Finite Group Databasebeta

← C127×#8481 #44572154

Subgroups — C127×#8481 #44572154

Order 32512.

844 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3536C211yesmaximal, characteristic
2C127×#1964C211yesmaximal, characteristic, complemented
3C127×#1900C211yesmaximal, characteristic, complemented
4C127×#1894C211yesmaximal, characteristic, complemented
5C127×#1871C211yesmaximal, characteristic, complemented
6C127×#1513C211yesmaximal, characteristic, complemented
7C127×#1508C211yesmaximal, characteristic, complemented
8C22×M16×C127C2211yescharacteristic
9#562×C127—22no—
10#554×C127—21no—
11#548×C127—21no—
12#547×C127—21no—
13#546×C127—21no—
14#546×C127—22no—
15#543×C127C412yescomplemented
16#542×C127—21no—
17#539×C127—21no—
18#538×C127C412yescomplemented
19#537×C127—21no—
20#537×C127—21no—
21#525×C127C2211yescharacteristic
22C2×C22⋊Q8×C127C2211yescharacteristic
23C2×#121×C127C2211yescharacteristic
24C2×#104×C127—21no—
25C2×#103×C127—21no—
26C2×#100×C127—21no—
27C2×#99×C127—22no—
28#407×C127C2211yescharacteristic
29#380×C127C2211yescharacteristic
30C4×C22⋊C4×C127C2211yescharacteristic
31#343×C127—21no—
32#340×C127—21no—
33#339×C127—21no—
34#328×C127—22no—
35#328×C127—21no—
36#327×C127—21no—
37C2×#41×C127—22no—
38C2×#41×C127—21no—
39C2×#41×C127D411yescharacteristic
40C22×Q8×C127D411yescharacteristic
41C22×D4×C127D412yes—
42C22×D4×C127D411yescharacteristic
43C23×C4×C127C2311yescharacteristic
44C2×M16×C127—21no—
45C2×M16×C127—21no—
46C2×M16×C127—21no—
47C2×M16×C127—42no—
48C22×C8×C127—21no—
49C4⋊Q8×C127—21no—
50#126×C127—22no—
51#125×C127—22no—
52#124×C127—21no—
53#124×C127—22no—
54#124×C127—22no—
55#123×C127—22no—
56#123×C127—22no—
57#123×C127—22no—
58#123×C127—21no—
59#123×C127—22no—
60C22⋊Q8×C127—21no—
61C22⋊Q8×C127—22no—
62C22⋊Q8×C127—22no—
63C22⋊Q8×C127—22no—
64C22⋊Q8×C127—22no—
65C22⋊Q8×C127—21no—
66C22⋊Q8×C127—21no—
67C22⋊Q8×C127—22no—
68C22⋊Q8×C127—22no—
69C22⋊Q8×C127C2×C412yes—
70C22⋊Q8×C127C2×C411yescharacteristic
71C22⋊Q8×C127D412yes—
72C22⋊Q8×C127D411yescharacteristic
73#121×C127—21no—
74#121×C127—22no—
75#121×C127—22no—
76#121×C127—22no—
77#121×C127—22no—
78#121×C127—22no—
79#121×C127—21no—
80#121×C127—21no—
81#121×C127—21no—
82#121×C127—21no—
83#121×C127C2×C411yescharacteristic
84#121×C127D411yescharacteristic
85#120×C127—22no—
86#120×C127—21no—
87C4×Q8×C127—21no—
88C4×D4×C127—22no—
89C4×D4×C127—21no—
90C4×D4×C127—22no—
91C4×D4×C127—21no—
92C4×D4×C127—21no—
93#117×C127D411yescharacteristic
94C2×C4⋊C4×C127—21no—
95C2×C4⋊C4×C127—21no—
96C2×C4⋊C4×C127—21no—
97C2×C4⋊C4×C127D411yescharacteristic
98C2×C4⋊C4×C127D411yescharacteristic
99C2×C22⋊C4×C127—22no—
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#103×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×C127C22⋊C412yes—
114C24×C127C2×D411yescharacteristic
115#41×C127—41no—
116#41×C127—41no—
117#41×C127—82no—
118#41×C127—82no—
119#41×C127—81no—
120#41×C127—81no—
121C2×Q8×C127—22no—
122C2×Q8×C127—21no—
123C2×Q8×C127—41no—
124C2×Q8×C127—41no—
125C2×Q8×C127C22⋊C411yescharacteristic
126C2×Q8×C127C22⋊C412yes—
127C2×D4×C127—21no—
128C2×D4×C127—21no—
129C2×D4×C127—22no—
130C2×D4×C127—22no—
131C2×D4×C127—22no—
132C2×D4×C127—21no—
133C2×D4×C127—22no—
134C2×D4×C127—21no—
135C2×D4×C127—21no—
136C2×D4×C127—41no—
