Finite Group Databasebeta

← C127×#8489 #44572162

Subgroups — C127×#8489 #44572162

Order 32512.

690 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3560C211yesmaximal, characteristic
2C127×#1553C211yesmaximal, characteristic, complemented
3C127×#1535C211yesmaximal, characteristic, complemented
4C127×#1496C211yesmaximal, characteristic, complemented
5C127×#1482C211yesmaximal, characteristic, complemented
6C127×#1473C211yesmaximal, characteristic, complemented
7C127×#1473C211yesmaximal, characteristic, complemented
8#563×C127—21no—
9#560×C127—21no—
10#553×C127—21no—
11#553×C127—21no—
12#551×C127—21no—
13#547×C127—21no—
14#546×C127—21no—
15#546×C127—21no—
16#542×C127—21no—
17#539×C127—21no—
18#539×C127C411yescharacteristic
19#538×C127—21no—
20#538×C127—21no—
21#538×C127C411yescharacteristic
22#537×C127C411yescharacteristic
23#534×C127C411yescharacteristic
24#532×C127C2211yescharacteristic
25#529×C127C2211yescharacteristic
26C2×#126×C127C2211yescharacteristic
27#432×C127C2211yescharacteristic, complemented
28#432×C127C2211yescharacteristic, complemented
29#431×C127C2211yescharacteristic, complemented
30#431×C127C2211yescharacteristic, complemented
31#332×C127—21no—
32#331×C127—21no—
33#330×C127—21no—
34#329×C127—21no—
35Q8⋊C8×C127—21no—
36D4⋊C8×C127—21no—
37D4⋊C8×C127—21no—
38D4⋊C8×C127—21no—
39#324×C127—21no—
40#324×C127—21no—
41#323×C127—21no—
42#323×C127—21no—
43C2×#41×C127—21no—
44C2×#41×C127—21no—
45C22×D4×C127—21no—
46C4⋊Q8×C127—21no—
47C4⋊Q8×C127D411yescharacteristic
48#127×C127D411yescharacteristic
49#126×C127—21no—
50#126×C127—21no—
51#126×C127—21no—
52#126×C127—21no—
53#126×C127—21no—
54#126×C127—21no—
55#126×C127—21no—
56#126×C127—21no—
57#126×C127—21no—
58#125×C127—21no—
59#125×C127—21no—
60#125×C127D411yescharacteristic
61#124×C127—21no—
62#124×C127—21no—
63#124×C127—21no—
64#124×C127—21no—
65#124×C127D411yescharacteristic
66#123×C127—21no—
67#123×C127—21no—
68#123×C127—21no—
69#123×C127—21no—
70#123×C127—21no—
71#123×C127—21no—
72#123×C127—21no—
73#123×C127—21no—
74#123×C127—21no—
75#123×C127—21no—
76#123×C127—21no—
77#123×C127—21no—
78C22⋊Q8×C127—21no—
79C22⋊Q8×C127—21no—
80C22⋊Q8×C127—21no—
81C22⋊Q8×C127—21no—
82C22⋊Q8×C127—21no—
83C22⋊Q8×C127—21no—
84C22⋊Q8×C127—21no—
85C22⋊Q8×C127C2×C411yescharacteristic
86#121×C127—21no—
87#121×C127—21no—
88#121×C127—21no—
89#121×C127—21no—
90#121×C127—21no—
91#121×C127—21no—
92#121×C127—21no—
93#121×C127—21no—
94#121×C127—21no—
95#121×C127—21no—
96#121×C127—21no—
97#121×C127—21no—
98#121×C127C2×C411yescharacteristic
99#121×C127C2×C411yescharacteristic
100#121×C127C2×C411yescharacteristic
101#120×C127—21no—
102#120×C127—21no—
103#120×C127—21no—
104#120×C127—21no—
105#120×C127—21no—
106C4×Q8×C127D411yescharacteristic
107C4×D4×C127—21no—
108C4×D4×C127—21no—
109C4×D4×C127—21no—
110C4×D4×C127—21no—
111C4×D4×C127—21no—
112C4×D4×C127—21no—
113C4×D4×C127—21no—
114C4×D4×C127—21no—
115C4×D4×C127D411yescharacteristic
