Finite Group Databasebeta

← C2×D3×D12 #64303

Subgroups — C2×D3×D12 #64303

Order 288.

499 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 499 conjugacy classes of subgroups — too many to draw. Only its 132 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×D32C212yesmaximal, complemented
2C2×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3C2×C3×D12C211yesmaximal, characteristic, complemented
4C2×C3×C4×D3C211yesmaximal, characteristic, complemented
5C2×#626C212yesmaximal, complemented
6D3×D12C218yesmaximal, direct product factor
7C2×D3×D4—31nomaximal
8C22×D12—31nomaximal
9C22×C3⋊D3C2212yescomplemented
10C22×C3×D3C2211yescharacteristic
11C22×C3×D3C2212yescomplemented
12C2×D32—28no—
13C2×D32C2218yescomplemented
14C2×C32×C4C2211yescharacteristic, complemented
15C4⋊(C3⋊D3)C2214yescomplemented
16C2×C3×Dic3C2211yescharacteristic, complemented
17C3×D12C2214yescomplemented
18C3×C4×D3C2214yescomplemented
19#626C2218yescomplemented
20C23×D3—32no—
21C23×D3—32no—
22C2×C3×D4—31no—
23C22×C3×C4—31no—
24C2×#67—32no—
25D3×D4—38no—
26C2×D12—32no—
27C2×D12—31no—
28C2×D12—31no—
29C2×D12—38no—
30C2×D12—61no—
31C2×D12D311yescharacteristic, direct product factor
32C2×C4×D3D311yescharacteristic, complemented
33C22×C32C2311yescharacteristic
34C2×C3⋊D3—24no—
35C2×C3⋊D3C2314yescomplemented
36C2×C3×D3—24no—
37C2×C3×D3D414yescomplemented
38C2×C3×D3C2312yes—
39C2×C3×D3C2314yescomplemented
40D32—216no—
41C32×C4C2312yescomplemented
42C3×Dic3C2312yescomplemented
43C22×D4—91noSylow
44C23×C3—31no—
45C23×C3—32no—
46C22×D3—32no—
47C22×D3—32no—
48C22×D3—38no—
49C22×D3—38no—
50C22×D3—62no—
51C22×D3—68no—
52C22×D3—68no—
53C22×D3C2×D311yescharacteristic
54C22×D3C2×D312yescomplemented
55C3×D4—34no—
56C2×C3×C4—21no—
57C2×C3×C4—31no—
58C2×C3×C4—34no—
59C2×C3×C4C2×D311yescharacteristic, complemented
60C2×C3×C4C2×D311yescharacteristic, complemented
61#67—38no—
62C2×Dic3C2×D311yescharacteristic, complemented
63D12—38no—
64D12—34no—
65D12—34no—
66D12—64no—
67D12C2×D314yesdirect product factor
68C4×D3C2×D314yescomplemented
69C2×C32C2×D412yescomplemented
70C2×C32C2411yescharacteristic
71C3⋊D3—24no—
72C3×D3—24no—
73C3×D3C2×D414yescomplemented
74C24—92no—
75C2×D4—31no—
76C2×D4—98no—
77C2×D4—92no—
78C2×D4—91no—
79C22×C4—31no—
80C22×C3—21no—
81C22×C3—34no—
82C22×C3—32no—
83C22×C3—34no—
84C22×C3—64no—
85C22×C3C22×D311yescharacteristic
86C22×C3C22×D311yescharacteristic
87C2×D3—24no—
88C2×D3—34no—
89C2×D3—34no—
90C2×D3—64no—
91C2×D3—616no—
92C2×D3—64no—
93C2×D3—64no—
94C2×D3—616no—
95C2×D3—124no—
96C2×D3D1214yesdirect product factor
97C2×D3C22×D312yes—
98C2×D3C22×D314yescomplemented
99C3×C4—22no—
100C3×C4—32no—
101C3×C4C22×D312yescomplemented
102C3×C4C22×D312yescomplemented
103Dic3C22×D312yescomplemented
104C32C22×D411yescharacteristic, complemented, Sylow
105C23—31no—
106C23—32no—
107C23—98no—
108C23—92no—
109C23—188no—
110D4—34no—
111D4—98no—
112D4—94no—
113C2×C4—31no—
114C2×C4—34no—
115C2×C4D3211yescharacteristic, complemented
116C2×C3—21no—
117C2×C3—22no—
118C2×C3—34no—
119C2×C3—64no—
120C2×C3C2×D1212yescomplemented
121C2×C3D3×D412yescomplemented
122C2×C3C23×D311yescharacteristic
123C2×C3C23×D311yescharacteristic
124D3—24no—
125D3—64no—
126D3—64no—
127D3—124no—
128D3C2×D1214yesdirect product factor
129C22—32no—
130C22—34no—
131C22—34no—
132C22—64no—
133C22—94no—
134C22—1816no—
135C22—184no—
136C22C2×D3211yescharacteristic
137C4—32no—
138C4C2×D3212yescomplemented
139C3—21no—
140C3C22×D1211yescharacteristic, complemented
141C3C2×D3×D411yescharacteristic, complemented
142C2—34no—
143C2—64no—
144C2—184no—
145C2D3×D1212yesdirect product factor
146C2C22×D3211yescharacteristic
subgroupG/H
centerC22C2×D32
commutator, cosocleC2×C32C24
FrattiniC2C22×D32
FittingC2×C32×C4C22
socleC22×C32C23
hypercenterC2×C4D32
hypocenterC32C22×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C22×D32C2semidirect
2. C2×C4⋊(C3⋊D3)C2semidirect
3. C2×C3×D12C2semidirect
4. C2×C3×C4×D3C2semidirect
5. C2×#626C2semidirect
6. D3×D12C2direct (N × H)
9. C22×C3⋊D3C22semidirect
11. C22×C3×D3C22semidirect
13. C2×D32C22semidirect
14. C2×C32×C4C22semidirect
15. C4⋊(C3⋊D3)C22semidirect
16. C2×C3×Dic3C22semidirect
17. C3×D12C22semidirect
18. C3×C4×D3C22semidirect
19. #626C22semidirect
31. C2×D12D3direct (N × H)
32. C2×C4×D3D3semidirect
35. C2×C3⋊D3C23semidirect
37. C2×C3×D3D4semidirect
39. C2×C3×D3C23semidirect
41. C32×C4C23semidirect
42. C3×Dic3C23semidirect
54. C22×D3C2×D3semidirect
59. C2×C3×C4C2×D3semidirect
60. C2×C3×C4C2×D3semidirect
62. C2×Dic3C2×D3semidirect
67. D12C2×D3direct (N × H)
68. C4×D3C2×D3semidirect
69. C2×C32C2×D4semidirect
73. C3×D3C2×D4semidirect
96. C2×D3D12direct (N × H)
98. C2×D3C22×D3semidirect
101. C3×C4C22×D3semidirect
102. C3×C4C22×D3semidirect
103. Dic3C22×D3semidirect
104. C32C22×D4semidirect
115. C2×C4D32semidirect
120. C2×C3C2×D12semidirect
121. C2×C3D3×D4semidirect
128. D3C2×D12direct (N × H)
138. C4C2×D32semidirect
140. C3C22×D12semidirect
141. C3C2×D3×D4semidirect
145. C2D3×D12direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D322
C2×C4⋊(C3⋊D3)2
C2×C3×D122
C2×C3×C4×D32
C2×#6262
D3×D122
C2×D3×D43
C22×D123