Finite Group Databasebeta

← C127×#21536 #44585209

Subgroups — C127×#21536 #44585209

Order 32512.

1066 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C127C211yesmaximal, characteristic
2C2×C4×D8×C127C211yesmaximal, characteristic, complemented
3C2×#405×C127C211yesmaximal, characteristic, complemented
4C127×#2324C212yesmaximal, complemented
5C127×#1972C211yesmaximal, characteristic, complemented
6C127×#1944C211yesmaximal, characteristic, complemented
7C127×#1934C212yesmaximal, complemented
8C127×#1893C212yesmaximal, complemented
9C127×#1809C211yesmaximal, characteristic, complemented
10C4×#106×C127C211yesmaximal, characteristic, complemented
11C127×#1762C212yesmaximal, complemented
12C22×D8×C127C2211yescharacteristic
13C22×M16×C127C2211yescharacteristic
14C23×C8×C127C2211yescharacteristic
15C2×#121×C127C2212yes—
16C2×C4×D4×C127C2212yes—
17C2×#117×C127C2211yescharacteristic
18#469×C127C418yescomplemented
19C4×D8×C127—24no—
20C2×#107×C127C2211yescharacteristic
21C2×#106×C127C2211yescharacteristic
22C2×#106×C127C2211yescharacteristic
23C2×#102×C127C2212yes—
24C2×#102×C127C2212yes—
25C2×#102×C127C2212yes—
26#405×C127—24no—
27C2×#97×C127C2211yescharacteristic
28C2×#97×C127C2211yescharacteristic
29C2×C4×C8×C127C2211yescharacteristic
30C2×C4×C8×C127C2211yescharacteristic
31#390×C127—22no—
32#390×C127C2212yes—
33#389×C127C2212yes—
34#388×C127—22no—
35#386×C127—22no—
36#385×C127—22no—
37#380×C127C2212yes—
38C4×C4⋊C4×C127C2212yes—
39#340×C127C2212yes—
40#340×C127C2212yes—
41#340×C127C2212yes—
42C22×D4×C127—22no—
43C22×D4×C127C2312yes—
44C23×C4×C127—22no—
45C23×C4×C127C2311yescharacteristic
46C2×D8×C127—22no—
47C2×D8×C127—22no—
48C2×D8×C127C2×C414yes—
49C2×M16×C127—22no—
50C2×M16×C127—22no—
51C2×M16×C127C2×C414yescomplemented
52C22×C8×C127—22no—
53C22×C8×C127—22no—
54C22×C8×C127—22no—
55C22×C8×C127C2311yescharacteristic
56C22×C8×C127C2311yescharacteristic
57C22×C8×C127C2311yescharacteristic
58C22×C8×C127C2311yescharacteristic
59#121×C127—24no—
60#121×C127C2×C418yescomplemented
61C4×D4×C127—24no—
62C4×D4×C127—24no—
63#117×C127—22no—
64#117×C127—22no—
65C2×C4⋊C4×C127—22no—
66C2×C4⋊C4×C127D411yescharacteristic
67C2×C4⋊C4×C127D411yescharacteristic
68C2×C4⋊C4×C127C2312yes—
69C2×C4⋊C4×C127C2312yes—
70C2×C4⋊C4×C127C2312yes—
71C2×C22⋊C4×C127—22no—
72C2×C22⋊C4×C127—22no—
73C2×C22⋊C4×C127—22no—
74C2×C22⋊C4×C127—22no—
75C2×C22⋊C4×C127—22no—
76C2×C22⋊C4×C127D411yescharacteristic
77C2×C22⋊C4×C127D411yescharacteristic
78C2×C42×C127—22no—
79C2×C42×C127C2311yescharacteristic
80C2×C42×C127C2311yescharacteristic
81#107×C127—22no—
82#106×C127—22no—
83#106×C127C2×C414yescomplemented
84#102×C127—24no—
85#102×C127—24no—
86#102×C127C2×C418yescomplemented
87#97×C127—22no—
88#97×C127—22no—
89C4×C8×C127—22no—
90C4×C8×C127D414yescomplemented
91#95×C127—22no—
92#95×C127—22no—
93#95×C127—22no—
94C24×C127—22no—
95C24×C127C2×D411yescharacteristic
96C2×D4×C127—28no—
97C2×D4×C127—22no—
98C2×D4×C127—22no—
99C2×D4×C127—22no—
100C2×D4×C127—22no—
101C2×D4×C127—22no—
102C2×D4×C127—82no—
103C2×D4×C127—82no—
104C2×D4×C127C22×C414yes—
105C22×C4×C127—21no—
106C22×C4×C127—21no—
107C22×C4×C127—21no—
108C22×C4×C127—21no—
109C22×C4×C127—22no—
110C22×C4×C127—22no—
111C22×C4×C127—22no—
