Finite Group Databasebeta

← C127×#21529 #44585202

Subgroups — C127×#21529 #44585202

Order 32512.

1066 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#466×C127C211yesmaximal, characteristic
2C2×#442×C127C211yesmaximal, characteristic, complemented
3C2×#405×C127C211yesmaximal, characteristic, complemented
4C127×#2324C212yesmaximal, complemented
5C127×#1972C211yesmaximal, characteristic, complemented
6C127×#1943C211yesmaximal, characteristic, complemented
7C127×#1934C212yesmaximal, complemented
8C127×#1895C212yesmaximal, complemented
9C127×#1807C211yesmaximal, characteristic, complemented
10C127×#1776C211yesmaximal, characteristic, complemented
11C4×#102×C127C212yesmaximal, complemented
12C22×D8×C127C2211yescharacteristic
13C22×M16×C127C2211yescharacteristic
14C23×C8×C127C2211yescharacteristic
15C2×#121×C127C2212yes—
16C2×C4×D4×C127C2212yes—
17C2×#117×C127C2211yescharacteristic
18#466×C127C418yescomplemented
19#442×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×C127—22no—
52C22×C8×C127—22no—
53C22×C8×C127—22no—
54C22×C8×C127C2×C414yescomplemented
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×C127D412yes—
67C2×C4⋊C4×C127C2312yes—
68C2×C4⋊C4×C127C2312yes—
69C2×C4⋊C4×C127C2312yes—
70C2×C22⋊C4×C127—22no—
71C2×C22⋊C4×C127—22no—
72C2×C22⋊C4×C127—22no—
73C2×C22⋊C4×C127—22no—
74C2×C22⋊C4×C127—22no—
75C2×C22⋊C4×C127D412yes—
76C2×C42×C127—22no—
77C2×C42×C127C2311yescharacteristic
78C2×C42×C127C2311yescharacteristic
79#107×C127C2×C414yescomplemented
80#106×C127—22no—
81#106×C127—22no—
82#102×C127—24no—
83#102×C127—24no—
84#102×C127C2×C418yescomplemented
85#97×C127—22no—
86#97×C127D414yescomplemented
87C4×C8×C127—22no—
88C4×C8×C127—22no—
89#95×C127—22no—
90#95×C127—22no—
91#95×C127—22no—
92C24×C127—22no—
93C24×C127C2×D411yescharacteristic
94C2×D4×C127—28no—
95C2×D4×C127—22no—
96C2×D4×C127—22no—
97C2×D4×C127—22no—
98C2×D4×C127—22no—
99C2×D4×C127—22no—
100C2×D4×C127—82no—
101C2×D4×C127—82no—
102C2×D4×C127C22×C414yes—
103C22×C4×C127—21no—
104C22×C4×C127—21no—
105C22×C4×C127—21no—
106C22×C4×C127—21no—
107C22×C4×C127—22no—
108C22×C4×C127—22no—
109C22×C4×C127—22no—
110C22×C4×C127—44no—
111C22×C4×C127—82no—
112C22×C4×C127—82no—
113C22×C4×C127C22×C412yes—
114C22×C4×C127C2×D412yes—
115C22×C4×C127C2×D411yescharacteristic
116C22×C4×C127C2×D412yes—
117C22×C4×C127#4112yes—
118C22×C4×C127C2411yescharacteristic
119D8×C127—28no—
120M16×C127—28no—
121C2×C8×C127—21no—
122C2×C8×C127—21no—
123C2×C8×C127—21no—
124C2×C8×C127—21no—
125C2×C8×C127—21no—
126C2×C8×C127—21no—
127C2×C8×C127—28no—
128C2×C8×C127C22×C412yes—
129C2×C8×C127C22×C412yes—
130C2×C8×C127C2×D412yes—
131C2×C8×C127C2×D412yes—
132C2×C8×C127#4112yes—
133C2×C8×C127#4112yes—
134C4⋊C4×C127—24no—
135C4⋊C4×C127—22no—
136C4⋊C4×C127—22no—
137C4⋊C4×C127—22no—
138C4⋊C4×C127—22no—
139C4⋊C4×C127—22no—
