Finite Group Databasebeta

← C127×#8359 #44572032

Subgroups — C127×#8359 #44572032

Order 32512.

1208 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C127C211yesmaximal, characteristic
2C127×#1789C212yesmaximal, complemented
3C4×#99×C127C211yesmaximal, characteristic, complemented
4C127×#1507C212yesmaximal, complemented
5C127×#1465C211yesmaximal, characteristic, complemented
6C22×#41×C127C2211yescharacteristic
7C23×D4×C127C411yescharacteristic, complemented
8#546×C127—24no—
9#546×C127—24no—
10C2×#124×C127C411yescharacteristic, complemented
11C2×#123×C127—21no—
12C2×C22⋊Q8×C127C411yescharacteristic, complemented
13C2×#121×C127—21no—
14C2×#121×C127C2211yescharacteristic
15C2×#120×C127—21no—
16C2×C4×D4×C127C411yescharacteristic, complemented
17C2×C4×D4×C127C2211yescharacteristic
18C22×C22⋊C4×C127—21no—
19C2×#104×C127—24no—
20C2×#99×C127—21no—
21#407×C127C2212yescomplemented
22C4×C22⋊C4×C127C2212yescomplemented
23#342×C127—21no—
24#327×C127—24no—
25#324×C127—21no—
26#323×C127—21no—
27C25×C127—21no—
28C2×#41×C127—22no—
29C2×#41×C127—44no—
30C2×#41×C127D414yes—
31C22×Q8×C127C2×C411yescharacteristic
32C22×D4×C127—21no—
33C22×D4×C127—21no—
34C22×D4×C127—22no—
35C22×D4×C127—22no—
36C22×D4×C127—21no—
37C22×D4×C127—44no—
38C22×D4×C127C2×C411yescharacteristic
39C22×D4×C127C2×C411yescharacteristic
40C22×D4×C127D411yescharacteristic
41C23×C4×C127—21no—
42C23×C4×C127—21no—
43C23×C4×C127C2×C411yescharacteristic
44C23×C4×C127C2311yescharacteristic
45C2×M16×C127—22no—
46#124×C127—22no—
47#124×C127—22no—
48#123×C127—28no—
49C22⋊Q8×C127—22no—
50C22⋊Q8×C127—22no—
51#121×C127—28no—
52#121×C127—22no—
53#121×C127D414yes—
54#120×C127—28no—
55C4×D4×C127—22no—
56C4×D4×C127—22no—
57C4×D4×C127—22no—
58C4×D4×C127—22no—
59C2×C4⋊C4×C127—21no—
60C2×C4⋊C4×C127C2×C411yescharacteristic
61C2×C4⋊C4×C127D411yescharacteristic
62C2×C22⋊C4×C127—28no—
63C2×C22⋊C4×C127—21no—
64C2×C22⋊C4×C127—21no—
65C2×C22⋊C4×C127—21no—
66C2×C22⋊C4×C127—21no—
67C2×C22⋊C4×C127—21no—
68C2×C22⋊C4×C127—22no—
69C2×C22⋊C4×C127D411yescharacteristic
70C2×C22⋊C4×C127D411yescharacteristic
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—24no—
80C24×C127—21no—
81C24×C127—44no—
82C24×C127—42no—
83C24×C127—42no—
84C24×C127—82no—
85C24×C127C22⋊C411yescharacteristic
86C24×C127C2×D411yescharacteristic
87#41×C127—28no—
88#41×C127—44no—
89#41×C127—48no—
90C2×Q8×C127—21no—
91C2×Q8×C127—42no—
92C2×Q8×C127C22⋊C412yes—
93C2×D4×C127—24no—
94C2×D4×C127—24no—
95C2×D4×C127—22no—
96C2×D4×C127—22no—
97C2×D4×C127—24no—
98C2×D4×C127—24no—
99C2×D4×C127—21no—
100C2×D4×C127—21no—
101C2×D4×C127—41no—
102C2×D4×C127—42no—
103C2×D4×C127—48no—
104C2×D4×C127—44no—
105C2×D4×C127—44no—
106C2×D4×C127—44no—
107C2×D4×C127—44no—
108C2×D4×C127—82no—
109C2×D4×C127C22⋊C412yes—
110C2×D4×C127C22⋊C412yes—
111C22×C4×C127—21no—
112C22×C4×C127—21no—
113C22×C4×C127—24no—
114C22×C4×C127—21no—
115C22×C4×C127—21no—
