Finite Group Databasebeta

← C127×#14231 #44577904

Subgroups — C127×#14231 #44577904

Order 32512.

1670 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#399×C127C211yesmaximal, characteristic
2C2×#388×C127C212yesmaximal
3C2×#388×C127C211yesmaximal, characteristic
4C2×#387×C127C212yesmaximal, complemented
5C2×C4×C4⋊C4×C127C211yesmaximal, characteristic, complemented
6C127×#1445C211yesmaximal, characteristic, complemented
7C127×#1444C211yesmaximal, characteristic, complemented
8C127×#1439C211yesmaximal, characteristic
9C127×#1437C212yesmaximal
10C127×C4⋊#95C212yesmaximal, complemented
11C4×#95×C127C211yesmaximal, characteristic, complemented
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2212yes—
15C22×C4⋊C4×C127C2212yes—
16C22×C4⋊C4×C127C2211yescharacteristic
17C22×C22⋊C4×C127C2211yescharacteristic
18C22×C22⋊C4×C127C2211yescharacteristic
19C22×C22⋊C4×C127C2212yes—
20C22×C22⋊C4×C127C2212yes—
21C22×C22⋊C4×C127C2211yescharacteristic
22C22×C42×C127C2212yes—
23C22×C42×C127C2212yes—
24C22×C42×C127C2211yescharacteristic
25#399×C127C418yescomplemented
26#388×C127—24no—
27#388×C127—28no—
28#387×C127—28no—
29C4×C4⋊C4×C127—24no—
30C2×#95×C127C2211yescharacteristic
31C2×#95×C127C2211yescharacteristic
32C2×#95×C127C2212yes—
33C2×#95×C127C2212yes—
34C2×#95×C127C2212yes—
35C2×#95×C127C2212yes—
36C2×#95×C127C2212yes—
37C2×#95×C127C2211yescharacteristic
38C2×#95×C127C2211yescharacteristic
39C2×#95×C127C2212yes—
40C25×C127C2311yescharacteristic
41C23×C4×C127C2311yescharacteristic
42C23×C4×C127C2311yescharacteristic
43C23×C4×C127C2312yes—
44C23×C4×C127C2311yescharacteristic
45C23×C4×C127C2312yes—
46C23×C4×C127C2312yes—
47C23×C4×C127C2311yescharacteristic
48C23×C4×C127C2312yes—
49C23×C4×C127C2311yescharacteristic
50C23×C4×C127C2311yescharacteristic
51C2×C4⋊C4×C127—22no—
52C2×C4⋊C4×C127—22no—
53C2×C4⋊C4×C127—24no—
54C2×C4⋊C4×C127—24no—
55C2×C4⋊C4×C127—22no—
56C2×C4⋊C4×C127—24no—
57C2×C4⋊C4×C127—24no—
58C2×C4⋊C4×C127—24no—
59C2×C4⋊C4×C127—22no—
60C2×C4⋊C4×C127—24no—
61C2×C4⋊C4×C127—42no—
62C2×C4⋊C4×C127C2×C418yes—
63C2×C4⋊C4×C127C2×C414yes—
64C2×C22⋊C4×C127—24no—
65C2×C22⋊C4×C127—22no—
66C2×C22⋊C4×C127—22no—
67C2×C22⋊C4×C127—24no—
68C2×C22⋊C4×C127—24no—
69C2×C22⋊C4×C127—22no—
70C2×C22⋊C4×C127—22no—
71C2×C22⋊C4×C127—24no—
72C2×C22⋊C4×C127—24no—
73C2×C22⋊C4×C127—24no—
74C2×C22⋊C4×C127—42no—
75C2×C22⋊C4×C127C2×C418yes—
76C2×C22⋊C4×C127C2×C414yes—
77C2×C42×C127—24no—
78C2×C42×C127—24no—
79C2×C42×C127—24no—
80C2×C42×C127—24no—
81C2×C42×C127—24no—
82C2×C42×C127—24no—
83C2×C42×C127—42no—
84C2×C42×C127D414yes—
85#95×C127—24no—
86#95×C127—24no—
87#95×C127—24no—
88#95×C127—24no—
89#95×C127—24no—
90#95×C127—22no—
91#95×C127—22no—
92#95×C127—22no—
93#95×C127C2×C414yes—
94#95×C127D418yes—
95C24×C127—21no—
96C24×C127—22no—
97C24×C127—21no—
98C24×C127—22no—
99C24×C127—22no—
100C24×C127—22no—
101C24×C127—21no—
102C24×C127—21no—
103C24×C127—21no—
104C24×C127—21no—
105C24×C127C22×C412yes—
106C24×C127C2411yescharacteristic
107C22×C4×C127—22no—
108C22×C4×C127—22no—
109C22×C4×C127—22no—
110C22×C4×C127—22no—
111C22×C4×C127—22no—
112C22×C4×C127—22no—
113C22×C4×C127—21no—
114C22×C4×C127—22no—
115C22×C4×C127—22no—
116C22×C4×C127—21no—
117C22×C4×C127—21no—
118C22×C4×C127—21no—
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—22no—
126C22×C4×C127—22no—
