Finite Group Databasebeta

← #14516499

Subgroups — #14516499

Order 1944.

146 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 23 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#11757460C211yesmaximal, characteristic, complemented
2#10619983—31nomaximal
3C3×(C22⋊C27)⋊C2—31nomaximal
4((C22⋊C27)⋊C2)⋊C3—32nomaximal
5#92214—41nomaximal
6C22×#737D311yescharacteristic
7C2×#4207—31no—
8#66409—31no—
9#66353D312yescomplemented
10C3×C22⋊C27D311yescharacteristic, complemented
11#6873—41noSylow
12#6233—31no—
13#611⋊C3—92no—
14#638⋊C3—91no—
15C3×#611—91no—
16(C22⋊C27)⋊C2—32no—
17(C22⋊C27)⋊C2—31no—
18C2×#737—31no—
19#4207—61no—
20D27⋊C3—122no—
21C3×D27—121no—
22C22×3−1+2—61no—
23C22×3−1+2D912yes—
24C22×H(3,𝔽3)D911yescharacteristic
25C22×C3×C9—31no—
26C22×C3×C9C3⋊D311yescharacteristic
27C2×C3⋊D9—31no—
28C2×AGL(1,ℤ/9)—92no—
29C2×(C3⋊D3)⋊C3—91no—
30C2×C3×D9—91no—
31C3⋊Dic9—31no—
323−1+2⋊C4—92no—
33(C3⋊Dic3)⋊C3—91no—
34C3×Dic9—91no—
35C22⋊C27—31no—
36C22⋊C27—32no—
37#737S411yescharacteristic
38C27⋊C3—42no—
39C3×C27—41no—
40#638—91no—
41C3×#67—271no—
42#611—92no—
43#611—91no—
44C2×3−1+2—32no—
45C2×3−1+2—62no—
46C2×3−1+2—61no—
47C2×H(3,𝔽3)—31no—
48C2×C3×C9—31no—
49C2×C3×C9—31no—
50C2×C3×C9—61no—
51C3⋊D9—61no—
52AGL(1,ℤ/9)—182no—
53(C3⋊D3)⋊C3—181no—
54C3×D9—181no—
55D27—121no—
56D27—122no—
57C22×C32—31no—
58C22×C32C3⋊D911yescharacteristic
59C2×C3⋊D3—91no—
60C2×C3×D3—271no—
61C3⋊Dic3—91no—
62C3×Dic3—271no—
63C22×C9—21no—
64C22×C9—32no—
65C22×C9#27211yescharacteristic
66C2×D9—91no—
67C2×D9—92no—
68Dic9—91no—
69Dic9—92no—
703−1+2—61no—
713−1+2(C22⋊C9)⋊C212yes—
72H(3,𝔽3)(C22⋊C9)⋊C211yescharacteristic
73C3×C9—31no—
74C3×C9C3⋊S411yescharacteristic
75C27—121no—
76C27—122no—
77C3×D4—811no—
78#67—271no—
79#67—811no—
80C2×C32—31no—
81C2×C32—31no—
82C2×C32—61no—
83C3⋊D3—181no—
84C3×D3—541no—
85C2×C9—32no—
86C2×C9—31no—
87C2×C9—61no—
88C2×C9—62no—
89D9—182no—
90D9—181no—
91C22×C3—31no—
92C22×C3—91no—
93C22×C3—811no—
94C22×C3#418111yescharacteristic
95C2×D3—271no—
96C2×D3—811no—
97C3×C4—811no—
98Dic3—271no—
99Dic3—811no—
100C32—31no—
101C32C3⋊((C22⋊C9)⋊C2)11yescharacteristic
102C9—21no—
103C9—32no—
104C9#625811yescharacteristic
105D4—811noSylow
106C2×C3—31no—
107C2×C3—91no—
108C2×C3—91no—
109C2×C3—181no—
110C2×C3—1621no—
111D3—541no—
112D3—1621no—
113C22—811no—
114C22#9221411yescharacteristic, complemented
115C4—811no—
116C3—31no—
117C3—91no—
118C3#1061976111yescharacteristic
119C2—31no—
120C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenter#11757460C2
FrattiniC3×C9C3⋊S4
FittingC22×#737D3
socleC22×C3#4181
LCSG ▷ #11757460
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11757460C2semidirect
9. #66353D3semidirect
10. C3×C22⋊C27D3semidirect
114. C22#92214semidirect

Maximal subgroups

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

subgroupindex
#117574602
#106199833
C3×(C22⋊C27)⋊C23
((C22⋊C27)⋊C2)⋊C33
#922144