Finite Group Databasebeta

← C127×#8479 #44572152

Subgroups — C127×#8479 #44572152

Order 32512.

912 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3537C211yesmaximal, characteristic
2C127×#1964C211yesmaximal, characteristic, complemented
3C127×#1900C211yesmaximal, characteristic, complemented
4C127×#1895C211yesmaximal, characteristic, complemented
5C127×#1871C211yesmaximal, characteristic, complemented
6C127×#1513C211yesmaximal, characteristic, complemented
7C127×#1507C211yesmaximal, characteristic, complemented
8C22×M16×C127C2211yescharacteristic, complemented
9#560×C127—22no—
10#553×C127—21no—
11#553×C127—21no—
12D42×C127—22no—
13D42×C127—21no—
14D42×C127—21no—
15#540×C127—21no—
16#538×C127—21no—
17#538×C127C412yescomplemented
18#535×C127—21no—
19#534×C127—21no—
20#534×C127C412yescomplemented
21#525×C127C2211yescharacteristic
22C2×#121×C127C2211yescharacteristic
23C2×#121×C127C2211yescharacteristic
24C2×#104×C127—21no—
25C2×#102×C127—21no—
26C2×#100×C127—21no—
27C2×#99×C127—22no—
28#407×C127C2211yescharacteristic, complemented
29#380×C127C2211yescharacteristic, complemented
30C4×C22⋊C4×C127C2211yescharacteristic, complemented
31#343×C127—21no—
32#340×C127—21no—
33#339×C127—21no—
34#328×C127—21no—
35#327×C127—22no—
36#327×C127—21no—
37C2×#41×C127D411yescharacteristic
38C22×D4×C127—22no—
39C22×D4×C127—21no—
40C22×D4×C127—22no—
41C22×D4×C127—21no—
42C22×D4×C127D412yes—
43C22×D4×C127D411yescharacteristic
44C22×D4×C127D411yescharacteristic
45C23×C4×C127C2311yescharacteristic
46C2×M16×C127—21no—
47C2×M16×C127—21no—
48C2×M16×C127—21no—
49C2×M16×C127—42no—
50C22×C8×C127—21no—
51#127×C127—22no—
52#127×C127—21no—
53#126×C127—22no—
54#126×C127—22no—
55#125×C127—21no—
56#124×C127—22no—
57#123×C127—22no—
58#123×C127—21no—
59#123×C127—22no—
60#123×C127—22no—
61#123×C127—22no—
62C22⋊Q8×C127C2×C411yescharacteristic
63C22⋊Q8×C127D411yescharacteristic
64#121×C127—22no—
65#121×C127—21no—
66#121×C127—21no—
67#121×C127—22no—
68#121×C127—22no—
69#121×C127—22no—
70#121×C127—22no—
71#121×C127—22no—
72#121×C127—21no—
73#121×C127—21no—
74#121×C127—21no—
75#121×C127—21no—
76#121×C127—21no—
77#121×C127—21no—
78#121×C127C2×C412yes—
79#121×C127C2×C411yescharacteristic
80#121×C127D412yes—
81#121×C127D411yescharacteristic
82#120×C127—22no—
83#120×C127—22no—
84#120×C127—22no—
85#120×C127—22no—
86#120×C127—21no—
87#120×C127—22no—
88#120×C127—22no—
89C4×D4×C127—22no—
90C4×D4×C127—21no—
91C4×D4×C127—21no—
92C4×D4×C127—22no—
93C4×D4×C127—21no—
94C4×D4×C127—21no—
95#117×C127—21no—
96#117×C127D411yescharacteristic
97C2×C4⋊C4×C127—21no—
98C2×C4⋊C4×C127D411yescharacteristic
99C2×C4⋊C4×C127D411yescharacteristic
100C2×C22⋊C4×C127—21no—
101C2×C22⋊C4×C127—21no—
102C2×C22⋊C4×C127—21no—
103C2×C22⋊C4×C127C2×C412yes—
104C2×C42×C127—21no—
105#104×C127—42no—
