Finite Group Databasebeta

← C127×#21486 #44585159

Subgroups — C127×#21486 #44585159

Order 32512.

1110 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#435×C127C212yesmaximal, complemented
2C2×C8×D4×C127C211yesmaximal, characteristic, complemented
3C2×C4×M16×C127C211yesmaximal, characteristic, complemented
4C4×#121×C127C211yesmaximal, characteristic
5C127×#1954C211yesmaximal, characteristic, complemented
6C127×#1939C211yesmaximal, characteristic, complemented
7C127×#1924C212yesmaximal, complemented
8C127×#1870C212yesmaximal, complemented
9C127×#1797C211yesmaximal, characteristic, complemented
10C127×#1770C211yesmaximal, characteristic, complemented
11C127×#1752C212yesmaximal, complemented
12C22×M16×C127C2211yescharacteristic
13C22×M16×C127C2211yescharacteristic
14C23×C8×C127C2212yes—
15C2×#121×C127C411yescharacteristic
16C2×C4×D4×C127C2212yes—
17C2×C4×D4×C127C2211yescharacteristic
18C22×C42×C127C2211yescharacteristic
19#435×C127—28no—
20C8×D4×C127—24no—
21C2×C4⋊C8×C127C2211yescharacteristic
22C2×C4⋊C8×C127C2212yes—
23C2×C4⋊C8×C127C2211yescharacteristic
24C2×C22⋊C8×C127C2212yes—
25C2×C22⋊C8×C127C2212yes—
26C2×C22⋊C8×C127C2212yes—
27C2×C22⋊C8×C127C2212yes—
28C4×M16×C127—24no—
29C2×#97×C127C2211yescharacteristic
30C2×#97×C127C2211yescharacteristic
31C2×#97×C127C2212yes—
32C2×C4×C8×C127C2211yescharacteristic
33C2×C4×C8×C127C2211yescharacteristic
34#390×C127C411yescharacteristic
35#389×C127C411yescharacteristic
36#388×C127C412yes—
37#386×C127C412yes—
38#380×C127C411yescharacteristic
39C4×C4⋊C4×C127C2211yescharacteristic
40C4×C22⋊C4×C127C2212yes—
41#336×C127C2212yes—
42#336×C127C2212yes—
43#336×C127C2212yes—
44C22×D4×C127C2×C412yes—
45C22×D4×C127C2×C411yescharacteristic
46C23×C4×C127C2×C411yescharacteristic
47C23×C4×C127C2×C411yescharacteristic
48C23×C4×C127C2312yes—
49C23×C4×C127C2311yescharacteristic
50C2×M16×C127—22no—
51C2×M16×C127—22no—
52C2×M16×C127—22no—
53C2×M16×C127—22no—
54C2×M16×C127—22no—
55C2×M16×C127D414yescomplemented
56C22×C8×C127—24no—
57C22×C8×C127—24no—
58C22×C8×C127—24no—
59C22×C8×C127C2312yes—
60C22×C8×C127C2312yes—
61C22×C8×C127C2311yescharacteristic
62C22×C8×C127C2311yescharacteristic
63C22×C8×C127C2311yescharacteristic
64C22×C8×C127C2311yescharacteristic
65#121×C127—24no—
66C4×D4×C127—24no—
67C4×D4×C127—24no—
68C4×D4×C127—22no—
69C4×D4×C127—22no—
70C2×C4⋊C4×C127C2×C411yescharacteristic
71C2×C4⋊C4×C127C2×C412yes—
72C2×C4⋊C4×C127C2×C411yescharacteristic
73C2×C4⋊C4×C127C2×C411yescharacteristic
74C2×C22⋊C4×C127C2×C412yes—
75C2×C22⋊C4×C127C2×C412yes—
76C2×C22⋊C4×C127C2×C412yes—
77C2×C22⋊C4×C127C2×C412yes—
78C2×C22⋊C4×C127C2×C412yes—
79C2×C42×C127—22no—
80C2×C42×C127—22no—
81C2×C42×C127C2×C411yescharacteristic
82C2×C42×C127C2×C411yescharacteristic
83C2×C42×C127C2311yescharacteristic
84C2×C42×C127C2312yes—
85C2×C42×C127C2311yescharacteristic
86C4⋊C8×C127—24no—
87C4⋊C8×C127—22no—
88C4⋊C8×C127—22no—
89C22⋊C8×C127—24no—
