Finite Group Databasebeta

← C127×#17448 #44581121

Subgroups — C127×#17448 #44581121

Order 32512.

1646 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C127C211yesmaximal, characteristic
2C127×#2920C211yesmaximal, characteristic, complemented
3C127×#2920C211yesmaximal, characteristic, complemented
4C127×#1490C214yesmaximal, complemented
5C127×#1486C214yesmaximal, complemented
6C127×#1478C214yesmaximal, complemented
7C23×D4×C127C411yescharacteristic
8C24×C4×C127—21no—
9C2×C4×D4×C127—21no—
10C2×C4×D4×C127—21no—
11C2×C4×D4×C127—21no—
12C2×C4×D4×C127—21no—
13C2×C4×D4×C127—21no—
14C2×C4×D4×C127—21no—
15C2×C4×D4×C127C412yes—
16C2×C4×D4×C127C412yes—
17C2×C4×D4×C127C412yes—
18C2×C4×D4×C127C2212yes—
19C2×C4×D4×C127C2212yes—
20C2×C4×D4×C127C2212yes—
21C22×C4⋊C4×C127C411yescharacteristic
22C22×C22⋊C4×C127—21no—
23C22×C42×C127C2211yescharacteristic
24#432×C127—21no—
25#432×C127—21no—
26#432×C127—21no—
27#432×C127C2212yescomplemented
28#431×C127—21no—
29#431×C127C2212yescomplemented
30#431×C127C2212yescomplemented
31#431×C127C2212yescomplemented
32#423×C127—21no—
33#423×C127C2212yescomplemented
34#407×C127—21no—
35#407×C127—21no—
36C4×M16×C127—21no—
37C4×M16×C127C2212yescomplemented
38D4⋊C8×C127C22116yescomplemented
39C25×C127—21no—
40C22×D4×C127—28no—
41C22×D4×C127—21no—
42C22×D4×C127—21no—
43C22×D4×C127—21no—
44C22×D4×C127C2×C412yes—
45C22×D4×C127C2×C412yes—
46C22×D4×C127C2×C412yes—
47C23×C4×C127—21no—
48C23×C4×C127—22no—
49C23×C4×C127—22no—
50C23×C4×C127—22no—
51C23×C4×C127—22no—
52C23×C4×C127—22no—
53C23×C4×C127—22no—
54C23×C4×C127—48no—
55C23×C4×C127C2×C411yescharacteristic
56C23×C4×C127D411yescharacteristic
57C23×C4×C127D411yescharacteristic
58C2×M16×C127—22no—
59C2×M16×C127—22no—
60C4×D4×C127—22no—
61C4×D4×C127—22no—
62C4×D4×C127—22no—
63C4×D4×C127—22no—
64C4×D4×C127—22no—
65C4×D4×C127—22no—
66C4×D4×C127—22no—
67C4×D4×C127—22no—
68C4×D4×C127—22no—
69C4×D4×C127—22no—
70C4×D4×C127—22no—
71C4×D4×C127—22no—
72C4×D4×C127C2×C414yes—
73C4×D4×C127C2×C414yes—
74C4×D4×C127C2×C414yes—
75C4×D4×C127C2314yes—
76C2×C4⋊C4×C127—21no—
77C2×C4⋊C4×C127—21no—
78C2×C4⋊C4×C127—21no—
79C2×C4⋊C4×C127C2×C412yes—
80C2×C4⋊C4×C127C2×C412yes—
81C2×C4⋊C4×C127C2×C412yes—
82C2×C22⋊C4×C127—22no—
83C2×C22⋊C4×C127—22no—
84C2×C22⋊C4×C127—22no—
85C2×C22⋊C4×C127—22no—
86C2×C22⋊C4×C127—22no—
87C2×C22⋊C4×C127—22no—
88C2×C42×C127C2×C411yescharacteristic
89C2×C42×C127C2×C411yescharacteristic
90C2×C42×C127C2×C411yescharacteristic
91C2×C42×C127D411yescharacteristic
92C2×C42×C127D411yescharacteristic
93C2×C42×C127D411yescharacteristic
94C2×C42×C127D411yescharacteristic
95C2×C42×C127D411yescharacteristic
96C2×C42×C127D411yescharacteristic
97C2×C42×C127C2311yescharacteristic
98C2×C42×C127C2311yescharacteristic
99C2×C42×C127C2311yescharacteristic
100C4⋊C8×C127—22no—
101C4⋊C8×C127—22no—
102C4⋊C8×C127—22no—
103C4⋊C8×C127C2314yescomplemented
104C22⋊C8×C127—22no—
105C22⋊C8×C127—22no—
106C22⋊C8×C127—22no—
107C22⋊C8×C127—22no—
108#97×C127—22no—
109#97×C127—22no—
110C4×C8×C127—22no—
111C4×C8×C127C2314yescomplemented
