Finite Group Databasebeta

← C3×D32⋊C4 #88927

Subgroups — C3×D32⋊C4 #88927

Order 432.

132 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 26 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×C3×D32C211yesmaximal, characteristic
2C2×C3×#157C211yesmaximal, characteristic, complemented
3C3×#624C211yesmaximal, characteristic, complemented
4D32⋊C4C311yesmaximal, characteristic, direct product factor
5C2×C3×C3⋊D3C2211yescharacteristic
6C2×C32×D3—21no—
7C3×D32—21no—
8C3×D32C412yescomplemented
9C3×#157—21no—
10C32×Dic3—21no—
11C22×C3×D3—61no—
12C2×D32C2×C311yescharacteristic
13C2×#157C2×C311yescharacteristic, complemented
14C3×C4×D3—61no—
15#624C2×C311yescharacteristic, complemented
16C2×C33D411yescharacteristic
17C3×C3⋊D3C2×C411yescharacteristic
18C3×C3⋊D3D411yescharacteristic
19C32×D3—22no—
20C3×C22⋊C4—91nomaximal
21C22×C32—61no—
22C2×C3⋊D3C22×C311yescharacteristic
23C2×C3×D3—21no—
24C2×C3×D3—21no—
25C2×C3×D3—41no—
26C2×C3×D3—62no—
27C2×C3×D3—61no—
28C2×C3×D3—61no—
29C2×C3×D3—62no—
30D32—21no—
31D32C3×C412yescomplemented
32#157—21no—
33C32×C4—61no—
34C3×Dic3—21no—
35C3×Dic3—21no—
36C3×Dic3—41no—
37C33C22⋊C411yescharacteristic, complemented, Sylow
38C23×C3—91no—
39C22×D3—61no—
40C2×C3×C4—91no—
41C2×C3×C4—91no—
42C4×D3—61no—
43C2×C32—21no—
44C2×C32—21no—
45C2×C32—41no—
46C2×C32—41no—
47C2×C32—62no—
48C2×C32C3×D411yescharacteristic
49C3⋊D3C2×C3×C411yescharacteristic
50C3⋊D3C3×D411yescharacteristic
51C3×D3—22no—
52C3×D3—22no—
53C3×D3—42no—
54C3×D3—61no—
55C3×D3—61no—
56C3×D3—61no—
57C3×D3—61no—
58C22⋊C4—91noSylow
59C22×C3—61no—
60C22×C3—61no—
61C22×C3—92no—
62C22×C3—91no—
63C22×C3—121no—
64C22×C3—181no—
65C2×D3—21no—
66C2×D3—62no—
67C2×D3—61no—
68C2×D3—61no—
69C2×D3—62no—
70C3×C4—61no—
71C3×C4—61no—
72C3×C4—121no—
73C3×C4—181no—
74Dic3—21no—
75C32—21no—
76C32—21no—
77C32—41no—
78C32—41no—
79C32C3×C22⋊C411yescharacteristic, complemented
80C23—91no—
81C2×C4—91no—
82C2×C4—91no—
83C2×C3—21no—
84C2×C3—21no—
85C2×C3—41no—
86C2×C3—41no—
87C2×C3—62no—
88C2×C3—62no—
89C2×C3—91no—
90C2×C3—91no—
91C2×C3—122no—
92C2×C3GO+(4,𝔽2)11yescharacteristic
93D3—22no—
94D3—61no—
95D3—61no—
96D3—61no—
97D3—61no—
98C22—61no—
99C22—92no—
100C22—91no—
101C22—181no—
102C4—61no—
103C4—181no—
104C3—21no—
105C3—21no—
106C3—41no—
107C3—41no—
108C3D32⋊C411yescharacteristic, direct product factor
109C2—62no—
110C2—91no—
111C2—91no—
112C2C3×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
center, hypercenterC2×C3GO+(4,𝔽2)
commutatorC3⋊D3C2×C3×C4
FrattiniC2C3×GO+(4,𝔽2)
Fitting, socleC2×C33D4
prime radicalC2×C3×D32C2
cosocleC2×C3⋊D3C22×C3
hypocenterC32C3×C22⋊C4
LCSG ▷ C3⋊D3 ▷ C32
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
2. C2×C3×#157C2semidirect
3. C3×#624C2semidirect
4. D32⋊C4C3direct (N × H)
8. C3×D32C4semidirect
13. C2×#157C2×C3semidirect
15. #624C2×C3semidirect
31. D32C3×C4semidirect
37. C33C22⋊C4semidirect
79. C32C3×C22⋊C4semidirect
108. C3D32⋊C4direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D322
C2×C3×#1572
C3×#6242
D32⋊C43
C3×C22⋊C49