Finite Group Databasebeta

← #14518086

Subgroups — #14518086

Order 1944.

287 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 287 conjugacy classes of subgroups — too many to draw. Only its 37 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#11757857C211yesmaximal, characteristic, complemented
2C3⋊(C9⋊S4)C311yesmaximal, characteristic, complemented
3C3⋊((C3⋊S4)⋊C3)—31nomaximal
4#10619980—31nomaximal
5#10619746—32nomaximal
6#92303—41nomaximal
7C22×C3×3−1+2D311yescharacteristic, complemented
8C2×C3⋊AGL(1,ℤ/9)—31no—
9C3×C22⋊H(3,𝔽3)D311yescharacteristic
10C3×C9⋊A4—21no—
11C3×C9×A4C2×C311yescharacteristic, complemented
12C3⋊(3−1+2⋊C4)—31no—
13C32⋊(C22⋊C9)D312yescomplemented
14(C3×A4)⋊C9—21no—
15(C3×A4)⋊C9—22no—
16C9⋊H(3,𝔽3)—41noSylow
17C3⋊(C3⋊S4)—31no—
18C3×#638—91no—
19C3⋊((C22⋊C9)⋊C2)—32no—
20C9⋊S4—93no—
21(C3⋊S4)⋊C3—93no—
22#6233—31no—
23#611⋊C3—93no—
24C2×C3×3−1+2—31no—
25C3⋊(C3⋊D9)—41no—
26C3⋊AGL(1,ℤ/9)—61no—
27C3⋊((C3⋊D3)⋊C3)—121no—
28#4169—122no—
29C22×C33C3⋊D311yescharacteristic
30C2×C3×C3⋊D3—91no—
31C32×A4—21no—
32C32×A4C3×D311yescharacteristic
33C3×C3⋊Dic3—91no—
34C22×3−1+2—33no—
35C22×C3×C9—21no—
36C22×C3×C9C3×D311yescharacteristic
37C2×C3⋊D9—31no—
38C2×AGL(1,ℤ/9)—93no—
39C22⋊H(3,𝔽3)—33no—
40C3×C22⋊C9—22no—
41C3×C22⋊C9C3×D312yes—
42C9⋊A4—63no—
43C9×A4—33no—
44C3⋊Dic9—31no—
453−1+2⋊C4—93no—
46C3×3−1+2—81no—
47C3×3−1+2S411yescharacteristic, complemented
48C3×H(3,𝔽3)—41no—
49C32×C9—41no—
50C32⋊C9—42no—
51C32⋊C9—82no—
52C32⋊C9—81no—
53C3⋊S4—93no—
54C3⋊S4—271no—
55C3⋊S4—272no—
56#638—91no—
57C3×#67—271no—
58C3×#67—271no—
59C3×#67—272no—
60(C22⋊C9)⋊C2—272no—
61#611—93no—
62C2×C33—31no—
63C3⋊(C3⋊D3)—121no—
64C3×C3⋊D3—181no—
65C2×3−1+2—33no—
66C2×3−1+2—63no—
67C2×C3×C9—31no—
68C2×C3×C9—61no—
69C3⋊D9—61no—
70C3⋊D9—122no—
71C3⋊D9—363no—
72AGL(1,ℤ/9)—183no—
73(C3⋊D3)⋊C3—363no—
74C22×C32—31no—
75C22×C32—31no—
76C22×C32—32no—
77C22×C32C3×C3⋊D311yescharacteristic
78C2×C3⋊D3—91no—
79C2×C3×D3—271no—
80C2×C3×D3—271no—
81C2×C3×D3—272no—
82C3×A4—31no—
83C3×A4—32no—
84C3×A4—61no—
85C3×A4—61no—
86C3×A4—62no—
87C3×A4AGL(1,ℤ/9)13yescomplemented
88C3⋊Dic3—91no—
89C3×Dic3—271no—
90C3×Dic3—271no—
91C3×Dic3—272no—
92C22×C9—61no—
93C22×C9(C3⋊D3)⋊C313yescomplemented
94C2×D9—93no—
95C22⋊C9—32no—
96C22⋊C9—62no—
97Dic9—93no—
98C33—41no—
99C33—81no—
100C33C3⋊S411yescharacteristic
1013−1+2—33no—
1023−1+2—243no—
103H(3,𝔽3)—123no—
104C3×C9—21no—
105C3×C9—42no—
106C3×C9—82no—
107C3×C9—123no—
108C3×C9C3×S411yescharacteristic
109S4—813no—
110C3×D4—811no—
111#67—271no—
112#67—271no—
113#67—272no—
114C2×C32—31no—
115C2×C32—31no—
116C2×C32—61no—
117C2×C32—92no—
118C2×C32—91no—
119C3⋊D3—181no—
120C3⋊D3—363no—
121C3⋊D3—1081no—
122C3⋊D3—1082no—
123C3×D3—541no—
124C3×D3—541no—
125C3×D3—542no—
126C2×C9—33no—
127C2×C9—63no—
128D9—183no—
129D9—1082no—
130C22×C3—91no—
131C22×C3—811no—
132C22×C3C3⋊((C3⋊D3)⋊C3)11yescharacteristic
133C22×C3C3⋊AGL(1,ℤ/9)11yescharacteristic
134C22×C3#420712yes—
135C2×D3—271no—
136C2×D3—272no—
137C2×D3—271no—
138A4—33no—
139A4—181no—
140C3×C4—811no—
141Dic3—271no—
142Dic3—272no—
143Dic3—271no—
144C32—32no—
145C32—31no—
146C32—31no—
147C32—43no—
148C32—122no—
149C32—121no—
150C32—242no—
151C32—241no—
152C32—241no—
153C32C3×C3⋊S411yescharacteristic
154C9—61no—
155C9—122no—
156C9—242no—
157C9(C3⋊S4)⋊C313yescomplemented
158D4—811noSylow
159C2×C3—32no—
160C2×C3—31no—
161C2×C3—31no—
162C2×C3—91no—
163C2×C3—181no—
164C2×C3—1621no—
165D3—542no—
166D3—541no—
167D3—541no—
168D3—3243no—
169C22—811no—
170C22#9230311yescharacteristic, complemented
171C4—811no—
172C3—91no—
173C3—123no—
174C3—721no—
175C3#66440⋊C212yes—
176C3A4⋊AGL(1,ℤ/9)11yescharacteristic
177C3C3⋊((C3⋊S4)⋊C3)11yescharacteristic
178C2—31no—
179C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC3×C9×A4C2×C3
FrattiniC32C3×C3⋊S4
FittingC22×C3×3−1+2D3
socleC22×C32C3×C3⋊D3
LCSG ▷ C3×C9×A4
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11757857C2semidirect
2. C3⋊(C9⋊S4)C3semidirect
7. C22×C3×3−1+2D3semidirect
11. C3×C9×A4C2×C3semidirect
13. C32⋊(C22⋊C9)D3semidirect
47. C3×3−1+2S4semidirect
87. C3×A4AGL(1,ℤ/9)semidirect
93. C22×C9(C3⋊D3)⋊C3semidirect
157. C9(C3⋊S4)⋊C3semidirect
170. C22#92303semidirect

Maximal subgroups

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

subgroupindex
#117578572
C3⋊(C9⋊S4)3
C3⋊((C3⋊S4)⋊C3)3
#106199803
#106197463
#923034