90C22⋊C8×C127—24no—
91C22⋊C8×C127—24no—
92C22⋊C8×C127—24no—
93#97×C127—22no—
94#97×C127—22no—
95#97×C127—24no—
96C4×C8×C127—22no—
97C4×C8×C127D414yescomplemented
98#95×C127C2×C412yes—
99#95×C127C2×C412yes—
100#95×C127C2×C412yes—
101C24×C127C22×C411yescharacteristic
102C24×C127C22×C412yes—
103C2×D4×C127—24no—
104C2×D4×C127—24no—
105C2×D4×C127—22no—
106C2×D4×C127—22no—
107C2×D4×C127—42no—
108C2×D4×C127M1614yescomplemented
109C22×C4×C127—21no—
110C22×C4×C127—21no—
111C22×C4×C127—21no—
112C22×C4×C127—21no—
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—41no—
124C22×C4×C127—41no—
125C22×C4×C127C22×C411yescharacteristic
126C22×C4×C127C22×C411yescharacteristic
127C22×C4×C127C22×C412yes—
128C22×C4×C127C22×C412yes—
129C22×C4×C127C22×C412yes—
130C22×C4×C127C22×C411yescharacteristic
131C22×C4×C127C22×C411yescharacteristic
132C22×C4×C127C22×C411yescharacteristic
133C22×C4×C127C2×D412yes—
134C22×C4×C127#4112yes—
135C22×C4×C127C2411yescharacteristic
136M16×C127—28no—
137M16×C127—28no—
138C2×C8×C127—21no—
139C2×C8×C127—21no—
140C2×C8×C127—21no—
141C2×C8×C127—21no—
142C2×C8×C127—21no—
143C2×C8×C127—21no—
144C2×C8×C127—22no—
145C2×C8×C127—22no—
146C2×C8×C127—22no—
147C2×C8×C127—22no—
148C2×C8×C127—22no—
149C2×C8×C127—22no—
150C2×C8×C127—48no—
151C2×C8×C127C2×D412yes—
152C2×C8×C127C2×D412yes—
153C2×C8×C127C2×D412yes—
154C2×C8×C127C2×D412yes—
155C2×C8×C127#4112yes—
156C2×C8×C127#4112yes—
157C4⋊C4×C127—24no—
158C4⋊C4×C127—22no—
159C4⋊C4×C127—22no—
160C4⋊C4×C127—22no—
161C22⋊C4×C127—24no—
162C22⋊C4×C127—24no—
163C22⋊C4×C127—24no—
164C22⋊C4×C127—24no—
165C22⋊C4×C127—42no—
166C42×C127—22no—
167C42×C127—22no—
168C42×C127—21no—
169C42×C127—22no—
170C42×C127—21no—
171C42×C127—22no—
172C42×C127C2×D412yes—
173C42×C127#4112yes—
174C23×C127—22no—
175C23×C127—22no—
176C23×C127—21no—
177C23×C127—22no—
178C23×C127—21no—
179C23×C127—21no—
180C23×C127—21no—
181C23×C127—22no—
182C23×C127—22no—
183C23×C127—21no—
184C23×C127—21no—
185C23×C127—22no—
186C23×C127C4×D412yes—
187C23×C127C2×M1614yes—
188C23×C127C23×C411yescharacteristic
189D4×C127—28no—
190D4×C127—48no—
191C2×C4×C127—21no—
192C2×C4×C127—21no—
193C2×C4×C127—21no—
194C2×C4×C127—21no—
195C2×C4×C127—22no—
196C2×C4×C127—22no—
197C2×C4×C127—22no—
198C2×C4×C127—22no—
199C2×C4×C127—21no—
200C2×C4×C127—21no—
201C2×C4×C127—22no—
202C2×C4×C127—22no—
203C2×C4×C127—22no—
204C2×C4×C127—22no—
205C2×C4×C127—22no—
206C2×C4×C127—21no—
207C2×C4×C127—22no—
208C2×C4×C127—22no—
209C2×C4×C127—21no—
210C2×C4×C127—21no—
211C2×C4×C127—22no—
212C2×C4×C127—21no—
213C2×C4×C127—22no—
214C2×C4×C127—44no—
215C2×C4×C127—42no—
216C2×C4×C127—42no—
217C2×C4×C127—42no—
218C2×C4×C127—42no—
219C2×C4×C127—44no—
220C2×C4×C127C4×D412yes—
221C2×C4×C127C4×D412yes—
222C2×C4×C127C4×D412yes—
223C2×C4×C127C2×M1612yes—
224C2×C4×C127#13112yes—
225C2×C4×C127C22×D411yescharacteristic
226C2×C4×C127C22×D411yescharacteristic
227C2×C4×C127C2×#4111yescharacteristic
