Finite Group Databasebeta

← C127×#18291 #44581964

Subgroups — C127×#18291 #44581964

Order 32512.

984 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3459C211yesmaximal, characteristic
2C127×#3190C212yesmaximal, complemented
3C127×#2638C211yesmaximal, characteristic, complemented
4C127×#1609C212yesmaximal, complemented
5C127×#1608C211yesmaximal, characteristic, complemented
6C127×#1607C211yesmaximal, characteristic, complemented
7C127×#1603C212yesmaximal, complemented
8C127×#1602C211yesmaximal, characteristic, complemented
9C127×#1601C211yesmaximal, 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×C22⋊Q8×C127C2211yescharacteristic, complemented
24C2×C4×D4×C127—21no—
25C2×C4×D4×C127C2211yescharacteristic
26#485×C127—22no—
27#483×C127C2212yescomplemented
28#480×C127C2212yes—
29#467×C127—22no—
30#465×C127—22no—
31#452×C127—22no—
32#451×C127C2212yescomplemented
33#448×C127C2212yes—
34C2×C22⋊C8×C127C2212yescomplemented
35#398×C127C2211yescharacteristic, complemented
36#397×C127—21no—
37#397×C127C2211yescharacteristic
38#395×C127C2211yescharacteristic, complemented
39#394×C127—21no—
40#393×C127C2211yescharacteristic
41#387×C127—21no—
42#385×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×C127D412yes—
52C22×Q8×C127C2311yescharacteristic
53C22×D4×C127—21no—
54C22×D4×C127D411yescharacteristic
55C23×C4×C127—21no—
56C23×C4×C127D411yescharacteristic
57C23×C4×C127C2311yescharacteristic
58C2×Q16×C127—22no—
59C2×SD16×C127—22no—
60C22×C8×C127—22no—
61#126×C127—22no—
62#126×C127—22no—
63#126×C127—22no—
64#125×C127—21no—
65#125×C127—22no—
66#124×C127—22no—
67#124×C127—21no—
68#123×C127—22no—
69#123×C127—22no—
70#123×C127—22no—
71#123×C127—22no—
72#123×C127—22no—
73#123×C127—22no—
74C22⋊Q8×C127—22no—
75C22⋊Q8×C127—22no—
76C22⋊Q8×C127—21no—
77C22⋊Q8×C127—22no—
78C22⋊Q8×C127—22no—
79C22⋊Q8×C127—22no—
80C22⋊Q8×C127D412yes—
81C22⋊Q8×C127C2312yes—
82#121×C127—22no—
83#121×C127—22no—
84#121×C127—22no—
85#121×C127—21no—
86#121×C127D412yes—
87#121×C127C2312yes—
88#120×C127—22no—
89#120×C127—22no—
90#120×C127—22no—
91C4×Q8×C127—21no—
92C4×D4×C127—22no—
93C4×D4×C127—22no—
94C4×D4×C127—21no—
95C4×D4×C127—22no—
96C4×D4×C127—22no—
97C4×D4×C127—22no—
98C4×D4×C127—22no—
99C4×D4×C127—22no—
100#117×C127—22no—
101#117×C127D412yes—
102C2×C4⋊C4×C127—21no—
103C2×C4⋊C4×C127—21no—
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×C127D411yescharacteristic
115C2×C22⋊C4×C127C2311yescharacteristic
116C2×C42×C127—21no—
117C2×C42×C127D411yescharacteristic
118#107×C127—22no—
119#106×C127—22no—
120#103×C127—22no—
121#103×C127—22no—
122#103×C127—22no—
123#102×C127—22no—
124C22⋊C8×C127—22no—
125C22⋊C8×C127C2312yes—
126C22⋊C8×C127C2312yes—
127#95×C127—21no—
128#95×C127—21no—
129#95×C127—21no—
130#95×C127—21no—
131#95×C127—21no—
132#95×C127C2311yescharacteristic
133#95×C127C2311yescharacteristic
134C24×C127—21no—
135C24×C127C2×D411yescharacteristic
136C24×C127C2×D411yescharacteristic
137#41×C127—82no—
138C2×Q8×C127—21no—
139C2×Q8×C127—22no—
140C2×Q8×C127—81no—
141C2×Q8×C127C2×D412yes—
142C2×D4×C127—22no—
143C2×D4×C127—22no—
144C2×D4×C127—22no—
145C2×D4×C127—22no—
146C2×D4×C127—21no—
147C2×D4×C127—22no—
148C2×D4×C127—22no—
149C2×D4×C127—41no—
150C2×D4×C127—42no—
151C2×D4×C127—42no—
152C2×D4×C127C2×D412yes—
153C22×C4×C127—21no—
154C22×C4×C127—21no—
155C22×C4×C127—21no—
156C22×C4×C127—22no—
