Finite Group Databasebeta

← C127×#16094 #44579767

Subgroups — C127×#16094 #44579767

Order 32512.

1906 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#124×C127C211yesmaximal, characteristic
2C2×#391×C127C211yesmaximal, characteristic, complemented
3C2×#388×C127C212yesmaximal, complemented
4C127×#1446C211yesmaximal, characteristic, complemented
5C127×#1440C212yesmaximal, complemented
6C127×#1439C212yesmaximal, complemented
7C127×#1439C212yesmaximal, complemented
8C127×#1438C212yesmaximal
9C127×#1436C212yesmaximal, complemented
10C23×Q8×C127C2211yescharacteristic
11C23×D4×C127C2211yescharacteristic
12C2×#124×C127—24no—
13C2×#124×C127—28no—
14C22×C4⋊C4×C127C2212yes—
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C22⋊C4×C127C2212yes—
17C22×C22⋊C4×C127C2212yes—
18C22×C22⋊C4×C127C2212yes—
19C22×C22⋊C4×C127C2212yes—
20C22×C22⋊C4×C127C2212yes—
21C22×C22⋊C4×C127C2212yes—
22C22×C42×C127C2211yescharacteristic
23C22×C42×C127C2211yescharacteristic
24#391×C127—24no—
25#388×C127—28no—
26C2×#95×C127C2212yes—
27C2×#95×C127C2212yes—
28C2×#95×C127C2212yes—
29C2×#95×C127C2212yes—
30C2×#95×C127C2212yes—
31C2×#95×C127C2212yes—
32C2×#95×C127C2212yes—
33C2×#95×C127C2211yescharacteristic
34C2×#95×C127C2211yescharacteristic
35C25×C127C2312yes—
36C22×Q8×C127—24no—
37C22×Q8×C127—24no—
38C22×Q8×C127—41no—
39C22×Q8×C127—41no—
40C22×Q8×C127D414yes—
41C22×D4×C127—24no—
42C22×D4×C127—22no—
43C22×D4×C127—24no—
44C22×D4×C127—41no—
45C22×D4×C127—41no—
46C23×C4×C127C2312yes—
47C23×C4×C127C2312yes—
48C23×C4×C127C2312yes—
49C23×C4×C127C2311yescharacteristic
50C23×C4×C127C2312yes—
51C23×C4×C127C2312yes—
52C23×C4×C127C2311yescharacteristic
53C23×C4×C127C2311yescharacteristic
54#124×C127—232no—
55C2×C4⋊C4×C127—24no—
56C2×C4⋊C4×C127—22no—
57C2×C4⋊C4×C127—24no—
58C2×C4⋊C4×C127—42no—
59C2×C4⋊C4×C127—41no—
60C2×C4⋊C4×C127—41no—
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—24no—
68C2×C22⋊C4×C127—24no—
69C2×C22⋊C4×C127—24no—
70C2×C22⋊C4×C127—24no—
71C2×C22⋊C4×C127—24no—
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—42no—
78C2×C22⋊C4×C127D418yes—
79C2×C42×C127—24no—
80C2×C42×C127—22no—
81C2×C42×C127—24no—
82C2×C42×C127—22no—
83#95×C127—24no—
84#95×C127—24no—
85#95×C127—24no—
86#95×C127—24no—
87#95×C127—24no—
88#95×C127—24no—
89#95×C127—41no—
90#95×C127—42no—
91#95×C127—41no—
92C24×C127—22no—
93C24×C127—22no—
94C24×C127—22no—
95C24×C127—22no—
96C24×C127—22no—
97C24×C127—22no—
98C24×C127—22no—
99C24×C127—22no—
100C24×C127—22no—
101C24×C127—22no—
102C24×C127—22no—
103C24×C127—22no—
104C24×C127—22no—
105C24×C127—22no—
106C24×C127C2×D414yes—
107C24×C127C2411yescharacteristic
108C2×Q8×C127—28no—
109C2×Q8×C127—28no—
110C2×Q8×C127—44no—
111C2×Q8×C127—48no—
112C2×Q8×C127—48no—
113C2×D4×C127—28no—
114C2×D4×C127—48no—
115C2×D4×C127—48no—
116C2×D4×C127—44no—
117C2×D4×C127—44no—
118C22×C4×C127—22no—
