Finite Group Databasebeta

← C127×#13960 #44577633

Subgroups — C127×#13960 #44577633

Order 32512.

2590 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C127C211yesmaximal, characteristic
2C2×#386×C127C212yesmaximal
3C2×#380×C127C211yesmaximal, characteristic, complemented
4C22×#95×C127C211yesmaximal, characteristic, complemented
5C127×#1441C212yesmaximal, complemented
6C127×#1439C212yesmaximal, complemented
7C127×#1434C212yesmaximal, complemented
8C127×C22⋊#95C212yesmaximal, complemented
9C127×C22⋊#95C212yesmaximal, complemented
10C23×D4×C127C2211yescharacteristic
11C24×C4×C127C2212yes—
12C24×C4×C127C2211yescharacteristic
13C24×C4×C127C2211yescharacteristic
14C2×C4×D4×C127—24no—
15C2×C4×D4×C127—24no—
16C2×C4×D4×C127C418yescomplemented
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C4⋊C4×C127C2212yes—
19C22×C22⋊C4×C127C2212yes—
20C22×C22⋊C4×C127C2214yes—
21C22×C22⋊C4×C127C2211yescharacteristic
22C22×C22⋊C4×C127C2211yescharacteristic
23C22×C42×C127C2211yescharacteristic
24#386×C127—28no—
25#380×C127—24no—
26C2×#95×C127—24no—
27C2×#95×C127C2214yes—
28C2×#95×C127C2212yes—
29C2×#95×C127C2212yes—
30C2×#95×C127C2214yes—
31C2×#95×C127C2212yes—
32C2×#95×C127C2214yes—
33C25×C127C2311yescharacteristic
34C25×C127C2311yescharacteristic
35C22×D4×C127—22no—
36C22×D4×C127—22no—
37C22×D4×C127—22no—
38C22×D4×C127—22no—
39C22×D4×C127C2×C414yes—
40C22×D4×C127D414yes—
41C22×D4×C127Q814yes—
42C23×C4×C127—24no—
43C23×C4×C127—22no—
44C23×C4×C127—22no—
45C23×C4×C127—28no—
46C23×C4×C127—24no—
47C23×C4×C127—24no—
48C23×C4×C127—44no—
49C23×C4×C127—44no—
50C23×C4×C127—44no—
51C23×C4×C127C2×C414yes—
52C23×C4×C127C2×C414yescomplemented
53C23×C4×C127D414yes—
54C23×C4×C127D414yes—
55C23×C4×C127C2314yes—
56C23×C4×C127C2311yescharacteristic
57C23×C4×C127C2311yescharacteristic
58C23×C4×C127C2314yes—
59C23×C4×C127C2311yescharacteristic
60C23×C4×C127C2311yescharacteristic
61C23×C4×C127C2311yescharacteristic
62C4×D4×C127—232no—
63C2×C4⋊C4×C127—22no—
64C2×C4⋊C4×C127—22no—
65C2×C4⋊C4×C127—24no—
66C2×C4⋊C4×C127—44no—
67C2×C4⋊C4×C127C2×C414yescomplemented
68C2×C22⋊C4×C127—22no—
69C2×C22⋊C4×C127—22no—
70C2×C22⋊C4×C127—22no—
71C2×C22⋊C4×C127—22no—
72C2×C22⋊C4×C127—24no—
73C2×C22⋊C4×C127—28no—
74C2×C22⋊C4×C127—24no—
75C2×C22⋊C4×C127—24no—
76C2×C22⋊C4×C127—28no—
77C2×C22⋊C4×C127—44no—
78C2×C22⋊C4×C127C2×C414yes—
79C2×C22⋊C4×C127C2×C414yescomplemented
80C2×C42×C127—22no—
81C2×C42×C127—22no—
82C2×C42×C127C2×C414yescomplemented
83#95×C127—24no—
84#95×C127—24no—
85#95×C127—24no—
86#95×C127—28no—
87#95×C127—28no—
88#95×C127—44no—
89C24×C127—24no—
90C24×C127—24no—
91C24×C127—21no—
92C24×C127—21no—
93C24×C127—24no—
94C24×C127—21no—
95C24×C127—21no—
96C24×C127—24no—
97C24×C127C22×C412yes—
98C24×C127C22×C412yes—
99C24×C127C2×D412yes—
100C24×C127C2×D412yes—
101C24×C127C2×D412yes—
102C24×C127C2×D412yes—
103C24×C127C2×Q812yes—
104C24×C127C2×Q812yes—
