Finite Group Databasebeta

← C127×#18335 #44582008

Subgroups — C127×#18335 #44582008

Order 32512.

1194 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3459C211yesmaximal, characteristic, complemented
2C127×#3217C212yesmaximal, complemented
3C127×#2541C211yesmaximal, characteristic, complemented
4C127×#1600C214yesmaximal, complemented
5C127×#1596C212yesmaximal, complemented
6C127×#1595C212yesmaximal, complemented
7C127×#1509C212yesmaximal, complemented
8C127×#1466C211yesmaximal, characteristic, complemented
9#543×C127C2211yescharacteristic
10#539×C127—22no—
11#539×C127—21no—
12#538×C127—22no—
13#538×C127C2212yes—
14#534×C127—21no—
15#534×C127C2211yescharacteristic
16C2×#127×C127—21no—
17C2×#127×C127C2211yescharacteristic, complemented
18#529×C127—22no—
19#529×C127C2212yes—
20#525×C127—21no—
21#525×C127—22no—
22C2×#121×C127—21no—
23C2×#121×C127—21no—
24C2×C4×D4×C127—21no—
25C2×C4×D4×C127C2211yescharacteristic
26#496×C127—22no—
27#490×C127—22no—
28#460×C127—22no—
29#459×C127—22no—
30#450×C127C2214yescomplemented
31#447×C127C2214yes—
32#432×C127C2212yescomplemented
33#392×C127C2212yes—
34#392×C127C2212yescomplemented
35#390×C127—21no—
36C4×C4⋊C4×C127C2211yescharacteristic, complemented
37#328×C127C2214yescomplemented
38#327×C127C2214yes—
39#323×C127C2212yes—
40#323×C127C2212yescomplemented
41C2×#41×C127—21no—
42C22×D4×C127—21no—
43C22×D4×C127—22no—
44C22×D4×C127—22no—
45C22×D4×C127—21no—
46C22×D4×C127—21no—
47C22×D4×C127D411yescharacteristic
48C22×D4×C127C2312yes—
49C23×C4×C127—21no—
50C23×C4×C127D411yescharacteristic
51C23×C4×C127D411yescharacteristic
52C2×SD16×C127—24no—
53C2×D8×C127—24no—
54#127×C127—22no—
55#127×C127—22no—
56#127×C127—44no—
57#126×C127—22no—
58#126×C127—22no—
59#126×C127—22no—
60#125×C127—22no—
61#125×C127D412yescomplemented
62#124×C127—22no—
63#124×C127D412yescomplemented
64#123×C127—22no—
65#123×C127—22no—
66#123×C127—22no—
67#123×C127—22no—
68#123×C127—22no—
69#123×C127—22no—
70C22⋊Q8×C127—21no—
71C22⋊Q8×C127—22no—
72C22⋊Q8×C127—22no—
73C22⋊Q8×C127—21no—
74C22⋊Q8×C127—22no—
75C22⋊Q8×C127C2312yes—
76#121×C127—22no—
77#121×C127—21no—
78#121×C127—22no—
79#121×C127—22no—
80#121×C127—21no—
81#121×C127—44no—
82#121×C127—44no—
83#121×C127C2312yes—
84#120×C127—22no—
85#120×C127—22no—
86#120×C127—22no—
87C4×Q8×C127D412yescomplemented
88C4×D4×C127—22no—
89C4×D4×C127—22no—
90C4×D4×C127—22no—
91C4×D4×C127—22no—
92C4×D4×C127—22no—
93C4×D4×C127—22no—
94C4×D4×C127—22no—
95C4×D4×C127D412yescomplemented
96#117×C127—21no—
97#117×C127—22no—
98C2×C4⋊C4×C127—21no—
99C2×C4⋊C4×C127—21no—
100C2×C4⋊C4×C127D411yescharacteristic
101C2×C22⋊C4×C127—21no—
102C2×C22⋊C4×C127—21no—
103C2×C22⋊C4×C127—22no—
104C2×C22⋊C4×C127—22no—
105C2×C22⋊C4×C127C2311yescharacteristic