116C22×C4×C127—24no—
117C22×C4×C127—42no—
118C22×C4×C127—42no—
119C22×C4×C127—44no—
120C22×C4×C127—42no—
121C22×C4×C127—82no—
122C22×C4×C127C22⋊C411yescharacteristic
123C22×C4×C127C22⋊C411yescharacteristic
124C22×C4×C127C22⋊C411yescharacteristic
125C22×C4×C127C22×C411yescharacteristic
126C22×C4×C127C2×D412yes—
127C22×C4×C127C2×D412yes—
128C22×C4×C127C2×D411yescharacteristic
129M16×C127—44no—
130C2×C8×C127—42no—
131C4⋊C4×C127—24no—
132C4⋊C4×C127—21no—
133C4⋊C4×C127—22no—
134C4⋊C4×C127C22⋊C412yes—
135C22⋊C4×C127—24no—
136C22⋊C4×C127—24no—
137C22⋊C4×C127—24no—
138C22⋊C4×C127—24no—
139C22⋊C4×C127—22no—
140C22⋊C4×C127—22no—
141C22⋊C4×C127—24no—
142C22⋊C4×C127—24no—
143C22⋊C4×C127—42no—
144C42×C127—21no—
145C42×C127—21no—
146C42×C127—44no—
147C23×C127—24no—
148C23×C127—21no—
149C23×C127—22no—
150C23×C127—21no—
151C23×C127—21no—
152C23×C127—21no—
153C23×C127—22no—
154C23×C127—41no—
155C23×C127—41no—
156C23×C127—41no—
157C23×C127—41no—
158C23×C127—42no—
159C23×C127—42no—
160C23×C127—48no—
161C23×C127—42no—
162C23×C127—48no—
163C23×C127—41no—
164C23×C127—41no—
165C23×C127—41no—
166C23×C127—41no—
167C23×C127—84no—
168C23×C127—88no—
169C23×C127—88no—
170C23×C127#10412yescomplemented
171C23×C127C2×C22⋊C411yescharacteristic
172C23×C127#12012yes—
173Q8×C127—24no—
174Q8×C127—42no—
175D4×C127—24no—
176D4×C127—22no—
177D4×C127—42no—
178D4×C127—44no—
179D4×C127—48no—
180D4×C127—48no—
181D4×C127—42no—
182D4×C127—84no—
183D4×C127#9914yescomplemented
184C2×C4×C127—24no—
185C2×C4×C127—22no—
186C2×C4×C127—21no—
187C2×C4×C127—21no—
188C2×C4×C127—22no—
189C2×C4×C127—22no—
190C2×C4×C127—21no—
191C2×C4×C127—21no—
192C2×C4×C127—21no—
193C2×C4×C127—41no—
194C2×C4×C127—42no—
195C2×C4×C127—48no—
196C2×C4×C127—42no—
197C2×C4×C127—42no—
198C2×C4×C127—42no—
199C2×C4×C127—42no—
200C2×C4×C127—41no—
201C2×C4×C127—41no—
202C2×C4×C127—44no—
203C2×C4×C127—84no—
204C2×C4×C127—82no—
205C2×C4×C127—82no—
206C2×C4×C127C2×C22⋊C411yescharacteristic
207C2×C4×C127C2×C22⋊C411yescharacteristic
208C2×C4×C127#12012yes—
209C8×C127—82no—
210C22×C127—21no—
211C22×C127—21no—
212C22×C127—22no—
213C22×C127—22no—
214C22×C127—24no—
215C22×C127—22no—
216C22×C127—22no—
217C22×C127—42no—
218C22×C127—44no—
219C22×C127—44no—
220C22×C127—42no—
221C22×C127—42no—
222C22×C127—41no—
223C22×C127—41no—
224C22×C127—42no—
225C22×C127—42no—
226C22×C127—42no—
227C22×C127—42no—
228C22×C127—81no—
229C22×C127—81no—
230C22×C127—82no—
231C22×C127—82no—
232C22×C127—816no—
233C22×C127#37911yescharacteristic
234C22×C127C2×#10411yescharacteristic
235C22×C127#42111yescharacteristic
236C4×C127—22no—
237C4×C127—21no—
238C4×C127—42no—
239C4×C127—41no—
240C4×C127—42no—
241C4×C127—41no—
242C4×C127—41no—
243C4×C127—84no—
244C4×C127C2×#9912yes—
245#8359C12711yesmaximal, characteristic, direct product factor, Sylow
246C2×C127—21no—
247C2×C127—21no—
248C2×C127—42no—
249C2×C127—44no—
