Finite Group Databasebeta

← C127×#18290 #44581963

Subgroups — C127×#18290 #44581963

Order 32512.

1034 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3459C211yesmaximal, characteristic, complemented
2C127×#3188C212yesmaximal, complemented
3C127×#2635C211yesmaximal, characteristic, complemented
4C127×#1615C212yesmaximal, complemented
5C127×#1614C211yesmaximal, characteristic, complemented
6C127×#1613C211yesmaximal, characteristic, complemented
7C127×#1597C212yesmaximal, complemented
8C127×#1596C211yesmaximal, characteristic, complemented
9C127×#1595C211yesmaximal, characteristic, complemented
10C127×#1516C212yesmaximal, complemented
11C127×#1459C211yesmaximal, characteristic, complemented
12#543×C127C2211yescharacteristic
13#539×C127—22no—
14#539×C127C2212yes—
15#538×C127—22no—
16#538×C127—21no—
17#534×C127—21no—
18#534×C127C2211yescharacteristic
19#529×C127—22no—
20#529×C127—21no—
21#525×C127—22no—
22#525×C127C2212yes—
23C2×#121×C127C2211yescharacteristic, complemented
24C2×C4×D4×C127—21no—
25C2×C4×D4×C127C2211yescharacteristic
26#484×C127C2212yescomplemented
27#482×C127—22no—
28#481×C127C2212yes—
29#466×C127—22no—
30#465×C127—22no—
31#450×C127C2212yescomplemented
32#449×C127—22no—
33#447×C127C2212yes—
34C2×C22⋊C8×C127C2212yescomplemented
35#400×C127C2211yescharacteristic, complemented
36#399×C127C2211yescharacteristic
37#394×C127—21no—
38#394×C127C2211yescharacteristic, complemented
39#392×C127—21no—
40#392×C127C2211yescharacteristic
41#388×C127—21no—
42#386×C127—21no—
43#381×C127C2211yescharacteristic, complemented
44#328×C127C2212yescomplemented
45#328×C127C2212yescomplemented
46#327×C127C2212yes—
47#327×C127C2212yes—
48#324×C127C2212yescomplemented
49#323×C127C2211yescharacteristic
50#323×C127C2211yescharacteristic
51C2×#41×C127D412yescomplemented
52C22×D4×C127—21no—
53C22×D4×C127—21no—
54C22×D4×C127—21no—
55C22×D4×C127D411yescharacteristic
56C22×D4×C127C2311yescharacteristic
57C23×C4×C127—21no—
58C23×C4×C127D411yescharacteristic
59C23×C4×C127C2311yescharacteristic
60C2×SD16×C127—22no—
61C2×D8×C127—22no—
62C22×C8×C127—22no—
63#126×C127—22no—
64#126×C127—22no—
65#126×C127—22no—
66#125×C127—21no—
67#125×C127—22no—
68#124×C127—22no—
69#124×C127—21no—
70#123×C127—22no—
71#123×C127—22no—
72#123×C127—22no—
73#123×C127—22no—
74#123×C127—22no—
75#123×C127—22no—
76C22⋊Q8×C127—22no—
77C22⋊Q8×C127—22no—
78C22⋊Q8×C127—21no—
79C22⋊Q8×C127—22no—
80C22⋊Q8×C127D412yescomplemented
81C22⋊Q8×C127C2312yes—
82#121×C127—22no—
83#121×C127—22no—
84#121×C127—22no—
85#121×C127—21no—
86#121×C127—22no—
87#121×C127—22no—
88#121×C127D412yescomplemented
89#121×C127C2312yes—
90#120×C127—22no—
91#120×C127—22no—
92#120×C127—22no—
93C4×Q8×C127—21no—
94C4×D4×C127—22no—
95C4×D4×C127—22no—
96C4×D4×C127—21no—
97C4×D4×C127—22no—
98C4×D4×C127—22no—
99C4×D4×C127—22no—
100C4×D4×C127—22no—
101C4×D4×C127—22no—
102#117×C127—22no—
103#117×C127D412yescomplemented
104C2×C4⋊C4×C127—21no—
105C2×C4⋊C4×C127—21no—
106C2×C4⋊C4×C127C2311yescharacteristic
107C2×C4⋊C4×C127C2311yescharacteristic
108C2×C22⋊C4×C127—21no—
109C2×C22⋊C4×C127—21no—
