Finite Group Databasebeta

← C127×#3200 #30636152

Subgroups — C127×#3200 #30636152

Order 16256.

410 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#536×C127C211yesmaximal, characteristic, complemented
2#535×C127C211yesmaximal, characteristic
3#485×C127C212yesmaximal, complemented
4#482×C127C212yesmaximal, complemented
5#468×C127C212yesmaximal, complemented
6#465×C127C212yesmaximal, complemented
7#450×C127C212yesmaximal, complemented
8#448×C127C212yesmaximal, complemented
9#408×C127C211yesmaximal, characteristic, complemented
10C2×#41×C127C2211yescharacteristic
11C22×Q8×C127C2211yescharacteristic, complemented
12C22×D4×C127C2211yescharacteristic
13C2×SD16×C127C2212yes—
14C2×SD16×C127C2212yes—
15C2×M16×C127C2211yescharacteristic, complemented
16C22×C8×C127C2211yescharacteristic, complemented
17C4⋊Q8×C127—21no—
18#127×C127—21no—
19#124×C127—21no—
20#124×C127—21no—
21#123×C127—21no—
22#123×C127—21no—
23C22⋊Q8×C127C2212yes—
24C22⋊Q8×C127C2212yescomplemented
25#121×C127C2212yes—
26#121×C127C2212yes—
27#120×C127—21no—
28#120×C127—21no—
29#117×C127C2211yescharacteristic
30#117×C127C2211yescharacteristic, complemented
31#107×C127C2212yescomplemented
32#106×C127C2212yescomplemented
33#103×C127C2212yescomplemented
34#103×C127C2212yescomplemented
35#102×C127C2212yes—
36#102×C127C2212yes—
37C22⋊C8×C127C2212yes—
38C22⋊C8×C127C2212yescomplemented
39C24×C127—21no—
40#41×C127—41no—
41#41×C127—41no—
42C2×Q8×C127—21no—
43C2×Q8×C127—41no—
44C2×Q8×C127—41no—
45C2×Q8×C127D411yescharacteristic
46C2×Q8×C127C2312yes—
47C2×D4×C127—22no—
48C2×D4×C127—22no—
49C2×D4×C127—21no—
50C2×D4×C127—41no—
51C2×D4×C127—41no—
52C2×D4×C127D411yescharacteristic
53C2×D4×C127D411yescharacteristic
54C2×D4×C127D411yescharacteristic
55C2×D4×C127C2312yes—
56C22×C4×C127—21no—
57C22×C4×C127C2311yescharacteristic
58C22×C4×C127C2311yescharacteristic
59C22×C4×C127C2311yescharacteristic
60SD16×C127—42no—
61SD16×C127—42no—
62M16×C127—41no—
63C2×C8×C127—41no—
64C2×C8×C127C2312yes—
65C2×C8×C127C2312yes—
66C4⋊C4×C127—22no—
67C4⋊C4×C127—22no—
68C4⋊C4×C127C2312yes—
69C4⋊C4×C127C2312yes—
70C22⋊C4×C127—21no—
71C22⋊C4×C127—21no—
72C22⋊C4×C127—22no—
73C22⋊C4×C127—22no—
74C22⋊C4×C127—22no—
75C22⋊C4×C127—22no—
76C42×C127—21no—
77C42×C127—21no—
78C23×C127—22no—
79C23×C127—42no—
80C23×C127—82no—
81C23×C127C2×D411yescharacteristic
82C23×C127C2×D411yescharacteristic
83C23×C127C2×D411yescharacteristic
84Q8×C127—22no—
85Q8×C127—22no—
86Q8×C127—41no—
87Q8×C127—42no—
88D4×C127—22no—
89D4×C127—22no—
90D4×C127—41no—
91D4×C127—41no—
92D4×C127—41no—
93D4×C127—42no—
94D4×C127—82no—
95D4×C127—82no—
96C2×C4×C127—21no—
97C2×C4×C127—21no—
98C2×C4×C127—21no—
99C2×C4×C127—21no—
100C2×C4×C127—21no—
101C2×C4×C127—21no—
102C2×C4×C127—22no—
103C2×C4×C127—22no—
104C2×C4×C127—22no—
105C2×C4×C127—42no—
106C2×C4×C127C2×D411yescharacteristic
107C2×C4×C127C2×D411yescharacteristic
108C2×C4×C127C2×D411yescharacteristic
109C2×C4×C127C2411yescharacteristic
110C8×C127—22no—
111C8×C127—22no—
112C22×C127—21no—
113C22×C127—21no—
114C22×C127—21no—
115C22×C127—22no—
116C22×C127—22no—
117C22×C127—22no—
118C22×C127—42no—
119C22×C127—42no—
120C22×C127—42no—
121C22×C127—84no—
122C22×C127C22×D411yescharacteristic
123C4×C127—21no—
124C4×C127—21no—
125C4×C127—21no—
126C4×C127—42no—
127C4×C127—42no—
128C4×C127—42no—
129C4×C127H(5,𝔽2)11yescharacteristic
130C4×C127H(5,𝔽2)11yescharacteristic
131C2×C127—41no—
132C2×C127—41no—
133C2×C127—41no—
134C2×C127—82no—
135C2×C127#53411yescharacteristic
136C2×C127#57712yes—
137#3200C12711yesmaximal, characteristic, direct product factor, Sylow
138C127#320011yescharacteristic, direct product factor, Sylow
139#536C2×C12711yescharacteristic, complemented
140#535C2×C12711yescharacteristic
141#485C2×C12712yescomplemented
142#482C2×C12712yescomplemented
143#468C2×C12712yescomplemented
144#465C2×C12712yescomplemented
145#450C2×C12712yescomplemented
146#448C2×C12712yescomplemented
147#408C2×C12711yescharacteristic, complemented
148C2×#41C22×C12711yescharacteristic