127C22×C4×C127—22no—
128C22×C4×C127—22no—
129C22×C4×C127—22no—
130C22×C4×C127—21no—
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—21no—
142C22×C4×C127—22no—
143C22×C4×C127—21no—
144C22×C4×C127—22no—
145C22×C4×C127—22no—
146C22×C4×C127—22no—
147C22×C4×C127—21no—
148C22×C4×C127—21no—
149C22×C4×C127—21no—
150C22×C4×C127—21no—
151C22×C4×C127C22×C414yes—
152C22×C4×C127C22×C412yes—
153C22×C4×C127C22×C412yes—
154C22×C4×C127C22×C414yes—
155C22×C4×C127C2×D414yes—
156C22×C4×C127C2×D414yes—
157C22×C4×C127C2×D412yes—
158C22×C4×C127C2×D412yes—
159C22×C4×C127C2×D414yes—
160C22×C4×C127C2×D412yes—
161C22×C4×C127#4114yes—
162C22×C4×C127#4112yes—
163C22×C4×C127#4114yes—
164C22×C4×C127#4114yes—
165C4⋊C4×C127—28no—
166C4⋊C4×C127—28no—
167C4⋊C4×C127—216no—
168C4⋊C4×C127—48no—
169C4⋊C4×C127—44no—
170C22⋊C4×C127—28no—
171C22⋊C4×C127—216no—
172C22⋊C4×C127—48no—
173C22⋊C4×C127—44no—
174C22⋊C4×C127—44no—
175C42×C127—28no—
176C42×C127—48no—
177C42×C127—48no—
178C23×C127—22no—
179C23×C127—24no—
180C23×C127—24no—
181C23×C127—22no—
182C23×C127—22no—
183C23×C127—41no—
184C23×C127—41no—
185C23×C127—42no—
186C23×C127—41no—
187C23×C127—41no—
188C23×C127—42no—
189C23×C127—41no—
190C23×C127—41no—
191C23×C127—41no—
192C23×C127—41no—
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×C127C23×C411yescharacteristic
202C23×C127C22×D411yescharacteristic
203C23×C127C22×D412yes—
204C23×C127C2×#4111yescharacteristic
205C23×C127C2×#4112yes—
206C23×C127C2×#4112yes—
207C23×C127C2×#4112yes—
208C23×C127H(5,𝔽2)11yescharacteristic
209C23×C1272−1+411yescharacteristic
210C23×C1272−1+411yescharacteristic
211C23×C1272−1+411yescharacteristic
212C2×C4×C127—24no—
213C2×C4×C127—24no—
214C2×C4×C127—24no—
215C2×C4×C127—22no—
216C2×C4×C127—22no—
217C2×C4×C127—22no—
218C2×C4×C127—24no—
219C2×C4×C127—22no—
220C2×C4×C127—22no—
221C2×C4×C127—22no—
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—22no—
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—24no—
240C2×C4×C127—24no—
241C2×C4×C127—42no—
242C2×C4×C127—42no—
243C2×C4×C127—42no—
244C2×C4×C127—41no—
245C2×C4×C127—42no—
246C2×C4×C127—41no—
247C2×C4×C127—42no—
248C2×C4×C127—42no—
249C2×C4×C127—42no—
250C2×C4×C127—42no—
251C2×C4×C127—42no—
252C2×C4×C127—42no—
253C2×C4×C127—42no—
254C2×C4×C127—42no—
255C2×C4×C127—42no—
256C2×C4×C127—41no—
257C2×C4×C127—41no—
258C2×C4×C127—41no—
259C2×C4×C127—41no—
260C2×C4×C127—41no—
261C2×C4×C127—41no—
262C2×C4×C127—42no—
263C2×C4×C127—42no—
264C2×C4×C127—42no—
265C2×C4×C127—42no—
266C2×C4×C127C4×D418yes—
267C2×C4×C127C4×D414yes—
268C2×C4×C127#12314yes—
269C2×C4×C127#12714yes—
270C22×C127—42no—
271C22×C127—42no—
272C22×C127—44no—
273C22×C127—44no—
274C22×C127—42no—
275C22×C127—81no—
276C22×C127—81no—
277C22×C127—81no—
278C22×C127—82no—
279C22×C127—82no—
280C22×C127—81no—
281C22×C127C2×C4×D411yescharacteristic
282C22×C127C2×C4×D412yes—
283C22×C127C4×#4112yes—
284C22×C127#51911yescharacteristic
285C22×C127#52011yescharacteristic
286C22×C127C2×#12311yescharacteristic
287C22×C127#52511yescharacteristic
288C22×C127#52912yes—
289C22×C127C2×#12711yescharacteristic
290C22×C127#53211yescharacteristic
291C22×C127#53212yes—
292C22×C127#53611yescharacteristic
293C22×C127#53711yescharacteristic
294C22×C127#54111yescharacteristic
295C22×C127#54211yescharacteristic
296C22×C127#54612yes—
297C22×C127#54712yes—