250C2×C127—42no—
251C2×C127—82no—
252C2×C127#178111yescharacteristic
253C2×C127#178911yescharacteristic
254C2×C127#179511yescharacteristic
255C2×#546C2×C12711yescharacteristic
256#1789C2×C12712yescomplemented
257C4×#99C2×C12711yescharacteristic, complemented
258#1507C2×C12712yescomplemented
259#1465C2×C12711yescharacteristic, complemented
260C127#835911yescharacteristic, direct product factor, Sylow
261C22×#41C22×C12711yescharacteristic
262C23×D4C4×C12711yescharacteristic, complemented
263#546—24no—
264#546—24no—
265C2×#124C4×C12711yescharacteristic, complemented
266C2×#123—21no—
267C2×C22⋊Q8C4×C12711yescharacteristic, complemented
268C2×#121—21no—
269C2×#121C22×C12711yescharacteristic
270C2×#120—21no—
271C2×C4×D4C4×C12711yescharacteristic, complemented
272C2×C4×D4C22×C12711yescharacteristic
273C22×C22⋊C4—21no—
274C2×#104—24no—
275C2×#99—21no—
276#407C22×C12712yescomplemented
277C4×C22⋊C4C22×C12712yescomplemented
278#342—21no—
279#327—24no—
280#324—21no—
281#323—21no—
282C25—21no—
283C2×#41—22no—
284C2×#41—44no—
285C2×#41D4×C12714yes—
286C22×Q8C2×C4×C12711yescharacteristic
287C22×D4—21no—
288C22×D4—21no—
289C22×D4—22no—
290C22×D4—22no—
291C22×D4—21no—
292C22×D4—44no—
293C22×D4C2×C4×C12711yescharacteristic
294C22×D4C2×C4×C12711yescharacteristic
295C22×D4D4×C12711yescharacteristic
296C23×C4—21no—
297C23×C4—21no—
298C23×C4C2×C4×C12711yescharacteristic
299C23×C4C23×C12711yescharacteristic
300C2×M16—22no—
301#124—22no—
302#124—22no—
303#123—28no—
304C22⋊Q8—22no—
305C22⋊Q8—22no—
306#121—28no—
307#121—22no—
308#121D4×C12714yes—
309#120—28no—
310C4×D4—22no—
311C4×D4—22no—
312C4×D4—22no—
313C4×D4—22no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4C2×C4×C12711yescharacteristic
316C2×C4⋊C4D4×C12711yescharacteristic
317C2×C22⋊C4—28no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4D4×C12711yescharacteristic
325C2×C22⋊C4D4×C12711yescharacteristic
326C2×C42—22no—
327C2×C42C2×C4×C12711yescharacteristic
328#104—48no—
329#99—24no—
330C22⋊C8—22no—
331C22⋊C8—22no—
332#95—22no—
333C24—21no—
334C24—24no—
335C24—21no—
336C24—44no—
337C24—42no—
338C24—42no—
339C24—82no—
340C24C22⋊C4×C12711yescharacteristic
341C24C2×D4×C12711yescharacteristic
342#41—28no—
343#41—44no—
344#41—48no—
345C2×Q8—21no—
346C2×Q8—42no—
347C2×Q8C22⋊C4×C12712yes—
348C2×D4—24no—
349C2×D4—24no—
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—24no—
353C2×D4—24no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—41no—
357C2×D4—42no—
358C2×D4—48no—
359C2×D4—44no—
360C2×D4—44no—
361C2×D4—44no—
362C2×D4—44no—
363C2×D4—82no—
364C2×D4C22⋊C4×C12712yes—
365C2×D4C22⋊C4×C12712yes—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—24no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—24no—
372C22×C4—42no—
373C22×C4—42no—
374C22×C4—44no—
375C22×C4—42no—
376C22×C4—82no—
377C22×C4C22⋊C4×C12711yescharacteristic
378C22×C4C22⋊C4×C12711yescharacteristic
