Finite Group Databasebeta

← C127×#2611 #30635563

Subgroups — C127×#2611 #30635563

Order 16256.

476 conjugacy classes of subgroups.

The subgroup lattice has 252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×C127C211yesmaximal, characteristic, complemented
2C2×#117×C127C211yesmaximal, characteristic
3#400×C127C211yesmaximal, characteristic, complemented
4#399×C127C211yesmaximal, characteristic
5#398×C127C211yesmaximal, characteristic, complemented
6#397×C127C211yesmaximal, characteristic
7#389×C127C212yesmaximal, complemented
8#388×C127C212yesmaximal
9#387×C127C212yesmaximal, complemented
10#385×C127C212yesmaximal
11#376×C127C211yesmaximal, characteristic, complemented
12C23×C4×C127C2211yescharacteristic
13#125×C127—24no—
14#117×C127—24no—
15C2×C4⋊C4×C127C2211yescharacteristic
16C2×C4⋊C4×C127C2211yescharacteristic
17C2×C4⋊C4×C127C2212yes—
18C2×C4⋊C4×C127C2212yes—
19C2×C4⋊C4×C127C2211yescharacteristic
20C2×C4⋊C4×C127C2211yescharacteristic
21C2×C4⋊C4×C127C2212yes—
22C2×C4⋊C4×C127C2212yes—
23C2×C22⋊C4×C127C2211yescharacteristic
24C2×C22⋊C4×C127C2211yescharacteristic
25C2×C22⋊C4×C127C2212yes—
26C2×C22⋊C4×C127C2212yes—
27C2×C42×C127C2211yescharacteristic
28C2×C42×C127C2212yes—
29C2×C42×C127C2211yescharacteristic
30#95×C127C2212yes—
31#95×C127C2211yescharacteristic
32#95×C127C2211yescharacteristic
33#95×C127C2212yes—
34#95×C127C2212yes—
35#95×C127C2212yes—
36#95×C127C2212yes—
37C24×C127C2311yescharacteristic
38C22×C4×C127—22no—
39C22×C4×C127—22no—
40C22×C4×C127—22no—
41C22×C4×C127C2312yes—
42C22×C4×C127C2311yescharacteristic
43C22×C4×C127C2311yescharacteristic
44C22×C4×C127C2312yes—
45C22×C4×C127C2312yes—
46C22×C4×C127C2311yescharacteristic
47C22×C4×C127C2311yescharacteristic
48C22×C4×C127C2311yescharacteristic
49C22×C4×C127C2312yes—
50C22×C4×C127C2311yescharacteristic
51C4⋊C4×C127—22no—
52C4⋊C4×C127—22no—
53C4⋊C4×C127—24no—
54C4⋊C4×C127—24no—
55C4⋊C4×C127—22no—
56C4⋊C4×C127—22no—
57C4⋊C4×C127—24no—
58C4⋊C4×C127—24no—
59C22⋊C4×C127—24no—
60C22⋊C4×C127—22no—
61C22⋊C4×C127—22no—
62C22⋊C4×C127—24no—
63C42×C127—22no—
64C42×C127—24no—
65C42×C127D414yes—
66C23×C127—21no—
67C23×C127—22no—
68C23×C127—21no—
69C23×C127—22no—
70C23×C127#4112yes—
71C23×C127C2411yescharacteristic
72C2×C4×C127—28no—
73C2×C4×C127—21no—
74C2×C4×C127—22no—
75C2×C4×C127—22no—
76C2×C4×C127—21no—
77C2×C4×C127—21no—
78C2×C4×C127—21no—
79C2×C4×C127—22no—
80C2×C4×C127—22no—
81C2×C4×C127—21no—
82C2×C4×C127—21no—
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—22no—
93C2×C4×C127—22no—
94C2×C4×C127C2×D412yes—
95C2×C4×C127C2×D412yes—
96C2×C4×C127C2×D412yes—
97C2×C4×C127#4114yes—
98C2×C4×C127#4112yes—
99C22×C127—22no—
100C22×C127—24no—
101C22×C127—41no—
102C22×C127—41no—
103C22×C127—42no—
104C22×C127C22×D411yescharacteristic
105C22×C127C2×#4111yescharacteristic
106C22×C127C2×#4111yescharacteristic
107C22×C127C2×#4112yes—
108C22×C1272−1+412yes—
109C4×C127—22no—
110C4×C127—22no—
111C4×C127—22no—
112C4×C127—22no—
113C4×C127—24no—
114C4×C127—42no—
115C4×C127—41no—
116C4×C127—42no—
117C4×C127—41no—
118C4×C127—42no—
119C2×C127—42no—
120C2×C127#52511yescharacteristic
121C2×C127#53211yescharacteristic
122C2×C127#53611yescharacteristic
123C2×C127#55212yes—
124C2×C127#55212yes—
125#2611C12711yesmaximal, characteristic, direct product factor, Sylow
126C127#261111yescharacteristic, direct product factor, Sylow