149C22×Q8C22×C12711yescharacteristic, complemented
150C22×D4C22×C12711yescharacteristic
151C2×SD16C22×C12712yes—
152C2×SD16C22×C12712yes—
153C2×M16C22×C12711yescharacteristic, complemented
154C22×C8C22×C12711yescharacteristic, complemented
155C4⋊Q8—21no—
156#127—21no—
157#124—21no—
158#124—21no—
159#123—21no—
160#123—21no—
161C22⋊Q8C22×C12712yes—
162C22⋊Q8C22×C12712yescomplemented
163#121C22×C12712yes—
164#121C22×C12712yes—
165#120—21no—
166#120—21no—
167#117C22×C12711yescharacteristic
168#117C22×C12711yescharacteristic, complemented
169#107C22×C12712yescomplemented
170#106C22×C12712yescomplemented
171#103C22×C12712yescomplemented
172#103C22×C12712yescomplemented
173#102C22×C12712yes—
174#102C22×C12712yes—
175C22⋊C8C22×C12712yes—
176C22⋊C8C22×C12712yescomplemented
177C24—21no—
178#41—41no—
179#41—41no—
180C2×Q8—21no—
181C2×Q8—41no—
182C2×Q8—41no—
183C2×Q8D4×C12711yescharacteristic
184C2×Q8C23×C12712yes—
185C2×D4—22no—
186C2×D4—22no—
187C2×D4—21no—
188C2×D4—41no—
189C2×D4—41no—
190C2×D4D4×C12711yescharacteristic
191C2×D4D4×C12711yescharacteristic
192C2×D4D4×C12711yescharacteristic
193C2×D4C23×C12712yes—
194C22×C4—21no—
195C22×C4C23×C12711yescharacteristic
196C22×C4C23×C12711yescharacteristic
197C22×C4C23×C12711yescharacteristic
198SD16—42no—
199SD16—42no—
200M16—41no—
201C2×C8—41no—
202C2×C8C23×C12712yes—
203C2×C8C23×C12712yes—
204C4⋊C4—22no—
205C4⋊C4—22no—
206C4⋊C4C23×C12712yes—
207C4⋊C4C23×C12712yes—
208C22⋊C4—21no—
209C22⋊C4—21no—
210C22⋊C4—22no—
211C22⋊C4—22no—
212C22⋊C4—22no—
213C22⋊C4—22no—
214C42—21no—
215C42—21no—
216C23—22no—
217C23—42no—
218C23—82no—
219C23C2×D4×C12711yescharacteristic
220C23C2×D4×C12711yescharacteristic
221C23C2×D4×C12711yescharacteristic
222Q8—22no—
223Q8—22no—
224Q8—41no—
225Q8—42no—
226D4—22no—
227D4—22no—
228D4—41no—
229D4—41no—
230D4—41no—
231D4—42no—
232D4—82no—
233D4—82no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—42no—
244C2×C4C2×D4×C12711yescharacteristic
245C2×C4C2×D4×C12711yescharacteristic
246C2×C4C2×D4×C12711yescharacteristic
247C2×C4C24×C12711yescharacteristic
248C8—22no—
249C8—22no—
250C22—21no—
251C22—21no—
252C22—21no—
253C22—22no—
254C22—22no—
255C22—22no—
256C22—42no—
257C22—42no—
258C22—42no—
259C22—84no—
260C22C22×D4×C12711yescharacteristic
261C4—21no—
262C4—21no—
263C4—21no—
264C4—42no—
265C4—42no—
266C4—42no—
267C4H(5,𝔽2)×C12711yescharacteristic
268C4H(5,𝔽2)×C12711yescharacteristic
269C2—41no—
270C2—41no—
271C2—41no—
272C2—82no—
273C2#534×C12711yescharacteristic
274C2#577×C12712yes—
subgroupG/H
center, socleC22×C127C22×D4
commutator, Frattini, cosocleC2×C4C24×C127
prime radical#535×C127C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×#41×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. #536×C127C2semidirect
3. #485×C127C2semidirect
4. #482×C127C2semidirect
5. #468×C127C2semidirect
6. #465×C127C2semidirect
7. #450×C127C2semidirect
8. #448×C127C2semidirect
9. #408×C127C2semidirect
11. C22×Q8×C127C22semidirect
15. C2×M16×C127C22semidirect
16. C22×C8×C127C22semidirect
24. C22⋊Q8×C127C22semidirect
30. #117×C127C22semidirect
31. #107×C127C22semidirect
32. #106×C127C22semidirect
33. #103×C127C22semidirect
34. #103×C127C22semidirect
38. C22⋊C8×C127C22semidirect
137. #3200C127direct (N × H)
138. C127#3200direct (N × H)
139. #536C2×C127semidirect
141. #485C2×C127semidirect
142. #482C2×C127semidirect
143. #468C2×C127semidirect
144. #465C2×C127semidirect
145. #450C2×C127semidirect
146. #448C2×C127semidirect
147. #408C2×C127semidirect
149. C22×Q8C22×C127semidirect
153. C2×M16C22×C127semidirect
154. C22×C8C22×C127semidirect
162. C22⋊Q8C22×C127semidirect
168. #117C22×C127semidirect
169. #107C22×C127semidirect
170. #106C22×C127semidirect
171. #103C22×C127semidirect
172. #103C22×C127semidirect
176. C22⋊C8C22×C127semidirect

Maximal subgroups

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

subgroupindex
#536×C1272
#535×C1272
#485×C1272
#482×C1272
#468×C1272
#465×C1272
#450×C1272
#448×C1272
#408×C1272
#3200127