Finite Group Databasebeta

← C127×#21813 #44585486

Subgroups — C127×#21813 #44585486

Order 32512.

1442 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#535×C127C211yesmaximal, characteristic
2C2×#433×C127C211yesmaximal, characteristic, complemented
3C127×#2314C211yesmaximal, characteristic, complemented
4C127×#1983C212yesmaximal, complemented
5C127×#1982C212yesmaximal, complemented
6C127×#1961C211yesmaximal, characteristic, complemented
7C127×#1959C211yesmaximal, characteristic, complemented
8C127×#1958C211yesmaximal, characteristic, complemented
9C127×#1957C211yesmaximal, characteristic, complemented
10C127×#1788C212yesmaximal, complemented
11C127×#1786C212yesmaximal, complemented
12C22×#41×C127C2211yescharacteristic
13C23×D4×C127C2211yescharacteristic
14#535×C127—24no—
15#535×C127C418yescomplemented
16C2×#127×C127C2211yescharacteristic
17C2×#127×C127C2211yescharacteristic
18C2×#124×C127C2211yescharacteristic
19C2×#124×C127C2211yescharacteristic
20C2×#121×C127—22no—
21C2×#120×C127—22no—
22C2×#117×C127C2211yescharacteristic
23#433×C127—24no—
24C2×C4⋊C8×C127C2212yescomplemented
25C2×#103×C127C2212yescomplemented
26C2×#103×C127C2212yescomplemented
27C2×#102×C127C2212yes—
28C2×#102×C127C2212yes—
29C2×#102×C127C2212yes—
30C2×#102×C127C2212yes—
31C2×#102×C127C2212yescomplemented
32C2×#102×C127C2212yescomplemented
33C2×C22⋊C8×C127C2212yes—
34C2×#97×C127C2211yescharacteristic, complemented
35C2×C4×C8×C127C2211yescharacteristic, complemented
36#388×C127—22no—
37#387×C127—22no—
38#384×C127C2211yescharacteristic, complemented
39#382×C127C2211yescharacteristic, complemented
40#380×C127C2212yes—
41C4×C4⋊C4×C127C2212yescomplemented
42C25×C127—21no—
43C2×#41×C127—22no—
44C2×#41×C127—42no—
45C2×#41×C127—42no—
46C2×#41×C127C2×C414yes—
47C22×Q8×C127C2311yescharacteristic
48C22×D4×C127—21no—
49C22×D4×C127—21no—
50C22×D4×C127—22no—
51C22×D4×C127—22no—
52C22×D4×C127—22no—
53C22×D4×C127—42no—
54C22×D4×C127—42no—
55C22×D4×C127C2×C414yes—
56C22×D4×C127C2311yescharacteristic
57C22×D4×C127C2311yescharacteristic
58C22×D4×C127C2311yescharacteristic
59C23×C4×C127—21no—
60C23×C4×C127C2311yescharacteristic
61C22×C8×C127C2312yes—
62C22×C8×C127C2312yes—
63#127×C127—22no—
64#127×C127—22no—
65#127×C127C2×C414yes—
66#127×C127C2×C414yes—
67#124×C127—22no—
68#124×C127—22no—
69#124×C127C2×C414yes—
70#124×C127C2×C414yes—
71#121×C127—216no—
72#120×C127—216no—
73#117×C127C2×C414yes—
74#117×C127D414yes—
75C2×C4⋊C4×C127—22no—
76C2×C4⋊C4×C127D412yes—
77C2×C4⋊C4×C127C2312yes—
78C2×C4⋊C4×C127C2312yes—
79C2×C22⋊C4×C127—22no—
80C2×C22⋊C4×C127—22no—
81C2×C22⋊C4×C127—22no—
82C2×C22⋊C4×C127D412yes—
83C2×C42×C127—22no—
84C2×C42×C127C2311yescharacteristic
85C2×C42×C127C2311yescharacteristic
86C4⋊C8×C127—24no—
87#103×C127—42no—
88#103×C127—42no—
89#102×C127—42no—
