Finite Group Databasebeta

← C127×#18307 #44581980

Subgroups — C127×#18307 #44581980

Order 32512.

934 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3461C211yesmaximal, characteristic, complemented
2C127×#3211C212yesmaximal, complemented
3C127×#2632C211yesmaximal, characteristic, complemented
4C127×#1605C211yesmaximal, characteristic, complemented
5C127×#1604C211yesmaximal, characteristic, complemented
6C127×#1603C212yesmaximal, complemented
7C127×#1599C211yesmaximal, characteristic, complemented
8C127×#1598C211yesmaximal, characteristic
9C127×#1597C212yesmaximal, complemented
10C127×#1521C212yesmaximal, complemented
11C127×#1461C211yesmaximal, characteristic, complemented
12#544×C127C2211yescharacteristic
13#542×C127—22no—
14#541×C127—22no—
15#539×C127—21no—
16#539×C127C2212yes—
17#537×C127C2211yescharacteristic
18#536×C127—21no—
19#533×C127—22no—
20#529×C127—22no—
21#529×C127—21no—
22#529×C127C2212yes—
23C2×#124×C127C2211yescharacteristic
24C4×#41×C127—21no—
25C2×C4×Q8×C127C2211yescharacteristic
26#495×C127—22no—
27#488×C127—22no—
28#464×C127—22no—
29#463×C127—22no—
30#451×C127C2212yes—
31#450×C127C2212yes—
32#448×C127C2212yes—
33#447×C127C2212yes—
34#431×C127C2212yes—
35#399×C127—21no—
36#395×C127C2211yescharacteristic
37#395×C127C2211yescharacteristic
38#394×C127C2211yescharacteristic
39#394×C127C2211yescharacteristic
40#393×C127—21no—
41#388×C127—21no—
42#388×C127—21no—
43#383×C127C2211yescharacteristic
44#328×C127C2212yes—
45#328×C127C2212yes—
46#327×C127C2212yes—
47#327×C127C2212yes—
48#324×C127C2212yes—
49#324×C127C2211yescharacteristic
50#324×C127C2211yescharacteristic
51C2×#41×C127—21no—
52C22×Q8×C127D411yescharacteristic
53C22×Q8×C127C2311yescharacteristic
54C22×D4×C127C2311yescharacteristic
55C2×Q16×C127—22no—
56C2×SD16×C127—22no—
57C2×SD16×C127—22no—
58C2×D8×C127—22no—
59C4⋊Q8×C127—22no—
60C4⋊Q8×C127—22no—
61#126×C127—22no—
62#126×C127—22no—
63#126×C127—22no—
64#126×C127—22no—
65#125×C127—21no—
66#125×C127—22no—
67#125×C127—22no—
68#125×C127—22no—
69#125×C127D412yes—
70#124×C127—22no—
71#124×C127—21no—
72#124×C127—22no—
73#124×C127—22no—
74#124×C127D412yes—
75#123×C127—22no—
76#123×C127—22no—
77#123×C127—22no—
78#123×C127—22no—
79C22⋊Q8×C127—22no—
80C22⋊Q8×C127—22no—
81C22⋊Q8×C127—22no—
82C22⋊Q8×C127—22no—
83C22⋊Q8×C127—21no—
84C22⋊Q8×C127—22no—
85C22⋊Q8×C127C2312yes—
86#121×C127—22no—
87#121×C127—21no—
88#121×C127C2312yes—
89C4×Q8×C127—21no—
90C4×Q8×C127—21no—
91C4×Q8×C127—21no—
92C4×Q8×C127—22no—
93C4×Q8×C127—22no—
94C4×Q8×C127D412yes—
95C4×D4×C127—21no—
96C4×D4×C127—21no—
97C4×D4×C127—21no—
98C4×D4×C127—22no—
99C4×D4×C127—22no—
100C4×D4×C127D412yes—
101#117×C127—22no—
102#117×C127—22no—
103#117×C127—21no—
104#117×C127—22no—
105C2×C4⋊C4×C127—21no—
106C2×C4⋊C4×C127—21no—
107C2×C4⋊C4×C127D411yescharacteristic
108C2×C4⋊C4×C127C2311yescharacteristic
109C2×C4⋊C4×C127C2311yescharacteristic
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×C42×C127—22no—
117C2×C42×C127D411yescharacteristic
118C2×C42×C127D411yescharacteristic
119C2×C42×C127C2311yescharacteristic
120C4⋊C8×C127—22no—
121#103×C127—22no—
122#103×C127—22no—
123#102×C127—22no—
124#102×C127—22no—
125C22⋊C8×C127C2312yes—
126C22⋊C8×C127C2312yes—
127C4×C8×C127—22no—
