Finite Group Databasebeta

← #14516491

Subgroups — #14516491

Order 1944.

263 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 263 conjugacy classes of subgroups — too many to draw. Only its 29 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
1H(3,𝔽3)⋊(C22⋊C9)C211yesmaximal, characteristic, complemented
2C3×C3⋊((C22⋊C9)⋊C2)—31nomaximal
3#10619977—31nomaximal
4#10619746—32nomaximal
5#92211—41nomaximal
6C22×C3×H(3,𝔽3)D311yescharacteristic
7C2×C3⋊((C3⋊D3)⋊C3)—31no—
8C32×C22⋊C9D311yescharacteristic, complemented
9C3⋊((C3⋊Dic3)⋊C3)—31no—
10C32⋊(C22⋊C9)D312yescomplemented
11H(3,𝔽3)⋊C9—41noSylow
12#6312—31no—
13C3×#638—91no—
14C3⋊((C22⋊C9)⋊C2)—31no—
15C3⋊((C22⋊C9)⋊C2)—32no—
16C3×(C22⋊C9)⋊C2—93no—
17#638⋊C3—93no—
18C2×C3×H(3,𝔽3)—31no—
19C3⋊((C3⋊D3)⋊C3)—61no—
20C3×C3⋊D9—121no—
21#4169—122no—
22C22×C33—31no—
23C22×C33C3⋊D311yescharacteristic
24C2×C3⋊(C3⋊D3)—31no—
25C2×C3×C3⋊D3—91no—
26C3⋊(C3⋊Dic3)—31no—
27C3×C3⋊Dic3—91no—
28C22×H(3,𝔽3)—61no—
29C22×H(3,𝔽3)D913yescomplemented
30C2×(C3⋊D3)⋊C3—93no—
31C3×C22⋊C9—31no—
32C3×C22⋊C9—33no—
33C3×C22⋊C9—32no—
34(C3⋊Dic3)⋊C3—93no—
35C3×H(3,𝔽3)S411yescharacteristic
36C32×C9—41no—
37C32⋊C9—42no—
38#638—91no—
39#638—93no—
40#638—271no—
41#638—271no—
42#638—271no—
43C3×#67—271no—
44C3×#67—271no—
45C3×#67—271no—
46C3×#67—271no—
47(C22⋊C9)⋊C2—93no—
48(C22⋊C9)⋊C2—272no—
49C2×C33—31no—
50C2×C33—31no—
51C2×C33—61no—
52C3⋊(C3⋊D3)—61no—
53C3×C3⋊D3—181no—
54C2×H(3,𝔽3)—33no—
55C2×H(3,𝔽3)—63no—
56C3⋊D9—121no—
57C3⋊D9—122no—
58(C3⋊D3)⋊C3—183no—
59C3×D9—363no—
60C22×C32—21no—
61C22×C32—31no—
62C22×C32—31no—
63C22×C32—31no—
64C22×C32—33no—
65C22×C32—91no—
66C22×C32—91no—
67C22×C32—91no—
68C22×C32C3⋊D911yescharacteristic
69C22×C32#27211yescharacteristic
70C2×C3⋊D3—91no—
71C2×C3⋊D3—93no—
72C2×C3⋊D3—271no—
73C2×C3⋊D3—271no—
74C2×C3⋊D3—271no—
75C2×C3×D3—271no—
76C2×C3×D3—271no—
77C2×C3×D3—271no—
78C2×C3×D3—271no—
79C3⋊Dic3—91no—
80C3⋊Dic3—93no—
81C3⋊Dic3—271no—
82C3⋊Dic3—271no—
83C3⋊Dic3—271no—
84C3×Dic3—271no—
85C3×Dic3—271no—
86C3×Dic3—271no—
87C3×Dic3—271no—
88C22⋊C9—33no—
89C22⋊C9—92no—
90C33—31no—
91C33C3⋊S411yescharacteristic
92H(3,𝔽3)—61no—
93H(3,𝔽3)(C22⋊C9)⋊C213yescomplemented
94C3×C9—121no—
95C3×C9—123no—
96C3×C9—122no—
97C3×D4—811no—
98#67—271no—
99#67—271no—
100#67—271no—
101#67—271no—
102#67—813no—
103C2×C32—31no—
104C2×C32—33no—
105C2×C32—31no—
106C2×C32—61no—
107C2×C32—63no—
108C2×C32—91no—
109C2×C32—91no—
110C2×C32—91no—
111C2×C32—91no—
112C2×C32—91no—
113C2×C32—91no—
114C2×C32—181no—
115C2×C32—181no—
116C2×C32—181no—
117C3⋊D3—181no—
118C3⋊D3—183no—
119C3⋊D3—541no—
120C3⋊D3—541no—
121C3⋊D3—541no—
122C3×D3—541no—
123C3×D3—541no—
124C3×D3—541no—
125C3×D3—541no—
126D9—363no—
127D9—1082no—
128C22×C3—31no—
129C22×C3—61no—
130C22×C3—93no—
131C22×C3—811no—
132C22×C3#418111yescharacteristic
133C22×C3#418311yescharacteristic
134C22×C3#418411yescharacteristic
135C22×C3#418511yescharacteristic
136C2×D3—271no—
137C2×D3—271no—
138C2×D3—271no—
139C2×D3—271no—
140C2×D3—813no—
141C3×C4—811no—
142Dic3—271no—
143Dic3—271no—
144Dic3—271no—
145Dic3—271no—
146Dic3—813no—
147C32—21no—
148C32—31no—
149C32—31no—
150C32—31no—
151C32—33no—
152C32—91no—
153C32—91no—
154C32—91no—
155C32C3⋊((C22⋊C9)⋊C2)11yescharacteristic
156C32#625811yescharacteristic
157C9—123no—
158C9—362no—
159D4—811noSylow
160C2×C3—31no—
161C2×C3—31no—
162C2×C3—31no—
163C2×C3—31no—
164C2×C3—91no—
165C2×C3—93no—
166C2×C3—181no—
167C2×C3—183no—
168C2×C3—1621no—
169D3—541no—
170D3—541no—
171D3—541no—
172D3—541no—
173D3—1623no—
174C22—811no—
175C22#9221111yescharacteristic, complemented
176C4—811no—
177C3—31no—
178C3—61no—
179C3—93no—
180C3#1061975511yescharacteristic
181C3#1061975611yescharacteristic
182C3#1061975711yescharacteristic
183C3#1061976111yescharacteristic
184C2—31no—
185C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterH(3,𝔽3)⋊(C22⋊C9)C2
FrattiniC33C3⋊S4
FittingC22×C3×H(3,𝔽3)D3
socleC22×C32#272
LCSG ▷ H(3,𝔽3)⋊(C22⋊C9)
UCSC1

Complements

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

NH ≅ G/Ntype
1. H(3,𝔽3)⋊(C22⋊C9)C2semidirect
8. C32×C22⋊C9D3semidirect
10. C32⋊(C22⋊C9)D3semidirect
29. C22×H(3,𝔽3)D9semidirect
93. H(3,𝔽3)(C22⋊C9)⋊C2semidirect
175. C22#92211semidirect

Maximal subgroups

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

subgroupindex
H(3,𝔽3)⋊(C22⋊C9)2
C3×C3⋊((C22⋊C9)⋊C2)3
#106199773
#106197463
#922114