112C24×C127—28no—
113C24×C127—22no—
114C24×C127—22no—
115C24×C127—22no—
116C24×C127—44no—
117C24×C127—44no—
118C24×C127C22⋊C411yescharacteristic
119C2×D4×C127—28no—
120C2×D4×C127—28no—
121C2×D4×C127—28no—
122C2×D4×C127—28no—
123C2×D4×C127—28no—
124C2×D4×C127—22no—
125C2×D4×C127—22no—
126C2×D4×C127—22no—
127C2×D4×C127—24no—
128C2×D4×C127M1618yescomplemented
129C2×D4×C127C22×C414yes—
130C22×C4×C127—24no—
131C22×C4×C127—24no—
132C22×C4×C127—22no—
133C22×C4×C127—22no—
134C22×C4×C127—22no—
135C22×C4×C127—24no—
136C22×C4×C127—24no—
137C22×C4×C127—24no—
138C22×C4×C127—24no—
139C22×C4×C127—42no—
140C22×C4×C127—48no—
141C22×C4×C127—48no—
142C22×C4×C127—48no—
143C22×C4×C127—48no—
144C22×C4×C127—48no—
145C22×C4×C127—44no—
146C22×C4×C127—48no—
147C22×C4×C127C22⋊C411yescharacteristic
148C22×C4×C127C22⋊C411yescharacteristic
149C22×C4×C127C22⋊C411yescharacteristic
150C22×C4×C127C22⋊C411yescharacteristic
151C22×C4×C127C22⋊C411yescharacteristic
152C22×C4×C127C22⋊C411yescharacteristic
153C22×C4×C127C22⋊C411yescharacteristic
154C22×C4×C127C22⋊C411yescharacteristic
155C22×C4×C127C22⋊C411yescharacteristic
156C22×C4×C127C22×C411yescharacteristic
157C22×C4×C127C22×C411yescharacteristic
158C22×C4×C127C22×C411yescharacteristic
159C22×C4×C127C2×D411yescharacteristic
160C22×C4×C127C2×D411yescharacteristic
161C22×C4×C127C2×D411yescharacteristic
162C22×C4×C127C2×D411yescharacteristic
163C22×C4×C127C2×D411yescharacteristic
164C22×C4×C127C2×D411yescharacteristic
165M16×C127—44no—
166M16×C127—44no—
167C2×C8×C127—24no—
168C2×C8×C127—24no—
169C4⋊C4×C127—22no—
170C4⋊C4×C127—22no—
171C4⋊C4×C127—22no—
172C4⋊C4×C127C22×C414yes—
173C22⋊C4×C127—24no—
174C22⋊C4×C127—24no—
175C22⋊C4×C127—24no—
176C22⋊C4×C127—24no—
177C42×C127C22⋊C411yescharacteristic
178C42×C127C22⋊C411yescharacteristic
179C42×C127C22⋊C411yescharacteristic
180C42×C127C22⋊C411yescharacteristic
181C42×C127C22⋊C411yescharacteristic
182C42×C127C22⋊C411yescharacteristic
183C42×C127C22×C411yescharacteristic
184C42×C127C22×C411yescharacteristic
185C42×C127C22×C411yescharacteristic
186C42×C127C2×D411yescharacteristic
187C42×C127C2×D411yescharacteristic
188C42×C127C2×D411yescharacteristic
189C42×C127C2×D411yescharacteristic
190C42×C127C2×D411yescharacteristic
191C42×C127C2×D411yescharacteristic
192C42×C127C2411yescharacteristic
193C23×C127—22no—
194C23×C127—22no—
195C23×C127—22no—
196C23×C127—28no—
197C23×C127—28no—
198C23×C127—24no—
199C23×C127—28no—
200C23×C127—44no—
201C23×C127—44no—
202C23×C127—432no—
203C23×C127—44no—
204C23×C127—44no—
205C23×C127—44no—
206C23×C127—44no—
207C23×C127C2×C22⋊C411yescharacteristic
208C23×C127C2×C22⋊C411yescharacteristic
209C23×C127C2×C22⋊C411yescharacteristic
210D4×C127—28no—
211D4×C127—28no—
212D4×C127—24no—
213D4×C127—28no—
214D4×C127C2×M1618yes—
215C2×C4×C127—22no—
216C2×C4×C127—22no—
217C2×C4×C127—22no—
218C2×C4×C127—22no—
219C2×C4×C127—22no—
220C2×C4×C127—22no—
221C2×C4×C127—22no—
222C2×C4×C127—22no—
223C2×C4×C127—22no—
224C2×C4×C127—22no—
225C2×C4×C127—22no—
226C2×C4×C127—22no—
227C2×C4×C127—24no—
