Finite Group Databasebeta

← #14516825

Subgroups — #14516825

Order 1944.

159 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 159 conjugacy classes of subgroups — too many to draw. Only its 40 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#11757613C211yesmaximal, characteristic
2#11757568C212yesmaximal
3#6189⋊C3—32nomaximal
4#10619531C311yesmaximal, characteristic, complemented
5C2×#6896C2211yescharacteristic
6C3⋊(3−1+2⋊C4)—32no—
7Dic3×3−1+2—32no—
8C3×3−1+2⋊C4D312yes—
9C9⋊Dic9C2×C311yescharacteristic
10Dic9⋊C9—22no—
11#66316—61no—
12C9×Dic9C2×C312yes—
13#6896Q811yescharacteristic, complemented, Sylow
14C3×#627—91no—
153−1+2⋊Q8—92no—
16#6189—32no—
17C2×C3×3−1+2C2×D312yes—
18C2×C9⋊C9—22no—
19C2×C9⋊C9—41no—
20C2×C32⋊C9—21no—
21C2×C92C22×C311yescharacteristic
22C3×C3⋊Dic3—91no—
23C32×Dic3—32no—
24C4×3−1+2—92no—
25C3⋊Dic9—32no—
26C3⋊Dic9—61no—
273−1+2⋊C4—32no—
283−1+2⋊C4—92no—
293−1+2⋊C4—182no—
30C9×Dic3—32no—
31C9×Dic3—62no—
32C3×Dic9C3×D312yes—
33C3×3−1+2Dic612yes—
34C9⋊C9—22no—
35C9⋊C9—41no—
36C32⋊C9—21no—
37C92C3×Q811yescharacteristic, complemented
38C3×Dic6—272no—
39#627—91no—
40Dic18—92no—
41C2×C33D3211yescharacteristic
42C2×3−1+2—32no—
43C2×3−1+2—62no—
44C2×C3×C9—22no—
45C2×C3×C9—21no—
46C2×C3×C9—41no—
47C2×C3×C9C2×C3×D312yes—
48C32×C4—92no—
49C3⋊Dic3—91no—
50C3×Dic3—32no—
51C3×Dic3—92no—
52C3×Dic3—272no—
53C3×Dic3—541no—
54C4×C9—92no—
55C4×C9—182no—
56Dic9—92no—
57Dic9—182no—
58Dic9—541no—
59Dic9AGL(1,ℤ/9)12yes—
60C33#62711yescharacteristic
613−1+2—32no—
623−1+2—62no—
63C3×C9—21no—
64C3×C9—22no—
65C3×C9—41no—
66C3×C9C3×Dic612yes—
67C3×Q8—811no—
68Dic6—272no—
69C2×C32—32no—
70C2×C32—61no—
71C2×C32C3×D3211yescharacteristic
72C2×C9—22no—
73C2×C9—61no—
74C2×C9—62no—
75C2×C9—121no—
76C2×C9C2×AGL(1,ℤ/9)12yes—
77C3×C4—92no—
78C3×C4—272no—
79C3×C4—811no—
80Dic3—32no—
81Dic3—272no—
82Dic3—541no—
83C32—32no—
84C32—61no—
85C32C3×#62711yescharacteristic
86C9—22no—
87C9—61no—
88C9—62no—
89C9—121no—
90C93−1+2⋊Q812yescomplemented
91Q8—811noSylow
92C2×C3—21no—
93C2×C3—91no—
94C2×C3D3×AGL(1,ℤ/9)12yes—
95C4—92no—
96C4—811no—
97C3—21no—
98C3—91no—
99C3#6189⋊C312yes—
100C2#92264⋊C211yescharacteristic
subgroupG/H
center, hypercenterC2#92264⋊C2
commutator, cosocleC2×C92C22×C3
Frattini, socleC2×C32C3×D32
FittingC2×#6896C22
prime radicalC2×C33D32
hypocenterC92C3×Q8
LCSG ▷ C2×C92 ▷ C92
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
4. #10619531C3semidirect
13. #6896Q8semidirect
37. C92C3×Q8semidirect
90. C93−1+2⋊Q8semidirect

Maximal subgroups

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

subgroupindex
#117576132
#117575682
#6189⋊C33
#106195313