Finite Group Databasebeta

← C127×#18341 #44582014

Subgroups — C127×#18341 #44582014

Order 32512.

898 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3455C211yesmaximal, characteristic
2C127×#3236C211yesmaximal, characteristic, complemented
3C127×#3234C211yesmaximal, characteristic, complemented
4C127×#2611C211yesmaximal, characteristic, complemented
5C127×#1618C212yesmaximal, complemented
6C127×#1615C212yesmaximal, complemented
7C127×#1612C212yesmaximal, complemented
8C127×#1609C212yesmaximal, complemented
9C127×#1506C211yesmaximal, characteristic, complemented
10C127×#1505C211yesmaximal, characteristic, complemented
11C127×#1464C211yesmaximal, characteristic, complemented
12#542×C127—21no—
13#542×C127—21no—
14#541×C127—21no—
15#540×C127—21no—
16#539×C127—21no—
17#539×C127C2212yes—
18#538×C127—21no—
19#538×C127C2212yes—
20#533×C127C2211yescharacteristic
21#532×C127C2211yescharacteristic
22#529×C127—22no—
23#529×C127—22no—
24C2×#125×C127C2211yescharacteristic
25#525×C127—21no—
26C4×#41×C127—21no—
27C2×#117×C127C2211yescharacteristic
28#501×C127—21no—
29#501×C127—21no—
30#491×C127—21no—
31#490×C127—21no—
32#484×C127C2212yes—
33#483×C127C2212yes—
34#481×C127C2212yes—
35#480×C127C2212yes—
36#479×C127—22no—
37#478×C127—22no—
38#432×C127C2211yescharacteristic
39#432×C127C2211yescharacteristic
40#400×C127C2211yescharacteristic
41#399×C127C2211yescharacteristic
42#398×C127C2211yescharacteristic
43#397×C127C2211yescharacteristic
44#389×C127—21no—
45#388×C127—21no—
46#387×C127—21no—
47#385×C127—21no—
48#376×C127C2211yescharacteristic
49#328×C127C2212yes—
50#328×C127C2212yes—
51#327×C127C2212yes—
52#327×C127C2212yes—
53#324×C127C2212yes—
54#323×C127C2212yes—
55C2×#41×C127—21no—
56C23×C4×C127D411yescharacteristic
57C4⋊Q8×C127D411yescharacteristic
58C4⋊Q8×C127D411yescharacteristic
59C4⋊Q8×C127D411yescharacteristic
60#127×C127D411yescharacteristic
61#126×C127—22no—
62#126×C127—22no—
63#126×C127—22no—
64#126×C127—22no—
65#125×C127—22no—
66#125×C127—22no—
67#125×C127—21no—
68#125×C127—21no—
69#125×C127—21no—
70#125×C127—21no—
71#125×C127—21no—
72#124×C127—22no—
73#124×C127—22no—
74#124×C127—21no—
75#123×C127—22no—
76#123×C127—22no—
77#123×C127—22no—
78#123×C127—22no—
79#123×C127—22no—
80C22⋊Q8×C127—21no—
81C22⋊Q8×C127—21no—
82C22⋊Q8×C127—22no—
83C22⋊Q8×C127—22no—
84C22⋊Q8×C127—21no—
85C22⋊Q8×C127C2312yes—
86#121×C127—21no—
87#121×C127—21no—
88#121×C127—22no—
89#121×C127—22no—
90#121×C127—21no—
91#121×C127C2312yes—
92#120×C127—22no—
93C4×Q8×C127—21no—
94C4×Q8×C127—21no—
95C4×Q8×C127—21no—
96C4×Q8×C127D412yes—
97C4×D4×C127—21no—
98C4×D4×C127—21no—
99C4×D4×C127—22no—
100C4×D4×C127—22no—
101C4×D4×C127—22no—
102C4×D4×C127—22no—
103C4×D4×C127—21no—
104C4×D4×C127D412yes—
105#117×C127—22no—
106#117×C127—21no—
107#117×C127—21no—
108#117×C127—21no—
109#117×C127—21no—
