Finite Group Databasebeta

← #10593429

Subgroups — #10593429

Order 576.

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

normal subgroups only

This group has 224 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×#3788C211yesmaximal, characteristic, complemented
2C2×#3774C211yesmaximal, characteristic, complemented
3#63912C212yesmaximal, complemented
4#63742C211yesmaximal, characteristic, complemented
5#63739C212yesmaximal, complemented
6C2×C4×C3⋊D3C2211yescharacteristic
7C2×#626—22no—
8C2×#625C2212yes—
9C2×#622C2211yescharacteristic
10C2×#622C2211yescharacteristic
11#3788—22no—
12#3774—22no—
13C3×(C2×D3)⋊C4—22no—
14#3724C2212yes—
15#884—62no—
16C22×C3⋊D3D411yescharacteristic
17C22×C3×D3—22no—
18C2×C32×C4D411yescharacteristic
19C2×C3⋊Dic3C2311yescharacteristic
20C4×C3⋊D3—21no—
21C4×C3⋊D3—21no—
22C2×C3×Dic3—22no—
23#626—44no—
24#625—22no—
25#625—22no—
26#622—21no—
27#622D412yescomplemented
28#469—91nomaximal, Sylow
29C2×#67—62no—
30C2×#67—62no—
31C2×D12—62no—
32C2×C4×D3—62no—
33C3×C22⋊C4—62no—
34(C2×D3)⋊C4—22no—
35Dic3⋊C4—62no—
36C22×C32C2×D411yescharacteristic
37C2×C3⋊D3—22no—
38C2×C3⋊D3—21no—
39C2×C3×D3—42no—
40C2×C3×D3—42no—
41C2×C3×D3—42no—
42C32×C4—21no—
43C3⋊Dic3C2×D411yescharacteristic
44C3⋊Dic3#4111yescharacteristic
45C3×Dic3—42no—
46C2×D8—91no—
47C2×M16—91no—
48#121—92no—
49#106—91no—
50#102—92no—
51C23×C3—62no—
52C22×D3—22no—
53C22×D3—62no—
54C2×C3×C4—22no—
55C2×C3×C4—62no—
56#67—122no—
57#67—122no—
58#67—124no—
59C2×Dic3—22no—
60C2×Dic3—62no—
61D12—124no—
62C4×D3—122no—
63C4×D3—122no—
64C2×C32#12111yescharacteristic
65C2×C32AGL(1,ℤ/8)12yes—
66C3⋊D3—41no—
67C3×D3—82no—
68C2×D4—92no—
69C2×D4—182no—
70C22×C4—91no—
71D8—182no—
72M16—182no—
73C2×C8—91no—
74C2×C8—91no—
75C4⋊C4—92no—
76C22⋊C4—62no—
77C22×C3—22no—
78C22×C3—122no—
79C22×C3—122no—
80C22×C3—122no—
81C2×D3—42no—
82C2×D3—42no—
83C2×D3—42no—
84C2×D3—64no—
85C2×D3—122no—
86C2×D3—122no—
87C3×C4—42no—
88C3×C4—122no—
89Dic3—42no—
90Dic3—62no—
91Dic3—62no—
92C32#46911yescharacteristic, complemented, Sylow
93C23—62no—
94C23—91no—
95D4—182no—
96D4—182no—
97D4—364no—
98C2×C4—62no—
99C2×C4—91no—
100C2×C4—181no—
101C2×C4—181no—
102C2×C4GO+(4,𝔽2)11yescharacteristic
103C8—92no—
104C8—181no—
105C2×C3—22no—
106C2×C3—22no—
107C2×C3—22no—
108C2×C3—242no—
109D3—82no—
110D3—124no—
111C22—122no—
112C22—122no—
113C22—122no—
114C22—182no—
115C22—181no—
116C22C2×GO+(4,𝔽2)11yescharacteristic
117C4—21no—
118C4—91no—
119C4—91no—
120C4—122no—
121C3—22no—
122C2—242no—
123C2—361no—
124C2#6422412yes—
125C2#6424211yescharacteristic
subgroupG/H
center, FrattiniC22C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C23
FittingC2×C32×C4D4
socleC22×C32C2×D4
hypercenterC2×C4GO+(4,𝔽2)
hypocenterC32#469
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#3788C2semidirect
2. C2×#3774C2semidirect
3. #63912C2semidirect
4. #63742C2semidirect
5. #63739C2semidirect
27. #622D4semidirect
92. C32#469semidirect

Maximal subgroups

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

subgroupindex
C2×#37882
C2×#37742
#639122
#637422
#637392
#4699