Finite Group Databasebeta

← C127×#8416 #44572089

Subgroups — C127×#8416 #44572089

Order 32512.

852 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3519C211yesmaximal, characteristic
2C127×#1980C211yesmaximal, characteristic, complemented
3C127×#1762C211yesmaximal, characteristic, complemented
4C127×#1530C211yesmaximal, characteristic, complemented
5C127×#1524C211yesmaximal, characteristic, complemented
6C127×#1509C211yesmaximal, characteristic, complemented
7C127×#1490C211yesmaximal, characteristic, complemented
8#555×C127C411yescharacteristic, complemented
9#554×C127C411yescharacteristic, complemented
10#553×C127—21no—
11#553×C127—21no—
12#550×C127C411yescharacteristic, complemented
13#546×C127—22no—
14#546×C127—21no—
15D42×C127—21no—
16D42×C127C411yescharacteristic, complemented
17#540×C127—21no—
18#538×C127—22no—
19#532×C127C2211yescharacteristic
20#529×C127C2211yescharacteristic
21#525×C127—21no—
22C2×#121×C127—21no—
23#518×C127—21no—
24C2×C4×D4×C127C2211yescharacteristic
25#432×C127C2211yescharacteristic, complemented
26C2×#104×C127—22no—
27C2×#102×C127—21no—
28C4×M16×C127C2211yescharacteristic, complemented
29C2×#97×C127C2211yescharacteristic, complemented
30C4×C4⋊C4×C127C2211yescharacteristic, complemented
31#340×C127—21no—
32#330×C127—21no—
33#329×C127—21no—
34#329×C127—22no—
35#328×C127—21no—
36#327×C127—21no—
37D4⋊C8×C127—21no—
38D4⋊C8×C127—21no—
39C2×#41×C127—21no—
40C2×#41×C127D412yes—
41C22×D4×C127—22no—
42C22×D4×C127—21no—
43C22×D4×C127—21no—
44C22×D4×C127D411yescharacteristic
45C23×C4×C127—21no—
46C2×M16×C127—21no—
47C22×C8×C127—21no—
48C4⋊Q8×C127C2×C411yescharacteristic
49#127×C127—21no—
50#127×C127C2×C411yescharacteristic
51#126×C127—22no—
52#126×C127—21no—
53#125×C127—21no—
54#125×C127D411yescharacteristic
55#124×C127—22no—
56#124×C127D411yescharacteristic
57#124×C127D412yes—
58#123×C127—22no—
59#123×C127—22no—
60#123×C127—22no—
61#123×C127—21no—
62C22⋊Q8×C127—21no—
63C22⋊Q8×C127—22no—
64C22⋊Q8×C127D411yescharacteristic
65#121×C127—22no—
66#121×C127—22no—
67#121×C127—22no—
68#121×C127—22no—
69#121×C127—21no—
70#121×C127—22no—
71#121×C127—21no—
72#121×C127—21no—
73#121×C127—21no—
74#121×C127—21no—
75#121×C127—21no—
76#121×C127—21no—
77#121×C127D411yescharacteristic
78#120×C127—22no—
79#120×C127—22no—
80#120×C127—22no—
81C4×Q8×C127C2×C411yescharacteristic
82C4×D4×C127—22no—
83C4×D4×C127—22no—
84C4×D4×C127—22no—
85C4×D4×C127—21no—
86C4×D4×C127—21no—
87C4×D4×C127—21no—
88C4×D4×C127—21no—
89C4×D4×C127—21no—
90C4×D4×C127—21no—
91C4×D4×C127—21no—
92C4×D4×C127C2×C411yescharacteristic
93C4×D4×C127C2×C411yescharacteristic
94C4×D4×C127C2×C411yescharacteristic
95C4×D4×C127D411yescharacteristic
96C4×D4×C127D411yescharacteristic
97#117×C127—21no—
98#117×C127—21no—
99#117×C127—21no—
100C2×C4⋊C4×C127—21no—
101C2×C4⋊C4×C127—21no—
102C2×C4⋊C4×C127D411yescharacteristic
