Finite Group Databasebeta

← C127×#21080 #44584753

Subgroups — C127×#21080 #44584753

Order 32512.

1000 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#430×C127C211yesmaximal, characteristic, complemented
2C2×#421×C127C211yesmaximal, characteristic
3C2×#421×C127C211yesmaximal, characteristic
4C2×#413×C127C211yesmaximal, characteristic
5C127×#2873C211yesmaximal, characteristic, complemented
6C127×#1932C218yesmaximal, complemented
7C2×#344×C127C211yesmaximal, characteristic, complemented
8C127×#1733C211yesmaximal, characteristic, complemented
9C22×#41×C127C2211yescharacteristic
10C22×M16×C127C2211yescharacteristic
11C22×M16×C127C2211yescharacteristic
12C22×M16×C127C2211yescharacteristic
13C22×M16×C127C2211yescharacteristic
14C2×#117×C127C2211yescharacteristic
15C2×#117×C127C2211yescharacteristic
16#430×C127—22no—
17#430×C127C2214yescomplemented
18C2×#108×C127—22no—
19#421×C127—22no—
20#421×C127—22no—
21#421×C127—22no—
22#421×C127C2214yes—
23C2×#104×C127—22no—
24C2×#104×C127C2214yes—
25#413×C127C414yescomplemented
26#413×C127C2214yes—
27C2×#101×C127C412yescomplemented
28C2×#100×C127C412yescomplemented
29#405×C127—22no—
30#405×C127—22no—
31C4×M16×C127C2214yescomplemented
32#344×C127C2214yescomplemented
33#339×C127C2214yescomplemented
34C2×#41×C127—21no—
35C2×#41×C127—21no—
36C2×#41×C127—21no—
37C2×#41×C127—21no—
38C2×#41×C127—21no—
39C2×#41×C127—21no—
40C2×#41×C127—21no—
41C2×#41×C127—21no—
42C2×#41×C127—21no—
43C2×#41×C127—21no—
44C2×#41×C127C2×C412yes—
45C2×#41×C127C2312yes—
46C22×Q8×C127C2×C411yescharacteristic
47C22×D4×C127—21no—
48C22×D4×C127C2×C411yescharacteristic
49C23×C4×C127—21no—
50C23×C4×C127C2311yescharacteristic
51C2×M16×C127—21no—
52C2×M16×C127—21no—
53C2×M16×C127—21no—
54C2×M16×C127—21no—
55C2×M16×C127—21no—
56C2×M16×C127—21no—
57C2×M16×C127—21no—
58C2×M16×C127—21no—
59C2×M16×C127—21no—
60C2×M16×C127—21no—
61C2×M16×C127—21no—
62C2×M16×C127—21no—
63C2×M16×C127—21no—
64C2×M16×C127—21no—
65C2×M16×C127C2×C412yes—
66C2×M16×C127C2×C412yes—
67C2×M16×C127C2×C412yes—
68C2×M16×C127C2×C412yes—
69C2×M16×C127D412yes—
70C2×M16×C127D412yes—
71C2×M16×C127C2312yes—
72C2×M16×C127C2312yes—
73C2×M16×C127C2312yes—
74C2×M16×C127C2312yes—
75C22×C8×C127—21no—
76C22×C8×C127—21no—
77C22×C8×C127—21no—
78C22×C8×C127—21no—
79#117×C127—21no—
80#117×C127—21no—
81#117×C127—21no—
82#117×C127—21no—
83#117×C127—21no—
84#117×C127D412yes—
85#117×C127D412yes—
86#117×C127C2312yes—
87C2×C4⋊C4×C127—21no—
88C2×C4⋊C4×C127—21no—
89C2×C22⋊C4×C127—21no—
90C2×C22⋊C4×C127—21no—
91C2×C42×C127—21no—
92C2×C42×C127C2312yes—
93#108×C127—28no—
94#104×C127—28no—
95#104×C127—28no—
96#101×C127C2×C418yescomplemented
97#100×C127C2×C418yescomplemented
98#97×C127—24no—
99C4×C8×C127—24no—
100C24×C127—21no—
101C24×C127#4111yescharacteristic
102#41×C127—22no—
103#41×C127—22no—
104#41×C127—22no—
105#41×C127—22no—
106#41×C127—22no—
107#41×C127—22no—
108#41×C127—22no—
109#41×C127—22no—
110#41×C127—41no—
111#41×C127—41no—
112#41×C127—41no—
113#41×C127—41no—
114#41×C127—41no—
115#41×C127—41no—
116#41×C127—41no—
