Finite Group Databasebeta

← #11772545

Subgroups — #11772545

Order 1152.

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

normal subgroups only

This group has 162 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
3C2×#63733C211yesmaximal, characteristic
4#64286—21no—
5C2×#3787C2211yescharacteristic
6#64218C412yescomplemented
7#64214—21no—
8#64213—21no—
9C2×#3712—21no—
10#63746—21no—
11#63745C412yes—
12#63733—21no—
13#63733C412yescomplemented
14C2×C4×C3⋊D3D411yescharacteristic
15C22⋊#157—41no—
16C2×#622C2×C411yescharacteristic
17C2×#622Q811yescharacteristic
18C4⋊#157—22no—
19C4×#157—41no—
20#3787C2×C411yescharacteristic
21#3787C2×C411yescharacteristic
22#3787D411yescharacteristic
23#3787D411yescharacteristic
24#3771—22no—
25C2×C3×C3⋊C8—41no—
26#3712—22no—
27#3712—41no—
28#1389—91nomaximal, Sylow
29C2×ΓL(1,𝔽25)—121no—
30C22×C3⋊D3SD1611yescharacteristic
31C2×#157—42no—
32C2×C32×C4SD1611yescharacteristic
33C2×C3⋊Dic3C4⋊C411yescharacteristic
34C4×C3⋊D3C22⋊C411yescharacteristic
35C4×C3⋊D3C22⋊C411yescharacteristic
36C4×C3⋊D3D811yescharacteristic
37C4×C3⋊D3Q1611yescharacteristic
38#622C4211yescharacteristic
39#622C22⋊C411yescharacteristic
40#622C4⋊C411yescharacteristic
41#622C4⋊C411yescharacteristic
42C3×C3⋊C8—42no—
43C2×M32—91no—
44C2×#108—91no—
45#427—91no—
46C2×C4×D3—121no—
47C2×C3×C8—121no—
48C2×C3⋊C8—41no—
49ΓL(1,𝔽25)—122no—
50ΓL(1,𝔽25)—122no—
51C22×C32#10611yescharacteristic
52C2×C3⋊D3—41no—
53C2×C3⋊D3#10211yescharacteristic
54C2×C3⋊D3#10311yescharacteristic
55#157—82no—
56C32×C4#10211yescharacteristic
57C32×C4#10311yescharacteristic
58C3⋊Dic3#9511yescharacteristic
59C3⋊Dic3#10711yescharacteristic
60C2×M16—181no—
61C22×C8—91no—
62#117—181no—
63M32—92no—
64M32—181no—
65C2×C16—181no—
66#108—92no—
67#108—181no—
68#107—181no—
69#106—92no—
70C22×D3—121no—
71C2×C3×C4—41no—
72C2×Dic3—121no—
73C4×D3—121no—
74C4×D3—121no—
75C4×D3—121no—
76C4×D3—121no—
77C3×C8—122no—
78C3⋊C8—42no—
79C2×C32—21no—
80C2×C32#34011yescharacteristic
81C3⋊D3—21no—
82C3⋊D3—21no—
83C22×C4—91no—
84M16—182no—
85M16—361no—
86C2×C8—91no—
87C2×C8—91no—
88C2×C8—91no—
89C2×C8—91no—
90C2×C8—91no—
91C2×C8—91no—
92C2×C8—121no—
93C4⋊C4—182no—
94C22⋊C4—361no—
95C42—361no—
96C16—182no—
97C22×C3—41no—
98C2×D3—121no—
99C2×D3—121no—
100C2×D3—242no—
101C3×C4—41no—
102C3×C4—41no—
103Dic3—121no—
104Dic3—121no—
105C32#138911yescharacteristic, complemented, Sylow
106C23—91no—
107C2×C4—91no—
108C2×C4—91no—
109C2×C4—91no—
110C2×C4—91no—
111C2×C4—91no—
112C2×C4—362no—
113C2×C4AΓL(1,𝔽9)11yescharacteristic
114C8—91no—
115C8—91no—
116C8—91no—
117C8—91no—
118C8—122no—
119C2×C3—42no—
120C2×C3—41no—
121D3—241no—
122D3—241no—
123C22—91no—
124C22—91no—
125C22—361no—
126C22AGL(1,𝔽9)⋊C411yescharacteristic
127C4—91no—
128C4—91no—
129C4—722no—
130C4GO+(4,𝔽2)⋊C411yescharacteristic
131C4PSU(3,𝔽2)⋊C411yescharacteristic
132C3—41no—
133C2—21no—
134C2—181no—
135C2—181no—
136C2#1059316611yescharacteristic
subgroupG/H
centerC4GO+(4,𝔽2)⋊C4
commutator#622C42
Frattini, hypercenterC2×C4AΓL(1,𝔽9)
FittingC2×C32×C4SD16
socleC2×C32#340
prime radicalC22×C3⋊D3SD16
cosocleC2×#3787C22
hypocenterC32#1389
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
6. #64218C4semidirect
13. #63733C4semidirect
105. C32#1389semidirect

Maximal subgroups

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

subgroupindex
#105964812
#105935432
C2×#637332
#13899