Finite Group Databasebeta

← C127×#17136 #44580809

Subgroups — C127×#17136 #44580809

Order 32512.

1594 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#399×C127C212yesmaximal, complemented
2C2×#396×C127C212yesmaximal, complemented
3C127×#1441C212yesmaximal, complemented
4C127×#1441C212yesmaximal, complemented
5C127×#1439C212yesmaximal, complemented
6C127×#1439C212yesmaximal, complemented
7C127×#1438C211yesmaximal, characteristic
8C127×#1438C211yesmaximal, characteristic
9C127×#1438C211yesmaximal, characteristic
10C23×D4×C127C2211yescharacteristic
11C22×C4⋊C4×C127C2212yes—
12C22×C4⋊C4×C127C2212yes—
13C22×C4⋊C4×C127C2212yes—
14C22×C4⋊C4×C127C2212yes—
15C22×C22⋊C4×C127C2211yescharacteristic
16C22×C22⋊C4×C127C2211yescharacteristic
17C22×C22⋊C4×C127C2212yes—
18C22×C22⋊C4×C127C2211yescharacteristic
19C22×C22⋊C4×C127C2212yes—
20C22×C22⋊C4×C127C2212yes—
21C22×C22⋊C4×C127C2212yes—
22C22×C22⋊C4×C127C2211yescharacteristic
23#399×C127—28no—
24#396×C127—28no—
25C2×#95×C127C2212yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2211yescharacteristic
28C2×#95×C127C2212yes—
29C2×#95×C127C2212yes—
30C2×#95×C127C2211yescharacteristic
31C2×#95×C127C2212yes—
32C2×#95×C127C2212yes—
33C25×C127C2311yescharacteristic
34C25×C127C2311yescharacteristic
35C22×D4×C127—42no—
36C22×D4×C127—42no—
37C22×D4×C127—41no—
38C22×D4×C127—41no—
39C22×D4×C127Q814yes—
40C23×C4×C127C2312yes—
41C23×C4×C127C2312yes—
42C23×C4×C127C2312yes—
43C23×C4×C127C2312yes—
44C23×C4×C127C2312yes—
45C23×C4×C127C2311yescharacteristic
46C23×C4×C127C2312yes—
47C2×C4⋊C4×C127—24no—
48C2×C4⋊C4×C127—24no—
49C2×C4⋊C4×C127—24no—
50C2×C4⋊C4×C127—24no—
51C2×C4⋊C4×C127—24no—
52C2×C4⋊C4×C127—42no—
53C2×C4⋊C4×C127—42no—
54C2×C4⋊C4×C127—42no—
55C2×C4⋊C4×C127—42no—
56C2×C4⋊C4×C127—42no—
57C2×C4⋊C4×C127—42no—
58C2×C4⋊C4×C127D418yescomplemented
59C2×C22⋊C4×C127—24no—
60C2×C22⋊C4×C127—24no—
61C2×C22⋊C4×C127—24no—
62C2×C22⋊C4×C127—24no—
63C2×C22⋊C4×C127—24no—
64C2×C22⋊C4×C127—24no—
65C2×C22⋊C4×C127—24no—
66C2×C22⋊C4×C127—24no—
67C2×C22⋊C4×C127—41no—
68C2×C22⋊C4×C127—41no—
69C2×C22⋊C4×C127—41no—
70C2×C22⋊C4×C127—42no—
71C2×C22⋊C4×C127—42no—
72C2×C22⋊C4×C127—42no—
73C2×C22⋊C4×C127—42no—
74C2×C22⋊C4×C127—42no—
75C2×C22⋊C4×C127—42no—
76C2×C22⋊C4×C127—42no—
77C2×C22⋊C4×C127—41no—
78C2×C22⋊C4×C127—42no—
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—
87C24×C127—22no—
88C24×C127—22no—
89C24×C127—22no—
90C24×C127—22no—
91C24×C127—22no—
92C24×C127—22no—
93C24×C127—22no—
94C24×C127—22no—
95C24×C127—22no—
96C24×C127—22no—
97C24×C127—21no—
98C24×C127—21no—
99C24×C127—21no—
100C24×C127—21no—
101C24×C127—22no—
102C24×C127—22no—
103C24×C127C2×Q812yes—
104C24×C127C2×Q812yes—
105C24×C127C2411yescharacteristic
106C2×D4×C127—44no—
107C2×D4×C127—44no—
108C2×D4×C127—44no—
109C2×D4×C127—48no—
