Finite Group Databasebeta

← #23748601

Subgroups — #23748601

Order 9477.

948 conjugacy classes of subgroups; only the 268 normal subgroups are shown.

normal subgroups only

This group has 948 conjugacy classes of subgroups — too many to draw. Only its 268 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
1#15691697C313yesmaximal, complemented
2C3×#11760453C311yesmaximal, characteristic, complemented
3#15691681C319yesmaximal, complemented
4#15691680C319yesmaximal, complemented
5#15691662C313yesmaximal, complemented
6#15691657C313yesmaximal, complemented
7#15691652C319yesmaximal, complemented
8C3×#11760443C311yesmaximal, characteristic, complemented
9C3×#11760441C311yesmaximal, characteristic, complemented
10C3×C13×#733C311yesmaximal, characteristic, complemented
11#11760454—39no—
12#11760454C32127yescomplemented
13#11760453—33no—
14#11760453—33no—
15#11760453—33no—
16#11760453—39no—
17C3×#66851C3213yes—
18C3×#66851C3211yescharacteristic
19C3×#66851C3211yescharacteristic
20C3×#66848C3213yescomplemented
21C3×#66849C3213yescomplemented
223−1+2×C13⋊C3—39no—
23C3×C32⋊(C13⋊C3)C3211yescharacteristic
24C3×C32⋊(C13⋊C3)C3213yes—
25C3×C9×C13⋊C3C3213yescomplemented
26#11760443C3213yescomplemented
27#11760443C3213yescomplemented
28#11760443C3213yescomplemented
29#11760441C3213yes—
30#11760441C3213yes—
31#11760441C3213yes—
32#11760439C32127yescomplemented
33#11760436C32127yescomplemented
34C3×C13×3−1+2C3213yes—
35C32×C9×C13C3211yescharacteristic
36C13×#733C3213yescomplemented
37C13×#733C3213yescomplemented
38C13×#733C3213yescomplemented
39#10624936—131nomaximal, Sylow
40C33×C13C3311yescharacteristic
41C32×C13⋊C3—33no—
42C32×C13⋊C3C3313yes—
43C13×3−1+2—33no—
44C13×3−1+2—33no—
45C13×3−1+2C3319yes—
46C3×C9×C13—31no—
47C3×C9×C13—31no—
48C3×C9×C13—31no—
49C3×C9×C13—33no—
50C3×C9×C13C3311yescharacteristic
51C3×C9×C13C3311yescharacteristic
52C3×C9×C13C3311yescharacteristic
53C32⋊(C13⋊C3)—31no—
54C32⋊(C13⋊C3)—31no—
55C32⋊(C13⋊C3)—31no—
56C32⋊(C13⋊C3)—33no—
57C32⋊(C13⋊C3)—33no—
58C32⋊(C13⋊C3)C3319yes—
59#66851—33no—
60#66851—33no—
61#66851—31no—
62#66851—31no—
63#66851—31no—
64#66851H(3,𝔽3)13yes—
65#66851H(3,𝔽3)13yes—
66#66851H(3,𝔽3)13yes—
67#66851C3319yes—
68C3×C13⋊C9—33no—
69C3×C13⋊C9C3313yes—
70C3×C13⋊C9C3313yes—
71#66849—327no—
72#66849—39no—
73#66848—327no—
74#66848—39no—
75C9×C13⋊C3—39no—
76C9×C13⋊C3—327no—
773−1+4—133no—
78C3×#737—131no—
79#6913—139no—
80#6913—139no—
81#6910—133no—
82#6909—133no—
83#6908—139no—
84C3×#733—131no—
85C3×#733C13⋊C311yescharacteristic, complemented
86C3×#732—131no—
87C32×C13—91no—
88C32×C13C3×H(3,𝔽3)11yescharacteristic
89C32×C13C3×H(3,𝔽3)11yescharacteristic
90C32×C13C3×H(3,𝔽3)11yescharacteristic
91C32×C13C3411yescharacteristic
92C3×C13⋊C3—33no—
93C3×C13⋊C3—39no—
94C3×C13⋊C3—93no—
95C3×C13⋊C3—273no—
96C9×C13—31no—
97C9×C13—39no—
98C9×C13—31no—
99C9×C13—31no—
100C13⋊C9—39no—
101C13⋊C9—33no—
102C13⋊C9C3×H(3,𝔽3)19yes—
103#737—1327no—
