Finite Group Databasebeta

← C127×#13784 #44577457

Subgroups — C127×#13784 #44577457

Order 32512.

2686 conjugacy classes of subgroups.

The subgroup lattice has 590 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×C4×C22⋊C4×C127C211yesmaximal, characteristic, complemented
4C22×#95×C127C211yesmaximal, characteristic, complemented
5C127×#1437C212yesmaximal, complemented
6C127×#1436C212yesmaximal, complemented
7C127×#1434C212yesmaximal, complemented
8C127×C22⋊#95C212yesmaximal, complemented
9C127×C22⋊#95C212yesmaximal, complemented
10C23×D4×C127C2211yescharacteristic
11C24×C4×C127C2211yescharacteristic
12C24×C4×C127C2212yes—
13C24×C4×C127C2211yescharacteristic
14C2×C4×D4×C127—24no—
15C2×C4×D4×C127—24no—
16C2×C4×D4×C127C418yescomplemented
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C22⋊C4×C127C2211yescharacteristic
19C22×C22⋊C4×C127C2211yescharacteristic
20C22×C22⋊C4×C127C2212yes—
21C22×C22⋊C4×C127C2214yes—
22C22×C42×C127C2211yescharacteristic
23C22×C42×C127C2212yes—
24#386×C127C4116yescomplemented
25C4×C22⋊C4×C127—24no—
26C2×#95×C127—24no—
27C2×#95×C127C2212yes—
28C2×#95×C127C2212yes—
29C2×#95×C127C2212yes—
30C2×#95×C127C2214yes—
31C2×#95×C127C2214yes—
32C2×#95×C127C2214yes—
33C25×C127C2311yescharacteristic
34C25×C127C2311yescharacteristic
35C22×D4×C127—22no—
36C22×D4×C127—22no—
37C22×D4×C127—24no—
38C22×D4×C127C2×C414yes—
39C22×D4×C127C2×C418yes—
40C23×C4×C127—24no—
41C23×C4×C127—24no—
42C23×C4×C127—22no—
43C23×C4×C127—22no—
44C23×C4×C127—44no—
45C23×C4×C127—44no—
46C23×C4×C127—44no—
47C23×C4×C127—44no—
48C23×C4×C127C2×C414yes—
49C23×C4×C127C2×C414yescomplemented
50C23×C4×C127C2×C418yescomplemented
51C23×C4×C127D414yes—
52C23×C4×C127D414yes—
53C23×C4×C127C2314yes—
54C23×C4×C127C2311yescharacteristic
55C23×C4×C127C2311yescharacteristic
56C23×C4×C127C2314yes—
57C23×C4×C127C2311yescharacteristic
58C23×C4×C127C2311yescharacteristic
59C23×C4×C127C2311yescharacteristic
60C4×D4×C127—232no—
61C2×C4⋊C4×C127—22no—
62C2×C4⋊C4×C127—22no—
63C2×C4⋊C4×C127C2×C414yescomplemented
64C2×C22⋊C4×C127—22no—
65C2×C22⋊C4×C127—22no—
66C2×C22⋊C4×C127—24no—
67C2×C22⋊C4×C127—24no—
68C2×C22⋊C4×C127—22no—
69C2×C22⋊C4×C127—22no—
70C2×C22⋊C4×C127—44no—
71C2×C22⋊C4×C127—44no—
72C2×C22⋊C4×C127C2×C414yes—
73C2×C22⋊C4×C127C2×C414yescomplemented
74C2×C22⋊C4×C127C2×C418yescomplemented
75C2×C22⋊C4×C127C2×C4116yescomplemented
76C2×C42×C127—22no—
77C2×C42×C127—22no—
78C2×C42×C127—24no—
79C2×C42×C127—44no—
80C2×C42×C127C2×C414yescomplemented
81#95×C127—24no—
82#95×C127—24no—
83#95×C127—24no—
84#95×C127—44no—
85#95×C127—44no—
86#95×C127C2×C4116yescomplemented
87C24×C127—24no—
88C24×C127—22no—
89C24×C127—22no—
90C24×C127—21no—
91C24×C127—21no—
92C24×C127—22no—
93C24×C127—22no—
94C24×C127—24no—
95C24×C127—22no—
96C24×C127C22×C414yes—
97C24×C127C22×C412yes—
98C24×C127C22×C412yes—
99C24×C127C22×C414yes—
100C24×C127C2×D412yes—
