Finite Group Databasebeta

← C127×#21017 #44584690

Subgroups — C127×#21017 #44584690

Order 32512.

1692 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#568×C127C211yesmaximal, characteristic, complemented
2C127×#3449C211yesmaximal, characteristic
3C2×#413×C127C211yesmaximal, characteristic, complemented
4C2×#413×C127C212yesmaximal, complemented
5C127×#1915C214yesmaximal, complemented
6C127×#1914C214yesmaximal, complemented
7C2×#344×C127C212yesmaximal, complemented
8C22×#41×C127C2211yescharacteristic
9C22×#41×C127C2211yescharacteristic
10#568×C127—22no—
11#568×C127—24no—
12#568×C127C2214yes—
13C2×#131×C127—24no—
14C22×M16×C127—22no—
15C22×M16×C127C2212yes—
16C22×M16×C127C2212yes—
17#537×C127—22no—
18#536×C127—21no—
19#536×C127C2212yes—
20#535×C127—21no—
21#535×C127C2212yes—
22#534×C127C414yes—
23#532×C127—22no—
24#525×C127—22no—
25#525×C127C414yes—
26C2×#117×C127C2211yescharacteristic
27#413×C127—22no—
28#413×C127—24no—
29#413×C127—24no—
30#413×C127C2214yes—
31C2×#101×C127—21no—
32C2×#101×C127C2214yescomplemented
33C2×#100×C127—21no—
34C2×#100×C127C2214yescomplemented
35#344×C127C2218yescomplemented
36C2×#41×C127—22no—
37C2×#41×C127—22no—
38C2×#41×C127—21no—
39C2×#41×C127—21no—
40C2×#41×C127—21no—
41C2×#41×C127—21no—
42C2×#41×C127—22no—
43C2×#41×C127—22no—
44C2×#41×C127—22no—
45C2×#41×C127—22no—
46C2×#41×C127—22no—
47C2×#41×C127—22no—
48C2×#41×C127C2×C412yes—
49C2×#41×C127D412yes—
50C2×#41×C127D412yes—
51C2×#41×C127C2312yes—
52C22×Q8×C127D411yescharacteristic
53C22×Q8×C127C2311yescharacteristic
54C22×D4×C127C2×C412yes—
55C22×D4×C127C2×C412yes—
56C22×D4×C127D411yescharacteristic
57C22×D4×C127C2311yescharacteristic
58C23×C4×C127C2×C412yes—
59C23×C4×C127D412yes—
60C23×C4×C127C2311yescharacteristic
61#131×C127—216no—
62#131×C127—216no—
63C2×M16×C127—24no—
64C2×M16×C127—28no—
65C2×M16×C127—22no—
66C2×M16×C127—28no—
67C2×M16×C127—22no—
68C2×M16×C127—22no—
69C2×M16×C127—22no—
70C2×M16×C127—22no—
71C2×M16×C127—22no—
72C2×M16×C127—22no—
73C2×M16×C127—22no—
74C2×M16×C127D414yescomplemented
75C2×M16×C127D414yescomplemented
76C2×M16×C127C2314yes—
77C2×M16×C127C2314yes—
78C22×C8×C127—24no—
79C22×C8×C127—22no—
80C22×C8×C127—22no—
81C4⋊Q8×C127—22no—
82#127×C127—22no—
83#124×C127—22no—
84#124×C127—22no—
85#123×C127—24no—
86#123×C127C2×C418yes—
87C22⋊Q8×C127—24no—
88C22⋊Q8×C127—24no—
89#121×C127—24no—
90#121×C127—28no—
91#121×C127—24no—
92#120×C127—24no—
93#120×C127C2×C418yes—
94C4×D4×C127—28no—
95#117×C127—21no—
96#117×C127—21no—
97#117×C127C2×C412yes—
98#117×C127C2312yes—
99C2×C4⋊C4×C127—21no—
100C2×C22⋊C4×C127C2×C412yes—
101C2×C42×C127—21no—
102#101×C127—24no—
103#101×C127—28no—
104#100×C127—24no—
105#100×C127—28no—
106C24×C127C22⋊C412yes—
107C24×C127C22×C412yes—
108C24×C127C22×C411yescharacteristic
109#41×C127—24no—
110#41×C127—24no—