103C2×C22⋊C4×C127—22no—
104C2×C22⋊C4×C127—22no—
105C2×C22⋊C4×C127—21no—
106C2×C42×C127—21no—
107C2×C42×C127C2311yescharacteristic
108C4⋊C8×C127—21no—
109#104×C127—44no—
110#102×C127—24no—
111C22⋊C8×C127—21no—
112#97×C127—21no—
113#97×C127—21no—
114#97×C127—21no—
115#97×C127—21no—
116C4×C8×C127—21no—
117#95×C127—21no—
118C24×C127—22no—
119C24×C127—21no—
120#41×C127—42no—
121#41×C127—42no—
122#41×C127—82no—
123C2×Q8×C127C22⋊C411yescharacteristic
124C2×Q8×C127C22⋊C412yes—
125C2×D4×C127—22no—
126C2×D4×C127—22no—
127C2×D4×C127—22no—
128C2×D4×C127—21no—
129C2×D4×C127—22no—
130C2×D4×C127—22no—
131C2×D4×C127—22no—
132C2×D4×C127—22no—
133C2×D4×C127—21no—
134C2×D4×C127—21no—
135C2×D4×C127—21no—
136C2×D4×C127—41no—
137C2×D4×C127—42no—
138C2×D4×C127—42no—
139C2×D4×C127—82no—
140C2×D4×C127—82no—
141C2×D4×C127—82no—
142C2×D4×C127C22⋊C411yescharacteristic
143C2×D4×C127C22⋊C411yescharacteristic
144C2×D4×C127C22⋊C411yescharacteristic
145C2×D4×C127C22⋊C412yes—
146C22×C4×C127—22no—
147C22×C4×C127—22no—
148C22×C4×C127—21no—
149C22×C4×C127—21no—
150C22×C4×C127—21no—
151C22×C4×C127—21no—
152C22×C4×C127—21no—
153C22×C4×C127—22no—
154C22×C4×C127—21no—
155C22×C4×C127—41no—
156C22×C4×C127—82no—
157C22×C4×C127C2×D411yescharacteristic
158C22×C4×C127C2×D411yescharacteristic
159C22×C4×C127C2×D411yescharacteristic
160M16×C127—22no—
161M16×C127—41no—
162C2×C8×C127—22no—
163C2×C8×C127—41no—
164C2×C8×C127—41no—
165C2×C8×C127—41no—
166C2×C8×C127—41no—
167C4⋊C4×C127—22no—
168C4⋊C4×C127—22no—
169C4⋊C4×C127—21no—
170C4⋊C4×C127—21no—
171C4⋊C4×C127—21no—
172C4⋊C4×C127—21no—
173C4⋊C4×C127—21no—
174C4⋊C4×C127—21no—
175C4⋊C4×C127—21no—
176C4⋊C4×C127—22no—
177C4⋊C4×C127—41no—
178C4⋊C4×C127C22⋊C411yescharacteristic
179C4⋊C4×C127C22⋊C411yescharacteristic
180C4⋊C4×C127C22⋊C411yescharacteristic
181C4⋊C4×C127C22⋊C411yescharacteristic
182C22⋊C4×C127—22no—
183C22⋊C4×C127—22no—
184C22⋊C4×C127—22no—
185C22⋊C4×C127—22no—
186C22⋊C4×C127—22no—
187C22⋊C4×C127—21no—
188C22⋊C4×C127—21no—
189C22⋊C4×C127—21no—
190C22⋊C4×C127—21no—
191C22⋊C4×C127—21no—
192C22⋊C4×C127—21no—
193C22⋊C4×C127—21no—
194C22⋊C4×C127—22no—
195C22⋊C4×C127—21no—
196C22⋊C4×C127—21no—
197C22⋊C4×C127—22no—
198C42×C127—22no—
199C42×C127—21no—
200C42×C127—42no—
201C42×C127C22×C411yescharacteristic
202C42×C127C2×D411yescharacteristic
203C42×C127C2×D411yescharacteristic
204C42×C127C2×D411yescharacteristic
205C23×C127—21no—
206C23×C127—21no—
207C23×C127—22no—
208C23×C127—21no—
209C23×C127—42no—
210C23×C127—44no—
211C23×C127—41no—
212C23×C127—41no—
213C23×C127—81no—
214C23×C127—82no—
215C23×C127—82no—
216C23×C127#12011yescharacteristic
217Q8×C127—42no—
218Q8×C127—41no—
219D4×C127—21no—
220D4×C127—21no—
221D4×C127—21no—
222D4×C127—42no—
223D4×C127—41no—
224D4×C127—42no—
225D4×C127—42no—
226D4×C127—44no—
227D4×C127—41no—
228D4×C127—42no—
229D4×C127—41no—
