Finite Group Databasebeta

← C127×#13979 #44577652

Subgroups — C127×#13979 #44577652

Order 32512.

2358 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C127C211yesmaximal, characteristic
2C2×#390×C127C211yesmaximal, characteristic
3C2×#390×C127C211yesmaximal, characteristic
4C2×#389×C127C211yesmaximal, characteristic, complemented
5C2×#382×C127C211yesmaximal, characteristic, complemented
6C127×#1439C214yesmaximal, complemented
7C127×C4⋊#95C211yesmaximal, characteristic, complemented
8C127×C22⋊#95C214yesmaximal, complemented
9C4×#95×C127C211yesmaximal, characteristic, complemented
10C23×D4×C127C2211yescharacteristic
11C24×C4×C127C2212yes—
12C2×C4×D4×C127—24no—
13C2×C4×D4×C127—24no—
14C2×C4×D4×C127—24no—
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C4⋊C4×C127C2211yescharacteristic
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C4⋊C4×C127C2212yes—
19C22×C22⋊C4×C127C2212yes—
20C22×C22⋊C4×C127C2214yes—
21C22×C22⋊C4×C127C2214yes—
22C22×C42×C127C2211yescharacteristic
23C22×C42×C127C2211yescharacteristic
24C22×C42×C127C2211yescharacteristic
25#390×C127—24no—
26#390×C127C418yescomplemented
27#389×C127—24no—
28#382×C127—24no—
29C2×#95×C127C2212yes—
30C2×#95×C127C2212yes—
31C2×#95×C127C2212yes—
32C2×#95×C127C2214yes—
33C2×#95×C127C2214yes—
34C25×C127C2312yes—
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—24no—
44C23×C4×C127—24no—
45C23×C4×C127—28no—
46C23×C4×C127—44no—
47C23×C4×C127C2312yes—
48C23×C4×C127C2312yes—
49C23×C4×C127C2312yes—
50C23×C4×C127C2311yescharacteristic
51C23×C4×C127C2312yes—
52C23×C4×C127C2312yes—
53C23×C4×C127C2311yescharacteristic
54C23×C4×C127C2311yescharacteristic
55C4×D4×C127—232no—
56C2×C4⋊C4×C127—22no—
57C2×C4⋊C4×C127—22no—
58C2×C4⋊C4×C127—22no—
59C2×C4⋊C4×C127—22no—
60C2×C4⋊C4×C127—22no—
61C2×C4⋊C4×C127—24no—
62C2×C4⋊C4×C127—22no—
63C2×C4⋊C4×C127—22no—
64C2×C4⋊C4×C127—44no—
65C2×C4⋊C4×C127C2×C414yescomplemented
66C2×C4⋊C4×C127D414yes—
67C2×C22⋊C4×C127—24no—
68C2×C22⋊C4×C127—24no—
69C2×C22⋊C4×C127—24no—
70C2×C22⋊C4×C127—28no—
71C2×C22⋊C4×C127—28no—
72C2×C22⋊C4×C127—44no—
73C2×C22⋊C4×C127—44no—
74C2×C22⋊C4×C127—44no—
75C2×C22⋊C4×C127C2×C4116yescomplemented
76C2×C42×C127—22no—
77C2×C42×C127—22no—
78C2×C42×C127—22no—
79C2×C42×C127—22no—
80C2×C42×C127—22no—
81C2×C42×C127—22no—
82C2×C42×C127—22no—
83C2×C42×C127C2×C414yescomplemented
84C2×C42×C127D414yes—
85#95×C127—28no—
86#95×C127—24no—
87#95×C127—24no—
88#95×C127—24no—
89#95×C127—44no—
90C24×C127—22no—
91C24×C127—22no—
92C24×C127—24no—
93C24×C127—24no—
94C24×C127—22no—
95C24×C127—22no—
96C24×C127—24no—
97C24×C127—24no—
98C24×C127C22×C414yes—
99C24×C127C2×D414yes—
100C24×C127C2×Q814yes—
101C24×C127C2411yescharacteristic
102C2×D4×C127—28no—
103C2×D4×C127—28no—
104C2×D4×C127—28no—