110#117×C127—21no—
111C2×C4⋊C4×C127—21no—
112C2×C4⋊C4×C127—21no—
113C2×C4⋊C4×C127—21no—
114C2×C4⋊C4×C127—21no—
115C2×C4⋊C4×C127D411yescharacteristic
116C2×C4⋊C4×C127C2311yescharacteristic
117C2×C4⋊C4×C127C2311yescharacteristic
118C2×C4⋊C4×C127C2311yescharacteristic
119C2×C22⋊C4×C127—21no—
120C2×C22⋊C4×C127—21no—
121C2×C22⋊C4×C127D411yescharacteristic
122C2×C22⋊C4×C127C2311yescharacteristic
123C2×C42×C127—22no—
124C2×C42×C127—21no—
125C2×C42×C127D411yescharacteristic
126C2×C42×C127C2311yescharacteristic
127#107×C127—22no—
128#107×C127—22no—
129#106×C127—22no—
130#106×C127—22no—
131C4⋊C8×C127—21no—
132C4⋊C8×C127—21no—
133#103×C127—22no—
134#103×C127—22no—
135#102×C127—22no—
136#102×C127—22no—
137C22⋊C8×C127C2312yes—
138C22⋊C8×C127C2312yes—
139#97×C127—21no—
140#97×C127—21no—
141#95×C127—21no—
142#95×C127—21no—
143#95×C127—21no—
144#95×C127—21no—
145#95×C127—21no—
146#95×C127C2311yescharacteristic
147#95×C127C2311yescharacteristic
148C24×C127C2×D411yescharacteristic
149#41×C127—42no—
150#41×C127—42no—
151C2×Q8×C127—21no—
152C2×Q8×C127—21no—
153C2×Q8×C127C2×D412yes—
154C2×D4×C127—22no—
155C2×D4×C127—22no—
156C2×D4×C127—22no—
157C2×D4×C127—21no—
158C2×D4×C127—21no—
159C2×D4×C127C2×D412yes—
160C22×C4×C127—21no—
161C22×C4×C127—22no—
162C22×C4×C127—22no—
163C22×C4×C127—22no—
164C22×C4×C127—21no—
165C22×C4×C127—21no—
166C22×C4×C127—21no—
167C22×C4×C127—21no—
168C22×C4×C127—21no—
169C22×C4×C127—41no—
170C22×C4×C127—41no—
171C22×C4×C127C2×D411yescharacteristic
172C22×C4×C127C2×D411yescharacteristic
173C22×C4×C127C2×D411yescharacteristic
174C22×C4×C127C2×D411yescharacteristic
175C22×C4×C127C2×D411yescharacteristic
176C22×C4×C127C2411yescharacteristic
177C2×C8×C127—22no—
178C2×C8×C127—22no—
179C4⋊C4×C127—22no—
180C4⋊C4×C127—22no—
181C4⋊C4×C127—22no—
182C4⋊C4×C127—22no—
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—22no—
190C4⋊C4×C127—21no—
191C4⋊C4×C127—21no—
192C4⋊C4×C127—22no—
193C4⋊C4×C127—21no—
194C4⋊C4×C127—21no—
195C4⋊C4×C127—21no—
196C4⋊C4×C127—21no—
197C4⋊C4×C127—42no—
198C4⋊C4×C127—42no—
199C4⋊C4×C127—41no—
200C4⋊C4×C127—41no—
201C4⋊C4×C127—41no—
202C4⋊C4×C127—41no—
203C4⋊C4×C127C2×D412yes—
204C4⋊C4×C127C2×D412yes—
205C22⋊C4×C127—22no—
206C22⋊C4×C127—22no—
207C22⋊C4×C127—22no—
208C22⋊C4×C127—22no—
209C22⋊C4×C127—22no—
210C22⋊C4×C127—22no—
211C22⋊C4×C127—22no—
212C22⋊C4×C127—21no—
213C22⋊C4×C127—21no—
214C22⋊C4×C127—22no—
215C22⋊C4×C127—21no—
216C22⋊C4×C127—21no—
217C22⋊C4×C127—22no—
218C22⋊C4×C127—42no—
219C22⋊C4×C127—42no—
220C42×C127—22no—
221C42×C127—22no—
222C42×C127—21no—
223C42×C127—22no—
224C42×C127—21no—
225C42×C127—42no—
226C42×C127C2×D411yescharacteristic
227C42×C127C2×D411yescharacteristic
228C42×C127C2×D411yescharacteristic
229C42×C127C2×D411yescharacteristic
230C23×C127—21no—
231C23×C127—22no—
232C23×C127—21no—
