Finite Group Databasebeta

← #11797580

Subgroups — #11797580

Order 1152.

230 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 51 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#10593297C211yesmaximal, characteristic
2#10590227C212yesmaximal, complemented
3C16×#157C211yesmaximal, characteristic, complemented
4#10590023C211yesmaximal, characteristic, complemented
5#10590015C212yesmaximal, complemented
6#64223C411yescharacteristic
7#63803C2212yes—
8C8×#157C2211yescharacteristic
9#63764C2211yescharacteristic
10#63733C411yescharacteristic
11#63731C412yes—
12C16×C3⋊D3C2211yescharacteristic
13C3×D3×C16—22no—
14#63544C2212yes—
15#63543—22no—
16#4901—62no—
17#3798C2×C412yes—
18C4×#157C2×C411yescharacteristic
19#3787C2×C411yescharacteristic
20#3776C811yescharacteristic
21#3775C812yes—
22#3774C811yescharacteristic
23C8×C3⋊D3C2311yescharacteristic
24C3×D3×C8—22no—
25#3712C2×C412yes—
26#3711—22no—
27#3708—21no—
28C32×C16D411yescharacteristic
29C3⋊(C3⋊C16)D411yescharacteristic
30C3×C3⋊C16—22no—
31#2170—91nomaximal, Sylow
32#901—62no—
33C2×C3×C16—62no—
34#812—62no—
35#798—62no—
36#798—62no—
37D3×C16—22no—
38D3×C16—62no—
39C2×#157—21no—
40C4×C3⋊D3C22×C411yescharacteristic
41C3×C4×D3—22no—
42#627C2×C812yes—
43#626—22no—
44#625C2×C812yes—
45#622C2×C811yescharacteristic
46#622C2×C811yescharacteristic
47C32×C8C2×D411yescharacteristic
48C3⋊(C3⋊C8)#4111yescharacteristic
49C3×C3⋊C8—22no—
50#504—92no—
51#443—91no—
52#364—91no—
53#350—92no—
54C4×C16—91no—
55#235—62no—
56C2×C3×C8—62no—
57#208—62no—
58ΓL(1,𝔽25)—62no—
59ΓL(1,𝔽25)—62no—
60D3×C8—22no—
61D3×C8—62no—
62C3×C16—22no—
63C3×C16—62no—
64C3⋊C16—22no—
65C3⋊C16—62no—
66C2×C3⋊D3#13111yescharacteristic
67C2×C3×D3—22no—
68#157—22no—
69C32×C4C4×D411yescharacteristic
70C3⋊Dic3C22×C811yescharacteristic
71C3×Dic3—22no—
72#135—91no—
73#131—92no—
74M32—92no—
75M32—182no—
76C2×C16—62no—
77C2×C16—91no—
78C2×C16—91no—
79#108—91no—
80#104—92no—
81C4×C8—91no—
82C2×C3×C4—62no—
83#67—62no—
84#67—62no—
85D12—62no—
86C4×D3—22no—
87C4×D3—62no—
88Dic6—62no—
89C3×C8—22no—
90C3×C8—62no—
91C3⋊C8—22no—
92C3⋊C8—62no—
93C2×C32C8×D411yescharacteristic
94C3⋊D3—21no—
95C3×D3—42no—
96#41—92no—
97Q16—91no—
98SD16—92no—
99D8—91no—
100M16—92no—
101M16—182no—
102C2×C8—62no—
103C2×C8—91no—
104C2×C8—91no—
105C42—91no—
106C16—62no—
107C16—91no—
108C16—181no—
109C16GO+(4,𝔽2)11yescharacteristic
110C22×C3—62no—
111C2×D3—22no—
112C2×D3—62no—
113C3×C4—22no—
114C3×C4—62no—
115Dic3—22no—
116Dic3—62no—
117C32#217011yescharacteristic, complemented, Sylow
118Q8—92no—
119D4—92no—
120D4—182no—
121C2×C4—62no—
122C2×C4—91no—
123C2×C4—181no—
124C8—62no—
125C8—91no—
126C8—91no—
127C8—91no—
128C8C2×GO+(4,𝔽2)11yescharacteristic
129C2×C3—22no—
130C2×C3—122no—
131D3—42no—
132D3—122no—
133C22—62no—
134C22—91no—
135C4—62no—
136C4—91no—
137C4—182no—
138C4C4×GO+(4,𝔽2)11yescharacteristic
139C3—22no—
140C2—122no—
141C2—181no—
142C2C8×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
center, hypercenterC16GO+(4,𝔽2)
commutatorC3⋊Dic3C22×C8
FrattiniC8C2×GO+(4,𝔽2)
FittingC32×C16D4
socleC2×C32C8×D4
prime radical#64223C4
cosocleC8×C3⋊D3C23
hypocenterC32#2170
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C16

Complements

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

NH ≅ G/Ntype
2. #10590227C2semidirect
3. C16×#157C2semidirect
4. #10590023C2semidirect
5. #10590015C2semidirect
117. C32#2170semidirect

Maximal subgroups

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

subgroupindex
#105932972
#105902272
C16×#1572
#105900232
#105900152
#21709