137C2×D4×C127—41no—
138C2×D4×C127—42no—
139C2×D4×C127—42no—
140C2×D4×C127C22⋊C411yescharacteristic
141C22×C4×C127—21no—
142C22×C4×C127—22no—
143C22×C4×C127—22no—
144C22×C4×C127—22no—
145C22×C4×C127—21no—
146C22×C4×C127—21no—
147C22×C4×C127—41no—
148C22×C4×C127—41no—
149C22×C4×C127—41no—
150C22×C4×C127—41no—
151C22×C4×C127C22⋊C412yes—
152C22×C4×C127C22×C411yescharacteristic
153C22×C4×C127C2×D411yescharacteristic
154C22×C4×C127C2×D411yescharacteristic
155C22×C4×C127C2×D411yescharacteristic
156C22×C4×C127C2×D411yescharacteristic
157C22×C4×C127C2×D411yescharacteristic
158M16×C127—22no—
159M16×C127—22no—
160M16×C127—41no—
161M16×C127—41no—
162M16×C127—41no—
163M16×C127—41no—
164C2×C8×C127—22no—
165C2×C8×C127—41no—
166C2×C8×C127—41no—
167C2×C8×C127—41no—
168C4⋊C4×C127—22no—
169C4⋊C4×C127—22no—
170C4⋊C4×C127—22no—
171C4⋊C4×C127—22no—
172C4⋊C4×C127—22no—
173C4⋊C4×C127—21no—
174C4⋊C4×C127—21no—
175C4⋊C4×C127—21no—
176C4⋊C4×C127—22no—
177C4⋊C4×C127—21no—
178C4⋊C4×C127—21no—
179C4⋊C4×C127—41no—
180C4⋊C4×C127—41no—
181C4⋊C4×C127C22⋊C412yes—
182C4⋊C4×C127C22⋊C411yescharacteristic
183C4⋊C4×C127C22⋊C411yescharacteristic
184C22⋊C4×C127—22no—
185C22⋊C4×C127—22no—
186C22⋊C4×C127—22no—
187C22⋊C4×C127—22no—
188C22⋊C4×C127—22no—
189C22⋊C4×C127—22no—
190C22⋊C4×C127—21no—
191C22⋊C4×C127—22no—
192C22⋊C4×C127—21no—
193C22⋊C4×C127—21no—
194C22⋊C4×C127—22no—
195C22⋊C4×C127—22no—
196C22⋊C4×C127—21no—
197C22⋊C4×C127—21no—
198C22⋊C4×C127—22no—
199C22⋊C4×C127—41no—
200C22⋊C4×C127—42no—
201C42×C127—22no—
202C42×C127—21no—
203C42×C127—41no—
204C42×C127—41no—
205C23×C127—21no—
206C23×C127—21no—
207C23×C127—22no—
208C23×C127—21no—
209C23×C127—41no—
210C23×C127—41no—
211C23×C127—42no—
212C23×C127—42no—
213C23×C127—42no—
214C23×C127C2×C22⋊C411yescharacteristic
215C23×C127#12011yescharacteristic
216C23×C127#12011yescharacteristic
217Q8×C127—42no—
218Q8×C127—41no—
219Q8×C127—41no—
220Q8×C127—41no—
221Q8×C127—82no—
222D4×C127—41no—
223D4×C127—42no—
224D4×C127—42no—
225D4×C127—41no—
226D4×C127—42no—
227D4×C127—41no—
228D4×C127—41no—
229D4×C127—41no—
230D4×C127—81no—
231D4×C127—82no—
232D4×C127—81no—
233D4×C127—82no—
234D4×C127—82no—
235C2×C4×C127—21no—
236C2×C4×C127—21no—
237C2×C4×C127—21no—
238C2×C4×C127—21no—
239C2×C4×C127—21no—
240C2×C4×C127—21no—
241C2×C4×C127—21no—
242C2×C4×C127—22no—
243C2×C4×C127—21no—
244C2×C4×C127—22no—
245C2×C4×C127—21no—
246C2×C4×C127—22no—
247C2×C4×C127—41no—
248C2×C4×C127—41no—
249C2×C4×C127—41no—
250C2×C4×C127—41no—
251C2×C4×C127—41no—
252C2×C4×C127—41no—
253C2×C4×C127—41no—
254C2×C4×C127—42no—
255C2×C4×C127—42no—
256C2×C4×C127—81no—
257C2×C4×C127—82no—
258C2×C4×C127—82no—
259C2×C4×C127—82no—
260C2×C4×C127—81no—
261C2×C4×C127—81no—
262C2×C4×C127—81no—
263C2×C4×C127—81no—
264C2×C4×C127—81no—
265C2×C4×C127C2×C22⋊C411yescharacteristic
266C2×C4×C127C2×C22⋊C411yescharacteristic
267C2×C4×C127#12011yescharacteristic
268C2×C4×C127#12011yescharacteristic
269C8×C127—42no—
270C8×C127—81no—
271C22×C127—21no—
272C22×C127—21no—
273C22×C127—21no—
274C22×C127—21no—
275C22×C127—21no—
276C22×C127—21no—
277C22×C127—21no—
278C22×C127—21no—
279C22×C127—41no—
280C22×C127—42no—
281C22×C127—41no—
282C22×C127—42no—
283C22×C127—41no—
284C22×C127—42no—
285C22×C127—81no—
286C22×C127—81no—
287C22×C127—162no—
