Finite Group Databasebeta

← C127×#16666 #44580339

Subgroups — C127×#16666 #44580339

Order 32512.

1462 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#393×C127C211yesmaximal, characteristic
2C2×#381×C127C211yesmaximal, characteristic
3C127×#1446C212yesmaximal, complemented
4C127×#1445C212yesmaximal, complemented
5C127×#1443C212yesmaximal, complemented
6C127×#1441C212yesmaximal, complemented
7C127×#1439C212yesmaximal
8C127×#1439C211yesmaximal, characteristic
9C127×C22⋊#95C212yesmaximal
10C23×Q8×C127C2211yescharacteristic
11C24×C4×C127C2211yescharacteristic
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2212yes—
14C22×C22⋊C4×C127C2212yes—
15C22×C22⋊C4×C127C2212yes—
16C22×C22⋊C4×C127C2211yescharacteristic
17C22×C22⋊C4×C127C2211yescharacteristic
18#393×C127—24no—
19#381×C127—24no—
20C2×#95×C127C2212yes—
21C2×#95×C127C2211yescharacteristic
22C2×#95×C127C2212yes—
23C2×#95×C127C2212yes—
24C2×#95×C127C2212yes—
25C2×#95×C127C2212yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2212yes—
28C2×#95×C127C2212yes—
29C2×#95×C127C2212yes—
30C2×#95×C127C2211yescharacteristic
31C2×#95×C127C2212yes—
32C2×#95×C127C2212yes—
33C25×C127C2311yescharacteristic
34C22×Q8×C127—22no—
35C22×Q8×C127—24no—
36C22×Q8×C127—42no—
37C22×Q8×C127—41no—
38C22×Q8×C127—41no—
39C23×C4×C127—22no—
40C23×C4×C127—22no—
41C23×C4×C127—41no—
42C23×C4×C127—41no—
43C23×C4×C127—41no—
44C23×C4×C127—41no—
45C23×C4×C127Q814yescomplemented
46C23×C4×C127C2312yes—
47C23×C4×C127C2312yes—
48C23×C4×C127C2312yes—
49C23×C4×C127C2311yescharacteristic
50C23×C4×C127C2311yescharacteristic
51C23×C4×C127C2312yes—
52C23×C4×C127C2312yes—
53C23×C4×C127C2312yes—
54C2×C4⋊C4×C127—24no—
55C2×C4⋊C4×C127—24no—
56C2×C4⋊C4×C127—41no—
57C2×C4⋊C4×C127—42no—
58C2×C4⋊C4×C127—42no—
59C2×C22⋊C4×C127—22no—
60C2×C22⋊C4×C127—24no—
61C2×C22⋊C4×C127—24no—
62C2×C22⋊C4×C127—24no—
63C2×C22⋊C4×C127—24no—
64C2×C22⋊C4×C127—41no—
65C2×C22⋊C4×C127—41no—
66C2×C22⋊C4×C127—42no—
67C2×C22⋊C4×C127—42no—
68C2×C22⋊C4×C127—41no—
69C2×C22⋊C4×C127—41no—
70C2×C22⋊C4×C127D414yes—
71#95×C127—24no—
72#95×C127—24no—
73#95×C127—24no—
74#95×C127—22no—
75#95×C127—24no—
76#95×C127—42no—
77#95×C127—41no—
78#95×C127—42no—
79#95×C127—42no—
80#95×C127—42no—
81#95×C127—42no—
82#95×C127—42no—
83#95×C127—42no—
84C24×C127—22no—
85C24×C127—22no—
86C24×C127—22no—
87C24×C127—21no—
88C24×C127—21no—
89C24×C127—21no—
90C24×C127—21no—
91C24×C127—22no—
92C24×C127C2×D412yes—
93C24×C127C2×Q812yes—
94C24×C127#4112yes—
95C24×C127C2411yescharacteristic
96C2×Q8×C127—48no—
97C2×Q8×C127—44no—
98C2×Q8×C127—44no—
99C2×Q8×C127—48no—
100C2×Q8×C127—44no—
101C22×C4×C127—28no—
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—22no—
109C22×C4×C127—22no—
110C22×C4×C127—21no—
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—21no—
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—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—44no—
152C22×C4×C127—44no—
153C22×C4×C127—44no—
154C22×C4×C127—44no—
155C22×C4×C127C2×D412yes—
156C22×C4×C127C2×D412yes—
157C22×C4×C127C2×Q814yes—
158C22×C4×C127#4114yes—
159C22×C4×C127#4114yes—
160C4⋊C4×C127—44no—
161C4⋊C4×C127—48no—
162C22⋊C4×C127—44no—
163C22⋊C4×C127—48no—
164C22⋊C4×C127—48no—
165C22⋊C4×C127—44no—
166C23×C127—24no—
167C23×C127—22no—
168C23×C127—22no—
169C23×C127—22no—
170C23×C127—22no—
171C23×C127—22no—
172C23×C127—22no—
173C23×C127—24no—
174C23×C127—24no—
175C23×C127—24no—
176C23×C127—24no—
177C23×C127—24no—
178C23×C127—42no—
179C23×C127—42no—
180C23×C127—42no—
181C23×C127—42no—
182C23×C127—41no—
183C23×C127—41no—
184C23×C127—42no—
185C23×C127—41no—
186C23×C127—42no—
187C23×C127—41no—
188C23×C127C22⋊Q814yes—
189C23×C127C22×D411yescharacteristic
190C23×C127C22×Q811yescharacteristic
