Finite Group Databasebeta

← #11772482

Subgroups — #11772482

Order 1152.

178 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 48 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
1C2×#64214C211yesmaximal, characteristic
2C2×#63745C211yesmaximal, characteristic
3#10593389C211yesmaximal, characteristic
4C2×C4⋊#157—21no—
5C2×#3787C2211yescharacteristic
6C2×#3771—21no—
7#64214—21no—
8#64214C412yescomplemented
9#63874—21no—
10#63745—21no—
11#63745C412yescomplemented
12#63743C412yescomplemented
13#63742—21no—
14C22×#157—41no—
15C2×C4×C3⋊D3D411yescharacteristic
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#1386—91nomaximal, Sylow
29#872—121no—
30C22×C3⋊D3D811yescharacteristic
31C2×#157—42no—
32C2×#157—82no—
33C2×C32×C4SD1611yescharacteristic
34C2×C3⋊Dic3C22⋊C411yescharacteristic
35C4×C3⋊D3C22⋊C411yescharacteristic
36C4×C3⋊D3C4⋊C411yescharacteristic
37C4×C3⋊D3SD1611yescharacteristic
38C4×C3⋊D3Q1611yescharacteristic
39C2×C3×Dic3—42no—
40#622C4211yescharacteristic
41#622C22⋊C411yescharacteristic
42#622C4⋊C411yescharacteristic
43#622C4⋊C411yescharacteristic
44C2×M32—91no—
45#427—91no—
46C2×#106—91no—
47C2×C4×D3—121no—
48C3×C42—121no—
49(C2×D3)⋊C4—122no—
50Dic3⋊C4—122no—
51C4×Dic3—41no—
52C22×C32#10211yescharacteristic
53C2×C3⋊D3—22no—
54C2×C3⋊D3#10211yescharacteristic
55C2×C3⋊D3#10711yescharacteristic
56#157—82no—
57C32×C4#10311yescharacteristic
58C32×C4#10611yescharacteristic
59C3⋊Dic3#9511yescharacteristic
60C3⋊Dic3#10311yescharacteristic
61C3×Dic3—82no—
62C22×C8—91no—
63#117—181no—
64C2×C4⋊C4—181no—
65M32—92no—
66M32—181no—
67C2×C16—181no—
68#107—92no—
69#106—92no—
70#106—181no—
71#106—181no—
72C22×D3—121no—
73C2×C3×C4—41no—
74C2×C3×C4—122no—
75C2×Dic3—42no—
76C2×Dic3—121no—
77C4×D3—121no—
78C4×D3—121no—
79C4×D3—121no—
80C4×D3—121no—
81C2×C32#34011yescharacteristic
82C2×C32#36012yes—
83C3⋊D3—21no—
84C3⋊D3—21no—
85C22×C4—91no—
86C22×C4—361no—
87C2×C8—91no—
88C2×C8—91no—
89C2×C8—91no—
90C2×C8—91no—
91C2×C8—91no—
92C2×C8—91no—
93C4⋊C4—182no—
94C4⋊C4—182no—
95C4⋊C4—361no—
96C22⋊C4—361no—
97C42—121no—
98C16—182no—
99C22×C3—41no—
100C2×D3—121no—
101C2×D3—121no—
102C2×D3—242no—
103C3×C4—41no—
104C3×C4—41no—
105C3×C4—242no—
106Dic3—82no—
107Dic3—121no—
108Dic3—121no—
109C32#138611yescharacteristic, complemented, Sylow
110C23—91no—
111C2×C4—91no—
112C2×C4—91no—
113C2×C4—91no—
114C2×C4—91no—
115C2×C4—91no—
116C2×C4—122no—
117C2×C4—362no—
118C2×C4—722no—
119C2×C4AΓL(1,𝔽9)11yescharacteristic
120C8—91no—
121C8—91no—
122C8—91no—
123C8—91no—
124C2×C3—42no—
125C2×C3—41no—
126D3—241no—
127D3—241no—
128C22—91no—
129C22—91no—
130C22—182no—
131C22GO+(4,𝔽2)⋊C411yescharacteristic
132C4—91no—
133C4—91no—
134C4—242no—
135C4—722no—
136C4PSU(3,𝔽2)⋊C411yescharacteristic
137C4AGL(1,𝔽9)⋊C411yescharacteristic
138C3—41no—
139C2—181no—
140C2—181no—
141C2#1059316212yes—
142C2#1059316611yescharacteristic
subgroupG/H
centerC22GO+(4,𝔽2)⋊C4
commutator#622C42
Frattini, hypercenterC2×C4AΓL(1,𝔽9)
FittingC2×C32×C4SD16
socleC22×C32#102
prime radicalC22×C3⋊D3D8
cosocleC2×#3787C22
hypocenterC32#1386
LCSG ▷ #622 ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
8. #64214C4semidirect
11. #63745C4semidirect
12. #63743C4semidirect
109. C32#1386semidirect

Maximal subgroups

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

subgroupindex
C2×#642142
C2×#637452
#105933892
#13869