Finite Group Databasebeta

← C2×D32⋊D3 #89108

Subgroups — C2×D32⋊D3 #89108

Order 432.

192 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 31 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×#1113C211yesmaximal, characteristic, complemented
2C2×C3×D32C211yesmaximal, characteristic, complemented
3C2×C3⋊#157C211yesmaximal, characteristic, complemented
4D32⋊D3C214yesmaximal, direct product factor
5C2×GO+(4,𝔽2)—31nomaximal
6C2×C3×C3⋊D3—21no—
7C2×C3×C3⋊D3C2211yescharacteristic
8C2×C32×D3—21no—
9#1113—21no—
10#1113C2212yescomplemented
11C3×D32—21no—
12C3×D32C2212yescomplemented
13C3⋊#157C2212yescomplemented
14C22×C3×D3—61no—
15C2×D32—31no—
16C2×D32—61no—
17C2×D32D311yescharacteristic, complemented
18C2×#157—31no—
19GO+(4,𝔽2)—34no—
20C2×C33D411yescharacteristic, complemented
21C3×C3⋊D3—22no—
22C3×C3⋊D3D411yescharacteristic, complemented
23C3×C3⋊D3C2311yescharacteristic
24C32×D3—22no—
25C2×#67—91nomaximal
26C22×C32—61no—
27C2×C3⋊D3—21no—
28C2×C3⋊D3C2×D311yescharacteristic
29C2×C3×D3—21no—
30C2×C3×D3—21no—
31C2×C3×D3—41no—
32C2×C3×D3—62no—
33C2×C3×D3—61no—
34C2×C3×D3—61no—
35C2×C3×D3—62no—
36C2×C3×D3—61no—
37C2×C3×D3—61no—
38C2×C3×D3—121no—
39D32—21no—
40D32—32no—
41D32—62no—
42D32—62no—
43D32—61no—
44D32C2×D312yescomplemented
45#157—32no—
46C33C2×D411yescharacteristic, complemented, Sylow
47C23×C3—91no—
48C22×D3—61no—
49C22×D3—91no—
50C22×D3—181no—
51#67—94no—
52C2×Dic3—91no—
53C2×C32—21no—
54C2×C32—21no—
55C2×C32—41no—
56C2×C32—41no—
57C2×C32—62no—
58C2×C32#6711yescharacteristic, complemented
59C3⋊D3—22no—
60C3⋊D3#6711yescharacteristic, complemented
61C3⋊D3C22×D311yescharacteristic
62C3×D3—22no—
63C3×D3—22no—
64C3×D3—42no—
65C3×D3—61no—
66C3×D3—61no—
67C3×D3—61no—
68C3×D3—61no—
69C3×D3—62no—
70C3×D3—62no—
71C3×D3—122no—
72C2×D4—271noSylow
73C22×C3—61no—
74C22×C3—61no—
75C22×C3—92no—
76C22×C3—91no—
77C22×C3—121no—
78C22×C3—181no—
79C22×C3—181no—
80C2×D3—21no—
81C2×D3—62no—
82C2×D3—61no—
83C2×D3—61no—
84C2×D3—62no—
85C2×D3—61no—
86C2×D3—61no—
87C2×D3—92no—
88C2×D3—121no—
89C2×D3—182no—
90C2×D3—181no—
91C2×D3—182no—
92Dic3—92no—
93C32—21no—
94C32—21no—
95C32—41no—
96C32—41no—
97C32C2×#6711yescharacteristic, complemented
98C23—91no—
99C23—271no—
100D4—274no—
101C2×C4—271no—
102C2×C3—21no—
103C2×C3—21no—
104C2×C3—41no—
105C2×C3—41no—
106C2×C3—62no—
107C2×C3—62no—
108C2×C3—91no—
109C2×C3—91no—
110C2×C3—122no—
111C2×C3—182no—
112C2×C3GO+(4,𝔽2)11yescharacteristic, complemented
113D3—22no—
114D3—61no—
115D3—61no—
116D3—61no—
117D3—61no—
118D3—62no—
119D3—62no—
120D3—122no—
121C22—61no—
122C22—92no—
123C22—91no—
124C22—181no—
125C22—181no—
126C22—272no—
127C22—541no—
128C4—272no—
129C3—21no—
130C3—21no—
131C3—41no—
132C3—41no—
133C3C2×GO+(4,𝔽2)11yescharacteristic, complemented
134C2—62no—
135C2—91no—
136C2—91no—
137C2—182no—
138C2D32⋊D311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2D32⋊D3
commutator, cosocleC3×C3⋊D3C23
FrattiniC1G
Fitting, socleC2×C33D4
hypocenterC33C2×D4
LCSG ▷ C3×C3⋊D3 ▷ C33
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×#1113C2semidirect
2. C2×C3×D32C2semidirect
3. C2×C3⋊#157C2semidirect
4. D32⋊D3C2direct (N × H)
10. #1113C22semidirect
12. C3×D32C22semidirect
13. C3⋊#157C22semidirect
17. C2×D32D3semidirect
20. C2×C33D4semidirect
22. C3×C3⋊D3D4semidirect
44. D32C2×D3semidirect
46. C33C2×D4semidirect
58. C2×C32#67semidirect
60. C3⋊D3#67semidirect
97. C32C2×#67semidirect
112. C2×C3GO+(4,𝔽2)semidirect
133. C3C2×GO+(4,𝔽2)semidirect
138. C2D32⋊D3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#11132
C2×C3×D322
C2×C3⋊#1572
D32⋊D32
C2×GO+(4,𝔽2)3
C2×#679