117#41×C127—41no—
118C2×Q8×C127—21no—
119C2×Q8×C127—21no—
120C2×Q8×C127—21no—
121C2×Q8×C127—21no—
122C2×Q8×C127—21no—
123C2×Q8×C127C22×C412yes—
124C2×D4×C127—22no—
125C2×D4×C127—22no—
126C2×D4×C127—21no—
127C2×D4×C127—21no—
128C2×D4×C127—21no—
129C2×D4×C127—21no—
130C2×D4×C127—21no—
131C2×D4×C127—41no—
132C2×D4×C127—41no—
133C2×D4×C127—41no—
134C2×D4×C127—41no—
135C2×D4×C127C22×C412yes—
136C22×C4×C127—21no—
137C22×C4×C127—22no—
138C22×C4×C127—22no—
139C22×C4×C127—22no—
140C22×C4×C127—41no—
141C22×C4×C127—41no—
142C22×C4×C127—41no—
143C22×C4×C127—41no—
144C22×C4×C127—41no—
145C22×C4×C127C22×C411yescharacteristic
146C22×C4×C127C22×C411yescharacteristic
147C22×C4×C127C2×D411yescharacteristic
148C22×C4×C127C2×D411yescharacteristic
149C22×C4×C127C2×D411yescharacteristic
150C22×C4×C127C2×D411yescharacteristic
151C22×C4×C127#4111yescharacteristic
152C22×C4×C127#4111yescharacteristic
153C22×C4×C127#4111yescharacteristic
154C22×C4×C127#4111yescharacteristic
155C22×C4×C127#4111yescharacteristic
156C22×C4×C127#4111yescharacteristic
157C22×C4×C127#4111yescharacteristic
158C22×C4×C127C2411yescharacteristic
159M16×C127—22no—
160M16×C127—22no—
161M16×C127—22no—
162M16×C127—22no—
163M16×C127—22no—
164M16×C127—22no—
165M16×C127—22no—
166M16×C127—22no—
167M16×C127—22no—
168M16×C127—22no—
169M16×C127—22no—
170M16×C127—41no—
171M16×C127—41no—
172M16×C127C22×C414yes—
173M16×C127C22×C414yes—
174M16×C127C2×D414yes—
175C2×C8×C127—22no—
176C2×C8×C127—22no—
177C2×C8×C127—22no—
178C2×C8×C127—22no—
179C2×C8×C127—22no—
180C2×C8×C127—22no—
181C2×C8×C127—22no—
182C2×C8×C127—22no—
183C2×C8×C127—22no—
184C2×C8×C127—22no—
185C2×C8×C127—41no—
186C2×C8×C127—41no—
187C4⋊C4×C127—22no—
188C4⋊C4×C127—22no—
189C4⋊C4×C127—22no—
190C4⋊C4×C127—41no—
191C22⋊C4×C127—22no—
192C22⋊C4×C127—22no—
193C22⋊C4×C127—22no—
194C22⋊C4×C127—41no—
195C42×C127—22no—
196C42×C127—22no—
197C42×C127—41no—
198C42×C127C2×D414yes—
199C23×C127—22no—
200C23×C127—41no—
201C23×C127—41no—
202C23×C127—81no—
203C23×C127—82no—
204C23×C127#11711yescharacteristic
205C23×C127#11711yescharacteristic
206C23×C127#12311yescharacteristic
207C23×C127#12311yescharacteristic
208C23×C127#12411yescharacteristic
209C23×C127#12411yescharacteristic
210C23×C127C2×#4111yescharacteristic
211Q8×C127—22no—
212Q8×C127—22no—
213Q8×C127—41no—
214Q8×C127—41no—
215D4×C127—22no—
216D4×C127—22no—
217D4×C127—42no—
218D4×C127—42no—
219D4×C127—42no—
220D4×C127—42no—
221D4×C127—41no—
222D4×C127—41no—
223C2×C4×C127—22no—
224C2×C4×C127—24no—
225C2×C4×C127—41no—
226C2×C4×C127—41no—
227C2×C4×C127—42no—
228C2×C4×C127—42no—
229C2×C4×C127—42no—
230C2×C4×C127—42no—
231C2×C4×C127—42no—
232C2×C4×C127—82no—
233C2×C4×C127—82no—
234C2×C4×C127#11711yescharacteristic
235C2×C4×C127#11711yescharacteristic
236C2×C4×C127C4×D411yescharacteristic
237C2×C4×C127C4×D411yescharacteristic
238C2×C4×C127C4×D411yescharacteristic
239C2×C4×C127C4×D411yescharacteristic
240C2×C4×C127C4×D411yescharacteristic
241C2×C4×C127C4×D411yescharacteristic
242C2×C4×C127C4×D411yescharacteristic
