Finite Group Databasebeta

← C127×#10969 #44574642

Subgroups — C127×#10969 #44574642

Order 32512.

1922 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C127C211yesmaximal, characteristic
2C22×#102×C127C212yesmaximal, complemented
3C22×C22⋊C8×C127C211yesmaximal, characteristic, complemented
4C2×#380×C127C211yesmaximal, characteristic, complemented
5C2×#340×C127C212yesmaximal, complemented
6C23×D4×C127—21no—
7C23×D4×C127C2211yescharacteristic
8C24×C4×C127C2211yescharacteristic
9C23×C8×C127C2212yes—
10C2×#121×C127—24no—
11C2×#121×C127—22no—
12C2×#121×C127—24no—
13C2×#121×C127C414yescomplemented
14C22×C4⋊C4×C127C2212yes—
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C22⋊C4×C127—21no—
17C22×C22⋊C4×C127—21no—
18C2×#102×C127—24no—
19C2×#102×C127—24no—
20C2×#102×C127—24no—
21C2×C22⋊C8×C127—22no—
22C2×C22⋊C8×C127—24no—
23#380×C127—24no—
24C2×#95×C127—21no—
25#340×C127—24no—
26C25×C127—21no—
27C25×C127D411yescharacteristic
28C22×D4×C127—28no—
29C22×D4×C127—24no—
30C22×D4×C127—22no—
31C22×D4×C127—22no—
32C22×D4×C127—22no—
33C22×D4×C127—21no—
34C22×D4×C127—22no—
35C22×D4×C127—22no—
36C22×D4×C127—44no—
37C22×D4×C127—42no—
38C22×D4×C127—42no—
39C22×D4×C127C2×C412yes—
40C22×D4×C127D414yes—
41C23×C4×C127—21no—
42C23×C4×C127—22no—
43C23×C4×C127—22no—
44C23×C4×C127—22no—
45C23×C4×C127—22no—
46C23×C4×C127—22no—
47C23×C4×C127—22no—
48C23×C4×C127—22no—
49C23×C4×C127C2×C412yes—
50C23×C4×C127D411yescharacteristic
51C23×C4×C127D412yes—
52C23×C4×C127C2311yescharacteristic
53C22×C8×C127—22no—
54C22×C8×C127—22no—
55C22×C8×C127—22no—
56C22×C8×C127—22no—
57C22×C8×C127—22no—
58C22×C8×C127—22no—
59C22×C8×C127D414yescomplemented
60#121×C127—216no—
61#121×C127—28no—
62#121×C127—28no—
63C2×C4⋊C4×C127—22no—
64C2×C4⋊C4×C127—21no—
65C2×C4⋊C4×C127—22no—
66C2×C4⋊C4×C127—22no—
67C2×C4⋊C4×C127—22no—
68C2×C4⋊C4×C127—22no—
69C2×C4⋊C4×C127—22no—
70C2×C4⋊C4×C127C2×C412yes—
71C2×C4⋊C4×C127D414yes—
72C2×C4⋊C4×C127D414yescomplemented
73C2×C22⋊C4×C127—28no—
74C2×C22⋊C4×C127—24no—
75C2×C22⋊C4×C127—24no—
76C2×C22⋊C4×C127—42no—
77C2×C22⋊C4×C127—42no—
78#102×C127—216no—
79C22⋊C8×C127—28no—
80#95×C127—24no—
81C24×C127—21no—
82C24×C127—22no—
83C24×C127—22no—
84C24×C127—21no—
85C24×C127—22no—
86C24×C127—21no—
87C24×C127—22no—
88C24×C127—21no—
89C24×C127—22no—
90C24×C127—24no—
91C24×C127—41no—
92C24×C127—42no—
93C24×C127—41no—
94C24×C127—41no—
95C24×C127—41no—
96C24×C127—42no—
97C24×C127—42no—
98C24×C127—41no—
99C24×C127—41no—
100C24×C127C22⋊C412yes—
101C24×C127D812yes—
102C24×C127SD1612yes—
103C24×C127C2×D411yescharacteristic
104C2×D4×C127—216no—
105C2×D4×C127—22no—
106C2×D4×C127—24no—
107C2×D4×C127—24no—
108C2×D4×C127—24no—
109C2×D4×C127—24no—
110C2×D4×C127—24no—
111C2×D4×C127—24no—
112C2×D4×C127—24no—
113C2×D4×C127—48no—
114C2×D4×C127—416no—
115C2×D4×C127—416no—
116C2×D4×C127—48no—
117C2×D4×C127—41no—
118C2×D4×C127—42no—
119C2×D4×C127—42no—
120C2×D4×C127—42no—
121C2×D4×C127—41no—
122C2×D4×C127—42no—
123C2×D4×C127—42no—
124C2×D4×C127C22⋊C414yescomplemented
125C22×C4×C127—22no—