110C2×C22⋊C4×C127—21no—
111C2×C22⋊C4×C127—21no—
112C2×C22⋊C4×C127—21no—
113C2×C22⋊C4×C127—21no—
114C2×C22⋊C4×C127—21no—
115C2×C22⋊C4×C127—21no—
116C2×C22⋊C4×C127D411yescharacteristic
117C2×C22⋊C4×C127C2311yescharacteristic
118C2×C42×C127—21no—
119C2×C42×C127D411yescharacteristic
120#107×C127—22no—
121#106×C127—22no—
122#103×C127—22no—
123#102×C127—22no—
124#102×C127—22no—
125#102×C127—22no—
126C22⋊C8×C127—22no—
127C22⋊C8×C127C2312yes—
128C22⋊C8×C127C2312yes—
129#95×C127—21no—
130#95×C127—21no—
131#95×C127—21no—
132#95×C127C2311yescharacteristic
133#95×C127C2311yescharacteristic
134C24×C127—21no—
135C24×C127—21no—
136C24×C127C2×D411yescharacteristic
137C24×C127C2×D411yescharacteristic
138#41×C127—82no—
139C2×Q8×C127—21no—
140C2×Q8×C127C2×D412yes—
141C2×D4×C127—22no—
142C2×D4×C127—22no—
143C2×D4×C127—22no—
144C2×D4×C127—22no—
145C2×D4×C127—21no—
146C2×D4×C127—22no—
147C2×D4×C127—22no—
148C2×D4×C127—22no—
149C2×D4×C127—41no—
150C2×D4×C127—42no—
151C2×D4×C127—42no—
152C2×D4×C127—42no—
153C2×D4×C127—42no—
154C2×D4×C127—81no—
155C2×D4×C127—81no—
156C2×D4×C127—81no—
157C2×D4×C127—81no—
158C2×D4×C127—81no—
159C2×D4×C127C2×D412yes—
160C22×C4×C127—21no—
161C22×C4×C127—21no—
162C22×C4×C127—21no—
163C22×C4×C127—22no—
164C22×C4×C127—21no—
165C22×C4×C127—22no—
166C22×C4×C127—21no—
167C22×C4×C127—21no—
168C22×C4×C127—21no—
169C22×C4×C127—21no—
170C22×C4×C127—81no—
171C22×C4×C127—81no—
172C22×C4×C127—82no—
173C22×C4×C127C2×D411yescharacteristic
174C22×C4×C127C2×D411yescharacteristic
175C22×C4×C127C2×D411yescharacteristic
176C22×C4×C127C2×D411yescharacteristic
177C22×C4×C127C2×D412yes—
178C22×C4×C127C2×D412yes—
179C22×C4×C127C2411yescharacteristic
180SD16×C127—82no—
181D8×C127—82no—
182C2×C8×C127—22no—
183C2×C8×C127—22no—
184C2×C8×C127—82no—
185C4⋊C4×C127—22no—
186C4⋊C4×C127—22no—
187C4⋊C4×C127—22no—
188C4⋊C4×C127—21no—
189C4⋊C4×C127—21no—
190C4⋊C4×C127—22no—
191C4⋊C4×C127—22no—
192C4⋊C4×C127—22no—
193C4⋊C4×C127—22no—
194C4⋊C4×C127—22no—
195C4⋊C4×C127—81no—
196C4⋊C4×C127C2×D412yes—
197C4⋊C4×C127C2×D412yes—
198C22⋊C4×C127—22no—
199C22⋊C4×C127—22no—
200C22⋊C4×C127—22no—
201C22⋊C4×C127—22no—
202C22⋊C4×C127—22no—
203C22⋊C4×C127—22no—
204C22⋊C4×C127—22no—
205C22⋊C4×C127—22no—
206C22⋊C4×C127—22no—
207C22⋊C4×C127—22no—
208C22⋊C4×C127—22no—
209C22⋊C4×C127—22no—
210C22⋊C4×C127—42no—
211C22⋊C4×C127—41no—
212C22⋊C4×C127—41no—
213C22⋊C4×C127—81no—
214C22⋊C4×C127—81no—
215C22⋊C4×C127—81no—
216C22⋊C4×C127—81no—
217C42×C127—22no—
218C42×C127—22no—
219C42×C127—21no—
220C42×C127—21no—
221C23×C127—21no—
222C23×C127—21no—
223C23×C127—21no—
224C23×C127—21no—
225C23×C127—22no—
226C23×C127—41no—
227C23×C127—41no—
228C23×C127—41no—
229C23×C127—41no—
230C23×C127—42no—
231C23×C127—41no—
232C23×C127—41no—
233C23×C127—41no—
234C23×C127—41no—
235C23×C127—41no—
236C23×C127—41no—
237C23×C127—41no—
238C23×C127—81no—
239C23×C127—81no—
240C23×C127#12012yes—
241C23×C127#13512yes—
242C23×C127C22×D411yescharacteristic
243Q8×C127—42no—
244Q8×C127—81no—
245D4×C127—42no—
246D4×C127—42no—
247D4×C127—42no—
248D4×C127—44no—
249D4×C127—44no—
250D4×C127—42no—
251D4×C127—42no—