106C2×C22⋊C4×C127C2311yescharacteristic
107C2×C42×C127—21no—
108C2×C42×C127—21no—
109C2×C42×C127C2311yescharacteristic
110C4⋊C8×C127—22no—
111#102×C127—24no—
112#102×C127—24no—
113C22⋊C8×C127C2314yes—
114#97×C127—22no—
115#95×C127C2312yes—
116C24×C127—21no—
117C24×C127—22no—
118C24×C127C2×D411yescharacteristic
119C24×C127C2×D411yescharacteristic
120#41×C127—82no—
121C2×Q8×C127—21no—
122C2×Q8×C127C2×D412yes—
123C2×D4×C127—22no—
124C2×D4×C127—22no—
125C2×D4×C127—22no—
126C2×D4×C127—22no—
127C2×D4×C127—21no—
128C2×D4×C127—22no—
129C2×D4×C127—22no—
130C2×D4×C127—24no—
131C2×D4×C127—41no—
132C2×D4×C127—42no—
133C2×D4×C127—42no—
134C2×D4×C127—44no—
135C2×D4×C127—44no—
136C2×D4×C127—42no—
137C2×D4×C127—42no—
138C2×D4×C127—42no—
139C2×D4×C127—42no—
140C2×D4×C127—44no—
141C2×D4×C127—44no—
142C2×D4×C127—42no—
143C2×D4×C127—41no—
144C2×D4×C127—41no—
145C2×D4×C127—82no—
146C2×D4×C127—82no—
147C2×D4×C127—82no—
148C2×D4×C127C2×D412yes—
149C22×C4×C127—21no—
150C22×C4×C127—22no—
151C22×C4×C127—21no—
152C22×C4×C127—21no—
153C22×C4×C127—22no—
154C22×C4×C127—21no—
155C22×C4×C127—21no—
156C22×C4×C127—22no—
157C22×C4×C127—21no—
158C22×C4×C127—21no—
159C22×C4×C127—42no—
160C22×C4×C127—42no—
161C22×C4×C127—82no—
162C22×C4×C127C2×D411yescharacteristic
163C22×C4×C127C2×D411yescharacteristic
164C22×C4×C127C2×D411yescharacteristic
165C22×C4×C127C2×D411yescharacteristic
166C22×C4×C127C2411yescharacteristic
167SD16×C127—84no—
168D8×C127—84no—
169C2×C8×C127—24no—
170C4⋊C4×C127—22no—
171C4⋊C4×C127—24no—
172C4⋊C4×C127—21no—
173C4⋊C4×C127—21no—
174C4⋊C4×C127—22no—
175C4⋊C4×C127—22no—
176C4⋊C4×C127—22no—
177C4⋊C4×C127—22no—
178C4⋊C4×C127—22no—
179C4⋊C4×C127—22no—
180C4⋊C4×C127C2×D412yes—
181C4⋊C4×C127C2×D412yes—
182C22⋊C4×C127—22no—
183C22⋊C4×C127—22no—
184C22⋊C4×C127—22no—
185C22⋊C4×C127—22no—
186C22⋊C4×C127—22no—
187C22⋊C4×C127—22no—
188C22⋊C4×C127—22no—
189C22⋊C4×C127—22no—
190C22⋊C4×C127—22no—
191C22⋊C4×C127—22no—
192C22⋊C4×C127—22no—
193C22⋊C4×C127—22no—
194C22⋊C4×C127—44no—
195C22⋊C4×C127—44no—
196C42×C127—22no—
197C42×C127—22no—
198C42×C127—42no—
199C42×C127C2×D412yes—
200C42×C127C2×D412yes—
201C23×C127—21no—
202C23×C127—21no—
203C23×C127—21no—
204C23×C127—22no—
205C23×C127—21no—
206C23×C127—21no—
207C23×C127—41no—
208C23×C127—41no—
209C23×C127—41no—
210C23×C127—41no—
211C23×C127—42no—
212C23×C127—42no—
213C23×C127—42no—
214C23×C127—42no—
215C23×C127—42no—
216C23×C127—42no—
217C23×C127—42no—
218C23×C127—42no—
219C23×C127—81no—
220C23×C127—81no—
221C23×C127AGL(1,ℤ/8)12yes—
222C23×C127C22×D411yescharacteristic
223Q8×C127—42no—
224Q8×C127—81no—
225D4×C127—44no—
226D4×C127—42no—
227D4×C127—44no—
228D4×C127—44no—
229D4×C127—44no—
230D4×C127—42no—
231D4×C127—42no—
232D4×C127—84no—
233D4×C127—82no—
234D4×C127—82no—
235D4×C127—81no—