105C2×D4×C127—28no—
106C2×D4×C127—28no—
107C2×D4×C127—28no—
108C2×D4×C127C4⋊C4116yescomplemented
109C22×C4×C127—21no—
110C22×C4×C127—21no—
111C22×C4×C127—22no—
112C22×C4×C127—216no—
113C22×C4×C127—22no—
114C22×C4×C127—22no—
115C22×C4×C127—21no—
116C22×C4×C127—21no—
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—22no—
124C22×C4×C127—22no—
125C22×C4×C127—22no—
126C22×C4×C127—22no—
127C22×C4×C127—22no—
128C22×C4×C127—24no—
129C22×C4×C127—22no—
130C22×C4×C127—24no—
131C22×C4×C127—24no—
132C22×C4×C127—22no—
133C22×C4×C127—22no—
134C22×C4×C127—22no—
135C22×C4×C127—24no—
136C22×C4×C127—22no—
137C22×C4×C127—22no—
138C22×C4×C127—22no—
139C22×C4×C127—22no—
140C22×C4×C127—24no—
141C22×C4×C127—24no—
142C22×C4×C127—416no—
143C22×C4×C127—416no—
144C22×C4×C127—48no—
145C22×C4×C127—48no—
146C22×C4×C127C22×C414yes—
147C22×C4×C127C22×C414yes—
148C22×C4×C127C22×C412yes—
149C22×C4×C127C2×D414yes—
150C22×C4×C127C2×D412yes—
151C22×C4×C127C2×D412yes—
152C22×C4×C127C2×D412yes—
153C22×C4×C127C2×D412yes—
154C22×C4×C127C2×D412yes—
155C22×C4×C127C2×Q812yes—
156C22×C4×C127#4114yes—
157C22×C4×C127#4114yes—
158C22×C4×C127#4112yes—
159C22×C4×C127#4112yes—
160C4⋊C4×C127—28no—
161C4⋊C4×C127—28no—
162C4⋊C4×C127—48no—
163C4⋊C4×C127—44no—
164C22⋊C4×C127—216no—
165C22⋊C4×C127—416no—
166C22⋊C4×C127—416no—
167C42×C127—28no—
168C42×C127—28no—
169C42×C127—44no—
170C23×C127—24no—
171C23×C127—24no—
172C23×C127—28no—
173C23×C127—28no—
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—42no—
183C23×C127—44no—
184C23×C127—42no—
185C23×C127—42no—
186C23×C127—42no—
187C23×C127—44no—
188C23×C127—44no—
189C23×C127—44no—
190C23×C127—44no—
191C23×C127—44no—
192C23×C127C2×C4⋊C418yes—
193C23×C127C23×C411yescharacteristic
194C23×C127C22×D411yescharacteristic
195C23×C127C22×D411yescharacteristic
196C23×C127C22×D411yescharacteristic
197C23×C127C22×Q811yescharacteristic
198C23×C127C2×#4111yescharacteristic
199C23×C127C2×#4111yescharacteristic
200C23×C127C2×#4112yes—
201C23×C127C2×#4112yes—
202C23×C127H(5,𝔽2)12yes—
203C23×C127H(5,𝔽2)12yes—
204D4×C127—232no—
205C2×C4×C127—22no—
206C2×C4×C127—22no—
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—28no—
214C2×C4×C127—22no—
215C2×C4×C127—24no—
216C2×C4×C127—24no—
217C2×C4×C127—22no—
218C2×C4×C127—22no—
219C2×C4×C127—24no—
220C2×C4×C127—28no—
221C2×C4×C127—24no—
222C2×C4×C127—432no—
223C2×C4×C127—42no—
224C2×C4×C127—42no—
225C2×C4×C127—42no—
226C2×C4×C127—42no—
227C2×C4×C127—42no—
228C2×C4×C127—44no—
229C2×C4×C127—42no—
230C2×C4×C127—42no—
231C2×C4×C127—42no—
232C2×C4×C127—42no—
233C2×C4×C127—44no—
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—44no—
243C2×C4×C127—44no—
244C2×C4×C127C2×C4⋊C414yes—
245C2×C4×C127C4×D414yes—
246C2×C4×C127C4×D414yes—
