Finite Group Databasebeta

← C127×#8247 #44571920

Subgroups — C127×#8247 #44571920

Order 32512.

444 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2966C211yesmaximal, characteristic
2C127×#1726C211yesmaximal, characteristic, complemented
3C127×#1524C211yesmaximal, characteristic
4C127×#1500C211yesmaximal, characteristic
5C8×M16×C127C211yesmaximal, characteristic, complemented
6C127×#1302C211yesmaximal, characteristic, complemented
7C127×#1300C211yesmaximal, characteristic, complemented
8#529×C127C2211yescharacteristic
9#446×C127C411yescharacteristic, complemented
10C8×Q8×C127C411yescharacteristic, complemented
11#436×C127C411yescharacteristic, complemented
12#435×C127—21no—
13C8×D4×C127—21no—
14C8×D4×C127C411yescharacteristic, complemented
15#433×C127—21no—
16#432×C127C2211yescharacteristic
17#431×C127C2211yescharacteristic
18#405×C127—21no—
19C4×M16×C127C2211yescharacteristic
20C2×#97×C127—21no—
21C2×#97×C127C2211yescharacteristic
22C2×C4×C8×C127—21no—
23C2×C4×C8×C127C2211yescharacteristic
24#376×C127C2211yescharacteristic
25#330×C127C412yescomplemented
26#329×C127C412yescomplemented
27#328×C127C412yes—
28#327×C127C412yes—
29#322×C127—21no—
30C82×C127—21no—
31C2×M16×C127—21no—
32C2×M16×C127—21no—
33C22×C8×C127—21no—
34C22×C8×C127—21no—
35C22×C8×C127D411yescharacteristic
36C22×C8×C127D411yescharacteristic
37#126×C127—21no—
38#125×C127C2×C411yescharacteristic
39#124×C127C2×C411yescharacteristic
40#123×C127—21no—
41C22⋊Q8×C127C2×C411yescharacteristic
42#121×C127C2×C411yescharacteristic
43C4×Q8×C127C2×C411yescharacteristic
44C4×D4×C127—21no—
45C4×D4×C127C2×C411yescharacteristic
46#117×C127—21no—
47C2×C42×C127—21no—
48C2×C42×C127C2311yescharacteristic
49C4⋊C8×C127—21no—
50C4⋊C8×C127—21no—
51C4⋊C8×C127—21no—
52C4⋊C8×C127C2×C411yescharacteristic
53C4⋊C8×C127C2×C411yescharacteristic
54C22⋊C8×C127—21no—
55C22⋊C8×C127—21no—
56C22⋊C8×C127—21no—
57C22⋊C8×C127C2×C412yes—
58#97×C127—24no—
59#97×C127—21no—
60#97×C127—21no—
61#97×C127—21no—
62#97×C127C2×C412yes—
63#97×C127C2×C412yes—
64C4×C8×C127—24no—
65C4×C8×C127—21no—
66C4×C8×C127—21no—
67C4×C8×C127—21no—
68C4×C8×C127C2×C411yescharacteristic
69C4×C8×C127C2×C411yescharacteristic
70C4×C8×C127D411yescharacteristic
71C4×C8×C127D411yescharacteristic
72#95×C127—21no—
73#95×C127C2×C412yes—
74C2×Q8×C127C4211yescharacteristic
75C2×D4×C127—21no—
76C2×D4×C127C4211yescharacteristic
77C22×C4×C127—22no—
78C22×C4×C127—21no—
79C22×C4×C127C22×C411yescharacteristic
80C22×C4×C127C2×D411yescharacteristic
81C22×C4×C127#4111yescharacteristic
82M16×C127—24no—
83M16×C127—42no—
84C2×C8×C127—22no—
85C2×C8×C127—22no—
86C2×C8×C127—22no—
87C2×C8×C127—22no—
88C2×C8×C127—22no—
89C2×C8×C127—22no—
90C2×C8×C127—21no—
91C2×C8×C127—21no—
92C2×C8×C127—22no—
93C2×C8×C127—42no—
94C2×C8×C127C22⋊C411yescharacteristic
95C2×C8×C127C22⋊C411yescharacteristic
96C2×C8×C127C22⋊C411yescharacteristic
97C2×C8×C127C22⋊C411yescharacteristic
98C4⋊C4×C127—21no—
99C4⋊C4×C127—21no—
100C4⋊C4×C127—21no—
101C4⋊C4×C127—21no—
102C4⋊C4×C127C4211yescharacteristic
103C4⋊C4×C127C4211yescharacteristic
104C22⋊C4×C127—21no—
105C22⋊C4×C127—21no—
106C22⋊C4×C127—21no—
107C22⋊C4×C127—21no—
108C22⋊C4×C127—21no—
109C42×C127—22no—
110C42×C127—22no—
