Finite Group Databasebeta

← C22×D32×C9 #13049313

Subgroups — C22×D32×C9 #13049313

Order 1296.

1000 conjugacy classes of subgroups; only the 312 normal subgroups are shown.

normal subgroups only

This group has 1000 conjugacy classes of subgroups — too many to draw. Only its 312 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×C3⋊D3C211yesmaximal, characteristic, complemented
2C22×C3×D3×C9C212yesmaximal, complemented
3C2×D32×C9C2112yesmaximal, direct product factor
4C22×C3×D32C311yesmaximal, characteristic
5C23×D3×C9—32nomaximal
6C22×C32×C9C2211yescharacteristic, complemented
7C2×C9×C3⋊D3C2216yescomplemented
8C2×C3×D3×C9C22112yescomplemented
9D32×C9C22116yesdirect product factor
10C22×C3×C3⋊D3C2×C311yescharacteristic
11C22×C32×D3C2×C312yes—
12C2×C3×D32C2×C3112yes—
13C23×C3×C9—32no—
14C22×D3×C9—22no—
15C22×D3×C9—32no—
16C22×D3×C9—324no—
17C22×D3×C9—61no—
18C22×D3×C9D312yesdirect product factor
19C2×C32×C9C2313yescomplemented
20C9×C3⋊D3C2314yescomplemented
21C3×D3×C9C2318yescomplemented
22C23×C3×D3—32no—
23C22×D32C911yescharacteristic, direct product factor
24C24×C9—91no—
25C22×C33C22×C311yescharacteristic
26C2×C3×C3⋊D3C22×C316yes—
27C2×C32×D3C22×C3112yes—
28C3×D32C22×C3116yes—
29C22×C3×C9—22no—
30C22×C3×C9—21no—
31C22×C3×C9—312no—
32C22×C3×C9—41no—
33C22×C3×C9C2×D312yescomplemented
34C2×D3×C9—212no—
35C2×D3×C9—312no—
36C2×D3×C9—332no—
37C2×D3×C9—66no—
38C2×D3×C9C2×D3112yesdirect product factor
39C32×C9C2411yescharacteristic, complemented, Sylow
40C23×C32—32no—
41C22×C3⋊D3C2×C911yescharacteristic, complemented
42C22×C3×D3—22no—
43C22×C3×D3—32no—
44C22×C3×D3—324no—
45C22×C3×D3—61no—
46C22×C3×D3C2×C912yescomplemented
47C22×C3×D3C3×D312yes—
48C2×D32C2×C9112yesdirect product factor
49C23×C9—32no—
50C23×C9—62no—
51C23×C9—912no—
52C23×C9—91no—
53C2×C33C23×C313yes—
54C3×C3⋊D3C23×C314yes—
55C32×D3C23×C318yes—
56C2×C3×C9—26no—
57C2×C3×C9—23no—
58C2×C3×C9—38no—
59C2×C3×C9—43no—
60C2×C3×C9C22×D316yescomplemented
61D3×C9—28no—
62D3×C9—38no—
63D3×C9—64no—
64D3×C9C22×D318yesdirect product factor
65C24×C3—91no—
66C23×D3—32no—
67C22×C32—22no—
68C22×C32—21no—
69C22×C32—312no—
70C22×C32—41no—
71C22×C32C22×C911yescharacteristic, complemented
72C22×C32C2×C3×D312yes—
73C2×C3⋊D3C22×C916yescomplemented
74C2×C3×D3—212no—
75C2×C3×D3—312no—
76C2×C3×D3—332no—
77C2×C3×D3—66no—
78C2×C3×D3C22×C9112yescomplemented
79C2×C3×D3C2×C3×D3112yes—
80D32C22×C9116yesdirect product factor
81C22×C9—22no—
82C22×C9—312no—
83C22×C9—41no—
84C22×C9—612no—
85C22×C9—916no—
86C22×C9—96no—
87C22×C9D3211yescharacteristic, direct product factor
88C33C24×C311yescharacteristic
89C3×C9—22no—
90C3×C9—21no—
91C3×C9—41no—
92C3×C9C23×D312yescomplemented
93C23×C3—32no—
94C23×C3—32no—
95C23×C3—62no—
96C23×C3—912no—
97C23×C3—91no—
98C22×D3—32no—
99C22×D3—324no—
100C22×D3—61no—
101C22×D3D3×C912yesdirect product factor
102C2×C32—26no—
103C2×C32—23no—
104C2×C32—38no—
105C2×C32—43no—
106C2×C32C23×C913yescomplemented
107C2×C32C22×C3×D316yes—
108C3⋊D3C23×C914yescomplemented
109C3×D3—28no—
110C3×D3—38no—
111C3×D3—64no—
112C3×D3C23×C918yescomplemented
113C3×D3C22×C3×D318yes—
114C2×C9—26no—
115C2×C9—38no—
116C2×C9—43no—
117C2×C9—68no—
118C2×C9—94no—
119C2×C9C2×D3213yesdirect product factor
120C24—91noSylow
121C22×C3—21no—
122C22×C3—22no—
123C22×C3—312no—
124C22×C3—312no—
125C22×C3—41no—
126C22×C3—612no—
127C22×C3—916no—
128C22×C3—96no—
129C22×C3C2×D3×C912yescomplemented
130C22×C3C3×D3211yescharacteristic
131C2×D3—312no—
132C2×D3—332no—
133C2×D3—66no—
134C2×D3C2×D3×C9112yesdirect product factor
135C32—21no—
136C32—22no—
137C32—41no—
138C32C24×C911yescharacteristic, complemented
139C32C23×C3×D312yes—
140C9—22no—
141C9—41no—
142C9C22×D3211yescharacteristic, direct product factor
143C23—32no—
144C23—912no—
145C23—91no—
146C2×C3—23no—
147C2×C3—26no—
148C2×C3—38no—
149C2×C3—38no—
150C2×C3—43no—
151C2×C3—68no—
152C2×C3—94no—
153C2×C3C22×D3×C916yescomplemented
154C2×C3C2×C3×D3213yes—
155D3—38no—
156D3—64no—
157D3C22×D3×C918yesdirect product factor
158C22—312no—
159C22—916no—
160C22—96no—
161C22D32×C911yescharacteristic, direct product factor
162C3—21no—
163C3—22no—
164C3—41no—
165C3C23×D3×C912yescomplemented
166C3C22×C3×D3211yescharacteristic
167C2—38no—
168C2—94no—
169C2C2×D32×C913yesdirect product factor
subgroupG/H
center, hypercenterC22×C9D32
commutator, hypocenterC32C24×C9
FrattiniC3C22×C3×D32
FittingC22×C32×C9C22
socleC22×C33C22×C3
prime radicalC22×C3×D32C3
cosocleC33C24×C3
LCSG ▷ C32
UCSC1 ◁ C22×C9