191C23×C127C2×#4111yescharacteristic
192C23×C127C2×#4112yes—
193C23×C127C2×#4112yes—
194C23×C127H(5,𝔽2)11yescharacteristic
195C23×C127H(5,𝔽2)11yescharacteristic
196C23×C127H(5,𝔽2)11yescharacteristic
197C23×C127H(5,𝔽2)11yescharacteristic
198C23×C127H(5,𝔽2)12yes—
199C23×C1272−1+412yes—
200Q8×C127—416no—
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—42no—
222C2×C4×C127—42no—
223C2×C4×C127—42no—
224C2×C4×C127—42no—
225C2×C4×C127—42no—
226C2×C4×C127—41no—
227C2×C4×C127—42no—
228C2×C4×C127—41no—
229C2×C4×C127—42no—
230C2×C4×C127—41no—
231C2×C4×C127—42no—
232C2×C4×C127—41no—
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—
254C22×C127—24no—
255C22×C127—28no—
256C22×C127—42no—
257C22×C127—42no—
258C22×C127—44no—
259C22×C127—42no—
260C22×C127—44no—
261C22×C127—42no—
262C22×C127—44no—
263C22×C127—42no—
264C22×C127—42no—
265C22×C127C2×C22⋊Q811yescharacteristic
266C22×C127#53312yes—
267C22×C127#53411yescharacteristic
268C22×C127#53511yescharacteristic
269C22×C127#53811yescharacteristic
270C22×C127#53811yescharacteristic
271C22×C127#53812yes—
272C22×C127#53812yes—
273C22×C127#54212yes—
274C22×C127#54212yes—
275C22×C127#54311yescharacteristic
276C22×C127#54311yescharacteristic
277C22×C127#54412yes—
278C22×C127#54612yes—
279C22×C127#54712yes—
280C22×C127#55111yescharacteristic
281C22×C127#55111yescharacteristic
282C22×C127#55112yes—
283C22×C127#55212yes—
284C22×C127#55912yes—
285C22×C127#56011yescharacteristic
286C22×C127#56212yes—
287C22×C127#56311yescharacteristic
288C4×C127—44no—
289C4×C127—42no—
290C4×C127—44no—
291C4×C127—42no—
292C4×C127—44no—
293C4×C127—82no—
294C4×C127—82no—
295C4×C127—82no—
296#16666C12711yesmaximal, characteristic, direct product factor, Sylow
297C2×C127—44no—
298C2×C127#243812yes—
299C2×C127#260711yescharacteristic
300C2×C127#262611yescharacteristic
301C2×C127#266512yes—
302C2×C127#269711yescharacteristic
303C2×C127#271012yes—
304C2×C127#271711yescharacteristic
305C2×C127#275112yes—
306C2×C127#276011yescharacteristic
307C2×C127#276411yescharacteristic
308C2×C127#284111yescharacteristic
309C2×#393C2×C12711yescharacteristic
310C2×#381C2×C12711yescharacteristic
311#1446C2×C12712yescomplemented
312#1445C2×C12712yescomplemented
313#1443C2×C12712yescomplemented
314#1441C2×C12712yescomplemented
315#1439C2×C12712yes—
316#1439C2×C12711yescharacteristic
317C22⋊#95C2×C12712yes—
318C127#1666611yescharacteristic, direct product factor, Sylow
319C23×Q8C22×C12711yescharacteristic
320C24×C4C22×C12711yescharacteristic
321C22×C4⋊C4C22×C12711yescharacteristic
322C22×C4⋊C4C22×C12712yes—
323C22×C22⋊C4C22×C12712yes—
324C22×C22⋊C4C22×C12712yes—
325C22×C22⋊C4C22×C12711yescharacteristic
326C22×C22⋊C4C22×C12711yescharacteristic
327#393—24no—
328#381—24no—
329C2×#95C22×C12712yes—
330C2×#95C22×C12711yescharacteristic
331C2×#95C22×C12712yes—
332C2×#95C22×C12712yes—
333C2×#95C22×C12712yes—
334C2×#95C22×C12712yes—
335C2×#95C22×C12712yes—
336C2×#95C22×C12712yes—
337C2×#95C22×C12712yes—
338C2×#95C22×C12712yes—
339C2×#95C22×C12711yescharacteristic
340C2×#95C22×C12712yes—
341C2×#95C22×C12712yes—
342C25C23×C12711yescharacteristic
343C22×Q8—22no—
344C22×Q8—24no—
345C22×Q8—42no—
346C22×Q8—41no—
347C22×Q8—41no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—41no—
351C23×C4—41no—
352C23×C4—41no—
353C23×C4—41no—
354C23×C4Q8×C12714yescomplemented
355C23×C4C23×C12712yes—
356C23×C4C23×C12712yes—
357C23×C4C23×C12712yes—
358C23×C4C23×C12711yescharacteristic
359C23×C4C23×C12711yescharacteristic
360C23×C4C23×C12712yes—
361C23×C4C23×C12712yes—
362C23×C4C23×C12712yes—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—41no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—42no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—41no—