298C22×C127#54712yes—
299C22×C127#54812yes—
300C22×C127#55112yes—
301C22×C127#55212yes—
302C22×C127#55212yes—
303C22×C127#55612yes—
304C4×C127—28no—
305C4×C127—24no—
306C4×C127—24no—
307C4×C127—24no—
308C4×C127—44no—
309C4×C127—42no—
310C4×C127—44no—
311C4×C127—44no—
312C4×C127—81no—
313C4×C127—81no—
314#14231C12711yesmaximal, characteristic, direct product factor, Sylow
315C2×C127—82no—
316C2×C127C4×#12311yescharacteristic
317C2×C127C4×#12711yescharacteristic
318C2×C127#232311yescharacteristic
319C2×C127#235912yes—
320C2×C127#236212yes—
321C2×C127#249811yescharacteristic
322C2×C127#250111yescharacteristic
323C2×C127#251912yes—
324C2×C127#252112yes—
325C2×C127#254011yescharacteristic
326C2×C127#260411yescharacteristic
327C2×#399C2×C12711yescharacteristic
328C2×#388C2×C12711yescharacteristic
329C2×#388C2×C12712yes—
330C2×#387C2×C12712yescomplemented
331C2×C4×C4⋊C4C2×C12711yescharacteristic, complemented
332#1445C2×C12711yescharacteristic, complemented
333#1444C2×C12711yescharacteristic, complemented
334#1439C2×C12711yescharacteristic
335#1437C2×C12712yes—
336C4⋊#95C2×C12712yescomplemented
337C4×#95C2×C12711yescharacteristic, complemented
338C127#1423111yescharacteristic, direct product factor, Sylow
339C22×C4⋊C4C22×C12711yescharacteristic
340C22×C4⋊C4C22×C12711yescharacteristic
341C22×C4⋊C4C22×C12712yes—
342C22×C4⋊C4C22×C12712yes—
343C22×C4⋊C4C22×C12711yescharacteristic
344C22×C22⋊C4C22×C12711yescharacteristic
345C22×C22⋊C4C22×C12711yescharacteristic
346C22×C22⋊C4C22×C12712yes—
347C22×C22⋊C4C22×C12712yes—
348C22×C22⋊C4C22×C12711yescharacteristic
349C22×C42C22×C12712yes—
350C22×C42C22×C12712yes—
351C22×C42C22×C12711yescharacteristic
352#399C4×C12718yescomplemented
353#388—24no—
354#388—28no—
355#387—28no—
356C4×C4⋊C4—24no—
357C2×#95C22×C12711yescharacteristic
358C2×#95C22×C12711yescharacteristic
359C2×#95C22×C12712yes—
360C2×#95C22×C12712yes—
361C2×#95C22×C12712yes—
362C2×#95C22×C12712yes—
363C2×#95C22×C12712yes—
364C2×#95C22×C12711yescharacteristic
365C2×#95C22×C12711yescharacteristic
366C2×#95C22×C12712yes—
367C25C23×C12711yescharacteristic
368C23×C4C23×C12711yescharacteristic
369C23×C4C23×C12711yescharacteristic
370C23×C4C23×C12711yescharacteristic
371C23×C4C23×C12712yes—
372C23×C4C23×C12712yes—
373C23×C4C23×C12712yes—
374C23×C4C23×C12711yescharacteristic
375C23×C4C23×C12712yes—
376C23×C4C23×C12711yescharacteristic
377C23×C4C23×C12711yescharacteristic
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—24no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—42no—
389C2×C4⋊C4C2×C4×C12718yes—
390C2×C4⋊C4C2×C4×C12714yes—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4C2×C4×C12718yes—
403C2×C22⋊C4C2×C4×C12714yes—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—24no—
407C2×C42—24no—
408C2×C42—24no—
409C2×C42—24no—
410C2×C42—42no—
411C2×C42D4×C12714yes—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—22no—
418#95—22no—
419#95—22no—
420#95C2×C4×C12714yes—
421#95D4×C12718yes—
422C24—21no—
423C24—22no—
424C24—21no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—21no—
429C24—21no—
430C24—21no—
431C24—21no—
432C24C22×C4×C12712yes—
433C24C24×C12711yescharacteristic
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—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
