Finite Group Databasebeta

← C2×#64225 #10596498

Subgroups — C2×#64225 #10596498

Order 576.

574 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 97 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×#3802C212yesmaximal, complemented
2C2×#3787C211yesmaximal, characteristic, complemented
3C2×#3774C214yesmaximal, complemented
4#64225C218yesmaximal, direct product factor
5C22×D32—22no—
6C2×C4×C3⋊D3C2211yescharacteristic
7C2×C3×D12—22no—
8C2×#625C2214yescomplemented
9#3802—24no—
10#3802C2218yescomplemented
11C2×#622C2212yescomplemented
12#3787C2214yescomplemented
13#3774C22116yescomplemented
14C2×D3×D4—62no—
15C22×C3⋊D3D411yescharacteristic
16C22×C3×D3—24no—
17C2×D32—28no—
18C2×D32—48no—
19C2×C32×C4D411yescharacteristic
20C2×C3⋊Dic3C2311yescharacteristic
21C4×C3⋊D3D412yes—
22C4×C3⋊D3C2312yes—
23C3×D12—28no—
24#625—24no—
25#625C2318yescomplemented
26#622C2314yescomplemented
27C22×D8—91nomaximal, Sylow
28C23×D3—64no—
29C2×C3×D4—62no—
30C2×#67—64no—
31D3×D4—68no—
32D3×D4—68no—
33C2×D12—22no—
34C2×C4×D3—62no—
35C22×C32C2×D411yescharacteristic
36C2×C3⋊D3D814yescomplemented
37C2×C3⋊D3C2×D412yes—
38C2×C3×D3—28no—
39C2×C3×D3—48no—
40D32—416no—
41C32×C4C2×D412yes—
42C3⋊Dic3C2×D411yescharacteristic
43C3⋊Dic3C2411yescharacteristic
44C22×D4—92no—
45C2×D8—98no—
46C2×D8—94no—
47C22×C8—91no—
48C23×C3—64no—
49C22×D3—24no—
50C22×D3—62no—
51C22×D3—616no—
52C22×D3—1216no—
53C3×D4—68no—
54C2×C3×C4—22no—
55#67—68no—
56#67—68no—
57C2×Dic3—62no—
58D12—28no—
59C4×D3—64no—
60C4×D3—64no—
61C2×C32C2×D812yescomplemented
62C2×C32C22×D411yescharacteristic
63C3⋊D3C2×D814yescomplemented
64C3×D3—48no—
65C24—182no—
66C2×D4—62no—
67C2×D4—98no—
68C2×D4—94no—
69C2×D4—184no—
70C22×C4—91no—
71D8—916no—
72C2×C8—94no—
73C2×C8—92no—
74C22×C3—22no—
75C22×C3—68no—
76C22×C3—128no—
77C2×D3—28no—
78C2×D3—48no—
79C2×D3—64no—
80C2×D3—68no—
81C2×D3—1232no—
82C3×C4—24no—
83Dic3—62no—
84Dic3—62no—
85C32C22×D811yescharacteristic, complemented, Sylow
86C23—64no—
87C23—91no—
88C23—188no—
89C23—368no—
90D4—68no—
91D4—98no—
92D4—184no—
93C2×C4—91no—
94C2×C4—92no—
95C2×C4—92no—
96C2×C4GO+(4,𝔽2)11yescharacteristic
97C8—94no—
98C2×C3—22no—
99C2×C3—24no—
100C2×C3—128no—
101D3—48no—
102D3—68no—
103C22—68no—
104C22—92no—
105C22—94no—
106C22—128no—
107C22—3616no—
108C22C2×GO+(4,𝔽2)11yescharacteristic
109C4—91no—
110C4—91no—
111C4C2×GO+(4,𝔽2)12yes—
112C3—22no—
113C2—94no—
114C2—128no—
115C2#6422512yesdirect product factor
116C2C22×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
centerC22C2×GO+(4,𝔽2)
commutator, cosocleC3⋊Dic3C24
FrattiniC2C22×GO+(4,𝔽2)
FittingC2×C32×C4D4
socleC22×C32C2×D4
hypercenterC2×C4GO+(4,𝔽2)
hypocenterC32C22×D8
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#3802C2semidirect
2. C2×#3787C2semidirect
3. C2×#3774C2semidirect
4. #64225C2direct (N × H)
8. C2×#625C22semidirect
10. #3802C22semidirect
11. C2×#622C22semidirect
12. #3787C22semidirect
13. #3774C22semidirect
25. #625C23semidirect
26. #622C23semidirect
36. C2×C3⋊D3D8semidirect
61. C2×C32C2×D8semidirect
63. C3⋊D3C2×D8semidirect
85. C32C22×D8semidirect
115. C2#64225direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#38022
C2×#37872
C2×#37742
#642252
C22×D89