Finite Group Databasebeta

← D3×C9×D8 #11721532

Subgroups — D3×C9×D8 #11721532

Order 864.

250 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 87 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
1D3×D4×C9C212yesmaximal, complemented
2C3×C9×D8C211yesmaximal, characteristic, complemented
3C9×#213C212yesmaximal, complemented
4C9×D24C211yesmaximal, characteristic, complemented
5D3×C8×C9C211yesmaximal, characteristic, complemented
6C3×D3×D8C311yesmaximal, characteristic
7C2×C9×D8—31nomaximal
8C22×D3×C9—22no—
9C3×D4×C9C2212yescomplemented
10C9×#67—22no—
11C9×D12C2212yescomplemented
12C4×D3×C9C2211yescharacteristic
13C3×C8×C9C2211yescharacteristic, complemented
14C9×C3⋊C8C2211yescharacteristic, complemented
15C3×D3×D4C2×C312yes—
16C32×D8C2×C311yescharacteristic
17C3×#213C2×C312yes—
18C3×D24C2×C311yescharacteristic
19C3×D3×C8C2×C311yescharacteristic
20C2×D4×C9—32no—
21C9×D8—21no—
22C9×D8—32no—
23C9×D8—31no—
24C9×D8D311yescharacteristic, direct product factor
25C2×C8×C9—31no—
26C22×C3×C9—22no—
27C2×D3×C9—22no—
28C2×D3×C9—44no—
29C2×D3×C9D411yescharacteristic
30C3×C4×C9C2311yescharacteristic
31C9×Dic3D411yescharacteristic
32C2×C3×D8—31no—
33D3×D8C911yescharacteristic, direct product factor
34C22×C3×D3—22no—
35C32×D4C22×C312yes—
36C3×#67—22no—
37C3×D12C22×C312yes—
38C3×C4×D3C22×C311yescharacteristic
39C23×C9—62no—
40C32×C8C22×C311yescharacteristic
41C3×C3⋊C8C22×C311yescharacteristic
42D4×C9—22no—
43D4×C9—32no—
44D4×C9—62no—
45D4×C9C2×D312yescomplemented
46C2×C4×C9—31no—
47C8×C9—21no—
48C8×C9—31no—
49C8×C9C2×D311yescharacteristic, complemented
50C2×C3×C9—42no—
51C2×C3×C9C2×D411yescharacteristic
52D3×C9—42no—
53D3×C9D812yesdirect product factor
54C2×C3×D4—32no—
55D3×D4C2×C912yescomplemented
56C3×D8—21no—
57C3×D8—32no—
58C3×D8—31no—
59C3×D8C2×C911yescharacteristic, complemented
60C3×D8C3×D311yescharacteristic
61C2×C3×C8—31no—
62#213C2×C912yescomplemented
63D24C2×C911yescharacteristic, complemented
64D3×C8C2×C911yescharacteristic, complemented
65C22×C32—22no—
66C2×C3×D3—22no—
67C2×C3×D3—44no—
68C2×C3×D3C3×D411yescharacteristic
69C32×C4C23×C311yescharacteristic
70C3×Dic3C3×D411yescharacteristic
71C22×C9—22no—
72C22×C9—31no—
73C22×C9—42no—
74C22×C9—62no—
75C22×C9—124no—
76C4×C9—21no—
77C4×C9—31no—
78C4×C9C22×D311yescharacteristic
79C2×D8—31noSylow
80C3×C9C2×D811yescharacteristic, complemented, Sylow
81C23×C3—62no—
82C22×D3—22no—
83C3×D4—22no—
84C3×D4—32no—
85C3×D4—62no—
86C3×D4C22×C912yescomplemented
87C3×D4C2×C3×D312yes—
88C2×C3×C4—31no—
89#67—22no—
90D12C22×C912yescomplemented
91C4×D3C22×C911yescharacteristic
92C3×C8—21no—
93C3×C8—31no—
94C3×C8C22×C911yescharacteristic, complemented
95C3×C8C2×C3×D311yescharacteristic
96C3⋊C8C22×C911yescharacteristic, complemented
97C2×C32—42no—
98C2×C32C2×C3×D411yescharacteristic
99C3×D3—42no—
100C3×D3C3×D812yes—
101C2×C9—21no—
102C2×C9—32no—
103C2×C9—42no—
104C2×C9—82no—
105C2×C9—122no—
106C2×C9D3×D411yescharacteristic
107C2×D4—32no—
108D8—32no—
109D8—31no—
110D8D3×C911yescharacteristic, direct product factor
111C2×C8—31no—
112C22×C3—22no—
113C22×C3—22no—
114C22×C3—31no—
115C22×C3—42no—
116C22×C3—62no—
117C22×C3—124no—
118C2×D3—22no—
119C2×D3—44no—
120C2×D3D4×C911yescharacteristic
121C3×C4—21no—
122C3×C4—31no—
123C3×C4C23×C911yescharacteristic
124C3×C4C22×C3×D311yescharacteristic
125Dic3D4×C911yescharacteristic
126C32C2×C3×D811yescharacteristic
127C9—21no—
128C9D3×D811yescharacteristic, direct product factor
129C23—62no—
130D4—32no—
131D4—62no—
132D4C2×D3×C912yescomplemented
133C2×C4—31no—
134C8—31no—
135C8C2×D3×C911yescharacteristic, complemented
136C2×C3—21no—
137C2×C3—32no—
138C2×C3—42no—
139C2×C3—42no—
140C2×C3—82no—
141C2×C3—122no—
142C2×C3C2×D4×C911yescharacteristic
143C2×C3C3×D3×D411yescharacteristic
144D3—42no—
145D3C9×D812yesdirect product factor
146C22—22no—
147C22—31no—
148C22—62no—
149C22—124no—
150C4—31no—
151C4C22×D3×C911yescharacteristic
152C3—21no—
153C3C2×C9×D811yescharacteristic, complemented
154C3C3×D3×D811yescharacteristic
155C2—32no—
156C2—42no—
157C2—122no—
158C2D3×D4×C911yescharacteristic
subgroupG/H
centerC2×C9D3×D4
commutatorC3×C4C23×C9
FrattiniC3×C4C22×C3×D3
FittingC3×C9×D8C2
socleC2×C32C2×C3×D4
prime radicalC3×D3×D8C3
cosocleC32×C4C23×C3
hypercenterC9×D8D3
hypocenterC3C2×C9×D8
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C9 ◁ C4×C9 ◁ C9×D8

