Finite Group Databasebeta

← #10624906⋊C2 #13091535

Subgroups — #10624906⋊C2 #13091535

Order 1458.

272 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 49 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
1#10624906C211yesmaximal, characteristic, complemented, Sylow
2#92312C311yesmaximal, characteristic, complemented
3#6897⋊C2C311yesmaximal, characteristic, complemented
4#92299C312yesmaximal, complemented
5#4169⋊C3—32nomaximal
6C3×#4169—32nomaximal
7#6898—22no—
8#6898—22no—
9#6898C2×C311yescharacteristic, complemented
10#6897—22no—
11#6897—22no—
12#6897C2×C311yescharacteristic, complemented
13#6894—22no—
14#6894—22no—
15#6894—22no—
16#6891D312yes—
17C9×3−1+2—22no—
18C9×3−1+2C2×C312yescomplemented
19C3×C32⋊C9D312yes—
20C32×C3⋊D3—91no—
21C3⋊AGL(1,ℤ/9)—32no—
22C3×C3⋊D9—32no—
23C9⋊D9C3211yescharacteristic, complemented
24#4169—32no—
25#4169—32no—
26#4169—32no—
27#4169—32no—
28#4169—32no—
29#4169—32no—
30C34C3⋊D311yescharacteristic
31C3×3−1+2—22no—
32C3×3−1+2C3×D312yes—
33C32×C9—22no—
34C32×C9C3×D312yes—
35C9⋊C9—22no—
36C9⋊C9—22no—
37C9⋊C9—22no—
38C9⋊C9—22no—
39C9⋊C9—22no—
40C9⋊C9—22no—
41C9⋊C9—22no—
42C9⋊C9—22no—
43C9⋊C9—22no—
44C9⋊C9—22no—
45C9⋊C9—22no—
46C9⋊C9—22no—
47C9⋊C9—22no—
48C9⋊C9—22no—
49C9⋊C9—22no—
50C9⋊C9—22no—
51C9⋊C9—22no—
52C9⋊C9—22no—
53C32⋊C9—22no—
54C32⋊C9—22no—
55C32⋊C9—22no—
56C32⋊C9—22no—
57C32⋊C9—22no—
58C32⋊C9—22no—
59C32⋊C9C3×D312yes—
60C32⋊C9C3×D312yes—
61C32⋊C9C3×D312yes—
62C32⋊C9C3×D312yes—
63C32⋊C9C3×D312yes—
64C32⋊C9C3×D312yes—
65C92—22no—
66C92—22no—
67C92C2×C3211yescharacteristic, complemented
68C3×C3⋊D3—91no—
69C3×C3⋊D3—91no—
70C3×C3⋊D3—92no—
71C32×D3—272no—
72C32×D3—272no—
73C3⋊D9—32no—
74C3⋊D9—32no—
75AGL(1,ℤ/9)—272no—
76C3×D9—272no—
77C33—32no—
78C33—62no—
79C33—92no—
80C33C3×C3⋊D312yes—
81C33C3×C3⋊D311yescharacteristic
82C33C3×C3⋊D311yescharacteristic
833−1+2—32no—
843−1+2—62no—
853−1+2—64no—
863−1+2—62no—
87C3×C9—22no—
88C3×C9—22no—
89C3×C9—22no—
90C3×C9—22no—
91C3×C9—22no—
92C3×C9—22no—
93C3×C9—22no—
94C3×C9—22no—
95C3×C9—92no—
96C3×C9—182no—
97C3×C9C32×D312yes—
98C3×C9C32×D312yes—
99C2×C32—811no—
100C3⋊D3—91no—
101C3×D3—272no—
102C3×D3—272no—
103C3×D3—272no—
104C3×D3—272no—
105C3×D3—272no—
106C3×D3—272no—
107C3×D3—272no—
108C3×D3—272no—
109D9—272no—
110D9—272no—
111C32—22no—
112C32—32no—
113C32—32no—
114C32—32no—
115C32—32no—
116C32—32no—
117C32—32no—
118C32—32no—
119C32—91no—
120C32—182no—
121C32—182no—
122C32#420712yes—
123C32C32×C3⋊D311yescharacteristic
124C9—32no—
125C9—32no—
126C9—62no—
127C9—62no—
128C9—62no—
129C9—62no—
130C9—62no—
131C9—62no—
132C9—62no—
133C9—62no—
134C2×C3—812no—
135C2×C3—811no—
136C2×C3—811no—
137D3—272no—
138D3—272no—
139C3—32no—
140C3—62no—
141C3—91no—
142C3—91no—
143C3C3×#420712yes—
144C3#4207⋊C312yes—
145C2—811noSylow
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC92C2×C32
Frattini, socleC32C32×C3⋊D3
Fitting#10624906C2
LCSG ▷ C92
UCSC1

Complements

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

NH ≅ G/Ntype
1. #10624906C2semidirect
2. #92312C3semidirect
3. #6897⋊C2C3semidirect
4. #92299C3semidirect
9. #6898C2×C3semidirect
12. #6897C2×C3semidirect
18. C9×3−1+2C2×C3semidirect
23. C9⋊D9C32semidirect
67. C92C2×C32semidirect

Maximal subgroups

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

subgroupindex
#106249062
#923123
#6897⋊C23
#922993
#4169⋊C33
C3×#41693