140C4⋊C4×C127—82no—
141C4⋊C4×C127C22×C414yes—
142C22⋊C4×C127—28no—
143C22⋊C4×C127—24no—
144C22⋊C4×C127—44no—
145C22⋊C4×C127—82no—
146C22⋊C4×C127—82no—
147C22⋊C4×C127—82no—
148C42×C127—21no—
149C42×C127—21no—
150C42×C127—82no—
151C42×C127C2×D412yes—
152C42×C127#4112yes—
153C23×C127—21no—
154C23×C127—21no—
155C23×C127—22no—
156C23×C127—22no—
157C23×C127—24no—
158C23×C127—42no—
159C23×C127—42no—
160C23×C127—42no—
161C23×C127—42no—
162C23×C127—42no—
163C23×C127—42no—
164C23×C127C4×D412yes—
165C23×C127C22×D411yescharacteristic
166D4×C127—24no—
167D4×C127—24no—
168D4×C127—42no—
169D4×C127—42no—
170D4×C127—88no—
171C2×C4×C127—21no—
172C2×C4×C127—21no—
173C2×C4×C127—22no—
174C2×C4×C127—22no—
175C2×C4×C127—22no—
176C2×C4×C127—22no—
177C2×C4×C127—22no—
178C2×C4×C127—22no—
179C2×C4×C127—24no—
180C2×C4×C127—22no—
181C2×C4×C127—22no—
182C2×C4×C127—22no—
183C2×C4×C127—42no—
184C2×C4×C127—42no—
185C2×C4×C127—42no—
186C2×C4×C127—42no—
187C2×C4×C127—42no—
188C2×C4×C127—42no—
189C2×C4×C127—42no—
190C2×C4×C127—42no—
191C2×C4×C127—88no—
192C2×C4×C127C4×D412yes—
193C2×C4×C127#12114yes—
194C2×C4×C127C23×C411yescharacteristic
195C2×C4×C127C22×D411yescharacteristic
196C2×C4×C127C2×#4111yescharacteristic
197C2×C4×C127C2×#4111yescharacteristic
198C2×C4×C127C2×#4111yescharacteristic
199C2×C4×C127C2×#4111yescharacteristic
200C8×C127—22no—
201C8×C127—22no—
202C8×C127—22no—
203C8×C127C4×D414yes—
204C22×C127—22no—
205C22×C127—22no—
206C22×C127—22no—
207C22×C127—42no—
208C22×C127—42no—
209C22×C127—44no—
210C22×C127—44no—
211C22×C127—44no—
212C22×C127—82no—
213C22×C127—82no—
214C22×C127—82no—
215C22×C127—82no—
216C22×C127C2×C4×D411yescharacteristic
217C22×C127C2×#12111yescharacteristic
218C22×C127#53211yescharacteristic
219C22×C127#57612yes—
220C22×C127#57712yes—
221C4×C127—24no—
222C4×C127—22no—
223C4×C127—44no—
224C4×C127—42no—
225C4×C127—82no—
226C4×C127—82no—
227C4×C127C2×C4×D411yescharacteristic
228C4×C127C4×#4111yescharacteristic
229C4×C127#52511yescharacteristic
230C4×C127#52911yescharacteristic
231#21529C12711yesmaximal, characteristic, direct product factor, Sylow
232C2×C127—42no—
233C2×C127—84no—
234C2×C127C4×#12111yescharacteristic
235C2×C127#294811yescharacteristic
236C2×C127#295211yescharacteristic
237C2×C127#306212yes—
238C2×C127#317912yes—
239C2×#466C2×C12711yescharacteristic
240C2×#442C2×C12711yescharacteristic, complemented
241C2×#405C2×C12711yescharacteristic, complemented
242#2324C2×C12712yescomplemented
243#1972C2×C12711yescharacteristic, complemented
244#1943C2×C12711yescharacteristic, complemented
245#1934C2×C12712yescomplemented
246#1895C2×C12712yescomplemented
247#1807C2×C12711yescharacteristic, complemented
248#1776C2×C12711yescharacteristic, complemented
249C4×#102C2×C12712yescomplemented
250C127#2152911yescharacteristic, direct product factor, Sylow