247C2×C4×C127#12014yes—
248C2×C4×C127C22⋊Q814yes—
249C2×C4×C127C22⋊Q814yes—
250C2×C4×C127#12314yes—
251C2×C4×C127#12414yes—
252C22×C127—216no—
253C22×C127—28no—
254C22×C127—44no—
255C22×C127—44no—
256C22×C127—44no—
257C22×C127—48no—
258C22×C127—48no—
259C22×C127—44no—
260C22×C127—44no—
261C22×C127—48no—
262C22×C127—44no—
263C22×C127C22×C4⋊C411yescharacteristic
264C22×C127C2×C4×D411yescharacteristic
265C22×C127C2×C4×D411yescharacteristic
266C22×C127C4×#4112yes—
267C22×C127#51812yes—
268C22×C127C2×#12011yescharacteristic
269C22×C127C2×C22⋊Q811yescharacteristic
270C22×C127C2×C22⋊Q811yescharacteristic
271C22×C127C2×#12311yescharacteristic
272C22×C127C2×#12411yescharacteristic
273C22×C127#52912yes—
274C22×C127#53211yescharacteristic
275C22×C127#53511yescharacteristic
276C22×C127#53511yescharacteristic
277C22×C127#54012yes—
278C22×C127#54612yes—
279C22×C127#54612yes—
280C22×C127#54612yes—
281C22×C127#55012yes—
282C22×C127#55312yes—
283C22×C127#55412yes—
284C22×C127#55412yes—
285C22×C127#55512yes—
286C4×C127—24no—
287C4×C127—44no—
288C4×C127—44no—
289C4×C127—44no—
290C4×C127—42no—
291C4×C127—44no—
292C4×C127—82no—
293C4×C127#38518yes—
294#13979C12711yesmaximal, characteristic, direct product factor, Sylow
295C2×C127—48no—
296C2×C127C2×#38511yescharacteristic
297C2×C127C4×#12411yescharacteristic
298C2×C127#232811yescharacteristic
299C2×C127#234912yes—
300C2×C127#236312yes—
301C2×C127#242012yes—
302C2×C127#243111yescharacteristic
303C2×C127#243511yescharacteristic
304C2×C127#245412yes—
305C2×C127#256311yescharacteristic
306C2×C127#256611yescharacteristic
307C22×C4×D4C2×C12711yescharacteristic
308C2×#390C2×C12711yescharacteristic
309C2×#390C2×C12711yescharacteristic
310C2×#389C2×C12711yescharacteristic, complemented
311C2×#382C2×C12711yescharacteristic, complemented
312#1439C2×C12714yescomplemented
313C4⋊#95C2×C12711yescharacteristic, complemented
314C22⋊#95C2×C12714yescomplemented
315C4×#95C2×C12711yescharacteristic, complemented
316C127#1397911yescharacteristic, direct product factor, Sylow
317C23×D4C22×C12711yescharacteristic
318C24×C4C22×C12712yes—
319C2×C4×D4—24no—
320C2×C4×D4—24no—
321C2×C4×D4—24no—
322C22×C4⋊C4C22×C12711yescharacteristic
323C22×C4⋊C4C22×C12711yescharacteristic
324C22×C4⋊C4C22×C12711yescharacteristic
325C22×C4⋊C4C22×C12712yes—
326C22×C22⋊C4C22×C12712yes—
327C22×C22⋊C4C22×C12714yes—
328C22×C22⋊C4C22×C12714yes—
329C22×C42C22×C12711yescharacteristic
330C22×C42C22×C12711yescharacteristic
331C22×C42C22×C12711yescharacteristic
332#390—24no—
333#390C4×C12718yescomplemented
334#389—24no—
335#382—24no—
336C2×#95C22×C12712yes—
337C2×#95C22×C12712yes—
338C2×#95C22×C12712yes—
339C2×#95C22×C12714yes—
340C2×#95C22×C12714yes—
341C25C23×C12712yes—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4C2×C4×C12714yes—