112C22×C4×C127—44no—
113C22×C4×C127—82no—
114C22×C4×C127—82no—
115C22×C4×C127C22×C412yes—
116C22×C4×C127C2×D411yescharacteristic
117C22×C4×C127C2×D411yescharacteristic
118C22×C4×C127C2×D411yescharacteristic
119C22×C4×C127C2×D411yescharacteristic
120C22×C4×C127C2×D411yescharacteristic
121C22×C4×C127#4112yes—
122C22×C4×C127C2411yescharacteristic
123D8×C127—28no—
124M16×C127—28no—
125C2×C8×C127—28no—
126C2×C8×C127—21no—
127C2×C8×C127—21no—
128C2×C8×C127—21no—
129C2×C8×C127—21no—
130C2×C8×C127—21no—
131C2×C8×C127—21no—
132C2×C8×C127C22×C412yes—
133C2×C8×C127C22×C412yes—
134C2×C8×C127C2×D412yes—
135C2×C8×C127C2×D412yes—
136C2×C8×C127#4112yes—
137C2×C8×C127#4112yes—
138C4⋊C4×C127—22no—
139C4⋊C4×C127—22no—
140C4⋊C4×C127—22no—
141C4⋊C4×C127—22no—
142C4⋊C4×C127—22no—
143C4⋊C4×C127—22no—
144C4⋊C4×C127—22no—
145C4⋊C4×C127—82no—
146C4⋊C4×C127C22×C414yes—
147C22⋊C4×C127—28no—
148C22⋊C4×C127—22no—
149C22⋊C4×C127—22no—
150C22⋊C4×C127—44no—
151C22⋊C4×C127—82no—
152C22⋊C4×C127—82no—
153C22⋊C4×C127—82no—
154C42×C127—21no—
155C42×C127—21no—
156C42×C127—82no—
157C42×C127C2×D412yes—
158C42×C127#4112yes—
159C23×C127—21no—
160C23×C127—21no—
161C23×C127—22no—
162C23×C127—22no—
163C23×C127—24no—
164C23×C127—42no—
165C23×C127—42no—
166C23×C127—42no—
167C23×C127—42no—
168C23×C127—42no—
169C23×C127—42no—
170C23×C127C4×D412yes—
171C23×C127C22×D411yescharacteristic
172D4×C127—24no—
173D4×C127—24no—
174D4×C127—42no—
175D4×C127—42no—
176D4×C127—88no—
177C2×C4×C127—21no—
178C2×C4×C127—21no—
179C2×C4×C127—22no—
180C2×C4×C127—22no—
181C2×C4×C127—22no—
182C2×C4×C127—22no—
183C2×C4×C127—22no—
184C2×C4×C127—22no—
185C2×C4×C127—24no—
186C2×C4×C127—21no—
187C2×C4×C127—21no—
188C2×C4×C127—22no—
189C2×C4×C127—22no—
190C2×C4×C127—42no—
191C2×C4×C127—42no—
192C2×C4×C127—42no—
193C2×C4×C127—42no—
194C2×C4×C127—42no—
195C2×C4×C127—42no—
196C2×C4×C127—42no—
197C2×C4×C127—42no—
198C2×C4×C127—88no—
199C2×C4×C127C4×D412yes—
200C2×C4×C127#12112yes—
201C2×C4×C127#12112yes—
202C2×C4×C127C23×C411yescharacteristic
203C2×C4×C127C22×D411yescharacteristic
204C2×C4×C127C2×#4111yescharacteristic
205C2×C4×C127C2×#4111yescharacteristic
206C2×C4×C127C2×#4111yescharacteristic
207C2×C4×C127C2×#4111yescharacteristic
208C8×C127—22no—
209C8×C127—22no—
210C8×C127—22no—
211C8×C127C4×D414yes—
212C22×C127—24no—
213C22×C127—22no—
214C22×C127—42no—
215C22×C127—41no—
216C22×C127—41no—
217C22×C127—44no—
218C22×C127—44no—
219C22×C127—44no—
220C22×C127—82no—
221C22×C127—82no—
222C22×C127—82no—
223C22×C127—82no—
224C22×C127C2×C4×D411yescharacteristic
225C22×C127C2×#12111yescharacteristic
226C22×C127#53211yescharacteristic
227C22×C127#57612yes—
228C22×C127#57712yes—
229C4×C127—22no—
230C4×C127—22no—
231C4×C127—22no—
232C4×C127—44no—
233C4×C127—41no—
234C4×C127—41no—
235C4×C127—82no—
236C4×C127—82no—
237C4×C127C2×C4×D411yescharacteristic
238C4×C127C4×#4111yescharacteristic
239C4×C127#52511yescharacteristic
240C4×C127#52911yescharacteristic
241#21536C12711yesmaximal, characteristic, direct product factor, Sylow
242C2×C127—42no—
243C2×C127—84no—
244C2×C127C4×#12111yescharacteristic
245C2×C127#294612yes—
246C2×C127#305811yescharacteristic
247C2×C127#306011yescharacteristic
248C2×C127#317912yes—
249C2×#469C2×C12711yescharacteristic
