Finite Group Databasebeta

← C11×#2901 #13065739

Subgroups — C11×#2901 #13065739

Order 1408.

738 conjugacy classes of subgroups; only the 340 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 340 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
1C11×#585C211yesmaximal, characteristic
2C11×#568C211yesmaximal, characteristic, complemented
3C4×C11×#41C211yesmaximal, characteristic, complemented
4C11×#421C216yesmaximal, complemented
5C2×C11×#104C216yesmaximal, complemented
6C11×2−1+4—21no—
7C11×2−1+4C414yescomplemented
8C11×H(5,𝔽2)—23no—
9C11×H(5,𝔽2)C414yescomplemented
10C2×C11×#41—24no—
11C2×C11×#41C2216yes—
12C2×C11×#41C2211yescharacteristic
13C11×#131—24no—
14C2×C11×M16C2216yescomplemented
15C4×Q8×C11—21no—
16C4×D4×C11—23no—
17C11×#117C2213yescomplemented
18C2×C42×C11C2213yescomplemented
19C11×#104C2214yescomplemented
20C11×#104C22112yescomplemented
21C11×#41—24no—
22C11×#41—212no—
23C11×#41—26no—
24C11×#41—26no—
25C11×#41C2×C414yes—
26C11×#41C2×C4112yescomplemented
27C11×#41D414yes—
28C11×#41C2314yes—
29C2×Q8×C11—24no—
30C2×Q8×C11C2×C416yescomplemented
31C2×Q8×C11D411yescharacteristic
32C2×D4×C11—26no—
33C2×D4×C11—212no—
34C2×D4×C11C2×C416yescomplemented
35C2×D4×C11D413yes—
36C22×C4×C11—26no—
37C22×C4×C11—23no—
38C22×C4×C11C2313yes—
39C11×M16—26no—
40C11×M16C2314yes—
41C2×C8×C11—26no—
42C11×C4⋊C4—23no—
43C11×C22⋊C4—23no—
44C42×C11—23no—
45C42×C11C2311yescharacteristic
46C42×C11C2313yes—
47#2901C1111yesmaximal, characteristic, direct product factor, Sylow
48C23×C11—26no—
49C23×C11C2×D413yes—
50Q8×C11—26no—
51Q8×C11C22⋊C414yes—
52Q8×C11C22×C414yes—
53D4×C11—212no—
54D4×C11—24no—
55D4×C11—26no—
56D4×C11C22⋊C4112yes—
57D4×C11C22×C414yes—
58C2×C4×C11—26no—
59C2×C4×C11—21no—
60C2×C4×C11—212no—
61C2×C4×C11—24no—
62C2×C4×C11—23no—
63C2×C4×C11—46no—
64C2×C4×C11C22×C416yes—
65C2×C4×C11C2×D413yes—
66C2×C4×C11C2×D416yes—
67C2×C4×C11C2411yescharacteristic
68C8×C11—24no—
69#585C2×C1111yescharacteristic
70#568C2×C1111yescharacteristic, complemented
71C4×#41C2×C1111yescharacteristic, complemented
72#421C2×C1116yescomplemented
73C2×#104C2×C1116yescomplemented
74C22×C11—24no—
75C22×C11—43no—
76C22×C11—86no—
77C22×C11C2×C22⋊C416yes—
78C22×C11C22×D411yescharacteristic
79C4×C11—22no—
80C4×C11—24no—
81C4×C11—43no—
82C4×C11C2×C22⋊C416yes—
83C4×C11C23×C411yescharacteristic
84C4×C11C22×D411yescharacteristic
852−1+4—21no—
862−1+4C4×C1114yescomplemented
87H(5,𝔽2)—23no—
88H(5,𝔽2)C4×C1114yescomplemented
89C2×#41—24no—
90C2×#41C22×C1116yes—
91C2×#41C22×C1111yescharacteristic
92#131—24no—
93C2×M16C22×C1116yescomplemented
94C4×Q8—21no—
95C4×D4—23no—
96#117C22×C1113yescomplemented