252D4×C127—82no—
253D4×C127—82no—
254D4×C127—81no—
255D4×C127—84no—
256D4×C127—84no—
257C2×C4×C127—21no—
258C2×C4×C127—22no—
259C2×C4×C127—21no—
260C2×C4×C127—22no—
261C2×C4×C127—21no—
262C2×C4×C127—22no—
263C2×C4×C127—21no—
264C2×C4×C127—21no—
265C2×C4×C127—42no—
266C2×C4×C127—41no—
267C2×C4×C127—42no—
268C2×C4×C127—41no—
269C2×C4×C127—42no—
270C2×C4×C127—44no—
271C2×C4×C127—42no—
272C2×C4×C127—41no—
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—41no—
280C2×C4×C127—41no—
281C2×C4×C127—41no—
282C2×C4×C127—41no—
283C2×C4×C127—81no—
284C2×C4×C127—81no—
285C2×C4×C127—82no—
286C2×C4×C127—81no—
287C2×C4×C127#12011yescharacteristic
288C2×C4×C127#12011yescharacteristic
289C2×C4×C127C22×D412yes—
290C8×C127—42no—
291C8×C127—42no—
292C22×C127—21no—
293C22×C127—21no—
294C22×C127—22no—
295C22×C127—22no—
296C22×C127—22no—
297C22×C127—22no—
298C22×C127—42no—
299C22×C127—41no—
300C22×C127—41no—
301C22×C127—42no—
302C22×C127—42no—
303C22×C127—42no—
304C22×C127—81no—
305C22×C127—81no—
306C22×C127—81no—
307C22×C127—81no—
308C22×C127—81no—
309C22×C127—81no—
310C22×C127—81no—
311C22×C127—84no—
312C22×C127—81no—
313C22×C127—81no—
314C22×C127—81no—
315C22×C127C2×#12011yescharacteristic
316C22×C127C2×#13511yescharacteristic
317C22×C127#57511yescharacteristic
318C4×C127—22no—
319C4×C127—21no—
320C4×C127—21no—
321C4×C127—41no—
322C4×C127—42no—
323C4×C127—41no—
324C4×C127—42no—
325C4×C127—41no—
326C4×C127—42no—
327C4×C127—81no—
328C4×C127—81no—
329C4×C127—81no—
330#18290C12711yesmaximal, characteristic, direct product factor, Sylow
331C2×C127—21no—
332C2×C127—21no—
333C2×C127—42no—
334C2×C127—42no—
335C2×C127—82no—
336C2×C127—161no—
337C2×C127#300211yescharacteristic
338C2×C127#302111yescharacteristic
339C2×C127#302611yescharacteristic
340#3459C2×C12711yescharacteristic, complemented
341#3188C2×C12712yescomplemented
342#2635C2×C12711yescharacteristic, complemented
343#1615C2×C12712yescomplemented
344#1614C2×C12711yescharacteristic, complemented
345#1613C2×C12711yescharacteristic, complemented
346#1597C2×C12712yescomplemented
347#1596C2×C12711yescharacteristic, complemented
348#1595C2×C12711yescharacteristic, complemented
349#1516C2×C12712yescomplemented
350#1459C2×C12711yescharacteristic, complemented
351C127#1829011yescharacteristic, direct product factor, Sylow
352#543C22×C12711yescharacteristic
353#539—22no—
354#539C22×C12712yes—
355#538—22no—
356#538—21no—
357#534—21no—
358#534C22×C12711yescharacteristic
359#529—22no—
360#529—21no—
361#525—22no—
362#525C22×C12712yes—
363C2×#121C22×C12711yescharacteristic, complemented
364C2×C4×D4—21no—
365C2×C4×D4C22×C12711yescharacteristic
366#484C22×C12712yescomplemented
367#482—22no—
368#481C22×C12712yes—
369#466—22no—
370#465—22no—
371#450C22×C12712yescomplemented
372#449—22no—
373#447C22×C12712yes—
374C2×C22⋊C8C22×C12712yescomplemented
375#400C22×C12711yescharacteristic, complemented
376#399C22×C12711yescharacteristic
377#394—21no—
378#394C22×C12711yescharacteristic, complemented
379#392—21no—
380#392C22×C12711yescharacteristic
381#388—21no—
382#386—21no—
