Finite Group Databasebeta

← C22×D3×Dic9 #11722527

Subgroups — C22×D3×Dic9 #11722527

Order 864.

762 conjugacy classes of subgroups; only the 311 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 311 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
1C23×D3×C9C211yesmaximal, characteristic
2C22×C3⋊Dic9C211yesmaximal, characteristic, complemented
3C22×C3×Dic9C211yesmaximal, characteristic, complemented
4C2×D3×Dic9C2112yesmaximal, direct product factor
5C22×D3×Dic3—31nomaximal
6C23×Dic9—31nomaximal
7C23×C3×C9C2211yescharacteristic
8C22×D3×C9C418yescomplemented
9C22×D3×C9C2216yes—
10C2×C3⋊Dic9C2216yescomplemented
11C2×C3×Dic9C2216yescomplemented
12D3×Dic9C22116yesdirect product factor
13C23×C3×D3D311yescharacteristic
14C22×C3⋊Dic3—31no—
15C22×C3×Dic3—31no—
16C2×D3×Dic3—312no—
17C24×C9—31no—
18C22×Dic9—31no—
19C22×Dic9—312no—
20C22×Dic9—61no—
21C22×Dic9D311yescharacteristic, direct product factor
22C22×C3×C9C2×C414yescomplemented
23C22×C3×C9C2313yes—
24C2×D3×C9C2×C4124yescomplemented
25C2×D3×C9C2314yes—
26C3⋊Dic9C2314yescomplemented
27C3×Dic9C2314yescomplemented
28C23×Dic3—91no—
29C22×C4×D3—91no—
30C23×C32C2×D311yescharacteristic
31C22×C3×D3Dic318yes—
32C22×C3×D3C2×D316yes—
33C2×C3⋊Dic3—36no—
34C2×C3×Dic3—36no—
35D3×Dic3—316no—
36C23×C9—21no—
37C23×C9—38no—
38C23×C9—36no—
39C23×C9C2×D311yescharacteristic
40C2×Dic9—36no—
41C2×Dic9—316no—
42C2×Dic9—66no—
43C2×Dic9C2×D316yesdirect product factor
44C2×C3×C9C22×C416yescomplemented
45C2×C3×C9C2411yescharacteristic
46D3×C9C22×C418yescomplemented
47C24×C3—31no—
48C23×D3D911yescharacteristic
49C22×C3×C4—91no—
50C22×Dic3—31no—
51C22×Dic3—912no—
52C22×Dic3—91no—
53C22×Dic3—91no—
54C22×Dic3—181no—
55C2×C4×D3—912no—
56C22×C32C2×Dic314yes—
57C22×C32C22×D313yes—
58C2×C3×D3C2×Dic3124yes—
59C2×C3×D3C22×D314yes—
60C3⋊Dic3—34no—
61C3×Dic3—34no—
62C22×C9—24no—
63C22×C9—23no—
64C22×C9—324no—
65C22×C9—34no—
66C22×C9C4×D314yescomplemented
67C22×C9C22×D313yes—
68Dic9—34no—
69Dic9—64no—
70Dic9C22×D314yesdirect product factor
71C23×C4—271noSylow
72C3×C9C23×C411yescharacteristic, complemented, Sylow
73C23×C3—21no—
74C23×C3—38no—
75C23×C3—36no—
76C23×C3C2×D911yescharacteristic
77C23×C3D3211yescharacteristic
78C22×D3Dic918yesdirect product factor
79C22×D3C2×D916yes—
80C2×C3×C4—96no—
81C2×Dic3—36no—
82C2×Dic3—916no—
83C2×Dic3—96no—
84C2×Dic3—96no—
85C2×Dic3—186no—
86C4×D3—916no—
87C2×C32C22×Dic316yes—
88C2×C32C23×D311yescharacteristic
89C3×D3C22×Dic318yes—
90C2×C9—21no—
91C2×C9—26no—
92C2×C9—38no—
93C2×C9C2×C4×D316yescomplemented
94C2×C9C23×D311yescharacteristic
95C24—31no—
96C22×C4—91no—
97C22×C4—2712no—
98C22×C4—271no—
99C22×C3—24no—
100C22×C3—23no—
101C22×C3—34no—
102C22×C3—324no—
103C22×C3C2×Dic914yescomplemented
104C22×C3C22×D913yes—
105C22×C3D3×Dic314yes—
106C22×C3C2×D3213yes—
107C2×D3C2×Dic9124yesdirect product factor
108C2×D3C22×D914yes—
109C3×C4—94no—
110Dic3—34no—
111Dic3—94no—
112Dic3—94no—
113Dic3—184no—
114C32C23×Dic311yescharacteristic
115C9—21no—
116C9C22×C4×D311yescharacteristic, complemented
117C23—38no—
118C23—36no—
119C23D3×D911yescharacteristic
120C2×C4—96no—
121C2×C4—2716no—
122C2×C4—276no—
123C2×C3—21no—
124C2×C3—26no—
125C2×C3—38no—
126C2×C3C22×Dic916yescomplemented
127C2×C3C23×D911yescharacteristic
128C2×C3C2×D3×Dic316yes—
129C2×C3C22×D3211yescharacteristic
130D3C22×Dic918yesdirect product factor
131C22—34no—
132C22—324no—
133C22D3×Dic914yesdirect product factor
134C22C2×D3×D913yes—
135C4—94no—
136C4—274no—
137C3—21no—
138C3C23×Dic911yescharacteristic, complemented
139C3C22×D3×Dic311yescharacteristic
140C2—38no—
141C2C2×D3×Dic916yesdirect product factor
142C2C22×D3×D911yescharacteristic
subgroupG/H
center, hypercenterC23D3×D9
commutator, hypocenterC3×C9C23×C4
FrattiniC2×C3C22×D32
FittingC23×C3×C9C22
socleC23×C32C2×D3
prime radicalC23×C3×D3D3
cosocleC2×C3×C9C24
LCSG ▷ C3×C9
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C22×C3⋊Dic9C2semidirect
3. C22×C3×Dic9C2semidirect
4. C2×D3×Dic9C2direct (N × H)
8. C22×D3×C9C4semidirect
10. C2×C3⋊Dic9C22semidirect
11. C2×C3×Dic9C22semidirect
12. D3×Dic9C22direct (N × H)
21. C22×Dic9D3direct (N × H)
22. C22×C3×C9C2×C4semidirect
24. C2×D3×C9C2×C4semidirect
26. C3⋊Dic9C23semidirect
27. C3×Dic9C23semidirect
43. C2×Dic9C2×D3direct (N × H)
44. C2×C3×C9C22×C4semidirect
46. D3×C9C22×C4semidirect
66. C22×C9C4×D3semidirect
70. Dic9C22×D3direct (N × H)
72. C3×C9C23×C4semidirect
78. C22×D3Dic9direct (N × H)
93. C2×C9C2×C4×D3semidirect
103. C22×C3C2×Dic9semidirect
107. C2×D3C2×Dic9direct (N × H)
116. C9C22×C4×D3semidirect
126. C2×C3C22×Dic9semidirect
130. D3C22×Dic9direct (N × H)
133. C22D3×Dic9direct (N × H)
138. C3C23×Dic9semidirect
141. C2C2×D3×Dic9direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D3×C92
C22×C3⋊Dic92
C22×C3×Dic92
C2×D3×Dic92
C22×D3×Dic33
C23×Dic93