250C2×C4×D8C2×C12711yescharacteristic, complemented
251C2×#405C2×C12711yescharacteristic, complemented
252#2324C2×C12712yescomplemented
253#1972C2×C12711yescharacteristic, complemented
254#1944C2×C12711yescharacteristic, complemented
255#1934C2×C12712yescomplemented
256#1893C2×C12712yescomplemented
257#1809C2×C12711yescharacteristic, complemented
258C4×#106C2×C12711yescharacteristic, complemented
259#1762C2×C12712yescomplemented
260C127#2153611yescharacteristic, direct product factor, Sylow
261C22×D8C22×C12711yescharacteristic
262C22×M16C22×C12711yescharacteristic
263C23×C8C22×C12711yescharacteristic
264C2×#121C22×C12712yes—
265C2×C4×D4C22×C12712yes—
266C2×#117C22×C12711yescharacteristic
267#469C4×C12718yescomplemented
268C4×D8—24no—
269C2×#107C22×C12711yescharacteristic
270C2×#106C22×C12711yescharacteristic
271C2×#106C22×C12711yescharacteristic
272C2×#102C22×C12712yes—
273C2×#102C22×C12712yes—
274C2×#102C22×C12712yes—
275#405—24no—
276C2×#97C22×C12711yescharacteristic
277C2×#97C22×C12711yescharacteristic
278C2×C4×C8C22×C12711yescharacteristic
279C2×C4×C8C22×C12711yescharacteristic
280#390—22no—
281#390C22×C12712yes—
282#389C22×C12712yes—
283#388—22no—
284#386—22no—
285#385—22no—
286#380C22×C12712yes—
287C4×C4⋊C4C22×C12712yes—
288#340C22×C12712yes—
289#340C22×C12712yes—
290#340C22×C12712yes—
291C22×D4—22no—
292C22×D4C23×C12712yes—
293C23×C4—22no—
294C23×C4C23×C12711yescharacteristic
295C2×D8—22no—
296C2×D8—22no—
297C2×D8C2×C4×C12714yes—
298C2×M16—22no—
299C2×M16—22no—
300C2×M16C2×C4×C12714yescomplemented
301C22×C8—22no—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8C23×C12711yescharacteristic
305C22×C8C23×C12711yescharacteristic
306C22×C8C23×C12711yescharacteristic
307C22×C8C23×C12711yescharacteristic
308#121—24no—
309#121C2×C4×C12718yescomplemented
310C4×D4—24no—
311C4×D4—24no—
312#117—22no—
313#117—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4D4×C12711yescharacteristic
316C2×C4⋊C4D4×C12711yescharacteristic
317C2×C4⋊C4C23×C12712yes—
318C2×C4⋊C4C23×C12712yes—
319C2×C4⋊C4C23×C12712yes—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4D4×C12711yescharacteristic
326C2×C22⋊C4D4×C12711yescharacteristic
327C2×C42—22no—
328C2×C42C23×C12711yescharacteristic
329C2×C42C23×C12711yescharacteristic
330#107—22no—
331#106—22no—
332#106C2×C4×C12714yescomplemented
333#102—24no—
334#102—24no—
335#102C2×C4×C12718yescomplemented
336#97—22no—
337#97—22no—
338C4×C8—22no—
339C4×C8D4×C12714yescomplemented
340#95—22no—
341#95—22no—
342#95—22no—
343C24—22no—
344C24C2×D4×C12711yescharacteristic
345C2×D4—28no—
346C2×D4—22no—
347C2×D4—22no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—82no—
352C2×D4—82no—
353C2×D4C22×C4×C12714yes—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—44no—
362C22×C4—82no—
363C22×C4—82no—
364C22×C4C22×C4×C12712yes—
365C22×C4C2×D4×C12711yescharacteristic
366C22×C4C2×D4×C12711yescharacteristic
367C22×C4C2×D4×C12711yescharacteristic
368C22×C4C2×D4×C12711yescharacteristic
369C22×C4C2×D4×C12711yescharacteristic
370C22×C4#41×C12712yes—
371C22×C4C24×C12711yescharacteristic
372D8—28no—
373M16—28no—
374C2×C8—28no—
375C2×C8—21no—
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—21no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8C22×C4×C12712yes—