111#41×C127—24no—
112#41×C127—24no—
113#41×C127—24no—
114#41×C127—24no—
115#41×C127—24no—
116#41×C127—24no—
117#41×C127—42no—
118#41×C127—41no—
119#41×C127—41no—
120#41×C127—42no—
121#41×C127—42no—
122#41×C127—42no—
123#41×C127—42no—
124#41×C127—41no—
125#41×C127—42no—
126#41×C127—41no—
127C2×Q8×C127—22no—
128C2×Q8×C127—22no—
129C2×Q8×C127—22no—
130C2×Q8×C127—21no—
131C2×Q8×C127—21no—
132C2×Q8×C127—22no—
133C2×Q8×C127C22⋊C412yes—
134C2×Q8×C127C2×D412yes—
135C2×D4×C127—24no—
136C2×D4×C127—24no—
137C2×D4×C127—22no—
138C2×D4×C127—22no—
139C2×D4×C127—24no—
140C2×D4×C127—24no—
141C2×D4×C127—28no—
142C2×D4×C127—22no—
143C2×D4×C127—22no—
144C2×D4×C127—22no—
145C2×D4×C127—21no—
146C2×D4×C127—21no—
147C2×D4×C127—22no—
148C2×D4×C127C22⋊C414yes—
149C2×D4×C127C22⋊C412yes—
150C2×D4×C127C22×C414yes—
151C2×D4×C127C2×D412yes—
152C22×C4×C127—22no—
153C22×C4×C127—22no—
154C22×C4×C127—22no—
155C22×C4×C127—22no—
156C22×C4×C127—22no—
157C22×C4×C127—22no—
158C22×C4×C127—22no—
159C22×C4×C127—24no—
160C22×C4×C127—24no—
161C22×C4×C127C22⋊C414yes—
162C22×C4×C127C22⋊C412yes—
163C22×C4×C127C22×C412yes—
164C22×C4×C127C22×C411yescharacteristic
165C22×C4×C127C2×D414yes—
166C22×C4×C127C2×D411yescharacteristic
167C22×C4×C127C2×D411yescharacteristic
168C22×C4×C127C2×D411yescharacteristic
169C22×C4×C127C2×D411yescharacteristic
170C22×C4×C127C2×D412yes—
171C22×C4×C127C2×D412yes—
172C22×C4×C127#4112yes—
173C22×C4×C127#4112yes—
174C22×C4×C127C2411yescharacteristic
175M16×C127—216no—
176M16×C127—24no—
177M16×C127—24no—
178M16×C127—24no—
179M16×C127—24no—
180M16×C127—24no—
181M16×C127—42no—
182M16×C127—42no—
183M16×C127C2×D418yes—
184C2×C8×C127—216no—
185C2×C8×C127—24no—
186C2×C8×C127—24no—
187C2×C8×C127—24no—
188C2×C8×C127—24no—
189C2×C8×C127—42no—
190C2×C8×C127—42no—
191C4⋊C4×C127—22no—
192C4⋊C4×C127—28no—
193C4⋊C4×C127—22no—
194C22⋊C4×C127—22no—
195C22⋊C4×C127—28no—
196C22⋊C4×C127—28no—
197C22⋊C4×C127C22×C414yes—
198C42×C127—22no—
199C42×C127—22no—
200C23×C127—22no—
201C23×C127—22no—
202C23×C127—22no—
203C23×C127—24no—
204C23×C127—81no—
205C23×C127—82no—
206C23×C127—82no—
207C23×C127C2×C22⋊C414yes—
208C23×C127C2×C22⋊C411yescharacteristic
209C23×C127C2×C22⋊C411yescharacteristic
210C23×C127C4×D412yes—
211C23×C127C4×D412yes—
212C23×C127C23×C411yescharacteristic
213Q8×C127—24no—
214Q8×C127—24no—
215Q8×C127—41no—
216Q8×C127—42no—
217Q8×C127—41no—
218D4×C127—28no—
219D4×C127—28no—
220D4×C127—24no—
221D4×C127—24no—
222D4×C127—42no—
223D4×C127—42no—
224D4×C127—44no—
225D4×C127—41no—
226D4×C127—42no—
227D4×C127—41no—
228D4×C127—88no—
229C2×C4×C127—22no—
230C2×C4×C127—22no—
231C2×C4×C127—24no—
232C2×C4×C127—24no—
233C2×C4×C127—24no—
234C2×C4×C127—24no—
235C2×C4×C127—24no—
236C2×C4×C127—22no—
237C2×C4×C127—24no—
238C2×C4×C127—42no—
239C2×C4×C127—44no—
240C2×C4×C127—42no—