106#102×C127—42no—
107#100×C127—42no—
108#99×C127—44no—
109C22⋊C8×C127—21no—
110C22⋊C8×C127—21no—
111#95×C127—21no—
112#95×C127—21no—
113C24×C127—22no—
114C24×C127—21no—
115C24×C127C22⋊C412yes—
116C24×C127C2×D411yescharacteristic
117#41×C127—41no—
118#41×C127—41no—
119C2×Q8×C127C22⋊C411yescharacteristic
120C2×D4×C127—22no—
121C2×D4×C127—21no—
122C2×D4×C127—22no—
123C2×D4×C127—21no—
124C2×D4×C127—22no—
125C2×D4×C127—22no—
126C2×D4×C127—22no—
127C2×D4×C127—22no—
128C2×D4×C127—22no—
129C2×D4×C127—21no—
130C2×D4×C127—22no—
131C2×D4×C127—22no—
132C2×D4×C127—21no—
133C2×D4×C127—21no—
134C2×D4×C127—21no—
135C2×D4×C127—41no—
136C2×D4×C127—41no—
137C2×D4×C127—41no—
138C2×D4×C127—41no—
139C2×D4×C127—42no—
140C2×D4×C127—42no—
141C2×D4×C127—81no—
142C2×D4×C127—81no—
143C2×D4×C127—82no—
144C2×D4×C127—84no—
145C2×D4×C127—82no—
146C2×D4×C127—82no—
147C2×D4×C127C22⋊C411yescharacteristic
148C2×D4×C127C22⋊C412yes—
149C22×C4×C127—22no—
150C22×C4×C127—22no—
151C22×C4×C127—21no—
152C22×C4×C127—21no—
153C22×C4×C127—41no—
154C22×C4×C127—41no—
155C22×C4×C127—41no—
156C22×C4×C127—41no—
157C22×C4×C127C22⋊C412yes—
158C22×C4×C127C22×C411yescharacteristic
159C22×C4×C127C2×D411yescharacteristic
160C22×C4×C127C2×D411yescharacteristic
161C22×C4×C127C2×D411yescharacteristic
162C22×C4×C127C2×D411yescharacteristic
163C22×C4×C127C2×D411yescharacteristic
164M16×C127—22no—
165M16×C127—22no—
166M16×C127—41no—
167M16×C127—41no—
168M16×C127—41no—
169M16×C127—41no—
170C2×C8×C127—22no—
171C2×C8×C127—41no—
172C2×C8×C127—41no—
173C2×C8×C127—41no—
174C4⋊C4×C127—22no—
175C4⋊C4×C127—22no—
176C4⋊C4×C127—21no—
177C4⋊C4×C127—21no—
178C4⋊C4×C127—21no—
179C4⋊C4×C127—21no—
180C4⋊C4×C127—21no—
181C4⋊C4×C127—41no—
182C4⋊C4×C127—41no—
183C4⋊C4×C127C22⋊C412yes—
184C4⋊C4×C127C22⋊C411yescharacteristic
185C4⋊C4×C127C22⋊C411yescharacteristic
186C22⋊C4×C127—22no—
187C22⋊C4×C127—22no—
188C22⋊C4×C127—22no—
189C22⋊C4×C127—22no—
190C22⋊C4×C127—22no—
191C22⋊C4×C127—21no—
192C22⋊C4×C127—21no—
193C22⋊C4×C127—21no—
194C22⋊C4×C127—22no—
195C22⋊C4×C127—22no—
196C22⋊C4×C127—22no—
197C22⋊C4×C127—21no—
198C22⋊C4×C127—22no—
199C22⋊C4×C127—21no—
200C22⋊C4×C127—22no—
201C22⋊C4×C127—41no—
202C22⋊C4×C127—42no—
203C42×C127—22no—
204C42×C127—21no—
205C42×C127—41no—
206C42×C127—41no—
207C23×C127—21no—
208C23×C127—21no—
209C23×C127—22no—
210C23×C127—22no—
211C23×C127—21no—
212C23×C127—41no—
213C23×C127—41no—
214C23×C127—42no—
215C23×C127—42no—
216C23×C127—42no—
217C23×C127—41no—
218C23×C127—41no—
219C23×C127—81no—
220C23×C127—81no—
221C23×C127—82no—
222C23×C127—82no—
223C23×C127—82no—
224C23×C127C2×C22⋊C411yescharacteristic
225C23×C127#12011yescharacteristic
226C23×C127#12011yescharacteristic
227Q8×C127—41no—
228D4×C127—42no—
229D4×C127—41no—
230D4×C127—44no—
231D4×C127—42no—
232D4×C127—42no—
233D4×C127—41no—