251C22×D8C22×C12711yescharacteristic
252C22×M16C22×C12711yescharacteristic
253C23×C8C22×C12711yescharacteristic
254C2×#121C22×C12712yes—
255C2×C4×D4C22×C12712yes—
256C2×#117C22×C12711yescharacteristic
257#466C4×C12718yescomplemented
258#442—24no—
259C2×#107C22×C12711yescharacteristic
260C2×#106C22×C12711yescharacteristic
261C2×#106C22×C12711yescharacteristic
262C2×#102C22×C12712yes—
263C2×#102C22×C12712yes—
264C2×#102C22×C12712yes—
265#405—24no—
266C2×#97C22×C12711yescharacteristic
267C2×#97C22×C12711yescharacteristic
268C2×C4×C8C22×C12711yescharacteristic
269C2×C4×C8C22×C12711yescharacteristic
270#390—22no—
271#390C22×C12712yes—
272#389C22×C12712yes—
273#388—22no—
274#386—22no—
275#385—22no—
276#380C22×C12712yes—
277C4×C4⋊C4C22×C12712yes—
278#340C22×C12712yes—
279#340C22×C12712yes—
280#340C22×C12712yes—
281C22×D4—22no—
282C22×D4C23×C12712yes—
283C23×C4—22no—
284C23×C4C23×C12711yescharacteristic
285C2×D8—22no—
286C2×D8—22no—
287C2×D8C2×C4×C12714yes—
288C2×M16—22no—
289C2×M16—22no—
290C2×M16—22no—
291C22×C8—22no—
292C22×C8—22no—
293C22×C8C2×C4×C12714yescomplemented
294C22×C8C23×C12711yescharacteristic
295C22×C8C23×C12711yescharacteristic
296C22×C8C23×C12711yescharacteristic
297C22×C8C23×C12711yescharacteristic
298#121—24no—
299#121C2×C4×C12718yescomplemented
300C4×D4—24no—
301C4×D4—24no—
302#117—22no—
303#117—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4D4×C12712yes—
306C2×C4⋊C4C23×C12712yes—
307C2×C4⋊C4C23×C12712yes—
308C2×C4⋊C4C23×C12712yes—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4D4×C12712yes—
315C2×C42—22no—
316C2×C42C23×C12711yescharacteristic
317C2×C42C23×C12711yescharacteristic
318#107C2×C4×C12714yescomplemented
319#106—22no—
320#106—22no—
321#102—24no—
322#102—24no—
323#102C2×C4×C12718yescomplemented
324#97—22no—
325#97D4×C12714yescomplemented
326C4×C8—22no—
327C4×C8—22no—
328#95—22no—
329#95—22no—
330#95—22no—
331C24—22no—
332C24C2×D4×C12711yescharacteristic
333C2×D4—28no—
334C2×D4—22no—
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—22no—
338C2×D4—22no—
339C2×D4—82no—
340C2×D4—82no—
341C2×D4C22×C4×C12714yes—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—44no—
350C22×C4—82no—
351C22×C4—82no—
352C22×C4C22×C4×C12712yes—
353C22×C4C2×D4×C12712yes—
354C22×C4C2×D4×C12711yescharacteristic
355C22×C4C2×D4×C12712yes—
356C22×C4#41×C12712yes—
357C22×C4C24×C12711yescharacteristic
358D8—28no—
359M16—28no—
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—21no—
366C2×C8—28no—
367C2×C8C22×C4×C12712yes—
368C2×C8C22×C4×C12712yes—
369C2×C8C2×D4×C12712yes—
370C2×C8C2×D4×C12712yes—
371C2×C8#41×C12712yes—
372C2×C8#41×C12712yes—
373C4⋊C4—24no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—82no—
380C4⋊C4C22×C4×C12714yes—
381C22⋊C4—28no—
382C22⋊C4—24no—
383C22⋊C4—44no—
384C22⋊C4—82no—
385C22⋊C4—82no—
386C22⋊C4—82no—