241C2×C4×C127—82no—
242C2×C4×C127C2×C22⋊C414yes—
243C2×C4×C127C2×C22⋊C411yescharacteristic
244C2×C4×C127C2×C22⋊C411yescharacteristic
245C2×C4×C127C4×D412yes—
246C2×C4×C127C4×D412yes—
247C2×C4×C127#12012yes—
248C2×C4×C127#12011yescharacteristic
249C2×C4×C127#12011yescharacteristic
250C2×C4×C127#12112yes—
251C2×C4×C127#12112yes—
252C2×C4×C127#12112yes—
253C2×C4×C127#12112yes—
254C2×C4×C127#12311yescharacteristic
255C2×C4×C127#12312yes—
256C2×C4×C127#12311yescharacteristic
257C2×C4×C127C22×D412yes—
258C2×C4×C127C22×D411yescharacteristic
259C2×C4×C127C22×D411yescharacteristic
260C2×C4×C127C2×#4112yes—
261C8×C127—28no—
262C8×C127—44no—
263C22×C127—24no—
264C22×C127—41no—
265C22×C127—41no—
266C22×C127—41no—
267C22×C127—42no—
268C22×C127—42no—
269C22×C127—44no—
270C22×C127—44no—
271C22×C127—44no—
272C22×C127—42no—
273C22×C127—82no—
274C22×C127—84no—
275C22×C127#38611yescharacteristic
276C22×C127#38611yescharacteristic
277C22×C127#38612yes—
278C22×C127C22×C22⋊C411yescharacteristic
279C22×C127C2×C4×D412yes—
280C4×C127—24no—
281C4×C127—44no—
282C4×C127—42no—
283C4×C127#38611yescharacteristic
284C4×C127#38612yes—
285C4×C127#38611yescharacteristic
286C4×C127C2×#12011yescharacteristic
287C4×C127C2×#12112yes—
288C4×C127C2×#12311yescharacteristic
289#21017C12711yesmaximal, characteristic, direct product factor, Sylow
290C2×C127—21no—
291C2×C127—21no—
292C2×C127—22no—
293C2×C127—21no—
294C2×C127—22no—
295C2×C127—44no—
296C2×C127—82no—
297C2×C127C2×#38611yescharacteristic
298C2×#568C2×C12711yescharacteristic, complemented
299#3449C2×C12711yescharacteristic
300C2×#413C2×C12711yescharacteristic, complemented
301C2×#413C2×C12712yescomplemented
302#1915C2×C12714yescomplemented
303#1914C2×C12714yescomplemented
304C2×#344C2×C12712yescomplemented
305C127#2101711yescharacteristic, direct product factor, Sylow
306C22×#41C22×C12711yescharacteristic
307C22×#41C22×C12711yescharacteristic
308#568—22no—
309#568—24no—
310#568C22×C12714yes—
311C2×#131—24no—
312C22×M16—22no—
313C22×M16C22×C12712yes—
314C22×M16C22×C12712yes—
315#537—22no—
316#536—21no—
317#536C22×C12712yes—
318#535—21no—
319#535C22×C12712yes—
320#534C4×C12714yes—
321#532—22no—
322#525—22no—
323#525C4×C12714yes—
324C2×#117C22×C12711yescharacteristic
325#413—22no—
326#413—24no—
327#413—24no—
328#413C22×C12714yes—
329C2×#101—21no—
330C2×#101C22×C12714yescomplemented
331C2×#100—21no—
332C2×#100C22×C12714yescomplemented
333#344C22×C12718yescomplemented
334C2×#41—22no—
335C2×#41—22no—
336C2×#41—21no—
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—21no—
340C2×#41—22no—
341C2×#41—22no—
342C2×#41—22no—
343C2×#41—22no—
344C2×#41—22no—
345C2×#41—22no—
346C2×#41C2×C4×C12712yes—
347C2×#41D4×C12712yes—
348C2×#41D4×C12712yes—
349C2×#41C23×C12712yes—
350C22×Q8D4×C12711yescharacteristic
351C22×Q8C23×C12711yescharacteristic
