Finite Group Databasebeta

← #10593386

Subgroups — #10593386

Order 576.

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

normal subgroups only

This group has 187 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
1#63900C211yesmaximal, characteristic
2#63865C211yesmaximal, characteristic
3#63778C211yesmaximal, characteristic
4#63742C212yesmaximal, complemented
5#63740C212yesmaximal, complemented
6C2×C4×C3⋊D3C2211yescharacteristic
7C2×#627C2211yescharacteristic
8C2×#624—21no—
9C2×#622C2212yes—
10C3×C4⋊Dic3—21no—
11C3×Dic3⋊C4—21no—
12#3724C2211yescharacteristic
13#3724C2212yes—
14#3722—21no—
15#896—61no—
16D3×C4⋊C4—61no—
17C22×C3⋊D3D411yescharacteristic
18C2×C32×C4D411yescharacteristic
19C2×C3⋊Dic3C2311yescharacteristic
20C4×C3⋊D3—22no—
21C2×C3×Dic3—21no—
22C2×C3×Dic3—21no—
23C2×C3×Dic3—22no—
24#627—22no—
25#624—42no—
26#622—22no—
27#483—91nomaximal, Sylow
28C2×C4×D3—61no—
29C2×C4×D3—61no—
30C2×C4×D3—62no—
31C2×Dic6—61no—
32C3×C4⋊C4—61no—
33C3×C4⋊C4—61no—
34(C2×D3)⋊C4—61no—
35(C2×D3)⋊C4—61no—
36C4⋊Dic3—21no—
37Dic3⋊C4—21no—
38Dic3⋊C4—62no—
39Dic3⋊C4—61no—
40C22×C32C2×D411yescharacteristic
41C2×C3⋊D3—21no—
42C2×C3⋊D3—21no—
43C2×C3⋊D3SD1612yes—
44C32×C4—21no—
45C3⋊Dic3#4112yes—
46C3×Dic3—41no—
47C3×Dic3—42no—
48C3×Dic3—41no—
49C22⋊Q8—91no—
50C2×C4⋊C4—91no—
51#106—92no—
52#103—92no—
53C22⋊C8—91no—
54C22×D3—61no—
55C22×D3—61no—
56C2×C3×C4—21no—
57C2×C3×C4—21no—
58C2×C3×C4—61no—
59C2×C3×C4—62no—
60C2×C3×C4—61no—
61C2×Dic3—21no—
62C2×Dic3—21no—
63C2×Dic3—22no—
64C2×Dic3—61no—
65C2×Dic3—61no—
66C4×D3—64no—
67C4×D3—122no—
68C4×D3—124no—
69Dic6—122no—
70C2×C32#12311yescharacteristic
71C2×C32C2×SD1611yescharacteristic
72C2×C32#13711yescharacteristic
73C3⋊D3—22no—
74C2×Q8—91no—
75C22×C4—91no—
76C22×C4—181no—
77C2×C8—92no—
78C4⋊C4—61no—
79C4⋊C4—61no—
80C4⋊C4—92no—
81C4⋊C4—91no—
82C22⋊C4—181no—
83C22×C3—21no—
84C22×C3—21no—
85C2×D3—62no—
86C2×D3—62no—
87C2×D3—62no—
88C2×D3—62no—
89C2×D3—121no—
90C2×D3—121no—
91C3×C4—22no—
92C3×C4—41no—
93C3×C4—121no—
94C3×C4—122no—
95C3×C4—121no—
96Dic3—41no—
97Dic3—42no—
98Dic3—41no—
99Dic3—62no—
100Dic3—62no—
101C32#48311yescharacteristic, complemented, Sylow
102C23—91no—
103Q8—182no—
104C2×C4—61no—
105C2×C4—61no—
106C2×C4—62no—
107C2×C4—91no—
108C2×C4—182no—
109C2×C4—362no—
110C2×C4GO+(4,𝔽2)11yescharacteristic
111C8—182no—
112C2×C3—21no—
113C2×C3—21no—
114C2×C3—21no—
115C2×C3—21no—
116C2×C3—21no—
117C2×C3—21no—
118D3—64no—
119D3—122no—
120C22—92no—
121C22—181no—
122C22—181no—
123C22C2×GO+(4,𝔽2)11yescharacteristic
124C4—21no—
125C4—92no—
126C4—121no—
127C4—122no—
128C4—121no—
129C3—21no—
130C3—21no—
131C2—182no—
132C2#6422611yescharacteristic
133C2#6422711yescharacteristic
134C2#6423311yescharacteristic
subgroupG/H
center, FrattiniC22C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C23
FittingC2×C32×C4D4
socleC22×C32C2×D4
prime radicalC22×C3⋊D3D4
hypercenterC2×C4GO+(4,𝔽2)
hypocenterC32#483
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
4. #63742C2semidirect
5. #63740C2semidirect
101. C32#483semidirect

Maximal subgroups

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

subgroupindex
#639002
#638652
#637782
#637422
#637402
#4839