Finite Group Databasebeta

← C127×#14514 #44578187

Subgroups — C127×#14514 #44578187

Order 32512.

1550 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#388×C127C212yesmaximal
2C2×#385×C127C211yesmaximal, characteristic
3C127×#1442C212yesmaximal, complemented
4C127×#1441C212yesmaximal, complemented
5C127×#1439C211yesmaximal, characteristic
6C127×#1439C211yesmaximal, characteristic
7C127×#1436C212yesmaximal, complemented
8C127×C4⋊#95C212yesmaximal, complemented
9C127×C22⋊#95C212yesmaximal
10C24×C4×C127C2211yescharacteristic
11C22×C4⋊C4×C127C2212yes—
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2212yes—
15C22×C22⋊C4×C127C2212yes—
16C22×C22⋊C4×C127C2212yes—
17C22×C22⋊C4×C127C2211yescharacteristic
18C22×C22⋊C4×C127C2211yescharacteristic
19C22×C42×C127C2212yes—
20#388×C127—28no—
21#385×C127C418yescomplemented
22C2×#95×C127C2212yes—
23C2×#95×C127C2212yes—
24C2×#95×C127C2212yes—
25C2×#95×C127C2212yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2212yes—
28C2×#95×C127C2212yes—
29C2×#95×C127C2211yescharacteristic
30C2×#95×C127C2212yes—
31C2×#95×C127C2211yescharacteristic
32C2×#95×C127C2212yes—
33C25×C127C2311yescharacteristic
34C23×C4×C127—41no—
35C23×C4×C127—41no—
36C23×C4×C127—42no—
37C23×C4×C127—42no—
38C23×C4×C127C2×C414yes—
39C23×C4×C127C2312yes—
40C23×C4×C127C2312yes—
41C23×C4×C127C2311yescharacteristic
42C23×C4×C127C2311yescharacteristic
43C23×C4×C127C2312yes—
44C23×C4×C127C2312yes—
45C23×C4×C127C2312yes—
46C23×C4×C127C2312yes—
47C2×C4⋊C4×C127—24no—
48C2×C4⋊C4×C127—24no—
49C2×C4⋊C4×C127—24no—
50C2×C4⋊C4×C127—42no—
51C2×C4⋊C4×C127—42no—
52C2×C4⋊C4×C127—42no—
53C2×C4⋊C4×C127—41no—
54C2×C4⋊C4×C127—41no—
55C2×C4⋊C4×C127—42no—
56C2×C4⋊C4×C127C2×C418yes—
57C2×C22⋊C4×C127—24no—
58C2×C22⋊C4×C127—24no—
59C2×C22⋊C4×C127—24no—
60C2×C22⋊C4×C127—24no—
61C2×C22⋊C4×C127—41no—
62C2×C22⋊C4×C127—41no—
63C2×C22⋊C4×C127—42no—
64C2×C22⋊C4×C127—42no—
65C2×C22⋊C4×C127C2×C414yes—
66C2×C22⋊C4×C127C2×C414yes—
67C2×C22⋊C4×C127D414yes—
68C2×C22⋊C4×C127Q814yes—
69C2×C42×C127—24no—
70C2×C42×C127—24no—
71C2×C42×C127—42no—
72#95×C127—24no—
73#95×C127—24no—
74#95×C127—24no—
75#95×C127—41no—
76#95×C127—42no—
77#95×C127—42no—
78#95×C127—42no—
79#95×C127—41no—
80#95×C127—42no—
81#95×C127—42no—
82#95×C127C2×C418yes—
83C24×C127—22no—
84C24×C127—22no—
85C24×C127—21no—
86C24×C127—21no—
87C24×C127—22no—
88C24×C127—22no—
89C24×C127—21no—
90C24×C127—21no—
91C24×C127C22×C412yes—
92C24×C127C2×D412yes—
93C24×C127C2×Q812yes—
94C24×C127C2411yescharacteristic
95C22×C4×C127—22no—
96C22×C4×C127—22no—
97C22×C4×C127—22no—
98C22×C4×C127—22no—
99C22×C4×C127—22no—
100C22×C4×C127—22no—
101C22×C4×C127—22no—
102C22×C4×C127—22no—
103C22×C4×C127—22no—
104C22×C4×C127—22no—
105C22×C4×C127—22no—
106C22×C4×C127—22no—
107C22×C4×C127—22no—
108C22×C4×C127—21no—
109C22×C4×C127—21no—
110C22×C4×C127—22no—
111C22×C4×C127—22no—
112C22×C4×C127—22no—
113C22×C4×C127—22no—
114C22×C4×C127—22no—
115C22×C4×C127—22no—
116C22×C4×C127—22no—
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—22no—
125C22×C4×C127—22no—
126C22×C4×C127—22no—