126C22×C4×C127—21no—
127C22×C4×C127—22no—
128C22×C4×C127—24no—
129C22×C4×C127—22no—
130C22×C4×C127—21no—
131C22×C4×C127—22no—
132C22×C4×C127—22no—
133C22×C4×C127—24no—
134C22×C4×C127—24no—
135C22×C4×C127—22no—
136C22×C4×C127—24no—
137C22×C4×C127—24no—
138C22×C4×C127—22no—
139C22×C4×C127—24no—
140C22×C4×C127—41no—
141C22×C4×C127—41no—
142C22×C4×C127—42no—
143C22×C4×C127—42no—
144C22×C4×C127—42no—
145C22×C4×C127—42no—
146C22×C4×C127—42no—
147C22×C4×C127—42no—
148C22×C4×C127—42no—
149C22×C4×C127—42no—
150C22×C4×C127—42no—
151C22×C4×C127—42no—
152C22×C4×C127—42no—
153C22×C4×C127—42no—
154C22×C4×C127—42no—
155C22×C4×C127—42no—
156C22×C4×C127—42no—
157C22×C4×C127C22⋊C412yes—
158C22×C4×C127C22×C411yescharacteristic
159C22×C4×C127C2×D412yes—
160C22×C4×C127C2×D412yes—
161C22×C4×C127C2×D412yes—
162C22×C4×C127C2×D412yes—
163C22×C4×C127C2×D411yescharacteristic
164C22×C4×C127#4112yes—
165C22×C4×C127#4112yes—
166C2×C8×C127—24no—
167C2×C8×C127—24no—
168C2×C8×C127—24no—
169C2×C8×C127—42no—
170C2×C8×C127—42no—
171C2×C8×C127—42no—
172C2×C8×C127—42no—
173C4⋊C4×C127—22no—
174C4⋊C4×C127—24no—
175C4⋊C4×C127—24no—
176C4⋊C4×C127—24no—
177C4⋊C4×C127—42no—
178C4⋊C4×C127—42no—
179C4⋊C4×C127C22⋊C414yescomplemented
180C22⋊C4×C127—216no—
181C22⋊C4×C127—48no—
182C23×C127—22no—
183C23×C127—22no—
184C23×C127—22no—
185C23×C127—22no—
186C23×C127—22no—
187C23×C127—22no—
188C23×C127—22no—
189C23×C127—24no—
190C23×C127—22no—
191C23×C127—24no—
192C23×C127—24no—
193C23×C127—24no—
194C23×C127—22no—
195C23×C127—22no—
196C23×C127—24no—
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—44no—
208C23×C127—44no—
209C23×C127—42no—
210C23×C127—42no—
211C23×C127—42no—
212C23×C127—42no—
213C23×C127—44no—
214C23×C127—44no—
215C23×C127—44no—
216C23×C127—44no—
217C23×C127—81no—
218C23×C127—81no—
219C23×C127—82no—
220C23×C127—82no—
221C23×C127—82no—
222C23×C127—82no—
223C23×C127—82no—
224C23×C127—81no—
225C23×C127—81no—
226C23×C127—82no—
227C23×C127#10214yescomplemented
228C23×C127C2×C22⋊C411yescharacteristic
229C23×C127#12012yes—
230C23×C127#12011yescharacteristic
231C23×C127#12112yes—
232C23×C127#12311yescharacteristic
233C23×C127C2×D811yescharacteristic
234C23×C127C2×SD1611yescharacteristic
235C23×C127#13512yes—
236C23×C127AGL(1,ℤ/8)11yescharacteristic
237C23×C127AGL(1,ℤ/8)12yes—
238C23×C127#13711yescharacteristic
239D4×C127—28no—
240D4×C127—432no—
241D4×C127—44no—
242D4×C127—44no—
243D4×C127—44no—
244C2×C4×C127—22no—
245C2×C4×C127—24no—
246C2×C4×C127—22no—
247C2×C4×C127—22no—
248C2×C4×C127—42no—
249C2×C4×C127—42no—
250C2×C4×C127—42no—
251C2×C4×C127—42no—
252C2×C4×C127—44no—
253C2×C4×C127—44no—
254C2×C4×C127—44no—
255C2×C4×C127—44no—
256C2×C4×C127—44no—
257C2×C4×C127—44no—
258C2×C4×C127—44no—
259C2×C4×C127—44no—
260C2×C4×C127—44no—
261C2×C4×C127—82no—
262C2×C4×C127—82no—
263C2×C4×C127—82no—
264C2×C4×C127—82no—
265C2×C4×C127C2×C22⋊C411yescharacteristic
266C2×C4×C127C2×C22⋊C411yescharacteristic
267C2×C4×C127C4×D412yes—
268C2×C4×C127C4×D412yes—
269C2×C4×C127#12012yes—