116C4×D4×C127D411yescharacteristic
117C4×D4×C127D411yescharacteristic
118#117×C127—21no—
119#117×C127—21no—
120C2×C4⋊C4×C127—21no—
121C2×C4⋊C4×C127C2×C411yescharacteristic
122C2×C4⋊C4×C127D411yescharacteristic
123C2×C4⋊C4×C127D411yescharacteristic
124C2×C22⋊C4×C127—21no—
125C2×C22⋊C4×C127—21no—
126C2×C22⋊C4×C127C2×C411yescharacteristic
127C2×C22⋊C4×C127D411yescharacteristic
128C2×C22⋊C4×C127D411yescharacteristic
129C2×C42×C127C2311yescharacteristic
130C4⋊C8×C127—21no—
131C4⋊C8×C127—21no—
132C4⋊C8×C127—21no—
133C4⋊C8×C127—21no—
134C22⋊C8×C127—21no—
135C22⋊C8×C127—21no—
136C22⋊C8×C127—21no—
137C22⋊C8×C127—21no—
138#97×C127—21no—
139#97×C127—21no—
140C4×C8×C127—21no—
141C4×C8×C127—21no—
142C24×C127—21no—
143C24×C127C22⋊C411yescharacteristic
144#41×C127—82no—
145#41×C127—82no—
146C2×Q8×C127—21no—
147C2×Q8×C127—21no—
148C2×Q8×C127C22⋊C411yescharacteristic
149C2×D4×C127—21no—
150C2×D4×C127—21no—
151C2×D4×C127—21no—
152C2×D4×C127—21no—
153C2×D4×C127—21no—
154C2×D4×C127—21no—
155C2×D4×C127—21no—
156C2×D4×C127—21no—
157C2×D4×C127—21no—
158C2×D4×C127—21no—
159C2×D4×C127—21no—
160C2×D4×C127—21no—
161C2×D4×C127—82no—
162C2×D4×C127C22⋊C411yescharacteristic
163C2×D4×C127C22⋊C411yescharacteristic
164C2×D4×C127C22⋊C411yescharacteristic
165C22×C4×C127—21no—
166C22×C4×C127—21no—
167C22×C4×C127—21no—
168C22×C4×C127—21no—
169C22×C4×C127—21no—
170C22×C4×C127—21no—
171C22×C4×C127—21no—
172C22×C4×C127—21no—
173C22×C4×C127C22⋊C411yescharacteristic
174C22×C4×C127C22⋊C411yescharacteristic
175C22×C4×C127C22⋊C411yescharacteristic
176C22×C4×C127C22×C411yescharacteristic
177C22×C4×C127C2×D411yescharacteristic
178C22×C4×C127C2×D411yescharacteristic
179C2×C8×C127—41no—
180C2×C8×C127—41no—
181C2×C8×C127—41no—
182C2×C8×C127—41no—
183C4⋊C4×C127—21no—
184C4⋊C4×C127—21no—
185C4⋊C4×C127—21no—
186C4⋊C4×C127—21no—
187C4⋊C4×C127—21no—
188C4⋊C4×C127—21no—
189C4⋊C4×C127—21no—
190C4⋊C4×C127—21no—
191C4⋊C4×C127—21no—
192C4⋊C4×C127—21no—
193C4⋊C4×C127—21no—
194C4⋊C4×C127—21no—
195C4⋊C4×C127—21no—
196C4⋊C4×C127—21no—
197C4⋊C4×C127—21no—
198C4⋊C4×C127—21no—
199C4⋊C4×C127—21no—
200C4⋊C4×C127C22⋊C411yescharacteristic
201C4⋊C4×C127C22⋊C411yescharacteristic
202C4⋊C4×C127C22⋊C411yescharacteristic
203C4⋊C4×C127C22⋊C411yescharacteristic
204C22⋊C4×C127—21no—
205C22⋊C4×C127—21no—
206C22⋊C4×C127—21no—
207C22⋊C4×C127—21no—
208C22⋊C4×C127—21no—
209C22⋊C4×C127—21no—
210C22⋊C4×C127—21no—
211C22⋊C4×C127—21no—
212C22⋊C4×C127—21no—
213C22⋊C4×C127—21no—
214C22⋊C4×C127—21no—
215C22⋊C4×C127—21no—
216C22⋊C4×C127—21no—
217C22⋊C4×C127—21no—
218C22⋊C4×C127—21no—
219C22⋊C4×C127—21no—
220C22⋊C4×C127—21no—
221C22⋊C4×C127—21no—
222C22⋊C4×C127—21no—
223C22⋊C4×C127—21no—
224C22⋊C4×C127—21no—
225C22⋊C4×C127—21no—
226C22⋊C4×C127—21no—
227C22⋊C4×C127—21no—
228C22⋊C4×C127—21no—
229C42×C127—21no—
230C42×C127—21no—
231C42×C127—21no—
232C42×C127C2×D411yescharacteristic
233C42×C127C2×D411yescharacteristic
234C42×C127C2×D411yescharacteristic