352C22×D4C2×C4×C12712yes—
353C22×D4C2×C4×C12712yes—
354C22×D4D4×C12711yescharacteristic
355C22×D4C23×C12711yescharacteristic
356C23×C4C2×C4×C12712yes—
357C23×C4D4×C12712yes—
358C23×C4C23×C12711yescharacteristic
359#131—216no—
360#131—216no—
361C2×M16—24no—
362C2×M16—28no—
363C2×M16—22no—
364C2×M16—28no—
365C2×M16—22no—
366C2×M16—22no—
367C2×M16—22no—
368C2×M16—22no—
369C2×M16—22no—
370C2×M16—22no—
371C2×M16—22no—
372C2×M16D4×C12714yescomplemented
373C2×M16D4×C12714yescomplemented
374C2×M16C23×C12714yes—
375C2×M16C23×C12714yes—
376C22×C8—24no—
377C22×C8—22no—
378C22×C8—22no—
379C4⋊Q8—22no—
380#127—22no—
381#124—22no—
382#124—22no—
383#123—24no—
384#123C2×C4×C12718yes—
385C22⋊Q8—24no—
386C22⋊Q8—24no—
387#121—24no—
388#121—28no—
389#121—24no—
390#120—24no—
391#120C2×C4×C12718yes—
392C4×D4—28no—
393#117—21no—
394#117—21no—
395#117C2×C4×C12712yes—
396#117C23×C12712yes—
397C2×C4⋊C4—21no—
398C2×C22⋊C4C2×C4×C12712yes—
399C2×C42—21no—
400#101—24no—
401#101—28no—
402#100—24no—
403#100—28no—
404C24C22⋊C4×C12712yes—
405C24C22×C4×C12712yes—
406C24C22×C4×C12711yescharacteristic
407#41—24no—
408#41—24no—
409#41—24no—
410#41—24no—
411#41—24no—
412#41—24no—
413#41—24no—
414#41—24no—
415#41—41no—
416#41—42no—
417#41—41no—
418#41—42no—
419#41—42no—
420#41—42no—
421#41—42no—
422#41—41no—
423#41—41no—
424#41—42no—
425C2×Q8—22no—
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—22no—
431C2×Q8C22⋊C4×C12712yes—
432C2×Q8C2×D4×C12712yes—
433C2×D4—24no—
434C2×D4—24no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—24no—
438C2×D4—24no—
439C2×D4—28no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—22no—
446C2×D4C22⋊C4×C12714yes—
447C2×D4C22⋊C4×C12712yes—
448C2×D4C22×C4×C12714yes—
449C2×D4C2×D4×C12712yes—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4C22⋊C4×C12714yes—
460C22×C4C22⋊C4×C12712yes—
461C22×C4C22×C4×C12712yes—
462C22×C4C22×C4×C12711yescharacteristic
463C22×C4C2×D4×C12714yes—
464C22×C4C2×D4×C12711yescharacteristic
465C22×C4C2×D4×C12711yescharacteristic
466C22×C4C2×D4×C12711yescharacteristic
467C22×C4C2×D4×C12711yescharacteristic
468C22×C4C2×D4×C12712yes—
469C22×C4C2×D4×C12712yes—
470C22×C4#41×C12712yes—
471C22×C4#41×C12712yes—
472C22×C4C24×C12711yescharacteristic
473M16—216no—
474M16—24no—
475M16—24no—
476M16—24no—
477M16—24no—
478M16—24no—
479M16—42no—
480M16—42no—
481M16C2×D4×C12718yes—
482C2×C8—216no—
483C2×C8—24no—
484C2×C8—24no—
485C2×C8—24no—
486C2×C8—24no—
487C2×C8—42no—
488C2×C8—42no—
489C4⋊C4—22no—
490C4⋊C4—28no—
491C4⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—28no—
494C22⋊C4—28no—
495C22⋊C4C22×C4×C12714yes—
496C42—22no—
497C42—22no—
498C23—22no—
499C23—22no—
500C23—22no—
501C23—24no—
502C23—81no—
503C23—82no—
504C23—82no—
505C23C2×C22⋊C4×C12714yes—
506C23C2×C22⋊C4×C12711yescharacteristic