347C22×D4D4×C12714yes—
348C22×D4Q8×C12714yes—
349C23×C4—24no—
350C23×C4—24no—
351C23×C4—24no—
352C23×C4—28no—
353C23×C4—44no—
354C23×C4C23×C12712yes—
355C23×C4C23×C12712yes—
356C23×C4C23×C12712yes—
357C23×C4C23×C12711yescharacteristic
358C23×C4C23×C12712yes—
359C23×C4C23×C12712yes—
360C23×C4C23×C12711yescharacteristic
361C23×C4C23×C12711yescharacteristic
362C4×D4—232no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4C2×C4×C12714yescomplemented
373C2×C4⋊C4D4×C12714yes—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—28no—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4C2×C4×C127116yescomplemented
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42C2×C4×C12714yescomplemented
391C2×C42D4×C12714yes—
392#95—28no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—44no—
397C24—22no—
398C24—22no—
399C24—24no—
400C24—24no—
401C24—22no—
402C24—22no—
403C24—24no—
404C24—24no—
405C24C22×C4×C12714yes—
406C24C2×D4×C12714yes—
407C24C2×Q8×C12714yes—
408C24C24×C12711yescharacteristic
409C2×D4—28no—
410C2×D4—28no—
411C2×D4—28no—
412C2×D4—28no—
413C2×D4—28no—
414C2×D4—28no—
415C2×D4C4⋊C4×C127116yescomplemented
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—216no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—21no—
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—24no—
436C22×C4—22no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—24no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—416no—
450C22×C4—416no—
451C22×C4—48no—
452C22×C4—48no—
453C22×C4C22×C4×C12714yes—
454C22×C4C22×C4×C12714yes—
455C22×C4C22×C4×C12712yes—
456C22×C4C2×D4×C12714yes—
457C22×C4C2×D4×C12712yes—
458C22×C4C2×D4×C12712yes—
459C22×C4C2×D4×C12712yes—
460C22×C4C2×D4×C12712yes—
461C22×C4C2×D4×C12712yes—
462C22×C4C2×Q8×C12712yes—
463C22×C4#41×C12714yes—
464C22×C4#41×C12714yes—
465C22×C4#41×C12712yes—
466C22×C4#41×C12712yes—
467C4⋊C4—28no—
468C4⋊C4—28no—
469C4⋊C4—48no—
470C4⋊C4—44no—
471C22⋊C4—216no—
472C22⋊C4—416no—
473C22⋊C4—416no—
474C42—28no—
475C42—28no—
476C42—44no—
477C23—24no—
478C23—24no—
479C23—28no—
480C23—28no—
481C23—24no—
482C23—24no—
483C23—24no—
484C23—24no—
485C23—28no—
486C23—28no—
487C23—28no—
488C23—28no—
489C23—42no—
490C23—44no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—44no—
495C23—44no—
496C23—44no—
497C23—44no—
498C23—44no—
499C23C2×C4⋊C4×C12718yes—
500C23C23×C4×C12711yescharacteristic
501C23C22×D4×C12711yescharacteristic
502C23C22×D4×C12711yescharacteristic
503C23C22×D4×C12711yescharacteristic
504C23C22×Q8×C12711yescharacteristic
505C23C2×#41×C12711yescharacteristic
506C23C2×#41×C12711yescharacteristic
507C23C2×#41×C12712yes—
508C23C2×#41×C12712yes—
509C23H(5,𝔽2)×C12712yes—
510C23H(5,𝔽2)×C12712yes—