101C24×C127C2×D412yes—
102C24×C127#4114yes—
103C24×C127C2411yescharacteristic
104C2×D4×C127—28no—
105C2×D4×C127—28no—
106C2×D4×C127—216no—
107C2×D4×C127—216no—
108C2×D4×C127C42116yescomplemented
109C22×C4×C127—21no—
110C22×C4×C127—21no—
111C22×C4×C127—22no—
112C22×C4×C127—24no—
113C22×C4×C127—24no—
114C22×C4×C127—216no—
115C22×C4×C127—24no—
116C22×C4×C127—24no—
117C22×C4×C127—21no—
118C22×C4×C127—21no—
119C22×C4×C127—21no—
120C22×C4×C127—21no—
121C22×C4×C127—24no—
122C22×C4×C127—24no—
123C22×C4×C127—22no—
124C22×C4×C127—24no—
125C22×C4×C127—24no—
126C22×C4×C127—24no—
127C22×C4×C127—24no—
128C22×C4×C127—24no—
129C22×C4×C127—24no—
130C22×C4×C127—24no—
131C22×C4×C127—24no—
132C22×C4×C127—22no—
133C22×C4×C127—24no—
134C22×C4×C127—28no—
135C22×C4×C127—48no—
136C22×C4×C127—48no—
137C22×C4×C127—416no—
138C22×C4×C127—48no—
139C22×C4×C127—48no—
140C22×C4×C127—48no—
141C22×C4×C127—48no—
142C22×C4×C127—48no—
143C22×C4×C127—48no—
144C22×C4×C127—416no—
145C22×C4×C127C22⋊C4116yescomplemented
146C22×C4×C127C22×C418yes—
147C22×C4×C127C22×C418yes—
148C22×C4×C127C22×C412yes—
149C22×C4×C127C22×C412yes—
150C22×C4×C127C22×C414yes—
151C22×C4×C127C22×C412yes—
152C22×C4×C127C22×C412yes—
153C22×C4×C127C22×C412yes—
154C22×C4×C127C2×D412yes—
155C22×C4×C127C2×D412yes—
156C22×C4×C127C2×D412yes—
157C22×C4×C127C2×D412yes—
158C4⋊C4×C127—28no—
159C22⋊C4×C127—28no—
160C22⋊C4×C127—216no—
161C22⋊C4×C127—28no—
162C22⋊C4×C127—416no—
163C42×C127—28no—
164C42×C127—48no—
165C23×C127—24no—
166C23×C127—28no—
167C23×C127—24no—
168C23×C127—28no—
169C23×C127—24no—
170C23×C127—24no—
171C23×C127—22no—
172C23×C127—22no—
173C23×C127—24no—
174C23×C127—28no—
175C23×C127—28no—
176C23×C127—22no—
177C23×C127—22no—
178C23×C127—24no—
179C23×C127—24no—
180C23×C127—28no—
181C23×C127—24no—
182C23×C127—24no—
183C23×C127—28no—
184C23×C127—42no—
185C23×C127—42no—
186C23×C127—41no—
187C23×C127—41no—
188C23×C127—42no—
189C23×C127—44no—
190C23×C127—44no—
191C23×C127C2×C4214yes—
192C23×C127C2×C4214yes—
193C23×C127C2×C22⋊C414yes—
194C23×C127#11714yes—
195C23×C127C4×D418yes—
196C23×C127C4×D418yes—
197C23×C127C23×C411yescharacteristic
198C23×C127C23×C412yes—
199C23×C127C22×D411yescharacteristic
200C23×C127C22×D411yescharacteristic
201C23×C127C2×#4112yes—
202C23×C127H(5,𝔽2)14yes—
203C23×C127H(5,𝔽2)12yes—
204C23×C1272−1+412yes—
205D4×C127—232no—
206C2×C4×C127—22no—
207C2×C4×C127—22no—
208C2×C4×C127—24no—
209C2×C4×C127—24no—
210C2×C4×C127—24no—
211C2×C4×C127—24no—
212C2×C4×C127—24no—
213C2×C4×C127—24no—
214C2×C4×C127—24no—
215C2×C4×C127—24no—
216C2×C4×C127—22no—
217C2×C4×C127—22no—
218C2×C4×C127—28no—
219C2×C4×C127—28no—
220C2×C4×C127—28no—
221C2×C4×C127—28no—
222C2×C4×C127—24no—
223C2×C4×C127—28no—
224C2×C4×C127—24no—
225C2×C4×C127—28no—
226C2×C4×C127—416no—
227C2×C4×C127—416no—
228C2×C4×C127—432no—
229C2×C4×C127—44no—
230C2×C4×C127—42no—
231C2×C4×C127—42no—
232C2×C4×C127—44no—