234D4×C127—42no—
235D4×C127—41no—
236D4×C127—41no—
237D4×C127—41no—
238D4×C127—41no—
239D4×C127—41no—
240D4×C127—81no—
241D4×C127—82no—
242D4×C127—82no—
243D4×C127—81no—
244D4×C127—82no—
245D4×C127—82no—
246D4×C127—82no—
247D4×C127—82no—
248D4×C127—82no—
249C2×C4×C127—21no—
250C2×C4×C127—21no—
251C2×C4×C127—21no—
252C2×C4×C127—21no—
253C2×C4×C127—21no—
254C2×C4×C127—21no—
255C2×C4×C127—21no—
256C2×C4×C127—22no—
257C2×C4×C127—21no—
258C2×C4×C127—22no—
259C2×C4×C127—21no—
260C2×C4×C127—41no—
261C2×C4×C127—41no—
262C2×C4×C127—41no—
263C2×C4×C127—41no—
264C2×C4×C127—41no—
265C2×C4×C127—42no—
266C2×C4×C127—42no—
267C2×C4×C127—81no—
268C2×C4×C127—82no—
269C2×C4×C127—82no—
270C2×C4×C127—81no—
271C2×C4×C127—81no—
272C2×C4×C127—81no—
273C2×C4×C127—81no—
274C2×C4×C127—81no—
275C2×C4×C127C2×C22⋊C411yescharacteristic
276C2×C4×C127C2×C22⋊C411yescharacteristic
277C2×C4×C127#12011yescharacteristic
278C2×C4×C127#12011yescharacteristic
279C8×C127—42no—
280C8×C127—81no—
281C22×C127—21no—
282C22×C127—21no—
283C22×C127—21no—
284C22×C127—21no—
285C22×C127—21no—
286C22×C127—21no—
287C22×C127—21no—
288C22×C127—21no—
289C22×C127—42no—
290C22×C127—42no—
291C22×C127—41no—
292C22×C127—42no—
293C22×C127—42no—
294C22×C127—41no—
295C22×C127—41no—
296C22×C127—42no—
297C22×C127—42no—
298C22×C127—81no—
299C22×C127—81no—
300C22×C127—161no—
301C22×C127—161no—
302C22×C127—162no—
303C22×C127—164no—
304C22×C127#37911yescharacteristic
305C22×C127#45311yescharacteristic
306C22×C127#45511yescharacteristic
307C4×C127—21no—
308C4×C127—21no—
309C4×C127—21no—
310C4×C127—42no—
311C4×C127—41no—
312C4×C127—42no—
313C4×C127—41no—
314C4×C127—41no—
315C4×C127—82no—
316C4×C127—161no—
317C4×C127B(4,𝔽2)11yescharacteristic
318C4×C127#45811yescharacteristic
319#8479C12711yesmaximal, characteristic, direct product factor, Sylow
320C2×C127—21no—
321C2×C127—21no—
322C2×C127—41no—
323C2×C127—41no—
324C2×C127—82no—
325C2×C127—82no—
326C2×C127—81no—
327C2×C127#179011yescharacteristic
328C2×C127#179211yescharacteristic
329C2×C127#179511yescharacteristic
330#3537C2×C12711yescharacteristic
331#1964C2×C12711yescharacteristic, complemented
332#1900C2×C12711yescharacteristic, complemented
333#1895C2×C12711yescharacteristic, complemented
334#1871C2×C12711yescharacteristic, complemented
335#1513C2×C12711yescharacteristic, complemented
336#1507C2×C12711yescharacteristic, complemented
337C127#847911yescharacteristic, direct product factor, Sylow
338C22×M16C22×C12711yescharacteristic, complemented
339#560—22no—
340#553—21no—
341#553—21no—
342D42—22no—
343D42—21no—
344D42—21no—
345#540—21no—
346#538—21no—
347#538C4×C12712yescomplemented
348#535—21no—
349#534—21no—
350#534C4×C12712yescomplemented
351#525C22×C12711yescharacteristic
352C2×#121C22×C12711yescharacteristic
353C2×#121C22×C12711yescharacteristic
