Finite Group Databasebeta

← C11×#3192 #13066030

Subgroups — C11×#3192 #13066030

Order 1408.

514 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 176 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#121C212yesmaximal, complemented
2C11×#481C214yesmaximal, complemented
3C11×#469C214yesmaximal, complemented
4C11×#447C214yesmaximal, complemented
5C11×#407C211yesmaximal, characteristic, complemented
6C22×D4×C11—22no—
7C22×D4×C11C2212yescomplemented
8C23×C4×C11C2211yescharacteristic
9C2×C11×D8C2214yescomplemented
10C2×C11×M16C2212yescomplemented
11C11×#121—22no—
12C11×#121—22no—
13C11×#121C2214yes—
14C11×#121C2214yescomplemented
15C2×C11×C4⋊C4C2212yescomplemented
16C2×C11×C22⋊C4—22no—
17C11×#106C2214yescomplemented
18C11×#102C2218yescomplemented
19C11×C22⋊C8C2214yescomplemented
20C24×C11—22no—
21C24×C11D411yescharacteristic
22C2×D4×C11—24no—
23C2×D4×C11—24no—
24C2×D4×C11—22no—
25C2×D4×C11—44no—
26C2×D4×C11—48no—
27C2×D4×C11C2314yes—
28C22×C4×C11—22no—
29C22×C4×C11—42no—
30C22×C4×C11D412yes—
31C22×C4×C11D411yescharacteristic
32C22×C4×C11C2312yes—
33C22×C4×C11C2311yescharacteristic
34C11×D8—44no—
35C11×M16—42no—
36C2×C8×C11C2314yes—
37C11×C4⋊C4—22no—
38C11×C4⋊C4C2314yes—
39C11×C22⋊C4—24no—
40C11×C22⋊C4—24no—
41#3192C1111yesmaximal, characteristic, direct product factor, Sylow
42C23×C11—24no—
43C23×C11—24no—
44C23×C11—41no—
45C23×C11—44no—
46C23×C11—44no—
47C23×C11—44no—
48C23×C11C2×D411yescharacteristic
49C23×C11C2×D412yes—
50D4×C11—28no—
51D4×C11—44no—
52D4×C11—48no—
53D4×C11—48no—
54C2×C4×C11—22no—
55C2×C4×C11—24no—
56C2×C4×C11—24no—
57C2×C4×C11—42no—
58C2×C4×C11—41no—
59C2×C4×C11—44no—
60C2×C4×C11C2×D411yescharacteristic
61C2×C4×C11C2×D412yes—
62C2×C4×C11C2411yescharacteristic
63C8×C11—24no—
64C2×#121C2×C1112yescomplemented
65#481C2×C1114yescomplemented
66#469C2×C1114yescomplemented
67#447C2×C1114yescomplemented
68#407C2×C1111yescharacteristic, complemented
69C22×C11—22no—
70C22×C11—22no—
71C22×C11—21no—
72C22×C11—22no—
73C22×C11—44no—
74C22×C11—44no—
75C22×C11—44no—
76C22×C11—44no—
77C22×C11—88no—
78C22×C11AGL(1,ℤ/8)14yes—
79C22×C11C22×D411yescharacteristic
80C4×C11—21no—
81C4×C11—22no—
82C4×C11—44no—
83C4×C11H(5,𝔽2)12yes—
84C22×D4—22no—
85C22×D4C22×C1112yescomplemented
86C23×C4C22×C1111yescharacteristic
87C2×D8C22×C1114yescomplemented
88C2×M16C22×C1112yescomplemented
89#121—22no—
90#121—22no—
91#121C22×C1114yes—
92#121C22×C1114yescomplemented
93C2×C4⋊C4C22×C1112yescomplemented
94C2×C22⋊C4—22no—
95#106C22×C1114yescomplemented
96#102C22×C1118yescomplemented
97C22⋊C8C22×C1114yescomplemented
98C2×C11—24no—
99C2×C11—41no—
100C2×C11—84no—
101C2×C11#53411yescharacteristic
102C2×C11C2×AGL(1,ℤ/8)12yes—
103C24—22no—
104C24D4×C1111yescharacteristic
105C2×D4—24no—
106C2×D4—24no—
107C2×D4—22no—
108C2×D4—44no—
109C2×D4—48no—
110C2×D4C23×C1114yes—
111C22×C4—22no—
112C22×C4—42no—
113C22×C4D4×C1112yes—
114C22×C4D4×C1111yescharacteristic
115C22×C4C23×C1112yes—
116C22×C4C23×C1111yescharacteristic
117D8—44no—
118M16—42no—
119C2×C8C23×C1114yes—
120C4⋊C4—22no—
121C4⋊C4C23×C1114yes—
122C22⋊C4—24no—
123C22⋊C4—24no—
124C11#319211yescharacteristic, direct product factor, Sylow
125C23—24no—
126C23—24no—
127C23—41no—
128C23—44no—
129C23—44no—
130C23—44no—
131C23C2×D4×C1111yescharacteristic
132C23C2×D4×C1112yes—
133D4—28no—
134D4—44no—
135D4—48no—
136D4—48no—
137C2×C4—22no—
138C2×C4—24no—
139C2×C4—24no—
140C2×C4—41no—
141C2×C4—42no—
142C2×C4—44no—
143C2×C4C2×D4×C1111yescharacteristic
144C2×C4C2×D4×C1112yes—
145C2×C4C24×C1111yescharacteristic
146C8—24no—
147C22—22no—
148C22—22no—
149C22—21no—
150C22—22no—
151C22—44no—
152C22—44no—
153C22—44no—
154C22—44no—
155C22—88no—
156C22C11×AGL(1,ℤ/8)14yes—
157C22C22×D4×C1111yescharacteristic
158C4—22no—
159C4—21no—
160C4—44no—
161C4C11×H(5,𝔽2)12yes—
162C2—24no—
163C2—41no—
164C2—84no—
165C2C11×#53411yescharacteristic
166C2C2×C11×AGL(1,ℤ/8)12yes—
subgroupG/H
center, socleC22×C11C22×D4
commutator, Frattini, cosocleC2×C4C24×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#121C2semidirect
2. C11×#481C2semidirect
3. C11×#469C2semidirect
4. C11×#447C2semidirect
5. C11×#407C2semidirect
7. C22×D4×C11C22semidirect
9. C2×C11×D8C22semidirect
10. C2×C11×M16C22semidirect
14. C11×#121C22semidirect
15. C2×C11×C4⋊C4C22semidirect
17. C11×#106C22semidirect
18. C11×#102C22semidirect
19. C11×C22⋊C8C22semidirect
41. #3192C11direct (N × H)
64. C2×#121C2×C11semidirect
65. #481C2×C11semidirect
66. #469C2×C11semidirect
67. #447C2×C11semidirect
68. #407C2×C11semidirect
85. C22×D4C22×C11semidirect
87. C2×D8C22×C11semidirect
88. C2×M16C22×C11semidirect
92. #121C22×C11semidirect
93. C2×C4⋊C4C22×C11semidirect
95. #106C22×C11semidirect
96. #102C22×C11semidirect
97. C22⋊C8C22×C11semidirect
124. C11#3192direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#1212
C11×#4812
C11×#4692
C11×#4472
C11×#4072
#319211