243C2×C4×C127C4×D411yescharacteristic
244C2×C4×C127#12111yescharacteristic
245C2×C4×C127#12111yescharacteristic
246C2×C4×C127#12111yescharacteristic
247C2×C4×C127#12111yescharacteristic
248C2×C4×C127#12311yescharacteristic
249C2×C4×C127#12311yescharacteristic
250C2×C4×C127#12411yescharacteristic
251C2×C4×C127#12411yescharacteristic
252C2×C4×C127#12611yescharacteristic
253C2×C4×C127#12611yescharacteristic
254C2×C4×C127#12611yescharacteristic
255C2×C4×C127#12611yescharacteristic
256C2×C4×C127C23×C411yescharacteristic
257C2×C4×C127C22×D411yescharacteristic
258C2×C4×C127C22×D411yescharacteristic
259C2×C4×C127C2×#4111yescharacteristic
260C2×C4×C127C2×#4111yescharacteristic
261C2×C4×C127C2×#4111yescharacteristic
262C8×C127—24no—
263C8×C127—24no—
264C8×C127—24no—
265C8×C127—42no—
266C22×C127—41no—
267C22×C127—41no—
268C22×C127—41no—
269C22×C127—41no—
270C22×C127—41no—
271C22×C127—41no—
272C22×C127—41no—
273C22×C127—42no—
274C22×C127—82no—
275C22×C127—82no—
276C22×C127—82no—
277C22×C127#38811yescharacteristic
278C22×C127#38811yescharacteristic
279C22×C127#38811yescharacteristic
280C22×C127#38811yescharacteristic
281C22×C127C2×#11711yescharacteristic
282C22×C127C2×#12311yescharacteristic
283C22×C127C2×#12411yescharacteristic
284C4×C127—44no—
285C4×C127—42no—
286C4×C127—82no—
287C4×C127#38811yescharacteristic
288C4×C127#38811yescharacteristic
289C4×C127#38811yescharacteristic
290C4×C127#38811yescharacteristic
291C4×C127C2×C4×D411yescharacteristic
292C4×C127C2×C4×D411yescharacteristic
293C4×C127C2×#12111yescharacteristic
294C4×C127C2×#12611yescharacteristic
295#21080C12711yesmaximal, characteristic, direct product factor, Sylow
296C2×C127—21no—
297C2×C127—21no—
298C2×C127—21no—
299C2×C127—21no—
300C2×C127—21no—
301C2×C127—21no—
302C2×C127—21no—
303C2×C127—82no—
304C2×C127C2×#38811yescharacteristic
305C2×#430C2×C12711yescharacteristic, complemented
306C2×#421C2×C12711yescharacteristic
307C2×#421C2×C12711yescharacteristic
308C2×#413C2×C12711yescharacteristic
309#2873C2×C12711yescharacteristic, complemented
310#1932C2×C12718yescomplemented
311C2×#344C2×C12711yescharacteristic, complemented
312#1733C2×C12711yescharacteristic, complemented
313C127#2108011yescharacteristic, direct product factor, Sylow
314C22×#41C22×C12711yescharacteristic
315C22×M16C22×C12711yescharacteristic
316C22×M16C22×C12711yescharacteristic
317C22×M16C22×C12711yescharacteristic
318C22×M16C22×C12711yescharacteristic
319C2×#117C22×C12711yescharacteristic
320C2×#117C22×C12711yescharacteristic
321#430—22no—
322#430C22×C12714yescomplemented
323C2×#108—22no—
324#421—22no—
325#421—22no—
326#421—22no—
327#421C22×C12714yes—
328C2×#104—22no—
329C2×#104C22×C12714yes—
330#413C4×C12714yescomplemented
331#413C22×C12714yes—
332C2×#101C4×C12712yescomplemented
333C2×#100C4×C12712yescomplemented
334#405—22no—
335#405—22no—
336C4×M16C22×C12714yescomplemented
337#344C22×C12714yescomplemented
338#339C22×C12714yescomplemented
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—21no—
342C2×#41—21no—
343C2×#41—21no—
344C2×#41—21no—
345C2×#41—21no—