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—
135#41×C127—42no—
136#41×C127—42no—
137C2×Q8×C127—21no—
138C2×Q8×C127—21no—
139C2×Q8×C127—22no—
140C2×Q8×C127—22no—
141C2×Q8×C127—22no—
142C2×Q8×C127—41no—
143C2×Q8×C127—81no—
144C2×Q8×C127C2×D412yes—
145C2×D4×C127—21no—
146C2×D4×C127—22no—
147C2×D4×C127—21no—
148C2×D4×C127—22no—
149C2×D4×C127—81no—
150C2×D4×C127C2×D412yes—
151C22×C4×C127—22no—
152C22×C4×C127—22no—
153C22×C4×C127—22no—
154C22×C4×C127—21no—
155C22×C4×C127—21no—
156C22×C4×C127—21no—
157C22×C4×C127C2×D411yescharacteristic
158C22×C4×C127C2×D411yescharacteristic
159C22×C4×C127C2×D411yescharacteristic
160C22×C4×C127C2×D411yescharacteristic
161C22×C4×C127C2×D411yescharacteristic
162C22×C4×C127C2×D411yescharacteristic
163C22×C4×C127C2411yescharacteristic
164Q16×C127—82no—
165SD16×C127—82no—
166SD16×C127—82no—
167D8×C127—82no—
168C2×C8×C127—22no—
169C2×C8×C127—22no—
170C4⋊C4×C127—21no—
171C4⋊C4×C127—22no—
172C4⋊C4×C127—21no—
173C4⋊C4×C127—22no—
174C4⋊C4×C127—22no—
175C4⋊C4×C127—21no—
176C4⋊C4×C127—21no—
177C4⋊C4×C127—22no—
178C4⋊C4×C127—22no—
179C4⋊C4×C127—22no—
180C4⋊C4×C127—22no—
181C4⋊C4×C127—22no—
182C4⋊C4×C127—22no—
183C4⋊C4×C127—22no—
184C4⋊C4×C127—22no—
185C4⋊C4×C127—81no—
186C4⋊C4×C127—81no—
187C4⋊C4×C127C2×D412yes—
188C4⋊C4×C127C2×D412yes—
189C22⋊C4×C127—22no—
190C22⋊C4×C127—22no—
191C22⋊C4×C127—22no—
192C22⋊C4×C127—22no—
193C22⋊C4×C127—22no—
194C22⋊C4×C127—22no—
195C22⋊C4×C127—22no—
196C22⋊C4×C127—22no—
197C22⋊C4×C127—22no—
198C22⋊C4×C127—42no—
199C22⋊C4×C127—41no—
200C22⋊C4×C127—41no—
201C22⋊C4×C127—42no—
202C22⋊C4×C127—42no—
203C22⋊C4×C127—81no—
204C22⋊C4×C127—81no—
205C42×C127—22no—
206C42×C127—22no—
207C42×C127—21no—
208C42×C127—22no—
209C42×C127—21no—
210C42×C127—21no—
211C42×C127—21no—
212C42×C127C2×D412yes—
213C42×C127C2×D412yes—
214C23×C127—22no—
215C23×C127—41no—
216C23×C127—41no—
217C23×C127—41no—
218C23×C127—41no—
219C23×C127—41no—
220C23×C127—41no—
221C23×C127—41no—
222C23×C127C22×D411yescharacteristic
223Q8×C127—44no—
224Q8×C127—42no—
225Q8×C127—42no—
226Q8×C127—42no—
227Q8×C127—42no—
228Q8×C127—81no—
229D4×C127—42no—
230D4×C127—42no—
231D4×C127—42no—
232D4×C127—42no—
233D4×C127—42no—
234D4×C127—42no—
235D4×C127—81no—
236C2×C4×C127—21no—
237C2×C4×C127—21no—
238C2×C4×C127—21no—
239C2×C4×C127—21no—
240C2×C4×C127—21no—
241C2×C4×C127—22no—
242C2×C4×C127—22no—
243C2×C4×C127—21no—
244C2×C4×C127—21no—
245C2×C4×C127—22no—
246C2×C4×C127—21no—
247C2×C4×C127—21no—
248C2×C4×C127—41no—
249C2×C4×C127—41no—
250C2×C4×C127—44no—
251C2×C4×C127—44no—
252C2×C4×C127—41no—
253C2×C4×C127—41no—
254C2×C4×C127—41no—
255C2×C4×C127—41no—
256C2×C4×C127—41no—
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—82no—
264C2×C4×C127#12011yescharacteristic
265C2×C4×C127#12011yescharacteristic
266C2×C4×C127#12012yes—
267C2×C4×C127#13512yes—
268C2×C4×C127C22×D412yes—
269C8×C127—42no—
270C8×C127—42no—
271C22×C127—21no—
272C22×C127—21no—
273C22×C127—42no—
274C22×C127—42no—
275C22×C127—42no—
276C22×C127—81no—
277C22×C127—81no—
278C22×C127—81no—
279C22×C127—81no—
280C22×C127—81no—
281C22×C127—81no—
282C22×C127—81no—
283C22×C127C2×#12011yescharacteristic
284C22×C127C2×#13511yescharacteristic
285C22×C127#57511yescharacteristic
286C4×C127—22no—
287C4×C127—22no—