236D4×C127—82no—
237D4×C127—88no—
238D4×C127—88no—
239D4×C127—82no—
240C2×C4×C127—21no—
241C2×C4×C127—21no—
242C2×C4×C127—22no—
243C2×C4×C127—24no—
244C2×C4×C127—22no—
245C2×C4×C127—22no—
246C2×C4×C127—21no—
247C2×C4×C127—21no—
248C2×C4×C127—22no—
249C2×C4×C127—41no—
250C2×C4×C127—42no—
251C2×C4×C127—42no—
252C2×C4×C127—42no—
253C2×C4×C127—42no—
254C2×C4×C127—42no—
255C2×C4×C127—44no—
256C2×C4×C127—41no—
257C2×C4×C127—41no—
258C2×C4×C127—81no—
259C2×C4×C127—81no—
260C2×C4×C127—81no—
261C2×C4×C127—82no—
262C2×C4×C127—81no—
263C2×C4×C127#12012yes—
264C2×C4×C127#12011yescharacteristic
265C2×C4×C127#12011yescharacteristic
266C2×C4×C127C22×D412yes—
267C8×C127—44no—
268C22×C127—21no—
269C22×C127—21no—
270C22×C127—22no—
271C22×C127—42no—
272C22×C127—42no—
273C22×C127—41no—
274C22×C127—41no—
275C22×C127—41no—
276C22×C127—42no—
277C22×C127—41no—
278C22×C127—42no—
279C22×C127—42no—
280C22×C127—41no—
281C22×C127—81no—
282C22×C127—81no—
283C22×C127—82no—
284C22×C127—82no—
285C22×C127—82no—
286C22×C127—82no—
287C22×C127—84no—
288C22×C127—82no—
289C22×C127—82no—
290C22×C127—82no—
291C22×C127C2×#12011yescharacteristic
292C22×C127C2×AGL(1,ℤ/8)11yescharacteristic
293C22×C127#57511yescharacteristic
294C4×C127—22no—
295C4×C127—21no—
296C4×C127—22no—
297C4×C127—44no—
298C4×C127—42no—
299C4×C127—41no—
300C4×C127—41no—
301C4×C127—42no—
302C4×C127—42no—
303C4×C127#45312yes—
304#18335C12711yesmaximal, characteristic, direct product factor, Sylow
305C2×C127—21no—
306C2×C127—21no—
307C2×C127—42no—
308C2×C127—81no—
309C2×C127—82no—
310C2×C127—162no—
311C2×C127#300611yescharacteristic
312C2×C127C2×#45311yescharacteristic
313C2×C127#302711yescharacteristic
314#3459C2×C12711yescharacteristic, complemented
315#3217C2×C12712yescomplemented
316#2541C2×C12711yescharacteristic, complemented
317#1600C2×C12714yescomplemented
318#1596C2×C12712yescomplemented
319#1595C2×C12712yescomplemented
320#1509C2×C12712yescomplemented
321#1466C2×C12711yescharacteristic, complemented
322C127#1833511yescharacteristic, direct product factor, Sylow
323#543C22×C12711yescharacteristic
324#539—22no—
325#539—21no—
326#538—22no—
327#538C22×C12712yes—
328#534—21no—
329#534C22×C12711yescharacteristic
330C2×#127—21no—
331C2×#127C22×C12711yescharacteristic, complemented
332#529—22no—
333#529C22×C12712yes—
334#525—21no—
335#525—22no—
336C2×#121—21no—
337C2×#121—21no—
338C2×C4×D4—21no—
339C2×C4×D4C22×C12711yescharacteristic
340#496—22no—
341#490—22no—
342#460—22no—
343#459—22no—
344#450C22×C12714yescomplemented
345#447C22×C12714yes—
346#432C22×C12712yescomplemented
347#392C22×C12712yes—
348#392C22×C12712yescomplemented
349#390—21no—
350C4×C4⋊C4C22×C12711yescharacteristic, complemented
351#328C22×C12714yescomplemented
352#327C22×C12714yes—