119C22×C4×C127—22no—
120C22×C4×C127—21no—
121C22×C4×C127—21no—
122C22×C4×C127—21no—
123C22×C4×C127—21no—
124C22×C4×C127—22no—
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—22no—
135C22×C4×C127—22no—
136C22×C4×C127—22no—
137C22×C4×C127—22no—
138C22×C4×C127—22no—
139C22×C4×C127—22no—
140C22×C4×C127—21no—
141C22×C4×C127—21no—
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×C127—22no—
159C22×C4×C127—22no—
160C22×C4×C127C2×D412yes—
161C22×C4×C127C2×D414yes—
162C22×C4×C127C2×D414yes—
163C22×C4×C127C2×D412yes—
164C22×C4×C127C2×D412yes—
165C22×C4×C127#4114yes—
166C22×C4×C127#4114yes—
167C22×C4×C127#4114yes—
168C4⋊C4×C127—48no—
169C4⋊C4×C127—44no—
170C22⋊C4×C127—216no—
171C22⋊C4×C127—216no—
172C22⋊C4×C127—216no—
173C22⋊C4×C127—48no—
174C22⋊C4×C127—48no—
175C22⋊C4×C127—48no—
176C42×C127—28no—
177C42×C127—44no—
178C23×C127—24no—
179C23×C127—24no—
180C23×C127—24no—
181C23×C127—24no—
182C23×C127—24no—
183C23×C127—24no—
184C23×C127—24no—
185C23×C127—42no—
186C23×C127—42no—
187C23×C127—42no—
188C23×C127—42no—
189C23×C127—42no—
190C23×C127—42no—
191C23×C127—42no—
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×C127—42no—
204C23×C127—42no—
205C23×C127—42no—
206C23×C127—42no—
207C23×C127—42no—
208C23×C127—42no—
209C23×C127—42no—
210C23×C127—42no—
211C23×C127—42no—
212C23×C127—42no—
213C23×C127C22×D411yescharacteristic
214C23×C127C22×D412yes—
215C23×C127C2×#4112yes—
216C23×C127C2×#4112yes—
217C23×C127C2×#4112yes—
218C23×C127H(5,𝔽2)11yescharacteristic
219C23×C127H(5,𝔽2)11yescharacteristic
220C23×C127H(5,𝔽2)12yes—
221C23×C1272−1+412yes—
222Q8×C127—416no—
223D4×C127—416no—
224C2×C4×C127—22no—
225C2×C4×C127—22no—
226C2×C4×C127—22no—
227C2×C4×C127—22no—
228C2×C4×C127—24no—
229C2×C4×C127—24no—
230C2×C4×C127—24no—
231C2×C4×C127—24no—
232C2×C4×C127—24no—
233C2×C4×C127—22no—
234C2×C4×C127—22no—
235C2×C4×C127—24no—
236C2×C4×C127—24no—
237C2×C4×C127—24no—
238C2×C4×C127—22no—
239C2×C4×C127—24no—
240C2×C4×C127—24no—
241C2×C4×C127—24no—
242C2×C4×C127—24no—
243C2×C4×C127—24no—
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—
269C2×C4×C127—42no—
270C2×C4×C127—42no—
271C2×C4×C127—42no—
272C2×C4×C127#12014yes—
273C2×C4×C127#12314yes—
274C22×C127—44no—
275C22×C127—44no—
276C22×C127—44no—
277C22×C127—44no—
278C22×C127—44no—
279C22×C127—44no—
280C22×C127—44no—
281C22×C127—82no—
282C22×C127—82no—
283C22×C127—82no—
284C22×C127—82no—
285C22×C127—82no—
286C22×C127—82no—
287C22×C127—82no—
288C22×C127—82no—
289C22×C127C2×#12011yescharacteristic
290C22×C127C2×#12311yescharacteristic
291C22×C127#52512yes—
292C22×C127#52912yes—
293C22×C127#53411yescharacteristic
294C22×C127#53712yes—
295C22×C127#53812yes—
296C22×C127#54212yes—
297C22×C127#54212yes—
298C22×C127#54612yes—
299C22×C127#54612yes—
300C22×C127#54612yes—
301C22×C127#54712yes—
302C22×C127#54812yes—
303C22×C127#55012yes—