111C42×C127—21no—
112C42×C127C22×C411yescharacteristic
113C42×C127C22×C411yescharacteristic
114C42×C127C2×D411yescharacteristic
115C42×C127#4111yescharacteristic
116C23×C127—21no—
117C23×C127C4×D411yescharacteristic
118Q8×C127—41no—
119D4×C127—41no—
120D4×C127—42no—
121C2×C4×C127—22no—
122C2×C4×C127—21no—
123C2×C4×C127—21no—
124C2×C4×C127—24no—
125C2×C4×C127—21no—
126C2×C4×C127—21no—
127C2×C4×C127—21no—
128C2×C4×C127—41no—
129C2×C4×C127—42no—
130C2×C4×C127—42no—
131C2×C4×C127—41no—
132C2×C4×C127—41no—
133C2×C4×C127C2×C4211yescharacteristic
134C2×C4×C127C2×C22⋊C411yescharacteristic
135C2×C4×C127#11711yescharacteristic
136C2×C4×C127C4×D411yescharacteristic
137C2×C4×C127C4×D411yescharacteristic
138C2×C4×C127C4×D411yescharacteristic
139C8×C127—24no—
140C8×C127—24no—
141C8×C127—21no—
142C8×C127—21no—
143C8×C127—42no—
144C8×C127—41no—
145C8×C127—41no—
146C8×C127#10412yes—
147C8×C127#10412yes—
148C22×C127—21no—
149C22×C127—21no—
150C22×C127—41no—
151C22×C127—41no—
152C22×C127—41no—
153C22×C127C4×C22⋊C411yescharacteristic
154C22×C127#44312yes—
155C4×C127—21no—
156C4×C127—21no—
157C4×C127—21no—
158C4×C127—21no—
159C4×C127—21no—
160C4×C127—44no—
161C4×C127—41no—
162C4×C127—41no—
163C4×C127—41no—
164C4×C127C2×#10411yescharacteristic
165C4×C127C2×#10411yescharacteristic
166#8247C12711yesmaximal, characteristic, direct product factor, Sylow
167C2×C127—22no—
168C2×C127—81no—
169C2×C127#175711yescharacteristic
170C2×C127C4×#10411yescharacteristic
171C2×C127#176411yescharacteristic
172#2966C2×C12711yescharacteristic
173#1726C2×C12711yescharacteristic, complemented
174#1524C2×C12711yescharacteristic
175#1500C2×C12711yescharacteristic
176C8×M16C2×C12711yescharacteristic, complemented
177#1302C2×C12711yescharacteristic, complemented
178#1300C2×C12711yescharacteristic, complemented
179C127#824711yescharacteristic, direct product factor, Sylow
180#529C22×C12711yescharacteristic
181#446C4×C12711yescharacteristic, complemented
182C8×Q8C4×C12711yescharacteristic, complemented
183#436C4×C12711yescharacteristic, complemented
184#435—21no—
185C8×D4—21no—
186C8×D4C4×C12711yescharacteristic, complemented
187#433—21no—
188#432C22×C12711yescharacteristic
189#431C22×C12711yescharacteristic
190#405—21no—
191C4×M16C22×C12711yescharacteristic
192C2×#97—21no—
193C2×#97C22×C12711yescharacteristic
194C2×C4×C8—21no—
195C2×C4×C8C22×C12711yescharacteristic
196#376C22×C12711yescharacteristic
197#330C4×C12712yescomplemented
198#329C4×C12712yescomplemented
199#328C4×C12712yes—
200#327C4×C12712yes—
201#322—21no—
202C82—21no—
203C2×M16—21no—
204C2×M16—21no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8D4×C12711yescharacteristic
208C22×C8D4×C12711yescharacteristic
209#126—21no—
210#125C2×C4×C12711yescharacteristic
211#124C2×C4×C12711yescharacteristic
212#123—21no—
213C22⋊Q8C2×C4×C12711yescharacteristic
214#121C2×C4×C12711yescharacteristic
215C4×Q8C2×C4×C12711yescharacteristic
216C4×D4—21no—
217C4×D4C2×C4×C12711yescharacteristic
218#117—21no—
219C2×C42—21no—
220C2×C42C23×C12711yescharacteristic
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8C2×C4×C12711yescharacteristic
225C4⋊C8C2×C4×C12711yescharacteristic
226C22⋊C8—21no—
227C22⋊C8—21no—
228C22⋊C8—21no—