105C24×C127#4112yes—
106C24×C127#4112yes—
107C24×C127C2411yescharacteristic
108C2×D4×C127—28no—
109C2×D4×C127—28no—
110C2×D4×C127—28no—
111C2×D4×C127—28no—
112C2×D4×C127—28no—
113C2×D4×C127—28no—
114C2×D4×C127C4⋊C4116yescomplemented
115C22×C4×C127—21no—
116C22×C4×C127—21no—
117C22×C4×C127—21no—
118C22×C4×C127—21no—
119C22×C4×C127—24no—
120C22×C4×C127—24no—
121C22×C4×C127—216no—
122C22×C4×C127—24no—
123C22×C4×C127—24no—
124C22×C4×C127—21no—
125C22×C4×C127—21no—
126C22×C4×C127—21no—
127C22×C4×C127—21no—
128C22×C4×C127—24no—
129C22×C4×C127—24no—
130C22×C4×C127—24no—
131C22×C4×C127—24no—
132C22×C4×C127—24no—
133C22×C4×C127—24no—
134C22×C4×C127—28no—
135C22×C4×C127—24no—
136C22×C4×C127—24no—
137C22×C4×C127—24no—
138C22×C4×C127—24no—
139C22×C4×C127—24no—
140C22×C4×C127—24no—
141C22×C4×C127—24no—
142C22×C4×C127—48no—
143C22×C4×C127—48no—
144C22×C4×C127—48no—
145C22×C4×C127—48no—
146C22×C4×C127—416no—
147C22×C4×C127—416no—
148C22×C4×C127—48no—
149C22×C4×C127—48no—
150C22×C4×C127—48no—
151C22×C4×C127—48no—
152C22×C4×C127C22⋊C4116yescomplemented
153C22×C4×C127C22×C412yes—
154C22×C4×C127C22×C412yes—
155C22×C4×C127C22×C412yes—
156C22×C4×C127C22×C412yes—
157C22×C4×C127C22×C412yes—
158C22×C4×C127C2×D412yes—
159C22×C4×C127C2×D412yes—
160C22×C4×C127C2×D412yes—
161C22×C4×C127C2×D412yes—
162C22×C4×C127C2×D412yes—
163C22×C4×C127C2×Q812yes—
164C22×C4×C127#4118yes—
165C4⋊C4×C127—28no—
166C4⋊C4×C127—48no—
167C22⋊C4×C127—28no—
168C22⋊C4×C127—28no—
169C22⋊C4×C127—416no—
170C22⋊C4×C127—48no—
171C42×C127—28no—
172C23×C127—24no—
173C23×C127—24no—
174C23×C127—24no—
175C23×C127—24no—
176C23×C127—24no—
177C23×C127—24no—
178C23×C127—28no—
179C23×C127—28no—
180C23×C127—28no—
181C23×C127—28no—
182C23×C127—22no—
183C23×C127—22no—
184C23×C127—24no—
185C23×C127—24no—
186C23×C127—22no—
187C23×C127—22no—
188C23×C127—22no—
189C23×C127—22no—
190C23×C127—28no—
191C23×C127—28no—
192C23×C127—42no—
193C23×C127—42no—
194C23×C127—42no—
195C23×C127—42no—
196C23×C127—44no—
197C23×C127—44no—
198C23×C127C2×C22⋊C414yes—
199C23×C127C2×C4⋊C414yes—
200C23×C127C2×C4⋊C414yes—
201C23×C127#11714yes—
202C23×C127#12114yes—
203C23×C127#12114yes—
204C23×C127C22⋊Q814yes—
205C23×C127C22⋊Q814yes—
206C23×C127C23×C411yescharacteristic
207C23×C127C22×D411yescharacteristic
208C23×C127C22×D411yescharacteristic
209C23×C127C22×D411yescharacteristic
210C23×C127C22×Q811yescharacteristic
211C23×C127C2×#4111yescharacteristic
212C23×C127C2×#4111yescharacteristic
213C23×C127C2×#4114yes—
214C23×C127H(5,𝔽2)14yes—
215D4×C127—232no—
216C2×C4×C127—22no—
217C2×C4×C127—22no—
218C2×C4×C127—24no—
219C2×C4×C127—24no—
220C2×C4×C127—22no—
221C2×C4×C127—22no—
222C2×C4×C127—22no—
223C2×C4×C127—22no—
224C2×C4×C127—24no—
225C2×C4×C127—24no—
226C2×C4×C127—24no—
227C2×C4×C127—24no—
228C2×C4×C127—22no—
229C2×C4×C127—22no—
230C2×C4×C127—24no—
231C2×C4×C127—24no—
232C2×C4×C127—28no—
233C2×C4×C127—28no—
234C2×C4×C127—28no—
