Finite Group Databasebeta

← C127×#8361 #44572034

Subgroups — C127×#8361 #44572034

Order 32512.

1126 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C127C211yesmaximal, characteristic
2C127×#1789C212yesmaximal, complemented
3C4×#99×C127C211yesmaximal, characteristic, complemented
4C127×#1507C212yesmaximal, complemented
5C127×#1465C211yesmaximal, characteristic, complemented
6C22×#41×C127C411yescharacteristic, complemented
7C22×#41×C127C2211yescharacteristic
8#550×C127—24no—
9#550×C127—24no—
10C2×#127×C127—21no—
11C2×#127×C127C411yescharacteristic, complemented
12C2×#121×C127—21no—
13C2×#121×C127—21no—
14C2×#121×C127C411yescharacteristic, complemented
15C2×#121×C127C2211yescharacteristic
16C2×C4×Q8×C127C411yescharacteristic, complemented
17C2×C4×D4×C127—21no—
18C2×C4×D4×C127C2211yescharacteristic
19C2×#104×C127—24no—
20C2×#99×C127—21no—
21#407×C127C2212yes—
22C4×C22⋊C4×C127C2212yes—
23#342×C127—21no—
24#327×C127—24no—
25#324×C127—21no—
26#323×C127—21no—
27C2×#41×C127—22no—
28C2×#41×C127—22no—
29C2×#41×C127—22no—
30C2×#41×C127—44no—
31C2×#41×C127—44no—
32C2×#41×C127D414yes—
33C22×Q8×C127C2×C411yescharacteristic
34C22×D4×C127—21no—
35C22×D4×C127—21no—
36C22×D4×C127—21no—
37C22×D4×C127—21no—
38C22×D4×C127—21no—
39C22×D4×C127—21no—
40C22×D4×C127C2×C411yescharacteristic
41C22×D4×C127C2×C411yescharacteristic
42C22×D4×C127D411yescharacteristic
43C23×C4×C127—21no—
44C23×C4×C127—21no—
45C23×C4×C127C2×C411yescharacteristic
46C23×C4×C127C2311yescharacteristic
47C2×M16×C127—22no—
48#127×C127—28no—
49#127×C127—22no—
50#127×C127—22no—
51#121×C127—28no—
52#121×C127—28no—
53#121×C127—22no—
54#121×C127—22no—
55#121×C127—22no—
56#121×C127D414yes—
57C4×Q8×C127—22no—
58C4×Q8×C127—22no—
59C4×D4×C127—28no—
60C4×D4×C127—22no—
61C4×D4×C127—22no—
62C2×C4⋊C4×C127—21no—
63C2×C4⋊C4×C127C2×C411yescharacteristic
64C2×C4⋊C4×C127D411yescharacteristic
65C2×C22⋊C4×C127—21no—
66C2×C22⋊C4×C127—21no—
67C2×C22⋊C4×C127—22no—
68C2×C22⋊C4×C127D411yescharacteristic
69C2×C22⋊C4×C127D411yescharacteristic
70C2×C42×C127—21no—
71C2×C42×C127—22no—
72C2×C42×C127C2×C411yescharacteristic
73#104×C127—48no—
74#99×C127—24no—
75C22⋊C8×C127—22no—
76C22⋊C8×C127—22no—
77#95×C127—22no—
78C24×C127—21no—
79C24×C127—21no—
80C24×C127C22⋊C411yescharacteristic
81C24×C127C2×D411yescharacteristic
82#41×C127—28no—
83#41×C127—44no—
84#41×C127—48no—
85#41×C127—48no—
86#41×C127—44no—
87#41×C127—44no—
88C2×Q8×C127—24no—
89C2×Q8×C127—21no—
90C2×Q8×C127C22⋊C412yes—
91C2×D4×C127—24no—
92C2×D4×C127—24no—
93C2×D4×C127—22no—
94C2×D4×C127—24no—
95C2×D4×C127—24no—
96C2×D4×C127—24no—
97C2×D4×C127—24no—
98C2×D4×C127—22no—
99C2×D4×C127—21no—
100C2×D4×C127—21no—
101C2×D4×C127—42no—
102C2×D4×C127—41no—
103C2×D4×C127—42no—
104C2×D4×C127—44no—
105C2×D4×C127—44no—
106C2×D4×C127—42no—
107C2×D4×C127—42no—
108C2×D4×C127—82no—
109C2×D4×C127—82no—
110C2×D4×C127—82no—
111C2×D4×C127C22⋊C412yes—
112C2×D4×C127C22⋊C412yes—