110C2×D4×C127—48no—
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—22no—
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—22no—
150C22×C4×C127—22no—
151C22×C4×C127—22no—
152C22×C4×C127—22no—
153C22×C4×C127C2×D414yes—
154C22×C4×C127C2×D414yes—
155C22×C4×C127C2×D414yes—
156C22×C4×C127C2×Q812yes—
157C22×C4×C127#4114yes—
158C4⋊C4×C127—48no—
159C4⋊C4×C127—48no—
160C4⋊C4×C127—48no—
161C4⋊C4×C127—48no—
162C22⋊C4×C127—44no—
163C22⋊C4×C127—44no—
164C22⋊C4×C127—48no—
165C22⋊C4×C127—44no—
166C22⋊C4×C127—48no—
167C22⋊C4×C127—48no—
168C22⋊C4×C127—48no—
169C22⋊C4×C127—44no—
170C23×C127—22no—
171C23×C127—22no—
172C23×C127—22no—
173C23×C127—22no—
174C23×C127—22no—
175C23×C127—22no—
176C23×C127—24no—
177C23×C127—24no—
178C23×C127—24no—
179C23×C127—24no—
180C23×C127—42no—
181C23×C127—42no—
182C23×C127—42no—
183C23×C127—42no—
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×C127—41no—
193C23×C127—41no—
194C23×C127—42no—
195C23×C127—42no—
196C23×C127—42no—
197C23×C127—42no—
198C23×C127—41no—
199C23×C127—41no—
200C23×C127—41no—
201C23×C127—42no—
202C23×C127—42no—
203C23×C127—42no—
204C23×C127—42no—
205C23×C127—41no—
206C23×C127—42no—
207C23×C127—42no—
208C23×C127—42no—
209C23×C127—42no—
210C23×C127—41no—
211C23×C127—41no—
212C23×C127C22×D412yes—
213C23×C127C22×Q811yescharacteristic
214C23×C127C2×#4112yes—
215C23×C127H(5,𝔽2)12yes—
216C23×C127H(5,𝔽2)12yes—
217C23×C127H(5,𝔽2)12yes—
218C23×C127H(5,𝔽2)11yescharacteristic
219C23×C127H(5,𝔽2)11yescharacteristic
220C23×C1272−1+412yes—
221D4×C127—416no—
222C2×C4×C127—24no—
223C2×C4×C127—24no—
224C2×C4×C127—24no—
225C2×C4×C127—24no—
226C2×C4×C127—24no—
227C2×C4×C127—24no—
228C2×C4×C127—22no—
229C2×C4×C127—22no—
230C2×C4×C127—22no—
231C2×C4×C127—24no—
232C2×C4×C127—24no—
233C2×C4×C127—24no—
234C2×C4×C127—24no—
235C2×C4×C127—24no—
236C2×C4×C127—24no—
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×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—42no—
269C22×C127—42no—
270C22×C127—42no—
271C22×C127—42no—
272C22×C127—42no—
273C22×C127—44no—
274C22×C127—44no—
275C22×C127—44no—
276C22×C127—44no—
277C22×C127—42no—
278C22×C127—42no—
279C22×C127—82no—
280C22×C127—82no—
281C22×C127—82no—
282C22×C127—82no—
283C22×C127—82no—
284C22×C127—82no—
285C22×C127—82no—
286C22×C127—82no—
287C22×C127#53412yes—
288C22×C127#53512yes—
289C22×C127#53712yes—
290C22×C127#53912yes—
291C22×C127#54012yes—
292C22×C127#54212yes—
293C22×C127#54311yescharacteristic
294C22×C127#54311yescharacteristic
295C22×C127#54311yescharacteristic
296C22×C127D4211yescharacteristic
297C22×C127#54612yes—
298C22×C127D4×Q812yes—
299C22×C127#55012yes—
300C22×C127#55111yescharacteristic
301C22×C127#55412yes—
302C22×C127#56012yes—
303C22×C127#56012yes—
304C22×C127#56011yescharacteristic
305C22×C127#56212yes—
