Finite Group Databasebeta

← C3⋊D3×D36 #13048652

Subgroups — C3⋊D3×D36 #13048652

Order 1296.

614 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×D9×C3⋊D3C212yesmaximal, complemented
2C4⋊(C3⋊(C3⋊D9))C211yesmaximal, characteristic, complemented
3C4×C9×C3⋊D3C211yesmaximal, characteristic, complemented
4C32×D36C211yesmaximal, characteristic, complemented
5#10619873C212yesmaximal, complemented
6C3⋊D3×D12—31nomaximal
7D3×D36—34nomaximal
8C2×C3⋊(C3⋊D9)C2212yescomplemented
9C2×C9×C3⋊D3C2211yescharacteristic
10C2×C32×D9C2212yescomplemented
11D9×C3⋊D3—24no—
12C32×C4×C9C2211yescharacteristic, complemented
13C9×C3⋊Dic3C2211yescharacteristic, complemented
14C2×D3×C3⋊D3—32no—
15C4⋊(C3⋊(C3⋊D3))—31no—
16C3×C4×C3⋊D3D311yescharacteristic
17C32×D12—31no—
18#6291—32no—
19C2×D3×D9—38no—
20C4⋊(C3⋊D9)—34no—
21C4⋊(C3⋊D9)—64no—
22C4×D3×C9—34no—
23C3×D36D314yescomplemented
24#6192—38no—
25C2×C32×C9C2311yescharacteristic
26C3⋊(C3⋊D9)—22no—
27C9×C3⋊D3D412yescomplemented
28C32×D9—22no—
29D4×C3⋊D3—91no—
30D3×D12—94no—
31C2×D36—91no—
32C2×C3⋊(C3⋊D3)—32no—
33C2×C3×C3⋊D3C2×D311yescharacteristic
34C2×C32×D3—32no—
35D3×C3⋊D3—64no—
36C33×C4C2×D311yescharacteristic
37C3×C3⋊Dic3C2×D311yescharacteristic
38C2×C3⋊D9—38no—
39C2×C3⋊D9—68no—
40C2×D3×C9—34no—
41C2×C3×D9C2×D318yescomplemented
42D3×D9—616no—
43C3×C4×C9—24no—
44C3×C4×C9C2×D314yescomplemented
45C9×Dic3—34no—
46C32×C9C2×D411yescharacteristic, complemented, Sylow
47C22×C3⋊D3—92no—
48C2×D32—98no—
49C32×D4—91no—
50#638—92no—
51C4⋊(C3⋊D3)—91no—
52C4⋊(C3⋊D3)—94no—
53C4⋊(C3⋊D3)—184no—
54C4×C3⋊D3D911yescharacteristic, complemented
55C3×D12—34no—
56C3×C4×D3—34no—
57#626—98no—
58C22×D9—92no—
59C2×C4×C9—91no—
60D36—92no—
61D36—91no—
62D36—184no—
63D36C3⋊D311yescharacteristic, direct product factor
64C2×C33C22×D311yescharacteristic
65C3⋊(C3⋊D3)—62no—
66C3×C3⋊D3D1212yes—
67C32×D3—62no—
68C2×C3×C9—24no—
69C2×C3×C9C22×D314yes—
70C3⋊D9—68no—
71C3⋊D9—128no—
72D3×C9—38no—
73C3×D9—28no—
74D3×D4—274no—
75C2×D12—271no—
76C22×C32—92no—
77C2×C3⋊D3—92no—
78C2×C3⋊D3—98no—
79C2×C3⋊D3—188no—
80C2×C3⋊D3—184no—
81C2×C3⋊D3C2×D911yescharacteristic
82C2×C3×D3—34no—
83C2×C3×D3—38no—
84D32—1816no—
85C32×C4—24no—
86C32×C4C2×D911yescharacteristic, complemented
87C32×C4D3214yes—
88C3⋊Dic3C2×D911yescharacteristic, complemented
89C3×Dic3—34no—
90C22×C9—91no—
91C2×D9—92no—
92C2×D9—188no—
93C2×D9—184no—
94C2×D9C2×C3⋊D312yescomplemented
95C4×C9—24no—
96C4×C9—91no—
97C4×C9C2×C3⋊D311yescharacteristic, complemented
98C33C2×D1211yescharacteristic
99C3×C9—24no—
100C3×C9D3×D414yescomplemented
