Finite Group Databasebeta

← #23748558

Subgroups — #23748558

Order 9477.

1118 conjugacy classes of subgroups; only the 286 normal subgroups are shown.

normal subgroups only

This group has 1118 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#15691698C311yesmaximal, characteristic, complemented
2C13⋊H(5,𝔽3)C311yesmaximal, characteristic, complemented
3C3×H(3,𝔽3)×C13⋊C3C311yesmaximal, characteristic, complemented
4#15691657C3124yesmaximal, complemented
5C3×#11760436C3112yesmaximal, complemented
6C13×3−1+4C311yesmaximal, characteristic, complemented
7C33×C13⋊C3C3214yescomplemented
8#11760452—39no—
9C3×#66851C32112yescomplemented
10C3×C32⋊(C13⋊C3)C3218yescomplemented
11C3×C32⋊(C13⋊C3)C32112yescomplemented
12H(3,𝔽3)×C13⋊C3—39no—
13H(3,𝔽3)×C13⋊C3—39no—
14#11760436C3219yescomplemented
15#11760436C32172yescomplemented
16C13×#737—39no—
17C3×C13×3−1+2C32112yescomplemented
18C3×C13×H(3,𝔽3)C3211yescharacteristic
19#10624930—131nomaximal, Sylow
20C33×C13C3314yes—
21C32×C13⋊C3—312no—
22C32×C13⋊C3—312no—
23C32×C13⋊C3—912no—
24C32×C13⋊C3C3311yescharacteristic
25C32×C13⋊C3C3318yes—
26C13×3−1+2—324no—
27C13×3−1+2C3319yes—
28C13×H(3,𝔽3)H(3,𝔽3)19yes—
29C3×C9×C13—312no—
30C32⋊(C13⋊C3)—324no—
31C32⋊(C13⋊C3)—324no—
32C32⋊(C13⋊C3)C3319yes—
33#66851—324no—
34#66851C3319yes—
35C3×C13⋊C9—312no—
363−1+4—131no—
373−1+4C13⋊C311yescharacteristic, complemented
38H(5,𝔽3)—131no—
39C32×H(3,𝔽3)—131no—
40#6909—1324no—
41C3×AΣL(1,𝔽27)—1312no—
42C32×C13—94no—
43C32×C13C3×H(3,𝔽3)112yes—
44C32×C13C3411yescharacteristic
45C3×C13⋊C3—31no—
46C3×C13⋊C3—33no—
47C3×C13⋊C3—38no—
48C3×C13⋊C3—39no—
49C3×C13⋊C3—936no—
50C3×C13⋊C3—98no—
51C3×C13⋊C3—2712no—
52C9×C13—39no—
53C13⋊C9—39no—
54C34—134no—
55#737—39no—
56#737—399no—
57C3×3−1+2—1312no—
58C3×3−1+2C3×C13⋊C3112yescomplemented
59C3×H(3,𝔽3)—1312no—
60C3×H(3,𝔽3)—138no—
61C3×H(3,𝔽3)—399no—
62C3×H(3,𝔽3)—399no—
63C3×H(3,𝔽3)C3×C13⋊C311yescharacteristic
64AΣL(1,𝔽27)—139no—
65AΣL(1,𝔽27)—1372no—
66C3×C13—31no—
67C3×C13—312no—
68C3×C13C32×H(3,𝔽3)11yescharacteristic
69C13⋊C3—33no—
70C13⋊C3—98no—
71C13⋊C3—99no—
72C33—131no—
73C33—138no—
74C33—3912no—
75C33—3912no—
76C33—11712no—
77C33C32×C13⋊C314yes—
783−1+2—324no—
793−1+2—139no—
803−1+2—3924no—
813−1+2C32×C13⋊C319yes—
82H(3,𝔽3)—139no—
83H(3,𝔽3)—3924no—
84H(3,𝔽3)—3924no—
85H(3,𝔽3)C32⋊(C13⋊C3)19yes—
86C3×C9—312no—
87C3×C9—3912no—
88C13#1062493011yescharacteristic, complemented, Sylow
89C32—94no—
90C32—393no—
91C32—391no—
92C32—399no—
93C32—398no—
94C32—35112no—
95C32—11736no—
96C32—1178no—
97C32C3×C32⋊(C13⋊C3)112yes—
98C32C33×C13⋊C311yescharacteristic
99C9—39no—
100C9—399no—
101C3—31no—
102C3—312no—
103C3—393no—
104C3—1179no—
105C3—1178no—
106C3C32×C32⋊(C13⋊C3)11yescharacteristic
subgroupG/H
centerC3C32×C32⋊(C13⋊C3)
commutator, cosocleC32×C13C34
FrattiniC32C33×C13⋊C3
FittingC13×3−1+4C3
socleC3×C13C32×H(3,𝔽3)
hypercenter3−1+4C13⋊C3
hypocenterC13#10624930
LCSG ▷ C32×C13 ▷ C3×C13 ▷ C13
UCSC1 ◁ C3 ◁ C3×H(3,𝔽3) ◁ 3−1+4

Complements

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

NH ≅ G/Ntype
1. #15691698C3semidirect
2. C13⋊H(5,𝔽3)C3semidirect
3. C3×H(3,𝔽3)×C13⋊C3C3semidirect
4. #15691657C3semidirect
5. C3×#11760436C3semidirect
6. C13×3−1+4C3semidirect
7. C33×C13⋊C3C32semidirect
9. C3×#66851C32semidirect
10. C3×C32⋊(C13⋊C3)C32semidirect
11. C3×C32⋊(C13⋊C3)C32semidirect
14. #11760436C32semidirect
15. #11760436C32semidirect
17. C3×C13×3−1+2C32semidirect
37. 3−1+4C13⋊C3semidirect
58. C3×3−1+2C3×C13⋊C3semidirect
88. C13#10624930semidirect