Finite Group Databasebeta

← C127×#3197 #30636149

Subgroups — C127×#3197 #30636149

Order 16256.

418 conjugacy classes of subgroups.

The subgroup lattice has 238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#525×C127C212yesmaximal, complemented
2#485×C127C212yesmaximal, complemented
3#482×C127C212yesmaximal, complemented
4#470×C127C211yesmaximal, characteristic, complemented
5#469×C127C211yesmaximal, characteristic, complemented
6#468×C127C212yesmaximal, complemented
7#452×C127C212yesmaximal, complemented
8#449×C127C212yesmaximal, complemented
9#407×C127C211yesmaximal, characteristic, complemented
10C2×#41×C127C2212yes—
11C23×C4×C127C2211yescharacteristic
12C2×Q16×C127C2211yescharacteristic, complemented
13C2×SD16×C127C2212yescomplemented
14C2×D8×C127C2211yescharacteristic, complemented
15C2×M16×C127C2211yescharacteristic
16C2×M16×C127C2211yescharacteristic
17#123×C127—22no—
18C22⋊Q8×C127C2212yes—
19C22⋊Q8×C127C2212yes—
20#121×C127C2212yes—
21#121×C127C2212yes—
22#120×C127—22no—
23C4×D4×C127—22no—
24C4×D4×C127—22no—
25#117×C127C2212yes—
26#107×C127C2212yescomplemented
27#106×C127C2211yescharacteristic, complemented
28#106×C127C2211yescharacteristic, complemented
29#103×C127C2212yescomplemented
30#103×C127C2212yescomplemented
31#102×C127C2212yescomplemented
32#102×C127C2212yescomplemented
33C22⋊C8×C127C2212yes—
34C22⋊C8×C127C2212yes—
35C24×C127D411yescharacteristic
36#41×C127—42no—
37#41×C127—42no—
38C2×Q8×C127C2312yes—
39C2×D4×C127—22no—
40C2×D4×C127—22no—
41C2×D4×C127—22no—
42C2×D4×C127C2312yes—
43C22×C4×C127—22no—
44C22×C4×C127—41no—
45C22×C4×C127—41no—
46C22×C4×C127D411yescharacteristic
47C22×C4×C127D412yes—
48C22×C4×C127C2312yes—
49C22×C4×C127C2311yescharacteristic
50Q16×C127—41no—
51SD16×C127—42no—
52D8×C127—41no—
53M16×C127—41no—
54M16×C127—41no—
55C2×C8×C127C2311yescharacteristic
56C2×C8×C127C2312yes—
57C2×C8×C127C2311yescharacteristic
58C4⋊C4×C127—22no—
59C4⋊C4×C127—22no—
60C4⋊C4×C127C2312yes—
61C4⋊C4×C127C2312yes—
62C22⋊C4×C127—22no—
63C22⋊C4×C127—22no—
64C22⋊C4×C127—22no—
65C22⋊C4×C127—22no—
66C22⋊C4×C127—22no—
67C42×C127—22no—
68C23×C127—22no—
69C23×C127—41no—
70C23×C127—42no—
71C23×C127C2×D412yes—
72C23×C127C2×D411yescharacteristic
73Q8×C127—22no—
74Q8×C127—22no—
75D4×C127—22no—
76D4×C127—22no—
77D4×C127—44no—
78D4×C127—44no—
79D4×C127—44no—
80C2×C4×C127—21no—
81C2×C4×C127—21no—
82C2×C4×C127—22no—
83C2×C4×C127—22no—
84C2×C4×C127—22no—
85C2×C4×C127—22no—
86C2×C4×C127—22no—
87C2×C4×C127—41no—
88C2×C4×C127—42no—
89C2×C4×C127—44no—
90C2×C4×C127C2×D412yes—
91C2×C4×C127C2×D411yescharacteristic
92C2×C4×C127C2411yescharacteristic
93C8×C127—21no—
94C8×C127—22no—
95C8×C127—21no—
96C22×C127—22no—
97C22×C127—21no—
98C22×C127—22no—
99C22×C127—22no—
100C22×C127—22no—
101C22×C127—44no—
102C22×C127—42no—
103C22×C127—42no—
104C22×C127—42no—
105C22×C127C22×D411yescharacteristic
106C4×C127—22no—
107C4×C127—21no—
108C4×C127—42no—
109C4×C127—42no—
110C4×C127—42no—
111C4×C127H(5,𝔽2)11yescharacteristic
112C4×C127H(5,𝔽2)11yescharacteristic
113C2×C127—42no—
114C2×C127—41no—
115C2×C127—82no—
116C2×C127#53411yescharacteristic
117C2×C127#57512yes—
118#3197C12711yesmaximal, characteristic, direct product factor, Sylow
119C127#319711yescharacteristic, direct product factor, Sylow
120#525C2×C12712yescomplemented
121#485C2×C12712yescomplemented
122#482C2×C12712yescomplemented
123#470C2×C12711yescharacteristic, complemented
124#469C2×C12711yescharacteristic, complemented
125#468C2×C12712yescomplemented
126#452C2×C12712yescomplemented
127#449C2×C12712yescomplemented
128#407C2×C12711yescharacteristic, complemented
129C2×#41C22×C12712yes—
