Finite Group Databasebeta

← #11797613

Subgroups — #11797613

Order 1152.

175 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 175 conjugacy classes of subgroups — too many to draw. Only its 53 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#10596485C212yesmaximal, complemented
2#10593779C211yesmaximal, characteristic
3#10593269C212yesmaximal, complemented
4#10593256C211yesmaximal, characteristic, complemented
5#10593255C211yesmaximal, characteristic, complemented
6#64287C2212yes—
7#64218—22no—
8C2×#3771—22no—
9#64214C2212yes—
10#64213C2211yescharacteristic
11#64213C2211yescharacteristic
12#64121C411yescharacteristic
13#63783C412yes—
14#63771C411yescharacteristic
15C8×#157C2211yescharacteristic
16#3830C2×C412yes—
17#3792—22no—
18C2×#622—22no—
19C4×#157C2×C411yescharacteristic
20#3788C2×C412yes—
21#3787C2311yescharacteristic
22#3771—22no—
23#3771—21no—
24#3771D412yes—
25C32×D8C811yescharacteristic
26#3754C812yes—
27#3746C811yescharacteristic
28C8×C3⋊D3C2×C411yescharacteristic
29#2171—91nomaximal, Sylow
30#912—121no—
31C2×#157—21no—
32C32×D4C2×C812yes—
33#638—22no—
34C2×C3⋊Dic3—22no—
35C4×C3⋊D3C22×C411yescharacteristic
36#634C2×C812yes—
37#622—22no—
38#622C2×D411yescharacteristic
39#622#4111yescharacteristic
40C32×C8C2×C811yescharacteristic
41C3⋊(C3⋊C8)C2×C811yescharacteristic
42#504—92no—
43#443—91no—
44#364—91no—
45#350—92no—
46#346—91no—
47#237—122no—
48C3×D8—41no—
49#214—122no—
50Dic12—121no—
51D3×C8—121no—
52C22×C32—22no—
53C2×C3⋊D3#13111yescharacteristic
54#157—41no—
55C32×C4C22×C811yescharacteristic
56C3⋊Dic3—22no—
57C3⋊Dic3C4×D411yescharacteristic
58#135—91no—
59#131—92no—
60M32—92no—
61M32—182no—
62C2×C16—91no—
63C2×C16—91no—
64C2×C16—182no—
65#108—91no—
66#104—92no—
67C4×C8—91no—
68C3×D4—42no—
69#67—242no—
70C2×Dic3—242no—
71C4×D3—121no—
72Dic6—122no—
73C3×C8—41no—
74C3⋊C8—121no—
75C2×C32—42no—
76C2×C32C8×D411yescharacteristic
77C3⋊D3—21no—
78#41—92no—
79Q16—91no—
80SD16—92no—
81D8AGL(1,𝔽9)11yescharacteristic
82M16—92no—
83M16—182no—
84C2×C8—91no—
85C2×C8—91no—
86C2×C8—182no—
87C42—91no—
88C16—92no—
89C16—181no—
90C16—182no—
91C22×C3—82no—
92C2×D3—121no—
93C3×C4—41no—
94Dic3—121no—
95Dic3—242no—
96C32#217111yescharacteristic, complemented, Sylow
97Q8—92no—
98D4—182no—
99D4C2×AGL(1,𝔽9)12yes—
100C2×C4—91no—
101C2×C4—182no—
102C2×C4—181no—
103C8—91no—
104C8—91no—
105C8—91no—
106C8—182no—
107C8C2×AGL(1,𝔽9)11yescharacteristic
108C2×C3—41no—
109C2×C3—162no—
110D3—241no—
111C22—22no—
112C22—91no—
113C4—91no—
114C4—182no—
115C4—361no—
116C4C22×AGL(1,𝔽9)11yescharacteristic
117C3—41no—
118C2—42no—
119C2—181no—
120C2D4×AGL(1,𝔽9)11yescharacteristic
subgroupG/H
centerC2D4×AGL(1,𝔽9)
commutatorC32×C4C22×C8
FrattiniC4C22×AGL(1,𝔽9)
FittingC32×D8C8
socleC2×C32C8×D4
prime radical#64121C4
cosocle#3787C23
hypercenterD8AGL(1,𝔽9)
hypocenterC32#2171
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C4 ◁ D8

Complements

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

NH ≅ G/Ntype
1. #10596485C2semidirect
3. #10593269C2semidirect
4. #10593256C2semidirect
5. #10593255C2semidirect
96. C32#2171semidirect

Maximal subgroups

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

subgroupindex
#105964852
#105937792
#105932692
#105932562
#105932552
#21719