Finite Group Databasebeta

← #23748580

Subgroups — #23748580

Order 9477.

980 conjugacy classes of subgroups; only the 286 normal subgroups are shown.

normal subgroups only

This group has 980 conjugacy classes of subgroups — too many to draw. Only its 286 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
2#15691679C3118yesmaximal, complemented
3#15691670C312yesmaximal, complemented
4#15691666C311yesmaximal, characteristic, complemented
5#15691661C313yesmaximal, complemented
6#15691651C319yesmaximal, complemented
7C3×#11760435C313yesmaximal, complemented
8C32×C13×3−1+2C311yesmaximal, characteristic, complemented
9#11760454—318no—
10#11760453C32127yescomplemented
11C3×#66851C3216yes—
123−1+2×C13⋊C3—39no—
13C3×C32⋊(C13⋊C3)C3213yes—
14#11760443C32118yescomplemented
15#11760441C3219yescomplemented
16#11760438C32127yescomplemented
17#11760435C3219yescomplemented
18#11760435C32118yescomplemented
19C34×C13C3211yescharacteristic
20C3×C13×3−1+2—39no—
21C3×C13×3−1+2C3211yescharacteristic
22C3×C13×3−1+2C3211yescharacteristic
23C3×C13×3−1+2C3211yescharacteristic
24C3×C13×3−1+2C3216yescomplemented
25C32×C9×C13C3213yescomplemented
26#10624934—131nomaximal, Sylow
27C33×C13—33no—
28C33×C13—93no—
29C33×C13C3311yescharacteristic
30C33×C13C3312yes—
31C33×C13C3311yescharacteristic
32C32×C13⋊C3—33no—
33C13×3−1+2—33no—
34C13×3−1+2—33no—
35C13×3−1+2—318no—
36C13×3−1+2H(3,𝔽3)19yes—
37C3×C9×C13—39no—
38C3×C9×C13C3313yes—
39C3×C9×C13C3313yes—
40C3×C9×C13C3313yes—
41C32⋊(C13⋊C3)—36no—
42C32⋊(C13⋊C3)C3319yes—
43#66851—36no—
44#66851—36no—
45#66851C33118yes—
46C3×C13⋊C9—36no—
47#66849—327no—
48#66848—327no—
49C9×C13⋊C3—327no—
503−1+4—133no—
51C32×3−1+2C13⋊C311yescharacteristic, complemented
52#6913—1318no—
53#6912—132no—
54#6911—131no—
55#6910—133no—
56#6908—139no—
57C3×AΣL(1,𝔽27)—133no—
58C32×C13—33no—
59C32×C13—31no—
60C32×C13—32no—
61C32×C13—91no—
62C32×C13—99no—
63C32×C13—92no—
64C32×C13C3×H(3,𝔽3)13yes—
65C32×C13C3411yescharacteristic
66C3×C13⋊C3—39no—
67C3×C13⋊C3—273no—
68C9×C13—33no—
69C9×C13—33no—
70C9×C13C3×H(3,𝔽3)19yes—
71C13⋊C9—318no—
72C34C3×C13⋊C311yescharacteristic
73#737—1327no—
74#737—3918no—
75C3×3−1+2—39no—
76C3×3−1+2—136no—
77C3×3−1+2—399no—
78C3×3−1+2C3×C13⋊C311yescharacteristic
79C3×3−1+2C3×C13⋊C311yescharacteristic
80C3×3−1+2C3×C13⋊C311yescharacteristic
81C3×3−1+2C3×C13⋊C316yescomplemented
82C3×H(3,𝔽3)—133no—
83C32×C9C3×C13⋊C313yescomplemented
84#733—1318no—
85#732—139no—
86#731—1327no—
87AΣL(1,𝔽27)—1318no—
88AΣL(1,𝔽27)—139no—
89C3×C13—33no—
90C3×C13—33no—
91C3×C13—31no—
92C3×C13—92no—
93C3×C13C32×H(3,𝔽3)11yescharacteristic
94C13⋊C3—99no—
95C33—33no—
96C33—93no—
97C33—393no—
98C33C32×C13⋊C311yescharacteristic
99C33C32×C13⋊C312yes—
100C33C32×C13⋊C311yescharacteristic
1013−1+2—33no—
1023−1+2—33no—
1033−1+2—318no—
1043−1+2—1318no—
1053−1+2—396no—
1063−1+2—396no—
1073−1+2—3927no—
1083−1+2—3927no—
1093−1+2C32⋊(C13⋊C3)19yes—
110H(3,𝔽3)—139no—
111H(3,𝔽3)—396no—
112C3×C9—39no—
113C3×C9—396no—
114C3×C9—3927no—
115C3×C9C32×C13⋊C313yes—
116C3×C9C32×C13⋊C313yes—
117C3×C9C32×C13⋊C313yes—
118C13#1062493411yescharacteristic, complemented, Sylow
119C32—33no—
120C32—31no—
121C32—32no—
122C32—91no—
123C32—99no—
124C32—92no—
125C32—399no—
126C32—3513no—
127C32C3×C32⋊(C13⋊C3)13yes—
128C32C33×C13⋊C311yescharacteristic
129C9—33no—
130C9—33no—
131C9—3918no—
132C9C3×C32⋊(C13⋊C3)19yes—
133C3—31no—
134C3—33no—
135C3—33no—
136C3—92no—
137C3—1179no—
138C3C32×C32⋊(C13⋊C3)11yescharacteristic
subgroupG/H
centerC3C32×C32⋊(C13⋊C3)
commutator, cosocleC32×C13C34
FrattiniC32C33×C13⋊C3
FittingC32×C13×3−1+2C3
socleC3×C13C32×H(3,𝔽3)
hypercenterC32×3−1+2C13⋊C3
hypocenterC13#10624934
LCSG ▷ C32×C13 ▷ C3×C13 ▷ C13
UCSC1 ◁ C3 ◁ C3×3−1+2 ◁ C32×3−1+2

Complements

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

NH ≅ G/Ntype
1. #15691697C3semidirect
2. #15691679C3semidirect
3. #15691670C3semidirect
4. #15691666C3semidirect
5. #15691661C3semidirect
6. #15691651C3semidirect
7. C3×#11760435C3semidirect
8. C32×C13×3−1+2C3semidirect
10. #11760453C32semidirect
14. #11760443C32semidirect
15. #11760441C32semidirect
16. #11760438C32semidirect
17. #11760435C32semidirect
18. #11760435C32semidirect
24. C3×C13×3−1+2C32semidirect
25. C32×C9×C13C32semidirect
51. C32×3−1+2C13⋊C3semidirect
81. C3×3−1+2C3×C13⋊C3semidirect
83. C32×C9C3×C13⋊C3semidirect
118. C13#10624934semidirect