235C42×C127C2×D411yescharacteristic
236C23×C127—21no—
237C23×C127—21no—
238C23×C127—21no—
239C23×C127—21no—
240C23×C127—41no—
241C23×C127—41no—
242C23×C127—41no—
243C23×C127—81no—
244C23×C127—81no—
245C23×C127—81no—
246C23×C127C2×C22⋊C411yescharacteristic
247Q8×C127—41no—
248Q8×C127—81no—
249Q8×C127—81no—
250D4×C127—41no—
251D4×C127—41no—
252D4×C127—41no—
253D4×C127—42no—
254D4×C127—42no—
255D4×C127—42no—
256D4×C127—81no—
257D4×C127—81no—
258D4×C127—81no—
259D4×C127—81no—
260D4×C127—81no—
261D4×C127—81no—
262D4×C127—81no—
263D4×C127—81no—
264D4×C127—81no—
265C2×C4×C127—21no—
266C2×C4×C127—21no—
267C2×C4×C127—21no—
268C2×C4×C127—21no—
269C2×C4×C127—21no—
270C2×C4×C127—21no—
271C2×C4×C127—21no—
272C2×C4×C127—21no—
273C2×C4×C127—41no—
274C2×C4×C127—41no—
275C2×C4×C127—41no—
276C2×C4×C127—41no—
277C2×C4×C127—41no—
278C2×C4×C127—41no—
279C2×C4×C127—81no—
280C2×C4×C127—81no—
281C2×C4×C127—81no—
282C2×C4×C127—81no—
283C2×C4×C127—81no—
284C2×C4×C127—81no—
285C2×C4×C127—81no—
286C2×C4×C127—81no—
287C2×C4×C127C2×C22⋊C411yescharacteristic
288C2×C4×C127C2×C22⋊C411yescharacteristic
289C2×C4×C127#12011yescharacteristic
290C2×C4×C127#12011yescharacteristic
291C2×C4×C127#12011yescharacteristic
292C2×C4×C127#12011yescharacteristic
293C8×C127—81no—
294C8×C127—81no—
295C8×C127—81no—
296C8×C127—81no—
297C22×C127—21no—
298C22×C127—21no—
299C22×C127—21no—
300C22×C127—41no—
301C22×C127—41no—
302C22×C127—41no—
303C22×C127—41no—
304C22×C127—41no—
305C22×C127—41no—
306C22×C127—41no—
307C22×C127—41no—
308C22×C127—41no—
309C22×C127—41no—
310C22×C127—41no—
311C22×C127—41no—
312C22×C127—161no—
313C22×C127—162no—
314C22×C127#37911yescharacteristic
315C4×C127—21no—
316C4×C127—21no—
317C4×C127—21no—
318C4×C127—21no—
319C4×C127—21no—
320C4×C127—21no—
321C4×C127—41no—
322C4×C127—41no—
323C4×C127—41no—
324C4×C127—41no—
325C4×C127—41no—
326C4×C127—41no—
327C4×C127—41no—
328C4×C127—41no—
329#8489C12711yesmaximal, characteristic, direct product factor, Sylow
330C2×C127—41no—
331C2×C127—81no—
332C2×C127—81no—
333C2×C127—81no—
334C2×C127—81no—
335C2×C127#179111yescharacteristic
336C2×C127#179411yescharacteristic
337C2×C127#179511yescharacteristic
338#3560C2×C12711yescharacteristic
339#1553C2×C12711yescharacteristic, complemented
340#1535C2×C12711yescharacteristic, complemented
341#1496C2×C12711yescharacteristic, complemented
342#1482C2×C12711yescharacteristic, complemented
343#1473C2×C12711yescharacteristic, complemented
344#1473C2×C12711yescharacteristic, complemented
345C127#848911yescharacteristic, direct product factor, Sylow
346#563—21no—
347#560—21no—
348#553—21no—
349#553—21no—
350#551—21no—
351#547—21no—
352#546—21no—
353#546—21no—
354#542—21no—
355#539—21no—
356#539C4×C12711yescharacteristic
357#538—21no—
358#538—21no—
359#538C4×C12711yescharacteristic
360#537C4×C12711yescharacteristic
361#534C4×C12711yescharacteristic
362#532C22×C12711yescharacteristic
363#529C22×C12711yescharacteristic