270C2×C4×C127#12011yescharacteristic
271C2×C4×C127#12012yes—
272C2×C4×C127#12112yes—
273C2×C4×C127#12112yes—
274C2×C4×C127#12112yes—
275C2×C4×C127#12112yes—
276C2×C4×C127#12112yes—
277C2×C4×C127#12312yes—
278C2×C4×C127#12311yescharacteristic
279C2×C4×C127#12412yes—
280C2×C4×C127#12712yes—
281C8×C127—44no—
282C22×C127—24no—
283C22×C127—24no—
284C22×C127—24no—
285C22×C127—42no—
286C22×C127—42no—
287C22×C127—42no—
288C22×C127—44no—
289C22×C127—44no—
290C22×C127—44no—
291C22×C127—44no—
292C22×C127—42no—
293C22×C127—44no—
294C22×C127—44no—
295C22×C127—44no—
296C22×C127—82no—
297C22×C127—82no—
298C22×C127—82no—
299C22×C127—82no—
300C22×C127—84no—
301C22×C127—84no—
302C22×C127—84no—
303C22×C127—84no—
304C22×C127#37911yescharacteristic
305C22×C127#38611yescharacteristic
306C22×C127#38611yescharacteristic
307C22×C127#39212yes—
308C22×C127#39412yes—
309C22×C127C2×#10211yescharacteristic
310C22×C127#41611yescharacteristic
311C22×C127#41711yescharacteristic
312C22×C127#41811yescharacteristic
313C22×C127#44711yescharacteristic
314C22×C127#44712yes—
315C22×C127#44811yescharacteristic
316C22×C127#44912yes—
317C22×C127#44912yes—
318C22×C127#45012yes—
319C22×C127#45212yes—
320C22×C127#46512yes—
321C22×C127#46612yes—
322C22×C127#46812yes—
323C22×C127#46912yes—
324C22×C127#48011yescharacteristic
325C22×C127#48111yescharacteristic
326C22×C127#48212yes—
327C4×C127—42no—
328C4×C127—44no—
329C4×C127—84no—
330C4×C127#38612yes—
331C4×C127#39012yes—
332C4×C127#39212yes—
333C4×C127#39412yes—
334#10969C12711yesmaximal, characteristic, direct product factor, Sylow
335C2×C127—44no—
336C2×C127—84no—
337C2×C127#143811yescharacteristic
338C2×C127#178611yescharacteristic
339C2×C127#178811yescharacteristic
340C2×C127#187411yescharacteristic
341C2×C127#187511yescharacteristic
342C2×C127#189311yescharacteristic
343C2×C127#189511yescharacteristic
344C2×C127#199912yes—
345C2×C127#200012yes—
346C2×C127#203312yes—
347C2×C127#203412yes—
348C22×#121C2×C12711yescharacteristic
349C22×#102C2×C12712yescomplemented
350C22×C22⋊C8C2×C12711yescharacteristic, complemented
351C2×#380C2×C12711yescharacteristic, complemented
352C2×#340C2×C12712yescomplemented
353C127#1096911yescharacteristic, direct product factor, Sylow
354C23×D4—21no—
355C23×D4C22×C12711yescharacteristic
356C24×C4C22×C12711yescharacteristic
357C23×C8C22×C12712yes—
358C2×#121—24no—
359C2×#121—22no—
360C2×#121—24no—
361C2×#121C4×C12714yescomplemented
362C22×C4⋊C4C22×C12712yes—
363C22×C4⋊C4C22×C12711yescharacteristic
364C22×C22⋊C4—21no—
365C22×C22⋊C4—21no—
366C2×#102—24no—
367C2×#102—24no—
368C2×#102—24no—
369C2×C22⋊C8—22no—
370C2×C22⋊C8—24no—
371#380—24no—
372C2×#95—21no—
373#340—24no—
374C25—21no—
375C25D4×C12711yescharacteristic
376C22×D4—28no—
377C22×D4—24no—
378C22×D4—22no—
379C22×D4—22no—
380C22×D4—22no—
381C22×D4—21no—
382C22×D4—22no—
383C22×D4—22no—
384C22×D4—44no—
385C22×D4—42no—
386C22×D4—42no—
387C22×D4C2×C4×C12712yes—
388C22×D4D4×C12714yes—
389C23×C4—21no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4C2×C4×C12712yes—
