Finite Group Databasebeta

← #23748581

Subgroups — #23748581

Order 9477.

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

normal subgroups only

This group has 980 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
2C3×3−1+2×C13⋊C3C311yesmaximal, characteristic, complemented
3#15691681C319yesmaximal, complemented
4#15691680C319yesmaximal, complemented
5#15691670C311yesmaximal, characteristic, complemented
6#15691666C311yesmaximal, characteristic, complemented
7#15691662C313yesmaximal, complemented
8#15691652C319yesmaximal, complemented
9C3×#11760436C313yesmaximal, complemented
10C13×#6912C311yesmaximal, characteristic, complemented
11C33×C13⋊C3C3211yescharacteristic
12#11760454—39no—
13#11760454C32127yescomplemented
14#11760453—39no—
15C3×#66851C3213yes—
16C3×#66851C3211yescharacteristic
17C3×#66851C3211yescharacteristic
18C3×#66848C3213yescomplemented
19C3×#66849C3213yescomplemented
203−1+2×C13⋊C3—39no—
213−1+2×C13⋊C3—39no—
22C3×C32⋊(C13⋊C3)C3213yes—
23C3×C9×C13⋊C3C3213yescomplemented
24#11760443C3219yescomplemented
25#11760441C3219yescomplemented
26#11760439C32127yescomplemented
27#11760436C3219yescomplemented
28#11760436C3219yescomplemented
29#11760436C3219yescomplemented
30C3×C13×3−1+2C3213yes—
31C3×C13×3−1+2C3211yescharacteristic
32C13×#733C3219yescomplemented
33#10624934—131nomaximal, Sylow
34C33×C13C3311yescharacteristic
35C32×C13⋊C3—33no—
36C32×C13⋊C3—33no—
37C32×C13⋊C3—93no—
38C32×C13⋊C3C3311yescharacteristic
39C32×C13⋊C3C3311yescharacteristic
40C32×C13⋊C3C3311yescharacteristic
41C13×3−1+2—33no—
42C13×3−1+2—33no—
43C13×3−1+2—33no—
44C13×3−1+2C3319yes—
45C3×C9×C13—33no—
46C3×C9×C13C3313yes—
47C32⋊(C13⋊C3)—33no—
48C32⋊(C13⋊C3)—33no—
49C32⋊(C13⋊C3)C3319yes—
50#66851—33no—
51#66851—33no—
52#66851—33no—
53#66851H(3,𝔽3)19yes—
54#66851C3319yes—
55C3×C13⋊C9—33no—
56C3×C13⋊C9C3313yes—
57C3×C13⋊C9C3313yes—
58#66849—39no—
59#66849—327no—
60#66848—39no—
61#66848—327no—
62C9×C13⋊C3—39no—
63C9×C13⋊C3—327no—
643−1+4—133no—
65C32×3−1+2—131no—
66#6913—139no—
67#6913—139no—
68#6912—131no—
69#6912C13⋊C311yescharacteristic, complemented
70#6911—131no—
71#6910—133no—
72#6908—139no—
73C3×AΣL(1,𝔽27)—133no—
74C32×C13—91no—
75C32×C13C3×H(3,𝔽3)13yes—
76C32×C13C3411yescharacteristic
77C3×C13⋊C3—31no—
78C3×C13⋊C3—33no—
79C3×C13⋊C3—39no—
80C3×C13⋊C3—31no—
81C3×C13⋊C3—31no—
82C3×C13⋊C3—99no—
83C3×C13⋊C3—91no—
84C3×C13⋊C3—91no—
85C3×C13⋊C3—273no—
86C9×C13—39no—
87C9×C13—33no—
88C13⋊C9—39no—
89C13⋊C9—33no—
90C13⋊C9C3×H(3,𝔽3)19yes—
91C34—131no—
92#737—1327no—
93#737—399no—
94#737—399no—
95C3×3−1+2—131no—
96C3×3−1+2—131no—
97C3×3−1+2—133no—
98C3×3−1+2—133no—
99C3×3−1+2—133no—
100C3×3−1+2—399no—
101C3×3−1+2—399no—
102C3×3−1+2C3×C13⋊C313yes—
103C3×3−1+2C3×C13⋊C311yescharacteristic
104C3×H(3,𝔽3)—133no—
105C32×C9—133no—
106#733—139no—
107#733C3×C13⋊C319yescomplemented
108#732—139no—
109#731—1327no—
110AΣL(1,𝔽27)—139no—
111AΣL(1,𝔽27)—139no—
112AΣL(1,𝔽27)—139no—
113C3×C13—31no—
114C3×C13—33no—
115C3×C13C32×H(3,𝔽3)11yescharacteristic
116C13⋊C3—33no—
117C13⋊C3—91no—
118C13⋊C3—91no—
119C13⋊C3—99no—
120C33—131no—
121C33—131no—
122C33—131no—
123C33—393no—
124C33—393no—
125C33—1173no—
126C33C32×C13⋊C311yescharacteristic
1273−1+2—33no—
1283−1+2—33no—
1293−1+2—33no—
1303−1+2—139no—
1313−1+2—139no—
1323−1+2—399no—
1333−1+2—3927no—
1343−1+2—399no—
1353−1+2—3927no—
1363−1+2—393no—
1373−1+2—393no—
1383−1+2—393no—
1393−1+2C32×C13⋊C319yes—
140H(3,𝔽3)—139no—
141H(3,𝔽3)—393no—
142H(3,𝔽3)—393no—
143C3×C9—33no—
144C3×C9—133no—
145C3×C9—133no—
146C3×C9—399no—
147C3×C9—3927no—
148C3×C9—393no—
149C3×C9C32×C13⋊C313yes—
150C13#1062493411yescharacteristic, complemented, Sylow
151C32—91no—
152C32—393no—
153C32—391no—
154C32—399no—
155C32—391no—
156C32—391no—
157C32—3513no—
158C32—1179no—
159C32—1171no—
160C32—1171no—
161C32H(3,𝔽3)×C13⋊C313yes—
162C32C33×C13⋊C311yescharacteristic
163C9—39no—
164C9—33no—
165C9—139no—
166C9—393no—
167C9—399no—
168C3—31no—
169C3—33no—
170C3—393no—
171C3—1179no—
172C3—1171no—
173C3—1171no—
174C3C3×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)
hypercenter#6912C13⋊C3
hypocenterC13#10624934
LCSG ▷ C32×C13 ▷ C3×C13 ▷ C13
UCSC1 ◁ C3 ◁ C33 ◁ #6912

Complements

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

NH ≅ G/Ntype
1. #15691697C3semidirect
2. C3×3−1+2×C13⋊C3C3semidirect
3. #15691681C3semidirect
4. #15691680C3semidirect
5. #15691670C3semidirect
6. #15691666C3semidirect
7. #15691662C3semidirect
8. #15691652C3semidirect
9. C3×#11760436C3semidirect
10. C13×#6912C3semidirect
13. #11760454C32semidirect
18. C3×#66848C32semidirect
19. C3×#66849C32semidirect
23. C3×C9×C13⋊C3C32semidirect
24. #11760443C32semidirect
25. #11760441C32semidirect
26. #11760439C32semidirect
27. #11760436C32semidirect
28. #11760436C32semidirect
29. #11760436C32semidirect
32. C13×#733C32semidirect
69. #6912C13⋊C3semidirect
107. #733C3×C13⋊C3semidirect
150. C13#10624934semidirect