Finite Group Databasebeta

← C2×Dic9⋊H(3,𝔽3) #14517430

Subgroups — C2×Dic9⋊H(3,𝔽3) #14517430

Order 1944.

389 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 389 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C22×C9⋊H(3,𝔽3)C211yesmaximal, characteristic
2Dic9⋊H(3,𝔽3)C212yesmaximal, direct product factor
3C2×C3×3−1+2⋊C4C313yesmaximal, complemented
4C2×Dic3×H(3,𝔽3)—31nomaximal
5C2×C32×Dic9C311yesmaximal, characteristic, complemented
6C2×C9⋊H(3,𝔽3)C412yescomplemented
7C2×C9⋊H(3,𝔽3)C2211yescharacteristic
8C22×C3×3−1+2C2×C313yes—
9C22×C3×H(3,𝔽3)D311yescharacteristic
10C22×C32×C9C2×C311yescharacteristic
11C3×3−1+2⋊C4C2×C316yescomplemented
12Dic3×H(3,𝔽3)—32no—
13C32×Dic9C2×C312yescomplemented
14C22×C32⋊C9—23no—
15C22×C32⋊C9—21no—
16C9⋊H(3,𝔽3)C2×C411yescharacteristic, complemented, Sylow
17C2×C32×Dic3—31no—
18C2×C32×Dic3—33no—
19C2×C4×H(3,𝔽3)—91no—
20C2×3−1+2⋊C4—33no—
21C2×C3×Dic9—31no—
22C2×C3×Dic9C3211yescharacteristic
23C2×C3×3−1+2C3×C416yescomplemented
24C2×C3×3−1+2C22×C313yes—
25C2×C3×H(3,𝔽3)Dic312yes—
26C2×C3×H(3,𝔽3)C2×D311yescharacteristic
27C2×C32×C9C3×C412yescomplemented
28C2×C32×C9C22×C311yescharacteristic
29C2×C32⋊C9—26no—
30C2×C32⋊C9—22no—
31C2×C32⋊C9—23no—
32C2×C32⋊C9—21no—
33C22×C33C3×D311yescharacteristic
34C22×C33C3×D313yes—
35C32×Dic3—32no—
36C32×Dic3—36no—
37C22×3−1+2—33no—
38C22×3−1+2—63no—
39C22×H(3,𝔽3)—31no—
40C22×H(3,𝔽3)—61no—
41C22×C3×C9—21no—
42C22×C3×C9—23no—
43C22×C3×C9—31no—
44C22×C3×C9—61no—
45C22×C3×C9C2×C3211yescharacteristic
46C4×H(3,𝔽3)—92no—
473−1+2⋊C4—36no—
48C3×Dic9—32no—
49C3×Dic9C2×C3212yes—
50C3×3−1+2C2×C3×C413yescomplemented
51C3×H(3,𝔽3)C2×Dic311yescharacteristic
52C32×C9C2×C3×C411yescharacteristic, complemented
53C32⋊C9—23no—
54C32⋊C9—21no—
55C2×C32×C4—93no—
56C2×C32×C4—91no—
57C2×C3×Dic3—31no—
58C2×C3×Dic3—91no—
59C2×C3×Dic3—93no—
60C2×Dic9H(3,𝔽3)11yescharacteristic, complemented
61C2×C33C3×Dic312yes—
62C2×C33C3×Dic316yes—
63C2×C33C2×C3×D311yescharacteristic
64C2×C33C2×C3×D313yes—
65C2×3−1+2—36no—
66C2×3−1+2—33no—
67C2×3−1+2—66no—
68C2×3−1+2—63no—
69C2×H(3,𝔽3)—32no—
70C2×H(3,𝔽3)—31no—
71C2×H(3,𝔽3)—62no—
72C2×H(3,𝔽3)—61no—
73C2×C3×C9—22no—
74C2×C3×C9—26no—
75C2×C3×C9—21no—
76C2×C3×C9—23no—
77C2×C3×C9—32no—
78C2×C3×C9—31no—
79C2×C3×C9—62no—
80C2×C3×C9—61no—
81C2×C3×C9C32×C412yes—
82C2×C3×C9C22×C3211yescharacteristic
83C22×C32—21no—
84C22×C32—31no—
85C22×C32—33no—
86C22×C32—33no—
87C22×C32—61no—
88C22×C32—63no—
89C22×C32AGL(1,ℤ/9)11yescharacteristic
90C22×C32C32×D311yescharacteristic
91C32×C4—96no—
92C32×C4—92no—
93C3×Dic3—32no—
94C3×Dic3—92no—
95C3×Dic3—96no—
96C22×C9—21no—
97C22×C9—61no—
98C22×C9—63no—
99C22×C9C2×H(3,𝔽3)11yescharacteristic
100Dic9C2×H(3,𝔽3)12yescomplemented
101C33C2×C3×Dic311yescharacteristic
102C33C2×C3×Dic313yes—
1033−1+2—33no—
1043−1+2—63no—
105H(3,𝔽3)—31no—
106H(3,𝔽3)—61no—
107C3×C9—21no—
108C3×C9—23no—
109C3×C9—31no—
110C3×C9—61no—
111C3×C9C2×C32×C411yescharacteristic
112C2×C3×C4—91no—
113C2×C3×C4—271no—
114C2×C3×C4—273no—
115C2×Dic3—31no—
116C2×C32—22no—
117C2×C32—21no—
118C2×C32—32no—
119C2×C32—31no—
120C2×C32—36no—
121C2×C32—36no—
122C2×C32—33no—
123C2×C32—33no—
124C2×C32—62no—
125C2×C32—61no—
126C2×C32—66no—
127C2×C32—63no—
128C2×C323−1+2⋊C412yescomplemented
129C2×C32C2×AGL(1,ℤ/9)11yescharacteristic
130C2×C32C32×Dic312yes—
131C2×C32C2×C32×D311yescharacteristic
132C2×C9—22no—
133C2×C9—21no—
134C2×C9—62no—
135C2×C9—66no—
136C2×C9—61no—
137C2×C9—63no—
138C2×C9C4×H(3,𝔽3)12yescomplemented
139C2×C9C22×H(3,𝔽3)11yescharacteristic
140C22×C3—21no—
141C22×C3—31no—
142C22×C3—61no—
143C22×C3—93no—
144C22×C3D3×H(3,𝔽3)11yescharacteristic
145C22×C3C3×AGL(1,ℤ/9)11yescharacteristic
146C3×C4—92no—
147C3×C4—272no—
148C3×C4—276no—
149Dic3—32no—
150C32—21no—
151C32—31no—
152C32—33no—
153C32—33no—
154C32—61no—
155C32—63no—
156C32C2×3−1+2⋊C411yescharacteristic, complemented
157C32C2×C32×Dic311yescharacteristic
158C9—21no—
159C9—61no—
160C9—63no—
161C9C2×C4×H(3,𝔽3)11yescharacteristic, complemented
162C2×C4—91noSylow
163C2×C3—21no—
164C2×C3—22no—
165C2×C3—31no—
166C2×C3—32no—
167C2×C3—61no—
168C2×C3—62no—
169C2×C3—93no—
170C2×C3—96no—
171C2×C3Dic3×H(3,𝔽3)12yes—
172C2×C3C3×3−1+2⋊C412yes—
173C2×C3C2×D3×H(3,𝔽3)11yescharacteristic
174C2×C3C2×C3×AGL(1,ℤ/9)11yescharacteristic
175C22D9⋊H(3,𝔽3)11yescharacteristic
176C4—92no—
177C3—21no—
178C3—31no—
179C3—61no—
180C3—93no—
181C3C2×Dic3×H(3,𝔽3)11yescharacteristic
182C3C2×C3×3−1+2⋊C411yescharacteristic
183C2Dic9⋊H(3,𝔽3)12yesdirect product factor
184C2C2×D9⋊H(3,𝔽3)11yescharacteristic
subgroupG/H
centerC22×C3C3×AGL(1,ℤ/9)
commutatorC3×C9C2×C32×C4
FrattiniC2×C32C2×C32×D3
FittingC22×C9⋊H(3,𝔽3)C2
socleC22×C32C32×D3
prime radicalC22×C3×H(3,𝔽3)D3
cosocleC2×C3×C9C22×C32
hypercenterC22×C32AGL(1,ℤ/9)
hypocenterC9C2×C4×H(3,𝔽3)
LCSG ▷ C3×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C22×C32