511D4—232no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—28no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—28no—
528C2×C4—24no—
529C2×C4—432no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—44no—
536C2×C4—42no—
537C2×C4—44no—
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—44no—
550C2×C4—44no—
551C2×C4C2×C4⋊C4×C12714yes—
552C2×C4C4×D4×C12714yes—
553C2×C4C4×D4×C12714yes—
554C2×C4#120×C12714yes—
555C2×C4C22⋊Q8×C12714yes—
556C2×C4C22⋊Q8×C12714yes—
557C2×C4#123×C12714yes—
558C2×C4#124×C12714yes—
559C22—216no—
560C22—28no—
561C22—44no—
562C22—48no—
563C22—48no—
564C22—44no—
565C22—44no—
566C22—48no—
567C22—44no—
568C22—44no—
569C22—44no—
570C22C22×C4⋊C4×C12711yescharacteristic
571C22C2×C4×D4×C12711yescharacteristic
572C22C2×C4×D4×C12711yescharacteristic
573C22C4×#41×C12712yes—
574C22#518×C12712yes—
575C22C2×#120×C12711yescharacteristic
576C22C2×C22⋊Q8×C12711yescharacteristic
577C22C2×C22⋊Q8×C12711yescharacteristic
578C22C2×#123×C12711yescharacteristic
579C22C2×#124×C12711yescharacteristic
580C22#529×C12712yes—
581C22#532×C12711yescharacteristic
582C22#535×C12711yescharacteristic
583C22#535×C12711yescharacteristic
584C22#540×C12712yes—
585C22#546×C12712yes—
586C22#546×C12712yes—
587C22#546×C12712yes—
588C22#550×C12712yes—
589C22#553×C12712yes—
590C22#554×C12712yes—
591C22#554×C12712yes—
592C22#555×C12712yes—
593C4—24no—
594C4—44no—
595C4—44no—
596C4—44no—
597C4—42no—
598C4—44no—
599C4—82no—
600C4#385×C12718yes—
601C2—48no—
602C2C2×#385×C12711yescharacteristic
603C2C4×#124×C12711yescharacteristic
604C2C127×#232811yescharacteristic
605C2C127×#234912yes—
606C2C127×#236312yes—
607C2C127×#242012yes—
608C2C127×#243111yescharacteristic
609C2C127×#243511yescharacteristic
610C2C127×#245412yes—
611C2C127×#256311yescharacteristic
612C2C127×#256611yescharacteristic
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
4. C2×#389×C127C2semidirect
5. C2×#382×C127C2semidirect
6. C127×#1439C2semidirect
7. C127×C4⋊#95C2semidirect
8. C127×C22⋊#95C2semidirect
9. C4×#95×C127C2semidirect
26. #390×C127C4semidirect
65. C2×C4⋊C4×C127C2×C4semidirect
75. C2×C22⋊C4×C127C2×C4semidirect
83. C2×C42×C127C2×C4semidirect
108. C2×D4×C127C4⋊C4semidirect
294. #13979C127direct (N × H)
310. C2×#389C2×C127semidirect
311. C2×#382C2×C127semidirect
312. #1439C2×C127semidirect
313. C4⋊#95C2×C127semidirect
314. C22⋊#95C2×C127semidirect
315. C4×#95C2×C127semidirect
316. C127#13979direct (N × H)
333. #390C4×C127semidirect
372. C2×C4⋊C4C2×C4×C127semidirect
382. C2×C22⋊C4C2×C4×C127semidirect
390. C2×C42C2×C4×C127semidirect
415. C2×D4C4⋊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×#390×C1272
C2×#389×C1272
C2×#382×C1272
C127×#14392
C127×C4⋊#952
C127×C22⋊#952
C4×#95×C1272
#13979127