228C2×C4×C127—41no—
229C2×C4×C127—41no—
230C2×C4×C127—41no—
231C2×C4×C127—41no—
232C2×C4×C127—48no—
233C2×C4×C127—48no—
234C2×C4×C127—44no—
235C2×C4×C127—44no—
236C2×C4×C127—44no—
237C2×C4×C127—48no—
238C2×C4×C127—48no—
239C2×C4×C127C2×C22⋊C411yescharacteristic
240C2×C4×C127C2×C22⋊C411yescharacteristic
241C2×C4×C127C2×C22⋊C411yescharacteristic
242C2×C4×C127C2×C22⋊C411yescharacteristic
243C2×C4×C127C2×C22⋊C411yescharacteristic
244C2×C4×C127C2×C22⋊C411yescharacteristic
245C2×C4×C127C2×C22⋊C411yescharacteristic
246C2×C4×C127C2×C22⋊C411yescharacteristic
247C2×C4×C127C2×C22⋊C411yescharacteristic
248C2×C4×C127C2×M1614yes—
249C2×C4×C127AGL(1,ℤ/8)14yes—
250C2×C4×C127C23×C411yescharacteristic
251C2×C4×C127C22×D411yescharacteristic
252C2×C4×C127C22×D411yescharacteristic
253C8×C127—44no—
254C8×C127—44no—
255C22×C127—28no—
256C22×C127—21no—
257C22×C127—21no—
258C22×C127—21no—
259C22×C127—21no—
260C22×C127—21no—
261C22×C127—21no—
262C22×C127—28no—
263C22×C127—416no—
264C22×C127—416no—
265C22×C127—416no—
266C22×C127—44no—
267C22×C127—44no—
268C22×C127#40712yes—
269C22×C127#41812yes—
270C22×C127#42112yes—
271C22×C127C22×C22⋊C411yescharacteristic
272C4×C127—21no—
273C4×C127—21no—
274C4×C127—21no—
275C4×C127—21no—
276C4×C127—21no—
277C4×C127—21no—
278C4×C127—21no—
279C4×C127—21no—
280C4×C127—44no—
281C4×C127#40712yes—
282C4×C127#41812yes—
283C4×C127C22×M1612yes—
284C4×C127C2×AGL(1,ℤ/8)12yes—
285#17448C12711yesmaximal, characteristic, direct product factor, Sylow
286C2×C127—22no—
287C2×C127—22no—
288C2×C127—22no—
289C2×C127—48no—
290C2×C127C2×#40711yescharacteristic
291C2×C127C2×#41811yescharacteristic
292C2×C127C2×#42111yescharacteristic
293C22×C4×D4C2×C12711yescharacteristic
294#2920C2×C12711yescharacteristic, complemented
295#2920C2×C12711yescharacteristic, complemented
296#1490C2×C12714yescomplemented
297#1486C2×C12714yescomplemented
298#1478C2×C12714yescomplemented
299C127#1744811yescharacteristic, direct product factor, Sylow
300C23×D4C4×C12711yescharacteristic
301C24×C4—21no—
302C2×C4×D4—21no—
303C2×C4×D4—21no—
304C2×C4×D4—21no—
305C2×C4×D4—21no—
306C2×C4×D4—21no—
307C2×C4×D4—21no—
308C2×C4×D4C4×C12712yes—
309C2×C4×D4C4×C12712yes—
310C2×C4×D4C4×C12712yes—
311C2×C4×D4C22×C12712yes—
312C2×C4×D4C22×C12712yes—
313C2×C4×D4C22×C12712yes—
314C22×C4⋊C4C4×C12711yescharacteristic
315C22×C22⋊C4—21no—
316C22×C42C22×C12711yescharacteristic
317#432—21no—
318#432—21no—
319#432—21no—
320#432C22×C12712yescomplemented
321#431—21no—
322#431C22×C12712yescomplemented
323#431C22×C12712yescomplemented
324#431C22×C12712yescomplemented
325#423—21no—
326#423C22×C12712yescomplemented
327#407—21no—
328#407—21no—
329C4×M16—21no—
330C4×M16C22×C12712yescomplemented
331D4⋊C8C22×C127116yescomplemented
332C25—21no—
333C22×D4—28no—
334C22×D4—21no—
335C22×D4—21no—
336C22×D4—21no—
337C22×D4C2×C4×C12712yes—
338C22×D4C2×C4×C12712yes—
339C22×D4C2×C4×C12712yes—
340C23×C4—21no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—22no—
347C23×C4—48no—
348C23×C4C2×C4×C12711yescharacteristic
349C23×C4D4×C12711yescharacteristic