Complements

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

NH ≅ G/Ntype
2. Dic9⋊H(3,𝔽3)C2direct (N × H)
3. C2×C3×3−1+2⋊C4C3semidirect
5. C2×C32×Dic9C3semidirect
6. C2×C9⋊H(3,𝔽3)C4semidirect
11. C3×3−1+2⋊C4C2×C3semidirect
13. C32×Dic9C2×C3semidirect
16. C9⋊H(3,𝔽3)C2×C4semidirect
23. C2×C3×3−1+2C3×C4semidirect
27. C2×C32×C9C3×C4semidirect
50. C3×3−1+2C2×C3×C4semidirect
52. C32×C9C2×C3×C4semidirect
60. C2×Dic9H(3,𝔽3)semidirect
100. Dic9C2×H(3,𝔽3)semidirect
128. C2×C323−1+2⋊C4semidirect
138. C2×C9C4×H(3,𝔽3)semidirect
156. C32C2×3−1+2⋊C4semidirect
161. C9C2×C4×H(3,𝔽3)semidirect
183. C2Dic9⋊H(3,𝔽3)direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C9⋊H(3,𝔽3)2
Dic9⋊H(3,𝔽3)2
C2×C3×3−1+2⋊C43
C2×Dic3×H(3,𝔽3)3
C2×C32×Dic93