113C22×C4×C127—21no—
114C22×C4×C127—24no—
115C22×C4×C127—21no—
116C22×C4×C127—21no—
117C22×C4×C127—21no—
118C22×C4×C127—24no—
119C22×C4×C127—42no—
120C22×C4×C127—44no—
121C22×C4×C127—44no—
122C22×C4×C127—42no—
123C22×C4×C127—42no—
124C22×C4×C127C22⋊C411yescharacteristic
125C22×C4×C127C22⋊C411yescharacteristic
126C22×C4×C127C22⋊C411yescharacteristic
127C22×C4×C127C22×C411yescharacteristic
128C22×C4×C127C2×D412yes—
129C22×C4×C127C2×D412yes—
130C22×C4×C127C2×D411yescharacteristic
131M16×C127—44no—
132C2×C8×C127—42no—
133C4⋊C4×C127—24no—
134C4⋊C4×C127—21no—
135C4⋊C4×C127—22no—
136C4⋊C4×C127C22⋊C412yes—
137C22⋊C4×C127—24no—
138C22⋊C4×C127—22no—
139C22⋊C4×C127—24no—
140C22⋊C4×C127—22no—
141C22⋊C4×C127—24no—
142C22⋊C4×C127—42no—
143C42×C127—24no—
144C42×C127—21no—
145C42×C127—21no—
146C42×C127—44no—
147C23×C127—21no—
148C23×C127—21no—
149C23×C127—21no—
150C23×C127—22no—
151C23×C127—22no—
152C23×C127—21no—
153C23×C127—21no—
154C23×C127—41no—
155C23×C127—41no—
156C23×C127—42no—
157C23×C127—42no—
158C23×C127—42no—
159C23×C127—42no—
160C23×C127—41no—
161C23×C127—41no—
162C23×C127—41no—
163C23×C127—41no—
164C23×C127—41no—
165C23×C127—41no—
166C23×C127C2×C22⋊C411yescharacteristic
167C23×C127#12012yes—
168Q8×C127—24no—
169Q8×C127—22no—
170Q8×C127#9914yescomplemented
171D4×C127—24no—
172D4×C127—44no—
173D4×C127—48no—
174D4×C127—42no—
175D4×C127—48no—
176D4×C127—48no—
177D4×C127—42no—
178D4×C127—42no—
179D4×C127—84no—
180D4×C127—84no—
181D4×C127—84no—
182C2×C4×C127—24no—
183C2×C4×C127—21no—
184C2×C4×C127—22no—
185C2×C4×C127—21no—
186C2×C4×C127—24no—
187C2×C4×C127—22no—
188C2×C4×C127—21no—
189C2×C4×C127—22no—
190C2×C4×C127—21no—
191C2×C4×C127—41no—
192C2×C4×C127—42no—
193C2×C4×C127—48no—
194C2×C4×C127—48no—
195C2×C4×C127—42no—
196C2×C4×C127—42no—
197C2×C4×C127—42no—
198C2×C4×C127—41no—
199C2×C4×C127—41no—
200C2×C4×C127—44no—
201C2×C4×C127—82no—
202C2×C4×C127—82no—
203C2×C4×C127#10412yescomplemented
204C2×C4×C127C2×C22⋊C411yescharacteristic
205C2×C4×C127C2×C22⋊C411yescharacteristic
206C2×C4×C127#12012yes—
207C8×C127—82no—
208C22×C127—21no—
209C22×C127—21no—
210C22×C127—22no—
211C22×C127—22no—
212C22×C127—22no—
213C22×C127—41no—
214C22×C127—42no—
215C22×C127—42no—
216C22×C127—42no—
217C22×C127—41no—
218C22×C127—42no—
219C22×C127—41no—
220C22×C127—42no—
221C22×C127—42no—
222C22×C127—81no—
223C22×C127—81no—
224C22×C127—81no—
225C22×C127—81no—
226C22×C127—82no—
227C22×C127—82no—
228C22×C127—82no—
229C22×C127—82no—
230C22×C127#37911yescharacteristic
231C22×C127C2×#10411yescharacteristic
232C22×C127#42111yescharacteristic
233C4×C127—22no—
234C4×C127—24no—
235C4×C127—21no—
236C4×C127—22no—
237C4×C127—42no—
238C4×C127—41no—
239C4×C127—41no—
240C4×C127—84no—
241C4×C127C2×#9912yes—
242#8361C12711yesmaximal, characteristic, direct product factor, Sylow
243C2×C127—21no—
244C2×C127—21no—
245C2×C127—42no—
246C2×C127—81no—
247C2×C127—82no—
