Finite Group Databasebeta

← C11×#10624897 #22548420

Subgroups — C11×#10624897 #22548420

Order 8019.

950 conjugacy classes of subgroups; only the 482 normal subgroups are shown.

normal subgroups only

This group has 950 conjugacy classes of subgroups — too many to draw. Only its 482 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×H(3,𝔽3)C311yesmaximal, characteristic
2C11×C9⋊H(3,𝔽3)C3124yesmaximal, complemented
3C11×#6891C318yesmaximal, complemented
4C9×C11×H(3,𝔽3)C313yesmaximal, complemented
5C3×C11×C32⋊C9C314yesmaximal, complemented
6C34×C11C3214yes—
7C3×C11×3−1+2C32124yescomplemented
8C3×C11×H(3,𝔽3)—39no—
9C3×C11×H(3,𝔽3)C3218yes—
10C3×C11×H(3,𝔽3)C3211yescharacteristic
11C32×C9×C11C32112yescomplemented
12C11×C32⋊C9C3211yescharacteristic
13C11×C32⋊C9C3218yes—
14C11×C32⋊C9C32124yescomplemented
15C11×C32⋊C9C32124yescomplemented
16C11×C32⋊C9C32124yescomplemented
17#10624897C1111yesmaximal, characteristic, direct product factor, Sylow
18C33×C11—312no—
19C33×C11—312no—
20C33×C11—94no—
21C33×C11—94no—
22C33×C11C3318yes—
23C33×C11C3314yes—
24C33×C11C3311yescharacteristic
25C11×3−1+2—924no—
26C11×H(3,𝔽3)—324no—
27C11×H(3,𝔽3)3−1+219yescomplemented
28C3×C9×C11—912no—
29C3×C9×C11C3313yes—
30C3×C9×C11C33124yes—
31C32×H(3,𝔽3)C3×C1111yescharacteristic
32C9⋊H(3,𝔽3)C3×C11124yescomplemented
33#6891C3×C1118yescomplemented
34C9×H(3,𝔽3)C3×C1113yescomplemented
35C3×C32⋊C9C3×C1114yescomplemented
36C32×C11—31no—
37C32×C11—34no—
38C32×C11—34no—
39C32×C11—31no—
40C32×C11—31no—
41C32×C11—34no—
42C32×C11—38no—
43C32×C11—38no—
44C32×C11—38no—
45C32×C11—38no—
46C32×C11—936no—
47C32×C11C3×3−1+2112yes—
48C32×C11#73713yes—
49C32×C11C3411yescharacteristic
50C9×C11—33no—
51C9×C11—324no—
52C34C32×C1114yes—
53C3×3−1+2C32×C11124yescomplemented
54C3×H(3,𝔽3)—39no—
55C3×H(3,𝔽3)C32×C1118yes—
56C3×H(3,𝔽3)C32×C1111yescharacteristic
57C32×C9C32×C11112yescomplemented
58C32⋊C9C32×C1111yescharacteristic
59C32⋊C9C32×C1118yes—
60C32⋊C9C32×C11124yescomplemented
61C32⋊C9C32×C11124yescomplemented
62C32⋊C9C32×C11124yescomplemented
63C3×C11—33no—
64C3×C11—312no—
65C3×C11—98no—
66C3×C11C32×3−1+211yescharacteristic
67C3×C11C3×#73711yescharacteristic
68C3×C11H(5,𝔽3)11yescharacteristic
69C3×C113−1+411yescharacteristic
70C33—312no—
71C33—312no—
72C33—94no—
73C33—94no—
74C33C33×C1118yes—
75C33C33×C1114yes—
76C33C33×C1111yescharacteristic
773−1+2—924no—
78H(3,𝔽3)—324no—
79H(3,𝔽3)C11×3−1+219yescomplemented
80C3×C9—912no—
81C3×C9C33×C1113yes—
82C3×C9C33×C11124yes—
83C11#1062489711yescharacteristic, direct product factor, Sylow
84C32—34no—
85C32—34no—
86C32—31no—
87C32—31no—
88C32—34no—
89C32—31no—
90C32—38no—
91C32—38no—
92C32—38no—
93C32—38no—
94C32—936no—
95C32C3×C11×3−1+2112yes—
96C32C11×#73713yes—
97C32C34×C1111yescharacteristic
98C9—33no—
99C9—324no—
100C3—33no—
101C3—312no—
102C3—98no—
103C3C32×C11×3−1+211yescharacteristic
104C3C3×C11×#73711yescharacteristic
105C3C11×H(5,𝔽3)11yescharacteristic
106C3C11×3−1+411yescharacteristic
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
2. C11×C9⋊H(3,𝔽3)C3semidirect
3. C11×#6891C3semidirect
4. C9×C11×H(3,𝔽3)C3semidirect
5. C3×C11×C32⋊C9C3semidirect
7. C3×C11×3−1+2C32semidirect
11. C32×C9×C11C32semidirect
14. C11×C32⋊C9C32semidirect
15. C11×C32⋊C9C32semidirect
16. C11×C32⋊C9C32semidirect
17. #10624897C11direct (N × H)
27. C11×H(3,𝔽3)3−1+2semidirect
32. C9⋊H(3,𝔽3)C3×C11semidirect
33. #6891C3×C11semidirect
34. C9×H(3,𝔽3)C3×C11semidirect
35. C3×C32⋊C9C3×C11semidirect
53. C3×3−1+2C32×C11semidirect
57. C32×C9C32×C11semidirect
60. C32⋊C9C32×C11semidirect
61. C32⋊C9C32×C11semidirect
62. C32⋊C9C32×C11semidirect
79. H(3,𝔽3)C11×3−1+2semidirect
83. C11#10624897direct (N × H)