90#102×C127—42no—
91#102×C127—42no—
92#102×C127—42no—
93#102×C127—42no—
94#102×C127—42no—
95C22⋊C8×C127—24no—
96#97×C127—22no—
97C4×C8×C127—22no—
98#95×C127—22no—
99#95×C127—22no—
100#95×C127—22no—
101C24×C127—21no—
102C24×C127—21no—
103C24×C127—21no—
104C24×C127—24no—
105C24×C127—42no—
106C24×C127—42no—
107C24×C127—82no—
108C24×C127—82no—
109C24×C127C2×D411yescharacteristic
110#41×C127—48no—
111#41×C127—48no—
112C2×Q8×C127—21no—
113C2×Q8×C127—22no—
114C2×Q8×C127—22no—
115C2×Q8×C127C22×C412yes—
116C2×D4×C127—24no—
117C2×D4×C127—24no—
118C2×D4×C127—28no—
119C2×D4×C127—28no—
120C2×D4×C127—21no—
121C2×D4×C127—21no—
122C2×D4×C127—21no—
123C2×D4×C127—22no—
124C2×D4×C127—22no—
125C2×D4×C127—22no—
126C2×D4×C127—22no—
127C2×D4×C127—22no—
128C2×D4×C127—22no—
129C2×D4×C127—48no—
130C2×D4×C127—42no—
131C2×D4×C127—42no—
132C2×D4×C127—48no—
133C2×D4×C127—42no—
134C2×D4×C127—42no—
135C2×D4×C127—82no—
136C2×D4×C127—82no—
137C2×D4×C127—82no—
138C2×D4×C127—82no—
139C2×D4×C127C22×C412yes—
140C2×D4×C127C22×C412yes—
141C2×D4×C127C22×C412yes—
142C22×C4×C127—22no—
143C22×C4×C127—22no—
144C22×C4×C127—21no—
145C22×C4×C127—24no—
146C22×C4×C127—22no—
147C22×C4×C127—22no—
148C22×C4×C127—42no—
149C22×C4×C127—42no—
150C22×C4×C127C22×C412yes—
151C22×C4×C127C2×D411yescharacteristic
152C22×C4×C127C2×D412yes—
153C22×C4×C127C2×D412yes—
154C22×C4×C127C2×D412yes—
155C22×C4×C127C2411yescharacteristic
156C2×C8×C127—22no—
157C2×C8×C127—22no—
158C2×C8×C127—22no—
159C2×C8×C127—22no—
160C2×C8×C127—22no—
161C2×C8×C127—22no—
162C4⋊C4×C127—22no—
163C4⋊C4×C127—22no—
164C4⋊C4×C127—22no—
165C4⋊C4×C127—22no—
166C4⋊C4×C127—82no—
167C4⋊C4×C127C22⋊C418yes—
168C22⋊C4×C127—28no—
169C22⋊C4×C127—28no—
170C22⋊C4×C127—82no—
171C22⋊C4×C127C22⋊C418yes—
172C42×C127—82no—
173C42×C127C22×C412yes—
174C42×C127C22×C412yes—
175C42×C127C2×D412yes—
176C42×C127C2×D412yes—
177C23×C127—21no—
178C23×C127—21no—
179C23×C127—22no—
180C23×C127—22no—
181C23×C127—22no—
182C23×C127—22no—
183C23×C127—22no—
184C23×C127—48no—
185C23×C127—41no—
186C23×C127—41no—
187C23×C127—41no—
188C23×C127—41no—
189C23×C127—41no—
190C23×C127—41no—
191C23×C127—42no—
192C23×C127—42no—
193C23×C127—42no—
194C23×C127—42no—
195C23×C127—42no—
196C23×C127—42no—
197C23×C127—88no—
198C23×C127—84no—
199C23×C127—84no—
200C23×C127—88no—
201C23×C127C2×C22⋊C412yes—
202C23×C127C22×D411yescharacteristic
203Q8×C127—24no—
204Q8×C127—42no—
205D4×C127—24no—
206D4×C127—24no—
207D4×C127—24no—
208D4×C127—48no—
209D4×C127—48no—
210D4×C127—42no—
211D4×C127—42no—
212D4×C127—42no—
213D4×C127—88no—
214D4×C127—88no—
215C2×C4×C127—21no—
216C2×C4×C127—21no—
217C2×C4×C127—22no—
218C2×C4×C127—22no—
219C2×C4×C127—22no—
220C2×C4×C127—22no—
221C2×C4×C127—24no—
222C2×C4×C127—24no—
223C2×C4×C127—22no—
224C2×C4×C127—48no—
225C2×C4×C127—41no—
226C2×C4×C127—41no—