248C2×C127—82no—
249C2×C127#178111yescharacteristic
250C2×C127#178911yescharacteristic
251C2×C127#179511yescharacteristic
252C2×#550C2×C12711yescharacteristic
253#1789C2×C12712yescomplemented
254C4×#99C2×C12711yescharacteristic, complemented
255#1507C2×C12712yescomplemented
256#1465C2×C12711yescharacteristic, complemented
257C127#836111yescharacteristic, direct product factor, Sylow
258C22×#41C4×C12711yescharacteristic, complemented
259C22×#41C22×C12711yescharacteristic
260#550—24no—
261#550—24no—
262C2×#127—21no—
263C2×#127C4×C12711yescharacteristic, complemented
264C2×#121—21no—
265C2×#121—21no—
266C2×#121C4×C12711yescharacteristic, complemented
267C2×#121C22×C12711yescharacteristic
268C2×C4×Q8C4×C12711yescharacteristic, complemented
269C2×C4×D4—21no—
270C2×C4×D4C22×C12711yescharacteristic
271C2×#104—24no—
272C2×#99—21no—
273#407C22×C12712yes—
274C4×C22⋊C4C22×C12712yes—
275#342—21no—
276#327—24no—
277#324—21no—
278#323—21no—
279C2×#41—22no—
280C2×#41—22no—
281C2×#41—22no—
282C2×#41—44no—
283C2×#41—44no—
284C2×#41D4×C12714yes—
285C22×Q8C2×C4×C12711yescharacteristic
286C22×D4—21no—
287C22×D4—21no—
288C22×D4—21no—
289C22×D4—21no—
290C22×D4—21no—
291C22×D4—21no—
292C22×D4C2×C4×C12711yescharacteristic
293C22×D4C2×C4×C12711yescharacteristic
294C22×D4D4×C12711yescharacteristic
295C23×C4—21no—
296C23×C4—21no—
297C23×C4C2×C4×C12711yescharacteristic
298C23×C4C23×C12711yescharacteristic
299C2×M16—22no—
300#127—28no—
301#127—22no—
302#127—22no—
303#121—28no—
304#121—28no—
305#121—22no—
306#121—22no—
307#121—22no—
308#121D4×C12714yes—
309C4×Q8—22no—
310C4×Q8—22no—
311C4×D4—28no—
312C4×D4—22no—
313C4×D4—22no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4C2×C4×C12711yescharacteristic
316C2×C4⋊C4D4×C12711yescharacteristic
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4D4×C12711yescharacteristic
321C2×C22⋊C4D4×C12711yescharacteristic
322C2×C42—21no—
323C2×C42—22no—
324C2×C42C2×C4×C12711yescharacteristic
325#104—48no—
326#99—24no—
327C22⋊C8—22no—
328C22⋊C8—22no—
329#95—22no—
330C24—21no—
331C24—21no—
332C24C22⋊C4×C12711yescharacteristic
333C24C2×D4×C12711yescharacteristic
334#41—28no—
335#41—44no—
336#41—48no—
337#41—48no—
338#41—44no—
339#41—44no—
340C2×Q8—24no—
341C2×Q8—21no—
342C2×Q8C22⋊C4×C12712yes—
343C2×D4—24no—
344C2×D4—24no—
345C2×D4—22no—
346C2×D4—24no—
347C2×D4—24no—
348C2×D4—24no—
349C2×D4—24no—
350C2×D4—22no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—42no—
354C2×D4—41no—
355C2×D4—42no—
356C2×D4—44no—
357C2×D4—44no—
358C2×D4—42no—
359C2×D4—42no—
360C2×D4—82no—
361C2×D4—82no—
362C2×D4—82no—
363C2×D4C22⋊C4×C12712yes—
364C2×D4C22⋊C4×C12712yes—
365C22×C4—21no—
366C22×C4—24no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—24no—
371C22×C4—42no—
372C22×C4—44no—
373C22×C4—44no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4C22⋊C4×C12711yescharacteristic
377C22×C4C22⋊C4×C12711yescharacteristic
