Finite Group Databasebeta

← C2×#63735 #10593335

Subgroups — C2×#63735 #10593335

Order 576.

158 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 33 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
1C2×#3718C211yesmaximal, characteristic, complemented
2C2×#3713C211yesmaximal, characteristic
3C2×#3708C211yesmaximal, characteristic, complemented
4#63735C214yesmaximal, direct product factor
5C2×C3×D12—21no—
6C2×C3×Dic6—21no—
7C2×C3⋊(C3⋊C8)C2211yescharacteristic
8#3718—21no—
9#3718C2212yescomplemented
10#3713—21no—
11#3713C2212yes—
12#3708C2212yescomplemented
13C2×#216—61no—
14C2×#213—61no—
15C22×C3×D3—41no—
16C2×C32×C4D411yescharacteristic
17C2×C3×Dic3—41no—
18C3×D12—22no—
19C3×D12—41no—
20C3×Dic6—22no—
21C3×Dic6—41no—
22C3⋊(C3⋊C8)D411yescharacteristic
23C3⋊(C3⋊C8)C2311yescharacteristic
24C2×SD32—91nomaximal, Sylow
25C2×C3×Q8—61no—
26C2×C3×D4—61no—
27C2×D12—21no—
28C2×Dic6—21no—
29#216—62no—
30#216—62no—
31#213—62no—
32#213—62no—
33C2×C3⋊C8—61no—
34C2×C3⋊C8—61no—
35C22×C32D811yescharacteristic
36C2×C3×D3—42no—
37C2×C3×D3—82no—
38C32×C4D811yescharacteristic
39C32×C4C2×D411yescharacteristic
40C3×Dic3—42no—
41C2×Q16—91no—
42C2×D8—91no—
43SD32—94no—
44C2×C16—91no—
45C23×C3—121no—
46C22×D3—41no—
47C3×Q8—62no—
48C3×Q8—121no—
49C3×D4—62no—
50C3×D4—121no—
51C2×C3×C4—21no—
52C2×C3×C4—21no—
53C2×C3×C4—121no—
54C2×Dic3—41no—
55D12—22no—
56D12—41no—
57Dic6—22no—
58Dic6—41no—
59C3⋊C8—61no—
60C3⋊C8—61no—
61C3⋊C8—61no—
62C3⋊C8—61no—
63C2×C32SD3212yescomplemented
64C2×C32C2×D811yescharacteristic
65C3×D3—82no—
66C2×Q8—61no—
67C2×D4—61no—
68Q16—92no—
69Q16—181no—
70D8—92no—
71D8—181no—
72C2×C8—91no—
73C16—92no—
74C22×C3—21no—
75C22×C3—21no—
76C22×C3—122no—
77C22×C3—242no—
78C2×D3—42no—
79C2×D3—82no—
80C3×C4—21no—
81C3×C4—21no—
82C3×C4—21no—
83C3×C4—21no—
84C3×C4—122no—
85Dic3—42no—
86C32C2×SD3211yescharacteristic, complemented, Sylow
87C23—121no—
88Q8—62no—
89Q8—121no—
90D4—62no—
91D4—121no—
92C2×C4—121no—
93C2×C4GO+(4,𝔽2)11yescharacteristic
94C8—91no—
95C8—91no—
96C2×C3—21no—
97C2×C3—21no—
98C2×C3—22no—
99C2×C3—22no—
100C2×C3—242no—
101D3—82no—
102C22—122no—
103C22—242no—
104C22#377411yescharacteristic
105C4—122no—
106C4#377411yescharacteristic
107C4C2×GO+(4,𝔽2)11yescharacteristic
108C3—21no—
109C3—21no—
110C2—242no—
111C2#6373512yesdirect product factor
112C2C2×#377411yescharacteristic
subgroupG/H
centerC22#3774
commutator, cosocleC3⋊(C3⋊C8)C23
FrattiniC4C2×GO+(4,𝔽2)
FittingC2×C32×C4D4
socleC22×C32D8
prime radicalC2×#3713C2
hypercenterC2×C4GO+(4,𝔽2)
hypocenterC32C2×SD32
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#3718C2semidirect
3. C2×#3708C2semidirect
4. #63735C2direct (N × H)
9. #3718C22semidirect
12. #3708C22semidirect
63. C2×C32SD32semidirect
86. C32C2×SD32semidirect
111. C2#63735direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#37182
C2×#37132
C2×#37082
#637352
C2×SD329