Finite Group Databasebeta

← C2×#10620145 #13049679

Subgroups — C2×#10620145 #13049679

Order 1296.

2136 conjugacy classes of subgroups; only the 378 normal subgroups are shown.

normal subgroups only

This group has 2136 conjugacy classes of subgroups — too many to draw. Only its 378 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
1C22×C3×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C22×C33×D3C211yesmaximal, characteristic, complemented
3C2×C3⋊(C3⋊(C3⋊Dic3))C211yesmaximal, characteristic, complemented
4#10620145C214yesmaximal, direct product factor
5C2×#6312—31nomaximal
6C2×#6290—313nomaximal
7C22×C34C2211yescharacteristic
8C2×C3×C3⋊(C3⋊D3)—22no—
9C2×C3×C3⋊(C3⋊D3)C2212yescomplemented
10C2×C33×D3—22no—
11C2×C33×D3C2212yescomplemented
12C3⋊(C3⋊(C3⋊Dic3))C2212yescomplemented
13C23×C33—31no—
14C22×C3⋊(C3⋊D3)D311yescharacteristic, complemented
15C22×C3×C3⋊D3—313no—
16C22×C32×D3D3113yescomplemented
17#6312—34no—
18C2×C3⋊(C3⋊Dic3)—31no—
19C2×C3⋊(C3⋊Dic3)—313no—
20C2×C3⋊(C3⋊Dic3)—613no—
21#6290—352no—
22C2×C34D412yescomplemented
23C2×C34C2311yescharacteristic
24C3×C3⋊(C3⋊D3)—22no—
25C33×D3—22no—
26C2×#638—913no—
27C2×#625—913no—
28C22×C33—213no—
29C22×C33—32no—
30C22×C33—62no—
31C22×C33C2×D3113yes—
32C22×C33C2×D311yescharacteristic
33C2×C3⋊(C3⋊D3)—22no—
34C2×C3⋊(C3⋊D3)C2×D312yescomplemented
35C2×C3×C3⋊D3—326no—
36C2×C3×C3⋊D3—626no—
37C2×C32×D3—226no—
38C2×C32×D3C2×D3126yescomplemented
39C3⋊(C3⋊Dic3)—32no—
40C3⋊(C3⋊Dic3)—326no—
41C3⋊(C3⋊Dic3)—626no—
42C34C2×D411yescharacteristic, complemented, Sylow
43C23×C32—313no—
44C22×C3⋊D3—313no—
45C22×C3×D3—913no—
46C22×C3×D3C3⋊D3113yescomplemented
47#638—952no—
48C2×C3⋊Dic3—913no—
49C2×C3⋊Dic3—913no—
50C2×C3⋊Dic3—1852no—
51#625—952no—
52C2×C33—226no—
53C2×C33—213no—
54C2×C33—62no—
55C2×C33#67126yescomplemented
56C2×C33#6712yescomplemented
57C2×C33C22×D3113yes—
58C2×C33C22×D311yescharacteristic
59C3⋊(C3⋊D3)—22no—
60C3×C3⋊D3—626no—
61C32×D3—226no—
62C2×#67—2713no—
63C2×#67—271no—
64C22×C32—252no—
65C22×C32—326no—
66C22×C32—626no—
67C22×C32D32113yes—
68C22×C32C2×C3⋊D3113yes—
69C2×C3⋊D3—326no—
70C2×C3⋊D3—626no—
71C2×C3×D3—226no—
72C2×C3×D3—926no—
73C2×C3×D3—1826no—
74C2×C3×D3C2×C3⋊D3126yescomplemented
75C3⋊Dic3—926no—
76C3⋊Dic3—926no—
77C3⋊Dic3—18104no—
78C33—213no—
79C33C2×#67113yescomplemented
80C33C2×#6711yescharacteristic, complemented
81C23×C3—313no—
82C23×C3—271no—
83C22×D3—913no—
84C22×D3C3⋊(C3⋊D3)11yescharacteristic, complemented