354C2×#104—21no—
355C2×#102—21no—
356C2×#100—21no—
357C2×#99—22no—
358#407C22×C12711yescharacteristic, complemented
359#380C22×C12711yescharacteristic, complemented
360C4×C22⋊C4C22×C12711yescharacteristic, complemented
361#343—21no—
362#340—21no—
363#339—21no—
364#328—21no—
365#327—22no—
366#327—21no—
367C2×#41D4×C12711yescharacteristic
368C22×D4—22no—
369C22×D4—21no—
370C22×D4—22no—
371C22×D4—21no—
372C22×D4D4×C12712yes—
373C22×D4D4×C12711yescharacteristic
374C22×D4D4×C12711yescharacteristic
375C23×C4C23×C12711yescharacteristic
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16—42no—
380C22×C8—21no—
381#127—22no—
382#127—21no—
383#126—22no—
384#126—22no—
385#125—21no—
386#124—22no—
387#123—22no—
388#123—21no—
389#123—22no—
390#123—22no—
391#123—22no—
392C22⋊Q8C2×C4×C12711yescharacteristic
393C22⋊Q8D4×C12711yescharacteristic
394#121—22no—
395#121—21no—
396#121—21no—
397#121—22no—
398#121—22no—
399#121—22no—
400#121—22no—
401#121—22no—
402#121—21no—
403#121—21no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121—21no—
408#121C2×C4×C12712yes—
409#121C2×C4×C12711yescharacteristic
410#121D4×C12712yes—
411#121D4×C12711yescharacteristic
412#120—22no—
413#120—22no—
414#120—22no—
415#120—22no—
416#120—21no—
417#120—22no—
418#120—22no—
419C4×D4—22no—
420C4×D4—21no—
421C4×D4—21no—
422C4×D4—22no—
423C4×D4—21no—
424C4×D4—21no—
425#117—21no—
426#117D4×C12711yescharacteristic
427C2×C4⋊C4—21no—
428C2×C4⋊C4D4×C12711yescharacteristic
429C2×C4⋊C4D4×C12711yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4C2×C4×C12712yes—
434C2×C42—21no—
435#104—42no—
436#102—42no—
437#100—42no—
438#99—44no—
439C22⋊C8—21no—
440C22⋊C8—21no—
441#95—21no—
442#95—21no—
443C24—22no—
444C24—21no—
445C24C22⋊C4×C12712yes—
446C24C2×D4×C12711yescharacteristic
447#41—41no—
448#41—41no—
449C2×Q8C22⋊C4×C12711yescharacteristic
450C2×D4—22no—
451C2×D4—21no—
452C2×D4—22no—
453C2×D4—21no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—21no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—81no—
472C2×D4—81no—
473C2×D4—82no—
474C2×D4—84no—
475C2×D4—82no—
476C2×D4—82no—
477C2×D4C22⋊C4×C12711yescharacteristic
478C2×D4C22⋊C4×C12712yes—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4C22⋊C4×C12712yes—
488C22×C4C22×C4×C12711yescharacteristic
489C22×C4C2×D4×C12711yescharacteristic
490C22×C4C2×D4×C12711yescharacteristic
491C22×C4C2×D4×C12711yescharacteristic
492C22×C4C2×D4×C12711yescharacteristic
493C22×C4C2×D4×C12711yescharacteristic
494M16—22no—
495M16—22no—
496M16—41no—
497M16—41no—
498M16—41no—
499M16—41no—
500C2×C8—22no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8—41no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4C22⋊C4×C12712yes—
514C4⋊C4C22⋊C4×C12711yescharacteristic
515C4⋊C4C22⋊C4×C12711yescharacteristic