235C2×C4×C127—416no—
236C2×C4×C127—416no—
237C2×C4×C127—432no—
238C2×C4×C127—44no—
239C2×C4×C127—42no—
240C2×C4×C127—42no—
241C2×C4×C127—42no—
242C2×C4×C127—42no—
243C2×C4×C127—44no—
244C2×C4×C127—44no—
245C2×C4×C127—44no—
246C2×C4×C127—44no—
247C2×C4×C127—44no—
248C2×C4×C127—44no—
249C2×C4×C127—44no—
250C2×C4×C127—44no—
251C2×C4×C127—44no—
252C2×C4×C127—44no—
253C2×C4×C127C2×C22⋊C414yes—
254C2×C4×C127C2×C22⋊C414yes—
255C2×C4×C127C2×C4⋊C414yes—
256C22×C127—24no—
257C22×C127—28no—
258C22×C127—28no—
259C22×C127—28no—
260C22×C127—28no—
261C22×C127—28no—
262C22×C127—28no—
263C22×C127—24no—
264C22×C127—28no—
265C22×C127—24no—
266C22×C127—42no—
267C22×C127—44no—
268C22×C127—44no—
269C22×C127—44no—
270C22×C127—44no—
271C22×C127—44no—
272C22×C127—42no—
273C22×C127#38018yes—
274C22×C127C22×C22⋊C411yescharacteristic
275C22×C127C22×C4⋊C411yescharacteristic
276C22×C127C2×#11711yescharacteristic
277C22×C127C4×#4112yes—
278C22×C127#51812yes—
279C22×C127C2×#12111yescharacteristic
280C22×C127C2×#12111yescharacteristic
281C22×C127C2×C22⋊Q811yescharacteristic
282C22×C127C2×C22⋊Q811yescharacteristic
283C22×C127#52512yes—
284C22×C127#53212yes—
285C22×C127#53412yes—
286C22×C127#53412yes—
287C22×C127#54614yes—
288C22×C127#55114yes—
289C22×C127#55314yes—
290C22×C127#55414yes—
291C4×C127—24no—
292C4×C127—24no—
293C4×C127—24no—
294C4×C127—42no—
295C4×C127—48no—
296C4×C127—42no—
297C4×C127—84no—
298#13960C12711yesmaximal, characteristic, direct product factor, Sylow
299C2×C127—28no—
300C2×C127—44no—
301C2×C127C2×#38011yescharacteristic
302C2×C127#229711yescharacteristic
303C2×C127#230811yescharacteristic
304C2×C127#234912yes—
305C2×C127#235312yes—
306C2×C127#253412yes—
307C2×C127#254312yes—
308C2×C127#256412yes—
309C2×C127#257912yes—
310C22×C4×D4C2×C12711yescharacteristic
311C2×#386C2×C12712yes—
312C2×#380C2×C12711yescharacteristic, complemented
313C22×#95C2×C12711yescharacteristic, complemented
314#1441C2×C12712yescomplemented
315#1439C2×C12712yescomplemented
316#1434C2×C12712yescomplemented
317C22⋊#95C2×C12712yescomplemented
318C22⋊#95C2×C12712yescomplemented
319C127#1396011yescharacteristic, direct product factor, Sylow
320C23×D4C22×C12711yescharacteristic
321C24×C4C22×C12712yes—
322C24×C4C22×C12711yescharacteristic
323C24×C4C22×C12711yescharacteristic
324C2×C4×D4—24no—
325C2×C4×D4—24no—
326C2×C4×D4C4×C12718yescomplemented
327C22×C4⋊C4C22×C12711yescharacteristic
328C22×C4⋊C4C22×C12712yes—
329C22×C22⋊C4C22×C12712yes—
330C22×C22⋊C4C22×C12714yes—
331C22×C22⋊C4C22×C12711yescharacteristic
332C22×C22⋊C4C22×C12711yescharacteristic
333C22×C42C22×C12711yescharacteristic
334#386—28no—
335#380—24no—
336C2×#95—24no—
337C2×#95C22×C12714yes—
338C2×#95C22×C12712yes—
339C2×#95C22×C12712yes—
340C2×#95C22×C12714yes—
341C2×#95C22×C12712yes—
342C2×#95C22×C12714yes—
343C25C23×C12711yescharacteristic
344C25C23×C12711yescharacteristic