Complements

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

NH ≅ G/Ntype
1. D3×D4×C9C2semidirect
2. C3×C9×D8C2semidirect
3. C9×#213C2semidirect
4. C9×D24C2semidirect
5. D3×C8×C9C2semidirect
9. C3×D4×C9C22semidirect
11. C9×D12C22semidirect
13. C3×C8×C9C22semidirect
14. C9×C3⋊C8C22semidirect
24. C9×D8D3direct (N × H)
33. D3×D8C9direct (N × H)
45. D4×C9C2×D3semidirect
49. C8×C9C2×D3semidirect
53. D3×C9D8direct (N × H)
55. D3×D4C2×C9semidirect
59. C3×D8C2×C9semidirect
62. #213C2×C9semidirect
63. D24C2×C9semidirect
64. D3×C8C2×C9semidirect
80. C3×C9C2×D8semidirect
86. C3×D4C22×C9semidirect
90. D12C22×C9semidirect
94. C3×C8C22×C9semidirect
96. C3⋊C8C22×C9semidirect
110. D8D3×C9direct (N × H)
128. C9D3×D8direct (N × H)
132. D4C2×D3×C9semidirect
135. C8C2×D3×C9semidirect
145. D3C9×D8direct (N × H)
153. C3C2×C9×D8semidirect

Maximal subgroups

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

subgroupindex
D3×D4×C92
C3×C9×D82
C9×#2132
C9×D242
D3×C8×C92
C3×D3×D83
C2×C9×D83