Finite Group Databasebeta

← C2×#64223 #10596496

Subgroups — C2×#64223 #10596496

Order 576.

430 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 89 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×#3798C212yesmaximal, complemented
2C2×#3787C211yesmaximal, characteristic, complemented
3C2×#3776C211yesmaximal, characteristic, complemented
4C2×#3775C212yesmaximal, complemented
5C2×#3774C211yesmaximal, characteristic, complemented
6#64223C218yesmaximal, direct product factor
7C2×C4×C3⋊D3C2211yescharacteristic
8C2×C3×C4×D3—22no—
9C2×#627C2212yes—
10C2×#626—22no—
11C2×#625C2212yes—
12#3798—24no—
13#3798C2218yescomplemented
14C2×#622C2211yescharacteristic
15C2×#622C2211yescharacteristic
16#3787C2214yescomplemented
17#3776C2214yescomplemented
18#3775C2218yescomplemented
19#3774C2214yescomplemented
20C2×#235—62no—
21C22×C3⋊D3D411yescharacteristic
22C22×C3×D3—22no—
23C2×C32×C4D411yescharacteristic
24C2×C3⋊Dic3C2311yescharacteristic
25C4×C3⋊D3D412yes—
26C4×C3⋊D3C2312yes—
27C2×C3×Dic3—22no—
28C3×C4×D3—28no—
29#627—22no—
30#627C2314yes—
31#626—28no—
32#625—22no—
33#625C2314yes—
34#622C2312yes—
35#622C2312yes—
36C2×#135—91nomaximal, Sylow
37C22×C3×C4—62no—
38C2×#67—62no—
39C2×#67—62no—
40#235—68no—
41#235—68no—
42C2×D12—62no—
43C2×C4×D3—22no—
44C2×C4×D3—62no—
45C2×Dic6—62no—
46C22×C32C2×D411yescharacteristic
47C2×C3⋊D3—22no—
48C2×C3⋊D3C2×D412yes—
49C2×C3×D3—24no—
50C2×C3×D3—44no—
51C32×C4C2×D412yes—
52C3⋊Dic3C2×D411yescharacteristic
53C3⋊Dic3C2411yescharacteristic
54C3×Dic3—24no—
55C2×#41—92no—
56#135—98no—
57C2×Q16—91no—
58C2×SD16—92no—
59C2×D8—91no—
60C22×C8—91no—
61C23×C3—62no—
62C22×D3—22no—
63C22×D3—62no—
64C2×C3×C4—22no—
65C2×C3×C4—68no—
66C2×C3×C4—62no—
67#67—64no—
68#67—68no—
69#67—64no—
70C2×Dic3—22no—
71C2×Dic3—62no—
72D12—68no—
73C4×D3—28no—
74C4×D3—64no—
75C4×D3—64no—
76Dic6—64no—
77Dic6—64no—
78C2×C32#13512yescomplemented
79C2×C32C22×D411yescharacteristic
80C3⋊D3—22no—
81C3×D3—44no—
82#41—98no—
83#41—184no—
84C2×Q8—92no—
85C2×D4—92no—
86C2×D4—182no—
87C22×C4—62no—
88C22×C4—91no—
89Q16—94no—
90SD16—98no—
91D8—94no—
92C2×C8—91no—
93C2×C8—91no—
94C2×C8—94no—
95C22×C3—22no—
96C22×C3—64no—
97C22×C3—124no—
98C2×D3—24no—
99C2×D3—44no—
100C2×D3—64no—
101C2×D3—124no—
102C3×C4—24no—
103C3×C4—64no—
104Dic3—24no—
105Dic3—62no—
106Dic3—62no—
107C32C2×#13511yescharacteristic, complemented, Sylow
108C23—62no—
109C23—91no—
110Q8—94no—
111Q8—182no—
112D4—94no—
113D4—188no—
114D4—182no—
115C2×C4—62no—
116C2×C4—68no—
117C2×C4—91no—
118C2×C4—92no—
119C2×C4—92no—
120C2×C4GO+(4,𝔽2)11yescharacteristic
121C8—92no—
122C8—92no—
123C2×C3—22no—
124C2×C3—24no—
125C2×C3—124no—
126D3—44no—
127D3—124no—
128C22—64no—
129C22—92no—
130C22—124no—
131C22—182no—
132C22C2×GO+(4,𝔽2)11yescharacteristic
133C4—64no—
134C4—91no—
135C4—91no—
136C4C2×GO+(4,𝔽2)12yes—
137C3—22no—
138C2—124no—
139C2—182no—
140C2#6422312yesdirect product factor
141C2C22×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
center, hypercenterC2×C4GO+(4,𝔽2)
commutator, cosocleC3⋊Dic3C24
FrattiniC2C22×GO+(4,𝔽2)
FittingC2×C32×C4D4
socleC22×C32C2×D4
hypocenterC32C2×#135
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#3798C2semidirect
2. C2×#3787C2semidirect
3. C2×#3776C2semidirect
4. C2×#3775C2semidirect
5. C2×#3774C2semidirect
6. #64223C2direct (N × H)
13. #3798C22semidirect
16. #3787C22semidirect
17. #3776C22semidirect
18. #3775C22semidirect
19. #3774C22semidirect
78. C2×C32#135semidirect
107. C32C2×#135semidirect
140. C2#64223direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#37982
C2×#37872
C2×#37762
C2×#37752
C2×#37742
#642232
C2×#1359