Finite Group Databasebeta

← C127×#15928 #44579601

Subgroups — C127×#15928 #44579601

Order 32512.

1566 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#126×C127C211yesmaximal, characteristic
2C2×#400×C127C211yesmaximal, characteristic, complemented
3C2×#397×C127C211yesmaximal, characteristic
4C2×#384×C127C211yesmaximal, characteristic, complemented
5C127×#1445C211yesmaximal, characteristic, complemented
6C127×#1441C212yesmaximal, complemented
7C127×#1439C212yesmaximal
8C127×#1439C212yesmaximal
9C127×#1437C211yesmaximal, characteristic
10C127×#1436C212yesmaximal, complemented
11C127×#1436C211yesmaximal, characteristic, complemented
12C2×#126×C127—24no—
13C2×#126×C127—24no—
14C2×#126×C127—24no—
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C4⋊C4×C127C2211yescharacteristic
17C22×C4⋊C4×C127C2212yes—
18C22×C4⋊C4×C127C2212yes—
19C22×C4⋊C4×C127C2211yescharacteristic
20C22×C4⋊C4×C127C2211yescharacteristic
21C22×C22⋊C4×C127C2211yescharacteristic
22C22×C22⋊C4×C127C2211yescharacteristic
23C22×C22⋊C4×C127C2212yes—
24C22×C22⋊C4×C127C2211yescharacteristic
25C22×C22⋊C4×C127C2212yes—
26C22×C42×C127C2211yescharacteristic
27C22×C42×C127C2211yescharacteristic
28#400×C127—24no—
29#397×C127—24no—
30#384×C127—24no—
31C2×#95×C127C2212yes—
32C2×#95×C127C2211yescharacteristic
33C2×#95×C127C2212yes—
34C2×#95×C127C2211yescharacteristic
35C2×#95×C127C2212yes—
36C2×#95×C127C2212yes—
37C2×#95×C127C2212yes—
38C2×#95×C127C2212yes—
39C2×#95×C127C2212yes—
40C2×#95×C127C2212yes—
41C25×C127C2311yescharacteristic
42C23×C4×C127C2312yes—
43C23×C4×C127C2312yes—
44C23×C4×C127C2312yes—
45C23×C4×C127C2311yescharacteristic
46C23×C4×C127C2311yescharacteristic
47C23×C4×C127C2311yescharacteristic
48C23×C4×C127C2311yescharacteristic
49C23×C4×C127C2311yescharacteristic
50C23×C4×C127C2311yescharacteristic
51C23×C4×C127C2312yes—
52#126×C127—232no—
53C2×C4⋊C4×C127—22no—
54C2×C4⋊C4×C127—22no—
55C2×C4⋊C4×C127—22no—
56C2×C4⋊C4×C127—22no—
57C2×C4⋊C4×C127—22no—
58C2×C4⋊C4×C127—22no—
59C2×C4⋊C4×C127—22no—
60C2×C4⋊C4×C127—24no—
61C2×C4⋊C4×C127—24no—
62C2×C4⋊C4×C127—22no—
63C2×C4⋊C4×C127—22no—
64C2×C4⋊C4×C127—22no—
65C2×C4⋊C4×C127—24no—
66C2×C4⋊C4×C127—24no—
67C2×C4⋊C4×C127—42no—
68C2×C4⋊C4×C127—42no—
69C2×C4⋊C4×C127D414yes—
70C2×C4⋊C4×C127D414yes—
71C2×C22⋊C4×C127—22no—
72C2×C22⋊C4×C127—22no—
73C2×C22⋊C4×C127—22no—
74C2×C22⋊C4×C127—22no—
75C2×C22⋊C4×C127—22no—
76C2×C22⋊C4×C127—22no—
77C2×C22⋊C4×C127—22no—
78C2×C22⋊C4×C127—22no—
79C2×C22⋊C4×C127—24no—
80C2×C22⋊C4×C127—24no—
81C2×C22⋊C4×C127—24no—
82C2×C22⋊C4×C127—24no—
83C2×C22⋊C4×C127—42no—
84C2×C22⋊C4×C127—42no—
85C2×C22⋊C4×C127D414yes—
86C2×C42×C127—22no—
87C2×C42×C127—22no—
88C2×C42×C127—22no—
89C2×C42×C127—22no—
90C2×C42×C127—24no—
91#95×C127—22no—
92#95×C127—24no—
93#95×C127—22no—
94#95×C127—24no—
95#95×C127—24no—
96#95×C127—24no—
97#95×C127—24no—
98#95×C127—24no—
99#95×C127—42no—
100#95×C127—42no—
101C24×C127—21no—
102C24×C127—21no—
103C24×C127—22no—
104C24×C127—22no—
105C24×C127—22no—
106C24×C127—22no—
107C24×C127—22no—
108C24×C127—22no—
109C24×C127C2×D412yes—