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4C2×C4×C12714yes—
350C22×D4D4×C12714yes—
351C22×D4Q8×C12714yes—
352C23×C4—24no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—28no—
356C23×C4—24no—
357C23×C4—24no—
358C23×C4—44no—
359C23×C4—44no—
360C23×C4—44no—
361C23×C4C2×C4×C12714yes—
362C23×C4C2×C4×C12714yescomplemented
363C23×C4D4×C12714yes—
364C23×C4D4×C12714yes—
365C23×C4C23×C12714yes—
366C23×C4C23×C12711yescharacteristic
367C23×C4C23×C12711yescharacteristic
368C23×C4C23×C12714yes—
369C23×C4C23×C12711yescharacteristic
370C23×C4C23×C12711yescharacteristic
371C23×C4C23×C12711yescharacteristic
372C4×D4—232no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4C2×C4×C12714yescomplemented
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4C2×C4×C12714yes—
389C2×C22⋊C4C2×C4×C12714yescomplemented
390C2×C42—22no—
391C2×C42—22no—
392C2×C42C2×C4×C12714yescomplemented
393#95—24no—
394#95—24no—
395#95—24no—
396#95—28no—
397#95—28no—
398#95—44no—
399C24—24no—
400C24—24no—
401C24—21no—
402C24—21no—
403C24—24no—
404C24—21no—
405C24—21no—
406C24—24no—
407C24C22×C4×C12712yes—
408C24C22×C4×C12712yes—
409C24C2×D4×C12712yes—
410C24C2×D4×C12712yes—
411C24C2×D4×C12712yes—
412C24C2×D4×C12712yes—
413C24C2×Q8×C12712yes—
414C24C2×Q8×C12712yes—
415C24#41×C12712yes—
416C24#41×C12712yes—
417C24C24×C12711yescharacteristic
418C2×D4—28no—
419C2×D4—28no—
420C2×D4—28no—
421C2×D4—28no—
422C2×D4—28no—
423C2×D4—28no—
424C2×D4C4⋊C4×C127116yescomplemented
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—216no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—28no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—48no—
453C22×C4—48no—
454C22×C4—48no—
455C22×C4—48no—
456C22×C4—416no—
457C22×C4—416no—
458C22×C4—48no—
459C22×C4—48no—
460C22×C4—48no—
461C22×C4—48no—
462C22×C4C22⋊C4×C127116yescomplemented
463C22×C4C22×C4×C12712yes—
464C22×C4C22×C4×C12712yes—
465C22×C4C22×C4×C12712yes—
466C22×C4C22×C4×C12712yes—
467C22×C4C22×C4×C12712yes—
468C22×C4C2×D4×C12712yes—
469C22×C4C2×D4×C12712yes—
470C22×C4C2×D4×C12712yes—
471C22×C4C2×D4×C12712yes—
472C22×C4C2×D4×C12712yes—
473C22×C4C2×Q8×C12712yes—
474C22×C4#41×C12718yes—
475C4⋊C4—28no—
476C4⋊C4—48no—
477C22⋊C4—28no—
478C22⋊C4—28no—
479C22⋊C4—416no—
480C22⋊C4—48no—
481C42—28no—
482C23—24no—
483C23—24no—
484C23—24no—
485C23—24no—
486C23—24no—
487C23—24no—
488C23—28no—
489C23—28no—
490C23—28no—
491C23—28no—
492C23—22no—
493C23—22no—
494C23—24no—
495C23—24no—
496C23—22no—
497C23—22no—
498C23—22no—
499C23—22no—
500C23—28no—
501C23—28no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—44no—
507C23—44no—
508C23C2×C22⋊C4×C12714yes—
509C23C2×C4⋊C4×C12714yes—
510C23C2×C4⋊C4×C12714yes—
511C23#117×C12714yes—
512C23#121×C12714yes—
513C23#121×C12714yes—
514C23C22⋊Q8×C12714yes—
515C23C22⋊Q8×C12714yes—
516C23C23×C4×C12711yescharacteristic
517C23C22×D4×C12711yescharacteristic
518C23C22×D4×C12711yescharacteristic
