Finite Group Databasebeta

← C127×#2376 #30635328

Subgroups — C127×#2376 #30635328

Order 16256.

512 conjugacy classes of subgroups.

The subgroup lattice has 254 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#123×C127C211yesmaximal, characteristic
2#390×C127C211yesmaximal, characteristic
3#389×C127C212yesmaximal, complemented
4#388×C127C212yesmaximal, complemented
5#388×C127C212yesmaximal, complemented
6#387×C127C212yesmaximal, complemented
7#386×C127C211yesmaximal, characteristic
8#385×C127C212yesmaximal, complemented
9#380×C127C212yesmaximal, complemented
10C22×D4×C127C2211yescharacteristic
11C23×C4×C127C2211yescharacteristic
12C23×C4×C127C2211yescharacteristic
13#123×C127C418yescomplemented
14C2×C4⋊C4×C127C2212yes—
15C2×C4⋊C4×C127C2212yes—
16C2×C4⋊C4×C127C2212yes—
17C2×C4⋊C4×C127C2211yescharacteristic
18C2×C4⋊C4×C127C2212yes—
19C2×C22⋊C4×C127C2212yes—
20C2×C22⋊C4×C127C2212yes—
21C2×C22⋊C4×C127C2212yes—
22C2×C22⋊C4×C127C2211yescharacteristic
23C2×C22⋊C4×C127C2212yes—
24C2×C22⋊C4×C127C2211yescharacteristic
25C2×C42×C127C2211yescharacteristic
26C2×C42×C127C2212yes—
27#95×C127C2212yes—
28#95×C127C2212yes—
29#95×C127C2212yes—
30#95×C127C2212yes—
31#95×C127C2212yes—
32C24×C127C2311yescharacteristic
33C24×C127C2311yescharacteristic
34C2×D4×C127—41no—
35C2×D4×C127—41no—
36C2×D4×C127C2×C414yes—
37C22×C4×C127—41no—
38C22×C4×C127—41no—
39C22×C4×C127—42no—
40C22×C4×C127—41no—
41C22×C4×C127C2×C414yescomplemented
42C22×C4×C127C2312yes—
43C22×C4×C127C2312yes—
44C22×C4×C127C2312yes—
45C22×C4×C127C2312yes—
46C22×C4×C127C2312yes—
47C22×C4×C127C2311yescharacteristic
48C22×C4×C127C2312yes—
49C4⋊C4×C127—42no—
50C4⋊C4×C127—42no—
51C4⋊C4×C127—42no—
52C4⋊C4×C127—41no—
53C4⋊C4×C127C2×C418yescomplemented
54C22⋊C4×C127—42no—
55C22⋊C4×C127—42no—
56C22⋊C4×C127—42no—
57C22⋊C4×C127—41no—
58C22⋊C4×C127C2×C418yes—
59C22⋊C4×C127C2×C414yescomplemented
60C42×C127—42no—
61C42×C127—41no—
62C23×C127—22no—
63C23×C127—22no—
64C23×C127—21no—
65C23×C127—21no—
66C23×C127—21no—
67C23×C127—21no—
68C23×C127—22no—
69C23×C127—22no—
70C23×C127C22×C412yes—
71C23×C127C22×C412yes—
72C23×C127C2411yescharacteristic
73D4×C127—44no—
74C2×C4×C127—22no—
75C2×C4×C127—21no—
76C2×C4×C127—22no—
77C2×C4×C127—22no—
78C2×C4×C127—21no—
79C2×C4×C127—22no—
80C2×C4×C127—22no—
81C2×C4×C127—22no—
82C2×C4×C127—22no—
83C2×C4×C127—22no—
84C2×C4×C127—22no—
85C2×C4×C127—22no—
86C2×C4×C127—22no—
87C2×C4×C127—22no—
88C2×C4×C127—22no—
89C2×C4×C127—22no—
90C2×C4×C127—22no—
91C2×C4×C127—22no—
92C2×C4×C127—44no—
93C2×C4×C127—44no—
94C2×C4×C127C22×C414yes—
95C2×C4×C127C22×C414yes—
96C2×C4×C127C22×C412yes—
97C22×C127—22no—
98C22×C127—22no—
99C22×C127—24no—
100C22×C127—24no—
101C22×C127—41no—
102C22×C127—41no—
103C22×C127—42no—
104C22×C127—42no—
105C22×C127—41no—
106C22×C127—41no—
107C22×C127C23×C411yescharacteristic
108C22×C127H(5,𝔽2)11yescharacteristic
109C22×C127H(5,𝔽2)11yescharacteristic
110C22×C127H(5,𝔽2)12yes—
111C22×C1272−1+412yes—
112C4×C127—24no—
113C4×C127—22no—
114C4×C127—24no—
115C4×C127—42no—
116C4×C127—42no—
117C4×C127—42no—
118C4×C127—42no—
119C2×C127—42no—
120C2×C127—42no—
121C2×C127#51811yescharacteristic
122C2×C127#52012yes—
123C2×C127#56011yescharacteristic
124C2×C127#56212yes—
125C2×C127#56311yescharacteristic
126#2376C12711yesmaximal, characteristic, direct product factor, Sylow
127C127#237611yescharacteristic, direct product factor, Sylow
128C2×#123C2×C12711yescharacteristic
