Finite Group Databasebeta

← #14515804

Subgroups — #14515804

Order 1944.

134 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 25 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×#92182C211yesmaximal, characteristic, complemented
2C2×#92181C211yesmaximal, characteristic, complemented
3#11757336C211yesmaximal, characteristic, complemented
4#10619909—31nomaximal
5#10619545—31nomaximal
6C2×#6872C2211yescharacteristic
7#92182—21no—
8#92181—21no—
9C2×#4208D311yescharacteristic
10C2×#4207—31no—
11#66409—31no—
12C2×C3⋊D27D311yescharacteristic, complemented
13C2×D3×C27—31no—
14(C27⋊C3)⋊C4—61no—
15C3×Dic27—31no—
16#6872D411yescharacteristic, complemented, Sylow
17#6200—91no—
18#6195—91no—
19#6194—91no—
20#6171—91no—
21C2×#737C2×D311yescharacteristic
22#4208—21no—
23#4207—61no—
24C2×C27⋊C3—21no—
25C2×C3×C27C2×D311yescharacteristic
26C3⋊D27—21no—
27D3×C27—61no—
28C2×#272D911yescharacteristic
29C2×C3⋊D9—31no—
30C2×AGL(1,ℤ/9)—181no—
31C2×(C3⋊D3)⋊C3—91no—
32C2×D3×C9—31no—
33C2×D3×C9—91no—
34C2×C3×D9—91no—
35C3⋊Dic9—31no—
363−1+2⋊C4—181no—
37(C3⋊Dic3)⋊C3—91no—
38C3×Dic9—91no—
39C22×C27—91no—
40C2×D27—91no—
41Dic27—31no—
42Dic27—61no—
43#737#6711yescharacteristic
44C27⋊C3—21no—
45C3×C27#6711yescharacteristic, complemented
46#626—271no—
47#625—271no—
48#611—271no—
49C2×3−1+2—21no—
50C2×3−1+2—61no—
51C2×H(3,𝔽3)C2×D911yescharacteristic
52C2×C3×C9—31no—
53C2×C3×C9D3211yescharacteristic
54#272—21no—
55C3⋊D9—61no—
56AGL(1,ℤ/9)—182no—
57(C3⋊D3)⋊C3—181no—
58D3×C9—61no—
59D3×C9—181no—
60C3×D9—181no—
61C2×C27—31no—
62C2×C27—61no—
63C2×C27—181no—
64D27—181no—
65C2×C3⋊D3—91no—
66C2×C3×D3—31no—
67C2×C3×D3—91no—
68C2×C3×D3—271no—
69C3⋊Dic3—91no—
70C3×Dic3—271no—
71C22×C9—91no—
72C2×D9—91no—
73C2×D9—181no—
74Dic9—91no—
75Dic9—181no—
763−1+2—21no—
773−1+2—61no—
78H(3,𝔽3)#61111yescharacteristic
79C3×C9—31no—
80C3×C9#62511yescharacteristic
81C27—31no—
82C27—61no—
83#67—811no—
84#67—811no—
85D12—811no—
86C2×C32—31no—
87C2×C32D3×D911yescharacteristic
88C3⋊D3—181no—
89C3×D3—61no—
90C3×D3—181no—
91C3×D3—541no—
92C2×C9—21no—
93C2×C9—61no—
94C2×C9—181no—
95C2×C9((C3⋊D3)⋊C3)⋊C211yescharacteristic
96D9—182no—
97D9—181no—
98C22×C3—91no—
99C22×C3—811no—
100C2×D3—31no—
101C2×D3—91no—
102C2×D3—271no—
103C2×D3—811no—
104C3×C4—811no—
105Dic3—271no—
106Dic3—811no—
107C32—31no—
108C32#619411yescharacteristic
109C9—21no—
110C9—61no—
111C9#619811yescharacteristic
112D4—2431noSylow
113C2×C3—31no—
114C2×C3—91no—
115C2×C3—181no—
116C2×C3—1621no—
117C2×C3((C3⋊D3)⋊C9)⋊C211yescharacteristic
118D3—61no—
119D3—181no—
120D3—541no—
121D3—1621no—
122C22—91no—
123C22—811no—
124C4—811no—
125C3—31no—
126C3—91no—
127C3#1061953611yescharacteristic
128C2—181no—
129C2—1621no—
130C2#92181⋊C211yescharacteristic
subgroupG/H
center, hypercenterC2#92181⋊C2
commutator, Fitting, cosocleC2×#6872C22
FrattiniC2×C3×C9D32
socleC2×C3((C3⋊D3)⋊C9)⋊C2
hypocenter#6872D4
LCSG ▷ C2×#6872 ▷ #6872
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×#92182C2semidirect
2. C2×#92181C2semidirect
3. #11757336C2semidirect
12. C2×C3⋊D27D3semidirect
16. #6872D4semidirect
45. C3×C27#67semidirect

Maximal subgroups

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

subgroupindex
C2×#921822
C2×#921812
#117573362
#106199093
#106195453