110C24×C127C2411yescharacteristic
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—21no—
120C22×C4×C127—21no—
121C22×C4×C127—21no—
122C22×C4×C127—21no—
123C22×C4×C127—21no—
124C22×C4×C127—21no—
125C22×C4×C127—21no—
126C22×C4×C127—21no—
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—22no—
140C22×C4×C127—22no—
141C22×C4×C127—22no—
142C22×C4×C127—22no—
143C22×C4×C127—22no—
144C22×C4×C127—22no—
145C22×C4×C127—22no—
146C22×C4×C127—22no—
147C22×C4×C127—22no—
148C22×C4×C127—22no—
149C22×C4×C127—22no—
150C22×C4×C127—22no—
151C22×C4×C127—22no—
152C22×C4×C127—22no—
153C22×C4×C127—22no—
154C22×C4×C127—22no—
155C22×C4×C127—22no—
156C22×C4×C127—22no—
157C22×C4×C127—22no—
158C22×C4×C127C2×D412yes—
159C22×C4×C127C2×D412yes—
160C22×C4×C127C2×D412yes—
161C22×C4×C127C2×D412yes—
162C22×C4×C127C2×D412yes—
163C22×C4×C127C2×D412yes—
164C22×C4×C127C2×D412yes—
165C22×C4×C127C2×D412yes—
166C22×C4×C127#4114yes—
167C22×C4×C127#4114yes—
168C22×C4×C127#4114yes—
169C4⋊C4×C127—28no—
170C4⋊C4×C127—28no—
171C4⋊C4×C127—28no—
172C4⋊C4×C127—48no—
173C4⋊C4×C127—48no—
174C4⋊C4×C127—44no—
175C22⋊C4×C127—28no—
176C22⋊C4×C127—28no—
177C22⋊C4×C127—28no—
178C22⋊C4×C127—48no—
179C22⋊C4×C127—48no—
180C42×C127—28no—
181C42×C127—28no—
182C23×C127—22no—
183C23×C127—22no—
184C23×C127—22no—
185C23×C127—24no—
186C23×C127—24no—
187C23×C127—41no—
188C23×C127—42no—
189C23×C127—41no—
190C23×C127—41no—
191C23×C127—41no—
192C23×C127—42no—
193C23×C127—42no—
194C23×C127—42no—
195C23×C127—42no—
196C23×C127—42no—
197C23×C127—42no—
198C23×C127—42no—
199C23×C127—42no—
200C23×C127—42no—
201C23×C127—42no—
202C23×C127—42no—
203C23×C127C22×D411yescharacteristic
204C23×C127C22×D411yescharacteristic
205C23×C127C22×D411yescharacteristic
206C23×C127C2×#4112yes—
207C23×C127C2×#4112yes—
208C23×C127C2×#4112yes—
209C23×C127H(5,𝔽2)12yes—
210C23×C1272−1+412yes—
211C23×C1272−1+412yes—
212C2×C4×C127—22no—
213C2×C4×C127—24no—
214C2×C4×C127—22no—
215C2×C4×C127—24no—
216C2×C4×C127—24no—
217C2×C4×C127—24no—
218C2×C4×C127—24no—
219C2×C4×C127—24no—
220C2×C4×C127—24no—
221C2×C4×C127—24no—
222C2×C4×C127—22no—
223C2×C4×C127—22no—
224C2×C4×C127—22no—
225C2×C4×C127—22no—
226C2×C4×C127—22no—
227C2×C4×C127—22no—
228C2×C4×C127—22no—
229C2×C4×C127—24no—
230C2×C4×C127—24no—
231C2×C4×C127—24no—
232C2×C4×C127—24no—
233C2×C4×C127—41no—
234C2×C4×C127—41no—
235C2×C4×C127—41no—
236C2×C4×C127—41no—
237C2×C4×C127—41no—
238C2×C4×C127—41no—
239C2×C4×C127—41no—
240C2×C4×C127—41no—
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×C127—42no—
248C2×C4×C127—42no—
249C2×C4×C127—42no—
250C2×C4×C127—42no—
251C2×C4×C127—42no—
252C2×C4×C127—42no—
253C2×C4×C127—42no—
254C2×C4×C127—42no—
255C2×C4×C127—42no—
256C2×C4×C127—42no—
257C2×C4×C127—42no—
258C2×C4×C127—42no—
259C2×C4×C127—42no—
260C2×C4×C127—42no—
261C2×C4×C127—42no—
262C2×C4×C127—42no—
263C2×C4×C127—42no—
264C2×C4×C127—42no—
265C2×C4×C127—42no—
266C2×C4×C127—42no—
267C2×C4×C127—42no—
268C2×C4×C127#12014yes—
269C2×C4×C127#12618yescomplemented
270C22×C127—42no—
271C22×C127—42no—
272C22×C127—42no—