97C2×C42C22×C1113yescomplemented
98#104C22×C1114yescomplemented
99#104C22×C11112yescomplemented
100C2×C11—21no—
101C2×C11—26no—
102C2×C11—44no—
103C2×C11C22×C22⋊C411yescharacteristic
104#41—24no—
105#41—212no—
106#41—26no—
107#41—26no—
108#41C2×C4×C1114yes—
109#41C2×C4×C11112yescomplemented
110#41D4×C1114yes—
111#41C23×C1114yes—
112C2×Q8—24no—
113C2×Q8C2×C4×C1116yescomplemented
114C2×Q8D4×C1111yescharacteristic
115C2×D4—26no—
116C2×D4—212no—
117C2×D4C2×C4×C1116yescomplemented
118C2×D4D4×C1113yes—
119C22×C4—26no—
120C22×C4—23no—
121C22×C4C23×C1113yes—
122M16—26no—
123M16C23×C1114yes—
124C2×C8—26no—
125C4⋊C4—23no—
126C22⋊C4—23no—
127C42—23no—
128C42C23×C1111yescharacteristic
129C42C23×C1113yes—
130C11#290111yescharacteristic, direct product factor, Sylow
131C23—26no—
132C23C2×D4×C1113yes—
133Q8—26no—
134Q8C11×C22⋊C414yes—
135Q8C22×C4×C1114yes—
136D4—212no—
137D4—24no—
138D4—26no—
139D4C11×C22⋊C4112yes—
140D4C22×C4×C1114yes—
141C2×C4—26no—
142C2×C4—21no—
143C2×C4—212no—
144C2×C4—24no—
145C2×C4—23no—
146C2×C4—46no—
147C2×C4C22×C4×C1116yes—
148C2×C4C2×D4×C1113yes—
149C2×C4C2×D4×C1116yes—
150C2×C4C24×C1111yescharacteristic
151C8—24no—
152C22—24no—
153C22—43no—
154C22—86no—
155C22C2×C11×C22⋊C416yes—
156C22C22×D4×C1111yescharacteristic
157C4—22no—
158C4—24no—
159C4—43no—
160C4C2×C11×C22⋊C416yes—
161C4C23×C4×C1111yescharacteristic
162C4C22×D4×C1111yescharacteristic
163C2—21no—
164C2—26no—
165C2—44no—
166C2C22×C11×C22⋊C411yescharacteristic
subgroupG/H
centerC4×C11C22×D4
commutatorC4C23×C4×C11
Frattini, cosocleC2×C4C24×C11
socleC2×C11C22×C22⋊C4
prime radicalC11×#585C2
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C11 ◁ C2×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#568C2semidirect
3. C4×C11×#41C2semidirect
4. C11×#421C2semidirect
5. C2×C11×#104C2semidirect
7. C11×2−1+4C4semidirect
9. C11×H(5,𝔽2)C4semidirect
14. C2×C11×M16C22semidirect
17. C11×#117C22semidirect
18. C2×C42×C11C22semidirect
19. C11×#104C22semidirect
20. C11×#104C22semidirect
26. C11×#41C2×C4semidirect
30. C2×Q8×C11C2×C4semidirect
34. C2×D4×C11C2×C4semidirect
47. #2901C11direct (N × H)
70. #568C2×C11semidirect
71. C4×#41C2×C11semidirect
72. #421C2×C11semidirect
73. C2×#104C2×C11semidirect
86. 2−1+4C4×C11semidirect
88. H(5,𝔽2)C4×C11semidirect
93. C2×M16C22×C11semidirect
96. #117C22×C11semidirect
97. C2×C42C22×C11semidirect
98. #104C22×C11semidirect
99. #104C22×C11semidirect
109. #41C2×C4×C11semidirect
113. C2×Q8C2×C4×C11semidirect
117. C2×D4C2×C4×C11semidirect
130. C11#2901direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#5852
C11×#5682
C4×C11×#412
C11×#4212
C2×C11×#1042
#290111