Finite Group Databasebeta

← #14552004

Subgroups — #14552004

Order 2187.

120 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 38 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#10624841C311yesmaximal, characteristic, complemented
2#10624841C311yesmaximal, characteristic, complemented
3#10624840C311yesmaximal, characteristic, complemented
4#10624713C311yesmaximal, characteristic, complemented
5#10624541C311yesmaximal, characteristic, complemented
6#10624541C311yesmaximal, characteristic, complemented
7#10624541C311yesmaximal, characteristic, complemented
8#10624540C311yesmaximal, characteristic, complemented
9#10624539C311yesmaximal, characteristic, complemented
10#10624539C311yesmaximal, characteristic, complemented
11#10624538C311yesmaximal, characteristic, complemented
12#10624537C311yesmaximal, characteristic, complemented
13#10624536C311yesmaximal, characteristic, complemented
14#6908—31no—
15#6908—31no—
16C3×#733—31no—
17#6887C3211yescharacteristic
18#6880—32no—
19#6880C3211yescharacteristic
20#6880C3211yescharacteristic
21#6880C3211yescharacteristic
22#6880C3211yescharacteristic
23#6880C3211yescharacteristic
24#6880C3211yescharacteristic
25#6880C3211yescharacteristic
26#6879C3211yescharacteristic
27#6879C3211yescharacteristic
28#6878—32no—
29#6878—32no—
30C9⋊C27—32no—
31C32⋊C27—31no—
32#6864C3211yescharacteristic
33#6864C3211yescharacteristic
34C9×C27C3211yescharacteristic
35#737—91no—
36#737—91no—
37C3×3−1+2—91no—
38C32×C9H(3,𝔽3)11yescharacteristic
39#733—31no—
40#733—31no—
41#733—31no—
42#733—31no—
43#733—31no—
44#733—31no—
45#733—31no—
46#733—91no—
47#733—91no—
48#732—31no—
49#732—31no—
50#731—91no—
51#731—91no—
52AΣL(1,𝔽27)—91no—
53AΣL(1,𝔽27)—91no—
54C3×C27—31no—
55C3×C27—31no—
56C3×C27—31no—
57C9⋊C9—31no—
58C9⋊C9—31no—
59C32⋊C9—31no—
60C92H(3,𝔽3)12yes—
61C92C3311yescharacteristic
62C33#73211yescharacteristic
633−1+2—91no—
643−1+2—91no—
653−1+2—91no—
663−1+2—91no—
673−1+2—91no—
683−1+2—91no—
693−1+2—91no—
703−1+2—272no—
713−1+2—272no—
723−1+2—272no—
73H(3,𝔽3)—91no—
74H(3,𝔽3)—91no—
75C3×C9—32no—
76C3×C9—31no—
77C3×C9—91no—
78C3×C9—271no—
79C3×C9—271no—
80C3×C9—271no—
81C3×C9#73211yescharacteristic
82C3×C9#73211yescharacteristic
83C3×C9C3×H(3,𝔽3)11yescharacteristic
84C27—91no—
85C27—91no—
86C27—91no—
87C32—31no—
88C32—91no—
89C32—271no—
90C32—271no—
91C32C3×#73211yescharacteristic
92C9—31no—
93C9—31no—
94C9—31no—
95C9—92no—
96C9—91no—
97C9—271no—
98C9—271no—
99C9—271no—
100C9—271no—
101C9—271no—
102C9—271no—
103C9—271no—
104C3—31no—
105C3—91no—
106C3—811no—
107C3—811no—
108C3#1062483911yescharacteristic
subgroupG/H
center, socleC3#10624839
commutator, Frattini, cosocleC92C33
LCSG ▷ C92 ▷ C3×C9 ▷ C32 ▷ C3 ▷ C1
UCSC1 ◁ C3 ◁ C32 ◁ C32×C9 ◁ #6887 ◁ G
LECSG ▷ C92 ▷ C3×C9 ▷ C32 ▷ C3 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #10624841C3semidirect
2. #10624841C3semidirect
3. #10624840C3semidirect
4. #10624713C3semidirect
5. #10624541C3semidirect
6. #10624541C3semidirect
7. #10624541C3semidirect
8. #10624540C3semidirect
9. #10624539C3semidirect
10. #10624539C3semidirect
11. #10624538C3semidirect
12. #10624537C3semidirect
13. #10624536C3semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#106248413
#106248403
#106247133
#106245413
#106245403
#106245393
#106245383
#106245373
#106245363