230D4×C127—42no—
231D4×C127—41no—
232D4×C127—41no—
233D4×C127—82no—
234D4×C127—82no—
235D4×C127—82no—
236D4×C127—82no—
237D4×C127#10412yescomplemented
238C2×C4×C127—21no—
239C2×C4×C127—21no—
240C2×C4×C127—21no—
241C2×C4×C127—21no—
242C2×C4×C127—21no—
243C2×C4×C127—21no—
244C2×C4×C127—22no—
245C2×C4×C127—21no—
246C2×C4×C127—21no—
247C2×C4×C127—21no—
248C2×C4×C127—41no—
249C2×C4×C127—42no—
250C2×C4×C127—42no—
251C2×C4×C127—41no—
252C2×C4×C127—41no—
253C2×C4×C127—42no—
254C2×C4×C127—81no—
255C2×C4×C127—81no—
256C2×C4×C127—82no—
257C2×C4×C127—81no—
258C2×C4×C127—82no—
259C2×C4×C127—82no—
260C2×C4×C127—81no—
261C2×C4×C127—81no—
262C2×C4×C127C2×C22⋊C411yescharacteristic
263C2×C4×C127C2×C22⋊C411yescharacteristic
264C2×C4×C127C2×C22⋊C411yescharacteristic
265C2×C4×C127#12011yescharacteristic
266C2×C4×C127#12011yescharacteristic
267C2×C4×C127#12011yescharacteristic
268C8×C127—42no—
269C8×C127—42no—
270C8×C127—81no—
271C22×C127—21no—
272C22×C127—21no—
273C22×C127—22no—
274C22×C127—41no—
275C22×C127—41no—
276C22×C127—42no—
277C22×C127—41no—
278C22×C127—41no—
279C22×C127—41no—
280C22×C127—42no—
281C22×C127—41no—
282C22×C127—41no—
283C22×C127—41no—
284C22×C127—42no—
285C22×C127—82no—
286C22×C127—82no—
287C22×C127—164no—
288C22×C127#37911yescharacteristic
289C22×C127#45311yescharacteristic
290C22×C127#45511yescharacteristic
291C4×C127—21no—
292C4×C127—21no—
293C4×C127—21no—
294C4×C127—21no—
295C4×C127—21no—
296C4×C127—41no—
297C4×C127—42no—
298C4×C127—41no—
299C4×C127—41no—
300C4×C127—41no—
301C4×C127—41no—
302C4×C127—82no—
303C4×C127C2×#10411yescharacteristic
304C4×C127#42111yescharacteristic
305#8416C12711yesmaximal, characteristic, direct product factor, Sylow
306C2×C127—21no—
307C2×C127—21no—
308C2×C127—42no—
309C2×C127—81no—
310C2×C127—82no—
311C2×C127—81no—
312C2×C127#178911yescharacteristic
313C2×C127#179211yescharacteristic
314C2×C127#179511yescharacteristic
315#3519C2×C12711yescharacteristic
316#1980C2×C12711yescharacteristic, complemented
317#1762C2×C12711yescharacteristic, complemented
318#1530C2×C12711yescharacteristic, complemented
319#1524C2×C12711yescharacteristic, complemented
320#1509C2×C12711yescharacteristic, complemented
321#1490C2×C12711yescharacteristic, complemented
322C127#841611yescharacteristic, direct product factor, Sylow
323#555C4×C12711yescharacteristic, complemented
324#554C4×C12711yescharacteristic, complemented
325#553—21no—
326#553—21no—
327#550C4×C12711yescharacteristic, complemented
328#546—22no—
329#546—21no—
330D42—21no—
331D42C4×C12711yescharacteristic, complemented
332#540—21no—
333#538—22no—
334#532C22×C12711yescharacteristic
335#529C22×C12711yescharacteristic
336#525—21no—
337C2×#121—21no—
338#518—21no—
339C2×C4×D4C22×C12711yescharacteristic
340#432C22×C12711yescharacteristic, complemented
341C2×#104—22no—
342C2×#102—21no—
