Finite Group Databasebeta

← #11797579

Subgroups — #11797579

Order 1152.

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

normal subgroups only

This group has 177 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#10596487C212yesmaximal, complemented
2#10593787C211yesmaximal, characteristic
3#10593271C212yesmaximal, complemented
4#10593257C211yesmaximal, characteristic, complemented
5#10593254C211yesmaximal, characteristic, complemented
6#64289C2212yes—
7#64214—22no—
8#64214C2212yes—
9#64213—22no—
10#64213C2211yescharacteristic
11#64213C2211yescharacteristic
12#64128C411yescharacteristic
13#63785C412yes—
14#63771C411yescharacteristic
15C8×#157C2211yescharacteristic
16#3832C2×C412yes—
17C4×#157C2×C411yescharacteristic
18#3788—22no—
19#3788C2×C412yes—
20#3787—22no—
21#3787C2311yescharacteristic
22#3771—22no—
23#3771—21no—
24#3771D411yescharacteristic
25#3771D411yescharacteristic
26C32×Q16C811yescharacteristic
27#3755C812yes—
28#3745C811yescharacteristic
29C8×C3⋊D3C2×C411yescharacteristic
30#2170—91nomaximal, Sylow
31#919—121no—
32C2×#157—21no—
33C32×Q8C2×C812yes—
34C4⋊(C3⋊D3)—22no—
35C4⋊(C3⋊D3)C2×C812yes—
36C4×C3⋊D3—22no—
37C4×C3⋊D3C22×C411yescharacteristic
38#622—22no—
39#622C2×D411yescharacteristic
40#622#4111yescharacteristic
41C32×C8C2×C811yescharacteristic
42C3⋊(C3⋊C8)C2×C811yescharacteristic
43#504—92no—
44#443—91no—
45#364—91no—
46#350—92no—
47C4×C16—91no—
48#239—122no—
49C3×Q16—41no—
50#215—122no—
51D24—121no—
52D3×C8—121no—
53C2×C3⋊D3—22no—
54C2×C3⋊D3#13111yescharacteristic
55#157—22no—
56C32×C4—22no—
57C32×C4C22×C811yescharacteristic
58C3⋊Dic3C4×D411yescharacteristic
59#135—91no—
60#131—92no—
61M32—92no—
62M32—182no—
63C2×C16—91no—
64C2×C16—91no—
65C2×C16—182no—
66#108—91no—
67#104—92no—
68C4×C8—91no—
69C3×Q8—42no—
70D12—122no—
71D12—242no—
72C4×D3—121no—
73C4×D3—242no—
74C3×C8—41no—
75C3⋊C8—121no—
76C2×C32C8×D411yescharacteristic
77C3⋊D3—21no—
78C3⋊D3—42no—
79#41—92no—
80Q16AGL(1,𝔽9)11yescharacteristic
81SD16—92no—
82D8—91no—
83M16—92no—
84M16—182no—
85C2×C8—91no—
86C2×C8—91no—
87C2×C8—182no—
88C42—91no—
89C16—91no—
90C16—91no—
91C16—181no—
92C16—182no—
93C2×D3—121no—
94C2×D3—242no—
95C3×C4—41no—
96C3×C4—82no—
97Dic3—121no—
98C32#217011yescharacteristic, complemented, Sylow
99Q8C2×AGL(1,𝔽9)12yes—
100D4—92no—
101D4—182no—
102C2×C4—91no—
103C2×C4—182no—
104C2×C4—181no—
105C8—91no—
106C8—91no—
107C8—91no—
108C8—182no—
109C8C2×AGL(1,𝔽9)11yescharacteristic
110C2×C3—41no—
111D3—241no—
112D3—482no—
113C22—91no—
114C22—182no—
115C4—22no—
116C4—91no—
117C4—182no—
118C4C22×AGL(1,𝔽9)11yescharacteristic
119C3—41no—
120C2—181no—
121C2—362no—
122C2D4×AGL(1,𝔽9)11yescharacteristic
subgroupG/H
centerC2D4×AGL(1,𝔽9)
commutatorC32×C4C22×C8
FrattiniC4C22×AGL(1,𝔽9)
FittingC32×Q16C8
socleC2×C32C8×D4
prime radical#64128C4
cosocle#3787C23
hypercenterQ16AGL(1,𝔽9)
hypocenterC32#2170
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C4 ◁ Q16

Complements

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

NH ≅ G/Ntype
1. #10596487C2semidirect
3. #10593271C2semidirect
4. #10593257C2semidirect
5. #10593254C2semidirect
98. C32#2170semidirect

Maximal subgroups

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

subgroupindex
#105964872
#105937872
#105932712
#105932572
#105932542
#21709