Finite Group Databasebeta

← #88939

Subgroups — #88939

Order 432.

132 conjugacy classes of subgroups; only the 21 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 21 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
2C2×C3×#157C211yesmaximal, characteristic, complemented
3#6294C211yesmaximal, characteristic, complemented
4D32⋊C4—31nomaximal
5C2×C3×C3⋊D3—21no—
6C2×C3×C3⋊D3C2211yescharacteristic
7#1113—21no—
8#1113C412yescomplemented
9C3×#157—21no—
10C3×C3⋊Dic3—21no—
11C2×D32—31no—
12C2×D32—61no—
13C2×#157D311yescharacteristic, complemented
14#624—31no—
15D3×Dic3—61no—
16C2×C33D411yescharacteristic
17C3×C3⋊D3—22no—
18C3×C3⋊D3C2×C411yescharacteristic
19C3×C3⋊D3D411yescharacteristic
20(C2×D3)⋊C4—91nomaximal
21C2×C3⋊D3—21no—
22C2×C3⋊D3C2×D311yescharacteristic
23C2×C3×D3—61no—
24C2×C3×D3—61no—
25C2×C3×D3—61no—
26C2×C3×D3—61no—
27C2×C3×D3—121no—
28D32—32no—
29D32—62no—
30D32—62no—
31D32—61no—
32#157—21no—
33C3⋊Dic3—21no—
34C3×Dic3—61no—
35C3×Dic3—61no—
36C3×Dic3—121no—
37C33C22⋊C411yescharacteristic, complemented, Sylow
38C22×D3—91no—
39C22×D3—181no—
40C2×C3×C4—91no—
41C2×Dic3—91no—
42C4×D3—181no—
43C2×C32—21no—
44C2×C32—21no—
45C2×C32—41no—
46C2×C32—41no—
47C2×C32D1211yescharacteristic
48C3⋊D3—22no—
49C3⋊D3C4×D311yescharacteristic
50C3⋊D3#6711yescharacteristic
51C3×D3—61no—
52C3×D3—61no—
53C3×D3—61no—
54C3×D3—61no—
55C3×D3—62no—
56C3×D3—62no—
57C3×D3—122no—
58C22⋊C4—271noSylow
59C22×C3—91no—
60C22×C3—181no—
61C2×D3—61no—
62C2×D3—61no—
63C2×D3—61no—
64C2×D3—61no—
65C2×D3—92no—
66C2×D3—121no—
67C2×D3—182no—
68C2×D3—181no—
69C2×D3—182no—
70C3×C4—181no—
71C3×C4—181no—
72Dic3—61no—
73Dic3—61no—
74Dic3—121no—
75C32—21no—
76C32—21no—
77C32—41no—
78C32—41no—
79C32(C2×D3)⋊C411yescharacteristic, complemented
80C23—271no—
81C2×C4—91no—
82C2×C4—271no—
83C2×C3—21no—
84C2×C3—21no—
85C2×C3—41no—
86C2×C3—41no—
87C2×C3—91no—
88C2×C3—91no—
89C2×C3—182no—
90C2×C3GO+(4,𝔽2)11yescharacteristic
91D3—61no—
92D3—61no—
93D3—61no—
94D3—61no—
95D3—62no—
96D3—62no—
97D3—122no—
98C22—91no—
99C22—181no—
100C22—272no—
101C22—541no—
102C4—181no—
103C4—181no—
104C3—21no—
105C3—21no—
106C3—41no—
107C3—41no—
108C3D32⋊C411yescharacteristic, complemented
109C2—91no—
110C2—91no—
111C2—182no—
112C2#157⋊D311yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2#157⋊D3
commutatorC3×C3⋊D3C2×C4
Fitting, socleC2×C33D4
prime radicalC2×#1113C2
cosocleC2×C3×C3⋊D3C22
hypocenterC33C22⋊C4
LCSG ▷ C3×C3⋊D3 ▷ C33
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C2×C3×#157C2semidirect
3. #6294C2semidirect
8. #1113C4semidirect
13. C2×#157D3semidirect
37. C33C22⋊C4semidirect
79. C32(C2×D3)⋊C4semidirect
108. C3D32⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#11132
C2×C3×#1572
#62942
D32⋊C43
(C2×D3)⋊C49