343C4×M16C22×C12711yescharacteristic, complemented
344C2×#97C22×C12711yescharacteristic, complemented
345C4×C4⋊C4C22×C12711yescharacteristic, complemented
346#340—21no—
347#330—21no—
348#329—21no—
349#329—22no—
350#328—21no—
351#327—21no—
352D4⋊C8—21no—
353D4⋊C8—21no—
354C2×#41—21no—
355C2×#41D4×C12712yes—
356C22×D4—22no—
357C22×D4—21no—
358C22×D4—21no—
359C22×D4D4×C12711yescharacteristic
360C23×C4—21no—
361C2×M16—21no—
362C22×C8—21no—
363C4⋊Q8C2×C4×C12711yescharacteristic
364#127—21no—
365#127C2×C4×C12711yescharacteristic
366#126—22no—
367#126—21no—
368#125—21no—
369#125D4×C12711yescharacteristic
370#124—22no—
371#124D4×C12711yescharacteristic
372#124D4×C12712yes—
373#123—22no—
374#123—22no—
375#123—22no—
376#123—21no—
377C22⋊Q8—21no—
378C22⋊Q8—22no—
379C22⋊Q8D4×C12711yescharacteristic
380#121—22no—
381#121—22no—
382#121—22no—
383#121—22no—
384#121—21no—
385#121—22no—
386#121—21no—
387#121—21no—
388#121—21no—
389#121—21no—
390#121—21no—
391#121—21no—
392#121D4×C12711yescharacteristic
393#120—22no—
394#120—22no—
395#120—22no—
396C4×Q8C2×C4×C12711yescharacteristic
397C4×D4—22no—
398C4×D4—22no—
399C4×D4—22no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4C2×C4×C12711yescharacteristic
408C4×D4C2×C4×C12711yescharacteristic
409C4×D4C2×C4×C12711yescharacteristic
410C4×D4D4×C12711yescharacteristic
411C4×D4D4×C12711yescharacteristic
412#117—21no—
413#117—21no—
414#117—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4D4×C12711yescharacteristic
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—21no—
421C2×C42—21no—
422C2×C42C23×C12711yescharacteristic
423C4⋊C8—21no—
424#104—44no—
425#102—24no—
426C22⋊C8—21no—
427#97—21no—
428#97—21no—
429#97—21no—
430#97—21no—
431C4×C8—21no—
432#95—21no—
433C24—22no—
434C24—21no—
435#41—42no—
436#41—42no—
437#41—82no—
438C2×Q8C22⋊C4×C12711yescharacteristic
439C2×Q8C22⋊C4×C12712yes—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—21no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—41no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4—82no—
455C2×D4—82no—
456C2×D4—82no—
457C2×D4C22⋊C4×C12711yescharacteristic
458C2×D4C22⋊C4×C12711yescharacteristic
459C2×D4C22⋊C4×C12711yescharacteristic
460C2×D4C22⋊C4×C12712yes—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—82no—
472C22×C4C2×D4×C12711yescharacteristic
473C22×C4C2×D4×C12711yescharacteristic
474C22×C4C2×D4×C12711yescharacteristic
475M16—22no—
476M16—41no—
477C2×C8—22no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—22no—
492C4⋊C4—41no—
493C4⋊C4C22⋊C4×C12711yescharacteristic
494C4⋊C4C22⋊C4×C12711yescharacteristic
495C4⋊C4C22⋊C4×C12711yescharacteristic
496C4⋊C4C22⋊C4×C12711yescharacteristic
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—22no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—22no—
513C42—22no—
514C42—21no—
515C42—42no—
516C42C22×C4×C12711yescharacteristic
