Finite Group Databasebeta

← C127×#14448 #44578121

Subgroups — C127×#14448 #44578121

Order 32512.

1810 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊Q8×C127C211yesmaximal, characteristic
2C2×#387×C127C212yesmaximal, complemented
3C127×#1446C212yesmaximal, complemented
4C127×#1445C212yesmaximal, complemented
5C127×#1439C212yesmaximal
6C127×#1437C212yesmaximal
7C127×C4⋊#95C212yesmaximal, complemented
8C127×C22⋊#95C211yesmaximal, characteristic
9C127×C22⋊#95C211yesmaximal, characteristic
10C23×Q8×C127C2211yescharacteristic
11C24×C4×C127C2211yescharacteristic
12C2×C22⋊Q8×C127—28no—
13C2×C22⋊Q8×C127C418yescomplemented
14C22×C4⋊C4×C127C2212yes—
15C22×C4⋊C4×C127C2212yes—
16C22×C4⋊C4×C127C2211yescharacteristic
17C22×C22⋊C4×C127C2212yes—
18C22×C22⋊C4×C127C2212yes—
19C22×C22⋊C4×C127C2211yescharacteristic
20C22×C22⋊C4×C127C2211yescharacteristic
21C22×C42×C127C2212yes—
22#387×C127—28no—
23C2×#95×C127C2212yes—
24C2×#95×C127C2212yes—
25C2×#95×C127C2212yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2211yescharacteristic
28C2×#95×C127C2212yes—
29C2×#95×C127C2211yescharacteristic
30C2×#95×C127C2212yes—
31C2×#95×C127C2212yes—
32C2×#95×C127C2212yes—
33C2×#95×C127C2212yes—
34C25×C127C2311yescharacteristic
35C22×Q8×C127—24no—
36C22×Q8×C127—41no—
37C22×Q8×C127—41no—
38C22×Q8×C127—42no—
39C22×Q8×C127C2×C414yes—
40C23×C4×C127—24no—
41C23×C4×C127—41no—
42C23×C4×C127—41no—
43C23×C4×C127—42no—
44C23×C4×C127C2×C414yes—
45C23×C4×C127C2312yes—
46C23×C4×C127C2312yes—
47C23×C4×C127C2312yes—
48C23×C4×C127C2311yescharacteristic
49C23×C4×C127C2312yes—
50C23×C4×C127C2312yes—
51C23×C4×C127C2312yes—
52C23×C4×C127C2311yescharacteristic
53C22⋊Q8×C127—232no—
54C2×C4⋊C4×C127—24no—
55C2×C4⋊C4×C127—24no—
56C2×C4⋊C4×C127—24no—
57C2×C4⋊C4×C127—24no—
58C2×C4⋊C4×C127—42no—
59C2×C4⋊C4×C127C2×C418yes—
60C2×C4⋊C4×C127C2×C414yes—
61C2×C4⋊C4×C127D418yes—
62C2×C22⋊C4×C127—24no—
63C2×C22⋊C4×C127—24no—
64C2×C22⋊C4×C127—24no—
65C2×C22⋊C4×C127—22no—
66C2×C22⋊C4×C127—24no—
67C2×C22⋊C4×C127—41no—
68C2×C22⋊C4×C127—41no—
69C2×C22⋊C4×C127—42no—
70C2×C22⋊C4×C127—41no—
71C2×C22⋊C4×C127—41no—
72C2×C22⋊C4×C127C2×C418yes—
73C2×C22⋊C4×C127Q814yescomplemented
74C2×C42×C127—24no—
75C2×C42×C127—24no—
76C2×C42×C127—42no—
77#95×C127—24no—
78#95×C127—24no—
79#95×C127—24no—
80#95×C127—24no—
81#95×C127—41no—
82#95×C127—42no—
83#95×C127—42no—
84#95×C127—42no—
85#95×C127—42no—
86#95×C127—41no—
87#95×C127—42no—
88C24×C127—22no—
89C24×C127—22no—
90C24×C127—21no—
91C24×C127—21no—
92C24×C127—21no—
93C24×C127—22no—
94C24×C127—22no—
95C24×C127—21no—
96C24×C127C22×C412yes—
97C24×C127C2×Q812yes—
98C24×C127#4112yes—
99C24×C127C2411yescharacteristic
100C2×Q8×C127—28no—
101C2×Q8×C127—44no—
102C2×Q8×C127—44no—
103C2×Q8×C127—48no—
104C2×Q8×C127—48no—
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—22no—
118C22×C4×C127—22no—
119C22×C4×C127—22no—
120C22×C4×C127—22no—
121C22×C4×C127—22no—
122C22×C4×C127—22no—
123C22×C4×C127—21no—
124C22×C4×C127—21no—
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—28no—