398C23×C4D4×C12711yescharacteristic
399C23×C4D4×C12712yes—
400C23×C4C23×C12711yescharacteristic
401C22×C8—22no—
402C22×C8—22no—
403C22×C8—22no—
404C22×C8—22no—
405C22×C8—22no—
406C22×C8—22no—
407C22×C8D4×C12714yescomplemented
408#121—216no—
409#121—28no—
410#121—28no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4C2×C4×C12712yes—
419C2×C4⋊C4D4×C12714yes—
420C2×C4⋊C4D4×C12714yescomplemented
421C2×C22⋊C4—28no—
422C2×C22⋊C4—24no—
423C2×C22⋊C4—24no—
424C2×C22⋊C4—42no—
425C2×C22⋊C4—42no—
426#102—216no—
427C22⋊C8—28no—
428#95—24no—
429C24—21no—
430C24—22no—
431C24—22no—
432C24—21no—
433C24—22no—
434C24—21no—
435C24—22no—
436C24—21no—
437C24—22no—
438C24—24no—
439C24—41no—
440C24—42no—
441C24—41no—
442C24—41no—
443C24—41no—
444C24—42no—
445C24—42no—
446C24—41no—
447C24—41no—
448C24C22⋊C4×C12712yes—
449C24D8×C12712yes—
450C24SD16×C12712yes—
451C24C2×D4×C12711yescharacteristic
452C2×D4—216no—
453C2×D4—22no—
454C2×D4—24no—
455C2×D4—24no—
456C2×D4—24no—
457C2×D4—24no—
458C2×D4—24no—
459C2×D4—24no—
460C2×D4—24no—
461C2×D4—48no—
462C2×D4—416no—
463C2×D4—416no—
464C2×D4—48no—
465C2×D4—41no—
466C2×D4—42no—
467C2×D4—42no—
468C2×D4—42no—
469C2×D4—41no—
470C2×D4—42no—
471C2×D4—42no—
472C2×D4C22⋊C4×C12714yescomplemented
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—24no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4C22⋊C4×C12712yes—
506C22×C4C22×C4×C12711yescharacteristic
507C22×C4C2×D4×C12712yes—
508C22×C4C2×D4×C12712yes—
509C22×C4C2×D4×C12712yes—
510C22×C4C2×D4×C12712yes—
511C22×C4C2×D4×C12711yescharacteristic
512C22×C4#41×C12712yes—
513C22×C4#41×C12712yes—
514C2×C8—24no—
515C2×C8—24no—
516C2×C8—24no—
517C2×C8—42no—
518C2×C8—42no—
519C2×C8—42no—
520C2×C8—42no—
521C4⋊C4—22no—
522C4⋊C4—24no—
523C4⋊C4—24no—
524C4⋊C4—24no—
525C4⋊C4—42no—
526C4⋊C4—42no—
527C4⋊C4C22⋊C4×C12714yescomplemented
528C22⋊C4—216no—
529C22⋊C4—48no—
530C23—22no—
531C23—22no—
532C23—22no—
533C23—22no—
534C23—22no—
535C23—22no—
536C23—22no—
537C23—24no—
538C23—22no—
539C23—24no—
540C23—24no—
541C23—24no—
542C23—22no—
543C23—22no—
544C23—24no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23—42no—
554C23—42no—
555C23—44no—
556C23—44no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—44no—
562C23—44no—
563C23—44no—
564C23—44no—
565C23—81no—
566C23—81no—
567C23—82no—
568C23—82no—
569C23—82no—
570C23—82no—
571C23—82no—
572C23—81no—
573C23—81no—
574C23—82no—
575C23#102×C12714yescomplemented
576C23C2×C22⋊C4×C12711yescharacteristic
577C23#120×C12712yes—
578C23#120×C12711yescharacteristic
579C23#121×C12712yes—
580C23#123×C12711yescharacteristic
581C23C2×D8×C12711yescharacteristic
582C23C2×SD16×C12711yescharacteristic
583C23#135×C12712yes—
584C23AGL(1,ℤ/8)×C12711yescharacteristic
585C23AGL(1,ℤ/8)×C12712yes—
586C23#137×C12711yescharacteristic
587D4—28no—
588D4—432no—
589D4—44no—
590D4—44no—
591D4—44no—
592C2×C4—22no—
593C2×C4—24no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—44no—
601C2×C4—44no—
602C2×C4—44no—
603C2×C4—44no—
604C2×C4—44no—
