Finite Group Databasebeta

← #11772525

Subgroups — #11772525

Order 1152.

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

normal subgroups only

This group has 158 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
1C2×#64214C211yesmaximal, characteristic
2#10593546C211yesmaximal, characteristic
3#10593331C211yesmaximal, characteristic
4#64283—21no—
5C2×#3787C2211yescharacteristic
6C2×#3771—21no—
7#64214—21no—
8#64214C412yes—
9#63818—21no—
10#63748—21no—
11#63748C412yes—
12#63733—21no—
13#63733C412yes—
14C2×C4×C3⋊D3D411yescharacteristic
15#3792—22no—
16C2×#622C2×C411yescharacteristic
17C2×#622D411yescharacteristic
18#3788—41no—
19#3787—41no—
20#3787C2×C411yescharacteristic
21#3787C2×C411yescharacteristic
22#3787D411yescharacteristic
23#3787Q811yescharacteristic
24#3771—22no—
25C3×#208—41no—
26#3712—22no—
27#3710—41no—
28#1388—91nomaximal, Sylow
29D3×M16—121no—
30C22×C3⋊D3Q1611yescharacteristic
31C2×C32×C4SD1611yescharacteristic
32C2×C3⋊Dic3C22⋊C411yescharacteristic
33C4×C3⋊D3C22⋊C411yescharacteristic
34C4×C3⋊D3C4⋊C411yescharacteristic
35C4×C3⋊D3D811yescharacteristic
36C4×C3⋊D3SD1611yescharacteristic
37#622—42no—
38#622C4211yescharacteristic
39#622C22⋊C411yescharacteristic
40#622C4⋊C411yescharacteristic
41#622C4⋊C411yescharacteristic
42C3×C3⋊C8—42no—
43C2×M32—91no—
44C2×#108—91no—
45C2×#108—91no—
46C2×C4×D3—121no—
47C3×M16—121no—
48#208—41no—
49ΓL(1,𝔽25)—122no—
50D3×C8—122no—
51C22×C32#10311yescharacteristic
52C2×C3⋊D3—41no—
53C2×C3⋊D3#10311yescharacteristic
54C2×C3⋊D3#10711yescharacteristic
55C32×C4#10211yescharacteristic
56C32×C4#10611yescharacteristic
57C3⋊Dic3#9511yescharacteristic
58C3⋊Dic3#10211yescharacteristic
59C2×M16—181no—
60C2×M16—181no—
61C22×C8—91no—
62M32—92no—
63M32—181no—
64C2×C16—181no—
65#108—92no—
66#108—92no—
67#108—181no—
68#108—181no—
69C22×D3—121no—
70C2×C3×C4—41no—
71C2×Dic3—121no—
72C4×D3—121no—
73C4×D3—121no—
74C4×D3—121no—
75C4×D3—121no—
76C3×C8—122no—
77C3⋊C8—42no—
78C2×C32—21no—
79C2×C32#34011yescharacteristic
80C3⋊D3—21no—
81C3⋊D3—21no—
82C22×C4—91no—
83M16—121no—
84M16—182no—
85M16—182no—
86M16—361no—
87C2×C8—91no—
88C2×C8—91no—
89C2×C8—91no—
90C2×C8—91no—
91C2×C8—91no—
92C2×C8—91no—
93C2×C8—361no—
94C2×C8—361no—
95C16—182no—
96C22×C3—41no—
97C2×D3—121no—
98C2×D3—121no—
99C2×D3—242no—
100C3×C4—41no—
101C3×C4—41no—
102Dic3—121no—
103Dic3—121no—
104C32#138811yescharacteristic, complemented, Sylow
105C23—91no—
106C2×C4—91no—
107C2×C4—91no—
108C2×C4—91no—
109C2×C4—91no—
110C2×C4—91no—
111C2×C4AΓL(1,𝔽9)11yescharacteristic
112C8—91no—
113C8—91no—
114C8—91no—
115C8—91no—
116C8—122no—
117C8—362no—
118C2×C3—41no—
119C2×C3—81no—
120D3—122no—
121D3—241no—
122C22—91no—
123C22—91no—
124C22—361no—
125C22PSU(3,𝔽2)⋊C411yescharacteristic
126C4—91no—
127C4—91no—
128C4GO+(4,𝔽2)⋊C411yescharacteristic
129C4AGL(1,𝔽9)⋊C411yescharacteristic
130C3—41no—
131C2—21no—
132C2—181no—
133C2—181no—
134C2#1059316611yescharacteristic
subgroupG/H
centerC2#10593166
commutator#622C42
Frattini, hypercenterC2×C4AΓL(1,𝔽9)
FittingC2×C32×C4SD16
socleC2×C32#340
prime radicalC22×C3⋊D3Q16
cosocleC2×#3787C22
hypocenterC32#1388
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
104. C32#1388semidirect

Maximal subgroups

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

subgroupindex
C2×#642142
#105935462
#105933312
#13889