378C22×C4C22⋊C4×C12711yescharacteristic
379C22×C4C22×C4×C12711yescharacteristic
380C22×C4C2×D4×C12712yes—
381C22×C4C2×D4×C12712yes—
382C22×C4C2×D4×C12711yescharacteristic
383M16—44no—
384C2×C8—42no—
385C4⋊C4—24no—
386C4⋊C4—21no—
387C4⋊C4—22no—
388C4⋊C4C22⋊C4×C12712yes—
389C22⋊C4—24no—
390C22⋊C4—22no—
391C22⋊C4—24no—
392C22⋊C4—22no—
393C22⋊C4—24no—
394C22⋊C4—42no—
395C42—24no—
396C42—21no—
397C42—21no—
398C42—44no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23—22no—
403C23—22no—
404C23—21no—
405C23—21no—
406C23—41no—
407C23—41no—
408C23—42no—
409C23—42no—
410C23—42no—
411C23—42no—
412C23—41no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23C2×C22⋊C4×C12711yescharacteristic
419C23#120×C12712yes—
420Q8—24no—
421Q8—22no—
422Q8#99×C12714yescomplemented
423D4—24no—
424D4—44no—
425D4—48no—
426D4—42no—
427D4—48no—
428D4—42no—
429D4—48no—
430D4—42no—
431D4—84no—
432D4—84no—
433D4—84no—
434C2×C4—24no—
435C2×C4—21no—
436C2×C4—22no—
437C2×C4—21no—
438C2×C4—24no—
439C2×C4—22no—
440C2×C4—21no—
441C2×C4—22no—
442C2×C4—21no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—48no—
446C2×C4—48no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—44no—
453C2×C4—82no—
454C2×C4—82no—
455C2×C4#104×C12712yescomplemented
456C2×C4C2×C22⋊C4×C12711yescharacteristic
457C2×C4C2×C22⋊C4×C12711yescharacteristic
458C2×C4#120×C12712yes—
459C8—82no—
460C22—21no—
461C22—21no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—42no—
466C22—41no—
467C22—42no—
468C22—41no—
469C22—42no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22—41no—
474C22—81no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22—82no—
479C22—82no—
480C22—82no—
481C22—82no—
482C22#379×C12711yescharacteristic
483C22C2×#104×C12711yescharacteristic
484C22#421×C12711yescharacteristic
485C4—22no—
486C4—24no—
487C4—21no—
488C4—22no—
489C4—41no—
490C4—42no—
491C4—41no—
492C4—84no—
493C4C2×#99×C12712yes—
494C2—21no—
495C2—21no—
496C2—42no—
497C2—82no—
498C2—82no—
499C2—81no—
500C2C127×#178111yescharacteristic
501C2C127×#178911yescharacteristic
502C2C127×#179511yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC2×#550×C127C2
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×#1789C2semidirect
3. C4×#99×C127C2semidirect
4. C127×#1507C2semidirect
5. C127×#1465C2semidirect
6. C22×#41×C127C4semidirect
11. C2×#127×C127C4semidirect
14. C2×#121×C127C4semidirect
16. C2×C4×Q8×C127C4semidirect
170. Q8×C127#99semidirect
203. C2×C4×C127#104semidirect
242. #8361C127direct (N × H)
253. #1789C2×C127semidirect
254. C4×#99C2×C127semidirect
255. #1507C2×C127semidirect
256. #1465C2×C127semidirect
257. C127#8361direct (N × H)
258. C22×#41C4×C127semidirect
263. C2×#127C4×C127semidirect
266. C2×#121C4×C127semidirect
268. C2×C4×Q8C4×C127semidirect
422. Q8#99×C127semidirect
455. C2×C4#104×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#550×C1272
C127×#17892
C4×#99×C1272
C127×#15072
C127×#14652
#8361127