Finite Group Databasebeta

← C3×#15691662 #23748521

Subgroups — C3×#15691662 #23748521

Order 9477.

1088 conjugacy classes of subgroups; only the 292 normal subgroups are shown.

normal subgroups only

This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 292 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
1C32×#66851C311yesmaximal, characteristic, complemented
2C32×#66851C311yesmaximal, characteristic, complemented
3C32×C32⋊(C13⋊C3)C311yesmaximal, characteristic
4#15691662C3127yesmaximal, direct product factor
5C3×#11760439C319yesmaximal, complemented
6C32×C13×3−1+2C311yesmaximal, characteristic, complemented
7C33×C13⋊C3—31no—
8C3×#66851—31no—
9C3×#66851—31no—
10C3×#66851—36no—
11C3×#66851—31no—
12C3×#66851—31no—
13C3×#66851—31no—
14C3×#66851—36no—
15C3×#66851C3213yescomplemented
16C3×#66851C3219yescomplemented
17C3×#66851C3219yescomplemented
18C3×C32⋊(C13⋊C3)—31no—
19C3×C32⋊(C13⋊C3)—31no—
20C3×C32⋊(C13⋊C3)—36no—
21C3×C32⋊(C13⋊C3)C3213yes—
22C3×C32⋊(C13⋊C3)C3219yes—
23C32×C13⋊C9—31no—
24C32×C13⋊C9C3213yescomplemented
25#11760439C32181yescomplemented
26C34×C13C3211yescharacteristic
27C3×C13×3−1+2—31no—
28C3×C13×3−1+2—31no—
29C3×C13×3−1+2—36no—
30C3×C13×3−1+2C3213yescomplemented
31C3×C13×3−1+2C3219yescomplemented
32C32×C9×C13—31no—
33C3×#6910—131nomaximal, Sylow
34C33×C13—93no—
35C33×C13H(3,𝔽3)11yescharacteristic
36C33×C13H(3,𝔽3)11yescharacteristic
37C33×C13H(3,𝔽3)11yescharacteristic
38C33×C13H(3,𝔽3)16yes—
39C33×C13C3311yescharacteristic
40C33×C13C3313yes—
41C32×C13⋊C3—39no—
42C32×C13⋊C3—33no—
43C32×C13⋊C3—99no—
44C13×3−1+2—36no—
45C13×3−1+2—39no—
46C13×3−1+2—39no—
47C13×3−1+2C3319yescomplemented
48C3×C9×C13—39no—
49C3×C9×C13—33no—
50C32⋊(C13⋊C3)—36no—
51C32⋊(C13⋊C3)—39no—
52C32⋊(C13⋊C3)—39no—
53C32⋊(C13⋊C3)C3319yes—
54#66851—36no—
55#66851—39no—
56#66851—39no—
57#66851—39no—
58#66851—39no—
59#66851—39no—
60#66851C3319yescomplemented
61C3×C13⋊C9—39no—
62C3×C13⋊C9—33no—
63C3×C13⋊C9—36no—
64C3×C13⋊C9—33no—
65C3×C13⋊C9C3319yescomplemented
66C32×3−1+2—131no—
67C32×3−1+2—131no—
68C32×3−1+2C13⋊C311yescharacteristic, complemented
69C32×H(3,𝔽3)—131no—
70#6910—1327no—
71C3×#731—139no—
72C32×C13—33no—
73C32×C13—33no—
74C32×C13—33no—
75C32×C13—33no—
76C32×C13—96no—
77C32×C13—93no—
78C32×C13C3×H(3,𝔽3)13yes—
79C32×C13C3×H(3,𝔽3)12yes—
80C32×C13C3×H(3,𝔽3)13yes—
81C32×C13C3×H(3,𝔽3)13yes—
82C32×C13C3×H(3,𝔽3)11yescharacteristic
83C32×C13C3411yescharacteristic
84C3×C13⋊C3—39no—
85C3×C13⋊C3—927no—
86C3×C13⋊C3—99no—
87C9×C13—39no—
88C13⋊C9—39no—
89C13⋊C9—39no—
90C34—391no—
91C34C3×C13⋊C311yescharacteristic
92C3×3−1+2—36no—
93C3×3−1+2—31no—
94C3×3−1+2—31no—
95C3×3−1+2—139no—
96C3×3−1+2—133no—
97C3×3−1+2—139no—
98C3×3−1+2—396no—
99C3×3−1+2—396no—