228C2×C4×C127C2×#4111yescharacteristic
229C2×C4×C127C2×#4111yescharacteristic
230C2×C4×C127C2×#4111yescharacteristic
231C8×C127—22no—
232C8×C127—22no—
233C8×C127—22no—
234C8×C127—42no—
235C8×C127—42no—
236C8×C127#12114yescomplemented
237C22×C127—24no—
238C22×C127—22no—
239C22×C127—24no—
240C22×C127—22no—
241C22×C127—24no—
242C22×C127—22no—
243C22×C127—41no—
244C22×C127—41no—
245C22×C127—42no—
246C22×C127—42no—
247C22×C127—41no—
248C22×C127—42no—
249C22×C127—41no—
250C22×C127—42no—
251C22×C127C2×C4×D411yescharacteristic
252C22×C127C2×C4×D411yescharacteristic
253C22×C127C4×#4111yescharacteristic
254C22×C127C22×M1611yescharacteristic
255C22×C127C2×#13111yescharacteristic
256C22×C127#56811yescharacteristic
257C22×C127#56811yescharacteristic
258C4×C127—22no—
259C4×C127—22no—
260C4×C127—41no—
261C4×C127—41no—
262C4×C127—42no—
263C4×C127—42no—
264C4×C127—42no—
265C4×C127#43514yescomplemented
266C4×C127C2×#12111yescharacteristic
267C4×C127#52511yescharacteristic
268C4×C127#52911yescharacteristic
269C4×C127#53211yescharacteristic
270#21486C12711yesmaximal, characteristic, direct product factor, Sylow
271C2×C127—44no—
272C2×C127—42no—
273C2×C127C4×#12111yescharacteristic
274C2×C127C2×#43511yescharacteristic
275C2×C127#293011yescharacteristic
276C2×C127D4×M1611yescharacteristic
277C2×C127#293511yescharacteristic
278C2×C127#296911yescharacteristic
279C2×C127#297011yescharacteristic
280C2×#435C2×C12712yescomplemented
281C2×C8×D4C2×C12711yescharacteristic, complemented
282C2×C4×M16C2×C12711yescharacteristic, complemented
283C4×#121C2×C12711yescharacteristic
284#1954C2×C12711yescharacteristic, complemented
285#1939C2×C12711yescharacteristic, complemented
286#1924C2×C12712yescomplemented
287#1870C2×C12712yescomplemented
288#1797C2×C12711yescharacteristic, complemented
289#1770C2×C12711yescharacteristic, complemented
290#1752C2×C12712yescomplemented
291C127#2148611yescharacteristic, direct product factor, Sylow
292C22×M16C22×C12711yescharacteristic
293C22×M16C22×C12711yescharacteristic
294C23×C8C22×C12712yes—
295C2×#121C4×C12711yescharacteristic
296C2×C4×D4C22×C12712yes—
297C2×C4×D4C22×C12711yescharacteristic
298C22×C42C22×C12711yescharacteristic
299#435—28no—
300C8×D4—24no—
301C2×C4⋊C8C22×C12711yescharacteristic
302C2×C4⋊C8C22×C12711yescharacteristic
303C2×C4⋊C8C22×C12712yes—
304C2×C22⋊C8C22×C12712yes—
305C2×C22⋊C8C22×C12712yes—
306C2×C22⋊C8C22×C12712yes—
307C2×C22⋊C8C22×C12712yes—
308C4×M16—24no—
309C2×#97C22×C12711yescharacteristic
310C2×#97C22×C12711yescharacteristic
311C2×#97C22×C12712yes—
312C2×C4×C8C22×C12711yescharacteristic
313C2×C4×C8C22×C12711yescharacteristic
314#390C4×C12711yescharacteristic
315#389C4×C12711yescharacteristic
316#388C4×C12712yes—
317#386C4×C12712yes—
318#380C4×C12711yescharacteristic
319C4×C4⋊C4C22×C12711yescharacteristic
320C4×C22⋊C4C22×C12712yes—
321#336C22×C12712yes—
322#336C22×C12712yes—
323#336C22×C12712yes—
324C22×D4C2×C4×C12712yes—