346C2×#41—21no—
347C2×#41—21no—
348C2×#41—21no—
349C2×#41C2×C4×C12712yes—
350C2×#41C23×C12712yes—
351C22×Q8C2×C4×C12711yescharacteristic
352C22×D4—21no—
353C22×D4C2×C4×C12711yescharacteristic
354C23×C4—21no—
355C23×C4C23×C12711yescharacteristic
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16C2×C4×C12712yes—
371C2×M16C2×C4×C12712yes—
372C2×M16C2×C4×C12712yes—
373C2×M16C2×C4×C12712yes—
374C2×M16D4×C12712yes—
375C2×M16D4×C12712yes—
376C2×M16C23×C12712yes—
377C2×M16C23×C12712yes—
378C2×M16C23×C12712yes—
379C2×M16C23×C12712yes—
380C22×C8—21no—
381C22×C8—21no—
382C22×C8—21no—
383C22×C8—21no—
384#117—21no—
385#117—21no—
386#117—21no—
387#117—21no—
388#117—21no—
389#117D4×C12712yes—
390#117D4×C12712yes—
391#117C23×C12712yes—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C42—21no—
397C2×C42C23×C12712yes—
398#108—28no—
399#104—28no—
400#104—28no—
401#101C2×C4×C12718yescomplemented
402#100C2×C4×C12718yescomplemented
403#97—24no—
404C4×C8—24no—
405C24—21no—
406C24#41×C12711yescharacteristic
407#41—22no—
408#41—22no—
409#41—22no—
410#41—22no—
411#41—22no—
412#41—22no—
413#41—22no—
414#41—22no—
415#41—41no—
416#41—41no—
417#41—41no—
418#41—41no—
419#41—41no—
420#41—41no—
421#41—41no—
422#41—41no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8C22×C4×C12712yes—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4C22×C4×C12712yes—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4C22×C4×C12711yescharacteristic
451C22×C4C22×C4×C12711yescharacteristic
452C22×C4C2×D4×C12711yescharacteristic
453C22×C4C2×D4×C12711yescharacteristic
454C22×C4C2×D4×C12711yescharacteristic
455C22×C4C2×D4×C12711yescharacteristic
456C22×C4#41×C12711yescharacteristic
457C22×C4#41×C12711yescharacteristic
458C22×C4#41×C12711yescharacteristic
459C22×C4#41×C12711yescharacteristic
460C22×C4#41×C12711yescharacteristic
461C22×C4#41×C12711yescharacteristic
462C22×C4#41×C12711yescharacteristic
463C22×C4C24×C12711yescharacteristic
464M16—22no—
465M16—22no—
466M16—22no—
467M16—22no—
468M16—22no—
469M16—22no—
470M16—22no—
471M16—22no—
472M16—22no—
473M16—22no—
474M16—22no—
475M16—41no—
476M16—41no—
477M16C22×C4×C12714yes—
478M16C22×C4×C12714yes—
479M16C2×D4×C12714yes—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—41no—
491C2×C8—41no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—41no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—41no—
500C42—22no—
501C42—22no—
502C42—41no—
503C42C2×D4×C12714yes—
504C23—22no—
505C23—41no—
506C23—41no—
507C23—81no—
508C23—82no—
509C23#117×C12711yescharacteristic
510C23#117×C12711yescharacteristic
511C23#123×C12711yescharacteristic
512C23#123×C12711yescharacteristic
513C23#124×C12711yescharacteristic
514C23#124×C12711yescharacteristic
515C23C2×#41×C12711yescharacteristic
516Q8—22no—
517Q8—22no—
518Q8—41no—
519Q8—41no—
520D4—22no—
521D4—22no—
522D4—42no—
523D4—42no—
524D4—42no—
525D4—42no—
526D4—41no—
527D4—41no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—82no—
538C2×C4—82no—
539C2×C4#117×C12711yescharacteristic
540C2×C4#117×C12711yescharacteristic
