Finite Group Databasebeta

← C3×C3⋊D3×C22⋊C9 #14519264

Subgroups — C3×C3⋊D3×C22⋊C9 #14519264

Order 1944.

808 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 808 conjugacy classes of subgroups — too many to draw. Only its 112 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
1C33×C22⋊C9C211yesmaximal, characteristic, complemented
2C22×C32×C3⋊D3C311yesmaximal, characteristic
3C3⋊D3×C22⋊C9C313yesmaximal, direct product factor
4C3×D3×C22⋊C9—34nomaximal
5C3×C9×C3⋊D3—41nomaximal
6C22×C34C2×C311yescharacteristic
7C2×C32×C3⋊D3—31no—
8C2×C32×C3⋊D3—31no—
9C32×C22⋊C9—24no—
10C32×C22⋊C9—212no—
11C32×C22⋊C9D314yescomplemented
12C32×C22⋊C9C2×C313yescomplemented
13C33×C9—41noSylow
14C22×C3×C3⋊D3C913yescomplemented
15C22×C3×C3⋊D3C3211yescharacteristic
16C22×C32×D3—34no—
17C2×C3×C22⋊C9—91no—
18D3×C22⋊C9—312no—
19C2×C34—31no—
20C32×C3⋊D3—31no—
21C32×C3⋊D3A411yescharacteristic
22C9×C3⋊D3—43no—
23C3×D3×C9—124no—
24C22×C33—212no—
25C22×C33—24no—
26C22×C33C2×C913yescomplemented
27C22×C33C3×D314yes—
28C22×C33C2×C3211yescharacteristic
29C2×C3×C3⋊D3—33no—
30C2×C3×C3⋊D3—31no—
31C2×C3×C3⋊D3—33no—
32C2×C3×C3⋊D3—31no—
33C2×C32×D3—94no—
34C2×C32×D3—94no—
35C3×C22⋊C9—224no—
36C3×C22⋊C9—212no—
37C3×C22⋊C9—24no—
38C3×C22⋊C9—212no—
39C3×C22⋊C9C3×D3112yescomplemented
40C3×C22⋊C9C3⋊D311yescharacteristic, direct product factor
41C34C2×A411yescharacteristic
42C32×C9—44no—
43C32×C9—43no—
44C32×C9—812no—
45C32×C9—84no—
46C23×C32—91no—
47C22×C3⋊D3C3×C911yescharacteristic, complemented
48C22×C3×D3—312no—
49C22×C3×D3—34no—
50C2×C22⋊C9—93no—
51C2×C33—33no—
52C2×C33—34no—
53C2×C33—31no—
54C2×C33—612no—
55C2×C33—64no—
56C3×C3⋊D3—33no—
57C3×C3⋊D3—31no—
58C3×C3⋊D3C22⋊C913yesdirect product factor
59C3×C3⋊D3C3×A411yescharacteristic
60C32×D3—34no—
61C32×D3—94no—
62C2×C3×C9—361no—
63D3×C9—1212no—
64C22×C32—224no—
65C22×C32—212no—
66C22×C32—24no—
67C22×C32—212no—
68C22×C32—24no—
69C22×C32—271no—
70C22×C32—271no—
71C22×C32D3×C9112yescomplemented
72C22×C32C2×C3×C911yescharacteristic, complemented
73C22×C32C32×D314yes—
74C22×C32C3×C3⋊D311yescharacteristic
75C2×C3⋊D3—31no—
76C2×C3⋊D3—31no—
77C2×C3×D3—912no—
78C2×C3×D3—94no—
79C2×C3×D3—912no—
80C2×C3×D3—94no—
81C22⋊C9—212no—
82C22⋊C9C3×C3⋊D313yesdirect product factor
83C33—212no—
84C33—24no—
85C33C2×C22⋊C913yescomplemented
86C33D3×A414yes—
87C33C2×C3×A411yescharacteristic
88C3×C9—41no—
89C3×C9—412no—
90C3×C9—812no—
91C3×C9—824no—
92C3×C9—812no—
93C3×C9—84no—
94C23×C3—93no—
95C23×C3—91no—
96C22×D3—34no—
97C2×C32—31no—
98C2×C32—31no—
99C2×C32—312no—
100C2×C32—34no—
101C2×C32—64no—
102C2×C32—612no—
103C2×C32—64no—
104C2×C32—612no—
105C2×C32—624no—
106C2×C32—91no—
107C2×C32—271no—
108C3⋊D3—31no—
109C3⋊D3C3×C22⋊C911yescharacteristic, direct product factor
110C3×D3—312no—
111C3×D3—34no—
112C3×D3—912no—
113C3×D3—94no—
114C2×C9—363no—
115C22×C3—212no—
116C22×C3—24no—
117C22×C3—271no—
118C22×C3—273no—
119C22×C3—271no—
120C22×C3—273no—
121C22×C3C3×D3×C914yescomplemented
122C22×C3C9×C3⋊D313yescomplemented
123C22×C3C32×C3⋊D311yescharacteristic
124C2×D3—94no—
125C2×D3—94no—
126C32—224no—
127C32—24no—
128C32—212no—
129C32—24no—
130C32—212no—
131C32D3×C22⋊C9112yescomplemented
132C32C2×C3×C22⋊C911yescharacteristic, complemented
133C32C3×D3×A414yes—
134C32A4×C3⋊D311yescharacteristic
135C9—43no—
136C9—812no—
137C23—91noSylow
138C2×C3—31no—
139C2×C3—34no—
140C2×C3—33no—
141C2×C3—612no—
142C2×C3—64no—
143C2×C3—91no—
144C2×C3—93no—
145C2×C3—271no—
146C2×C3—273no—
147D3—34no—
148D3—94no—
149C22—271no—
150C22—271no—
151C22C3×C9×C3⋊D311yescharacteristic, complemented
152C3—212no—
153C3—24no—
154C3C3×D3×C22⋊C914yescomplemented
155C3C3⋊D3×C22⋊C913yesdirect product factor
156C3C3×A4×C3⋊D311yescharacteristic
157C2—31no—
158C2—91no—
159C2—271no—
subgroupG/H
center, hypercenterC32A4×C3⋊D3
commutator, hypocenterC22×C32C2×C3×C9
FrattiniC3C3×A4×C3⋊D3
Fitting, socleC22×C34C2×C3
prime radicalC22×C32×C3⋊D3C3
cosocleC22×C33C2×C32
LCSG ▷ C22×C32
UCSC1 ◁ C32