350C23×C4D4×C12711yescharacteristic
351C2×M16—22no—
352C2×M16—22no—
353C4×D4—22no—
354C4×D4—22no—
355C4×D4—22no—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4—22no—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4—22no—
362C4×D4—22no—
363C4×D4—22no—
364C4×D4—22no—
365C4×D4C2×C4×C12714yes—
366C4×D4C2×C4×C12714yes—
367C4×D4C2×C4×C12714yes—
368C4×D4C23×C12714yes—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4C2×C4×C12712yes—
373C2×C4⋊C4C2×C4×C12712yes—
374C2×C4⋊C4C2×C4×C12712yes—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C42C2×C4×C12711yescharacteristic
382C2×C42C2×C4×C12711yescharacteristic
383C2×C42C2×C4×C12711yescharacteristic
384C2×C42D4×C12711yescharacteristic
385C2×C42D4×C12711yescharacteristic
386C2×C42D4×C12711yescharacteristic
387C2×C42D4×C12711yescharacteristic
388C2×C42D4×C12711yescharacteristic
389C2×C42D4×C12711yescharacteristic
390C2×C42C23×C12711yescharacteristic
391C2×C42C23×C12711yescharacteristic
392C2×C42C23×C12711yescharacteristic
393C4⋊C8—22no—
394C4⋊C8—22no—
395C4⋊C8—22no—
396C4⋊C8C23×C12714yescomplemented
397C22⋊C8—22no—
398C22⋊C8—22no—
399C22⋊C8—22no—
400C22⋊C8—22no—
401#97—22no—
402#97—22no—
403C4×C8—22no—
404C4×C8C23×C12714yescomplemented
405C24—28no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—44no—
410C24—44no—
411C24C22⋊C4×C12711yescharacteristic
412C2×D4—28no—
413C2×D4—28no—
414C2×D4—28no—
415C2×D4—28no—
416C2×D4—28no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—24no—
421C2×D4M16×C12718yescomplemented
422C2×D4C22×C4×C12714yes—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—42no—
433C22×C4—48no—
434C22×C4—48no—
435C22×C4—48no—
436C22×C4—48no—
437C22×C4—48no—
438C22×C4—44no—
439C22×C4—48no—
440C22×C4C22⋊C4×C12711yescharacteristic
441C22×C4C22⋊C4×C12711yescharacteristic
442C22×C4C22⋊C4×C12711yescharacteristic
443C22×C4C22⋊C4×C12711yescharacteristic
444C22×C4C22⋊C4×C12711yescharacteristic
445C22×C4C22⋊C4×C12711yescharacteristic
446C22×C4C22⋊C4×C12711yescharacteristic
447C22×C4C22⋊C4×C12711yescharacteristic
448C22×C4C22⋊C4×C12711yescharacteristic
449C22×C4C22×C4×C12711yescharacteristic
450C22×C4C22×C4×C12711yescharacteristic
451C22×C4C22×C4×C12711yescharacteristic
452C22×C4C2×D4×C12711yescharacteristic
453C22×C4C2×D4×C12711yescharacteristic
454C22×C4C2×D4×C12711yescharacteristic
455C22×C4C2×D4×C12711yescharacteristic
456C22×C4C2×D4×C12711yescharacteristic
457C22×C4C2×D4×C12711yescharacteristic
458M16—44no—
459M16—44no—
460C2×C8—24no—
461C2×C8—24no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4C22×C4×C12714yes—
466C22⋊C4—24no—
467C22⋊C4—24no—
468C22⋊C4—24no—
469C22⋊C4—24no—
470C42C22⋊C4×C12711yescharacteristic
471C42C22⋊C4×C12711yescharacteristic
472C42C22⋊C4×C12711yescharacteristic
473C42C22⋊C4×C12711yescharacteristic
474C42C22⋊C4×C12711yescharacteristic
475C42C22⋊C4×C12711yescharacteristic
476C42C22×C4×C12711yescharacteristic
477C42C22×C4×C12711yescharacteristic
478C42C22×C4×C12711yescharacteristic
479C42C2×D4×C12711yescharacteristic
480C42C2×D4×C12711yescharacteristic