304C22×C127#55511yescharacteristic
305C22×C127#55511yescharacteristic
306C22×C127#55612yes—
307C22×C127#55912yes—
308C22×C127H(3,𝔽4)11yescharacteristic
309C22×C127#56311yescharacteristic
310C4×C127—24no—
311C4×C127—24no—
312C4×C127—42no—
313C4×C127—44no—
314C4×C127—44no—
315C4×C127—44no—
316C4×C127—82no—
317C4×C127—82no—
318#16094C12711yesmaximal, characteristic, direct product factor, Sylow
319C2×C127—84no—
320C2×C127#240511yescharacteristic
321C2×C127#240712yes—
322C2×C127#244812yes—
323C2×C127#245912yes—
324C2×C127#247412yes—
325C2×C127#271212yes—
326C2×C127#271512yes—
327C2×C127#273111yescharacteristic
328C2×C127#273311yescharacteristic
329C22×#124C2×C12711yescharacteristic
330C2×#391C2×C12711yescharacteristic, complemented
331C2×#388C2×C12712yescomplemented
332#1446C2×C12711yescharacteristic, complemented
333#1440C2×C12712yescomplemented
334#1439C2×C12712yescomplemented
335#1439C2×C12712yescomplemented
336#1438C2×C12712yes—
337#1436C2×C12712yescomplemented
338C127#1609411yescharacteristic, direct product factor, Sylow
339C23×Q8C22×C12711yescharacteristic
340C23×D4C22×C12711yescharacteristic
341C2×#124—24no—
342C2×#124—28no—
343C22×C4⋊C4C22×C12712yes—
344C22×C4⋊C4C22×C12711yescharacteristic
345C22×C22⋊C4C22×C12712yes—
346C22×C22⋊C4C22×C12712yes—
347C22×C22⋊C4C22×C12712yes—
348C22×C22⋊C4C22×C12712yes—
349C22×C22⋊C4C22×C12712yes—
350C22×C22⋊C4C22×C12712yes—
351C22×C42C22×C12711yescharacteristic
352C22×C42C22×C12711yescharacteristic
353#391—24no—
354#388—28no—
355C2×#95C22×C12712yes—
356C2×#95C22×C12712yes—
357C2×#95C22×C12712yes—
358C2×#95C22×C12712yes—
359C2×#95C22×C12712yes—
360C2×#95C22×C12712yes—
361C2×#95C22×C12712yes—
362C2×#95C22×C12711yescharacteristic
363C2×#95C22×C12711yescharacteristic
364C25C23×C12712yes—
365C22×Q8—24no—
366C22×Q8—24no—
367C22×Q8—41no—
368C22×Q8—41no—
369C22×Q8D4×C12714yes—
370C22×D4—24no—
371C22×D4—22no—
372C22×D4—24no—
373C22×D4—41no—
374C22×D4—41no—
375C23×C4C23×C12712yes—
376C23×C4C23×C12712yes—
377C23×C4C23×C12712yes—
378C23×C4C23×C12711yescharacteristic
379C23×C4C23×C12712yes—
380C23×C4C23×C12712yes—
381C23×C4C23×C12711yescharacteristic
382C23×C4C23×C12711yescharacteristic
383#124—232no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—42no—
388C2×C4⋊C4—41no—
389C2×C4⋊C4—41no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4D4×C12718yes—
408C2×C42—24no—
409C2×C42—22no—
410C2×C42—24no—
411C2×C42—22no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—41no—
419#95—42no—
420#95—41no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24C2×D4×C12714yes—
436C24C24×C12711yescharacteristic
437C2×Q8—28no—
438C2×Q8—28no—
439C2×Q8—44no—
440C2×Q8—48no—
441C2×Q8—48no—
442C2×D4—28no—
443C2×D4—48no—
444C2×D4—48no—
445C2×D4—44no—
446C2×D4—44no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
