Finite Group Databasebeta

← C2×D32⋊C4 #64232

Subgroups — C2×D32⋊C4 #64232

Order 288.

226 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 43 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
1C22×D32C211yesmaximal, characteristic
2C22×#157C211yesmaximal, characteristic, complemented
3C2×#624C211yesmaximal, characteristic, complemented
4D32⋊C4C214yesmaximal, direct product factor
5C22×C3⋊D3C2211yescharacteristic
6C22×C3×D3—21no—
7C2×D32—21no—
8C2×D32—22no—
9C2×D32C414yescomplemented
10C2×D32C2212yes—
11C2×#157—22no—
12C2×#157C2212yescomplemented
13C2×C3×Dic3—21no—
14#624—21no—
15#624C2212yescomplemented
16C23×D3—61no—
17C2×C4×D3—61no—
18C22×C32D411yescharacteristic
19C2×C3⋊D3C2×C412yes—
20C2×C3⋊D3D411yescharacteristic
21C2×C3⋊D3D412yes—
22C2×C3⋊D3C2311yescharacteristic
23C2×C3×D3—24no—
24C2×C3×D3—22no—
25D32—24no—
26D32—22no—
27D32C2×C414yescomplemented
28#157—22no—
29C3×Dic3—22no—
30C2×C22⋊C4—91nomaximal, Sylow
31C23×C3—61no—
32C22×D3—21no—
33C22×D3—64no—
34C22×D3—62no—
35C22×D3—61no—
36C22×D3—61no—
37C22×D3—62no—
38C22×D3—64no—
39C2×C3×C4—61no—
40C2×Dic3—21no—
41C4×D3—62no—
42C4×D3—62no—
43C2×C32C22⋊C412yescomplemented
44C2×C32C2×D411yescharacteristic
45C3⋊D3C22⋊C412yescomplemented
46C3⋊D3C22×C411yescharacteristic
47C3⋊D3C2×D411yescharacteristic
48C3×D3—24no—
49C24—91no—
50C22×C4—91no—
51C22×C4—91no—
52C22⋊C4—94no—
53C22×C3—21no—
54C22×C3—21no—
55C22×C3—62no—
56C22×C3—64no—
57C2×D3—22no—
58C2×D3—24no—
59C2×D3—64no—
60C2×D3—61no—
61C2×D3—61no—
62C2×D3—62no—
63C2×D3—61no—
64C2×D3—62no—
65C2×D3—61no—
66C2×D3—62no—
67C2×D3—62no—
68C2×D3—68no—
69C2×D3—64no—
70C3×C4—62no—
71Dic3—22no—
72C32C2×C22⋊C411yescharacteristic, complemented, Sylow
73C23—61no—
74C23—92no—
75C23—94no—
76C23—91no—
77C23—181no—
78C23—182no—
79C2×C4—61no—
80C2×C4—92no—
81C2×C4—92no—
82C2×C4—181no—
83C2×C4—182no—
84C2×C3—21no—
85C2×C3—21no—
86C2×C3—22no—
87C2×C3—22no—
88C2×C3—64no—
89D3—24no—
90D3—62no—
91D3—61no—
92D3—61no—
93D3—62no—
94D3—61no—
95D3—61no—
96C22—62no—
97C22—64no—
98C22—94no—
99C22—91no—
100C22—91no—
101C22—92no—
102C22—92no—
103C22—182no—
104C22—184no—
105C22GO+(4,𝔽2)11yescharacteristic
106C4—62no—
107C4—182no—
108C3—21no—
109C3—21no—
110C2—64no—
111C2—91no—
112C2—91no—
113C2—92no—
114C2D32⋊C412yesdirect product factor
115C2C2×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
center, hypercenterC22GO+(4,𝔽2)
commutatorC3⋊D3C22×C4
FrattiniC2C2×GO+(4,𝔽2)
Fitting, socleC22×C32D4
prime radicalC22×D32C2
cosocleC2×C3⋊D3C23
hypocenterC32C2×C22⋊C4
LCSG ▷ C3⋊D3 ▷ C32
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. C22×#157C2semidirect
3. C2×#624C2semidirect
4. D32⋊C4C2direct (N × H)
9. C2×D32C4semidirect
12. C2×#157C22semidirect
15. #624C22semidirect
27. D32C2×C4semidirect
43. C2×C32C22⋊C4semidirect
45. C3⋊D3C22⋊C4semidirect
72. C32C2×C22⋊C4semidirect
114. C2D32⋊C4direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D322
C22×#1572
C2×#6242
D32⋊C42
C2×C22⋊C49