Finite Group Databasebeta

← C127×#3041 #30635993

Subgroups — C127×#3041 #30635993

Order 16256.

526 conjugacy classes of subgroups.

The subgroup lattice has 244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×AGL(1,ℤ/8)×C127C211yesmaximal, characteristic, complemented
2C22×D8×C127C211yesmaximal, characteristic, complemented
3#535×C127C211yesmaximal, characteristic, complemented
4#518×C127C211yesmaximal, characteristic, complemented
5#463×C127C214yesmaximal, complemented
6#459×C127C214yesmaximal, complemented
7#424×C127C211yesmaximal, characteristic, complemented
8#418×C127C211yesmaximal, characteristic, complemented
9#416×C127C211yesmaximal, characteristic, complemented
10C2×#41×C127C2211yescharacteristic
11C22×D4×C127C2211yescharacteristic
12C22×D4×C127C2211yescharacteristic
13AGL(1,ℤ/8)×C127—24no—
14C2×SD16×C127C2212yescomplemented
15C2×D8×C127—24no—
16C2×D8×C127C2214yes—
17C2×D8×C127C2212yescomplemented
18C2×M16×C127C2211yescharacteristic
19C22×C8×C127C2211yescharacteristic
20#127×C127C2212yescomplemented
21#124×C127C2212yescomplemented
22#121×C127—22no—
23#120×C127—22no—
24C4×D4×C127—22no—
25C4×D4×C127C2214yescomplemented
26#117×C127C2211yescharacteristic
27#117×C127C2211yescharacteristic
28C2×C22⋊C4×C127—22no—
29C4⋊C8×C127C2214yescomplemented
30#103×C127C2212yescomplemented
31#102×C127C2212yescomplemented
32#102×C127C2214yescomplemented
33C24×C127—21no—
34C24×C127—21no—
35#41×C127—22no—
36#41×C127—22no—
37C2×Q8×C127C2311yescharacteristic
38C2×D4×C127—21no—
39C2×D4×C127—21no—
40C2×D4×C127—22no—
41C2×D4×C127—21no—
42C2×D4×C127—24no—
43C2×D4×C127—22no—
44C2×D4×C127—22no—
45C2×D4×C127D414yescomplemented
46C2×D4×C127C2312yes—
47C2×D4×C127C2311yescharacteristic
48C2×D4×C127C2312yes—
49C22×C4×C127—21no—
50C22×C4×C127—24no—
51C22×C4×C127C2311yescharacteristic
52SD16×C127—24no—
53D8×C127—28no—
54D8×C127—24no—
55M16×C127—22no—
56C2×C8×C127—22no—
57C2×C8×C127C2312yes—
58C2×C8×C127C2312yes—
59C4⋊C4×C127D412yes—
60C4⋊C4×C127C2312yes—
61C22⋊C4×C127—21no—
62C22⋊C4×C127—24no—
63C22⋊C4×C127—24no—
64C22⋊C4×C127D412yes—
65C42×C127—21no—
66C42×C127C2312yes—
67C23×C127—22no—
68C23×C127—24no—
69C23×C127—22no—
70C23×C127—21no—
71C23×C127—42no—
72C23×C127—82no—
73C23×C127—82no—
74C23×C127C2×D411yescharacteristic
75Q8×C127—21no—
76Q8×C127—21no—
77D4×C127—24no—
78D4×C127—22no—
79D4×C127—21no—
80D4×C127—22no—
81D4×C127—22no—
82D4×C127—21no—
83D4×C127—42no—
84D4×C127—42no—
85D4×C127—84no—
86D4×C127C2×D414yes—
87C2×C4×C127—22no—
88C2×C4×C127—21no—
89C2×C4×C127—42no—
90C2×C4×C127—84no—
91C2×C4×C127C2×D414yes—
92C2×C4×C127C2×D411yescharacteristic
93C2×C4×C127C2×D412yes—
94C2×C4×C127#4112yes—
95C2×C4×C127C2411yescharacteristic
96C8×C127—22no—
97C8×C127—22no—
98C22×C127—22no—
99C22×C127—24no—
100C22×C127—44no—
101C22×C127—41no—
102C22×C127—42no—
103C22×C127—42no—
104C22×C127—44no—
105C22×C127—84no—
106C22×C127—84no—
107C22×C127#12112yes—
108C22×C127C22×D411yescharacteristic
109C4×C127—24no—
110C4×C127—41no—
111C4×C127—42no—
112C4×C127#12112yes—
113C4×C127C22×D411yescharacteristic
114C4×C127C2×#4111yescharacteristic
115C2×C127—22no—
116C2×C127—44no—
117C2×C127—81no—
118C2×C127—82no—
119C2×C127C2×#12111yescharacteristic
120C2×C127#57612yes—
121#3041C12711yesmaximal, characteristic, direct product factor, Sylow
122C127#304111yescharacteristic, direct product factor, Sylow
123C2×AGL(1,ℤ/8)C2×C12711yescharacteristic, complemented
124C22×D8C2×C12711yescharacteristic, complemented
125#535C2×C12711yescharacteristic, complemented
126#518C2×C12711yescharacteristic, complemented
127#463C2×C12714yescomplemented
128#459C2×C12714yescomplemented
129#424C2×C12711yescharacteristic, complemented
130#418C2×C12711yescharacteristic, complemented
131#416C2×C12711yescharacteristic, complemented