233C2×C4×C127—41no—
234C2×C4×C127—44no—
235C2×C4×C127—41no—
236C2×C4×C127—42no—
237C2×C4×C127—44no—
238C2×C4×C127—44no—
239C2×C4×C127—44no—
240C2×C4×C127—44no—
241C2×C4×C127—44no—
242C2×C4×C127C2×C4214yes—
243C2×C4×C127C2×C22⋊C414yes—
244C2×C4×C127C2×C22⋊C414yes—
245C22×C127—24no—
246C22×C127—24no—
247C22×C127—28no—
248C22×C127—28no—
249C22×C127—28no—
250C22×C127—216no—
251C22×C127—28no—
252C22×C127—24no—
253C22×C127—28no—
254C22×C127—42no—
255C22×C127—42no—
256C22×C127—44no—
257C22×C127—44no—
258C22×C127—44no—
259C22×C127—48no—
260C22×C127C4×C22⋊C418yes—
261C22×C127C22×C4211yescharacteristic
262C22×C127C22×C22⋊C411yescharacteristic
263C22×C127C2×#11711yescharacteristic
264C22×C127C2×C4×D412yes—
265C22×C127C2×C4×D412yes—
266C22×C127#51812yes—
267C22×C127#51814yes—
268C22×C127#52012yes—
269C22×C127#52014yes—
270C22×C127#53412yes—
271C22×C127#53412yes—
272C22×C127#53511yescharacteristic
273C22×C127#53611yescharacteristic
274C22×C127#53712yes—
275C22×C127#53814yes—
276C22×C127#53914yes—
277C4×C127—24no—
278C4×C127—24no—
279C4×C127—24no—
280C4×C127—42no—
281C4×C127—42no—
282C4×C127—48no—
283C4×C127—48no—
284#13784C12711yesmaximal, characteristic, direct product factor, Sylow
285C2×C127—28no—
286C2×C127—44no—
287C2×C127C2×C4×C22⋊C411yescharacteristic
288C2×C127#227512yes—
289C2×C127#230811yescharacteristic
290C2×C127#231111yescharacteristic
291C2×C127#231812yes—
292C2×C127#232112yes—
293C2×C127#232212yes—
294C2×C127#232514yes—
295C22×C4×D4C2×C12711yescharacteristic
296C2×#386C2×C12712yes—
297C2×C4×C22⋊C4C2×C12711yescharacteristic, complemented
298C22×#95C2×C12711yescharacteristic, complemented
299#1437C2×C12712yescomplemented
300#1436C2×C12712yescomplemented
301#1434C2×C12712yescomplemented
302C22⋊#95C2×C12712yescomplemented
303C22⋊#95C2×C12712yescomplemented
304C127#1378411yescharacteristic, direct product factor, Sylow
305C23×D4C22×C12711yescharacteristic
306C24×C4C22×C12711yescharacteristic
307C24×C4C22×C12712yes—
308C24×C4C22×C12711yescharacteristic
309C2×C4×D4—24no—
310C2×C4×D4—24no—
311C2×C4×D4C4×C12718yescomplemented
312C22×C4⋊C4C22×C12711yescharacteristic
313C22×C22⋊C4C22×C12711yescharacteristic
314C22×C22⋊C4C22×C12711yescharacteristic
315C22×C22⋊C4C22×C12712yes—
316C22×C22⋊C4C22×C12714yes—
317C22×C42C22×C12711yescharacteristic
318C22×C42C22×C12712yes—
319#386C4×C127116yescomplemented
320C4×C22⋊C4—24no—
321C2×#95—24no—
322C2×#95C22×C12712yes—
323C2×#95C22×C12712yes—
324C2×#95C22×C12712yes—
325C2×#95C22×C12714yes—
326C2×#95C22×C12714yes—
327C2×#95C22×C12714yes—
328C25C23×C12711yescharacteristic
329C25C23×C12711yescharacteristic
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—24no—
333C22×D4C2×C4×C12714yes—
334C22×D4C2×C4×C12718yes—
335C23×C4—24no—
336C23×C4—24no—
337C23×C4—22no—
338C23×C4—22no—
339C23×C4—44no—
340C23×C4—44no—
341C23×C4—44no—
342C23×C4—44no—
343C23×C4C2×C4×C12714yes—