605C2×C4—44no—
606C2×C4—44no—
607C2×C4—44no—
608C2×C4—44no—
609C2×C4—82no—
610C2×C4—82no—
611C2×C4—82no—
612C2×C4—82no—
613C2×C4C2×C22⋊C4×C12711yescharacteristic
614C2×C4C2×C22⋊C4×C12711yescharacteristic
615C2×C4C4×D4×C12712yes—
616C2×C4C4×D4×C12712yes—
617C2×C4#120×C12712yes—
618C2×C4#120×C12711yescharacteristic
619C2×C4#120×C12712yes—
620C2×C4#121×C12712yes—
621C2×C4#121×C12712yes—
622C2×C4#121×C12712yes—
623C2×C4#121×C12712yes—
624C2×C4#121×C12712yes—
625C2×C4#123×C12712yes—
626C2×C4#123×C12711yescharacteristic
627C2×C4#124×C12712yes—
628C2×C4#127×C12712yes—
629C8—44no—
630C22—24no—
631C22—24no—
632C22—24no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—44no—
637C22—44no—
638C22—44no—
639C22—44no—
640C22—42no—
641C22—44no—
642C22—44no—
643C22—44no—
644C22—82no—
645C22—82no—
646C22—82no—
647C22—82no—
648C22—84no—
649C22—84no—
650C22—84no—
651C22—84no—
652C22#379×C12711yescharacteristic
653C22#386×C12711yescharacteristic
654C22#386×C12711yescharacteristic
655C22#392×C12712yes—
656C22#394×C12712yes—
657C22C2×#102×C12711yescharacteristic
658C22#416×C12711yescharacteristic
659C22#417×C12711yescharacteristic
660C22#418×C12711yescharacteristic
661C22#447×C12711yescharacteristic
662C22#447×C12712yes—
663C22#448×C12711yescharacteristic
664C22#449×C12712yes—
665C22#449×C12712yes—
666C22#450×C12712yes—
667C22#452×C12712yes—
668C22#465×C12712yes—
669C22#466×C12712yes—
670C22#468×C12712yes—
671C22#469×C12712yes—
672C22#480×C12711yescharacteristic
673C22#481×C12711yescharacteristic
674C22#482×C12712yes—
675C4—42no—
676C4—44no—
677C4—84no—
678C4#386×C12712yes—
679C4#390×C12712yes—
680C4#392×C12712yes—
681C4#394×C12712yes—
682C2—44no—
683C2—84no—
684C2C127×#143811yescharacteristic
685C2C127×#178611yescharacteristic
686C2C127×#178811yescharacteristic
687C2C127×#187411yescharacteristic
688C2C127×#187511yescharacteristic
689C2C127×#189311yescharacteristic
690C2C127×#189511yescharacteristic
691C2C127×#199912yes—
692C2C127×#200012yes—
693C2C127×#203312yes—
694C2C127×#203412yes—
subgroupG/H
center, socleC24×C127C2×D4
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC22×#121×C127C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C127 ◁ C24×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#102×C127C2semidirect
3. C22×C22⋊C8×C127C2semidirect
4. C2×#380×C127C2semidirect
5. C2×#340×C127C2semidirect
13. C2×#121×C127C4semidirect
59. C22×C8×C127D4semidirect
72. C2×C4⋊C4×C127D4semidirect
124. C2×D4×C127C22⋊C4semidirect
179. C4⋊C4×C127C22⋊C4semidirect
227. C23×C127#102semidirect
334. #10969C127direct (N × H)
349. C22×#102C2×C127semidirect
350. C22×C22⋊C8C2×C127semidirect
351. C2×#380C2×C127semidirect
352. C2×#340C2×C127semidirect
353. C127#10969direct (N × H)
361. C2×#121C4×C127semidirect
407. C22×C8D4×C127semidirect
420. C2×C4⋊C4D4×C127semidirect
472. C2×D4C22⋊C4×C127semidirect
527. C4⋊C4C22⋊C4×C127semidirect
575. C23#102×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C1272
C22×#102×C1272
C22×C22⋊C8×C1272
C2×#380×C1272
C2×#340×C1272
#10969127