374C2×C22⋊C4—41no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—41no—
378C2×C22⋊C4—41no—
379C2×C22⋊C4D4×C12714yes—
380#95—24no—
381#95—24no—
382#95—24no—
383#95—22no—
384#95—24no—
385#95—42no—
386#95—41no—
387#95—42no—
388#95—42no—
389#95—42no—
390#95—42no—
391#95—42no—
392#95—42no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—22no—
401C24C2×D4×C12712yes—
402C24C2×Q8×C12712yes—
403C24#41×C12712yes—
404C24C24×C12711yescharacteristic
405C2×Q8—48no—
406C2×Q8—44no—
407C2×Q8—44no—
408C2×Q8—48no—
409C2×Q8—44no—
410C22×C4—28no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—22no—
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—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
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—22no—
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—44no—
459C22×C4—44no—
460C22×C4—44no—
461C22×C4—44no—
462C22×C4—44no—
463C22×C4—44no—
464C22×C4C2×D4×C12712yes—
465C22×C4C2×D4×C12712yes—
466C22×C4C2×Q8×C12714yes—
467C22×C4#41×C12714yes—
468C22×C4#41×C12714yes—
469C4⋊C4—44no—
470C4⋊C4—48no—
471C22⋊C4—44no—
472C22⋊C4—48no—
473C22⋊C4—48no—
474C22⋊C4—44no—
475C23—24no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—24no—
483C23—24no—
484C23—24no—
485C23—24no—
486C23—24no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—41no—
492C23—41no—
493C23—42no—
494C23—41no—
495C23—42no—
496C23—41no—
497C23C22⋊Q8×C12714yes—
498C23C22×D4×C12711yescharacteristic
499C23C22×Q8×C12711yescharacteristic
500C23C2×#41×C12711yescharacteristic
501C23C2×#41×C12712yes—
502C23C2×#41×C12712yes—
503C23H(5,𝔽2)×C12711yescharacteristic
504C23H(5,𝔽2)×C12711yescharacteristic
505C23H(5,𝔽2)×C12711yescharacteristic
506C23H(5,𝔽2)×C12711yescharacteristic
507C23H(5,𝔽2)×C12712yes—
508C232−1+4×C12712yes—
509Q8—416no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—416no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—41no—
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—
563C22—24no—
564C22—28no—
565C22—42no—
566C22—42no—
567C22—44no—
568C22—42no—
569C22—44no—
570C22—42no—
571C22—44no—
572C22—42no—
573C22—42no—
574C22C2×C22⋊Q8×C12711yescharacteristic
575C22#533×C12712yes—
576C22#534×C12711yescharacteristic
577C22#535×C12711yescharacteristic
578C22#538×C12711yescharacteristic
579C22#538×C12711yescharacteristic
580C22#538×C12712yes—
581C22#538×C12712yes—
582C22#542×C12712yes—
583C22#542×C12712yes—
584C22#543×C12711yescharacteristic
585C22#543×C12711yescharacteristic
586C22#544×C12712yes—
587C22#546×C12712yes—
588C22#547×C12712yes—
589C22#551×C12711yescharacteristic
590C22#551×C12711yescharacteristic
591C22#551×C12712yes—
592C22#552×C12712yes—
593C22#559×C12712yes—
594C22#560×C12711yescharacteristic
595C22#562×C12712yes—
596C22#563×C12711yescharacteristic
597C4—44no—
598C4—42no—
599C4—44no—
600C4—42no—
601C4—44no—
602C4—82no—
603C4—82no—
604C4—82no—
605C2—44no—
606C2C127×#243812yes—
607C2C127×#260711yescharacteristic
608C2C127×#262611yescharacteristic
609C2C127×#266512yes—
610C2C127×#269711yescharacteristic
611C2C127×#271012yes—
612C2C127×#271711yescharacteristic
613C2C127×#275112yes—
614C2C127×#276011yescharacteristic
615C2C127×#276411yescharacteristic
616C2C127×#284111yescharacteristic
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
3. C127×#1446C2semidirect
4. C127×#1445C2semidirect
5. C127×#1443C2semidirect
6. C127×#1441C2semidirect
45. C23×C4×C127Q8semidirect
296. #16666C127direct (N × H)
311. #1446C2×C127semidirect
312. #1445C2×C127semidirect
313. #1443C2×C127semidirect
314. #1441C2×C127semidirect
318. C127#16666direct (N × H)
354. C23×C4Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#393×C1272
C2×#381×C1272
C127×#14462
C127×#14452
C127×#14432
C127×#14412
C127×#14392
C127×C22⋊#952
#16666127