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—44no—
150C22×C4×C127—44no—
151C22×C4×C127—48no—
152C22×C4×C127—48no—
153C22×C4×C127C22×C414yes—
154C22×C4×C127C22×C412yes—
155C22×C4×C127C22×C414yes—
156C22×C4×C127C22×C412yes—
157C22×C4×C127C2×D414yes—
158C22×C4×C127C2×D414yes—
159C22×C4×C127C2×D414yes—
160C22×C4×C127C2×Q814yes—
161C22×C4×C127#4114yes—
162C4⋊C4×C127—216no—
163C4⋊C4×C127—48no—
164C4⋊C4×C127C22⋊C4116yescomplemented
165C22⋊C4×C127—216no—
166C22⋊C4×C127—44no—
167C22⋊C4×C127—48no—
168C22⋊C4×C127—44no—
169C42×C127—48no—
170C23×C127—22no—
171C23×C127—22no—
172C23×C127—22no—
173C23×C127—22no—
174C23×C127—22no—
175C23×C127—22no—
176C23×C127—22no—
177C23×C127—22no—
178C23×C127—22no—
179C23×C127—22no—
180C23×C127—24no—
181C23×C127—24no—
182C23×C127—24no—
183C23×C127—24no—
184C23×C127—42no—
185C23×C127—42no—
186C23×C127—42no—
187C23×C127—42no—
188C23×C127—42no—
189C23×C127—42no—
190C23×C127—42no—
191C23×C127—42no—
192C23×C127C4×Q814yes—
193C23×C127C23×C411yescharacteristic
194C23×C127C22×D412yes—
195C23×C127C22×Q811yescharacteristic
196C23×C127C2×#4111yescharacteristic
197C23×C127C2×#4112yes—
198C23×C127H(5,𝔽2)11yescharacteristic
199C23×C127H(5,𝔽2)11yescharacteristic
200C23×C127H(5,𝔽2)12yes—
201C23×C127H(5,𝔽2)11yescharacteristic
202C23×C1272−1+412yes—
203C23×C1272−1+411yescharacteristic
204Q8×C127—416no—
205C2×C4×C127—24no—
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—22no—
219C2×C4×C127—24no—
220C2×C4×C127—24no—
221C2×C4×C127—24no—
222C2×C4×C127—24no—
223C2×C4×C127—24no—
224C2×C4×C127—24no—
225C2×C4×C127—24no—
226C2×C4×C127—24no—
227C2×C4×C127—416no—
228C2×C4×C127—42no—
229C2×C4×C127—42no—
230C2×C4×C127—42no—
231C2×C4×C127—42no—
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×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×C127C2×C22⋊C418yes—
257C2×C4×C127C2×C22⋊C414yes—
258C22×C127—24no—
259C22×C127—24no—
260C22×C127—24no—
261C22×C127—42no—
262C22×C127—42no—
263C22×C127—42no—
264C22×C127—42no—
265C22×C127—44no—
266C22×C127—44no—
267C22×C127—44no—
268C22×C127—44no—
269C22×C127C22×C22⋊C411yescharacteristic
270C22×C127C2×C4×Q811yescharacteristic
271C22×C127C4×#4111yescharacteristic
272C22×C127#51811yescharacteristic
273C22×C127#51811yescharacteristic
274C22×C127#51911yescharacteristic
275C22×C127#52011yescharacteristic
276C22×C127#53512yes—
277C22×C127#53512yes—
278C22×C127#53811yescharacteristic
279C22×C127#53911yescharacteristic
280C22×C127#53912yes—
281C22×C127#54212yes—
282C22×C127#54311yescharacteristic
283C22×C127#54411yescharacteristic
284C22×C127#54612yes—
285C22×C127#54712yes—
286C22×C127#54812yes—
287C22×C127D4×Q812yes—
288C22×C127#55112yes—
289C22×C127#55412yes—
290C22×C127#56212yes—
291C22×C127#56312yes—
292C4×C127—24no—
293C4×C127—28no—
294C4×C127—42no—
295C4×C127—44no—
296C4×C127—44no—
297C4×C127—44no—
298C4×C127—82no—
299C4×C127—82no—
300#14448C12711yesmaximal, characteristic, direct product factor, Sylow
301C2×C127—44no—
302C2×C127#230911yescharacteristic
303C2×C127#232911yescharacteristic