325C22×D4C2×C4×C12711yescharacteristic
326C23×C4C2×C4×C12711yescharacteristic
327C23×C4C2×C4×C12711yescharacteristic
328C23×C4C23×C12712yes—
329C23×C4C23×C12711yescharacteristic
330C2×M16—22no—
331C2×M16—22no—
332C2×M16—22no—
333C2×M16—22no—
334C2×M16—22no—
335C2×M16D4×C12714yescomplemented
336C22×C8—24no—
337C22×C8—24no—
338C22×C8—24no—
339C22×C8C23×C12712yes—
340C22×C8C23×C12712yes—
341C22×C8C23×C12711yescharacteristic
342C22×C8C23×C12711yescharacteristic
343C22×C8C23×C12711yescharacteristic
344C22×C8C23×C12711yescharacteristic
345#121—24no—
346C4×D4—24no—
347C4×D4—24no—
348C4×D4—22no—
349C4×D4—22no—
350C2×C4⋊C4C2×C4×C12711yescharacteristic
351C2×C4⋊C4C2×C4×C12712yes—
352C2×C4⋊C4C2×C4×C12711yescharacteristic
353C2×C4⋊C4C2×C4×C12711yescharacteristic
354C2×C22⋊C4C2×C4×C12712yes—
355C2×C22⋊C4C2×C4×C12712yes—
356C2×C22⋊C4C2×C4×C12712yes—
357C2×C22⋊C4C2×C4×C12712yes—
358C2×C22⋊C4C2×C4×C12712yes—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42C2×C4×C12711yescharacteristic
362C2×C42C2×C4×C12711yescharacteristic
363C2×C42C23×C12712yes—
364C2×C42C23×C12711yescharacteristic
365C2×C42C23×C12711yescharacteristic
366C4⋊C8—24no—
367C4⋊C8—22no—
368C4⋊C8—22no—
369C22⋊C8—24no—
370C22⋊C8—24no—
371C22⋊C8—24no—
372C22⋊C8—24no—
373#97—22no—
374#97—22no—
375#97—24no—
376C4×C8—22no—
377C4×C8D4×C12714yescomplemented
378#95C2×C4×C12712yes—
379#95C2×C4×C12712yes—
380#95C2×C4×C12712yes—
381C24C22×C4×C12711yescharacteristic
382C24C22×C4×C12712yes—
383C2×D4—24no—
384C2×D4—24no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—42no—
388C2×D4M16×C12714yescomplemented
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4C22×C4×C12711yescharacteristic
406C22×C4C22×C4×C12711yescharacteristic
407C22×C4C22×C4×C12712yes—
408C22×C4C22×C4×C12712yes—
409C22×C4C22×C4×C12712yes—
410C22×C4C22×C4×C12711yescharacteristic
411C22×C4C22×C4×C12711yescharacteristic
412C22×C4C22×C4×C12711yescharacteristic
413C22×C4C2×D4×C12712yes—
414C22×C4#41×C12712yes—
415C22×C4C24×C12711yescharacteristic
416M16—28no—
417M16—28no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8—21no—
423C2×C8—21no—
424C2×C8—22no—
425C2×C8—22no—
426C2×C8—22no—
427C2×C8—22no—
428C2×C8—22no—
429C2×C8—22no—
430C2×C8—48no—
431C2×C8C2×D4×C12712yes—
432C2×C8C2×D4×C12712yes—
433C2×C8C2×D4×C12712yes—
434C2×C8C2×D4×C12712yes—
435C2×C8#41×C12712yes—
436C2×C8#41×C12712yes—
437C4⋊C4—24no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C22⋊C4—24no—
442C22⋊C4—24no—
443C22⋊C4—24no—
444C22⋊C4—24no—
445C22⋊C4—42no—
446C42—22no—
447C42—22no—
448C42—21no—
449C42—22no—
450C42—21no—
451C42—22no—
452C42C2×D4×C12712yes—
453C42#41×C12712yes—
454C23—22no—
455C23—22no—
456C23—21no—
457C23—22no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—22no—
462C23—22no—
463C23—21no—
464C23—21no—
465C23—22no—
466C23C4×D4×C12712yes—
467C23C2×M16×C12714yes—
468C23C23×C4×C12711yescharacteristic
469D4—28no—
