Finite Group Databasebeta

← #11786102

Subgroups — #11786102

Order 1152.

314 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 69 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
1C4×#3787C211yesmaximal, characteristic
2#10590340C212yesmaximal
3#10590051C214yesmaximal
4C2×#3787C2212yes—
5C42×C3⋊D3C2211yescharacteristic
6C2×#3712C2214yes—
7C4×#622C412yes—
8C4×#622C412yes—
9C3×C4⋊(C3⋊C8)—22no—
10#63572—22no—
11#4837—62no—
12C2×C4×C3⋊D3Q811yescharacteristic
13C2×C4×C3⋊D3Q811yescharacteristic
14C2×C4×C3⋊D3C2311yescharacteristic
15C2×#622C2×C414yes—
16#3787—24no—
17C32×C42D411yescharacteristic
18C4×C3⋊Dic3C2×C411yescharacteristic
19C4×C3⋊Dic3C2×C411yescharacteristic
20C4×C3⋊Dic3D411yescharacteristic
21C2×C3×C3⋊C8—24no—
22#3712—28no—
23#1837—91nomaximal, Sylow
24C2×ΓL(1,𝔽25)—64no—
25C42×D3—62no—
26C3×C4⋊C8—62no—
27Dic3⋊C8—64no—
28C4⋊(C3⋊C8)—22no—
29C22×C3⋊D3C2×Q811yescharacteristic
30C2×C32×C4C4⋊C411yescharacteristic
31C2×C32×C4C4⋊C411yescharacteristic
32C2×C32×C4C2×D411yescharacteristic
33C2×C3⋊Dic3C4⋊C411yescharacteristic
34C2×C3⋊Dic3C4⋊C411yescharacteristic
35C2×C3⋊Dic3C22×C411yescharacteristic
36C4×C3⋊D3—22no—
37C4×C3⋊D3—22no—
38C4×C3⋊D3#4114yes—
39#622—24no—
40C3×C3⋊C8—44no—
41#423—92no—
42C2×C4×C8—91no—
43#341—94no—
44C2×C4×D3—62no—
45C2×C4×D3—62no—
46C2×C4×D3—62no—
47C2×C3×C8—64no—
48C3×C42—22no—
49C4×Dic3—62no—
50C4×Dic3—62no—
51C4×Dic3—62no—
52C2×C3⋊C8—24no—
53ΓL(1,𝔽25)—128no—
54C22×C32C2×C4⋊C411yescharacteristic
55C2×C3⋊D3—21no—
56C2×C3⋊D3—21no—
57C2×C3⋊D3#12512yes—
58C32×C4—21no—
59C32×C4#10812yes—
60C32×C4#12412yes—
61C3⋊Dic3—21no—
62C3⋊Dic3#10812yes—
63C3⋊Dic3#11712yes—
64C2×M16—94no—
65C22×C8—92no—
66C2×C42—91no—
67C4⋊C8—62no—
68C4⋊C8—182no—
69C4×C8—92no—
70C4×C8—92no—
71C22×D3—62no—
72C2×C3×C4—22no—
73C2×C3×C4—22no—
74C2×C3×C4—22no—
75C2×Dic3—62no—
76C2×Dic3—62no—
77C2×Dic3—62no—
78C4×D3—64no—
79C4×D3—64no—
80C4×D3—124no—
81C4×D3—124no—
82C3×C8—124no—
83C3⋊C8—44no—
84C2×C32#38211yescharacteristic
85C2×C32C2×#10811yescharacteristic
86C2×C32C2×#10811yescharacteristic
87C3⋊D3—22no—
88C22×C4—91no—
89C22×C4—91no—
90C22×C4—91no—
91M16—188no—
92C2×C8—64no—
93C2×C8—94no—
94C2×C8—184no—
95C42—91no—
96C42—91no—
97C42—91no—
98C42GO+(4,𝔽2)11yescharacteristic
99C22×C3—22no—
100C2×D3—64no—
101C2×D3—122no—
102C2×D3—122no—
103C3×C4—22no—
104C3×C4—22no—
105C3×C4—24no—
106C3×C4—42no—
107Dic3—64no—
108Dic3—64no—
109Dic3—122no—
110C32#183711yescharacteristic, complemented, Sylow
111C23—91no—
112C2×C4—91no—
113C2×C4—91no—
114C2×C4—94no—
115C2×C4—91no—
116C2×C4—182no—
117C2×C4—182no—
118C2×C4#377311yescharacteristic
119C2×C4#377311yescharacteristic
120C2×C4C2×GO+(4,𝔽2)11yescharacteristic
121C8—124no—
122C8—184no—
123C2×C3—22no—
124C2×C3—22no—
125C2×C3—22no—
126D3—124no—
127C22—92no—
128C22—181no—
129C22—181no—
130C22C2×#377311yescharacteristic
131C4—21no—
132C4—92no—
133C4—92no—
134C4—181no—
135C4#6373312yes—
136C4#6422112yes—
137C3—22no—
138C2—182no—
139C2C2×#6373311yescharacteristic
140C2#1059333111yescharacteristic
141C2#1059334411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC32×C42D4
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C2×Q8
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1837
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
110. C32#1837semidirect

Maximal subgroups

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

subgroupindex
C4×#37872
#105903402
#105900512
#18379