101C22×D3—272no—
102C22×D3—278no—
103C3×D4—94no—
104C2×C3×C4—91no—
105#67—278no—
106D12—31no—
107D12—272no—
108D12—274no—
109D12—271no—
110D12—544no—
111C4×D3—34no—
112C2×C32—24no—
113C2×C32—182no—
114C2×C32C22×D911yescharacteristic
115C2×C32C2×D3214yes—
116C3⋊D3—182no—
117C3⋊D3—188no—
118C3⋊D3—368no—
119C3⋊D3D3612yesdirect product factor
120C3×D3—38no—
121C3×D3—68no—
122C2×C9—24no—
123C2×C9—92no—
124C2×C9C22×C3⋊D311yescharacteristic
125D9—22no—
126D9—182no—
127D9—368no—
128C2×D4—811noSylow
129C22×C3—91no—
130C22×C3—98no—
131C2×D3—34no—
132C2×D3—32no—
133C2×D3—278no—
134C2×D3—272no—
135C2×D3—548no—
136C2×D3—5416no—
137C2×D3—544no—
138C3×C4—24no—
139C3×C4—91no—
140C3×C4D3×D914yescomplemented
141C3×C4D3×C3⋊D311yescharacteristic
142Dic3—34no—
143C32—24no—
144C32C2×D3611yescharacteristic, complemented
145C32D3×D1214yes—
146C9—24no—
147C9D4×C3⋊D311yescharacteristic, complemented
148C23—812no—
149D4—91no—
150D4—812no—
151D4—811no—
152C2×C4—91no—
153C2×C3—24no—
154C2×C3—92no—
155C2×C3—188no—
156C2×C3C2×D3×D914yes—
157C2×C3C2×D3×C3⋊D311yescharacteristic
158D3—38no—
159D3—62no—
160D3—548no—
161D3—542no—
162D3—1088no—
163C22—91no—
164C22—92no—
165C22—812no—
166C22—1624no—
167C4—91no—
168C4D9×C3⋊D311yescharacteristic, complemented
169C3—24no—
170C3D3×D3614yescomplemented
171C3C3⋊D3×D1211yescharacteristic
172C2—92no—
173C2—182no—
174C2—1622no—
175C2C2×D9×C3⋊D311yescharacteristic
subgroupG/H
centerC2C2×D9×C3⋊D3
commutator, cosocleC2×C32×C9C23
FrattiniC2×C3C2×D3×C3⋊D3
FittingC32×C4×C9C22
socleC2×C33C22×D3
hypercenterC4D9×C3⋊D3
hypocenterC32×C9C2×D4
LCSG ▷ C2×C32×C9 ▷ C32×C9
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C2×D9×C3⋊D3C2semidirect
2. C4⋊(C3⋊(C3⋊D9))C2semidirect
3. C4×C9×C3⋊D3C2semidirect
4. C32×D36C2semidirect
5. #10619873C2semidirect
8. C2×C3⋊(C3⋊D9)C22semidirect
10. C2×C32×D9C22semidirect
12. C32×C4×C9C22semidirect
13. C9×C3⋊Dic3C22semidirect
23. C3×D36D3semidirect
27. C9×C3⋊D3D4semidirect
41. C2×C3×D9C2×D3semidirect
44. C3×C4×C9C2×D3semidirect
46. C32×C9C2×D4semidirect
54. C4×C3⋊D3D9semidirect
63. D36C3⋊D3direct (N × H)
86. C32×C4C2×D9semidirect
88. C3⋊Dic3C2×D9semidirect
94. C2×D9C2×C3⋊D3semidirect
97. C4×C9C2×C3⋊D3semidirect
100. C3×C9D3×D4semidirect
119. C3⋊D3D36direct (N × H)
140. C3×C4D3×D9semidirect
144. C32C2×D36semidirect
147. C9D4×C3⋊D3semidirect
168. C4D9×C3⋊D3semidirect
170. C3D3×D36semidirect

Maximal subgroups

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

subgroupindex
C2×D9×C3⋊D32
C4⋊(C3⋊(C3⋊D9))2
C4×C9×C3⋊D32
C32×D362
#106198732
C3⋊D3×D123
D3×D363