Finite Group Databasebeta

← #10619537

Subgroups — #10619537

Order 648.

118 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 118 conjugacy classes of subgroups — too many to draw. Only its 23 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×#4181C211yesmaximal, characteristic, complemented
2C2×#4169C211yesmaximal, characteristic, complemented
3(C3⋊Dic3)⋊C9C211yesmaximal, characteristic, complemented
4#6295—31nomaximal
5#6192—31nomaximal
6C2×C32⋊C9C2211yescharacteristic
7#4181—21no—
8#4169—21no—
9C2×C3×C3⋊D3—31no—
10C2×C3×C3⋊D3—31no—
11C3×C3⋊Dic3D311yescharacteristic
12C2×C3⋊D9D311yescharacteristic, complemented
13C2×C3×D9—31no—
14C2×C3×D9—61no—
15C9×Dic3—31no—
16C32⋊C9D411yescharacteristic, complemented, Sylow
17#626—91no—
18#626—91no—
19#625—91no—
20D36—91no—
21C2×C33C2×D311yescharacteristic
22C3×C3⋊D3—61no—
23C3×C3⋊D3—61no—
24C2×C3×C9—21no—
25C2×C3×C9C2×D311yescharacteristic
26C3⋊D9—21no—
27C3×D9—62no—
28C3×D9—61no—
29C2×C3⋊D3—31no—
30C2×C3⋊D3—31no—
31C2×C3×D3—91no—
32C2×C3×D3—91no—
33C2×C3×D3—91no—
34C2×C3×D3—91no—
35C2×C3×D3—181no—
36C2×C3×D3—181no—
37C3⋊Dic3D911yescharacteristic, complemented
38C3×Dic3—31no—
39C3×Dic3—91no—
40C2×D9—31no—
41C2×D9—61no—
42C2×D9—181no—
43C4×C9—91no—
44C33D1211yescharacteristic
45C3×C9—21no—
46C3×C9#6711yescharacteristic, complemented
47#67—271no—
48#67—271no—
49D12—271no—
50C2×C32—21no—
51C2×C32—31no—
52C2×C32—61no—
53C2×C32C2×D911yescharacteristic
54C2×C32D3211yescharacteristic
55C3⋊D3—61no—
56C3⋊D3—61no—
57C3×D3—182no—
58C3×D3—181no—
59C3×D3—182no—
60C3×D3—181no—
61C3×D3—181no—
62C3×D3—181no—
63C2×C9—61no—
64C2×C9—61no—
65D9—61no—
66D9—62no—
67D9—181no—
68C22×C3—271no—
69C22×C3—271no—
70C2×D3—91no—
71C2×D3—91no—
72C2×D3—91no—
73C2×D3—91no—
74C2×D3—181no—
75C2×D3—181no—
76C3×C4—91no—
77Dic3—31no—
78Dic3—181no—
79C32—21no—
80C32—31no—
81C32—61no—
82C32D3611yescharacteristic, complemented
83C32#62611yescharacteristic
84C9—61no—
85C9—61no—
86D4—811noSylow
87C2×C3—21no—
88C2×C3—61no—
89C2×C3—61no—
90C2×C3—541no—
91C2×C3—541no—
92C2×C3D3×D911yescharacteristic
93C2×C3((C3⋊D3)⋊C3)⋊C211yescharacteristic
94D3—182no—
95D3—181no—
96D3—182no—
97D3—181no—
98D3—181no—
99D3—181no—
100C22—271no—
101C22—271no—
102C4—91no—
103C3—21no—
104C3—61no—
105C3—61no—
106C3#619211yescharacteristic
107C3#620011yescharacteristic
108C2—541no—
109C2—541no—
110C2((C3⋊D3)⋊C9)⋊C211yescharacteristic
subgroupG/H
center, hypercenterC2((C3⋊D3)⋊C9)⋊C2
commutator, Fitting, cosocleC2×C32⋊C9C22
Frattini, socleC2×C32D32
hypocenterC32⋊C9D4
LCSG ▷ C2×C32⋊C9 ▷ C32⋊C9
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×#4181C2semidirect
2. C2×#4169C2semidirect
3. (C3⋊Dic3)⋊C9C2semidirect
12. C2×C3⋊D9D3semidirect
16. C32⋊C9D4semidirect
37. C3⋊Dic3D9semidirect
46. C3×C9#67semidirect
82. C32D36semidirect

Maximal subgroups

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

subgroupindex
C2×#41812
C2×#41692
(C3⋊Dic3)⋊C92
#62953
#61923