Finite Group Databasebeta

← C11×#2664 #13065502

Subgroups — C11×#2664 #13065502

Order 1408.

434 conjugacy classes of subgroups.

The subgroup lattice has 248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#126C211yesmaximal, characteristic
2C2×C11×#125C211yesmaximal, characteristic, complemented
3C11×#400C211yesmaximal, characteristic, complemented
4C11×#399C211yesmaximal, characteristic
5C11×#398C211yesmaximal, characteristic, complemented
6C11×#398C212yesmaximal, complemented
7C11×#397C211yesmaximal, characteristic
8C11×#396C212yesmaximal
9C11×#389C212yesmaximal, complemented
10C11×#388C212yesmaximal
11C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
12C11×#126—24no—
13C11×#125—24no—
14C2×C11×C4⋊C4C2212yes—
15C2×C11×C4⋊C4C2212yes—
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C4⋊C4C2212yes—
18C2×C11×C4⋊C4C2212yes—
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C11×C4⋊C4C2211yescharacteristic
23C2×C11×C4⋊C4C2212yes—
24C2×C11×C22⋊C4C2211yescharacteristic
25C2×C11×C22⋊C4C2212yes—
26C2×C11×C22⋊C4C2211yescharacteristic
27C2×C11×C22⋊C4C2211yescharacteristic
28C2×C11×C22⋊C4C2212yes—
29C2×C42×C11C2212yes—
30C2×C42×C11C2211yescharacteristic
31C11×#95C2211yescharacteristic
32C11×#95C2211yescharacteristic
33C11×#95C2212yes—
34C11×#95C2212yes—
35C11×#95C2212yes—
36C11×#95C2212yes—
37C24×C11C2311yescharacteristic
38C22×C4×C11C2312yes—
39C22×C4×C11C2311yescharacteristic
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2312yes—
43C22×C4×C11C2312yes—
44C22×C4×C11C2311yescharacteristic
45C22×C4×C11C2311yescharacteristic
46C22×C4×C11C2311yescharacteristic
47C22×C4×C11C2312yes—
48C11×C4⋊C4—24no—
49C11×C4⋊C4—24no—
50C11×C4⋊C4—22no—
51C11×C4⋊C4—22no—
52C11×C4⋊C4—22no—
53C11×C4⋊C4—22no—
54C11×C4⋊C4—22no—
55C11×C4⋊C4—24no—
56C11×C4⋊C4—24no—
57C11×C4⋊C4—42no—
58C11×C22⋊C4—22no—
59C11×C22⋊C4—22no—
60C11×C22⋊C4—22no—
61C11×C22⋊C4—24no—
62C11×C22⋊C4—42no—
63C42×C11—42no—
64C42×C11D414yes—
65#2664C1111yesmaximal, characteristic, direct product factor, Sylow
66C23×C11—21no—
67C23×C11—22no—
68C23×C11—21no—
69C23×C11—22no—
70C23×C11—21no—
71C23×C11C2411yescharacteristic
72C2×C4×C11—22no—
73C2×C4×C11—21no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—21no—
77C2×C4×C11—22no—
78C2×C4×C11—21no—
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—21no—
90C2×C4×C11—22no—
91C2×C4×C11—21no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11C2×D412yes—
95C2×C4×C11C2×D412yes—
96C2×C4×C11C2×D412yes—
97C2×C4×C11#4114yes—
98C2×#126C2×C1111yescharacteristic
99C2×#125C2×C1111yescharacteristic, complemented
100#400C2×C1111yescharacteristic, complemented
101#399C2×C1111yescharacteristic
102#398C2×C1111yescharacteristic, complemented
103#398C2×C1112yescomplemented
104#397C2×C1111yescharacteristic
105#396C2×C1112yes—
106#389C2×C1112yescomplemented
107#388C2×C1112yes—
108C4×C4⋊C4C2×C1111yescharacteristic, complemented
109C22×C11—41no—
110C22×C11—41no—
111C22×C11—41no—
112C22×C11—42no—
113C22×C11—42no—
114C22×C11C22×D411yescharacteristic
115C22×C11C2×#4112yes—
116C22×C11H(5,𝔽2)11yescharacteristic
117C22×C112−1+412yes—
118C22×C112−1+411yescharacteristic
