Finite Group Databasebeta

← C127×#11741 #44575414

Subgroups — C127×#11741 #44575414

Order 32512.

356 conjugacy classes of subgroups.

The subgroup lattice has 288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3168C211yesmaximal, characteristic
2C127×#2162C211yesmaximal, characteristic, complemented
3C4×#106×C127C211yesmaximal, characteristic, complemented
4C127×#1348C212yesmaximal, complemented
5C127×#1347C212yesmaximal
6#529×C127—21no—
7#499×C127C411yescharacteristic, complemented
8#495×C127C411yescharacteristic, complemented
9#488×C127—21no—
10#467×C127C2211yescharacteristic
11#466×C127C2211yescharacteristic
12#465×C127—21no—
13C4×Q16×C127C411yescharacteristic, complemented
14C4×SD16×C127—21no—
15C4×D8×C127C411yescharacteristic, complemented
16C2×#106×C127—21no—
17C2×C4×C8×C127C2211yescharacteristic
18C4×C4⋊C4×C127—21no—
19C4⋊C16×C127—21no—
20C22⋊C16×C127C2212yes—
21C4×C16×C127—21no—
22#340×C127C2212yes—
23C2×Q16×C127C2×C411yescharacteristic
24C2×SD16×C127—21no—
25C2×D8×C127C2×C411yescharacteristic
26C22×C8×C127D411yescharacteristic
27C22×C8×C127C2311yescharacteristic
28#126×C127—41no—
29#125×C127—21no—
30#124×C127—21no—
31#123×C127—41no—
32C22⋊Q8×C127—21no—
33#121×C127—21no—
34C4×Q8×C127—21no—
35C4×D4×C127—21no—
36C4×D4×C127—41no—
37#117×C127—41no—
38C2×C4⋊C4×C127—22no—
39C2×C42×C127—41no—
40C2×C42×C127D411yescharacteristic
41C2×C16×C127—22no—
42#107×C127C2×C411yescharacteristic
43#107×C127C2×C411yescharacteristic
44#106×C127—24no—
45#106×C127—21no—
46#103×C127—21no—
47#103×C127—21no—
48#102×C127—21no—
49#102×C127—21no—
50C4×C8×C127C2×C411yescharacteristic
51C4×C8×C127C2×C411yescharacteristic
52C4×C8×C127D411yescharacteristic
53C4×C8×C127D411yescharacteristic
54#95×C127—41no—
55C2×Q8×C127—21no—
56C2×D4×C127—21no—
57C2×D4×C127—41no—
58C22×C4×C127—42no—
59C22×C4×C127—41no—
60C22×C4×C127D811yescharacteristic
61C22×C4×C127D811yescharacteristic
62C22×C4×C127C2×D411yescharacteristic
63Q16×C127—41no—
64SD16×C127—42no—
65D8×C127—41no—
66C2×C8×C127—22no—
67C2×C8×C127—41no—
68C2×C8×C127C22⋊C411yescharacteristic
69C2×C8×C127C22⋊C411yescharacteristic
70C2×C8×C127C22×C411yescharacteristic
71C2×C8×C127C2×D411yescharacteristic
72C4⋊C4×C127—24no—
73C4⋊C4×C127—21no—
74C4⋊C4×C127—21no—
75C4⋊C4×C127—42no—
76C4⋊C4×C127—41no—
77C4⋊C4×C127—41no—
78C4⋊C4×C127—41no—
79C4⋊C4×C127—41no—
80C22⋊C4×C127—41no—
81C22⋊C4×C127—41no—
82C22⋊C4×C127—41no—
83C22⋊C4×C127—41no—
84C22⋊C4×C127—41no—
85C42×C127—41no—
86C42×C127—82no—
87C42×C127C22⋊C411yescharacteristic
88C42×C127C22⋊C411yescharacteristic
89C42×C127SD1611yescharacteristic
90C42×C127SD1611yescharacteristic
91C16×C127—42no—
92C23×C127—41no—
93C23×C127C2×D811yescharacteristic
94Q8×C127—41no—
95Q8×C127—41no—
96D4×C127—41no—
97D4×C127—41no—
98D4×C127—82no—
99C2×C4×C127—22no—
100C2×C4×C127—22no—
101C2×C4×C127—21no—
102C2×C4×C127—21no—
103C2×C4×C127—44no—
104C2×C4×C127—41no—
105C2×C4×C127—41no—
106C2×C4×C127—41no—
107C2×C4×C127—82no—
108C2×C4×C127—82no—
109C2×C4×C127—82no—
110C2×C4×C127#10211yescharacteristic
111C2×C4×C127#10211yescharacteristic
112C2×C4×C127#10211yescharacteristic
113C2×C4×C127#10211yescharacteristic
114C2×C4×C127C2×C22⋊C411yescharacteristic
115C2×C4×C127C2×SD1611yescharacteristic
116C8×C127—21no—
117C8×C127—21no—
118C8×C127—21no—
119C8×C127#10412yes—
120C22×C127—21no—
121C22×C127—21no—
122C22×C127—81no—
123C22×C127—81no—
124C22×C127—81no—
125C22×C127C2×#10211yescharacteristic
126C22×C127#50812yes—
127C4×C127—21no—
128C4×C127—21no—
129C4×C127—21no—
130C4×C127—21no—
131C4×C127—84no—
132C4×C127—81no—
133C4×C127—81no—
134C4×C127—81no—
135C4×C127#36012yes—
136C4×C127#41011yescharacteristic
137C4×C127C2×#10411yescharacteristic
138#11741C12711yesmaximal, characteristic, direct product factor, Sylow
139C2×C127—22no—
140C2×C127—161no—
141C2×C127#150211yescharacteristic
142C2×C127#213811yescharacteristic
143C2×C127C2×#36011yescharacteristic
144#3168C2×C12711yescharacteristic
145#2162C2×C12711yescharacteristic, complemented