306C22×C127#56212yes—
307C22×C127#56311yescharacteristic
308C4×C127—42no—
309C4×C127—44no—
310C4×C127—44no—
311C4×C127—44no—
312C4×C127—44no—
313C4×C127—82no—
314C4×C127—82no—
315#17136C12711yesmaximal, characteristic, direct product factor, Sylow
316C2×C127—82no—
317C2×C127—82no—
318C2×C127#267312yes—
319C2×C127#268311yescharacteristic
320C2×C127#269212yes—
321C2×C127#270512yes—
322C2×C127#273212yes—
323C2×C127#274811yescharacteristic
324C2×C127#281312yes—
325C2×C127#283712yes—
326C2×C127#284211yescharacteristic
327C2×#399C2×C12712yescomplemented
328C2×#396C2×C12712yescomplemented
329#1441C2×C12712yescomplemented
330#1441C2×C12712yescomplemented
331#1439C2×C12712yescomplemented
332#1439C2×C12712yescomplemented
333#1438C2×C12711yescharacteristic
334#1438C2×C12711yescharacteristic
335#1438C2×C12711yescharacteristic
336C127#1713611yescharacteristic, direct product factor, Sylow
337C23×D4C22×C12711yescharacteristic
338C22×C4⋊C4C22×C12712yes—
339C22×C4⋊C4C22×C12712yes—
340C22×C4⋊C4C22×C12712yes—
341C22×C4⋊C4C22×C12712yes—
342C22×C22⋊C4C22×C12711yescharacteristic
343C22×C22⋊C4C22×C12711yescharacteristic
344C22×C22⋊C4C22×C12712yes—
345C22×C22⋊C4C22×C12711yescharacteristic
346C22×C22⋊C4C22×C12712yes—
347C22×C22⋊C4C22×C12712yes—
348C22×C22⋊C4C22×C12712yes—
349C22×C22⋊C4C22×C12711yescharacteristic
350#399—28no—
351#396—28no—
352C2×#95C22×C12712yes—
353C2×#95C22×C12712yes—
354C2×#95C22×C12711yescharacteristic
355C2×#95C22×C12712yes—
356C2×#95C22×C12712yes—
357C2×#95C22×C12711yescharacteristic
358C2×#95C22×C12712yes—
359C2×#95C22×C12712yes—
360C25C23×C12711yescharacteristic
361C25C23×C12711yescharacteristic
362C22×D4—42no—
363C22×D4—42no—
364C22×D4—41no—
365C22×D4—41no—
366C22×D4Q8×C12714yes—
367C23×C4C23×C12712yes—
368C23×C4C23×C12712yes—
369C23×C4C23×C12712yes—
370C23×C4C23×C12712yes—
371C23×C4C23×C12712yes—
372C23×C4C23×C12711yescharacteristic
373C23×C4C23×C12712yes—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—42no—
380C2×C4⋊C4—42no—
381C2×C4⋊C4—42no—
382C2×C4⋊C4—42no—
383C2×C4⋊C4—42no—
384C2×C4⋊C4—42no—
385C2×C4⋊C4D4×C12718yescomplemented
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—41no—
395C2×C22⋊C4—41no—
396C2×C22⋊C4—41no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—41no—
405C2×C22⋊C4—42no—
406#95—24no—
407#95—24no—
408#95—41no—
409#95—42no—
410#95—42no—
411#95—42no—
412#95—42no—
413#95—41no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—22no—
429C24—22no—
430C24C2×Q8×C12712yes—
431C24C2×Q8×C12712yes—
432C24C24×C12711yescharacteristic
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—44no—
436C2×D4—48no—
437C2×D4—48no—
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—21no—
452C22×C4—21no—
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×C4—22no—