104#737—393no—
105#737—393no—
106#737—393no—
107#737—399no—
108#737—399no—
109C3×3−1+2—131no—
110C3×3−1+2—131no—
111C3×3−1+2—133no—
112C3×3−1+2—133no—
113C3×3−1+2—133no—
114C3×3−1+2—399no—
115C3×3−1+2C3×C13⋊C313yes—
116C3×H(3,𝔽3)—133no—
117C3×H(3,𝔽3)—131no—
118C32×C9—133no—
119C32×C9C3×C13⋊C311yescharacteristic
120#733—133no—
121#733—133no—
122#733—133no—
123#733C3×C13⋊C313yescomplemented
124#733C3×C13⋊C313yescomplemented
125#733C3×C13⋊C313yescomplemented
126#732—133no—
127#732—133no—
128#732—133no—
129#731—1327no—
130AΣL(1,𝔽27)—1327no—
131C3×C13—31no—
132C3×C13—31no—
133C3×C13—31no—
134C3×C13—31no—
135C3×C13C32×H(3,𝔽3)11yescharacteristic
136C13⋊C3—93no—
137C13⋊C3—99no—
138C33—133no—
139C33—393no—
140C33C32×C13⋊C311yescharacteristic
1413−1+2—33no—
1423−1+2—33no—
1433−1+2—133no—
1443−1+2—133no—
1453−1+2—133no—
1463−1+2—139no—
1473−1+2—399no—
1483−1+2—3927no—
1493−1+2—399no—
1503−1+2—3927no—
1513−1+2—393no—
1523−1+2—391no—
1533−1+2—391no—
1543−1+2—391no—
1553−1+2—393no—
1563−1+2C32×C13⋊C319yes—
157H(3,𝔽3)—139no—
158H(3,𝔽3)—393no—
159H(3,𝔽3)—393no—
160H(3,𝔽3)—391no—
161H(3,𝔽3)—391no—
162H(3,𝔽3)—391no—
163C3×C9—31no—
164C3×C9—31no—
165C3×C9—31no—
166C3×C9—33no—
167C3×C9—133no—
168C3×C9—133no—
169C3×C9—399no—
170C3×C9—3927no—
171C3×C9—393no—
172C3×C9C32×C13⋊C311yescharacteristic
173C3×C9C32×C13⋊C311yescharacteristic
174C3×C9C32×C13⋊C311yescharacteristic
175C13#1062493611yescharacteristic, complemented, Sylow
176C32—91no—
177C32—399no—
178C32—393no—
179C32—3513no—
180C32—1173no—
181C32H(3,𝔽3)×C13⋊C311yescharacteristic
182C32H(3,𝔽3)×C13⋊C311yescharacteristic
183C32H(3,𝔽3)×C13⋊C311yescharacteristic
184C32C33×C13⋊C311yescharacteristic
185C9—31no—
186C9—31no—
187C9—31no—
188C9—39no—
189C9—139no—
190C9—393no—
191C9—399no—
192C3—31no—
193C3—31no—
194C3—31no—
195C3—31no—
196C3—1179no—
197C3—1173no—
198C3C3×H(3,𝔽3)×C13⋊C311yescharacteristic
subgroupG/H
centerC3C3×H(3,𝔽3)×C13⋊C3
commutator, cosocleC32×C13C34
FrattiniC32C33×C13⋊C3
FittingC3×C13×#733C3
socleC3×C13C32×H(3,𝔽3)
hypercenterC3×#733C13⋊C3
hypocenterC13#10624936
LCSG ▷ C32×C13 ▷ C3×C13 ▷ C13
UCSC1 ◁ C3 ◁ C33 ◁ C3×#733

Complements

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

NH ≅ G/Ntype
1. #15691697C3semidirect
2. C3×#11760453C3semidirect
3. #15691681C3semidirect
4. #15691680C3semidirect
5. #15691662C3semidirect
6. #15691657C3semidirect
7. #15691652C3semidirect
8. C3×#11760443C3semidirect
9. C3×#11760441C3semidirect
10. C3×C13×#733C3semidirect
12. #11760454C32semidirect
20. C3×#66848C32semidirect
21. C3×#66849C32semidirect
25. C3×C9×C13⋊C3C32semidirect
26. #11760443C32semidirect
27. #11760443C32semidirect
28. #11760443C32semidirect
32. #11760439C32semidirect
33. #11760436C32semidirect
36. C13×#733C32semidirect
37. C13×#733C32semidirect
38. C13×#733C32semidirect
85. C3×#733C13⋊C3semidirect
123. #733C3×C13⋊C3semidirect
124. #733C3×C13⋊C3semidirect
125. #733C3×C13⋊C3semidirect
175. C13#10624936semidirect