344C23×C4C2×C4×C12714yescomplemented
345C23×C4C2×C4×C12718yescomplemented
346C23×C4D4×C12714yes—
347C23×C4D4×C12714yes—
348C23×C4C23×C12714yes—
349C23×C4C23×C12711yescharacteristic
350C23×C4C23×C12711yescharacteristic
351C23×C4C23×C12714yes—
352C23×C4C23×C12711yescharacteristic
353C23×C4C23×C12711yescharacteristic
354C23×C4C23×C12711yescharacteristic
355C4×D4—232no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4C2×C4×C12714yescomplemented
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4C2×C4×C12714yes—
368C2×C22⋊C4C2×C4×C12714yescomplemented
369C2×C22⋊C4C2×C4×C12718yescomplemented
370C2×C22⋊C4C2×C4×C127116yescomplemented
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—24no—
374C2×C42—44no—
375C2×C42C2×C4×C12714yescomplemented
376#95—24no—
377#95—24no—
378#95—24no—
379#95—44no—
380#95—44no—
381#95C2×C4×C127116yescomplemented
382C24—24no—
383C24—22no—
384C24—22no—
385C24—21no—
386C24—21no—
387C24—22no—
388C24—22no—
389C24—24no—
390C24—22no—
391C24C22×C4×C12714yes—
392C24C22×C4×C12712yes—
393C24C22×C4×C12712yes—
394C24C22×C4×C12714yes—
395C24C2×D4×C12712yes—
396C24C2×D4×C12712yes—
397C24#41×C12714yes—
398C24C24×C12711yescharacteristic
399C2×D4—28no—
400C2×D4—28no—
401C2×D4—216no—
402C2×D4—216no—
403C2×D4C42×C127116yescomplemented
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—216no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—24no—
429C22×C4—28no—
430C22×C4—48no—
431C22×C4—48no—
432C22×C4—416no—
433C22×C4—48no—
434C22×C4—48no—
435C22×C4—48no—
436C22×C4—48no—
437C22×C4—48no—
438C22×C4—48no—
439C22×C4—416no—
440C22×C4C22⋊C4×C127116yescomplemented
441C22×C4C22×C4×C12718yes—
442C22×C4C22×C4×C12718yes—
443C22×C4C22×C4×C12712yes—
444C22×C4C22×C4×C12712yes—
445C22×C4C22×C4×C12714yes—
446C22×C4C22×C4×C12712yes—
447C22×C4C22×C4×C12712yes—
448C22×C4C22×C4×C12712yes—
449C22×C4C2×D4×C12712yes—
450C22×C4C2×D4×C12712yes—
451C22×C4C2×D4×C12712yes—
452C22×C4C2×D4×C12712yes—
453C4⋊C4—28no—
454C22⋊C4—28no—
455C22⋊C4—216no—
456C22⋊C4—28no—
457C22⋊C4—416no—
458C42—28no—
459C42—48no—
460C23—24no—
461C23—28no—
462C23—24no—
463C23—28no—
464C23—24no—
465C23—24no—
466C23—22no—
467C23—22no—
468C23—24no—
469C23—28no—
470C23—28no—
471C23—22no—
472C23—22no—
473C23—24no—
474C23—24no—
475C23—28no—
476C23—24no—
477C23—24no—
478C23—28no—
479C23—42no—
480C23—42no—
481C23—41no—
482C23—41no—
483C23—42no—
484C23—44no—
485C23—44no—
486C23C2×C42×C12714yes—
487C23C2×C42×C12714yes—
488C23C2×C22⋊C4×C12714yes—
489C23#117×C12714yes—
490C23C4×D4×C12718yes—
491C23C4×D4×C12718yes—
492C23C23×C4×C12711yescharacteristic
493C23C23×C4×C12712yes—
494C23C22×D4×C12711yescharacteristic
495C23C22×D4×C12711yescharacteristic
496C23C2×#41×C12712yes—
497C23H(5,𝔽2)×C12714yes—
498C23H(5,𝔽2)×C12712yes—
499C232−1+4×C12712yes—
500D4—232no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—28no—
514C2×C4—28no—
515C2×C4—28no—
516C2×C4—28no—
517C2×C4—28no—