119C4×C11—22no—
120C4×C11—22no—
121C4×C11—22no—
122C4×C11—24no—
123C4×C11—41no—
124C4×C11—42no—
125C4×C11—41no—
126C4×C11—41no—
127C4×C11—42no—
128C4×C11—42no—
129#126—24no—
130#125—24no—
131C2×C4⋊C4C22×C1112yes—
132C2×C4⋊C4C22×C1112yes—
133C2×C4⋊C4C22×C1111yescharacteristic
134C2×C4⋊C4C22×C1111yescharacteristic
135C2×C4⋊C4C22×C1111yescharacteristic
136C2×C4⋊C4C22×C1111yescharacteristic
137C2×C4⋊C4C22×C1111yescharacteristic
138C2×C4⋊C4C22×C1112yes—
139C2×C4⋊C4C22×C1112yes—
140C2×C4⋊C4C22×C1112yes—
141C2×C22⋊C4C22×C1111yescharacteristic
142C2×C22⋊C4C22×C1111yescharacteristic
143C2×C22⋊C4C22×C1111yescharacteristic
144C2×C22⋊C4C22×C1112yes—
145C2×C22⋊C4C22×C1112yes—
146C2×C42C22×C1112yes—
147C2×C42C22×C1111yescharacteristic
148#95C22×C1111yescharacteristic
149#95C22×C1111yescharacteristic
150#95C22×C1112yes—
151#95C22×C1112yes—
152#95C22×C1112yes—
153#95C22×C1112yes—
154C2×C11—81no—
155C2×C11#53211yescharacteristic
156C2×C11#53611yescharacteristic
157C2×C11#53711yescharacteristic
158C2×C11#53912yes—
159C2×C11#54112yes—
160C24C23×C1111yescharacteristic
161C22×C4C23×C1112yes—
162C22×C4C23×C1111yescharacteristic
163C22×C4C23×C1111yescharacteristic
164C22×C4C23×C1111yescharacteristic
165C22×C4C23×C1112yes—
166C22×C4C23×C1112yes—
167C22×C4C23×C1111yescharacteristic
168C22×C4C23×C1111yescharacteristic
169C22×C4C23×C1111yescharacteristic
170C22×C4C23×C1112yes—
171C4⋊C4—24no—
172C4⋊C4—24no—
173C4⋊C4—22no—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—22no—
177C4⋊C4—22no—
178C4⋊C4—24no—
179C4⋊C4—24no—
180C4⋊C4—42no—
181C22⋊C4—22no—
182C22⋊C4—22no—
183C22⋊C4—22no—
184C22⋊C4—24no—
185C22⋊C4—42no—
186C42—42no—
187C42D4×C1114yes—
188C11#266411yescharacteristic, direct product factor, Sylow
189C23—21no—
190C23—22no—
191C23—21no—
192C23—22no—
193C23—21no—
194C23C24×C1111yescharacteristic
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4C2×D4×C1112yes—
218C2×C4C2×D4×C1112yes—
219C2×C4C2×D4×C1112yes—
220C2×C4C11×#4114yes—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—42no—
225C22—42no—
226C22C22×D4×C1111yescharacteristic
227C22C2×C11×#4112yes—
228C22C11×H(5,𝔽2)11yescharacteristic
229C22C11×2−1+412yes—
230C22C11×2−1+411yescharacteristic
231C4—22no—
232C4—22no—
233C4—22no—
234C4—24no—
235C4—41no—
236C4—42no—
237C4—41no—
238C4—41no—
239C4—42no—
240C4—42no—
241C2—81no—
242C2C11×#53211yescharacteristic
243C2C11×#53611yescharacteristic
244C2C11×#53711yescharacteristic
245C2C11×#53912yes—
246C2C11×#54112yes—
subgroupG/H
center, socleC23×C11C24
commutator, Frattini, cosocleC23C24×C11
prime radicalC24×C11C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#125C2semidirect
3. C11×#400C2semidirect
5. C11×#398C2semidirect
6. C11×#398C2semidirect
9. C11×#389C2semidirect
11. C4×C11×C4⋊C4C2semidirect
65. #2664C11direct (N × H)
99. C2×#125C2×C11semidirect
100. #400C2×C11semidirect
102. #398C2×C11semidirect
103. #398C2×C11semidirect
106. #389C2×C11semidirect
108. C4×C4⋊C4C2×C11semidirect
188. C11#2664direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#1262
C2×C11×#1252
C11×#4002
C11×#3992
C11×#3982
C11×#3972
C11×#3962
C11×#3892
C11×#3882
C4×C11×C4⋊C42
#266411