353#323C22×C12712yes—
354#323C22×C12712yescomplemented
355C2×#41—21no—
356C22×D4—21no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—21no—
360C22×D4—21no—
361C22×D4D4×C12711yescharacteristic
362C22×D4C23×C12712yes—
363C23×C4—21no—
364C23×C4D4×C12711yescharacteristic
365C23×C4D4×C12711yescharacteristic
366C2×SD16—24no—
367C2×D8—24no—
368#127—22no—
369#127—22no—
370#127—44no—
371#126—22no—
372#126—22no—
373#126—22no—
374#125—22no—
375#125D4×C12712yescomplemented
376#124—22no—
377#124D4×C12712yescomplemented
378#123—22no—
379#123—22no—
380#123—22no—
381#123—22no—
382#123—22no—
383#123—22no—
384C22⋊Q8—21no—
385C22⋊Q8—22no—
386C22⋊Q8—22no—
387C22⋊Q8—21no—
388C22⋊Q8—22no—
389C22⋊Q8C23×C12712yes—
390#121—22no—
391#121—21no—
392#121—22no—
393#121—22no—
394#121—21no—
395#121—44no—
396#121—44no—
397#121C23×C12712yes—
398#120—22no—
399#120—22no—
400#120—22no—
401C4×Q8D4×C12712yescomplemented
402C4×D4—22no—
403C4×D4—22no—
404C4×D4—22no—
405C4×D4—22no—
406C4×D4—22no—
407C4×D4—22no—
408C4×D4—22no—
409C4×D4D4×C12712yescomplemented
410#117—21no—
411#117—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4D4×C12711yescharacteristic
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4C23×C12711yescharacteristic
420C2×C22⋊C4C23×C12711yescharacteristic
421C2×C42—21no—
422C2×C42—21no—
423C2×C42C23×C12711yescharacteristic
424C4⋊C8—22no—
425#102—24no—
426#102—24no—
427C22⋊C8C23×C12714yes—
428#97—22no—
429#95C23×C12712yes—
430C24—21no—
431C24—22no—
432C24C2×D4×C12711yescharacteristic
433C24C2×D4×C12711yescharacteristic
434#41—82no—
435C2×Q8—21no—
436C2×Q8C2×D4×C12712yes—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—21no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—24no—
445C2×D4—41no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—44no—
449C2×D4—44no—
450C2×D4—42no—
451C2×D4—42no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4—44no—
455C2×D4—44no—
456C2×D4—42no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—82no—
460C2×D4—82no—
461C2×D4—82no—
462C2×D4C2×D4×C12712yes—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—82no—
476C22×C4C2×D4×C12711yescharacteristic
477C22×C4C2×D4×C12711yescharacteristic
478C22×C4C2×D4×C12711yescharacteristic
479C22×C4C2×D4×C12711yescharacteristic
480C22×C4C24×C12711yescharacteristic
481SD16—84no—
482D8—84no—
483C2×C8—24no—
484C4⋊C4—22no—
485C4⋊C4—24no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4C2×D4×C12712yes—
495C4⋊C4C2×D4×C12712yes—
496C22⋊C4—22no—
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—22no—
507C22⋊C4—22no—
508C22⋊C4—44no—
509C22⋊C4—44no—
510C42—22no—
511C42—22no—
512C42—42no—
513C42C2×D4×C12712yes—
514C42C2×D4×C12712yes—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—22no—
519C23—21no—