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—21no—
470C22×C4—21no—
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×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4C2×D4×C12712yes—
490C22×C4C2×D4×C12714yes—
491C22×C4C2×D4×C12714yes—
492C22×C4C2×D4×C12712yes—
493C22×C4C2×D4×C12712yes—
494C22×C4#41×C12714yes—
495C22×C4#41×C12714yes—
496C22×C4#41×C12714yes—
497C4⋊C4—48no—
498C4⋊C4—44no—
499C22⋊C4—216no—
500C22⋊C4—216no—
501C22⋊C4—216no—
502C22⋊C4—48no—
503C22⋊C4—48no—
504C22⋊C4—48no—
505C42—28no—
506C42—44no—
507C23—24no—
508C23—24no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23C22×D4×C12711yescharacteristic
543C23C22×D4×C12712yes—
544C23C2×#41×C12712yes—
545C23C2×#41×C12712yes—
546C23C2×#41×C12712yes—
547C23H(5,𝔽2)×C12711yescharacteristic
548C23H(5,𝔽2)×C12711yescharacteristic
549C23H(5,𝔽2)×C12712yes—
550C232−1+4×C12712yes—
551Q8—416no—
552D4—416no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
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—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4#120×C12714yes—
602C2×C4#123×C12714yes—
603C22—44no—
604C22—44no—
605C22—44no—
606C22—44no—
607C22—44no—
608C22—44no—
609C22—44no—
610C22—82no—
611C22—82no—
612C22—82no—
613C22—82no—
614C22—82no—
615C22—82no—
616C22—82no—
617C22—82no—
618C22C2×#120×C12711yescharacteristic
619C22C2×#123×C12711yescharacteristic
620C22#525×C12712yes—
621C22#529×C12712yes—
622C22#534×C12711yescharacteristic
623C22#537×C12712yes—
624C22#538×C12712yes—
625C22#542×C12712yes—
626C22#542×C12712yes—
627C22#546×C12712yes—
628C22#546×C12712yes—
629C22#546×C12712yes—
630C22#547×C12712yes—
631C22#548×C12712yes—
632C22#550×C12712yes—
633C22#555×C12711yescharacteristic
634C22#555×C12711yescharacteristic
635C22#556×C12712yes—
636C22#559×C12712yes—
637C22H(3,𝔽4)×C12711yescharacteristic
638C22#563×C12711yescharacteristic
639C4—24no—
640C4—24no—
641C4—42no—
642C4—44no—
643C4—44no—
644C4—44no—
645C4—82no—
646C4—82no—
647C2—84no—
648C2C127×#240511yescharacteristic
649C2C127×#240712yes—
650C2C127×#244812yes—
651C2C127×#245912yes—
652C2C127×#247412yes—
653C2C127×#271212yes—
654C2C127×#271512yes—
655C2C127×#273111yescharacteristic
656C2C127×#273311yescharacteristic
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
2. C2×#391×C127C2semidirect
3. C2×#388×C127C2semidirect
4. C127×#1446C2semidirect
5. C127×#1440C2semidirect
6. C127×#1439C2semidirect
7. C127×#1439C2semidirect
9. C127×#1436C2semidirect
318. #16094C127direct (N × H)
330. C2×#391C2×C127semidirect
331. C2×#388C2×C127semidirect
332. #1446C2×C127semidirect
333. #1440C2×C127semidirect
334. #1439C2×C127semidirect
335. #1439C2×C127semidirect
337. #1436C2×C127semidirect
338. C127#16094direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#124×C1272
C2×#391×C1272
C2×#388×C1272
C127×#14462
C127×#14402
C127×#14392
C127×#14382
C127×#14362
#16094127