383#381C22×C12711yescharacteristic, complemented
384#328C22×C12712yescomplemented
385#328C22×C12712yescomplemented
386#327C22×C12712yes—
387#327C22×C12712yes—
388#324C22×C12712yescomplemented
389#323C22×C12711yescharacteristic
390#323C22×C12711yescharacteristic
391C2×#41D4×C12712yescomplemented
392C22×D4—21no—
393C22×D4—21no—
394C22×D4—21no—
395C22×D4D4×C12711yescharacteristic
396C22×D4C23×C12711yescharacteristic
397C23×C4—21no—
398C23×C4D4×C12711yescharacteristic
399C23×C4C23×C12711yescharacteristic
400C2×SD16—22no—
401C2×D8—22no—
402C22×C8—22no—
403#126—22no—
404#126—22no—
405#126—22no—
406#125—21no—
407#125—22no—
408#124—22no—
409#124—21no—
410#123—22no—
411#123—22no—
412#123—22no—
413#123—22no—
414#123—22no—
415#123—22no—
416C22⋊Q8—22no—
417C22⋊Q8—22no—
418C22⋊Q8—21no—
419C22⋊Q8—22no—
420C22⋊Q8D4×C12712yescomplemented
421C22⋊Q8C23×C12712yes—
422#121—22no—
423#121—22no—
424#121—22no—
425#121—21no—
426#121—22no—
427#121—22no—
428#121D4×C12712yescomplemented
429#121C23×C12712yes—
430#120—22no—
431#120—22no—
432#120—22no—
433C4×Q8—21no—
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—21no—
437C4×D4—22no—
438C4×D4—22no—
439C4×D4—22no—
440C4×D4—22no—
441C4×D4—22no—
442#117—22no—
443#117D4×C12712yescomplemented
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4C23×C12711yescharacteristic
447C2×C4⋊C4C23×C12711yescharacteristic
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4D4×C12711yescharacteristic
457C2×C22⋊C4C23×C12711yescharacteristic
458C2×C42—21no—
459C2×C42D4×C12711yescharacteristic
460#107—22no—
461#106—22no—
462#103—22no—
463#102—22no—
464#102—22no—
465#102—22no—
466C22⋊C8—22no—
467C22⋊C8C23×C12712yes—
468C22⋊C8C23×C12712yes—
469#95—21no—
470#95—21no—
471#95—21no—
472#95C23×C12711yescharacteristic
473#95C23×C12711yescharacteristic
474C24—21no—
475C24—21no—
476C24C2×D4×C12711yescharacteristic
477C24C2×D4×C12711yescharacteristic
478#41—82no—
479C2×Q8—21no—
480C2×Q8C2×D4×C12712yes—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—21no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—41no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—81no—
495C2×D4—81no—
496C2×D4—81no—
497C2×D4—81no—
498C2×D4—81no—
499C2×D4C2×D4×C12712yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—81no—
511C22×C4—81no—
512C22×C4—82no—
513C22×C4C2×D4×C12711yescharacteristic
514C22×C4C2×D4×C12711yescharacteristic
515C22×C4C2×D4×C12711yescharacteristic
516C22×C4C2×D4×C12711yescharacteristic
517C22×C4C2×D4×C12712yes—
518C22×C4C2×D4×C12712yes—
519C22×C4C24×C12711yescharacteristic
520SD16—82no—
521D8—82no—
522C2×C8—22no—
523C2×C8—22no—
524C2×C8—82no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—81no—
536C4⋊C4C2×D4×C12712yes—
537C4⋊C4C2×D4×C12712yes—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—42no—
551C22⋊C4—41no—
552C22⋊C4—41no—
553C22⋊C4—81no—
554C22⋊C4—81no—
555C22⋊C4—81no—
556C22⋊C4—81no—
557C42—22no—
558C42—22no—
559C42—21no—
560C42—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—22no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—42no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—81no—