541C2×C4C4×D4×C12711yescharacteristic
542C2×C4C4×D4×C12711yescharacteristic
543C2×C4C4×D4×C12711yescharacteristic
544C2×C4C4×D4×C12711yescharacteristic
545C2×C4C4×D4×C12711yescharacteristic
546C2×C4C4×D4×C12711yescharacteristic
547C2×C4C4×D4×C12711yescharacteristic
548C2×C4C4×D4×C12711yescharacteristic
549C2×C4#121×C12711yescharacteristic
550C2×C4#121×C12711yescharacteristic
551C2×C4#121×C12711yescharacteristic
552C2×C4#121×C12711yescharacteristic
553C2×C4#123×C12711yescharacteristic
554C2×C4#123×C12711yescharacteristic
555C2×C4#124×C12711yescharacteristic
556C2×C4#124×C12711yescharacteristic
557C2×C4#126×C12711yescharacteristic
558C2×C4#126×C12711yescharacteristic
559C2×C4#126×C12711yescharacteristic
560C2×C4#126×C12711yescharacteristic
561C2×C4C23×C4×C12711yescharacteristic
562C2×C4C22×D4×C12711yescharacteristic
563C2×C4C22×D4×C12711yescharacteristic
564C2×C4C2×#41×C12711yescharacteristic
565C2×C4C2×#41×C12711yescharacteristic
566C2×C4C2×#41×C12711yescharacteristic
567C8—24no—
568C8—24no—
569C8—24no—
570C8—42no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—42no—
579C22—82no—
580C22—82no—
581C22—82no—
582C22#388×C12711yescharacteristic
583C22#388×C12711yescharacteristic
584C22#388×C12711yescharacteristic
585C22#388×C12711yescharacteristic
586C22C2×#117×C12711yescharacteristic
587C22C2×#123×C12711yescharacteristic
588C22C2×#124×C12711yescharacteristic
589C4—44no—
590C4—42no—
591C4—82no—
592C4#388×C12711yescharacteristic
593C4#388×C12711yescharacteristic
594C4#388×C12711yescharacteristic
595C4#388×C12711yescharacteristic
596C4C2×C4×D4×C12711yescharacteristic
597C4C2×C4×D4×C12711yescharacteristic
598C4C2×#121×C12711yescharacteristic
599C4C2×#126×C12711yescharacteristic
600C2—21no—
601C2—21no—
602C2—21no—
603C2—21no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—82no—
608C2C2×#388×C12711yescharacteristic
subgroupG/H
centerC4×C127C2×#121
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC2×C127C2×#388
prime radicalC22×#41×C127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#430×C127C2semidirect
5. C127×#2873C2semidirect
6. C127×#1932C2semidirect
7. C2×#344×C127C2semidirect
8. C127×#1733C2semidirect
17. #430×C127C22semidirect
25. #413×C127C4semidirect
27. C2×#101×C127C4semidirect
28. C2×#100×C127C4semidirect
31. C4×M16×C127C22semidirect
32. #344×C127C22semidirect
33. #339×C127C22semidirect
96. #101×C127C2×C4semidirect
97. #100×C127C2×C4semidirect
295. #21080C127direct (N × H)
305. C2×#430C2×C127semidirect
309. #2873C2×C127semidirect
310. #1932C2×C127semidirect
311. C2×#344C2×C127semidirect
312. #1733C2×C127semidirect
313. C127#21080direct (N × H)
322. #430C22×C127semidirect
330. #413C4×C127semidirect
332. C2×#101C4×C127semidirect
333. C2×#100C4×C127semidirect
336. C4×M16C22×C127semidirect
337. #344C22×C127semidirect
338. #339C22×C127semidirect
401. #101C2×C4×C127semidirect
402. #100C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#430×C1272
C2×#421×C1272
C2×#413×C1272
C127×#28732
C127×#19322
C2×#344×C1272
C127×#17332
#21080127