Finite Group Databasebeta

← D32⋊C32 #11772697

Subgroups — D32⋊C32 #11772697

Order 1152.

148 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 31 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
1D32×C16C211yesmaximal, characteristic
2#10590132C211yesmaximal, characteristic, complemented
3#10589067C211yesmaximal, characteristic, complemented
4D32×C8C411yescharacteristic
5C16×C3⋊D3C2211yescharacteristic
6C3×D3×C16—21no—
7#63542C411yescharacteristic
8D3×C3⋊C16—21no—
9#63540—21no—
10C3×C3⋊C32—21no—
11C2×D3×C16—61no—
12D3×C32—61no—
13C4×D32C811yescharacteristic
14C8×C3⋊D3C2×C411yescharacteristic
15C3×D3×C8—21no—
16#3710C811yescharacteristic
17D3×C3⋊C8—21no—
18C32×C16D411yescharacteristic
19C3⋊(C3⋊C16)D411yescharacteristic
20C3×C3⋊C16—21no—
21C22⋊C32—91nomaximal, Sylow
22C2×D3×C8—61no—
23C2×C3×C16—61no—
24C2×C3⋊C16—61no—
25D3×C16—21no—
26D3×C16—61no—
27D3×C16—61no—
28D3×C16—61no—
29D3×C16—61no—
30C3×C32—61no—
31C3⋊C32—21no—
32C2×D32C1611yescharacteristic
33C4×C3⋊D3C2×C811yescharacteristic
34C3×C4×D3—21no—
35#624C1611yescharacteristic
36D3×Dic3—21no—
37C32×C8C22⋊C411yescharacteristic
38C3⋊(C3⋊C8)M1611yescharacteristic
39C3×C3⋊C8—21no—
40C22×C16—91no—
41C2×C32—91no—
42C2×C32—91no—
43C2×C4×D3—61no—
44C2×C3×C8—61no—
45C2×C3⋊C8—61no—
46D3×C8—21no—
47D3×C8—61no—
48D3×C8—61no—
49D3×C8—61no—
50D3×C8—61no—
51C3×C16—21no—
52C3×C16—21no—
53C3×C16—61no—
54C3⋊C16—21no—
55C3⋊C16—61no—
56C3⋊C16—61no—
57C2×C3⋊D3C2×C1611yescharacteristic
58C2×C3×D3—21no—
59D32—21no—
60D32C3212yescomplemented
61C32×C4C22⋊C811yescharacteristic
62C3⋊Dic3M3211yescharacteristic
63C3×Dic3—21no—
64C22×C8—91no—
65C2×C16—61no—
66C2×C16—91no—
67C2×C16—91no—
68C2×C16—181no—
69C32—61no—
70C32—181no—
71C22×D3—61no—
72C2×C3×C4—61no—
73C2×Dic3—61no—
74C4×D3—21no—
75C4×D3—61no—
76C4×D3—61no—
77C4×D3—61no—
78C4×D3—61no—
79C3×C8—21no—
80C3×C8—21no—
81C3×C8—61no—
82C3⋊C8—21no—
83C3⋊C8—61no—
84C3⋊C8—61no—
85C2×C32C22⋊C1611yescharacteristic
86C3⋊D3C2×C3211yescharacteristic
87C3⋊D3M6411yescharacteristic
88C3×D3—22no—
89C22×C4—91no—
90C2×C8—61no—
91C2×C8—91no—
92C2×C8—91no—
93C2×C8—181no—
94C16—61no—
95C16—91no—
96C16GO+(4,𝔽2)11yescharacteristic
97C22×C3—61no—
98C2×D3—21no—
99C2×D3—62no—
100C2×D3—61no—
101C2×D3—61no—
102C2×D3—62no—
103C3×C4—21no—
104C3×C4—21no—
105C3×C4—61no—
106Dic3—21no—
107Dic3—61no—
108Dic3—61no—
109C32C22⋊C3211yescharacteristic, complemented, Sylow
110C23—91no—
111C2×C4—61no—
112C2×C4—91no—
113C2×C4—91no—
114C2×C4—181no—
115C8—61no—
116C8—91no—
117C8D32⋊C411yescharacteristic
118C2×C3—21no—
119C2×C3—21no—
120C2×C3—62no—
121D3—22no—
122D3—61no—
123D3—61no—
124D3—61no—
125D3—61no—
126C22—61no—
127C22—92no—
128C22—91no—
129C22—181no—
130C4—61no—
131C4—91no—
132C4D32⋊C811yescharacteristic
133C3—21no—
134C3—21no—
135C2—62no—
136C2—91no—
137C2—91no—
138C2D32⋊C1611yescharacteristic
subgroupG/H
center, Frattini, hypercenterC16GO+(4,𝔽2)
commutatorC3⋊D3C2×C32
FittingC32×C16D4
socleC2×C32C22⋊C16
prime radicalC2×D32C16
cosocleC16×C3⋊D3C22
hypocenterC32C22⋊C32
LCSG ▷ C3⋊D3 ▷ C32
UCSC1 ◁ C16

Complements

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

NH ≅ G/Ntype
2. #10590132C2semidirect
3. #10589067C2semidirect
60. D32C32semidirect
109. C32C22⋊C32semidirect

Maximal subgroups

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

subgroupindex
D32×C162
#105901322
#105890672
C22⋊C329