304C2×C127#233211yescharacteristic
305C2×C127#233911yescharacteristic
306C2×C127Q8×C22⋊C411yescharacteristic
307C2×C127#236811yescharacteristic
308C2×C127#237811yescharacteristic
309C2×C127#269212yes—
310C2×C127#269612yes—
311C2×C127#272012yes—
312C2×C127#272312yes—
313C22×C22⋊Q8C2×C12711yescharacteristic
314C2×#387C2×C12712yescomplemented
315#1446C2×C12712yescomplemented
316#1445C2×C12712yescomplemented
317#1439C2×C12712yes—
318#1437C2×C12712yes—
319C4⋊#95C2×C12712yescomplemented
320C22⋊#95C2×C12711yescharacteristic
321C22⋊#95C2×C12711yescharacteristic
322C127#1444811yescharacteristic, direct product factor, Sylow
323C23×Q8C22×C12711yescharacteristic
324C24×C4C22×C12711yescharacteristic
325C2×C22⋊Q8—28no—
326C2×C22⋊Q8C4×C12718yescomplemented
327C22×C4⋊C4C22×C12712yes—
328C22×C4⋊C4C22×C12712yes—
329C22×C4⋊C4C22×C12711yescharacteristic
330C22×C22⋊C4C22×C12712yes—
331C22×C22⋊C4C22×C12712yes—
332C22×C22⋊C4C22×C12711yescharacteristic
333C22×C22⋊C4C22×C12711yescharacteristic
334C22×C42C22×C12712yes—
335#387—28no—
336C2×#95C22×C12712yes—
337C2×#95C22×C12712yes—
338C2×#95C22×C12712yes—
339C2×#95C22×C12712yes—
340C2×#95C22×C12711yescharacteristic
341C2×#95C22×C12712yes—
342C2×#95C22×C12711yescharacteristic
343C2×#95C22×C12712yes—
344C2×#95C22×C12712yes—
345C2×#95C22×C12712yes—
346C2×#95C22×C12712yes—
347C25C23×C12711yescharacteristic
348C22×Q8—24no—
349C22×Q8—41no—
350C22×Q8—41no—
351C22×Q8—42no—
352C22×Q8C2×C4×C12714yes—
353C23×C4—24no—
354C23×C4—41no—
355C23×C4—41no—
356C23×C4—42no—
357C23×C4C2×C4×C12714yes—
358C23×C4C23×C12712yes—
359C23×C4C23×C12712yes—
360C23×C4C23×C12712yes—
361C23×C4C23×C12711yescharacteristic
362C23×C4C23×C12712yes—
363C23×C4C23×C12712yes—
364C23×C4C23×C12712yes—
365C23×C4C23×C12711yescharacteristic
366C22⋊Q8—232no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4C2×C4×C12718yes—
373C2×C4⋊C4C2×C4×C12714yes—
374C2×C4⋊C4D4×C12718yes—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—41no—
381C2×C22⋊C4—41no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—41no—
384C2×C22⋊C4—41no—
385C2×C22⋊C4C2×C4×C12718yes—
386C2×C22⋊C4Q8×C12714yescomplemented
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—42no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—41no—
395#95—42no—
396#95—42no—
397#95—42no—
398#95—42no—
399#95—41no—
400#95—42no—
401C24—22no—
402C24—22no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—22no—
407C24—22no—
408C24—21no—
409C24C22×C4×C12712yes—
410C24C2×Q8×C12712yes—
411C24#41×C12712yes—
412C24C24×C12711yescharacteristic
413C2×Q8—28no—
414C2×Q8—44no—
415C2×Q8—44no—
416C2×Q8—48no—
417C2×Q8—48no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—21no—
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—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—28no—
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—44no—
463C22×C4—44no—
464C22×C4—48no—
465C22×C4—48no—
466C22×C4C22×C4×C12714yes—
467C22×C4C22×C4×C12712yes—
468C22×C4C22×C4×C12714yes—
469C22×C4C22×C4×C12712yes—