227C2×C4×C127—42no—
228C2×C4×C127—42no—
229C2×C4×C127—42no—
230C2×C4×C127—42no—
231C2×C4×C127—42no—
232C2×C4×C127—42no—
233C2×C4×C127C2×C22⋊C414yes—
234C2×C4×C127C2×C22⋊C414yes—
235C2×C4×C127C2×C22⋊C412yes—
236C2×C4×C127C23×C411yescharacteristic
237C2×C4×C127C22×D411yescharacteristic
238C2×C4×C127H(5,𝔽2)12yes—
239C2×C4×C127H(5,𝔽2)12yes—
240C8×C127—42no—
241C8×C127—42no—
242C22×C127—22no—
243C22×C127—24no—
244C22×C127—41no—
245C22×C127—41no—
246C22×C127—42no—
247C22×C127—42no—
248C22×C127—42no—
249C22×C127—42no—
250C22×C127—44no—
251C22×C127—44no—
252C22×C127—44no—
253C22×C127—816no—
254C22×C127—81no—
255C22×C127—81no—
256C22×C127—81no—
257C22×C127—81no—
258C22×C127—81no—
259C22×C127—81no—
260C22×C127—82no—
261C22×C127—82no—
262C22×C127—82no—
263C22×C127C22×C22⋊C411yescharacteristic
264C22×C127#53511yescharacteristic
265C22×C127#53511yescharacteristic
266C22×C127#57612yes—
267C22×C127#57712yes—
268C4×C127—22no—
269C4×C127—24no—
270C4×C127—24no—
271C4×C127—42no—
272C4×C127—82no—
273C4×C127—82no—
274C4×C127#51812yes—
275C4×C127#53512yes—
276#21813C12711yesmaximal, characteristic, direct product factor, Sylow
277C2×C127—42no—
278C2×C127—82no—
279C2×C127—82no—
280C2×C127—82no—
281C2×C127#230911yescharacteristic
282C2×C127#289712yes—
283C2×C127#322011yescharacteristic
284C2×C127#322211yescharacteristic
285C2×C127#322412yes—
286C2×#535C2×C12711yescharacteristic
287C2×#433C2×C12711yescharacteristic, complemented
288#2314C2×C12711yescharacteristic, complemented
289#1983C2×C12712yescomplemented
290#1982C2×C12712yescomplemented
291#1961C2×C12711yescharacteristic, complemented
292#1959C2×C12711yescharacteristic, complemented
293#1958C2×C12711yescharacteristic, complemented
294#1957C2×C12711yescharacteristic, complemented
295#1788C2×C12712yescomplemented
296#1786C2×C12712yescomplemented
297C127#2181311yescharacteristic, direct product factor, Sylow
298C22×#41C22×C12711yescharacteristic
299C23×D4C22×C12711yescharacteristic
300#535—24no—
301#535C4×C12718yescomplemented
302C2×#127C22×C12711yescharacteristic
303C2×#127C22×C12711yescharacteristic
304C2×#124C22×C12711yescharacteristic
305C2×#124C22×C12711yescharacteristic
306C2×#121—22no—
307C2×#120—22no—
308C2×#117C22×C12711yescharacteristic
309#433—24no—
310C2×C4⋊C8C22×C12712yescomplemented
311C2×#103C22×C12712yescomplemented
312C2×#103C22×C12712yescomplemented
313C2×#102C22×C12712yes—
314C2×#102C22×C12712yes—
315C2×#102C22×C12712yes—
316C2×#102C22×C12712yes—
317C2×#102C22×C12712yescomplemented
318C2×#102C22×C12712yescomplemented
319C2×C22⋊C8C22×C12712yes—
320C2×#97C22×C12711yescharacteristic, complemented
321C2×C4×C8C22×C12711yescharacteristic, complemented
322#388—22no—
323#387—22no—
324#384C22×C12711yescharacteristic, complemented
325#382C22×C12711yescharacteristic, complemented