127C2×#125C2×C12711yescharacteristic, complemented
128C2×#117C2×C12711yescharacteristic
129#400C2×C12711yescharacteristic, complemented
130#399C2×C12711yescharacteristic
131#398C2×C12711yescharacteristic, complemented
132#397C2×C12711yescharacteristic
133#389C2×C12712yescomplemented
134#388C2×C12712yes—
135#387C2×C12712yescomplemented
136#385C2×C12712yes—
137#376C2×C12711yescharacteristic, complemented
138C23×C4C22×C12711yescharacteristic
139#125—24no—
140#117—24no—
141C2×C4⋊C4C22×C12711yescharacteristic
142C2×C4⋊C4C22×C12711yescharacteristic
143C2×C4⋊C4C22×C12712yes—
144C2×C4⋊C4C22×C12712yes—
145C2×C4⋊C4C22×C12711yescharacteristic
146C2×C4⋊C4C22×C12711yescharacteristic
147C2×C4⋊C4C22×C12712yes—
148C2×C4⋊C4C22×C12712yes—
149C2×C22⋊C4C22×C12711yescharacteristic
150C2×C22⋊C4C22×C12711yescharacteristic
151C2×C22⋊C4C22×C12712yes—
152C2×C22⋊C4C22×C12712yes—
153C2×C42C22×C12711yescharacteristic
154C2×C42C22×C12712yes—
155C2×C42C22×C12711yescharacteristic
156#95C22×C12712yes—
157#95C22×C12711yescharacteristic
158#95C22×C12711yescharacteristic
159#95C22×C12712yes—
160#95C22×C12712yes—
161#95C22×C12712yes—
162#95C22×C12712yes—
163C24C23×C12711yescharacteristic
164C22×C4—22no—
165C22×C4—22no—
166C22×C4—22no—
167C22×C4C23×C12712yes—
168C22×C4C23×C12711yescharacteristic
169C22×C4C23×C12711yescharacteristic
170C22×C4C23×C12712yes—
171C22×C4C23×C12712yes—
172C22×C4C23×C12711yescharacteristic
173C22×C4C23×C12711yescharacteristic
174C22×C4C23×C12711yescharacteristic
175C22×C4C23×C12712yes—
176C22×C4C23×C12711yescharacteristic
177C4⋊C4—22no—
178C4⋊C4—22no—
179C4⋊C4—24no—
180C4⋊C4—24no—
181C4⋊C4—22no—
182C4⋊C4—22no—
183C4⋊C4—24no—
184C4⋊C4—24no—
185C22⋊C4—24no—
186C22⋊C4—22no—
187C22⋊C4—22no—
188C22⋊C4—24no—
189C42—22no—
190C42—24no—
191C42D4×C12714yes—
192C23—21no—
193C23—22no—
194C23—21no—
195C23—22no—
196C23#41×C12712yes—
197C23C24×C12711yescharacteristic
198C2×C4—28no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—21no—
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—22no—
220C2×C4C2×D4×C12712yes—
221C2×C4C2×D4×C12712yes—
222C2×C4C2×D4×C12712yes—
223C2×C4#41×C12714yes—
224C2×C4#41×C12712yes—
225C22—22no—
226C22—24no—
227C22—41no—
228C22—41no—
229C22—42no—
230C22C22×D4×C12711yescharacteristic
231C22C2×#41×C12711yescharacteristic
232C22C2×#41×C12711yescharacteristic
233C22C2×#41×C12712yes—
234C222−1+4×C12712yes—
235C4—22no—
236C4—22no—
237C4—22no—
238C4—22no—
239C4—24no—
240C4—42no—
241C4—41no—
242C4—42no—
243C4—41no—
244C4—42no—
245C2—42no—
246C2#525×C12711yescharacteristic
247C2#532×C12711yescharacteristic
248C2#536×C12711yescharacteristic
249C2#552×C12712yes—
250C2#552×C12712yes—
subgroupG/H
center, socleC23×C127C24
commutator, Frattini, cosocleC23C24×C127
prime radicalC24×C127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#125×C127C2semidirect
3. #400×C127C2semidirect
5. #398×C127C2semidirect
7. #389×C127C2semidirect
9. #387×C127C2semidirect
11. #376×C127C2semidirect
125. #2611C127direct (N × H)
126. C127#2611direct (N × H)
127. C2×#125C2×C127semidirect
129. #400C2×C127semidirect
131. #398C2×C127semidirect
133. #389C2×C127semidirect
135. #387C2×C127semidirect
137. #376C2×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#125×C1272
C2×#117×C1272
#400×C1272
#399×C1272
#398×C1272
#397×C1272
#389×C1272
#388×C1272
#387×C1272
#385×C1272
#376×C1272
#2611127