507C23C2×C22⋊C4×C12711yescharacteristic
508C23C4×D4×C12712yes—
509C23C4×D4×C12712yes—
510C23C23×C4×C12711yescharacteristic
511Q8—24no—
512Q8—24no—
513Q8—41no—
514Q8—42no—
515Q8—41no—
516D4—28no—
517D4—28no—
518D4—24no—
519D4—24no—
520D4—42no—
521D4—42no—
522D4—44no—
523D4—41no—
524D4—42no—
525D4—41no—
526D4—88no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—24no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—44no—
539C2×C4—82no—
540C2×C4C2×C22⋊C4×C12714yes—
541C2×C4C2×C22⋊C4×C12711yescharacteristic
542C2×C4C2×C22⋊C4×C12711yescharacteristic
543C2×C4C4×D4×C12712yes—
544C2×C4C4×D4×C12712yes—
545C2×C4#120×C12711yescharacteristic
546C2×C4#120×C12712yes—
547C2×C4#120×C12711yescharacteristic
548C2×C4#121×C12712yes—
549C2×C4#121×C12712yes—
550C2×C4#121×C12712yes—
551C2×C4#121×C12712yes—
552C2×C4#123×C12711yescharacteristic
553C2×C4#123×C12711yescharacteristic
554C2×C4#123×C12712yes—
555C2×C4C22×D4×C12712yes—
556C2×C4C22×D4×C12711yescharacteristic
557C2×C4C22×D4×C12711yescharacteristic
558C2×C4C2×#41×C12712yes—
559C8—28no—
560C8—44no—
561C22—24no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—42no—
566C22—42no—
567C22—44no—
568C22—44no—
569C22—44no—
570C22—42no—
571C22—82no—
572C22—84no—
573C22#386×C12711yescharacteristic
574C22#386×C12711yescharacteristic
575C22#386×C12712yes—
576C22C22×C22⋊C4×C12711yescharacteristic
577C22C2×C4×D4×C12712yes—
578C4—24no—
579C4—44no—
580C4—42no—
581C4#386×C12711yescharacteristic
582C4#386×C12711yescharacteristic
583C4#386×C12712yes—
584C4C2×#120×C12711yescharacteristic
585C4C2×#121×C12712yes—
586C4C2×#123×C12711yescharacteristic
587C2—21no—
588C2—21no—
589C2—22no—
590C2—21no—
591C2—22no—
592C2—44no—
593C2—82no—
594C2C2×#386×C12711yescharacteristic
subgroupG/H
centerC4×C127#386
commutatorC23C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC2×C127C2×#386
prime radicalC127×#3449C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ C23×C4×C127 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#568×C127C2semidirect
3. C2×#413×C127C2semidirect
4. C2×#413×C127C2semidirect
5. C127×#1915C2semidirect
6. C127×#1914C2semidirect
7. C2×#344×C127C2semidirect
32. C2×#101×C127C22semidirect
34. C2×#100×C127C22semidirect
35. #344×C127C22semidirect
74. C2×M16×C127D4semidirect
75. C2×M16×C127D4semidirect
289. #21017C127direct (N × H)
298. C2×#568C2×C127semidirect
300. C2×#413C2×C127semidirect
301. C2×#413C2×C127semidirect
302. #1915C2×C127semidirect
303. #1914C2×C127semidirect
304. C2×#344C2×C127semidirect
305. C127#21017direct (N × H)
330. C2×#101C22×C127semidirect
332. C2×#100C22×C127semidirect
333. #344C22×C127semidirect
372. C2×M16D4×C127semidirect
373. C2×M16D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#568×C1272
C127×#34492
C2×#413×C1272
C127×#19152
C127×#19142
C2×#344×C1272
#21017127