519C23C22×D4×C12711yescharacteristic
520C23C22×Q8×C12711yescharacteristic
521C23C2×#41×C12711yescharacteristic
522C23C2×#41×C12711yescharacteristic
523C23C2×#41×C12714yes—
524C23H(5,𝔽2)×C12714yes—
525D4—232no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—28no—
543C2×C4—28no—
544C2×C4—28no—
545C2×C4—416no—
546C2×C4—416no—
547C2×C4—432no—
548C2×C4—44no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—44no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—44no—
555C2×C4—44no—
556C2×C4—44no—
557C2×C4—44no—
558C2×C4—44no—
559C2×C4—44no—
560C2×C4—44no—
561C2×C4—44no—
562C2×C4—44no—
563C2×C4C2×C22⋊C4×C12714yes—
564C2×C4C2×C22⋊C4×C12714yes—
565C2×C4C2×C4⋊C4×C12714yes—
566C22—28no—
567C22—28no—
568C22—28no—
569C22—28no—
570C22—28no—
571C22—24no—
572C22—24no—
573C22—28no—
574C22—28no—
575C22—24no—
576C22—44no—
577C22—44no—
578C22—44no—
579C22—44no—
580C22—42no—
581C22—42no—
582C22—44no—
583C22#380×C12718yes—
584C22C22×C22⋊C4×C12711yescharacteristic
585C22C22×C4⋊C4×C12711yescharacteristic
586C22C2×#117×C12711yescharacteristic
587C22C4×#41×C12712yes—
588C22#518×C12712yes—
589C22C2×#121×C12711yescharacteristic
590C22C2×#121×C12711yescharacteristic
591C22C2×C22⋊Q8×C12711yescharacteristic
592C22C2×C22⋊Q8×C12711yescharacteristic
593C22#525×C12712yes—
594C22#532×C12712yes—
595C22#534×C12712yes—
596C22#534×C12712yes—
597C22#546×C12714yes—
598C22#551×C12714yes—
599C22#553×C12714yes—
600C22#554×C12714yes—
601C4—24no—
602C4—24no—
603C4—24no—
604C4—48no—
605C4—42no—
606C4—42no—
607C4—84no—
608C2—28no—
609C2—44no—
610C2C2×#380×C12711yescharacteristic
611C2C127×#229711yescharacteristic
612C2C127×#230811yescharacteristic
613C2C127×#234912yes—
614C2C127×#235312yes—
615C2C127×#253412yes—
616C2C127×#254312yes—
617C2C127×#256412yes—
618C2C127×#257912yes—
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
3. C2×#380×C127C2semidirect
4. C22×#95×C127C2semidirect
5. C127×#1441C2semidirect
6. C127×#1439C2semidirect
7. C127×#1434C2semidirect
8. C127×C22⋊#95C2semidirect
9. C127×C22⋊#95C2semidirect
16. C2×C4×D4×C127C4semidirect
52. C23×C4×C127C2×C4semidirect
67. C2×C4⋊C4×C127C2×C4semidirect
79. C2×C22⋊C4×C127C2×C4semidirect
82. C2×C42×C127C2×C4semidirect
114. C2×D4×C127C4⋊C4semidirect
152. C22×C4×C127C22⋊C4semidirect
298. #13960C127direct (N × H)
312. C2×#380C2×C127semidirect
313. C22×#95C2×C127semidirect
314. #1441C2×C127semidirect
315. #1439C2×C127semidirect
316. #1434C2×C127semidirect
317. C22⋊#95C2×C127semidirect
318. C22⋊#95C2×C127semidirect
319. C127#13960direct (N × H)
326. C2×C4×D4C4×C127semidirect
362. C23×C4C2×C4×C127semidirect
377. C2×C4⋊C4C2×C4×C127semidirect
389. C2×C22⋊C4C2×C4×C127semidirect
392. C2×C42C2×C4×C127semidirect
424. C2×D4C4⋊C4×C127semidirect
462. C22×C4C22⋊C4×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
C2×#386×C1272
C2×#380×C1272
C22×#95×C1272
C127×#14412
C127×#14392
C127×#14342
C127×C22⋊#952
#13960127