130C23×C4C22×C12711yescharacteristic
131C2×Q16C22×C12711yescharacteristic, complemented
132C2×SD16C22×C12712yescomplemented
133C2×D8C22×C12711yescharacteristic, complemented
134C2×M16C22×C12711yescharacteristic
135C2×M16C22×C12711yescharacteristic
136#123—22no—
137C22⋊Q8C22×C12712yes—
138C22⋊Q8C22×C12712yes—
139#121C22×C12712yes—
140#121C22×C12712yes—
141#120—22no—
142C4×D4—22no—
143C4×D4—22no—
144#117C22×C12712yes—
145#107C22×C12712yescomplemented
146#106C22×C12711yescharacteristic, complemented
147#106C22×C12711yescharacteristic, complemented
148#103C22×C12712yescomplemented
149#103C22×C12712yescomplemented
150#102C22×C12712yescomplemented
151#102C22×C12712yescomplemented
152C22⋊C8C22×C12712yes—
153C22⋊C8C22×C12712yes—
154C24D4×C12711yescharacteristic
155#41—42no—
156#41—42no—
157C2×Q8C23×C12712yes—
158C2×D4—22no—
159C2×D4—22no—
160C2×D4—22no—
161C2×D4C23×C12712yes—
162C22×C4—22no—
163C22×C4—41no—
164C22×C4—41no—
165C22×C4D4×C12711yescharacteristic
166C22×C4D4×C12712yes—
167C22×C4C23×C12712yes—
168C22×C4C23×C12711yescharacteristic
169Q16—41no—
170SD16—42no—
171D8—41no—
172M16—41no—
173M16—41no—
174C2×C8C23×C12711yescharacteristic
175C2×C8C23×C12712yes—
176C2×C8C23×C12711yescharacteristic
177C4⋊C4—22no—
178C4⋊C4—22no—
179C4⋊C4C23×C12712yes—
180C4⋊C4C23×C12712yes—
181C22⋊C4—22no—
182C22⋊C4—22no—
183C22⋊C4—22no—
184C22⋊C4—22no—
185C22⋊C4—22no—
186C42—22no—
187C23—22no—
188C23—41no—
189C23—42no—
190C23C2×D4×C12712yes—
191C23C2×D4×C12711yescharacteristic
192Q8—22no—
193Q8—22no—
194D4—22no—
195D4—22no—
196D4—44no—
197D4—44no—
198D4—44no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—42no—
208C2×C4—44no—
209C2×C4C2×D4×C12712yes—
210C2×C4C2×D4×C12711yescharacteristic
211C2×C4C24×C12711yescharacteristic
212C8—21no—
213C8—22no—
214C8—21no—
215C22—22no—
216C22—21no—
217C22—22no—
218C22—22no—
219C22—22no—
220C22—44no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22C22×D4×C12711yescharacteristic
225C4—22no—
226C4—21no—
227C4—42no—
228C4—42no—
229C4—42no—
230C4H(5,𝔽2)×C12711yescharacteristic
231C4H(5,𝔽2)×C12711yescharacteristic
232C2—42no—
233C2—41no—
234C2—82no—
235C2#534×C12711yescharacteristic
236C2#575×C12712yes—
subgroupG/H
center, socleC22×C127C22×D4
commutator, Frattini, cosocleC2×C4C24×C127
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. #525×C127C2semidirect
2. #485×C127C2semidirect
3. #482×C127C2semidirect
4. #470×C127C2semidirect
5. #469×C127C2semidirect
6. #468×C127C2semidirect
7. #452×C127C2semidirect
8. #449×C127C2semidirect
9. #407×C127C2semidirect
12. C2×Q16×C127C22semidirect
13. C2×SD16×C127C22semidirect
14. C2×D8×C127C22semidirect
26. #107×C127C22semidirect
27. #106×C127C22semidirect
28. #106×C127C22semidirect
29. #103×C127C22semidirect
30. #103×C127C22semidirect
31. #102×C127C22semidirect
32. #102×C127C22semidirect
118. #3197C127direct (N × H)
119. C127#3197direct (N × H)
120. #525C2×C127semidirect
121. #485C2×C127semidirect
122. #482C2×C127semidirect
123. #470C2×C127semidirect
124. #469C2×C127semidirect
125. #468C2×C127semidirect
126. #452C2×C127semidirect
127. #449C2×C127semidirect
128. #407C2×C127semidirect
131. C2×Q16C22×C127semidirect
132. C2×SD16C22×C127semidirect
133. C2×D8C22×C127semidirect
145. #107C22×C127semidirect
146. #106C22×C127semidirect
147. #106C22×C127semidirect
148. #103C22×C127semidirect
149. #103C22×C127semidirect
150. #102C22×C127semidirect
151. #102C22×C127semidirect

Maximal subgroups

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

subgroupindex
#525×C1272
#485×C1272
#482×C1272
#470×C1272
#469×C1272
#468×C1272
#452×C1272
#449×C1272
#407×C1272
#3197127