364C2×#126C22×C12711yescharacteristic
365#432C22×C12711yescharacteristic, complemented
366#432C22×C12711yescharacteristic, complemented
367#431C22×C12711yescharacteristic, complemented
368#431C22×C12711yescharacteristic, complemented
369#332—21no—
370#331—21no—
371#330—21no—
372#329—21no—
373Q8⋊C8—21no—
374D4⋊C8—21no—
375D4⋊C8—21no—
376D4⋊C8—21no—
377#324—21no—
378#324—21no—
379#323—21no—
380#323—21no—
381C2×#41—21no—
382C2×#41—21no—
383C22×D4—21no—
384C4⋊Q8—21no—
385C4⋊Q8D4×C12711yescharacteristic
386#127D4×C12711yescharacteristic
387#126—21no—
388#126—21no—
389#126—21no—
390#126—21no—
391#126—21no—
392#126—21no—
393#126—21no—
394#126—21no—
395#126—21no—
396#125—21no—
397#125—21no—
398#125D4×C12711yescharacteristic
399#124—21no—
400#124—21no—
401#124—21no—
402#124—21no—
403#124D4×C12711yescharacteristic
404#123—21no—
405#123—21no—
406#123—21no—
407#123—21no—
408#123—21no—
409#123—21no—
410#123—21no—
411#123—21no—
412#123—21no—
413#123—21no—
414#123—21no—
415#123—21no—
416C22⋊Q8—21no—
417C22⋊Q8—21no—
418C22⋊Q8—21no—
419C22⋊Q8—21no—
420C22⋊Q8—21no—
421C22⋊Q8—21no—
422C22⋊Q8—21no—
423C22⋊Q8C2×C4×C12711yescharacteristic
424#121—21no—
425#121—21no—
426#121—21no—
427#121—21no—
428#121—21no—
429#121—21no—
430#121—21no—
431#121—21no—
432#121—21no—
433#121—21no—
434#121—21no—
435#121—21no—
436#121C2×C4×C12711yescharacteristic
437#121C2×C4×C12711yescharacteristic
438#121C2×C4×C12711yescharacteristic
439#120—21no—
440#120—21no—
441#120—21no—
442#120—21no—
443#120—21no—
444C4×Q8D4×C12711yescharacteristic
445C4×D4—21no—
446C4×D4—21no—
447C4×D4—21no—
448C4×D4—21no—
449C4×D4—21no—
450C4×D4—21no—
451C4×D4—21no—
452C4×D4—21no—
453C4×D4D4×C12711yescharacteristic
454C4×D4D4×C12711yescharacteristic
455C4×D4D4×C12711yescharacteristic
456#117—21no—
457#117—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4C2×C4×C12711yescharacteristic
460C2×C4⋊C4D4×C12711yescharacteristic
461C2×C4⋊C4D4×C12711yescharacteristic
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4C2×C4×C12711yescharacteristic
465C2×C22⋊C4D4×C12711yescharacteristic
466C2×C22⋊C4D4×C12711yescharacteristic
467C2×C42C23×C12711yescharacteristic
468C4⋊C8—21no—
469C4⋊C8—21no—
470C4⋊C8—21no—
471C4⋊C8—21no—
472C22⋊C8—21no—
473C22⋊C8—21no—
474C22⋊C8—21no—
475C22⋊C8—21no—
476#97—21no—
477#97—21no—
478C4×C8—21no—
479C4×C8—21no—
480C24—21no—
481C24C22⋊C4×C12711yescharacteristic
482#41—82no—
483#41—82no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8C22⋊C4×C12711yescharacteristic
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—82no—
500C2×D4C22⋊C4×C12711yescharacteristic
501C2×D4C22⋊C4×C12711yescharacteristic
502C2×D4C22⋊C4×C12711yescharacteristic
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4C22⋊C4×C12711yescharacteristic
512C22×C4C22⋊C4×C12711yescharacteristic
513C22×C4C22⋊C4×C12711yescharacteristic
514C22×C4C22×C4×C12711yescharacteristic
515C22×C4C2×D4×C12711yescharacteristic
516C22×C4C2×D4×C12711yescharacteristic
