Finite Group Databasebeta

← C2×C3⋊D3×C22⋊C9 #13049305

Subgroups — C2×C3⋊D3×C22⋊C9 #13049305

Order 1296.

504 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 75 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×C32×C22⋊C9C211yesmaximal, characteristic, complemented
2C3⋊D3×C22⋊C9C212yesmaximal, direct product factor
3C23×C3×C3⋊D3C311yesmaximal, characteristic
4C2×D3×C22⋊C9—34nomaximal
5C2×C9×C3⋊D3—41nomaximal
6C32×C22⋊C9C2211yescharacteristic, complemented
7C23×C33C2×C311yescharacteristic
8C22×C3×C3⋊D3—31no—
9C22×C3×C3⋊D3—31no—
10C22×C3×C3⋊D3—32no—
11C22×C3×C3⋊D3C2×C312yes—
12C2×C3×C22⋊C9—24no—
13C2×C3×C22⋊C9D314yescomplemented
14D3×C22⋊C9—38no—
15C2×C32×C9—41no—
16C9×C3⋊D3—42no—
17C23×C3⋊D3C911yescharacteristic, complemented
18C23×C3×D3—34no—
19C22×C22⋊C9—91no—
20C22×C33—31no—
21C22×C33—31no—
22C22×C33C22×C311yescharacteristic
23C2×C3×C3⋊D3—32no—
24C2×C3×C3⋊D3—31no—
25C2×C3×C3⋊D3—32no—
26C2×C3×C3⋊D3—32no—
27C2×C3×C3⋊D3—32no—
28C2×C3×C3⋊D3A411yescharacteristic
29C2×D3×C9—124no—
30C3×C22⋊C9—24no—
31C3×C22⋊C9C2×D314yescomplemented
32C32×C9—41noSylow
33C23×C32—24no—
34C23×C32C2×C911yescharacteristic, complemented
35C23×C32C3×D314yes—
36C22×C3⋊D3—31no—
37C22×C3⋊D3—31no—
38C22×C3⋊D3—32no—
39C22×C3⋊D3C2×C912yescomplemented
40C22×C3×D3—38no—
41C22×C3×D3—94no—
42C22×C3×D3—98no—
43C22×C3×D3—94no—
44C2×C22⋊C9—24no—
45C2×C22⋊C9—92no—
46C2×C22⋊C9C3⋊D311yescharacteristic, direct product factor
47C2×C33—31no—
48C2×C33—31no—
49C2×C33C2×A411yescharacteristic
50C3×C3⋊D3—32no—
51C3×C3⋊D3C2×A412yes—
52C2×C3×C9—44no—
53C2×C3×C9—84no—
54D3×C9—128no—
55C24×C3—91no—
56C23×D3—34no—
57C22×C32—24no—
58C22×C32—31no—
59C22×C32—31no—
60C22×C32—34no—
61C22×C32—34no—
62C22×C32—64no—
63C22×C32—64no—
64C22×C32C22×C911yescharacteristic, complemented
65C22×C32C2×C3×D314yes—
66C2×C3⋊D3—32no—
67C2×C3⋊D3—31no—
68C2×C3⋊D3—32no—
69C2×C3⋊D3—32no—
70C2×C3⋊D3—32no—
71C2×C3⋊D3C22⋊C911yescharacteristic, direct product factor
72C2×C3×D3—34no—
73C2×C3×D3—98no—
74C2×C3×D3—98no—
75C2×C3×D3—98no—
76C2×C3×D3—94no—
77C2×C3×D3—98no—
78C22×C9—361no—
79C22⋊C9—24no—
80C22⋊C9C2×C3⋊D311yescharacteristic, direct product factor
81C33C22×A411yescharacteristic
82C3×C9—44no—
83C3×C9—84no—
84C23×C3—24no—
85C23×C3—92no—
86C23×C3—271no—
87C23×C3—272no—
88C23×C3—271no—
89C23×C3D3×C914yescomplemented
90C23×C3C3×C3⋊D311yescharacteristic
91C22×D3—38no—
92C22×D3—94no—
93C22×D3—98no—
94C22×D3—94no—
95C2×C32—24no—
96C2×C32—31no—
97C2×C32—31no—