157C22×C4×C127—21no—
158C22×C4×C127—22no—
159C22×C4×C127—21no—
160C22×C4×C127—21no—
161C22×C4×C127—21no—
162C22×C4×C127—21no—
163C22×C4×C127—21no—
164C22×C4×C127—81no—
165C22×C4×C127—81no—
166C22×C4×C127—82no—
167C22×C4×C127C2×D411yescharacteristic
168C22×C4×C127C2×D411yescharacteristic
169C22×C4×C127C2×D411yescharacteristic
170C22×C4×C127C2×D411yescharacteristic
171C22×C4×C127C2×D412yes—
172C22×C4×C127C2×D412yes—
173C22×C4×C127C2411yescharacteristic
174Q16×C127—82no—
175SD16×C127—82no—
176C2×C8×C127—22no—
177C2×C8×C127—22no—
178C2×C8×C127—82no—
179C4⋊C4×C127—22no—
180C4⋊C4×C127—22no—
181C4⋊C4×C127—22no—
182C4⋊C4×C127—21no—
183C4⋊C4×C127—21no—
184C4⋊C4×C127—22no—
185C4⋊C4×C127—22no—
186C4⋊C4×C127—22no—
187C4⋊C4×C127—22no—
188C4⋊C4×C127—22no—
189C4⋊C4×C127—42no—
190C4⋊C4×C127—41no—
191C4⋊C4×C127—41no—
192C4⋊C4×C127—81no—
193C4⋊C4×C127C2×D412yes—
194C4⋊C4×C127C2×D412yes—
195C22⋊C4×C127—22no—
196C22⋊C4×C127—22no—
197C22⋊C4×C127—22no—
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—42no—
208C22⋊C4×C127—42no—
209C22⋊C4×C127—81no—
210C22⋊C4×C127—81no—
211C42×C127—22no—
212C42×C127—22no—
213C42×C127—21no—
214C42×C127—21no—
215C23×C127—21no—
216C23×C127—21no—
217C23×C127—21no—
218C23×C127—21no—
219C23×C127—22no—
220C23×C127—41no—
221C23×C127—41no—
222C23×C127—41no—
223C23×C127—41no—
224C23×C127—42no—
225C23×C127—81no—
226C23×C127—81no—
227C23×C127#12012yes—
228C23×C127#13512yes—
229C23×C127C22×D411yescharacteristic
230Q8×C127—42no—
231Q8×C127—42no—
232Q8×C127—42no—
233Q8×C127—81no—
234D4×C127—42no—
235D4×C127—44no—
236D4×C127—44no—
237D4×C127—42no—
238D4×C127—42no—
239D4×C127—82no—
240D4×C127—82no—
241D4×C127—81no—
242C2×C4×C127—21no—
243C2×C4×C127—22no—
244C2×C4×C127—21no—
245C2×C4×C127—22no—
246C2×C4×C127—21no—
247C2×C4×C127—22no—
248C2×C4×C127—21no—
249C2×C4×C127—21no—
250C2×C4×C127—42no—
251C2×C4×C127—41no—
252C2×C4×C127—42no—
253C2×C4×C127—41no—
254C2×C4×C127—42no—
255C2×C4×C127—44no—
256C2×C4×C127—42no—
257C2×C4×C127—41no—
258C2×C4×C127—41no—
259C2×C4×C127—41no—
260C2×C4×C127—41no—
261C2×C4×C127—41no—
262C2×C4×C127—41no—
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—81no—
272C2×C4×C127—81no—
273C2×C4×C127—82no—
274C2×C4×C127—81no—
275C2×C4×C127#12011yescharacteristic
276C2×C4×C127#12011yescharacteristic
277C2×C4×C127C22×D412yes—
278C8×C127—42no—
279C8×C127—42no—
280C22×C127—21no—
281C22×C127—21no—
282C22×C127—22no—
283C22×C127—22no—
284C22×C127—22no—
285C22×C127—22no—
286C22×C127—42no—
287C22×C127—41no—
288C22×C127—41no—
289C22×C127—42no—
290C22×C127—42no—
291C22×C127—42no—
292C22×C127—81no—
293C22×C127—81no—
294C22×C127—81no—
295C22×C127—84no—
296C22×C127C2×#12011yescharacteristic
297C22×C127C2×#13511yescharacteristic
298C22×C127#57511yescharacteristic
299C4×C127—22no—
300C4×C127—21no—
301C4×C127—21no—
302C4×C127—41no—
303C4×C127—42no—
304C4×C127—41no—
305C4×C127—42no—
306C4×C127—41no—
307C4×C127—42no—
308C4×C127—81no—
309C4×C127—81no—
310C4×C127—81no—
311C4×C127—81no—
312#18291C12711yesmaximal, characteristic, direct product factor, Sylow
313C2×C127—21no—
314C2×C127—21no—
315C2×C127—42no—
316C2×C127—42no—
317C2×C127—82no—
318C2×C127#300211yescharacteristic
319C2×C127#302211yescharacteristic
320C2×C127#302611yescharacteristic
321#3459C2×C12711yescharacteristic
322#3190C2×C12712yescomplemented
323#2638C2×C12711yescharacteristic, complemented