288C4×C127—21no—
289C4×C127—21no—
290C4×C127—22no—
291C4×C127—41no—
292C4×C127—42no—
293C4×C127—42no—
294C4×C127—41no—
295C4×C127—41no—
296C4×C127—42no—
297C4×C127—81no—
298C4×C127—81no—
299C4×C127—81no—
300#18307C12711yesmaximal, characteristic, direct product factor, Sylow
301C2×C127—21no—
302C2×C127—21no—
303C2×C127—82no—
304C2×C127—161no—
305C2×C127#300211yescharacteristic
306C2×C127#302011yescharacteristic
307C2×C127#302711yescharacteristic
308#3461C2×C12711yescharacteristic, complemented
309#3211C2×C12712yescomplemented
310#2632C2×C12711yescharacteristic, complemented
311#1605C2×C12711yescharacteristic, complemented
312#1604C2×C12711yescharacteristic, complemented
313#1603C2×C12712yescomplemented
314#1599C2×C12711yescharacteristic, complemented
315#1598C2×C12711yescharacteristic
316#1597C2×C12712yescomplemented
317#1521C2×C12712yescomplemented
318#1461C2×C12711yescharacteristic, complemented
319C127#1830711yescharacteristic, direct product factor, Sylow
320#544C22×C12711yescharacteristic
321#542—22no—
322#541—22no—
323#539—21no—
324#539C22×C12712yes—
325#537C22×C12711yescharacteristic
326#536—21no—
327#533—22no—
328#529—22no—
329#529—21no—
330#529C22×C12712yes—
331C2×#124C22×C12711yescharacteristic
332C4×#41—21no—
333C2×C4×Q8C22×C12711yescharacteristic
334#495—22no—
335#488—22no—
336#464—22no—
337#463—22no—
338#451C22×C12712yes—
339#450C22×C12712yes—
340#448C22×C12712yes—
341#447C22×C12712yes—
342#431C22×C12712yes—
343#399—21no—
344#395C22×C12711yescharacteristic
345#395C22×C12711yescharacteristic
346#394C22×C12711yescharacteristic
347#394C22×C12711yescharacteristic
348#393—21no—
349#388—21no—
350#388—21no—
351#383C22×C12711yescharacteristic
352#328C22×C12712yes—
353#328C22×C12712yes—
354#327C22×C12712yes—
355#327C22×C12712yes—
356#324C22×C12712yes—
357#324C22×C12711yescharacteristic
358#324C22×C12711yescharacteristic
359C2×#41—21no—
360C22×Q8D4×C12711yescharacteristic
361C22×Q8C23×C12711yescharacteristic
362C22×D4C23×C12711yescharacteristic
363C2×Q16—22no—
364C2×SD16—22no—
365C2×SD16—22no—
366C2×D8—22no—
367C4⋊Q8—22no—
368C4⋊Q8—22no—
369#126—22no—
370#126—22no—
371#126—22no—
372#126—22no—
373#125—21no—
374#125—22no—
375#125—22no—
376#125—22no—
377#125D4×C12712yes—
378#124—22no—
379#124—21no—
380#124—22no—
381#124—22no—
382#124D4×C12712yes—
383#123—22no—
384#123—22no—
385#123—22no—
386#123—22no—
387C22⋊Q8—22no—
388C22⋊Q8—22no—
389C22⋊Q8—22no—
390C22⋊Q8—22no—
391C22⋊Q8—21no—
392C22⋊Q8—22no—
393C22⋊Q8C23×C12712yes—
394#121—22no—
395#121—21no—
396#121C23×C12712yes—
397C4×Q8—21no—
398C4×Q8—21no—
399C4×Q8—21no—
400C4×Q8—22no—
401C4×Q8—22no—
402C4×Q8D4×C12712yes—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—22no—
407C4×D4—22no—
408C4×D4D4×C12712yes—
409#117—22no—
410#117—22no—
411#117—21no—
412#117—22no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4D4×C12711yescharacteristic
416C2×C4⋊C4C23×C12711yescharacteristic
417C2×C4⋊C4C23×C12711yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C42—22no—
425C2×C42D4×C12711yescharacteristic
426C2×C42D4×C12711yescharacteristic
427C2×C42C23×C12711yescharacteristic
428C4⋊C8—22no—
429#103—22no—
430#103—22no—
431#102—22no—
432#102—22no—
433C22⋊C8C23×C12712yes—
434C22⋊C8C23×C12712yes—