481C42C2×D4×C12711yescharacteristic
482C42C2×D4×C12711yescharacteristic
483C42C2×D4×C12711yescharacteristic
484C42C2×D4×C12711yescharacteristic
485C42C24×C12711yescharacteristic
486C23—22no—
487C23—22no—
488C23—22no—
489C23—28no—
490C23—28no—
491C23—24no—
492C23—28no—
493C23—44no—
494C23—44no—
495C23—432no—
496C23—44no—
497C23—44no—
498C23—44no—
499C23—44no—
500C23C2×C22⋊C4×C12711yescharacteristic
501C23C2×C22⋊C4×C12711yescharacteristic
502C23C2×C22⋊C4×C12711yescharacteristic
503D4—28no—
504D4—28no—
505D4—24no—
506D4—28no—
507D4C2×M16×C12718yes—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—48no—
526C2×C4—48no—
527C2×C4—44no—
528C2×C4—44no—
529C2×C4—44no—
530C2×C4—48no—
531C2×C4—48no—
532C2×C4C2×C22⋊C4×C12711yescharacteristic
533C2×C4C2×C22⋊C4×C12711yescharacteristic
534C2×C4C2×C22⋊C4×C12711yescharacteristic
535C2×C4C2×C22⋊C4×C12711yescharacteristic
536C2×C4C2×C22⋊C4×C12711yescharacteristic
537C2×C4C2×C22⋊C4×C12711yescharacteristic
538C2×C4C2×C22⋊C4×C12711yescharacteristic
539C2×C4C2×C22⋊C4×C12711yescharacteristic
540C2×C4C2×C22⋊C4×C12711yescharacteristic
541C2×C4C2×M16×C12714yes—
542C2×C4AGL(1,ℤ/8)×C12714yes—
543C2×C4C23×C4×C12711yescharacteristic
544C2×C4C22×D4×C12711yescharacteristic
545C2×C4C22×D4×C12711yescharacteristic
546C8—44no—
547C8—44no—
548C22—28no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—28no—
556C22—416no—
557C22—416no—
558C22—416no—
559C22—44no—
560C22—44no—
561C22#407×C12712yes—
562C22#418×C12712yes—
563C22#421×C12712yes—
564C22C22×C22⋊C4×C12711yescharacteristic
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—44no—
574C4#407×C12712yes—
575C4#418×C12712yes—
576C4C22×M16×C12712yes—
577C4C2×AGL(1,ℤ/8)×C12712yes—
578C2—22no—
579C2—22no—
580C2—22no—
581C2—48no—
582C2C2×#407×C12711yescharacteristic
583C2C2×#418×C12711yescharacteristic
584C2C2×#421×C12711yescharacteristic
subgroupG/H
centerC2×C4×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC42C24×C127
socleC22×C127C22×C22⋊C4
prime radicalC23×D4×C127C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2920C2semidirect
3. C127×#2920C2semidirect
4. C127×#1490C2semidirect
5. C127×#1486C2semidirect
6. C127×#1478C2semidirect
27. #432×C127C22semidirect
29. #431×C127C22semidirect
30. #431×C127C22semidirect
31. #431×C127C22semidirect
33. #423×C127C22semidirect
37. C4×M16×C127C22semidirect
38. D4⋊C8×C127C22semidirect
103. C4⋊C8×C127C23semidirect
111. C4×C8×C127C23semidirect
128. C2×D4×C127M16semidirect
285. #17448C127direct (N × H)
294. #2920C2×C127semidirect
295. #2920C2×C127semidirect
296. #1490C2×C127semidirect
297. #1486C2×C127semidirect
298. #1478C2×C127semidirect
299. C127#17448direct (N × H)
320. #432C22×C127semidirect
322. #431C22×C127semidirect
323. #431C22×C127semidirect
324. #431C22×C127semidirect
326. #423C22×C127semidirect
330. C4×M16C22×C127semidirect
331. D4⋊C8C22×C127semidirect
396. C4⋊C8C23×C127semidirect
404. C4×C8C23×C127semidirect
421. C2×D4M16×C127semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C1272
C127×#29202
C127×#14902
C127×#14862
C127×#14782
#17448127