273C22×C127—44no—
274C22×C127—44no—
275C22×C127—82no—
276C22×C127—82no—
277C22×C127—82no—
278C22×C127—82no—
279C22×C127C2×#12011yescharacteristic
280C22×C127#52511yescharacteristic
281C22×C127C2×#12612yes—
282C22×C127#53211yescharacteristic
283C22×C127#53211yescharacteristic
284C22×C127#53511yescharacteristic
285C22×C127#53611yescharacteristic
286C22×C127#53611yescharacteristic
287C22×C127#53912yes—
288C22×C127#54112yes—
289C22×C127#54212yes—
290C22×C127#54612yes—
291C22×C127#54712yes—
292C22×C127#54712yes—
293C22×C127#54712yes—
294C22×C127#54812yes—
295C22×C127#55012yes—
296C22×C127#55212yes—
297C22×C127#55312yes—
298C22×C127#55612yes—
299C22×C127#56312yes—
300C4×C127—24no—
301C4×C127—28no—
302C4×C127—42no—
303C4×C127—42no—
304C4×C127—42no—
305C4×C127—42no—
306C4×C127—42no—
307C4×C127—82no—
308C4×C127—82no—
309C4×C127—82no—
310#15928C12711yesmaximal, characteristic, direct product factor, Sylow
311C2×C127—82no—
312C2×C127#240611yescharacteristic
313C2×C127#243111yescharacteristic
314C2×C127#243211yescharacteristic
315C2×C127#248112yes—
316C2×C127#249612yes—
317C2×C127#251212yes—
318C2×C127#271612yes—
319C2×C127#271812yes—
320C2×C127#272112yes—
321C22×#126C2×C12711yescharacteristic
322C2×#400C2×C12711yescharacteristic, complemented
323C2×#397C2×C12711yescharacteristic
324C2×#384C2×C12711yescharacteristic, complemented
325#1445C2×C12711yescharacteristic, complemented
326#1441C2×C12712yescomplemented
327#1439C2×C12712yes—
328#1439C2×C12712yes—
329#1437C2×C12711yescharacteristic
330#1436C2×C12712yescomplemented
331#1436C2×C12711yescharacteristic, complemented
332C127#1592811yescharacteristic, direct product factor, Sylow
333C2×#126—24no—
334C2×#126—24no—
335C2×#126—24no—
336C22×C4⋊C4C22×C12711yescharacteristic
337C22×C4⋊C4C22×C12711yescharacteristic
338C22×C4⋊C4C22×C12712yes—
339C22×C4⋊C4C22×C12712yes—
340C22×C4⋊C4C22×C12711yescharacteristic
341C22×C4⋊C4C22×C12711yescharacteristic
342C22×C22⋊C4C22×C12711yescharacteristic
343C22×C22⋊C4C22×C12711yescharacteristic
344C22×C22⋊C4C22×C12712yes—
345C22×C22⋊C4C22×C12711yescharacteristic
346C22×C22⋊C4C22×C12712yes—
347C22×C42C22×C12711yescharacteristic
348C22×C42C22×C12711yescharacteristic
349#400—24no—
350#397—24no—
351#384—24no—
352C2×#95C22×C12712yes—
353C2×#95C22×C12711yescharacteristic
354C2×#95C22×C12712yes—
355C2×#95C22×C12711yescharacteristic
356C2×#95C22×C12712yes—
357C2×#95C22×C12712yes—
358C2×#95C22×C12712yes—
359C2×#95C22×C12712yes—
360C2×#95C22×C12712yes—
361C2×#95C22×C12712yes—
362C25C23×C12711yescharacteristic
363C23×C4C23×C12712yes—
364C23×C4C23×C12712yes—
365C23×C4C23×C12712yes—
366C23×C4C23×C12711yescharacteristic
367C23×C4C23×C12711yescharacteristic
368C23×C4C23×C12711yescharacteristic
369C23×C4C23×C12711yescharacteristic
370C23×C4C23×C12711yescharacteristic
371C23×C4C23×C12711yescharacteristic
372C23×C4C23×C12712yes—
373#126—232no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—42no—
389C2×C4⋊C4—42no—
390C2×C4⋊C4D4×C12714yes—
391C2×C4⋊C4D4×C12714yes—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4D4×C12714yes—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—24no—