435C4×C8—22no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95C23×C12711yescharacteristic
441#95C23×C12711yescharacteristic
442C24—21no—
443#41—42no—
444#41—42no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—41no—
451C2×Q8—81no—
452C2×Q8C2×D4×C12712yes—
453C2×D4—21no—
454C2×D4—22no—
455C2×D4—21no—
456C2×D4—22no—
457C2×D4—81no—
458C2×D4C2×D4×C12712yes—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4C2×D4×C12711yescharacteristic
466C22×C4C2×D4×C12711yescharacteristic
467C22×C4C2×D4×C12711yescharacteristic
468C22×C4C2×D4×C12711yescharacteristic
469C22×C4C2×D4×C12711yescharacteristic
470C22×C4C2×D4×C12711yescharacteristic
471C22×C4C24×C12711yescharacteristic
472Q16—82no—
473SD16—82no—
474SD16—82no—
475D8—82no—
476C2×C8—22no—
477C2×C8—22no—
478C4⋊C4—21no—
479C4⋊C4—22no—
480C4⋊C4—21no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—81no—
494C4⋊C4—81no—
495C4⋊C4C2×D4×C12712yes—
496C4⋊C4C2×D4×C12712yes—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—42no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C22⋊C4—42no—
510C22⋊C4—42no—
511C22⋊C4—81no—
512C22⋊C4—81no—
513C42—22no—
514C42—22no—
515C42—21no—
516C42—22no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42C2×D4×C12712yes—
521C42C2×D4×C12712yes—
522C23—22no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23C22×D4×C12711yescharacteristic
531Q8—44no—
532Q8—42no—
533Q8—42no—
534Q8—42no—
535Q8—42no—
536Q8—81no—
537D4—42no—
538D4—42no—
539D4—42no—
540D4—42no—
541D4—42no—
542D4—42no—
543D4—81no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—44no—
559C2×C4—44no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—82no—
572C2×C4#120×C12711yescharacteristic
573C2×C4#120×C12711yescharacteristic
574C2×C4#120×C12712yes—
575C2×C4#135×C12712yes—
576C2×C4C22×D4×C12712yes—
577C8—42no—
578C8—42no—
579C22—21no—
580C22—21no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22C2×#120×C12711yescharacteristic
592C22C2×#135×C12711yescharacteristic
593C22#575×C12711yescharacteristic
594C4—22no—
595C4—22no—
596C4—21no—
597C4—21no—
598C4—22no—
599C4—41no—
600C4—42no—
601C4—42no—
602C4—41no—
603C4—41no—
604C4—42no—
605C4—81no—
606C4—81no—
607C4—81no—
608C2—21no—
609C2—21no—
610C2—82no—
611C2—161no—
612C2C127×#300211yescharacteristic
613C2C127×#302011yescharacteristic
614C2C127×#302711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC22×C4C24×C127
prime radicalC127×#1598C2
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
1. C127×#3461C2semidirect
2. C127×#3211C2semidirect
3. C127×#2632C2semidirect
4. C127×#1605C2semidirect
5. C127×#1604C2semidirect
6. C127×#1603C2semidirect
7. C127×#1599C2semidirect
9. C127×#1597C2semidirect
10. C127×#1521C2semidirect
11. C127×#1461C2semidirect
300. #18307C127direct (N × H)
308. #3461C2×C127semidirect
309. #3211C2×C127semidirect
310. #2632C2×C127semidirect
311. #1605C2×C127semidirect
312. #1604C2×C127semidirect
313. #1603C2×C127semidirect
314. #1599C2×C127semidirect
316. #1597C2×C127semidirect
317. #1521C2×C127semidirect
318. #1461C2×C127semidirect
319. C127#18307direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#34612
C127×#32112
C127×#26322
C127×#16052
C127×#16042
C127×#16032
C127×#15992
C127×#15982
C127×#15972
C127×#15212
C127×#14612
#18307127