324#1609C2×C12712yescomplemented
325#1608C2×C12711yescharacteristic, complemented
326#1607C2×C12711yescharacteristic, complemented
327#1603C2×C12712yescomplemented
328#1602C2×C12711yescharacteristic, complemented
329#1601C2×C12711yescharacteristic, complemented
330#1516C2×C12712yescomplemented
331#1459C2×C12711yescharacteristic, complemented
332C127#1829111yescharacteristic, direct product factor, Sylow
333#543C22×C12711yescharacteristic
334#539—22no—
335#539C22×C12712yes—
336#538—22no—
337#538—21no—
338#534—21no—
339#534C22×C12711yescharacteristic
340#529—22no—
341#529—21no—
342#525—22no—
343#525C22×C12712yes—
344C2×C22⋊Q8C22×C12711yescharacteristic, complemented
345C2×C4×D4—21no—
346C2×C4×D4C22×C12711yescharacteristic
347#485—22no—
348#483C22×C12712yescomplemented
349#480C22×C12712yes—
350#467—22no—
351#465—22no—
352#452—22no—
353#451C22×C12712yescomplemented
354#448C22×C12712yes—
355C2×C22⋊C8C22×C12712yescomplemented
356#398C22×C12711yescharacteristic, complemented
357#397—21no—
358#397C22×C12711yescharacteristic
359#395C22×C12711yescharacteristic, complemented
360#394—21no—
361#393C22×C12711yescharacteristic
362#387—21no—
363#385—21no—
364#381C22×C12711yescharacteristic, complemented
365#328C22×C12712yescomplemented
366#328C22×C12712yescomplemented
367#327C22×C12712yes—
368#327C22×C12712yes—
369#324C22×C12712yescomplemented
370#323C22×C12711yescharacteristic
371#323C22×C12711yescharacteristic
372C2×#41D4×C12712yes—
373C22×Q8C23×C12711yescharacteristic
374C22×D4—21no—
375C22×D4D4×C12711yescharacteristic
376C23×C4—21no—
377C23×C4D4×C12711yescharacteristic
378C23×C4C23×C12711yescharacteristic
379C2×Q16—22no—
380C2×SD16—22no—
381C22×C8—22no—
382#126—22no—
383#126—22no—
384#126—22no—
385#125—21no—
386#125—22no—
387#124—22no—
388#124—21no—
389#123—22no—
390#123—22no—
391#123—22no—
392#123—22no—
393#123—22no—
394#123—22no—
395C22⋊Q8—22no—
396C22⋊Q8—22no—
397C22⋊Q8—21no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8D4×C12712yes—
402C22⋊Q8C23×C12712yes—
403#121—22no—
404#121—22no—
405#121—22no—
406#121—21no—
407#121D4×C12712yes—
408#121C23×C12712yes—
409#120—22no—
410#120—22no—
411#120—22no—
412C4×Q8—21no—
413C4×D4—22no—
414C4×D4—22no—
415C4×D4—21no—
416C4×D4—22no—
417C4×D4—22no—
418C4×D4—22no—
419C4×D4—22no—
420C4×D4—22no—
421#117—22no—
422#117D4×C12712yes—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4C23×C12711yescharacteristic
428C2×C4⋊C4C23×C12711yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4D4×C12711yescharacteristic
436C2×C22⋊C4C23×C12711yescharacteristic
437C2×C42—21no—
438C2×C42D4×C12711yescharacteristic
439#107—22no—
440#106—22no—
441#103—22no—
442#103—22no—
443#103—22no—
444#102—22no—
445C22⋊C8—22no—
446C22⋊C8C23×C12712yes—
447C22⋊C8C23×C12712yes—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95C23×C12711yescharacteristic
454#95C23×C12711yescharacteristic
455C24—21no—
456C24C2×D4×C12711yescharacteristic
457C24C2×D4×C12711yescharacteristic
458#41—82no—
459C2×Q8—21no—
460C2×Q8—22no—
461C2×Q8—81no—
462C2×Q8C2×D4×C12712yes—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—21no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—41no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4C2×D4×C12712yes—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—81no—
486C22×C4—81no—
487C22×C4—82no—
488C22×C4C2×D4×C12711yescharacteristic
