Finite Group Databasebeta

← #10619535

Subgroups — #10619535

Order 648.

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

normal subgroups only

This group has 114 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×(C3⋊D3)⋊C9C211yesmaximal, characteristic, complemented
3#66316C211yesmaximal, characteristic, complemented
4#6295—31nomaximal
5#6194—31nomaximal
6C2×C32⋊C9C2211yescharacteristic
7#4181—21no—
8(C3⋊D3)⋊C9—21no—
9C2×C3×C3⋊D3—31no—
10C2×C3×C3⋊D3D311yescharacteristic
11C3×C3⋊Dic3—31no—
12C2×D3×C9—31no—
13C2×C3×D9—31no—
14C2×C3×D9—61no—
15C3⋊Dic9D311yescharacteristic, complemented
16C32⋊C9D411yescharacteristic, complemented, Sylow
17#626—91no—
18#626—91no—
19#625—91no—
20#611—91no—
21C2×C33C2×D311yescharacteristic
22C3×C3⋊D3—21no—
23C3×C3⋊D3—61no—
24C2×C3×C9—21no—
25C2×C3×C9C2×D311yescharacteristic
26D3×C9—61no—
27C3×D9—62no—
28C3×D9—61no—
29C2×C3⋊D3—31no—
30C2×C3⋊D3D911yescharacteristic, complemented
31C2×C3×D3—31no—
32C2×C3×D3—91no—
33C2×C3×D3—91no—
34C2×C3×D3—181no—
35C2×C3×D3—181no—
36C3⋊Dic3—31no—
37C3×Dic3—91no—
38C3×Dic3—91no—
39C3×Dic3—181no—
40C22×C9—91no—
41C2×D9—31no—
42C2×D9—61no—
43Dic9—181no—
44C33#6711yescharacteristic
45C3×C9—21no—
46C3×C9D1211yescharacteristic, complemented
47#67—271no—
48#67—271no—
49D12—271no—
50C2×C32—21no—
51C2×C32—61no—
52C2×C32—121no—
53C2×C32C2×D911yescharacteristic
54C2×C32D3211yescharacteristic
55C3⋊D3—21no—
56C3⋊D3—61no—
57C3×D3—61no—
58C3×D3—181no—
59C3×D3—182no—
60C3×D3—181no—
61C3×D3—181no—
62C2×C9—61no—
63C2×C9—121no—
64C2×C9—181no—
65D9—61no—
66D9—62no—
67C22×C3—91no—
68C22×C3—271no—
69C2×D3—31no—
70C2×D3—91no—
71C2×D3—91no—
72C2×D3—181no—
73C2×D3—181no—
74C3×C4—271no—
75Dic3—91no—
76Dic3—91no—
77Dic3—181no—
78C32—21no—
79C32—61no—
80C32—121no—
81C32#61111yescharacteristic, complemented
82C32#62611yescharacteristic
83C9—61no—
84C9—121no—
85D4—811noSylow
86C2×C3—21no—
87C2×C3—61no—
88C2×C3—121no—
89C2×C3—181no—
90C2×C3—541no—
91C2×C3D3×D911yescharacteristic
92C2×C3((C3⋊D3)⋊C3)⋊C211yescharacteristic
93D3—61no—
94D3—181no—
95D3—181no—
96D3—182no—
97D3—181no—
98C22—91no—
99C22—271no—
100C4—271no—
101C3—21no—
102C3—61no—
103C3—121no—
104C3#619511yescharacteristic
105C3#620011yescharacteristic
106C2—181no—
107C2—541no—
108C2((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×(C3⋊D3)⋊C9C2semidirect
3. #66316C2semidirect
15. C3⋊Dic9D3semidirect
16. C32⋊C9D4semidirect
30. C2×C3⋊D3D9semidirect
46. C3×C9D12semidirect
81. C32#611semidirect

Maximal subgroups

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

subgroupindex
C2×#41812
C2×(C3⋊D3)⋊C92
#663162
#62953
#61943