233C23×C127—21no—
234C23×C127—41no—
235C23×C127—41no—
236C23×C127C22×D411yescharacteristic
237Q8×C127—42no—
238Q8×C127—42no—
239Q8×C127—81no—
240D4×C127—42no—
241D4×C127—42no—
242D4×C127—42no—
243D4×C127—42no—
244D4×C127—81no—
245D4×C127—82no—
246D4×C127—82no—
247C2×C4×C127—21no—
248C2×C4×C127—21no—
249C2×C4×C127—22no—
250C2×C4×C127—21no—
251C2×C4×C127—21no—
252C2×C4×C127—22no—
253C2×C4×C127—22no—
254C2×C4×C127—22no—
255C2×C4×C127—21no—
256C2×C4×C127—21no—
257C2×C4×C127—21no—
258C2×C4×C127—41no—
259C2×C4×C127—41no—
260C2×C4×C127—42no—
261C2×C4×C127—42no—
262C2×C4×C127—44no—
263C2×C4×C127—41no—
264C2×C4×C127—41no—
265C2×C4×C127—41no—
266C2×C4×C127—41no—
267C2×C4×C127—41no—
268C2×C4×C127—41no—
269C2×C4×C127—41no—
270C2×C4×C127—41no—
271C2×C4×C127—41no—
272C2×C4×C127—41no—
273C2×C4×C127—41no—
274C2×C4×C127—41no—
275C2×C4×C127—41no—
276C2×C4×C127—82no—
277C2×C4×C127—82no—
278C2×C4×C127#12011yescharacteristic
279C2×C4×C127#12011yescharacteristic
280C2×C4×C127#12011yescharacteristic
281C2×C4×C127#12011yescharacteristic
282C2×C4×C127C22×D411yescharacteristic
283C2×C4×C127C22×D411yescharacteristic
284C8×C127—42no—
285C8×C127—42no—
286C22×C127—21no—
287C22×C127—21no—
288C22×C127—42no—
289C22×C127—41no—
290C22×C127—42no—
291C22×C127—42no—
292C22×C127—41no—
293C22×C127—42no—
294C22×C127—41no—
295C22×C127—81no—
296C22×C127C2×#12011yescharacteristic
297C22×C127#57511yescharacteristic
298C22×C127#57511yescharacteristic
299C4×C127—21no—
300C4×C127—21no—
301C4×C127—21no—
302C4×C127—21no—
303C4×C127—21no—
304C4×C127—21no—
305C4×C127—42no—
306C4×C127—41no—
307C4×C127—42no—
308C4×C127—41no—
309C4×C127—42no—
310C4×C127—41no—
311C4×C127—42no—
312C4×C127—81no—
313C4×C127—81no—
314C4×C127—81no—
315#18341C12711yesmaximal, characteristic, direct product factor, Sylow
316C2×C127—21no—
317C2×C127—21no—
318C2×C127—82no—
319C2×C127—81no—
320C2×C127#300511yescharacteristic
321C2×C127#301811yescharacteristic
322C2×C127#302811yescharacteristic
323#3455C2×C12711yescharacteristic
324#3236C2×C12711yescharacteristic, complemented
325#3234C2×C12711yescharacteristic, complemented
326#2611C2×C12711yescharacteristic, complemented
327#1618C2×C12712yescomplemented
328#1615C2×C12712yescomplemented
329#1612C2×C12712yescomplemented
330#1609C2×C12712yescomplemented
331#1506C2×C12711yescharacteristic, complemented
332#1505C2×C12711yescharacteristic, complemented
333#1464C2×C12711yescharacteristic, complemented
334C127#1834111yescharacteristic, direct product factor, Sylow
335#542—21no—
336#542—21no—
337#541—21no—
338#540—21no—
339#539—21no—
340#539C22×C12712yes—
341#538—21no—
342#538C22×C12712yes—
343#533C22×C12711yescharacteristic
344#532C22×C12711yescharacteristic
345#529—22no—
346#529—22no—
347C2×#125C22×C12711yescharacteristic
348#525—21no—
349C4×#41—21no—
350C2×#117C22×C12711yescharacteristic