132C2×#41C22×C12711yescharacteristic
133C22×D4C22×C12711yescharacteristic
134C22×D4C22×C12711yescharacteristic
135AGL(1,ℤ/8)—24no—
136C2×SD16C22×C12712yescomplemented
137C2×D8—24no—
138C2×D8C22×C12714yes—
139C2×D8C22×C12712yescomplemented
140C2×M16C22×C12711yescharacteristic
141C22×C8C22×C12711yescharacteristic
142#127C22×C12712yescomplemented
143#124C22×C12712yescomplemented
144#121—22no—
145#120—22no—
146C4×D4—22no—
147C4×D4C22×C12714yescomplemented
148#117C22×C12711yescharacteristic
149#117C22×C12711yescharacteristic
150C2×C22⋊C4—22no—
151C4⋊C8C22×C12714yescomplemented
152#103C22×C12712yescomplemented
153#102C22×C12712yescomplemented
154#102C22×C12714yescomplemented
155C24—21no—
156C24—21no—
157#41—22no—
158#41—22no—
159C2×Q8C23×C12711yescharacteristic
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—22no—
163C2×D4—21no—
164C2×D4—24no—
165C2×D4—22no—
166C2×D4—22no—
167C2×D4D4×C12714yescomplemented
168C2×D4C23×C12712yes—
169C2×D4C23×C12711yescharacteristic
170C2×D4C23×C12712yes—
171C22×C4—21no—
172C22×C4—24no—
173C22×C4C23×C12711yescharacteristic
174SD16—24no—
175D8—28no—
176D8—24no—
177M16—22no—
178C2×C8—22no—
179C2×C8C23×C12712yes—
180C2×C8C23×C12712yes—
181C4⋊C4D4×C12712yes—
182C4⋊C4C23×C12712yes—
183C22⋊C4—21no—
184C22⋊C4—24no—
185C22⋊C4—24no—
186C22⋊C4D4×C12712yes—
187C42—21no—
188C42C23×C12712yes—
189C23—22no—
190C23—24no—
191C23—22no—
192C23—21no—
193C23—42no—
194C23—82no—
195C23—82no—
196C23C2×D4×C12711yescharacteristic
197Q8—21no—
198Q8—21no—
199D4—24no—
200D4—22no—
201D4—21no—
202D4—22no—
203D4—22no—
204D4—21no—
205D4—42no—
206D4—42no—
207D4—84no—
208D4C2×D4×C12714yes—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—42no—
212C2×C4—84no—
213C2×C4C2×D4×C12714yes—
214C2×C4C2×D4×C12711yescharacteristic
215C2×C4C2×D4×C12712yes—
216C2×C4#41×C12712yes—
217C2×C4C24×C12711yescharacteristic
218C8—22no—
219C8—22no—
220C22—22no—
221C22—24no—
222C22—44no—
223C22—41no—
224C22—42no—
225C22—42no—
226C22—44no—
227C22—84no—
228C22—84no—
229C22#121×C12712yes—
230C22C22×D4×C12711yescharacteristic
231C4—24no—
232C4—41no—
233C4—42no—
234C4#121×C12712yes—
235C4C22×D4×C12711yescharacteristic
236C4C2×#41×C12711yescharacteristic
237C2—22no—
238C2—44no—
239C2—82no—
240C2—81no—
241C2C2×#121×C12711yescharacteristic
242C2#576×C12712yes—
subgroupG/H
center, socleC22×C127C22×D4
commutator, Frattini, cosocleC2×C4C24×C127
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ #117×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×AGL(1,ℤ/8)×C127C2semidirect
2. C22×D8×C127C2semidirect
3. #535×C127C2semidirect
4. #518×C127C2semidirect
5. #463×C127C2semidirect
6. #459×C127C2semidirect
7. #424×C127C2semidirect
8. #418×C127C2semidirect
9. #416×C127C2semidirect
14. C2×SD16×C127C22semidirect
17. C2×D8×C127C22semidirect
20. #127×C127C22semidirect
21. #124×C127C22semidirect
25. C4×D4×C127C22semidirect
29. C4⋊C8×C127C22semidirect
30. #103×C127C22semidirect
31. #102×C127C22semidirect
32. #102×C127C22semidirect
45. C2×D4×C127D4semidirect
121. #3041C127direct (N × H)
122. C127#3041direct (N × H)
123. C2×AGL(1,ℤ/8)C2×C127semidirect
124. C22×D8C2×C127semidirect
125. #535C2×C127semidirect
126. #518C2×C127semidirect
127. #463C2×C127semidirect
128. #459C2×C127semidirect
129. #424C2×C127semidirect
130. #418C2×C127semidirect
131. #416C2×C127semidirect
136. C2×SD16C22×C127semidirect
139. C2×D8C22×C127semidirect
142. #127C22×C127semidirect
143. #124C22×C127semidirect
147. C4×D4C22×C127semidirect
151. C4⋊C8C22×C127semidirect
152. #103C22×C127semidirect
153. #102C22×C127semidirect
154. #102C22×C127semidirect
167. C2×D4D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×AGL(1,ℤ/8)×C1272
C22×D8×C1272
#535×C1272
#518×C1272
#463×C1272
#459×C1272
#424×C1272
#418×C1272
#416×C1272
#3041127