379C22×C4C22⋊C4×C12711yescharacteristic
380C22×C4C22×C4×C12711yescharacteristic
381C22×C4C2×D4×C12712yes—
382C22×C4C2×D4×C12712yes—
383C22×C4C2×D4×C12711yescharacteristic
384M16—44no—
385C2×C8—42no—
386C4⋊C4—24no—
387C4⋊C4—21no—
388C4⋊C4—22no—
389C4⋊C4C22⋊C4×C12712yes—
390C22⋊C4—24no—
391C22⋊C4—24no—
392C22⋊C4—24no—
393C22⋊C4—24no—
394C22⋊C4—22no—
395C22⋊C4—22no—
396C22⋊C4—24no—
397C22⋊C4—24no—
398C22⋊C4—42no—
399C42—21no—
400C42—21no—
401C42—44no—
402C23—24no—
403C23—21no—
404C23—22no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—22no—
409C23—41no—
410C23—41no—
411C23—41no—
412C23—41no—
413C23—42no—
414C23—42no—
415C23—48no—
416C23—42no—
417C23—48no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—84no—
423C23—88no—
424C23—88no—
425C23#104×C12712yescomplemented
426C23C2×C22⋊C4×C12711yescharacteristic
427C23#120×C12712yes—
428Q8—24no—
429Q8—42no—
430D4—24no—
431D4—22no—
432D4—42no—
433D4—44no—
434D4—48no—
435D4—48no—
436D4—42no—
437D4—84no—
438D4#99×C12714yescomplemented
439C2×C4—24no—
440C2×C4—22no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—48no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—44no—
458C2×C4—84no—
459C2×C4—82no—
460C2×C4—82no—
461C2×C4C2×C22⋊C4×C12711yescharacteristic
462C2×C4C2×C22⋊C4×C12711yescharacteristic
463C2×C4#120×C12712yes—
464C8—82no—
465C22—21no—
466C22—21no—
467C22—22no—
468C22—24no—
469C22—22no—
470C22—22no—
471C22—22no—
472C22—42no—
473C22—42no—
474C22—44no—
475C22—44no—
476C22—41no—
477C22—42no—
478C22—42no—
479C22—41no—
480C22—42no—
481C22—42no—
482C22—42no—
483C22—81no—
484C22—81no—
485C22—82no—
486C22—82no—
487C22—816no—
488C22#379×C12711yescharacteristic
489C22C2×#104×C12711yescharacteristic
490C22#421×C12711yescharacteristic
491C4—22no—
492C4—21no—
493C4—42no—
494C4—41no—
495C4—41no—
496C4—42no—
497C4—41no—
498C4—84no—
499C4C2×#99×C12712yes—
500C2—21no—
501C2—21no—
502C2—42no—
503C2—44no—
504C2—42no—
505C2—82no—
506C2C127×#178111yescharacteristic
507C2C127×#178911yescharacteristic
508C2C127×#179511yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC2×#546×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
7. C23×D4×C127C4semidirect
10. C2×#124×C127C4semidirect
12. C2×C22⋊Q8×C127C4semidirect
16. C2×C4×D4×C127C4semidirect
21. #407×C127C22semidirect
22. C4×C22⋊C4×C127C22semidirect
170. C23×C127#104semidirect
183. D4×C127#99semidirect
245. #8359C127direct (N × H)
256. #1789C2×C127semidirect
257. C4×#99C2×C127semidirect
258. #1507C2×C127semidirect
259. #1465C2×C127semidirect
260. C127#8359direct (N × H)
262. C23×D4C4×C127semidirect
265. C2×#124C4×C127semidirect
267. C2×C22⋊Q8C4×C127semidirect
271. C2×C4×D4C4×C127semidirect
276. #407C22×C127semidirect
277. C4×C22⋊C4C22×C127semidirect
425. C23#104×C127semidirect
438. D4#99×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1272
C127×#17892
C4×#99×C1272
C127×#15072
C127×#14652
#8359127