127C22×C4×C127—22no—
128C22×C4×C127—22no—
129C22×C4×C127—22no—
130C22×C4×C127—22no—
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—48no—
140C22×C4×C127—44no—
141C22×C4×C127—48no—
142C22×C4×C127—44no—
143C22×C4×C127—44no—
144C22×C4×C127C22×C412yes—
145C22×C4×C127C22×C414yes—
146C22×C4×C127C22×C412yes—
147C22×C4×C127C22×C414yes—
148C22×C4×C127C2×D414yes—
149C22×C4×C127C2×Q814yes—
150C22×C4×C127#4114yes—
151C22×C4×C127#4114yes—
152C4⋊C4×C127—48no—
153C4⋊C4×C127—48no—
154C4⋊C4×C127—44no—
155C4⋊C4×C127—44no—
156C22⋊C4×C127—44no—
157C22⋊C4×C127—48no—
158C22⋊C4×C127—48no—
159C22⋊C4×C127C4⋊C4116yescomplemented
160C42×C127—48no—
161C23×C127—24no—
162C23×C127—22no—
163C23×C127—24no—
164C23×C127—22no—
165C23×C127—22no—
166C23×C127—22no—
167C23×C127—22no—
168C23×C127—22no—
169C23×C127—24no—
170C23×C127—24no—
171C23×C127—24no—
172C23×C127—24no—
173C23×C127—42no—
174C23×C127—42no—
175C23×C127—42no—
176C23×C127—42no—
177C23×C127—41no—
178C23×C127—42no—
179C23×C127—41no—
180C23×C127—42no—
181C23×C127—41no—
182C23×C127—41no—
183C23×C127C2×C4⋊C414yes—
184C23×C127C23×C411yescharacteristic
185C23×C127C22×D411yescharacteristic
186C23×C127C22×Q811yescharacteristic
187C23×C127C2×#4112yes—
188C23×C127C2×#4112yes—
189C23×C127H(5,𝔽2)11yescharacteristic
190C23×C127H(5,𝔽2)11yescharacteristic
191C23×C127H(5,𝔽2)12yes—
192C23×C127H(5,𝔽2)12yes—
193C23×C1272−1+411yescharacteristic
194C23×C1272−1+411yescharacteristic
195C2×C4×C127—24no—
196C2×C4×C127—24no—
197C2×C4×C127—24no—
198C2×C4×C127—24no—
199C2×C4×C127—24no—
200C2×C4×C127—24no—
201C2×C4×C127—24no—
202C2×C4×C127—22no—
203C2×C4×C127—22no—
204C2×C4×C127—24no—
205C2×C4×C127—24no—
206C2×C4×C127—24no—
207C2×C4×C127—24no—
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—416no—
215C2×C4×C127—42no—
216C2×C4×C127—42no—
217C2×C4×C127—42no—
218C2×C4×C127—42no—
219C2×C4×C127—42no—
220C2×C4×C127—42no—
221C2×C4×C127—41no—
222C2×C4×C127—42no—
223C2×C4×C127—41no—
224C2×C4×C127—42no—
225C2×C4×C127—41no—
226C2×C4×C127—42no—
227C2×C4×C127—42no—
228C2×C4×C127—42no—
229C2×C4×C127—42no—
230C2×C4×C127—42no—
231C2×C4×C127—41no—
232C2×C4×C127—42no—
233C2×C4×C127—42no—
234C2×C4×C127—42no—
235C2×C4×C127—42no—
236C2×C4×C127—42no—
237C2×C4×C127—42no—
238C2×C4×C127—42no—
239C2×C4×C127—42no—
240C2×C4×C127—42no—
241C2×C4×C127—42no—
242C2×C4×C127—42no—
243C2×C4×C127—42no—
244C2×C4×C127—42no—
245C2×C4×C127—42no—
246C2×C4×C127—42no—
247C2×C4×C127C2×C4⋊C418yes—
248C22×C127—24no—
249C22×C127—28no—
250C22×C127—44no—
251C22×C127—42no—
252C22×C127—42no—
253C22×C127—44no—
254C22×C127—42no—
255C22×C127—42no—
256C22×C127—42no—
257C22×C127—44no—
258C22×C127—42no—
259C22×C127C22×C4⋊C411yescharacteristic
260C22×C127C4×#4112yes—
261C22×C127#51811yescharacteristic
262C22×C127#51812yes—
263C22×C127#51911yescharacteristic
264C22×C127#53711yescharacteristic
265C22×C127#53711yescharacteristic
266C22×C127#53912yes—
267C22×C127#53912yes—
268C22×C127#54212yes—
269C22×C127#54212yes—
270C22×C127#54411yescharacteristic
271C22×C127#54411yescharacteristic
272C22×C127#54612yes—
273C22×C127#54612yes—