146C4×#106C2×C12711yescharacteristic, complemented
147#1348C2×C12712yescomplemented
148#1347C2×C12712yes—
149C127#1174111yescharacteristic, direct product factor, Sylow
150#529—21no—
151#499C4×C12711yescharacteristic, complemented
152#495C4×C12711yescharacteristic, complemented
153#488—21no—
154#467C22×C12711yescharacteristic
155#466C22×C12711yescharacteristic
156#465—21no—
157C4×Q16C4×C12711yescharacteristic, complemented
158C4×SD16—21no—
159C4×D8C4×C12711yescharacteristic, complemented
160C2×#106—21no—
161C2×C4×C8C22×C12711yescharacteristic
162C4×C4⋊C4—21no—
163C4⋊C16—21no—
164C22⋊C16C22×C12712yes—
165C4×C16—21no—
166#340C22×C12712yes—
167C2×Q16C2×C4×C12711yescharacteristic
168C2×SD16—21no—
169C2×D8C2×C4×C12711yescharacteristic
170C22×C8D4×C12711yescharacteristic
171C22×C8C23×C12711yescharacteristic
172#126—41no—
173#125—21no—
174#124—21no—
175#123—41no—
176C22⋊Q8—21no—
177#121—21no—
178C4×Q8—21no—
179C4×D4—21no—
180C4×D4—41no—
181#117—41no—
182C2×C4⋊C4—22no—
183C2×C42—41no—
184C2×C42D4×C12711yescharacteristic
185C2×C16—22no—
186#107C2×C4×C12711yescharacteristic
187#107C2×C4×C12711yescharacteristic
188#106—24no—
189#106—21no—
190#103—21no—
191#103—21no—
192#102—21no—
193#102—21no—
194C4×C8C2×C4×C12711yescharacteristic
195C4×C8C2×C4×C12711yescharacteristic
196C4×C8D4×C12711yescharacteristic
197C4×C8D4×C12711yescharacteristic
198#95—41no—
199C2×Q8—21no—
200C2×D4—21no—
201C2×D4—41no—
202C22×C4—42no—
203C22×C4—41no—
204C22×C4D8×C12711yescharacteristic
205C22×C4D8×C12711yescharacteristic
206C22×C4C2×D4×C12711yescharacteristic
207Q16—41no—
208SD16—42no—
209D8—41no—
210C2×C8—22no—
211C2×C8—41no—
212C2×C8C22⋊C4×C12711yescharacteristic
213C2×C8C22⋊C4×C12711yescharacteristic
214C2×C8C22×C4×C12711yescharacteristic
215C2×C8C2×D4×C12711yescharacteristic
216C4⋊C4—24no—
217C4⋊C4—21no—
218C4⋊C4—21no—
219C4⋊C4—42no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C22⋊C4—41no—
225C22⋊C4—41no—
226C22⋊C4—41no—
227C22⋊C4—41no—
228C22⋊C4—41no—
229C42—41no—
230C42—82no—
231C42C22⋊C4×C12711yescharacteristic
232C42C22⋊C4×C12711yescharacteristic
233C42SD16×C12711yescharacteristic
234C42SD16×C12711yescharacteristic
235C16—42no—
236C23—41no—
237C23C2×D8×C12711yescharacteristic
238Q8—41no—
239Q8—41no—
240D4—41no—
241D4—41no—
242D4—82no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—44no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—82no—
252C2×C4—82no—
253C2×C4—82no—
254C2×C4#102×C12711yescharacteristic
255C2×C4#102×C12711yescharacteristic
256C2×C4#102×C12711yescharacteristic
257C2×C4#102×C12711yescharacteristic
258C2×C4C2×C22⋊C4×C12711yescharacteristic
259C2×C4C2×SD16×C12711yescharacteristic
260C8—21no—
261C8—21no—
262C8—21no—
263C8#104×C12712yes—
264C22—21no—
265C22—21no—
266C22—81no—
267C22—81no—
268C22—81no—
269C22C2×#102×C12711yescharacteristic
270C22#508×C12712yes—
271C4—21no—
272C4—21no—
273C4—21no—
274C4—21no—
275C4—84no—
276C4—81no—
277C4—81no—
278C4—81no—
279C4#360×C12712yes—
280C4#410×C12711yescharacteristic
281C4C2×#104×C12711yescharacteristic
282C2—22no—
283C2—161no—
284C2C127×#150211yescharacteristic
285C2C127×#213811yescharacteristic
286C2C2×#360×C12711yescharacteristic
subgroupG/H
centerC2×C4×C127#102
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
socleC22×C127C2×#102
prime radical#466×C127C22
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C42×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2162C2semidirect
3. C4×#106×C127C2semidirect
4. C127×#1348C2semidirect
7. #499×C127C4semidirect
8. #495×C127C4semidirect
13. C4×Q16×C127C4semidirect
15. C4×D8×C127C4semidirect
138. #11741C127direct (N × H)
145. #2162C2×C127semidirect
146. C4×#106C2×C127semidirect
147. #1348C2×C127semidirect
149. C127#11741direct (N × H)
151. #499C4×C127semidirect
152. #495C4×C127semidirect
157. C4×Q16C4×C127semidirect
159. C4×D8C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#31682
C127×#21622
C4×#106×C1272
C127×#13482
C127×#13472
#11741127