480C22×C4C2×D4×C12714yes—
481C22×C4C2×D4×C12714yes—
482C22×C4C2×D4×C12714yes—
483C22×C4C2×Q8×C12712yes—
484C22×C4#41×C12714yes—
485C4⋊C4—48no—
486C4⋊C4—48no—
487C4⋊C4—48no—
488C4⋊C4—48no—
489C22⋊C4—44no—
490C22⋊C4—44no—
491C22⋊C4—48no—
492C22⋊C4—44no—
493C22⋊C4—48no—
494C22⋊C4—48no—
495C22⋊C4—48no—
496C22⋊C4—44no—
497C23—22no—
498C23—22no—
499C23—22no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—24no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—41no—
520C23—41no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—41no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—41no—
538C23—41no—
539C23C22×D4×C12712yes—
540C23C22×Q8×C12711yescharacteristic
541C23C2×#41×C12712yes—
542C23H(5,𝔽2)×C12712yes—
543C23H(5,𝔽2)×C12712yes—
544C23H(5,𝔽2)×C12712yes—
545C23H(5,𝔽2)×C12711yescharacteristic
546C23H(5,𝔽2)×C12711yescharacteristic
547C232−1+4×C12712yes—
548D4—416no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
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—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C22—42no—
597C22—42no—
598C22—42no—
599C22—42no—
600C22—44no—
601C22—44no—
602C22—44no—
603C22—44no—
604C22—42no—
605C22—42no—
606C22—82no—
607C22—82no—
608C22—82no—
609C22—82no—
610C22—82no—
611C22—82no—
612C22—82no—
613C22—82no—
614C22#534×C12712yes—
615C22#535×C12712yes—
616C22#537×C12712yes—
617C22#539×C12712yes—
618C22#540×C12712yes—
619C22#542×C12712yes—
620C22#543×C12711yescharacteristic
621C22#543×C12711yescharacteristic
622C22#543×C12711yescharacteristic
623C22D42×C12711yescharacteristic
624C22#546×C12712yes—
625C22D4×Q8×C12712yes—
626C22#550×C12712yes—
627C22#551×C12711yescharacteristic
628C22#554×C12712yes—
629C22#560×C12712yes—
630C22#560×C12712yes—
631C22#560×C12711yescharacteristic
632C22#562×C12712yes—
633C22#562×C12712yes—
634C22#563×C12711yescharacteristic
635C4—42no—
636C4—44no—
637C4—44no—
638C4—44no—
639C4—44no—
640C4—82no—
641C4—82no—
642C2—82no—
643C2—82no—
644C2C127×#267312yes—
645C2C127×#268311yescharacteristic
646C2C127×#269212yes—
647C2C127×#270512yes—
648C2C127×#273212yes—
649C2C127×#274811yescharacteristic
650C2C127×#281312yes—
651C2C127×#283712yes—
652C2C127×#284211yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#399×C127C2semidirect
2. C2×#396×C127C2semidirect
3. C127×#1441C2semidirect
4. C127×#1441C2semidirect
5. C127×#1439C2semidirect
6. C127×#1439C2semidirect
58. C2×C4⋊C4×C127D4semidirect
315. #17136C127direct (N × H)
327. C2×#399C2×C127semidirect
328. C2×#396C2×C127semidirect
329. #1441C2×C127semidirect
330. #1441C2×C127semidirect
331. #1439C2×C127semidirect
332. #1439C2×C127semidirect
336. C127#17136direct (N × H)
385. C2×C4⋊C4D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#399×C1272
C2×#396×C1272
C127×#14412
C127×#14392
C127×#14382
#17136127