Finite Group Databasebeta

← #11772483

Subgroups — #11772483

Order 1152.

186 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 46 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#10593387C211yesmaximal, characteristic
4#64286—21no—
5C2×#3787C2211yescharacteristic
6#64218—21no—
7#64214C412yescomplemented
8#64213—21no—
9#63900—21no—
10#63746C412yescomplemented
11#63745—21no—
12#63742—21no—
13#63742C412yescomplemented
14C2×C4×C3⋊D3D411yescharacteristic
15C2×#624—41no—
16C22⋊#157—41no—
17C2×#622C2×C411yescharacteristic
18C2×#622D411yescharacteristic
19C4⋊#157—22no—
20C4×#157—41no—
21#3787C2×C411yescharacteristic
22#3787C2×C411yescharacteristic
23#3787D411yescharacteristic
24#3787Q811yescharacteristic
25#3771—22no—
26C3×C4⋊Dic3—41no—
27#3724—22no—
28#1386—91nomaximal, Sylow
29D3×C4⋊C4—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#624—82no—
40#622C4211yescharacteristic
41#622C22⋊C411yescharacteristic
42#622C4⋊C411yescharacteristic
43#622C4⋊C411yescharacteristic
44C2×M32—91no—
45#427—91no—
46C2×#106—91no—
47C2×C4×D3—121no—
48C2×C4×D3—122no—
49C3×C4⋊C4—121no—
50C4⋊Dic3—41no—
51Dic3⋊C4—122no—
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—
81C4×D3—244no—
82C2×C32—21no—
83C2×C32#34011yescharacteristic
84C3⋊D3—21no—
85C3⋊D3#36012yes—
86C22×C4—91no—
87C22×C4—361no—
88C2×C8—91no—
89C2×C8—91no—
90C2×C8—91no—
91C2×C8—91no—
92C2×C8—91no—
93C2×C8—91no—
94C4⋊C4—121no—
95C4⋊C4—182no—
96C4⋊C4—182no—
97C22⋊C4—361no—
98C42—361no—
99C16—182no—
100C22×C3—41no—
101C2×D3—121no—
102C2×D3—121no—
103C2×D3—122no—
104C2×D3—122no—
105C3×C4—41no—
106C3×C4—41no—
107C3×C4—242no—
108Dic3—82no—
109Dic3—121no—
110Dic3—121no—
111C32#138611yescharacteristic, complemented, Sylow
112C23—91no—
113C2×C4—91no—
114C2×C4—91no—
115C2×C4—91no—
116C2×C4—91no—
117C2×C4—91no—
118C2×C4—122no—
119C2×C4—362no—
120C2×C4—722no—
121C2×C4AΓL(1,𝔽9)11yescharacteristic
122C8—91no—
123C8—91no—
124C8—91no—
125C8—91no—
126C2×C3—41no—
127C2×C3—41no—
128C2×C3—41no—
129D3—122no—
130D3—122no—
131C22—91no—
132C22—91no—
133C22—182no—
134C22GO+(4,𝔽2)⋊C411yescharacteristic
135C4—91no—
136C4—91no—
137C4—242no—
138C4—722no—
139C4PSU(3,𝔽2)⋊C411yescharacteristic
140C4AGL(1,𝔽9)⋊C411yescharacteristic
141C3—41no—
142C2—21no—
143C2—92no—
144C2—181no—
145C2#1059316611yescharacteristic
subgroupG/H
centerC2#10593166
commutator#622C42
Frattini, hypercenterC2×C4AΓL(1,𝔽9)
FittingC2×C32×C4SD16
socleC2×C32#340
prime radicalC22×C3⋊D3D8
cosocleC2×#3787C22
hypocenterC32#1386
LCSG ▷ #622 ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
7. #64214C4semidirect
10. #63746C4semidirect
13. #63742C4semidirect
111. C32#1386semidirect

Maximal subgroups

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

subgroupindex
#105964812
#105935432
#105933872
#13869