Finite Group Databasebeta

← #92265⋊C4 #14516826

Subgroups — #92265⋊C4 #14516826

Order 1944.

216 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 50 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×#92265C211yesmaximal, characteristic
2#11757618C211yesmaximal, characteristic, complemented
3#11757569C211yesmaximal, characteristic, complemented
4D3×3−1+2⋊C4—31nomaximal
5Dic3×AGL(1,ℤ/9)—31nomaximal
6D9×Dic9C311yesmaximal, characteristic, complemented
7C2×#6900C2211yescharacteristic
8#92265C412yescomplemented
9C2×D3×3−1+2—31no—
10C2×C3×AGL(1,ℤ/9)D311yescharacteristic
11C3⋊(3−1+2⋊C4)—31no—
12C3⋊(3−1+2⋊C4)—31no—
13C3⋊(3−1+2⋊C4)—61no—
14Dic3×3−1+2—31no—
15C3×3−1+2⋊C4D311yescharacteristic
16C2×D9⋊C9—21no—
17C2×C9×D9C2×C311yescharacteristic
18C9⋊Dic9C2×C311yescharacteristic, complemented
19Dic9⋊C9—21no—
20C9×Dic9C2×C311yescharacteristic, complemented
21#6900C2×C411yescharacteristic, complemented, Sylow
22C3×D3×Dic3—91no—
23C2×3−1+2⋊C4—91no—
24C4×AGL(1,ℤ/9)—91no—
25D3×Dic9—31no—
26Dic3×D9—31no—
27C2×C3×3−1+2—21no—
28C2×C3×3−1+2C2×D311yescharacteristic
29C2×C3×3−1+2C2×D311yescharacteristic
30D3×3−1+2—32no—
31C3×AGL(1,ℤ/9)Dic312yes—
32C2×C9⋊C9—21no—
33C2×C9⋊C9—21no—
34C2×C9⋊C9—41no—
35C2×C92C22×C311yescharacteristic
36D9⋊C9—22no—
37C9×D9C3×C412yescomplemented
38C2×C32×D3—31no—
39C3×C3⋊Dic3—91no—
40C32×Dic3—31no—
41C22×3−1+2—91no—
42C2×AGL(1,ℤ/9)—31no—
43C2×D3×C9—31no—
44C2×D3×C9—61no—
45C2×C3×D9C3×D311yescharacteristic
46C4×3−1+2—91no—
47C3⋊Dic9—31no—
48C3⋊Dic9—31no—
49C3⋊Dic9—61no—
503−1+2⋊C4—31no—
513−1+2⋊C4—91no—
523−1+2⋊C4—91no—
533−1+2⋊C4—181no—
543−1+2⋊C4—181no—
553−1+2⋊C4—183no—
56C9×Dic3—31no—
57C9×Dic3—61no—
58C3×Dic9C3×D311yescharacteristic
59C3×3−1+2—21no—
60C3×3−1+2C4×D311yescharacteristic
61C3×3−1+2C2×Dic311yescharacteristic
62C9⋊C9—21no—
63C9⋊C9—21no—
64C9⋊C9—41no—
65C92C2×C3×C411yescharacteristic, complemented
66C2×C3×Dic3—271no—
67C3×C4×D3—271no—
68D3×Dic3—91no—
69C2×Dic9—91no—
70C4×D9—91no—
71C2×C33D3211yescharacteristic
72C32×D3—32no—
73C2×3−1+2—31no—
74C2×3−1+2—31no—
75C2×3−1+2—61no—
76C2×3−1+2—61no—
77C2×3−1+2—63no—
78C2×3−1+2—92no—
79C2×C3×C9—21no—
80C2×C3×C9—21no—
81C2×C3×C9—21no—
82C2×C3×C9—41no—
83C2×C3×C9C2×C3×D311yescharacteristic
84C2×C3×C9C2×C3×D311yescharacteristic
85AGL(1,ℤ/9)—32no—
86D3×C9—32no—
87D3×C9—62no—
88C3×D9C3×Dic312yes—
89C22×C32—91no—
90C2×C3×D3—31no—
91C2×C3×D3—91no—
92C32×C4—91no—
93C3⋊Dic3—91no—
94C3×Dic3—31no—