Complements

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

NH ≅ G/Ntype
1. C22×C9×C3⋊D3C2semidirect
2. C22×C3×D3×C9C2semidirect
3. C2×D32×C9C2direct (N × H)
6. C22×C32×C9C22semidirect
7. C2×C9×C3⋊D3C22semidirect
8. C2×C3×D3×C9C22semidirect
9. D32×C9C22direct (N × H)
18. C22×D3×C9D3direct (N × H)
19. C2×C32×C9C23semidirect
20. C9×C3⋊D3C23semidirect
21. C3×D3×C9C23semidirect
23. C22×D32C9direct (N × H)
33. C22×C3×C9C2×D3semidirect
38. C2×D3×C9C2×D3direct (N × H)
39. C32×C9C24semidirect
41. C22×C3⋊D3C2×C9semidirect
46. C22×C3×D3C2×C9semidirect
48. C2×D32C2×C9direct (N × H)
60. C2×C3×C9C22×D3semidirect
64. D3×C9C22×D3direct (N × H)
71. C22×C32C22×C9semidirect
73. C2×C3⋊D3C22×C9semidirect
78. C2×C3×D3C22×C9semidirect
80. D32C22×C9direct (N × H)
87. C22×C9D32direct (N × H)
92. C3×C9C23×D3semidirect
101. C22×D3D3×C9direct (N × H)
106. C2×C32C23×C9semidirect
108. C3⋊D3C23×C9semidirect
112. C3×D3C23×C9semidirect
119. C2×C9C2×D32direct (N × H)
129. C22×C3C2×D3×C9semidirect
134. C2×D3C2×D3×C9direct (N × H)
138. C32C24×C9semidirect
142. C9C22×D32direct (N × H)
153. C2×C3C22×D3×C9semidirect
157. D3C22×D3×C9direct (N × H)
161. C22D32×C9direct (N × H)
165. C3C23×D3×C9semidirect
169. C2C2×D32×C9direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C9×C3⋊D32
C22×C3×D3×C92
C2×D32×C92
C22×C3×D323
C23×D3×C93