Finite Group Databasebeta

← C13⋊C3×#6912 #23748527

Subgroups — C13⋊C3×#6912 #23748527

Order 9477.

980 conjugacy classes of subgroups; only the 271 normal subgroups are shown.

normal subgroups only

This group has 980 conjugacy classes of subgroups — too many to draw. Only its 271 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
1C3×3−1+2×C13⋊C3C313yesmaximal
2C3×3−1+2×C13⋊C3C311yesmaximal, characteristic
3#15691670C312yesmaximal, complemented
4#15691669C316yesmaximal, complemented
5#15691668C319yesmaximal, complemented
6#15691667C319yesmaximal, complemented
7C13⋊C3×#733C319yesmaximal, complemented
8C13×#6912C311yesmaximal, characteristic, complemented
9C33×C13⋊C3C3211yescharacteristic
10C3×#66851C3216yes—
11C3×#66851C3212yes—
12C3×#66848—33no—
13C3×#66848C3213yes—
14C3×#66849—33no—
15C3×#66849C3213yes—
163−1+2×C13⋊C3—33no—
173−1+2×C13⋊C3—33no—
183−1+2×C13⋊C3—33no—
193−1+2×C13⋊C3—33no—
203−1+2×C13⋊C3—33no—
213−1+2×C13⋊C3—33no—
223−1+2×C13⋊C3—33no—
233−1+2×C13⋊C3—33no—
243−1+2×C13⋊C3—33no—
253−1+2×C13⋊C3C3219yes—
263−1+2×C13⋊C3C3219yes—
273−1+2×C13⋊C3C3219yes—
28C3×C9×C13⋊C3—33no—
29C3×C9×C13⋊C3C3213yes—
30#11760443C32118yescomplemented
31#11760442C32154yescomplemented
32C3×C13×3−1+2C3213yes—
33C3×C13×3−1+2C3211yescharacteristic
34C13×#733C3219yescomplemented
35C3×#6912—131nomaximal, Sylow
36C33×C13C3311yescharacteristic
37C32×C13⋊C3—93no—
38C32×C13⋊C3H(3,𝔽3)13yes—
39C32×C13⋊C3H(3,𝔽3)13yes—
40C32×C13⋊C3H(3,𝔽3)13yes—
41C32×C13⋊C3C3311yescharacteristic
42C32×C13⋊C3C3311yescharacteristic
43C32×C13⋊C3C3311yescharacteristic
44C13×3−1+2—33no—
45C13×3−1+2—33no—
46C13×3−1+2—33no—
47C13×3−1+2C3319yes—
48C3×C9×C13—33no—
49C3×C9×C13C3313yes—
50#66851—36no—
51#66851—36no—
52#66851—36no—
53#66851C33118yes—
54C3×C13⋊C9—36no—
55C3×C13⋊C9C3316yes—
56#66849—39no—
57#66849—39no—
58#66849—39no—
59#66849—39no—
60#66848—39no—
61#66848—39no—
62#66848—39no—
63#66848—39no—
64C9×C13⋊C3—39no—
65C9×C13⋊C3—39no—
66C9×C13⋊C3—39no—
67C9×C13⋊C3—33no—
68C9×C13⋊C3—33no—
69C9×C13⋊C3—33no—
70C32×3−1+2—131no—
71C32×3−1+2—133no—
72#6912—136no—
73#6912—132no—
74#6912—139no—
75#6912—139no—
76#6912C13⋊C311yescharacteristic, direct product factor
77C3×#733—139no—
78C32×C13—91no—
79C32×C13C3×H(3,𝔽3)13yes—
80C32×C13C3411yescharacteristic
81C3×C13⋊C3—39no—
82C3×C13⋊C3—33no—
83C3×C13⋊C3—93no—
84C3×C13⋊C3—93no—
85C3×C13⋊C3—91no—
86C3×C13⋊C3—91no—
87C3×C13⋊C3C3×H(3,𝔽3)11yescharacteristic
88C3×C13⋊C3C3×H(3,𝔽3)13yes—
89C3×C13⋊C3C3×H(3,𝔽3)13yes—
90C3×C13⋊C3C3×H(3,𝔽3)11yescharacteristic