100C3×3−1+2—391no—
101C3×3−1+2—391no—
102C3×3−1+2—391no—
103C3×3−1+2—391no—
104C3×3−1+2—391no—
105C3×3−1+2C3×C13⋊C313yescomplemented
106C3×3−1+2C3×C13⋊C319yescomplemented
107C3×H(3,𝔽3)—133no—
108C3×H(3,𝔽3)—139no—
109C3×H(3,𝔽3)—396no—
110C3×H(3,𝔽3)—391no—
111C3×H(3,𝔽3)—391no—
112C32×C9—31no—
113C32×C9—133no—
114C32×C9—391no—
115#731—1381no—
116C3×C13—33no—
117C3×C13—33no—
118C3×C13—33no—
119C3×C13—32no—
120C3×C13—31no—
121C3×C13#691013yescomplemented
122C3×C13C32×H(3,𝔽3)11yescharacteristic
123C13⋊C3—99no—
124C33—93no—
125C33—399no—
126C33—393no—
127C33—1179no—
128C33C32⋊(C13⋊C3)11yescharacteristic
129C33C32⋊(C13⋊C3)11yescharacteristic
130C33C32⋊(C13⋊C3)11yescharacteristic
131C33C32⋊(C13⋊C3)16yes—
132C33C32×C13⋊C311yescharacteristic
133C33C32×C13⋊C313yes—
1343−1+2—36no—
1353−1+2—39no—
1363−1+2—39no—
1373−1+2—139no—
1383−1+2—399no—
1393−1+2—399no—
1403−1+2—399no—
1413−1+2—399no—
1423−1+2—396no—
1433−1+2—399no—
1443−1+2C32×C13⋊C319yescomplemented
145H(3,𝔽3)—139no—
146H(3,𝔽3)—399no—
147H(3,𝔽3)—396no—
148H(3,𝔽3)—399no—
149C3×C9—39no—
150C3×C9—33no—
151C3×C9—139no—
152C3×C9—396no—
153C3×C9—399no—
154C3×C9—393no—
155C3×C9—393no—
156C13C3×#691011yescharacteristic, complemented, Sylow
157C32—33no—
158C32—33no—
159C32—33no—
160C32—33no—
161C32—96no—
162C32—93no—
163C32—399no—
164C32—11727no—
165C32—1179no—
166C32C3×C32⋊(C13⋊C3)13yes—
167C32C3×C32⋊(C13⋊C3)12yes—
168C32C3×C32⋊(C13⋊C3)13yes—
169C32C3×C32⋊(C13⋊C3)13yes—
170C32C3×C32⋊(C13⋊C3)11yescharacteristic
171C32C33×C13⋊C311yescharacteristic
172C9—39no—
173C9—399no—
174C9—399no—
175C3—33no—
176C3—33no—
177C3—33no—
178C3—32no—
179C3—31no—
180C3—1179no—
181C3#1569166213yesdirect product factor
182C3C32×C32⋊(C13⋊C3)11yescharacteristic
subgroupG/H
centerC32C3×C32⋊(C13⋊C3)
commutator, cosocleC32×C13C34
FrattiniC32C33×C13⋊C3
FittingC32×C13×3−1+2C3
socleC32×C13C3×H(3,𝔽3)
prime radicalC32×C32⋊(C13⋊C3)C3
hypercenterC32×3−1+2C13⋊C3
hypocenterC13C3×#6910
LCSG ▷ C32×C13 ▷ C3×C13 ▷ C13
UCSC1 ◁ C32 ◁ C34 ◁ C32×3−1+2

Complements

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

NH ≅ G/Ntype
1. C32×#66851C3semidirect
2. C32×#66851C3semidirect
4. #15691662C3direct (N × H)
5. C3×#11760439C3semidirect
6. C32×C13×3−1+2C3semidirect
15. C3×#66851C32semidirect
16. C3×#66851C32semidirect
17. C3×#66851C32semidirect
24. C32×C13⋊C9C32semidirect
25. #11760439C32semidirect
30. C3×C13×3−1+2C32semidirect
31. C3×C13×3−1+2C32semidirect
47. C13×3−1+2C33semidirect
60. #66851C33semidirect
65. C3×C13⋊C9C33semidirect
68. C32×3−1+2C13⋊C3semidirect
105. C3×3−1+2C3×C13⋊C3semidirect
106. C3×3−1+2C3×C13⋊C3semidirect
121. C3×C13#6910semidirect
144. 3−1+2C32×C13⋊C3semidirect
156. C13C3×#6910semidirect
181. C3#15691662direct (N × H)