326#380C22×C12712yes—
327C4×C4⋊C4C22×C12712yescomplemented
328C25—21no—
329C2×#41—22no—
330C2×#41—42no—
331C2×#41—42no—
332C2×#41C2×C4×C12714yes—
333C22×Q8C23×C12711yescharacteristic
334C22×D4—21no—
335C22×D4—21no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—42no—
340C22×D4—42no—
341C22×D4C2×C4×C12714yes—
342C22×D4C23×C12711yescharacteristic
343C22×D4C23×C12711yescharacteristic
344C22×D4C23×C12711yescharacteristic
345C23×C4—21no—
346C23×C4C23×C12711yescharacteristic
347C22×C8C23×C12712yes—
348C22×C8C23×C12712yes—
349#127—22no—
350#127—22no—
351#127C2×C4×C12714yes—
352#127C2×C4×C12714yes—
353#124—22no—
354#124—22no—
355#124C2×C4×C12714yes—
356#124C2×C4×C12714yes—
357#121—216no—
358#120—216no—
359#117C2×C4×C12714yes—
360#117D4×C12714yes—
361C2×C4⋊C4—22no—
362C2×C4⋊C4D4×C12712yes—
363C2×C4⋊C4C23×C12712yes—
364C2×C4⋊C4C23×C12712yes—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4D4×C12712yes—
369C2×C42—22no—
370C2×C42C23×C12711yescharacteristic
371C2×C42C23×C12711yescharacteristic
372C4⋊C8—24no—
373#103—42no—
374#103—42no—
375#102—42no—
376#102—42no—
377#102—42no—
378#102—42no—
379#102—42no—
380#102—42no—
381C22⋊C8—24no—
382#97—22no—
383C4×C8—22no—
384#95—22no—
385#95—22no—
386#95—22no—
387C24—21no—
388C24—21no—
389C24—21no—
390C24—24no—
391C24—42no—
392C24—42no—
393C24—82no—
394C24—82no—
395C24C2×D4×C12711yescharacteristic
396#41—48no—
397#41—48no—
398C2×Q8—21no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8C22×C4×C12712yes—
402C2×D4—24no—
403C2×D4—24no—
404C2×D4—28no—
405C2×D4—28no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—48no—
416C2×D4—42no—
417C2×D4—42no—
418C2×D4—48no—
419C2×D4—42no—
420C2×D4—42no—
421C2×D4—82no—
422C2×D4—82no—
423C2×D4—82no—
424C2×D4—82no—
425C2×D4C22×C4×C12712yes—
426C2×D4C22×C4×C12712yes—
427C2×D4C22×C4×C12712yes—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4C22×C4×C12712yes—
437C22×C4C2×D4×C12711yescharacteristic
438C22×C4C2×D4×C12712yes—
439C22×C4C2×D4×C12712yes—
440C22×C4C2×D4×C12712yes—
441C22×C4C24×C12711yescharacteristic
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—22no—
446C2×C8—22no—
447C2×C8—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—82no—
453C4⋊C4C22⋊C4×C12718yes—
454C22⋊C4—28no—
455C22⋊C4—28no—
456C22⋊C4—82no—
457C22⋊C4C22⋊C4×C12718yes—
458C42—82no—
459C42C22×C4×C12712yes—
460C42C22×C4×C12712yes—
461C42C2×D4×C12712yes—
462C42C2×D4×C12712yes—
463C23—21no—
464C23—21no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—22no—
469C23—22no—
470C23—48no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—42no—
481C23—42no—
482C23—42no—
483C23—88no—
484C23—84no—
485C23—84no—
486C23—88no—
487C23C2×C22⋊C4×C12712yes—
488C23C22×D4×C12711yescharacteristic
489Q8—24no—
490Q8—42no—
491D4—24no—
492D4—24no—
493D4—24no—
494D4—48no—
495D4—48no—