91C3×C13⋊C3C3×H(3,𝔽3)11yescharacteristic
92C9×C13—39no—
93C9×C13—33no—
94C13⋊C9—318no—
95C13⋊C9—36no—
96C34—131no—
97C3×3−1+2—132no—
98C3×3−1+2—133no—
99C3×3−1+2—133no—
100C3×3−1+2—136no—
101C3×3−1+2—139no—
102C3×3−1+2—139no—
103C3×3−1+2—139no—
104C3×3−1+2—393no—
105C3×3−1+2—393no—
106C3×3−1+2—393no—
107C3×3−1+2—393no—
108C3×3−1+2—393no—
109C3×3−1+2—393no—
110C3×3−1+2—393no—
111C3×3−1+2—393no—
112C3×3−1+2—393no—
113C3×3−1+2—393no—
114C3×3−1+2—393no—
115C3×3−1+2C3×C13⋊C313yes—
116C3×3−1+2C3×C13⋊C311yescharacteristic
117C32×C9—133no—
118C32×C9—393no—
119#733—1354no—
120#733—1318no—
121#733C3×C13⋊C319yescomplemented
122C3×C13—33no—
123C3×C13—31no—
124C3×C13C32×H(3,𝔽3)11yescharacteristic
125C13⋊C3—33no—
126C13⋊C3—33no—
127C13⋊C3—31no—
128C13⋊C3—31no—
129C13⋊C3#691213yesdirect product factor
130C33—133no—
131C33—131no—
132C33—133no—
133C33—133no—
134C33—131no—
135C33—131no—
136C33—1173no—
137C33C32×C13⋊C311yescharacteristic
1383−1+2—33no—
1393−1+2—33no—
1403−1+2—33no—
1413−1+2—1318no—
1423−1+2—399no—
1433−1+2—399no—
1443−1+2—399no—
1453−1+2—399no—
1463−1+2—399no—
1473−1+2—399no—
1483−1+2—399no—
1493−1+2—399no—
1503−1+2—396no—
1513−1+2—396no—
1523−1+2—396no—
1533−1+2C32×C13⋊C319yes—
154C3×C9—33no—
155C3×C9—136no—
156C3×C9—393no—
157C3×C9—393no—
158C3×C9—393no—
159C3×C9—399no—
160C3×C9—399no—
161C3×C9—399no—
162C3×C9—396no—
163C3×C9C32×C13⋊C313yes—
164C13C3×#691211yescharacteristic, complemented, Sylow
165C32—91no—
166C32—131no—
167C32—131no—
168C32—131no—
169C32—133no—
170C32—133no—
171C32—399no—
172C32—393no—
173C32—1173no—
174C32—1173no—
175C32—1171no—
176C32—1171no—
177C32H(3,𝔽3)×C13⋊C313yes—
178C32C33×C13⋊C311yescharacteristic
179C9—39no—
180C9—33no—
181C9—396no—
182C9—3918no—
183C3—33no—
184C3—31no—
185C3—133no—
186C3—391no—
187C3—391no—
188C3—393no—
189C3—393no—
190C3C3×H(3,𝔽3)×C13⋊C311yescharacteristic
subgroupG/H
centerC3C3×H(3,𝔽3)×C13⋊C3
commutator, cosocleC32×C13C34
FrattiniC32C33×C13⋊C3
FittingC13×#6912C3
socleC3×C13C32×H(3,𝔽3)
prime radicalC33×C13⋊C3C32
hypercenter#6912C13⋊C3
hypocenterC13C3×#6912
LCSG ▷ C32×C13 ▷ C3×C13 ▷ C13
UCSC1 ◁ C3 ◁ C33 ◁ #6912

Complements

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

NH ≅ G/Ntype
3. #15691670C3semidirect
4. #15691669C3semidirect
5. #15691668C3semidirect
6. #15691667C3semidirect
7. C13⋊C3×#733C3semidirect
8. C13×#6912C3semidirect
30. #11760443C32semidirect
31. #11760442C32semidirect
34. C13×#733C32semidirect
76. #6912C13⋊C3direct (N × H)
121. #733C3×C13⋊C3semidirect
129. C13⋊C3#6912direct (N × H)
164. C13C3×#6912semidirect