C2×C127#260311yescharacteristic
319C2×#397C2×C12711yescharacteristic
320C2×#388C2×C12711yescharacteristic
321C2×C4×C4⋊C4C2×C12711yescharacteristic, complemented
322#1445C2×C12711yescharacteristic, complemented
323#1442C2×C12711yescharacteristic, complemented
324#1439C2×C12711yescharacteristic
325#1437C2×C12712yes—
326#1437C2×C12712yes—
327#1436C2×C12712yescomplemented
328#1434C2×C12712yescomplemented
329C4×#95C2×C12711yescharacteristic, complemented
330C127#1424911yescharacteristic, direct product factor, Sylow
331C22×C4⋊C4C22×C12711yescharacteristic
332C22×C4⋊C4C22×C12711yescharacteristic
333C22×C4⋊C4C22×C12711yescharacteristic
334C22×C22⋊C4C22×C12711yescharacteristic
335C22×C22⋊C4C22×C12711yescharacteristic
336C22×C22⋊C4C22×C12712yes—
337C22×C22⋊C4C22×C12711yescharacteristic
338C22×C22⋊C4C22×C12712yes—
339C22×C42C22×C12712yes—
340C22×C42C22×C12711yescharacteristic
341C22×C42C22×C12712yes—
342#397C4×C12718yescomplemented
343#388—24no—
344C4×C4⋊C4—24no—
345C2×#95C22×C12712yes—
346C2×#95C22×C12711yescharacteristic
347C2×#95C22×C12711yescharacteristic
348C2×#95C22×C12712yes—
349C2×#95C22×C12712yes—
350C2×#95C22×C12712yes—
351C2×#95C22×C12711yescharacteristic
352C2×#95C22×C12712yes—
353C2×#95C22×C12712yes—
354C2×#95C22×C12712yes—
355C2×#95C22×C12711yescharacteristic
356C2×#95C22×C12712yes—
357C25C23×C12711yescharacteristic
358C23×C4C23×C12711yescharacteristic
359C23×C4C23×C12711yescharacteristic
360C23×C4C23×C12711yescharacteristic
361C23×C4C23×C12712yes—
362C23×C4C23×C12712yes—
363C23×C4C23×C12712yes—
364C23×C4C23×C12712yes—
365C23×C4C23×C12711yescharacteristic
366C23×C4C23×C12711yescharacteristic
367C23×C4C23×C12711yescharacteristic
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4C2×C4×C12714yes—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4C2×C4×C12714yes—
387C2×C22⋊C4C2×C4×C12718yes—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—42no—
393C2×C42—42no—
394C2×C42—42no—
395C2×C42D4×C12714yes—
396#95—24no—
397#95—22no—
398#95—22no—
399#95—24no—
400#95—22no—
401#95—24no—
402#95—24no—
403#95—42no—
404#95—42no—
405#95—42no—
406#95C2×C4×C12718yes—
407#95C2×C4×C12714yes—
408C24—21no—
409C24—21no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24C22×C4×C12712yes—
419C24C24×C12711yescharacteristic
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
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—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4C22×C4×C12712yes—
467C22×C4C22×C4×C12714yes—
468C22×C4C22×C4×C12714yes—
469C22×C4C22×C4×C12712yes—
470C22×C4C2×D4×C12712yes—
471C22×C4C2×D4×C12712yes—
472C22×C4C2×D4×C12712yes—
473C22×C4#41×C12714yes—
474C22×C4#41×C12714yes—
475C22×C4#41×C12712yes—
476C22×C4#41×C12714yes—
477C22×C4#41×C12714yes—
478C4⋊C4—28no—
479C4⋊C4—28no—
480C4⋊C4—44no—
481C22⋊C4—28no—
482C22⋊C4—48no—
483C22⋊C4—48no—
484C22⋊C4—44no—
485C22⋊C4—44no—
486C42—28no—
487C42—48no—
488C42—48no—
489C23—22no—
490C23—24no—
491C23—24no—
492C23—22no—
493C23—22no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—42no—
498C23—42no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23C23×C4×C12711yescharacteristic
513C23C22×D4×C12711yescharacteristic
514C23C2×#41×C12711yescharacteristic
515C23C2×#41×C12712yes—
516C23C2×#41×C12712yes—
517C23C2×#41×C12712yes—
518C23C2×#41×C12712yes—
519C23H(5,𝔽2)×C12711yescharacteristic
520C23H(5,𝔽2)×C12711yescharacteristic
521C23H(5,𝔽2)×C12711yescharacteristic
522C232−1+4×C12711yescharacteristic
523C2×C4—24no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—24no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4C4×D4×C12714yes—
579C2×C4#123×C12714yes—
580C2×C4#124×C12714yes—
581C22—42no—
582C22—44no—
583C22—44no—
584C22—42no—
585C22—42no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—82no—
591C22—82no—
592C22C2×C4×D4×C12711yescharacteristic
593C22C4×#41×C12712yes—
594C22C4×#41×C12712yes—
595C22#518×C12711yescharacteristic
596C22#520×C12711yescharacteristic
597C22C2×#123×C12711yescharacteristic
598C22#525×C12711yescharacteristic
599C22C2×#124×C12711yescharacteristic
600C22#529×C12712yes—
601C22#529×C12712yes—
602C22#532×C12711yescharacteristic
603C22#535×C12711yescharacteristic
604C22#537×C12711yescharacteristic
605C22#540×C12711yescharacteristic
606C22#542×C12711yescharacteristic
607C22#551×C12712yes—
608C22#551×C12712yes—
609C22#552×C12712yes—
610C22#553×C12712yes—
611C22#553×C12712yes—
612C22#553×C12712yes—
613C22#556×C12712yes—
614C22#559×C12712yes—
615C4—24no—
616C4—24no—
617C4—24no—
618C4—44no—
619C4—44no—
620C4—44no—
621C4—44no—
622C4—42no—
623C4—81no—
624C4—81no—
625C2—82no—
626C2C4×#123×C12711yescharacteristic
627C2C4×#124×C12711yescharacteristic
628C2C127×#232411yescharacteristic
629C2C127×#237312yes—
630C2C127×#237412yes—
631C2C127×#249811yescharacteristic
632C2C127×#250411yescharacteristic
633C2C127×#251612yes—
634C2C127×#252512yes—
635C2C127×#259211yescharacteristic
636C2C127×#260311yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C4×C4⋊C4×C127C2semidirect
4. C127×#1445C2semidirect
5. C127×#1442C2semidirect
9. C127×#1436C2semidirect
10. C127×#1434C2semidirect
11. C4×#95×C127C2semidirect
23. #397×C127C4semidirect
306. #14249C127direct (N × H)
321. C2×C4×C4⋊C4C2×C127semidirect
322. #1445C2×C127semidirect
323. #1442C2×C127semidirect
327. #1436C2×C127semidirect
328. #1434C2×C127semidirect
329. C4×#95C2×C127semidirect
330. C127#14249direct (N × H)
342. #397C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#397×C1272
C2×#388×C1272
C2×C4×C4⋊C4×C1272
C127×#14452
C127×#14422
C127×#14392
C127×#14372
C127×#14362
C127×#14342
C4×#95×C1272
#14249127