412#95—22no—
413#95—24no—
414#95—22no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—42no—
421#95—42no—
422C24—21no—
423C24—21no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24C2×D4×C12712yes—
431C24C24×C12711yescharacteristic
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4C2×D4×C12712yes—
480C22×C4C2×D4×C12712yes—
481C22×C4C2×D4×C12712yes—
482C22×C4C2×D4×C12712yes—
483C22×C4C2×D4×C12712yes—
484C22×C4C2×D4×C12712yes—
485C22×C4C2×D4×C12712yes—
486C22×C4C2×D4×C12712yes—
487C22×C4#41×C12714yes—
488C22×C4#41×C12714yes—
489C22×C4#41×C12714yes—
490C4⋊C4—28no—
491C4⋊C4—28no—
492C4⋊C4—28no—
493C4⋊C4—48no—
494C4⋊C4—48no—
495C4⋊C4—44no—
496C22⋊C4—28no—
497C22⋊C4—28no—
498C22⋊C4—28no—
499C22⋊C4—48no—
500C22⋊C4—48no—
501C42—28no—
502C42—28no—
503C23—22no—
504C23—22no—
505C23—22no—
506C23—24no—
507C23—24no—
508C23—41no—
509C23—42no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23C22×D4×C12711yescharacteristic
525C23C22×D4×C12711yescharacteristic
526C23C22×D4×C12711yescharacteristic
527C23C2×#41×C12712yes—
528C23C2×#41×C12712yes—
529C23C2×#41×C12712yes—
530C23H(5,𝔽2)×C12712yes—
531C232−1+4×C12712yes—
532C232−1+4×C12712yes—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4#120×C12714yes—
590C2×C4#126×C12718yescomplemented
591C22—42no—
592C22—42no—
593C22—42no—
594C22—44no—
595C22—44no—
596C22—82no—
597C22—82no—
598C22—82no—
599C22—82no—
600C22C2×#120×C12711yescharacteristic
601C22#525×C12711yescharacteristic
602C22C2×#126×C12712yes—
603C22#532×C12711yescharacteristic
604C22#532×C12711yescharacteristic
605C22#535×C12711yescharacteristic
606C22#536×C12711yescharacteristic
607C22#536×C12711yescharacteristic
608C22#539×C12712yes—
609C22#541×C12712yes—
610C22#542×C12712yes—
611C22#546×C12712yes—
612C22#547×C12712yes—
613C22#547×C12712yes—
614C22#547×C12712yes—
615C22#548×C12712yes—
616C22#550×C12712yes—
617C22#552×C12712yes—
618C22#553×C12712yes—
619C22#556×C12712yes—
620C22#563×C12712yes—
621C4—24no—
622C4—28no—
623C4—42no—
624C4—42no—
625C4—42no—
626C4—42no—
627C4—42no—
628C4—82no—
629C4—82no—
630C4—82no—
631C2—82no—
632C2C127×#240611yescharacteristic
633C2C127×#243111yescharacteristic
634C2C127×#243211yescharacteristic
635C2C127×#248112yes—
636C2C127×#249612yes—
637C2C127×#251212yes—
638C2C127×#271612yes—
639C2C127×#271812yes—
640C2C127×#272112yes—
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#400×C127C2semidirect
4. C2×#384×C127C2semidirect
5. C127×#1445C2semidirect
6. C127×#1441C2semidirect
10. C127×#1436C2semidirect
11. C127×#1436C2semidirect
269. C2×C4×C127#126semidirect
310. #15928C127direct (N × H)
322. C2×#400C2×C127semidirect
324. C2×#384C2×C127semidirect
325. #1445C2×C127semidirect
326. #1441C2×C127semidirect
330. #1436C2×C127semidirect
331. #1436C2×C127semidirect
332. C127#15928direct (N × H)
590. C2×C4#126×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#126×C1272
C2×#400×C1272
C2×#397×C1272
C2×#384×C1272
C127×#14452
C127×#14412
C127×#14392
C127×#14372
C127×#14362
#15928127