579C23—81no—
580C23#120×C12712yes—
581C23#135×C12712yes—
582C23C22×D4×C12711yescharacteristic
583Q8—42no—
584Q8—81no—
585D4—42no—
586D4—42no—
587D4—42no—
588D4—44no—
589D4—44no—
590D4—42no—
591D4—42no—
592D4—82no—
593D4—82no—
594D4—81no—
595D4—84no—
596D4—84no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—42no—
606C2×C4—41no—
607C2×C4—42no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—44no—
611C2×C4—42no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—81no—
624C2×C4—82no—
625C2×C4—81no—
626C2×C4—81no—
627C2×C4#120×C12711yescharacteristic
628C2×C4#120×C12711yescharacteristic
629C2×C4C22×D4×C12712yes—
630C8—42no—
631C8—42no—
632C22—21no—
633C22—21no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—42no—
639C22—41no—
640C22—41no—
641C22—42no—
642C22—42no—
643C22—42no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—84no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22C2×#120×C12711yescharacteristic
656C22C2×#135×C12711yescharacteristic
657C22#575×C12711yescharacteristic
658C4—22no—
659C4—21no—
660C4—21no—
661C4—41no—
662C4—42no—
663C4—41no—
664C4—42no—
665C4—41no—
666C4—42no—
667C4—81no—
668C4—81no—
669C4—81no—
670C2—21no—
671C2—21no—
672C2—42no—
673C2—42no—
674C2—82no—
675C2—161no—
676C2C127×#300211yescharacteristic
677C2C127×#302111yescharacteristic
678C2C127×#302611yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC22×C4C24×C127
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
1. C127×#3459C2semidirect
2. C127×#3188C2semidirect
3. C127×#2635C2semidirect
4. C127×#1615C2semidirect
5. C127×#1614C2semidirect
6. C127×#1613C2semidirect
7. C127×#1597C2semidirect
8. C127×#1596C2semidirect
9. C127×#1595C2semidirect
10. C127×#1516C2semidirect
11. C127×#1459C2semidirect
23. C2×#121×C127C22semidirect
26. #484×C127C22semidirect
31. #450×C127C22semidirect
34. C2×C22⋊C8×C127C22semidirect
35. #400×C127C22semidirect
38. #394×C127C22semidirect
43. #381×C127C22semidirect
44. #328×C127C22semidirect
45. #328×C127C22semidirect
48. #324×C127C22semidirect
51. C2×#41×C127D4semidirect
80. C22⋊Q8×C127D4semidirect
88. #121×C127D4semidirect
103. #117×C127D4semidirect
330. #18290C127direct (N × H)
340. #3459C2×C127semidirect
341. #3188C2×C127semidirect
342. #2635C2×C127semidirect
343. #1615C2×C127semidirect
344. #1614C2×C127semidirect
345. #1613C2×C127semidirect
346. #1597C2×C127semidirect
347. #1596C2×C127semidirect
348. #1595C2×C127semidirect
349. #1516C2×C127semidirect
350. #1459C2×C127semidirect
351. C127#18290direct (N × H)
363. C2×#121C22×C127semidirect
366. #484C22×C127semidirect
371. #450C22×C127semidirect
374. C2×C22⋊C8C22×C127semidirect
375. #400C22×C127semidirect
378. #394C22×C127semidirect
383. #381C22×C127semidirect
384. #328C22×C127semidirect
385. #328C22×C127semidirect
388. #324C22×C127semidirect
391. C2×#41D4×C127semidirect
420. C22⋊Q8D4×C127semidirect
428. #121D4×C127semidirect
443. #117D4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#34592
C127×#31882
C127×#26352
C127×#16152
C127×#16142
C127×#16132
C127×#15972
C127×#15962
C127×#15952
C127×#15162
C127×#14592
#18290127