496D4—42no—
497D4—42no—
498D4—42no—
499D4—88no—
500D4—88no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—48no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4C2×C22⋊C4×C12714yes—
520C2×C4C2×C22⋊C4×C12714yes—
521C2×C4C2×C22⋊C4×C12712yes—
522C2×C4C23×C4×C12711yescharacteristic
523C2×C4C22×D4×C12711yescharacteristic
524C2×C4H(5,𝔽2)×C12712yes—
525C2×C4H(5,𝔽2)×C12712yes—
526C8—42no—
527C8—42no—
528C22—24no—
529C22—22no—
530C22—41no—
531C22—41no—
532C22—42no—
533C22—44no—
534C22—44no—
535C22—44no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—816no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22—82no—
547C22—82no—
548C22—82no—
549C22C22×C22⋊C4×C12711yescharacteristic
550C22#535×C12711yescharacteristic
551C22#535×C12711yescharacteristic
552C22#576×C12712yes—
553C22#577×C12712yes—
554C4—24no—
555C4—24no—
556C4—22no—
557C4—42no—
558C4—82no—
559C4—82no—
560C4#518×C12712yes—
561C4#535×C12712yes—
562C2—42no—
563C2—82no—
564C2—82no—
565C2—82no—
566C2C127×#230911yescharacteristic
567C2C127×#289712yes—
568C2C127×#322011yescharacteristic
569C2C127×#322211yescharacteristic
570C2C127×#322412yes—
subgroupG/H
center, socleC23×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC2×#535×C127C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×#117×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#433×C127C2semidirect
3. C127×#2314C2semidirect
4. C127×#1983C2semidirect
5. C127×#1982C2semidirect
6. C127×#1961C2semidirect
7. C127×#1959C2semidirect
8. C127×#1958C2semidirect
9. C127×#1957C2semidirect
10. C127×#1788C2semidirect
11. C127×#1786C2semidirect
15. #535×C127C4semidirect
24. C2×C4⋊C8×C127C22semidirect
25. C2×#103×C127C22semidirect
26. C2×#103×C127C22semidirect
31. C2×#102×C127C22semidirect
32. C2×#102×C127C22semidirect
34. C2×#97×C127C22semidirect
35. C2×C4×C8×C127C22semidirect
38. #384×C127C22semidirect
39. #382×C127C22semidirect
41. C4×C4⋊C4×C127C22semidirect
276. #21813C127direct (N × H)
287. C2×#433C2×C127semidirect
288. #2314C2×C127semidirect
289. #1983C2×C127semidirect
290. #1982C2×C127semidirect
291. #1961C2×C127semidirect
292. #1959C2×C127semidirect
293. #1958C2×C127semidirect
294. #1957C2×C127semidirect
295. #1788C2×C127semidirect
296. #1786C2×C127semidirect
297. C127#21813direct (N × H)
301. #535C4×C127semidirect
310. C2×C4⋊C8C22×C127semidirect
311. C2×#103C22×C127semidirect
312. C2×#103C22×C127semidirect
317. C2×#102C22×C127semidirect
318. C2×#102C22×C127semidirect
320. C2×#97C22×C127semidirect
321. C2×C4×C8C22×C127semidirect
324. #384C22×C127semidirect
325. #382C22×C127semidirect
327. C4×C4⋊C4C22×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#535×C1272
C2×#433×C1272
C127×#23142
C127×#19832
C127×#19822
C127×#19612
C127×#19592
C127×#19582
C127×#19572
C127×#17882
C127×#17862
#21813127