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—21no—
528C22⋊C4—22no—
529C22⋊C4—21no—
530C22⋊C4—22no—
531C22⋊C4—41no—
532C22⋊C4—42no—
533C42—22no—
534C42—21no—
535C42—41no—
536C42—41no—
537C23—21no—
538C23—21no—
539C23—22no—
540C23—21no—
541C23—22no—
542C23—41no—
543C23—41no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—41no—
548C23—41no—
549C23—81no—
550C23—81no—
551C23—82no—
552C23—82no—
553C23—82no—
554C23C2×C22⋊C4×C12711yescharacteristic
555C23#120×C12711yescharacteristic
556C23#120×C12711yescharacteristic
557Q8—41no—
558D4—42no—
559D4—41no—
560D4—44no—
561D4—42no—
562D4—42no—
563D4—41no—
564D4—42no—
565D4—41no—
566D4—41no—
567D4—41no—
568D4—41no—
569D4—41no—
570D4—81no—
571D4—82no—
572D4—82no—
573D4—81no—
574D4—82no—
575D4—82no—
576D4—82no—
577D4—82no—
578D4—82no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—81no—
598C2×C4—82no—
599C2×C4—82no—
600C2×C4—81no—
601C2×C4—81no—
602C2×C4—81no—
603C2×C4—81no—
604C2×C4—81no—
605C2×C4C2×C22⋊C4×C12711yescharacteristic
606C2×C4C2×C22⋊C4×C12711yescharacteristic
607C2×C4#120×C12711yescharacteristic
608C2×C4#120×C12711yescharacteristic
609C8—42no—
610C8—81no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—41no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—41no—
625C22—42no—
626C22—42no—
627C22—41no—
628C22—81no—
629C22—81no—
630C22—161no—
631C22—161no—
632C22—162no—
633C22—164no—
634C22#379×C12711yescharacteristic
635C22#453×C12711yescharacteristic
636C22#455×C12711yescharacteristic
637C4—21no—
638C4—21no—
639C4—21no—
640C4—41no—
641C4—42no—
642C4—41no—
643C4—42no—
644C4—41no—
645C4—82no—
646C4—161no—
647C4B(4,𝔽2)×C12711yescharacteristic
648C4#458×C12711yescharacteristic
649C2—21no—
650C2—21no—
651C2—41no—
652C2—41no—
653C2—81no—
654C2—82no—
655C2—82no—
656C2C127×#179011yescharacteristic
657C2C127×#179211yescharacteristic
658C2C127×#179511yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC127×#3537C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1964C2semidirect
3. C127×#1900C2semidirect
4. C127×#1895C2semidirect
5. C127×#1871C2semidirect
6. C127×#1513C2semidirect
7. C127×#1507C2semidirect
8. C22×M16×C127C22semidirect
17. #538×C127C4semidirect
20. #534×C127C4semidirect
28. #407×C127C22semidirect
29. #380×C127C22semidirect
30. C4×C22⋊C4×C127C22semidirect
319. #8479C127direct (N × H)
331. #1964C2×C127semidirect
332. #1900C2×C127semidirect
333. #1895C2×C127semidirect
334. #1871C2×C127semidirect
335. #1513C2×C127semidirect
336. #1507C2×C127semidirect
337. C127#8479direct (N × H)
338. C22×M16C22×C127semidirect
347. #538C4×C127semidirect
350. #534C4×C127semidirect
358. #407C22×C127semidirect
359. #380C22×C127semidirect
360. C4×C22⋊C4C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35372
C127×#19642
C127×#19002
C127×#18952
C127×#18712
C127×#15132
C127×#15072
#8479127