351#501—21no—
352#501—21no—
353#491—21no—
354#490—21no—
355#484C22×C12712yes—
356#483C22×C12712yes—
357#481C22×C12712yes—
358#480C22×C12712yes—
359#479—22no—
360#478—22no—
361#432C22×C12711yescharacteristic
362#432C22×C12711yescharacteristic
363#400C22×C12711yescharacteristic
364#399C22×C12711yescharacteristic
365#398C22×C12711yescharacteristic
366#397C22×C12711yescharacteristic
367#389—21no—
368#388—21no—
369#387—21no—
370#385—21no—
371#376C22×C12711yescharacteristic
372#328C22×C12712yes—
373#328C22×C12712yes—
374#327C22×C12712yes—
375#327C22×C12712yes—
376#324C22×C12712yes—
377#323C22×C12712yes—
378C2×#41—21no—
379C23×C4D4×C12711yescharacteristic
380C4⋊Q8D4×C12711yescharacteristic
381C4⋊Q8D4×C12711yescharacteristic
382C4⋊Q8D4×C12711yescharacteristic
383#127D4×C12711yescharacteristic
384#126—22no—
385#126—22no—
386#126—22no—
387#126—22no—
388#125—22no—
389#125—22no—
390#125—21no—
391#125—21no—
392#125—21no—
393#125—21no—
394#125—21no—
395#124—22no—
396#124—22no—
397#124—21no—
398#123—22no—
399#123—22no—
400#123—22no—
401#123—22no—
402#123—22no—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405C22⋊Q8—22no—
406C22⋊Q8—22no—
407C22⋊Q8—21no—
408C22⋊Q8C23×C12712yes—
409#121—21no—
410#121—21no—
411#121—22no—
412#121—22no—
413#121—21no—
414#121C23×C12712yes—
415#120—22no—
416C4×Q8—21no—
417C4×Q8—21no—
418C4×Q8—21no—
419C4×Q8D4×C12712yes—
420C4×D4—21no—
421C4×D4—21no—
422C4×D4—22no—
423C4×D4—22no—
424C4×D4—22no—
425C4×D4—22no—
426C4×D4—21no—
427C4×D4D4×C12712yes—
428#117—22no—
429#117—21no—
430#117—21no—
431#117—21no—
432#117—21no—
433#117—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4D4×C12711yescharacteristic
439C2×C4⋊C4C23×C12711yescharacteristic
440C2×C4⋊C4C23×C12711yescharacteristic
441C2×C4⋊C4C23×C12711yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4D4×C12711yescharacteristic
445C2×C22⋊C4C23×C12711yescharacteristic
446C2×C42—22no—
447C2×C42—21no—
448C2×C42D4×C12711yescharacteristic
449C2×C42C23×C12711yescharacteristic
450#107—22no—
451#107—22no—
452#106—22no—
453#106—22no—
454C4⋊C8—21no—
455C4⋊C8—21no—
456#103—22no—
457#103—22no—
458#102—22no—
459#102—22no—
460C22⋊C8C23×C12712yes—
461C22⋊C8C23×C12712yes—
462#97—21no—
463#97—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95C23×C12711yescharacteristic
470#95C23×C12711yescharacteristic
471C24C2×D4×C12711yescharacteristic
472#41—42no—
473#41—42no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8C2×D4×C12712yes—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4C2×D4×C12712yes—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4C2×D4×C12711yescharacteristic
495C22×C4C2×D4×C12711yescharacteristic
496C22×C4C2×D4×C12711yescharacteristic
497C22×C4C2×D4×C12711yescharacteristic
498C22×C4C2×D4×C12711yescharacteristic
499C22×C4C24×C12711yescharacteristic
500C2×C8—22no—