288C22×C127#37911yescharacteristic
289C22×C127#45311yescharacteristic
290C22×C127#45511yescharacteristic
291C4×C127—21no—
292C4×C127—21no—
293C4×C127—21no—
294C4×C127—42no—
295C4×C127—42no—
296C4×C127—41no—
297C4×C127—41no—
298C4×C127—41no—
299C4×C127—42no—
300C4×C127—82no—
301C4×C127—161no—
302C4×C127B(4,𝔽2)11yescharacteristic
303C4×C127#45811yescharacteristic
304#8481C12711yesmaximal, characteristic, direct product factor, Sylow
305C2×C127—21no—
306C2×C127—21no—
307C2×C127—41no—
308C2×C127—41no—
309C2×C127—81no—
310C2×C127—82no—
311C2×C127#179011yescharacteristic
312C2×C127#179211yescharacteristic
313C2×C127#179611yescharacteristic
314#3536C2×C12711yescharacteristic
315#1964C2×C12711yescharacteristic, complemented
316#1900C2×C12711yescharacteristic, complemented
317#1894C2×C12711yescharacteristic, complemented
318#1871C2×C12711yescharacteristic, complemented
319#1513C2×C12711yescharacteristic, complemented
320#1508C2×C12711yescharacteristic, complemented
321C127#848111yescharacteristic, direct product factor, Sylow
322C22×M16C22×C12711yescharacteristic
323#562—22no—
324#554—21no—
325#548—21no—
326#547—21no—
327#546—21no—
328#546—22no—
329#543C4×C12712yescomplemented
330#542—21no—
331#539—21no—
332#538C4×C12712yescomplemented
333#537—21no—
334#537—21no—
335#525C22×C12711yescharacteristic
336C2×C22⋊Q8C22×C12711yescharacteristic
337C2×#121C22×C12711yescharacteristic
338C2×#104—21no—
339C2×#103—21no—
340C2×#100—21no—
341C2×#99—22no—
342#407C22×C12711yescharacteristic
343#380C22×C12711yescharacteristic
344C4×C22⋊C4C22×C12711yescharacteristic
345#343—21no—
346#340—21no—
347#339—21no—
348#328—22no—
349#328—21no—
350#327—21no—
351C2×#41—22no—
352C2×#41—21no—
353C2×#41D4×C12711yescharacteristic
354C22×Q8D4×C12711yescharacteristic
355C22×D4D4×C12712yes—
356C22×D4D4×C12711yescharacteristic
357C23×C4C23×C12711yescharacteristic
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—42no—
362C22×C8—21no—
363C4⋊Q8—21no—
364#126—22no—
365#125—22no—
366#124—21no—
367#124—22no—
368#124—22no—
369#123—22no—
370#123—22no—
371#123—22no—
372#123—21no—
373#123—22no—
374C22⋊Q8—21no—
375C22⋊Q8—22no—
376C22⋊Q8—22no—
377C22⋊Q8—22no—
378C22⋊Q8—22no—
379C22⋊Q8—21no—
380C22⋊Q8—21no—
381C22⋊Q8—22no—
382C22⋊Q8—22no—
383C22⋊Q8C2×C4×C12712yes—
384C22⋊Q8C2×C4×C12711yescharacteristic
385C22⋊Q8D4×C12712yes—
386C22⋊Q8D4×C12711yescharacteristic
387#121—21no—
388#121—22no—
389#121—22no—
390#121—22no—
391#121—22no—
392#121—22no—
393#121—21no—
394#121—21no—
395#121—21no—
396#121—21no—
397#121C2×C4×C12711yescharacteristic
398#121D4×C12711yescharacteristic
399#120—22no—
400#120—21no—
401C4×Q8—21no—
402C4×D4—22no—
403C4×D4—21no—
404C4×D4—22no—
405C4×D4—21no—
406C4×D4—21no—
407#117D4×C12711yescharacteristic
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4D4×C12711yescharacteristic
412C2×C4⋊C4D4×C12711yescharacteristic
413C2×C22⋊C4—22no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4C2×C4×C12712yes—
418C2×C42—21no—
419#104—42no—
420#103—42no—
421#100—42no—
422#99—44no—
423C22⋊C8—21no—
424C22⋊C8—21no—
425#95—21no—
426#95—21no—
427C24C22⋊C4×C12712yes—
428C24C2×D4×C12711yescharacteristic
429#41—41no—
430#41—41no—
431#41—82no—
432#41—82no—
433#41—81no—
434#41—81no—
435C2×Q8—22no—
436C2×Q8—21no—
437C2×Q8—41no—
438C2×Q8—41no—