470C22×C4C2×D4×C12714yes—
471C22×C4C2×D4×C12714yes—
472C22×C4C2×D4×C12714yes—
473C22×C4C2×Q8×C12714yes—
474C22×C4#41×C12714yes—
475C4⋊C4—216no—
476C4⋊C4—48no—
477C4⋊C4C22⋊C4×C127116yescomplemented
478C22⋊C4—216no—
479C22⋊C4—44no—
480C22⋊C4—48no—
481C22⋊C4—44no—
482C42—48no—
483C23—22no—
484C23—22no—
485C23—22no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—24no—
494C23—24no—
495C23—24no—
496C23—24no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23C4×Q8×C12714yes—
506C23C23×C4×C12711yescharacteristic
507C23C22×D4×C12712yes—
508C23C22×Q8×C12711yescharacteristic
509C23C2×#41×C12711yescharacteristic
510C23C2×#41×C12712yes—
511C23H(5,𝔽2)×C12711yescharacteristic
512C23H(5,𝔽2)×C12711yescharacteristic
513C23H(5,𝔽2)×C12712yes—
514C23H(5,𝔽2)×C12711yescharacteristic
515C232−1+4×C12712yes—
516C232−1+4×C12711yescharacteristic
517Q8—416no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—416no—
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×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4C2×C22⋊C4×C12718yes—
570C2×C4C2×C22⋊C4×C12714yes—
571C22—24no—
572C22—24no—
573C22—24no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—44no—
578C22—44no—
579C22—44no—
580C22—44no—
581C22—42no—
582C22C22×C22⋊C4×C12711yescharacteristic
583C22C2×C4×Q8×C12711yescharacteristic
584C22C4×#41×C12711yescharacteristic
585C22#518×C12711yescharacteristic
586C22#518×C12711yescharacteristic
587C22#519×C12711yescharacteristic
588C22#520×C12711yescharacteristic
589C22#535×C12712yes—
590C22#535×C12712yes—
591C22#538×C12711yescharacteristic
592C22#539×C12711yescharacteristic
593C22#539×C12712yes—
594C22#542×C12712yes—
595C22#543×C12711yescharacteristic
596C22#544×C12711yescharacteristic
597C22#546×C12712yes—
598C22#547×C12712yes—
599C22#548×C12712yes—
600C22D4×Q8×C12712yes—
601C22#551×C12712yes—
602C22#554×C12712yes—
603C22#562×C12712yes—
604C22#563×C12712yes—
605C4—28no—
606C4—24no—
607C4—44no—
608C4—44no—
609C4—42no—
610C4—44no—
611C4—82no—
612C4—82no—
613C2—44no—
614C2C127×#230911yescharacteristic
615C2C127×#232911yescharacteristic
616C2C127×#233211yescharacteristic
617C2C127×#233911yescharacteristic
618C2Q8×C22⋊C4×C12711yescharacteristic
619C2C127×#236811yescharacteristic
620C2C127×#237811yescharacteristic
621C2C127×#269212yes—
622C2C127×#269612yes—
623C2C127×#272012yes—
624C2C127×#272312yes—
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
2. C2×#387×C127C2semidirect
3. C127×#1446C2semidirect
4. C127×#1445C2semidirect
7. C127×C4⋊#95C2semidirect
13. C2×C22⋊Q8×C127C4semidirect
73. C2×C22⋊C4×C127Q8semidirect
164. C4⋊C4×C127C22⋊C4semidirect
300. #14448C127direct (N × H)
314. C2×#387C2×C127semidirect
315. #1446C2×C127semidirect
316. #1445C2×C127semidirect
319. C4⋊#95C2×C127semidirect
322. C127#14448direct (N × H)
326. C2×C22⋊Q8C4×C127semidirect
386. C2×C22⋊C4Q8×C127semidirect
477. C4⋊C4C22⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊Q8×C1272
C2×#387×C1272
C127×#14462
C127×#14452
C127×#14392
C127×#14372
C127×C4⋊#952
C127×C22⋊#952
#14448127