517C42C2×D4×C12711yescharacteristic
518C42C2×D4×C12711yescharacteristic
519C42C2×D4×C12711yescharacteristic
520C23—21no—
521C23—21no—
522C23—21no—
523C23—22no—
524C23—42no—
525C23—44no—
526C23—41no—
527C23—41no—
528C23—81no—
529C23—82no—
530C23—82no—
531C23#120×C12711yescharacteristic
532Q8—42no—
533Q8—41no—
534D4—21no—
535D4—21no—
536D4—21no—
537D4—42no—
538D4—41no—
539D4—42no—
540D4—42no—
541D4—44no—
542D4—41no—
543D4—42no—
544D4—41no—
545D4—42no—
546D4—41no—
547D4—41no—
548D4—82no—
549D4—82no—
550D4—82no—
551D4—82no—
552D4#104×C12712yescomplemented
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—42no—
569C2×C4—81no—
570C2×C4—81no—
571C2×C4—82no—
572C2×C4—81no—
573C2×C4—82no—
574C2×C4—82no—
575C2×C4—81no—
576C2×C4—81no—
577C2×C4C2×C22⋊C4×C12711yescharacteristic
578C2×C4C2×C22⋊C4×C12711yescharacteristic
579C2×C4C2×C22⋊C4×C12711yescharacteristic
580C2×C4#120×C12711yescharacteristic
581C2×C4#120×C12711yescharacteristic
582C2×C4#120×C12711yescharacteristic
583C8—42no—
584C8—42no—
585C8—81no—
586C22—21no—
587C22—21no—
588C22—22no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—42no—
594C22—42no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—42no—
599C22—41no—
600C22—82no—
601C22—82no—
602C22—164no—
603C22#379×C12711yescharacteristic
604C22#453×C12711yescharacteristic
605C22#455×C12711yescharacteristic
606C4—21no—
607C4—21no—
608C4—21no—
609C4—21no—
610C4—21no—
611C4—41no—
612C4—41no—
613C4—42no—
614C4—41no—
615C4—41no—
616C4—41no—
617C4—82no—
618C4C2×#104×C12711yescharacteristic
619C4#421×C12711yescharacteristic
620C2—21no—
621C2—21no—
622C2—42no—
623C2—81no—
624C2—81no—
625C2—82no—
626C2C127×#178911yescharacteristic
627C2C127×#179211yescharacteristic
628C2C127×#179511yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC127×#3519C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1980C2semidirect
3. C127×#1762C2semidirect
4. C127×#1530C2semidirect
5. C127×#1524C2semidirect
6. C127×#1509C2semidirect
7. C127×#1490C2semidirect
8. #555×C127C4semidirect
9. #554×C127C4semidirect
12. #550×C127C4semidirect
16. D42×C127C4semidirect
25. #432×C127C22semidirect
28. C4×M16×C127C22semidirect
29. C2×#97×C127C22semidirect
30. C4×C4⋊C4×C127C22semidirect
237. D4×C127#104semidirect
305. #8416C127direct (N × H)
316. #1980C2×C127semidirect
317. #1762C2×C127semidirect
318. #1530C2×C127semidirect
319. #1524C2×C127semidirect
320. #1509C2×C127semidirect
321. #1490C2×C127semidirect
322. C127#8416direct (N × H)
323. #555C4×C127semidirect
324. #554C4×C127semidirect
327. #550C4×C127semidirect
331. D42C4×C127semidirect
340. #432C22×C127semidirect
343. C4×M16C22×C127semidirect
344. C2×#97C22×C127semidirect
345. C4×C4⋊C4C22×C127semidirect
552. D4#104×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35192
C127×#19802
C127×#17622
C127×#15302
C127×#15242
C127×#15092
C127×#14902
#8416127