520C23—21no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—81no—
534C23—81no—
535C23AGL(1,ℤ/8)×C12712yes—
536C23C22×D4×C12711yescharacteristic
537Q8—42no—
538Q8—81no—
539D4—44no—
540D4—42no—
541D4—44no—
542D4—44no—
543D4—44no—
544D4—42no—
545D4—42no—
546D4—84no—
547D4—82no—
548D4—81no—
549D4—82no—
550D4—82no—
551D4—88no—
552D4—88no—
553D4—82no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—44no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—81no—
573C2×C4—81no—
574C2×C4—82no—
575C2×C4—81no—
576C2×C4—81no—
577C2×C4#120×C12712yes—
578C2×C4#120×C12711yescharacteristic
579C2×C4#120×C12711yescharacteristic
580C2×C4C22×D4×C12712yes—
581C8—44no—
582C22—21no—
583C22—21no—
584C22—22no—
585C22—42no—
586C22—42no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—42no—
591C22—41no—
592C22—42no—
593C22—42no—
594C22—41no—
595C22—81no—
596C22—81no—
597C22—82no—
598C22—82no—
599C22—82no—
600C22—82no—
601C22—84no—
602C22—82no—
603C22—82no—
604C22—82no—
605C22C2×#120×C12711yescharacteristic
606C22C2×AGL(1,ℤ/8)×C12711yescharacteristic
607C22#575×C12711yescharacteristic
608C4—22no—
609C4—21no—
610C4—22no—
611C4—44no—
612C4—42no—
613C4—41no—
614C4—41no—
615C4—42no—
616C4—42no—
617C4#453×C12712yes—
618C2—21no—
619C2—21no—
620C2—42no—
621C2—81no—
622C2—82no—
623C2—162no—
624C2C127×#300611yescharacteristic
625C2C2×#453×C12711yescharacteristic
626C2C127×#302711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC22×C4C24×C127
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×#3459C2semidirect
2. C127×#3217C2semidirect
3. C127×#2541C2semidirect
4. C127×#1600C2semidirect
5. C127×#1596C2semidirect
6. C127×#1595C2semidirect
7. C127×#1509C2semidirect
8. C127×#1466C2semidirect
17. C2×#127×C127C22semidirect
30. #450×C127C22semidirect
32. #432×C127C22semidirect
34. #392×C127C22semidirect
36. C4×C4⋊C4×C127C22semidirect
37. #328×C127C22semidirect
40. #323×C127C22semidirect
61. #125×C127D4semidirect
63. #124×C127D4semidirect
87. C4×Q8×C127D4semidirect
95. C4×D4×C127D4semidirect
304. #18335C127direct (N × H)
314. #3459C2×C127semidirect
315. #3217C2×C127semidirect
316. #2541C2×C127semidirect
317. #1600C2×C127semidirect
318. #1596C2×C127semidirect
319. #1595C2×C127semidirect
320. #1509C2×C127semidirect
321. #1466C2×C127semidirect
322. C127#18335direct (N × H)
331. C2×#127C22×C127semidirect
344. #450C22×C127semidirect
346. #432C22×C127semidirect
348. #392C22×C127semidirect
350. C4×C4⋊C4C22×C127semidirect
351. #328C22×C127semidirect
354. #323C22×C127semidirect
375. #125D4×C127semidirect
377. #124D4×C127semidirect
401. C4×Q8D4×C127semidirect
409. C4×D4D4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#34592
C127×#32172
C127×#25412
C127×#16002
C127×#15962
C127×#15952
C127×#15092
C127×#14662
#18335127