489C22×C4C2×D4×C12711yescharacteristic
490C22×C4C2×D4×C12711yescharacteristic
491C22×C4C2×D4×C12711yescharacteristic
492C22×C4C2×D4×C12712yes—
493C22×C4C2×D4×C12712yes—
494C22×C4C24×C12711yescharacteristic
495Q16—82no—
496SD16—82no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—82no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—42no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—81no—
514C4⋊C4C2×D4×C12712yes—
515C4⋊C4C2×D4×C12712yes—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—42no—
529C22⋊C4—42no—
530C22⋊C4—81no—
531C22⋊C4—81no—
532C42—22no—
533C42—22no—
534C42—21no—
535C42—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—22no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—42no—
546C23—81no—
547C23—81no—
548C23#120×C12712yes—
549C23#135×C12712yes—
550C23C22×D4×C12711yescharacteristic
551Q8—42no—
552Q8—42no—
553Q8—42no—
554Q8—81no—
555D4—42no—
556D4—44no—
557D4—44no—
558D4—42no—
559D4—42no—
560D4—82no—
561D4—82no—
562D4—81no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—44no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—81no—
593C2×C4—82no—
594C2×C4—81no—
595C2×C4—81no—
596C2×C4#120×C12711yescharacteristic
597C2×C4#120×C12711yescharacteristic
598C2×C4C22×D4×C12712yes—
599C8—42no—
600C8—42no—
601C22—21no—
602C22—21no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—42no—
608C22—41no—
609C22—41no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—84no—
617C22C2×#120×C12711yescharacteristic
618C22C2×#135×C12711yescharacteristic
619C22#575×C12711yescharacteristic
620C4—22no—
621C4—21no—
622C4—21no—
623C4—41no—
624C4—42no—
625C4—41no—
626C4—42no—
627C4—41no—
628C4—42no—
629C4—81no—
630C4—81no—
631C4—81no—
632C4—81no—
633C2—21no—
634C2—21no—
635C2—42no—
636C2—42no—
637C2—82no—
638C2C127×#300211yescharacteristic
639C2C127×#302211yescharacteristic
640C2C127×#302611yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC22×C4C24×C127
prime radicalC127×#3459C2
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×#3190C2semidirect
3. C127×#2638C2semidirect
4. C127×#1609C2semidirect
5. C127×#1608C2semidirect
6. C127×#1607C2semidirect
7. C127×#1603C2semidirect
8. C127×#1602C2semidirect
9. C127×#1601C2semidirect
10. C127×#1516C2semidirect
11. C127×#1459C2semidirect
23. C2×C22⋊Q8×C127C22semidirect
27. #483×C127C22semidirect
32. #451×C127C22semidirect
34. C2×C22⋊C8×C127C22semidirect
35. #398×C127C22semidirect
38. #395×C127C22semidirect
43. #381×C127C22semidirect
44. #328×C127C22semidirect
45. #328×C127C22semidirect
48. #324×C127C22semidirect
312. #18291C127direct (N × H)
322. #3190C2×C127semidirect
323. #2638C2×C127semidirect
324. #1609C2×C127semidirect
325. #1608C2×C127semidirect
326. #1607C2×C127semidirect
327. #1603C2×C127semidirect
328. #1602C2×C127semidirect
329. #1601C2×C127semidirect
330. #1516C2×C127semidirect
331. #1459C2×C127semidirect
332. C127#18291direct (N × H)
344. C2×C22⋊Q8C22×C127semidirect
348. #483C22×C127semidirect
353. #451C22×C127semidirect
355. C2×C22⋊C8C22×C127semidirect
356. #398C22×C127semidirect
359. #395C22×C127semidirect
364. #381C22×C127semidirect
365. #328C22×C127semidirect
366. #328C22×C127semidirect
369. #324C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#34592
C127×#31902
C127×#26382
C127×#16092
C127×#16082
C127×#16072
C127×#16032
C127×#16022
C127×#16012
C127×#15162
C127×#14592
#18291127