274C22×C127#55111yescharacteristic
275C22×C127#55312yes—
276C22×C127#55412yes—
277C22×C127#55412yes—
278C22×C127#55911yescharacteristic
279C22×C127#56012yes—
280C22×C127#56011yescharacteristic
281C22×C127H(3,𝔽4)11yescharacteristic
282C4×C127—28no—
283C4×C127—42no—
284C4×C127—42no—
285C4×C127—44no—
286C4×C127—44no—
287C4×C127—44no—
288C4×C127—82no—
289C4×C127—82no—
290#14514C12711yesmaximal, characteristic, direct product factor, Sylow
291C2×C127—44no—
292C2×C127#231611yescharacteristic
293C2×C127#233212yes—
294C2×C127#234912yes—
295C2×C127#237411yescharacteristic
296C2×C127#237511yescharacteristic
297C2×C127#269112yes—
298C2×C127#269311yescharacteristic
299C2×C127#271211yescharacteristic
300C2×C127#276311yescharacteristic
301C2×C127#279012yes—
302C2×C127#280711yescharacteristic
303C2×#388C2×C12712yes—
304C2×#385C2×C12711yescharacteristic
305#1442C2×C12712yescomplemented
306#1441C2×C12712yescomplemented
307#1439C2×C12711yescharacteristic
308#1439C2×C12711yescharacteristic
309#1436C2×C12712yescomplemented
310C4⋊#95C2×C12712yescomplemented
311C22⋊#95C2×C12712yes—
312C127#1451411yescharacteristic, direct product factor, Sylow
313C24×C4C22×C12711yescharacteristic
314C22×C4⋊C4C22×C12712yes—
315C22×C4⋊C4C22×C12711yescharacteristic
316C22×C4⋊C4C22×C12711yescharacteristic
317C22×C4⋊C4C22×C12712yes—
318C22×C22⋊C4C22×C12712yes—
319C22×C22⋊C4C22×C12712yes—
320C22×C22⋊C4C22×C12711yescharacteristic
321C22×C22⋊C4C22×C12711yescharacteristic
322C22×C42C22×C12712yes—
323#388—28no—
324#385C4×C12718yescomplemented
325C2×#95C22×C12712yes—
326C2×#95C22×C12712yes—
327C2×#95C22×C12712yes—
328C2×#95C22×C12712yes—
329C2×#95C22×C12712yes—
330C2×#95C22×C12712yes—
331C2×#95C22×C12712yes—
332C2×#95C22×C12711yescharacteristic
333C2×#95C22×C12712yes—
334C2×#95C22×C12711yescharacteristic
335C2×#95C22×C12712yes—
336C25C23×C12711yescharacteristic
337C23×C4—41no—
338C23×C4—41no—
339C23×C4—42no—
340C23×C4—42no—
341C23×C4C2×C4×C12714yes—
342C23×C4C23×C12712yes—
343C23×C4C23×C12712yes—
344C23×C4C23×C12711yescharacteristic
345C23×C4C23×C12711yescharacteristic
346C23×C4C23×C12712yes—
347C23×C4C23×C12712yes—
348C23×C4C23×C12712yes—
349C23×C4C23×C12712yes—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—41no—
357C2×C4⋊C4—41no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4C2×C4×C12718yes—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4—41no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4C2×C4×C12714yes—
369C2×C22⋊C4C2×C4×C12714yes—
370C2×C22⋊C4D4×C12714yes—
371C2×C22⋊C4Q8×C12714yes—
372C2×C42—24no—
373C2×C42—24no—
374C2×C42—42no—
375#95—24no—
376#95—24no—
377#95—24no—
378#95—41no—
379#95—42no—
380#95—42no—
381#95—42no—
382#95—41no—
383#95—42no—
384#95—42no—
385#95C2×C4×C12718yes—
386C24—22no—
387C24—22no—
388C24—21no—
389C24—21no—
390C24—22no—
391C24—22no—
392C24—21no—
393C24—21no—
394C24C22×C4×C12712yes—
395C24C2×D4×C12712yes—
396C24C2×Q8×C12712yes—
397C24C24×C12711yescharacteristic
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—48no—
443C22×C4—44no—
444C22×C4—48no—
445C22×C4—44no—
