Finite Group Databasebeta

← C32×D3×C22⋊C9 #14519243

Subgroups — C32×D3×C22⋊C9 #14519243

Order 1944.

998 conjugacy classes of subgroups; only the 234 normal subgroups are shown.

normal subgroups only

This group has 998 conjugacy classes of subgroups — too many to draw. Only its 234 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×C33×D3C311yesmaximal, characteristic
3C2×C32×C22⋊C9—31nomaximal
4C3×D3×C22⋊C9C3112yesmaximal, direct product factor
5C32×D3×C9—41nomaximal
6C22×C34C2×C311yescharacteristic
7C2×C33×D3—31no—
8C2×C33×D3—31no—
9C32×C22⋊C9—21no—
10C32×C22⋊C9—212no—
11C32×C22⋊C9D311yescharacteristic, direct product factor
12C32×C22⋊C9C2×C3112yescomplemented
13C33×C9—41noSylow
14C23×C33—31no—
15C22×C32×D3C919yescomplemented
16C22×C32×D3C3214yes—
17C2×C3×C22⋊C9—312no—
18D3×C22⋊C9C3219yesdirect product factor
19C2×C34—31no—
20C33×D3—31no—
21C33×D3A411yescharacteristic
22C2×C32×C9—121no—
23C3×D3×C9—412no—
24C22×C33—29no—
25C22×C33—24no—
26C22×C33—91no—
27C22×C33—91no—
28C22×C33C2×C919yescomplemented
29C22×C33C3×D311yescharacteristic
30C22×C33C2×C3214yes—
31C2×C32×D3—39no—
32C2×C32×D3—34no—
33C2×C32×D3—39no—
34C2×C32×D3—34no—
35C3×C22⋊C9—212no—
36C3×C22⋊C9—236no—
37C3×C22⋊C9C3×D3112yesdirect product factor
38C3×C22⋊C9C2×C3219yescomplemented
39C34C2×A411yescharacteristic
40C32×C9—41no—
41C32×C9—412no—
42C32×C9—812no—
43C32×C9—81no—
44C23×C32—39no—
45C23×C32—34no—
46C22×C3×D3C3×C9112yescomplemented
47C22×C3×D3C3311yescharacteristic
48C2×C22⋊C9—39no—
49C2×C33—31no—
50C2×C33—31no—
51C2×C33—39no—
52C2×C33—34no—
53C2×C33—69no—
54C2×C33—64no—
55C2×C33—91no—
56C32×D3—39no—
57C32×D3—34no—
58C32×D3C22⋊C919yesdirect product factor
59C32×D3C3×A414yes—
60C2×C3×C9—1212no—
61D3×C9—49no—
62C22×C32—236no—
63C22×C32—212no—
64C22×C32—24no—
65C22×C32—99no—
66C22×C32—94no—
67C22×C32—99no—
68C22×C32—94no—
69C22×C32D3×C919yescomplemented
70C22×C32C2×C3×C9112yescomplemented
71C22×C32C32×D314yes—
72C22×C32C2×C3311yescharacteristic
73C2×C3×D3—312no—
74C2×C3×D3—31no—
75C2×C3×D3—312no—
76C2×C3×D3—31no—
77C22⋊C9—29no—
78C22⋊C9C32×D319yesdirect product factor
79C33—29no—
80C33—24no—
81C33C2×C22⋊C919yescomplemented
82C33D3×A411yescharacteristic
83C33C2×C3×A414yes—
84C3×C9—412no—
85C3×C9—49no—
86C3×C9—836no—
87C3×C9—812no—
88C23×C3—312no—
89C23×C3—31no—
90C22×D3C32×C911yescharacteristic, complemented
91C2×C32—39no—
92C2×C32—39no—
93C2×C32—34no—
94C2×C32—34no—
95C2×C32—312no—
96C2×C32—31no—
97C2×C32—64no—
98C2×C32—636no—
99C2×C32—612no—
100C2×C32—99no—
101C2×C32—94no—
102C3×D3—312no—
103C3×D3—31no—
104C3×D3C3×C22⋊C9112yesdirect product factor
105C3×D3C32×A411yescharacteristic
106C2×C9—129no—
107C22×C3—212no—
108C22×C3—21no—
109C22×C3—91no—
110C22×C3—912no—
111C22×C3—91no—
112C22×C3—912no—
113C22×C3C3×D3×C9112yescomplemented
114C22×C3C2×C32×C911yescharacteristic, complemented
115C22×C3C33×D311yescharacteristic
116C2×D3—31no—
117C2×D3—31no—
118C32—24no—
119C32—236no—
120C32—212no—
121C32D3×C22⋊C919yesdirect product factor
122C32C2×C3×C22⋊C9112yescomplemented
123C32C3×D3×A414yes—
124C32C2×C32×A411yescharacteristic
125C9—49no—
126C9—89no—
127C23—31noSylow
128C2×C3—31no—
129C2×C3—31no—
130C2×C3—312no—
131C2×C3—312no—
132C2×C3—31no—
133C2×C3—612no—
134C2×C3—61no—
135C2×C3—91no—
136C2×C3—912no—
137D3—31no—
138D3C32×C22⋊C911yescharacteristic, direct product factor
139C22—91no—
140C22—91no—
141C22C32×D3×C911yescharacteristic, complemented
142C3—212no—
143C3—21no—
144C3C3×D3×C22⋊C9112yesdirect product factor
145C3C2×C32×C22⋊C911yescharacteristic, complemented
146C3C32×D3×A411yescharacteristic
147C2—31no—
148C2—31no—
149C2—91no—
subgroupG/H
center, hypercenterC33D3×A4
commutator, hypocenterC22×C3C2×C32×C9
FrattiniC3C32×D3×A4
Fitting, socleC22×C34C2×C3
prime radicalC22×C33×D3C3
cosocleC22×C32C2×C33
LCSG ▷ C22×C3
UCSC1 ◁ C33

Complements

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

NH ≅ G/Ntype
1. C33×C22⋊C9C2semidirect
4. C3×D3×C22⋊C9C3direct (N × H)
11. C32×C22⋊C9D3direct (N × H)
12. C32×C22⋊C9C2×C3semidirect
15. C22×C32×D3C9semidirect
18. D3×C22⋊C9C32direct (N × H)
28. C22×C33C2×C9semidirect
37. C3×C22⋊C9C3×D3direct (N × H)
38. C3×C22⋊C9C2×C32semidirect
46. C22×C3×D3C3×C9semidirect
58. C32×D3C22⋊C9direct (N × H)
69. C22×C32D3×C9semidirect
70. C22×C32C2×C3×C9semidirect
78. C22⋊C9C32×D3direct (N × H)
81. C33C2×C22⋊C9semidirect
90. C22×D3C32×C9semidirect
104. C3×D3C3×C22⋊C9direct (N × H)
113. C22×C3C3×D3×C9semidirect
114. C22×C3C2×C32×C9semidirect
121. C32D3×C22⋊C9direct (N × H)
122. C32C2×C3×C22⋊C9semidirect
138. D3C32×C22⋊C9direct (N × H)
141. C22C32×D3×C9semidirect
144. C3C3×D3×C22⋊C9direct (N × H)
145. C3C2×C32×C22⋊C9semidirect

Maximal subgroups

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

subgroupindex
C33×C22⋊C92
C22×C33×D33
C2×C32×C22⋊C93
C3×D3×C22⋊C93
C32×D3×C94