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—21no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4C22×C4×C12712yes—
479C22×C4C22×C4×C12714yes—
480C22×C4C22×C4×C12712yes—
481C22×C4C22×C4×C12714yes—
482C22×C4C2×D4×C12714yes—
483C22×C4C2×D4×C12714yes—
484C22×C4C2×D4×C12712yes—
485C22×C4C2×D4×C12712yes—
486C22×C4C2×D4×C12714yes—
487C22×C4C2×D4×C12712yes—
488C22×C4#41×C12714yes—
489C22×C4#41×C12712yes—
490C22×C4#41×C12714yes—
491C22×C4#41×C12714yes—
492C4⋊C4—28no—
493C4⋊C4—28no—
494C4⋊C4—216no—
495C4⋊C4—48no—
496C4⋊C4—44no—
497C22⋊C4—28no—
498C22⋊C4—216no—
499C22⋊C4—48no—
500C22⋊C4—44no—
501C22⋊C4—44no—
502C42—28no—
503C42—48no—
504C42—48no—
505C23—22no—
506C23—24no—
507C23—24no—
508C23—22no—
509C23—22no—
510C23—41no—
511C23—41no—
512C23—42no—
513C23—41no—
514C23—41no—
515C23—42no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23C23×C4×C12711yescharacteristic
529C23C22×D4×C12711yescharacteristic
530C23C22×D4×C12712yes—
531C23C2×#41×C12711yescharacteristic
532C23C2×#41×C12712yes—
533C23C2×#41×C12712yes—
534C23C2×#41×C12712yes—
535C23H(5,𝔽2)×C12711yescharacteristic
536C232−1+4×C12711yescharacteristic
537C232−1+4×C12711yescharacteristic
538C232−1+4×C12711yescharacteristic
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4C4×D4×C12718yes—
594C2×C4C4×D4×C12714yes—
595C2×C4#123×C12714yes—
596C2×C4#127×C12714yes—
597C22—42no—
598C22—44no—
599C22—44no—
600C22—42no—
601C22—42no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—82no—
606C22—82no—
607C22—81no—
608C22C2×C4×D4×C12711yescharacteristic
609C22C2×C4×D4×C12712yes—
610C22C4×#41×C12712yes—
611C22#519×C12711yescharacteristic
612C22#520×C12711yescharacteristic
613C22C2×#123×C12711yescharacteristic
614C22#525×C12711yescharacteristic
615C22#529×C12712yes—
616C22C2×#127×C12711yescharacteristic
617C22#532×C12711yescharacteristic
618C22#532×C12712yes—
619C22#536×C12711yescharacteristic
620C22#537×C12711yescharacteristic
621C22#541×C12711yescharacteristic
622C22#542×C12711yescharacteristic
623C22#546×C12712yes—
624C22#547×C12712yes—
625C22#547×C12712yes—
626C22#548×C12712yes—
627C22#551×C12712yes—
628C22#552×C12712yes—
629C22#552×C12712yes—
630C22#556×C12712yes—
631C4—28no—
632C4—24no—
633C4—24no—
634C4—24no—
635C4—44no—
636C4—44no—
637C4—44no—
638C4—42no—
639C4—81no—
640C4—81no—
641C2—82no—
642C2C4×#123×C12711yescharacteristic
643C2C4×#127×C12711yescharacteristic
644C2C127×#232311yescharacteristic
645C2C127×#235912yes—
646C2C127×#236212yes—
647C2C127×#249811yescharacteristic
648C2C127×#250111yescharacteristic
649C2C127×#251912yes—
650C2C127×#252112yes—
651C2C127×#254011yescharacteristic
652C2C127×#260411yescharacteristic
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
4. C2×#387×C127C2semidirect
5. C2×C4×C4⋊C4×C127C2semidirect
6. C127×#1445C2semidirect
7. C127×#1444C2semidirect
10. C127×C4⋊#95C2semidirect
11. C4×#95×C127C2semidirect
25. #399×C127C4semidirect
314. #14231C127direct (N × H)
330. C2×#387C2×C127semidirect
331. C2×C4×C4⋊C4C2×C127semidirect
332. #1445C2×C127semidirect
333. #1444C2×C127semidirect
336. C4⋊#95C2×C127semidirect
337. C4×#95C2×C127semidirect
338. C127#14231direct (N × H)
352. #399C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#399×C1272
C2×#388×C1272
C2×#387×C1272
C2×C4×C4⋊C4×C1272
C127×#14452
C127×#14442
C127×#14392
C127×#14372
C127×C4⋊#952
C4×#95×C1272
#14231127