Finite Group Databasebeta

← C11×H(3,𝔽3)×3−1+2 #22548418

Subgroups — C11×H(3,𝔽3)×3−1+2 #22548418

Order 8019.

1244 conjugacy classes of subgroups; only the 518 normal subgroups are shown.

normal subgroups only

This group has 1244 conjugacy classes of subgroups — too many to draw. Only its 518 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
1C32×C11×3−1+2C314yesmaximal, complemented
2C32×C11×H(3,𝔽3)C311yesmaximal, characteristic
3C11×C9⋊H(3,𝔽3)C3124yesmaximal, complemented
4C11×#6891C318yesmaximal, complemented
5C9×C11×H(3,𝔽3)C313yesmaximal, complemented
6C34×C11C3214yes—
7C3×C11×3−1+2—336no—
8C3×C11×3−1+2C3218yes—
9C3×C11×3−1+2C3211yescharacteristic
10C3×C11×3−1+2C32124yescomplemented
11C3×C11×H(3,𝔽3)—39no—
12C3×C11×H(3,𝔽3)C3218yes—
13C3×C11×H(3,𝔽3)C3211yescharacteristic
14C32×C9×C11C32112yescomplemented
15C11×C32⋊C9C32124yescomplemented
16C11×C32⋊C9C32148yescomplemented
17H(3,𝔽3)×3−1+2C1111yesmaximal, characteristic, direct product factor, Sylow
18C33×C11—312no—
19C33×C11—312no—
20C33×C11—98no—
21C33×C11C3318yes—
22C33×C11C3311yescharacteristic
23C33×C11C3314yes—
24C11×3−1+2—324no—
25C11×3−1+2—372no—
26C11×3−1+2H(3,𝔽3)19yesdirect product factor
27C11×H(3,𝔽3)—324no—
28C11×H(3,𝔽3)3−1+219yesdirect product factor
29C3×C9×C11—336no—
30C3×C9×C11C33124yes—
31C3×C9×C11C3313yes—
32C32×3−1+2C3×C1114yescomplemented
33C32×H(3,𝔽3)C3×C1111yescharacteristic
34C9⋊H(3,𝔽3)C3×C11124yescomplemented
35#6891C3×C1118yescomplemented
36C9×H(3,𝔽3)C3×C1113yescomplemented
37C32×C11—34no—
38C32×C11—31no—
39C32×C11—32no—
40C32×C11—38no—
41C32×C11—38no—
42C32×C11—38no—
43C32×C11—316no—
44C32×C11—936no—
45C32×C11C3×H(3,𝔽3)13yes—
46C32×C11C3×3−1+2112yescomplemented
47C32×C11C3411yescharacteristic
48C9×C11—324no—
49C9×C11C3×H(3,𝔽3)19yescomplemented
50C34C32×C1114yes—
51C3×3−1+2—336no—
52C3×3−1+2C32×C1118yes—
53C3×3−1+2C32×C1111yescharacteristic
54C3×3−1+2C32×C11124yescomplemented
55C3×H(3,𝔽3)—39no—
56C3×H(3,𝔽3)C32×C1118yes—
57C3×H(3,𝔽3)C32×C1111yescharacteristic
58C32×C9C32×C11112yescomplemented
59C32⋊C9C32×C11124yescomplemented
60C32⋊C9C32×C11148yescomplemented
61C3×C11—33no—
62C3×C11—312no—
63C3×C11—98no—
64C3×C11C32×H(3,𝔽3)11yescharacteristic
65C3×C11C32×3−1+211yescharacteristic
66C3×C113−1+412yes—
67C33—312no—
68C33—312no—
69C33—98no—
70C33C33×C1118yes—
71C33C33×C1111yescharacteristic
72C33C33×C1114yes—
733−1+2—324no—
743−1+2—372no—
753−1+2C11×H(3,𝔽3)19yesdirect product factor
76H(3,𝔽3)—324no—
77H(3,𝔽3)C11×3−1+219yesdirect product factor
78C3×C9—336no—
79C3×C9C33×C11124yes—
80C3×C9C33×C1113yes—
81C11H(3,𝔽3)×3−1+211yescharacteristic, direct product factor, Sylow
82C32—32no—
83C32—38no—
84C32—34no—
85C32—31no—
86C32—316no—
87C32—38no—
88C32—38no—
89C32—936no—
90C32C3×C11×H(3,𝔽3)13yes—
91C32C3×C11×3−1+2112yescomplemented
92C32C34×C1111yescharacteristic
93C9—324no—
94C9C3×C11×H(3,𝔽3)19yescomplemented
95C3—33no—
96C3—312no—
97C3—98no—
98C3C32×C11×H(3,𝔽3)11yescharacteristic
99C3C32×C11×3−1+211yescharacteristic
100C3C11×3−1+412yes—
subgroupG/H
center, socleC32×C11C34
commutator, FrattiniC32C34×C11
LCSG ▷ C32 ▷ C1
UCSC1 ◁ C32×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C32×C11×3−1+2C3semidirect
3. C11×C9⋊H(3,𝔽3)C3semidirect
4. C11×#6891C3semidirect
5. C9×C11×H(3,𝔽3)C3semidirect
10. C3×C11×3−1+2C32semidirect
14. C32×C9×C11C32semidirect
15. C11×C32⋊C9C32semidirect
16. C11×C32⋊C9C32semidirect
17. H(3,𝔽3)×3−1+2C11direct (N × H)
26. C11×3−1+2H(3,𝔽3)direct (N × H)
28. C11×H(3,𝔽3)3−1+2direct (N × H)
32. C32×3−1+2C3×C11semidirect
34. C9⋊H(3,𝔽3)C3×C11semidirect
35. #6891C3×C11semidirect
36. C9×H(3,𝔽3)C3×C11semidirect
46. C32×C11C3×3−1+2semidirect
49. C9×C11C3×H(3,𝔽3)semidirect
54. C3×3−1+2C32×C11semidirect
58. C32×C9C32×C11semidirect
59. C32⋊C9C32×C11semidirect
60. C32⋊C9C32×C11semidirect
75. 3−1+2C11×H(3,𝔽3)direct (N × H)
77. H(3,𝔽3)C11×3−1+2direct (N × H)
81. C11H(3,𝔽3)×3−1+2direct (N × H)
91. C32C3×C11×3−1+2semidirect
94. C9C3×C11×H(3,𝔽3)semidirect