85#67—2752no—
86#67—274no—
87C2×Dic3—2713no—
88C2×Dic3—271no—
89C2×Dic3—5413no—
90C2×C32—2104no—
91C2×C32—252no—
92C2×C32—626no—
93C2×C32#625126yescomplemented
94C2×C32#638126yescomplemented
95C2×C32C2×D32113yes—
96C2×C32C22×C3⋊D3113yes—
97C3⋊D3—626no—
98C3×D3—226no—
99C3×D3—1826no—
100C2×D4—811noSylow
101C22×C3—213no—
102C22×C3—326no—
103C22×C3—626no—
104C22×C3—272no—
105C22×C3—542no—
106C22×C3D3×C3⋊D3113yes—
107C22×C3C2×C3⋊(C3⋊D3)11yescharacteristic
108C2×D3—22no—
109C2×D3—926no—
110C2×D3—1826no—
111C2×D3C2×C3⋊(C3⋊D3)12yescomplemented
112Dic3—2726no—
113Dic3—272no—
114Dic3—5426no—
115C32—252no—
116C32C2×#625113yescomplemented
117C32C2×#638113yescomplemented
118C23—31no—
119C23—271no—
120D4—814no—
121C2×C4—811no—
122C2×C3—213no—
123C2×C3—226no—
124C2×C3—626no—
125C2×C3—542no—
126C2×C3#6290126yescomplemented
127C2×C3#631212yescomplemented
128C2×C3C2×D3×C3⋊D3113yes—
129C2×C3C22×C3⋊(C3⋊D3)11yescharacteristic
130D3—22no—
131D3—1826no—
132C22—32no—
133C22—62no—
134C22—272no—
135C22—542no—
136C22D3×C3⋊(C3⋊D3)11yescharacteristic
137C4—812no—
138C3—213no—
139C3C2×#6290113yescomplemented
140C3C2×#631211yescharacteristic, complemented
141C2—62no—
142C2—542no—
143C2#1062014512yesdirect product factor
144C2C2×D3×C3⋊(C3⋊D3)11yescharacteristic
subgroupG/H
center, hypercenterC22D3×C3⋊(C3⋊D3)
commutator, cosocleC2×C34C23
FrattiniC2C2×D3×C3⋊(C3⋊D3)
Fitting, socleC22×C34C22
hypocenterC34C2×D4
LCSG ▷ C2×C34 ▷ C34
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C3×C3⋊(C3⋊D3)C2semidirect
2. C22×C33×D3C2semidirect
3. C2×C3⋊(C3⋊(C3⋊Dic3))C2semidirect
4. #10620145C2direct (N × H)
9. C2×C3×C3⋊(C3⋊D3)C22semidirect
11. C2×C33×D3C22semidirect
12. C3⋊(C3⋊(C3⋊Dic3))C22semidirect
14. C22×C3⋊(C3⋊D3)D3semidirect
16. C22×C32×D3D3semidirect
22. C2×C34D4semidirect
34. C2×C3⋊(C3⋊D3)C2×D3semidirect
38. C2×C32×D3C2×D3semidirect
42. C34C2×D4semidirect
46. C22×C3×D3C3⋊D3semidirect
55. C2×C33#67semidirect
56. C2×C33#67semidirect
74. C2×C3×D3C2×C3⋊D3semidirect
79. C33C2×#67semidirect
80. C33C2×#67semidirect
84. C22×D3C3⋊(C3⋊D3)semidirect
93. C2×C32#625semidirect
94. C2×C32#638semidirect
111. C2×D3C2×C3⋊(C3⋊D3)semidirect
116. C32C2×#625semidirect
117. C32C2×#638semidirect
126. C2×C3#6290semidirect
127. C2×C3#6312semidirect
139. C3C2×#6290semidirect
140. C3C2×#6312semidirect
143. C2#10620145direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C3⋊(C3⋊D3)2
C22×C33×D32
C2×C3⋊(C3⋊(C3⋊Dic3))2
#106201452
C2×#63123
C2×#62903