470D4—48no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—21no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—22no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—44no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—44no—
500C2×C4C4×D4×C12712yes—
501C2×C4C4×D4×C12712yes—
502C2×C4C4×D4×C12712yes—
503C2×C4C2×M16×C12712yes—
504C2×C4#131×C12712yes—
505C2×C4C22×D4×C12711yescharacteristic
506C2×C4C22×D4×C12711yescharacteristic
507C2×C4C2×#41×C12711yescharacteristic
508C2×C4C2×#41×C12711yescharacteristic
509C2×C4C2×#41×C12711yescharacteristic
510C2×C4C2×#41×C12711yescharacteristic
511C8—22no—
512C8—22no—
513C8—22no—
514C8—42no—
515C8—42no—
516C8#121×C12714yescomplemented
517C22—24no—
518C22—22no—
519C22—24no—
520C22—22no—
521C22—24no—
522C22—22no—
523C22—41no—
524C22—41no—
525C22—42no—
526C22—42no—
527C22—41no—
528C22—42no—
529C22—41no—
530C22—42no—
531C22C2×C4×D4×C12711yescharacteristic
532C22C2×C4×D4×C12711yescharacteristic
533C22C4×#41×C12711yescharacteristic
534C22C22×M16×C12711yescharacteristic
535C22C2×#131×C12711yescharacteristic
536C22#568×C12711yescharacteristic
537C22#568×C12711yescharacteristic
538C4—22no—
539C4—22no—
540C4—41no—
541C4—41no—
542C4—42no—
543C4—42no—
544C4—42no—
545C4#435×C12714yescomplemented
546C4C2×#121×C12711yescharacteristic
547C4#525×C12711yescharacteristic
548C4#529×C12711yescharacteristic
549C4#532×C12711yescharacteristic
550C2—44no—
551C2—42no—
552C2C4×#121×C12711yescharacteristic
553C2C2×#435×C12711yescharacteristic
554C2C127×#293011yescharacteristic
555C2D4×M16×C12711yescharacteristic
556C2C127×#293511yescharacteristic
557C2C127×#296911yescharacteristic
558C2C127×#297011yescharacteristic
subgroupG/H
centerC22×C4×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC23×C127C23×C4
prime radicalC2×#121×C127C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#435×C127C2semidirect
2. C2×C8×D4×C127C2semidirect
3. C2×C4×M16×C127C2semidirect
5. C127×#1954C2semidirect
6. C127×#1939C2semidirect
7. C127×#1924C2semidirect
8. C127×#1870C2semidirect
9. C127×#1797C2semidirect
10. C127×#1770C2semidirect
11. C127×#1752C2semidirect
55. C2×M16×C127D4semidirect
97. C4×C8×C127D4semidirect
108. C2×D4×C127M16semidirect
236. C8×C127#121semidirect
265. C4×C127#435semidirect
270. #21486C127direct (N × H)
280. C2×#435C2×C127semidirect
281. C2×C8×D4C2×C127semidirect
282. C2×C4×M16C2×C127semidirect
284. #1954C2×C127semidirect
285. #1939C2×C127semidirect
286. #1924C2×C127semidirect
287. #1870C2×C127semidirect
288. #1797C2×C127semidirect
289. #1770C2×C127semidirect
290. #1752C2×C127semidirect
291. C127#21486direct (N × H)
335. C2×M16D4×C127semidirect
377. C4×C8D4×C127semidirect
388. C2×D4M16×C127semidirect
516. C8#121×C127semidirect
545. C4#435×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#435×C1272
C2×C8×D4×C1272
C2×C4×M16×C1272
C4×#121×C1272
C127×#19542
C127×#19392
C127×#19242
C127×#18702
C127×#17972
C127×#17702
C127×#17522
#21486127