Finite Group Databasebeta

← #11772448

Subgroups — #11772448

Order 1152.

170 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 44 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#10596481C211yesmaximal, characteristic
2#10593543C211yesmaximal, characteristic
3#10593389C211yesmaximal, characteristic
4#64286—21no—
5C2×#3787C2211yescharacteristic
6#64218—21no—
7#64214—21no—
8#64213C412yescomplemented
9#63874—21no—
10#63746—21no—
11#63745C412yescomplemented
12#63743—21no—
13#63742C412yescomplemented
14C2×C4×C3⋊D3D411yescharacteristic
15C22⋊#157—41no—
16C2×#622C2×C411yescharacteristic
17C2×#622D411yescharacteristic
18C4⋊#157—22no—
19C4×#157—41no—
20#3787C2×C411yescharacteristic
21#3787C2×C411yescharacteristic
22#3787D411yescharacteristic
23#3787Q811yescharacteristic
24#3771—22no—
25C3×C4×Dic3—41no—
26#3724—22no—
27#3722—41no—
28#1384—91nomaximal, Sylow
29#872—121no—
30C22×C3⋊D3D811yescharacteristic
31C2×#157—42no—
32C2×C32×C4SD1611yescharacteristic
33C2×C3⋊Dic3C22⋊C411yescharacteristic
34C4×C3⋊D3C22⋊C411yescharacteristic
35C4×C3⋊D3C4⋊C411yescharacteristic
36C4×C3⋊D3SD1611yescharacteristic
37C4×C3⋊D3Q1611yescharacteristic
38C2×C3×Dic3—42no—
39#622C4211yescharacteristic
40#622C22⋊C411yescharacteristic
41#622C4⋊C411yescharacteristic
42#622C4⋊C411yescharacteristic
43C2×M32—91no—
44#427—91no—
45#427—91no—
46C2×C4×D3—121no—
47C3×C42—121no—
48(C2×D3)⋊C4—122no—
49Dic3⋊C4—122no—
50C4×Dic3—41no—
51C22×C32#10211yescharacteristic
52C2×C3⋊D3—41no—
53C2×C3⋊D3#10211yescharacteristic
54C2×C3⋊D3#10711yescharacteristic
55#157—82no—
56C32×C4#10311yescharacteristic
57C32×C4#10611yescharacteristic
58C3⋊Dic3#9511yescharacteristic
59C3⋊Dic3#10311yescharacteristic
60C3×Dic3—82no—
61C22×C8—91no—
62#117—181no—
63#117—181no—
64M32—181no—
65M32—181no—
66C2×C16—92no—
67#107—181no—
68#107—181no—
69#106—92no—
70#106—92no—
71C22×D3—121no—
72C2×C3×C4—41no—
73C2×C3×C4—122no—
74C2×Dic3—42no—
75C2×Dic3—121no—
76C4×D3—121no—
77C4×D3—121no—
78C4×D3—121no—
79C4×D3—121no—
80C2×C32—21no—
81C2×C32#34011yescharacteristic
82C3⋊D3—21no—
83C3⋊D3—21no—
84C22×C4—91no—
85C2×C8—91no—
86C2×C8—91no—
87C2×C8—91no—
88C2×C8—91no—
89C2×C8—91no—
90C2×C8—91no—
91C4⋊C4—182no—
92C4⋊C4—182no—
93C22⋊C4—361no—
94C22⋊C4—361no—
95C42—121no—
96C42—361no—
97C16—182no—
98C22×C3—41no—
99C2×D3—121no—
100C2×D3—121no—
101C2×D3—242no—
102C3×C4—41no—
103C3×C4—41no—
104C3×C4—242no—
105Dic3—82no—
106Dic3—121no—
107Dic3—121no—
108C32#138411yescharacteristic, complemented, Sylow
109C23—91no—
110C2×C4—91no—
111C2×C4—91no—
112C2×C4—91no—
113C2×C4—91no—
114C2×C4—91no—
115C2×C4—122no—
116C2×C4—362no—
117C2×C4AΓL(1,𝔽9)11yescharacteristic
118C8—91no—
119C8—91no—
120C8—91no—
121C8—91no—
122C2×C3—42no—
123C2×C3—41no—
124D3—241no—
125D3—241no—
126C22—91no—
127C22—91no—
128C22—361no—
129C22GO+(4,𝔽2)⋊C411yescharacteristic
130C4—91no—
131C4—91no—
132C4—242no—
133C4—722no—
134C4PSU(3,𝔽2)⋊C411yescharacteristic
135C4AGL(1,𝔽9)⋊C411yescharacteristic
136C3—41no—
137C2—21no—
138C2—181no—
139C2—181no—
140C2#1059316611yescharacteristic
subgroupG/H
centerC4AGL(1,𝔽9)⋊C4
commutator#622C42
Frattini, hypercenterC2×C4AΓL(1,𝔽9)
FittingC2×C32×C4SD16
socleC2×C32#340
prime radicalC22×C3⋊D3D8
cosocleC2×#3787C22
hypocenterC32#1384
LCSG ▷ #622 ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
8. #64213C4semidirect
11. #63745C4semidirect
13. #63742C4semidirect
108. C32#1384semidirect

Maximal subgroups

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

subgroupindex
#105964812
#105935432
#105933892
#13849