229C22⋊C8C2×C4×C12712yes—
230#97—24no—
231#97—21no—
232#97—21no—
233#97—21no—
234#97C2×C4×C12712yes—
235#97C2×C4×C12712yes—
236C4×C8—24no—
237C4×C8—21no—
238C4×C8—21no—
239C4×C8—21no—
240C4×C8C2×C4×C12711yescharacteristic
241C4×C8C2×C4×C12711yescharacteristic
242C4×C8D4×C12711yescharacteristic
243C4×C8D4×C12711yescharacteristic
244#95—21no—
245#95C2×C4×C12712yes—
246C2×Q8C42×C12711yescharacteristic
247C2×D4—21no—
248C2×D4C42×C12711yescharacteristic
249C22×C4—22no—
250C22×C4—21no—
251C22×C4C22×C4×C12711yescharacteristic
252C22×C4C2×D4×C12711yescharacteristic
253C22×C4#41×C12711yescharacteristic
254M16—24no—
255M16—42no—
256C2×C8—22no—
257C2×C8—22no—
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—22no—
265C2×C8—42no—
266C2×C8C22⋊C4×C12711yescharacteristic
267C2×C8C22⋊C4×C12711yescharacteristic
268C2×C8C22⋊C4×C12711yescharacteristic
269C2×C8C22⋊C4×C12711yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4C42×C12711yescharacteristic
275C4⋊C4C42×C12711yescharacteristic
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C42—22no—
282C42—22no—
283C42—21no—
284C42C22×C4×C12711yescharacteristic
285C42C22×C4×C12711yescharacteristic
286C42C2×D4×C12711yescharacteristic
287C42#41×C12711yescharacteristic
288C23—21no—
289C23C4×D4×C12711yescharacteristic
290Q8—41no—
291D4—41no—
292D4—42no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—24no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4C2×C42×C12711yescharacteristic
306C2×C4C2×C22⋊C4×C12711yescharacteristic
307C2×C4#117×C12711yescharacteristic
308C2×C4C4×D4×C12711yescharacteristic
309C2×C4C4×D4×C12711yescharacteristic
310C2×C4C4×D4×C12711yescharacteristic
311C8—24no—
312C8—24no—
313C8—21no—
314C8—21no—
315C8—42no—
316C8—41no—
317C8—41no—
318C8#104×C12712yes—
319C8#104×C12712yes—
320C22—21no—
321C22—21no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22C4×C22⋊C4×C12711yescharacteristic
326C22#443×C12712yes—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—44no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4C2×#104×C12711yescharacteristic
337C4C2×#104×C12711yescharacteristic
338C2—22no—
339C2—81no—
340C2C127×#175711yescharacteristic
341C2C4×#104×C12711yescharacteristic
342C2C127×#176411yescharacteristic
subgroupG/H
centerC2×C8×C127C22⋊C4
commutatorC2×C4C2×C42×C127
Frattini, cosocleC2×C42C23×C127
socleC22×C127C4×C22⋊C4
prime radical#121×C127C2×C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C8×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1726C2semidirect
5. C8×M16×C127C2semidirect
6. C127×#1302C2semidirect
7. C127×#1300C2semidirect
9. #446×C127C4semidirect
10. C8×Q8×C127C4semidirect
11. #436×C127C4semidirect
14. C8×D4×C127C4semidirect
25. #330×C127C4semidirect
26. #329×C127C4semidirect
166. #8247C127direct (N × H)
173. #1726C2×C127semidirect
176. C8×M16C2×C127semidirect
177. #1302C2×C127semidirect
178. #1300C2×C127semidirect
179. C127#8247direct (N × H)
181. #446C4×C127semidirect
182. C8×Q8C4×C127semidirect
183. #436C4×C127semidirect
186. C8×D4C4×C127semidirect
197. #330C4×C127semidirect
198. #329C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#29662
C127×#17262
C127×#15242
C127×#15002
C8×M16×C1272
C127×#13022
C127×#13002
#8247127