Finite Group Databasebeta

← #13091116

Subgroups — #13091116

Order 1458.

240 conjugacy classes of subgroups; only the 24 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 24 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#10624748C211yesmaximal, characteristic, complemented, Sylow
2#92391—31nomaximal
3C3⋊#4185C311yesmaximal, characteristic, complemented
4#4175⋊C3—32nomaximal
5C3×#4177—31nomaximal
6H(5,𝔽3)D311yescharacteristic, complemented
7#6910—21no—
8#6909—22no—
9#6909D312yescomplemented
10C3×#732C2×C311yescharacteristic, complemented
11C3×#731D311yescharacteristic, complemented
12#6893—21no—
13C3⋊((C3⋊D3)⋊C3)—33no—
14C3⋊((C3⋊D3)⋊C3)—31no—
15C3⋊((C3⋊D3)⋊C3)—32no—
16C3×C3⋊D9—31no—
17C3×(C3⋊D3)⋊C3—93no—
18C3×(C3⋊D3)⋊C3—91no—
19#4185—93no—
20#4177—33no—
21#4175—36no—
22C3×3−1+2—22no—
23C3×3−1+2—21no—
24C3×H(3,𝔽3)—21no—
25C3×H(3,𝔽3)—33no—
26C3×H(3,𝔽3)—33no—
27C3×H(3,𝔽3)—63no—
28C3×H(3,𝔽3)C3×D311yescharacteristic
29C3×H(3,𝔽3)C3×D312yescomplemented
30C3×H(3,𝔽3)C3⋊D311yescharacteristic
31C32×C9C3×D311yescharacteristic, complemented
32#732—33no—
33#731—33no—
34#731—63no—
35AΣL(1,𝔽27)—36no—
36AΣL(1,𝔽27)—66no—
37C32⋊C9—63no—
38C3⋊(C3⋊D3)—31no—
39C3⋊(C3⋊D3)—32no—
40C3×C3⋊D3—93no—
41C3×C3⋊D3—91no—
42C32×D3—271no—
43C3⋊D9—31no—
44(C3⋊D3)⋊C3—96no—
45(C3⋊D3)⋊C3—93no—
46(C3⋊D3)⋊C3—93no—
47(C3⋊D3)⋊C3—272no—
48C3×D9—271no—
49C33—23no—
50C33—31no—
51C33—31no—
52C33—33no—
53C33—32no—
54C33—63no—
55C33C3×C3⋊D311yescharacteristic
563−1+2—62no—
573−1+2—62no—
583−1+2—62no—
593−1+2—62no—
603−1+2—61no—
61H(3,𝔽3)—36no—
62H(3,𝔽3)—32no—
63H(3,𝔽3)—61no—
64H(3,𝔽3)—61no—
65H(3,𝔽3)—61no—
66H(3,𝔽3)—62no—
67H(3,𝔽3)—66no—
68H(3,𝔽3)—61no—
69H(3,𝔽3)—61no—
70H(3,𝔽3)(C3⋊D3)⋊C313yes—
71H(3,𝔽3)#27213yes—
72C3×C9—31no—
73C3×C9—31no—
74C3×C9—61no—
75C3×C9—62no—
76C3×C9—61no—
77C2×C32—811no—
78C3⋊D3—93no—
79C3⋊D3—91no—
80C3⋊D3—272no—
81C3⋊D3—811no—
82C3⋊D3—812no—
83C3×D3—273no—
84C3×D3—271no—
85C3×D3—811no—
86C3×D3—813no—
87D9—271no—
88C32—21no—
89C32—33no—
90C32—33no—
91C32—63no—
92C32—91no—
93C32—92no—
94C32—183no—
95C32—271no—
96C32—271no—
97C32—272no—
98C32—273no—
99C32—543no—
100C32C3⋊((C3⋊D3)⋊C3)11yescharacteristic
101C32C3×#27211yescharacteristic
102C9—91no—
103C9—182no—
104C9—181no—
105C2×C3—811no—
106C2×C3—813no—
107D3—271no—
108D3—811no—
109D3—813no—
110D3—2432no—
111C3—31no—
112C3—31no—
113C3—61no—
114C3—93no—
115C3—93no—
116C3—183no—
117C3—272no—
118C3#9230011yescharacteristic
119C2—811noSylow
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC3×#732C2×C3
FrattiniC33C3×C3⋊D3
Fitting#10624748C2
socleC3#92300
LCSG ▷ C3×#732
UCSC1

Complements

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

NH ≅ G/Ntype
1. #10624748C2semidirect
3. C3⋊#4185C3semidirect
6. H(5,𝔽3)D3semidirect
9. #6909D3semidirect
10. C3×#732C2×C3semidirect
11. C3×#731D3semidirect
29. C3×H(3,𝔽3)C3×D3semidirect
31. C32×C9C3×D3semidirect

Maximal subgroups

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

subgroupindex
#106247482
#923913
C3⋊#41853
#4175⋊C33
C3×#41773