129#390C2×C12711yescharacteristic
130#389C2×C12712yescomplemented
131#388C2×C12712yescomplemented
132#388C2×C12712yescomplemented
133#387C2×C12712yescomplemented
134#386C2×C12711yescharacteristic
135#385C2×C12712yescomplemented
136#380C2×C12712yescomplemented
137C22×D4C22×C12711yescharacteristic
138C23×C4C22×C12711yescharacteristic
139C23×C4C22×C12711yescharacteristic
140#123C4×C12718yescomplemented
141C2×C4⋊C4C22×C12712yes—
142C2×C4⋊C4C22×C12712yes—
143C2×C4⋊C4C22×C12712yes—
144C2×C4⋊C4C22×C12711yescharacteristic
145C2×C4⋊C4C22×C12712yes—
146C2×C22⋊C4C22×C12712yes—
147C2×C22⋊C4C22×C12712yes—
148C2×C22⋊C4C22×C12712yes—
149C2×C22⋊C4C22×C12711yescharacteristic
150C2×C22⋊C4C22×C12712yes—
151C2×C22⋊C4C22×C12711yescharacteristic
152C2×C42C22×C12711yescharacteristic
153C2×C42C22×C12712yes—
154#95C22×C12712yes—
155#95C22×C12712yes—
156#95C22×C12712yes—
157#95C22×C12712yes—
158#95C22×C12712yes—
159C24C23×C12711yescharacteristic
160C24C23×C12711yescharacteristic
161C2×D4—41no—
162C2×D4—41no—
163C2×D4C2×C4×C12714yes—
164C22×C4—41no—
165C22×C4—41no—
166C22×C4—42no—
167C22×C4—41no—
168C22×C4C2×C4×C12714yescomplemented
169C22×C4C23×C12712yes—
170C22×C4C23×C12712yes—
171C22×C4C23×C12712yes—
172C22×C4C23×C12712yes—
173C22×C4C23×C12712yes—
174C22×C4C23×C12711yescharacteristic
175C22×C4C23×C12712yes—
176C4⋊C4—42no—
177C4⋊C4—42no—
178C4⋊C4—42no—
179C4⋊C4—41no—
180C4⋊C4C2×C4×C12718yescomplemented
181C22⋊C4—42no—
182C22⋊C4—42no—
183C22⋊C4—42no—
184C22⋊C4—41no—
185C22⋊C4C2×C4×C12718yes—
186C22⋊C4C2×C4×C12714yescomplemented
187C42—42no—
188C42—41no—
189C23—22no—
190C23—22no—
191C23—21no—
192C23—21no—
193C23—21no—
194C23—21no—
195C23—22no—
196C23—22no—
197C23C22×C4×C12712yes—
198C23C22×C4×C12712yes—
199C23C24×C12711yescharacteristic
200D4—44no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—44no—
220C2×C4—44no—
221C2×C4C22×C4×C12714yes—
222C2×C4C22×C4×C12714yes—
223C2×C4C22×C4×C12712yes—
224C22—22no—
225C22—22no—
226C22—24no—
227C22—24no—
228C22—41no—
229C22—41no—
230C22—42no—
231C22—42no—
232C22—41no—
233C22—41no—
234C22C23×C4×C12711yescharacteristic
235C22H(5,𝔽2)×C12711yescharacteristic
236C22H(5,𝔽2)×C12711yescharacteristic
237C22H(5,𝔽2)×C12712yes—
238C222−1+4×C12712yes—
239C4—24no—
240C4—22no—
241C4—24no—
242C4—42no—
243C4—42no—
244C4—42no—
245C4—42no—
246C2—42no—
247C2—42no—
248C2#518×C12711yescharacteristic
249C2#520×C12712yes—
250C2#560×C12711yescharacteristic
251C2#562×C12712yes—
252C2#563×C12711yescharacteristic
subgroupG/H
center, socleC23×C127C24
commutatorC22C23×C4×C127
Frattini, cosocleC23C24×C127
prime radicalC22×D4×C127C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. #389×C127C2semidirect
4. #388×C127C2semidirect
5. #388×C127C2semidirect
6. #387×C127C2semidirect
8. #385×C127C2semidirect
9. #380×C127C2semidirect
13. #123×C127C4semidirect
41. C22×C4×C127C2×C4semidirect
53. C4⋊C4×C127C2×C4semidirect
59. C22⋊C4×C127C2×C4semidirect
126. #2376C127direct (N × H)
127. C127#2376direct (N × H)
130. #389C2×C127semidirect
131. #388C2×C127semidirect
132. #388C2×C127semidirect
133. #387C2×C127semidirect
135. #385C2×C127semidirect
136. #380C2×C127semidirect
140. #123C4×C127semidirect
168. C22×C4C2×C4×C127semidirect
180. C4⋊C4C2×C4×C127semidirect
186. C22⋊C4C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#123×C1272
#390×C1272
#389×C1272
#388×C1272
#387×C1272
#386×C1272
#385×C1272
#380×C1272
#2376127