439C2×Q8C22⋊C4×C12711yescharacteristic
440C2×Q8C22⋊C4×C12712yes—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—21no—
447C2×D4—22no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4C22⋊C4×C12711yescharacteristic
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4C22⋊C4×C12712yes—
466C22×C4C22×C4×C12711yescharacteristic
467C22×C4C2×D4×C12711yescharacteristic
468C22×C4C2×D4×C12711yescharacteristic
469C22×C4C2×D4×C12711yescharacteristic
470C22×C4C2×D4×C12711yescharacteristic
471C22×C4C2×D4×C12711yescharacteristic
472M16—22no—
473M16—22no—
474M16—41no—
475M16—41no—
476M16—41no—
477M16—41no—
478C2×C8—22no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—22no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4C22⋊C4×C12712yes—
496C4⋊C4C22⋊C4×C12711yescharacteristic
497C4⋊C4C22⋊C4×C12711yescharacteristic
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—21no—
505C22⋊C4—22no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—22no—
513C22⋊C4—41no—
514C22⋊C4—42no—
515C42—22no—
516C42—21no—
517C42—41no—
518C42—41no—
519C23—21no—
520C23—21no—
521C23—22no—
522C23—21no—
523C23—41no—
524C23—41no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23C2×C22⋊C4×C12711yescharacteristic
529C23#120×C12711yescharacteristic
530C23#120×C12711yescharacteristic
531Q8—42no—
532Q8—41no—
533Q8—41no—
534Q8—41no—
535Q8—82no—
536D4—41no—
537D4—42no—
538D4—42no—
539D4—41no—
540D4—42no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—81no—
545D4—82no—
546D4—81no—
547D4—82no—
548D4—82no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—81no—
571C2×C4—82no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4—81no—
575C2×C4—81no—
576C2×C4—81no—
577C2×C4—81no—
578C2×C4—81no—
579C2×C4C2×C22⋊C4×C12711yescharacteristic
580C2×C4C2×C22⋊C4×C12711yescharacteristic
581C2×C4#120×C12711yescharacteristic
582C2×C4#120×C12711yescharacteristic
583C8—42no—
584C8—81no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—21no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—41no—
594C22—42no—
595C22—41no—
596C22—42no—
597C22—41no—
598C22—42no—
599C22—81no—
600C22—81no—
601C22—162no—
602C22#379×C12711yescharacteristic
603C22#453×C12711yescharacteristic
604C22#455×C12711yescharacteristic
605C4—21no—
606C4—21no—
607C4—21no—
608C4—41no—
609C4—42no—
610C4—42no—
611C4—42no—
612C4—41no—
613C4—41no—
614C4—82no—
615C4—161no—
616C4B(4,𝔽2)×C12711yescharacteristic
617C4#458×C12711yescharacteristic
618C2—21no—
619C2—21no—
620C2—41no—
621C2—41no—
622C2—82no—
623C2—81no—
624C2C127×#179011yescharacteristic
625C2C127×#179211yescharacteristic
626C2C127×#179611yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC127×#3536C2
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×#1894C2semidirect
5. C127×#1871C2semidirect
6. C127×#1513C2semidirect
7. C127×#1508C2semidirect
15. #543×C127C4semidirect
18. #538×C127C4semidirect
304. #8481C127direct (N × H)
315. #1964C2×C127semidirect
316. #1900C2×C127semidirect
317. #1894C2×C127semidirect
318. #1871C2×C127semidirect
319. #1513C2×C127semidirect
320. #1508C2×C127semidirect
321. C127#8481direct (N × H)
329. #543C4×C127semidirect
332. #538C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35362
C127×#19642
C127×#19002
C127×#18942
C127×#18712
C127×#15132
C127×#15082
#8481127