501C2×C8—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—22no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—22no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—42no—
521C4⋊C4—42no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C4⋊C4C2×D4×C12712yes—
527C4⋊C4C2×D4×C12712yes—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—22no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—22no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C42—22no—
544C42—22no—
545C42—21no—
546C42—22no—
547C42—21no—
548C42—42no—
549C42C2×D4×C12711yescharacteristic
550C42C2×D4×C12711yescharacteristic
551C42C2×D4×C12711yescharacteristic
552C42C2×D4×C12711yescharacteristic
553C23—21no—
554C23—22no—
555C23—21no—
556C23—21no—
557C23—41no—
558C23—41no—
559C23C22×D4×C12711yescharacteristic
560Q8—42no—
561Q8—42no—
562Q8—81no—
563D4—42no—
564D4—42no—
565D4—42no—
566D4—42no—
567D4—81no—
568D4—82no—
569D4—82no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—44no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—82no—
600C2×C4—82no—
601C2×C4#120×C12711yescharacteristic
602C2×C4#120×C12711yescharacteristic
603C2×C4#120×C12711yescharacteristic
604C2×C4#120×C12711yescharacteristic
605C2×C4C22×D4×C12711yescharacteristic
606C2×C4C22×D4×C12711yescharacteristic
607C8—42no—
608C8—42no—
609C22—21no—
610C22—21no—
611C22—42no—
612C22—41no—
613C22—42no—
614C22—42no—
615C22—41no—
616C22—42no—
617C22—41no—
618C22—81no—
619C22C2×#120×C12711yescharacteristic
620C22#575×C12711yescharacteristic
621C22#575×C12711yescharacteristic
622C4—21no—
623C4—21no—
624C4—21no—
625C4—21no—
626C4—21no—
627C4—21no—
628C4—42no—
629C4—41no—
630C4—42no—
631C4—41no—
632C4—42no—
633C4—41no—
634C4—42no—
635C4—81no—
636C4—81no—
637C4—81no—
638C2—21no—
639C2—21no—
640C2—81no—
641C2—82no—
642C2C127×#300511yescharacteristic
643C2C127×#301811yescharacteristic
644C2C127×#302811yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC22×C4C24×C127
prime radicalC127×#3455C2
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×#3236C2semidirect
3. C127×#3234C2semidirect
4. C127×#2611C2semidirect
5. C127×#1618C2semidirect
6. C127×#1615C2semidirect
7. C127×#1612C2semidirect
8. C127×#1609C2semidirect
9. C127×#1506C2semidirect
10. C127×#1505C2semidirect
11. C127×#1464C2semidirect
315. #18341C127direct (N × H)
324. #3236C2×C127semidirect
325. #3234C2×C127semidirect
326. #2611C2×C127semidirect
327. #1618C2×C127semidirect
328. #1615C2×C127semidirect
329. #1612C2×C127semidirect
330. #1609C2×C127semidirect
331. #1506C2×C127semidirect
332. #1505C2×C127semidirect
333. #1464C2×C127semidirect
334. C127#18341direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#34552
C127×#32362
C127×#32342
C127×#26112
C127×#16182
C127×#16152
C127×#16122
C127×#16092
C127×#15062
C127×#15052
C127×#14642
#18341127