98C2×C32—34no—
99C2×C32—34no—
100C2×C32—64no—
101C2×C32—64no—
102C2×C32C2×C22⋊C911yescharacteristic, complemented
103C2×C32D3×A414yes—
104C3⋊D3—32no—
105C3⋊D3C2×C22⋊C912yesdirect product factor
106C3×D3—38no—
107C3×D3—98no—
108C2×C9—41no—
109C2×C9—84no—
110C2×C9—362no—
111C24—91noSylow
112C22×C3—24no—
113C22×C3—34no—
114C22×C3—31no—
115C22×C3—34no—
116C22×C3—31no—
117C22×C3—64no—
118C22×C3—64no—
119C22×C3—91no—
120C22×C3—272no—
121C22×C3—272no—
122C22×C3—272no—
123C22×C3—272no—
124C22×C3—271no—
125C22×C3C2×D3×C914yescomplemented
126C22×C3C2×C3×C3⋊D311yescharacteristic
127C2×D3—34no—
128C2×D3—98no—
129C2×D3—98no—
130C2×D3—98no—
131C2×D3—94no—
132C2×D3—98no—
133C32—24no—
134C32C22×C22⋊C911yescharacteristic, complemented
135C32C2×D3×A414yes—
136C9—41no—
137C9—84no—
138C23—92no—
139C23—271no—
140C23—272no—
141C23—271no—
142C23C9×C3⋊D311yescharacteristic, complemented
143C2×C3—24no—
144C2×C3—31no—
145C2×C3—31no—
146C2×C3—34no—
147C2×C3—34no—
148C2×C3—64no—
149C2×C3—64no—
150C2×C3—92no—
151C2×C3—272no—
152C2×C3D3×C22⋊C914yescomplemented
153C2×C3A4×C3⋊D311yescharacteristic
154D3—38no—
155D3—98no—
156C22—31no—
157C22—31no—
158C22—91no—
159C22—272no—
160C22—272no—
161C22—272no—
162C22—272no—
163C22—271no—
164C22C2×C9×C3⋊D311yescharacteristic, complemented
165C3—24no—
166C3C2×D3×C22⋊C914yescomplemented
167C3C2×A4×C3⋊D311yescharacteristic
168C2—31no—
169C2—31no—
170C2—92no—
171C2—272no—
172C2C3⋊D3×C22⋊C911yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3A4×C3⋊D3
commutator, hypocenterC22×C32C22×C9
FrattiniC3C2×A4×C3⋊D3
Fitting, socleC23×C33C2×C3
prime radicalC23×C3×C3⋊D3C3
cosocleC22×C33C22×C3
LCSG ▷ C22×C32
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C2×C32×C22⋊C9C2semidirect
2. C3⋊D3×C22⋊C9C2direct (N × H)
6. C32×C22⋊C9C22semidirect
13. C2×C3×C22⋊C9D3semidirect
17. C23×C3⋊D3C9semidirect
31. C3×C22⋊C9C2×D3semidirect
34. C23×C32C2×C9semidirect
39. C22×C3⋊D3C2×C9semidirect
46. C2×C22⋊C9C3⋊D3direct (N × H)
64. C22×C32C22×C9semidirect
71. C2×C3⋊D3C22⋊C9direct (N × H)
80. C22⋊C9C2×C3⋊D3direct (N × H)
89. C23×C3D3×C9semidirect
102. C2×C32C2×C22⋊C9semidirect
105. C3⋊D3C2×C22⋊C9direct (N × H)
125. C22×C3C2×D3×C9semidirect
134. C32C22×C22⋊C9semidirect
142. C23C9×C3⋊D3semidirect
152. C2×C3D3×C22⋊C9semidirect
164. C22C2×C9×C3⋊D3semidirect
166. C3C2×D3×C22⋊C9semidirect
172. C2C3⋊D3×C22⋊C9direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C22⋊C92
C3⋊D3×C22⋊C92
C23×C3×C3⋊D33
C2×D3×C22⋊C93
C2×C9×C3⋊D34