517C2×C8—41no—
518C2×C8—41no—
519C2×C8—41no—
520C2×C8—41no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4C22⋊C4×C12711yescharacteristic
539C4⋊C4C22⋊C4×C12711yescharacteristic
540C4⋊C4C22⋊C4×C12711yescharacteristic
541C4⋊C4C22⋊C4×C12711yescharacteristic
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—21no—
547C22⋊C4—21no—
548C22⋊C4—21no—
549C22⋊C4—21no—
550C22⋊C4—21no—
551C22⋊C4—21no—
552C22⋊C4—21no—
553C22⋊C4—21no—
554C22⋊C4—21no—
555C22⋊C4—21no—
556C22⋊C4—21no—
557C22⋊C4—21no—
558C22⋊C4—21no—
559C22⋊C4—21no—
560C22⋊C4—21no—
561C22⋊C4—21no—
562C22⋊C4—21no—
563C22⋊C4—21no—
564C22⋊C4—21no—
565C22⋊C4—21no—
566C22⋊C4—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42C2×D4×C12711yescharacteristic
571C42C2×D4×C12711yescharacteristic
572C42C2×D4×C12711yescharacteristic
573C42C2×D4×C12711yescharacteristic
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—81no—
582C23—81no—
583C23—81no—
584C23C2×C22⋊C4×C12711yescharacteristic
585Q8—41no—
586Q8—81no—
587Q8—81no—
588D4—41no—
589D4—41no—
590D4—41no—
591D4—42no—
592D4—42no—
593D4—42no—
594D4—81no—
595D4—81no—
596D4—81no—
597D4—81no—
598D4—81no—
599D4—81no—
600D4—81no—
601D4—81no—
602D4—81no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—81no—
618C2×C4—81no—
619C2×C4—81no—
620C2×C4—81no—
621C2×C4—81no—
622C2×C4—81no—
623C2×C4—81no—
624C2×C4—81no—
625C2×C4C2×C22⋊C4×C12711yescharacteristic
626C2×C4C2×C22⋊C4×C12711yescharacteristic
627C2×C4#120×C12711yescharacteristic
628C2×C4#120×C12711yescharacteristic
629C2×C4#120×C12711yescharacteristic
630C2×C4#120×C12711yescharacteristic
631C8—81no—
632C8—81no—
633C8—81no—
634C8—81no—
635C22—21no—
636C22—21no—
637C22—21no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—161no—
651C22—162no—
652C22#379×C12711yescharacteristic
653C4—21no—
654C4—21no—
655C4—21no—
656C4—21no—
657C4—21no—
658C4—21no—
659C4—41no—
660C4—41no—
661C4—41no—
662C4—41no—
663C4—41no—
664C4—41no—
665C4—41no—
666C4—41no—
667C2—41no—
668C2—81no—
669C2—81no—
670C2—81no—
671C2—81no—
672C2C127×#179111yescharacteristic
673C2C127×#179411yescharacteristic
674C2C127×#179511yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC127×#3560C2
LCSG ▷ C22×C4 ▷ 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×#1553C2semidirect
3. C127×#1535C2semidirect
4. C127×#1496C2semidirect
5. C127×#1482C2semidirect
6. C127×#1473C2semidirect
7. C127×#1473C2semidirect
27. #432×C127C22semidirect
28. #432×C127C22semidirect
29. #431×C127C22semidirect
30. #431×C127C22semidirect
329. #8489C127direct (N × H)
339. #1553C2×C127semidirect
340. #1535C2×C127semidirect
341. #1496C2×C127semidirect
342. #1482C2×C127semidirect
343. #1473C2×C127semidirect
344. #1473C2×C127semidirect
345. C127#8489direct (N × H)
365. #432C22×C127semidirect
366. #432C22×C127semidirect
367. #431C22×C127semidirect
368. #431C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35602
C127×#15532
C127×#15352
C127×#14962
C127×#14822
C127×#14732
#8489127