518C2×C4—24no—
519C2×C4—28no—
520C2×C4—24no—
521C2×C4—416no—
522C2×C4—416no—
523C2×C4—432no—
524C2×C4—44no—
525C2×C4—44no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—44no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—44no—
532C2×C4—42no—
533C2×C4—44no—
534C2×C4—44no—
535C2×C4—44no—
536C2×C4—44no—
537C2×C4C2×C42×C12714yes—
538C2×C4C2×C22⋊C4×C12714yes—
539C2×C4C2×C22⋊C4×C12714yes—
540C22—28no—
541C22—28no—
542C22—28no—
543C22—216no—
544C22—28no—
545C22—24no—
546C22—24no—
547C22—24no—
548C22—28no—
549C22—44no—
550C22—44no—
551C22—44no—
552C22—48no—
553C22—42no—
554C22—42no—
555C22C4×C22⋊C4×C12718yes—
556C22C22×C42×C12711yescharacteristic
557C22C22×C22⋊C4×C12711yescharacteristic
558C22C2×#117×C12711yescharacteristic
559C22C2×C4×D4×C12712yes—
560C22C2×C4×D4×C12712yes—
561C22#518×C12712yes—
562C22#518×C12714yes—
563C22#520×C12712yes—
564C22#520×C12714yes—
565C22#534×C12712yes—
566C22#534×C12712yes—
567C22#535×C12711yescharacteristic
568C22#536×C12711yescharacteristic
569C22#537×C12712yes—
570C22#538×C12714yes—
571C22#539×C12714yes—
572C4—24no—
573C4—24no—
574C4—24no—
575C4—48no—
576C4—48no—
577C4—42no—
578C4—42no—
579C2—28no—
580C2—44no—
581C2C2×C4×C22⋊C4×C12711yescharacteristic
582C2C127×#227512yes—
583C2C127×#230811yescharacteristic
584C2C127×#231111yescharacteristic
585C2C127×#231812yes—
586C2C127×#232112yes—
587C2C127×#232212yes—
588C2C127×#232514yes—
subgroupG/H
center, socleC24×C127C24
commutatorC22C22×C42×C127
Frattini, cosocleC24C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C4×C22⋊C4×C127C2semidirect
4. C22×#95×C127C2semidirect
5. C127×#1437C2semidirect
6. C127×#1436C2semidirect
7. C127×#1434C2semidirect
8. C127×C22⋊#95C2semidirect
9. C127×C22⋊#95C2semidirect
16. C2×C4×D4×C127C4semidirect
24. #386×C127C4semidirect
49. C23×C4×C127C2×C4semidirect
50. C23×C4×C127C2×C4semidirect
63. C2×C4⋊C4×C127C2×C4semidirect
73. C2×C22⋊C4×C127C2×C4semidirect
74. C2×C22⋊C4×C127C2×C4semidirect
75. C2×C22⋊C4×C127C2×C4semidirect
80. C2×C42×C127C2×C4semidirect
86. #95×C127C2×C4semidirect
108. C2×D4×C127C42semidirect
145. C22×C4×C127C22⋊C4semidirect
284. #13784C127direct (N × H)
297. C2×C4×C22⋊C4C2×C127semidirect
298. C22×#95C2×C127semidirect
299. #1437C2×C127semidirect
300. #1436C2×C127semidirect
301. #1434C2×C127semidirect
302. C22⋊#95C2×C127semidirect
303. C22⋊#95C2×C127semidirect
304. C127#13784direct (N × H)
311. C2×C4×D4C4×C127semidirect
319. #386C4×C127semidirect
344. C23×C4C2×C4×C127semidirect
345. C23×C4C2×C4×C127semidirect
358. C2×C4⋊C4C2×C4×C127semidirect
368. C2×C22⋊C4C2×C4×C127semidirect
369. C2×C22⋊C4C2×C4×C127semidirect
370. C2×C22⋊C4C2×C4×C127semidirect
375. C2×C42C2×C4×C127semidirect
381. #95C2×C4×C127semidirect
403. C2×D4C42×C127semidirect
440. 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×C4×C22⋊C4×C1272
C22×#95×C1272
C127×#14372
C127×#14362
C127×#14342
C127×C22⋊#952
#13784127