387C42—21no—
388C42—21no—
389C42—82no—
390C42C2×D4×C12712yes—
391C42#41×C12712yes—
392C23—21no—
393C23—21no—
394C23—22no—
395C23—22no—
396C23—24no—
397C23—42no—
398C23—42no—
399C23—42no—
400C23—42no—
401C23—42no—
402C23—42no—
403C23C4×D4×C12712yes—
404C23C22×D4×C12711yescharacteristic
405D4—24no—
406D4—24no—
407D4—42no—
408D4—42no—
409D4—88no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—24no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—88no—
431C2×C4C4×D4×C12712yes—
432C2×C4#121×C12714yes—
433C2×C4C23×C4×C12711yescharacteristic
434C2×C4C22×D4×C12711yescharacteristic
435C2×C4C2×#41×C12711yescharacteristic
436C2×C4C2×#41×C12711yescharacteristic
437C2×C4C2×#41×C12711yescharacteristic
438C2×C4C2×#41×C12711yescharacteristic
439C8—22no—
440C8—22no—
441C8—22no—
442C8C4×D4×C12714yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—42no—
447C22—42no—
448C22—44no—
449C22—44no—
450C22—44no—
451C22—82no—
452C22—82no—
453C22—82no—
454C22—82no—
455C22C2×C4×D4×C12711yescharacteristic
456C22C2×#121×C12711yescharacteristic
457C22#532×C12711yescharacteristic
458C22#576×C12712yes—
459C22#577×C12712yes—
460C4—24no—
461C4—22no—
462C4—44no—
463C4—42no—
464C4—82no—
465C4—82no—
466C4C2×C4×D4×C12711yescharacteristic
467C4C4×#41×C12711yescharacteristic
468C4#525×C12711yescharacteristic
469C4#529×C12711yescharacteristic
470C2—42no—
471C2—84no—
472C2C4×#121×C12711yescharacteristic
473C2C127×#294811yescharacteristic
474C2C127×#295211yescharacteristic
475C2C127×#306212yes—
476C2C127×#317912yes—
subgroupG/H
center, socleC23×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC2×#466×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×#442×C127C2semidirect
3. C2×#405×C127C2semidirect
4. C127×#2324C2semidirect
5. C127×#1972C2semidirect
6. C127×#1943C2semidirect
7. C127×#1934C2semidirect
8. C127×#1895C2semidirect
9. C127×#1807C2semidirect
10. C127×#1776C2semidirect
11. C4×#102×C127C2semidirect
18. #466×C127C4semidirect
54. C22×C8×C127C2×C4semidirect
60. #121×C127C2×C4semidirect
79. #107×C127C2×C4semidirect
84. #102×C127C2×C4semidirect
86. #97×C127D4semidirect
231. #21529C127direct (N × H)
240. C2×#442C2×C127semidirect
241. C2×#405C2×C127semidirect
242. #2324C2×C127semidirect
243. #1972C2×C127semidirect
244. #1943C2×C127semidirect
245. #1934C2×C127semidirect
246. #1895C2×C127semidirect
247. #1807C2×C127semidirect
248. #1776C2×C127semidirect
249. C4×#102C2×C127semidirect
250. C127#21529direct (N × H)
257. #466C4×C127semidirect
293. C22×C8C2×C4×C127semidirect
299. #121C2×C4×C127semidirect
318. #107C2×C4×C127semidirect
323. #102C2×C4×C127semidirect
325. #97D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#466×C1272
C2×#442×C1272
C2×#405×C1272
C127×#23242
C127×#19722
C127×#19432
C127×#19342
C127×#18952
C127×#18072
C127×#17762
C4×#102×C1272
#21529127