446C22×C4—44no—
447C22×C4C22×C4×C12712yes—
448C22×C4C22×C4×C12714yes—
449C22×C4C22×C4×C12712yes—
450C22×C4C22×C4×C12714yes—
451C22×C4C2×D4×C12714yes—
452C22×C4C2×Q8×C12714yes—
453C22×C4#41×C12714yes—
454C22×C4#41×C12714yes—
455C4⋊C4—48no—
456C4⋊C4—48no—
457C4⋊C4—44no—
458C4⋊C4—44no—
459C22⋊C4—44no—
460C22⋊C4—48no—
461C22⋊C4—48no—
462C22⋊C4C4⋊C4×C127116yescomplemented
463C42—48no—
464C23—24no—
465C23—22no—
466C23—24no—
467C23—22no—
468C23—22no—
469C23—22no—
470C23—22no—
471C23—22no—
472C23—24no—
473C23—24no—
474C23—24no—
475C23—24no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—41no—
481C23—42no—
482C23—41no—
483C23—42no—
484C23—41no—
485C23—41no—
486C23C2×C4⋊C4×C12714yes—
487C23C23×C4×C12711yescharacteristic
488C23C22×D4×C12711yescharacteristic
489C23C22×Q8×C12711yescharacteristic
490C23C2×#41×C12712yes—
491C23C2×#41×C12712yes—
492C23H(5,𝔽2)×C12711yescharacteristic
493C23H(5,𝔽2)×C12711yescharacteristic
494C23H(5,𝔽2)×C12712yes—
495C23H(5,𝔽2)×C12712yes—
496C232−1+4×C12711yescharacteristic
497C232−1+4×C12711yescharacteristic
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—416no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4C2×C4⋊C4×C12718yes—
551C22—24no—
552C22—28no—
553C22—44no—
554C22—42no—
555C22—42no—
556C22—44no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—44no—
561C22—42no—
562C22C22×C4⋊C4×C12711yescharacteristic
563C22C4×#41×C12712yes—
564C22#518×C12711yescharacteristic
565C22#518×C12712yes—
566C22#519×C12711yescharacteristic
567C22#537×C12711yescharacteristic
568C22#537×C12711yescharacteristic
569C22#539×C12712yes—
570C22#539×C12712yes—
571C22#542×C12712yes—
572C22#542×C12712yes—
573C22#544×C12711yescharacteristic
574C22#544×C12711yescharacteristic
575C22#546×C12712yes—
576C22#546×C12712yes—
577C22#551×C12711yescharacteristic
578C22#553×C12712yes—
579C22#554×C12712yes—
580C22#554×C12712yes—
581C22#559×C12711yescharacteristic
582C22#560×C12712yes—
583C22#560×C12711yescharacteristic
584C22H(3,𝔽4)×C12711yescharacteristic
585C4—28no—
586C4—42no—
587C4—44no—
588C4—42no—
589C4—44no—
590C4—44no—
591C4—82no—
592C4—82no—
593C2—44no—
594C2C127×#231611yescharacteristic
595C2C127×#233212yes—
596C2C127×#234912yes—
597C2C127×#237411yescharacteristic
598C2C127×#237511yescharacteristic
599C2C127×#269112yes—
600C2C127×#269311yescharacteristic
601C2C127×#271211yescharacteristic
602C2C127×#276311yescharacteristic
603C2C127×#279012yes—
604C2C127×#280711yescharacteristic
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
3. C127×#1442C2semidirect
4. C127×#1441C2semidirect
7. C127×#1436C2semidirect
8. C127×C4⋊#95C2semidirect
21. #385×C127C4semidirect
159. C22⋊C4×C127C4⋊C4semidirect
290. #14514C127direct (N × H)
305. #1442C2×C127semidirect
306. #1441C2×C127semidirect
309. #1436C2×C127semidirect
310. C4⋊#95C2×C127semidirect
312. C127#14514direct (N × H)
324. #385C4×C127semidirect
462. C22⋊C4C4⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#388×C1272
C2×#385×C1272
C127×#14422
C127×#14412
C127×#14392
C127×#14362
C127×C4⋊#952
C127×C22⋊#952
#14514127