382C2×C8C22×C4×C12712yes—
383C2×C8C2×D4×C12712yes—
384C2×C8C2×D4×C12712yes—
385C2×C8#41×C12712yes—
386C2×C8#41×C12712yes—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—82no—
395C4⋊C4C22×C4×C12714yes—
396C22⋊C4—28no—
397C22⋊C4—22no—
398C22⋊C4—22no—
399C22⋊C4—44no—
400C22⋊C4—82no—
401C22⋊C4—82no—
402C22⋊C4—82no—
403C42—21no—
404C42—21no—
405C42—82no—
406C42C2×D4×C12712yes—
407C42#41×C12712yes—
408C23—21no—
409C23—21no—
410C23—22no—
411C23—22no—
412C23—24no—
413C23—42no—
414C23—42no—
415C23—42no—
416C23—42no—
417C23—42no—
418C23—42no—
419C23C4×D4×C12712yes—
420C23C22×D4×C12711yescharacteristic
421D4—24no—
422D4—24no—
423D4—42no—
424D4—42no—
425D4—88no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—24no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—88no—
448C2×C4C4×D4×C12712yes—
449C2×C4#121×C12712yes—
450C2×C4#121×C12712yes—
451C2×C4C23×C4×C12711yescharacteristic
452C2×C4C22×D4×C12711yescharacteristic
453C2×C4C2×#41×C12711yescharacteristic
454C2×C4C2×#41×C12711yescharacteristic
455C2×C4C2×#41×C12711yescharacteristic
456C2×C4C2×#41×C12711yescharacteristic
457C8—22no—
458C8—22no—
459C8—22no—
460C8C4×D4×C12714yes—
461C22—24no—
462C22—22no—
463C22—42no—
464C22—41no—
465C22—41no—
466C22—44no—
467C22—44no—
468C22—44no—
469C22—82no—
470C22—82no—
471C22—82no—
472C22—82no—
473C22C2×C4×D4×C12711yescharacteristic
474C22C2×#121×C12711yescharacteristic
475C22#532×C12711yescharacteristic
476C22#576×C12712yes—
477C22#577×C12712yes—
478C4—22no—
479C4—22no—
480C4—22no—
481C4—44no—
482C4—41no—
483C4—41no—
484C4—82no—
485C4—82no—
486C4C2×C4×D4×C12711yescharacteristic
487C4C4×#41×C12711yescharacteristic
488C4#525×C12711yescharacteristic
489C4#529×C12711yescharacteristic
490C2—42no—
491C2—84no—
492C2C4×#121×C12711yescharacteristic
493C2C127×#294612yes—
494C2C127×#305811yescharacteristic
495C2C127×#306011yescharacteristic
496C2C127×#317912yes—
subgroupG/H
center, socleC23×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC2×#469×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×C4×D8×C127C2semidirect
3. C2×#405×C127C2semidirect
4. C127×#2324C2semidirect
5. C127×#1972C2semidirect
6. C127×#1944C2semidirect
7. C127×#1934C2semidirect
8. C127×#1893C2semidirect
9. C127×#1809C2semidirect
10. C4×#106×C127C2semidirect
11. C127×#1762C2semidirect
18. #469×C127C4semidirect
51. C2×M16×C127C2×C4semidirect
60. #121×C127C2×C4semidirect
83. #106×C127C2×C4semidirect
86. #102×C127C2×C4semidirect
90. C4×C8×C127D4semidirect
241. #21536C127direct (N × H)
250. C2×C4×D8C2×C127semidirect
251. C2×#405C2×C127semidirect
252. #2324C2×C127semidirect
253. #1972C2×C127semidirect
254. #1944C2×C127semidirect
255. #1934C2×C127semidirect
256. #1893C2×C127semidirect
257. #1809C2×C127semidirect
258. C4×#106C2×C127semidirect
259. #1762C2×C127semidirect
260. C127#21536direct (N × H)
267. #469C4×C127semidirect
300. C2×M16C2×C4×C127semidirect
309. #121C2×C4×C127semidirect
332. #106C2×C4×C127semidirect
335. #102C2×C4×C127semidirect
339. C4×C8D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#469×C1272
C2×C4×D8×C1272
C2×#405×C1272
C127×#23242
C127×#19722
C127×#19442
C127×#19342
C127×#18932
C127×#18092
C4×#106×C1272
C127×#17622
#21536127