95C3×Dic3—91no—
96C3×Dic3—271no—
97C3×Dic3—271no—
98C3×Dic3—541no—
99C22×C9—91no—
100C22×C9—181no—
101C2×D9AGL(1,ℤ/9)11yescharacteristic
102C4×C9—91no—
103C4×C9—181no—
104Dic9—91no—
105Dic9—91no—
106Dic9—181no—
107Dic9—181no—
108Dic9—183no—
109Dic9AGL(1,ℤ/9)11yescharacteristic, complemented
110C33D3×Dic311yescharacteristic
1113−1+2—31no—
1123−1+2—31no—
1133−1+2—61no—
1143−1+2—61no—
1153−1+2—63no—
116C3×C9—21no—
117C3×C9—21no—
118C3×C9—21no—
119C3×C9—41no—
120C3×C9C3×C4×D311yescharacteristic
121C3×C9C2×C3×Dic311yescharacteristic
122C2×C3×C4—811no—
123C2×Dic3—271no—
124C4×D3—271no—
125C2×C32—31no—
126C2×C32—31no—
127C2×C32—61no—
128C2×C32—92no—
129C2×C32C3×D3211yescharacteristic
130C3×D3—32no—
131C3×D3—92no—
132C2×C9—23no—
133C2×C9—21no—
134C2×C9—21no—
135C2×C9—61no—
136C2×C9—61no—
137C2×C9—92no—
138C2×C9—121no—
139C2×C9—182no—
140C2×C9C2×AGL(1,ℤ/9)11yescharacteristic
141C2×C9C2×AGL(1,ℤ/9)11yescharacteristic
142D93−1+2⋊C412yescomplemented
143C22×C3—91no—
144C22×C3—271no—
145C2×D3—31no—
146C3×C4—91no—
147C3×C4—271no—
148C3×C4—811no—
149Dic3—31no—
150Dic3—271no—
151Dic3—271no—
152Dic3—541no—
153C32—31no—
154C32—31no—
155C32—61no—
156C32C3×D3×Dic311yescharacteristic
157C9—23no—
158C9—21no—
159C9—21no—
160C9—61no—
161C9—61no—
162C9—121no—
163C9C4×AGL(1,ℤ/9)11yescharacteristic, complemented
164C9C2×3−1+2⋊C411yescharacteristic, complemented
165C2×C4—811noSylow
166C2×C3—21no—
167C2×C3—92no—
168C2×C3—91no—
169C2×C3—272no—
170C2×C3D3×AGL(1,ℤ/9)11yescharacteristic
171C2×C3D3×AGL(1,ℤ/9)11yescharacteristic
172D3—32no—
173C22—91no—
174C4—91no—
175C4—811no—
176C3—21no—
177C3—91no—
178C3Dic3×AGL(1,ℤ/9)11yescharacteristic
179C3D3×3−1+2⋊C411yescharacteristic
180C2—92no—
181C2#92265⋊C211yescharacteristic
subgroupG/H
center, hypercenterC2#92265⋊C2
commutator, hypocenterC92C2×C3×C4
Frattini, socleC2×C32C3×D32
FittingC2×#6900C22
prime radicalC2×C3×AGL(1,ℤ/9)D3
cosocleC2×C92C22×C3
LCSG ▷ C92
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. #11757618C2semidirect
3. #11757569C2semidirect
6. D9×Dic9C3semidirect
8. #92265C4semidirect
18. C9⋊Dic9C2×C3semidirect
20. C9×Dic9C2×C3semidirect
21. #6900C2×C4semidirect
37. C9×D9C3×C4semidirect
65. C92C2×C3×C4semidirect
109. Dic9AGL(1,ℤ/9)semidirect
142. D93−1+2⋊C4semidirect
163. C9C4×AGL(1,ℤ/9)semidirect
164. C9C2×3−1+2⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#922652
#117576182
#117575692
D3×3−1+2⋊C43
Dic3×AGL(1,ℤ/9)3
D9×Dic93