Complements

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

NH ≅ G/Ntype
1. C33×C22⋊C9C2semidirect
3. C3⋊D3×C22⋊C9C3direct (N × H)
11. C32×C22⋊C9D3semidirect
12. C32×C22⋊C9C2×C3semidirect
14. C22×C3×C3⋊D3C9semidirect
26. C22×C33C2×C9semidirect
39. C3×C22⋊C9C3×D3semidirect
40. C3×C22⋊C9C3⋊D3direct (N × H)
47. C22×C3⋊D3C3×C9semidirect
58. C3×C3⋊D3C22⋊C9direct (N × H)
71. C22×C32D3×C9semidirect
72. C22×C32C2×C3×C9semidirect
82. C22⋊C9C3×C3⋊D3direct (N × H)
85. C33C2×C22⋊C9semidirect
109. C3⋊D3C3×C22⋊C9direct (N × H)
121. C22×C3C3×D3×C9semidirect
122. C22×C3C9×C3⋊D3semidirect
131. C32D3×C22⋊C9semidirect
132. C32C2×C3×C22⋊C9semidirect
151. C22C3×C9×C3⋊D3semidirect
154. C3C3×D3×C22⋊C9semidirect
155. C3C3⋊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
C33×C22⋊C92
C22×C32×C3⋊D33
C3⋊D3×C22⋊C93
C3×D3×C22⋊C93
C3×C9×C3⋊D34