Finite Group Databasebeta

← #10590564

Subgroups — #10590564

Order 576.

208 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 66 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#64099C211yesmaximal, characteristic
2#63919C211yesmaximal, characteristic
3C3×#808C212yesmaximal
4#63575C212yesmaximal
5#63555C211yesmaximal, characteristic
6#4856—32nomaximal
7C2×#627—21no—
8C32×C4⋊C4C2211yescharacteristic
9C4⋊(C3⋊Dic3)—21no—
10C4⋊(C3⋊Dic3)C2211yescharacteristic
11#3750—21no—
12C4×C3⋊Dic3C2211yescharacteristic
13C3×C4⋊Dic3C2212yes—
14C2×C3×C3⋊C8C2212yes—
15#3724—21no—
16#890—32no—
17#890—61no—
18#888—32no—
19C3×#106—32no—
20#818—32no—
21#815—32no—
22#808D312yes—
23#807—32no—
24C2×C32×C4—21no—
25C2×C32×C4C2311yescharacteristic
26C2×C3⋊Dic3—21no—
27C2×C3⋊Dic3D411yescharacteristic
28C2×C3⋊Dic3D411yescharacteristic
29C2×C3×Dic3—22no—
30#627—42no—
31C3×C3⋊C8Q814yescomplemented
32#501—91noSylow
33C2×Dic6—62no—
34C2×C3×C8—32no—
35C3×C4⋊C4—21no—
36C3×C4⋊C4—32no—
37C3×C4⋊C4C2×D312yes—
38C4⋊Dic3—32no—
39C4⋊Dic3—61no—
40C4⋊Dic3—62no—
41C4⋊Dic3—62no—
42C4⋊Dic3C2×D312yes—
43Dic3⋊C4—62no—
44Dic3⋊C4—62no—
45Dic3⋊C4—62no—
46C4×Dic3—32no—
47C4×Dic3—61no—
48C2×C3⋊C8C2×D312yes—
49C22×C32C2×D411yescharacteristic
50C32×C4—41no—
51C32×C4C2×Q812yes—
52C3⋊Dic3—21no—
53C3⋊Dic3—21no—
54C3⋊Dic3—41no—
55C3×Dic3—42no—
56C4⋊Q8—91no—
57#125—91no—
58#107—92no—
59#106—32no—
60#97—91no—
61C2×C3×C4—22no—
62C2×C3×C4—22no—
63C2×C3×C4—21no—
64C2×C3×C4—62no—
65C2×C3×C4C22×D312yes—
66C2×Dic3—22no—
67C2×Dic3—32no—
68C2×Dic3—32no—
69C2×Dic3—61no—
70C2×Dic3—61no—
71C2×Dic3—62no—
72C2×Dic3—62no—
73Dic6—124no—
74C3×C8—34no—
75C3⋊C8Dic614yescomplemented
76C2×C32C4⋊Q811yescharacteristic
77C2×C32AGL(1,ℤ/8)11yescharacteristic
78C2×C32#13711yescharacteristic
79C2×Q8—181no—
80C2×C8—32no—
81C4⋊C4—32no—
82C4⋊C4—91no—
83C4⋊C4—181no—
84C4⋊C4—181no—
85C4⋊C4—181no—
86C4⋊C4D3211yescharacteristic
87C42—91no—
88C22×C3—21no—
89C22×C3D3×D412yes—
90C3×C4—22no—
91C3×C4—42no—
92C3×C4—42no—
93C3×C4—122no—
94C3×C4C2×Dic612yes—
95C3×C4D3×Q812yes—
96Dic3—42no—
97Dic3—62no—
98Dic3—62no—
99Dic3—121no—
100Dic3—121no—
101Dic3—122no—
102Dic3—122no—
103C32#50111yescharacteristic, complemented, Sylow
104Q8—362no—
105C2×C4—21no—
106C2×C4—62no—
107C2×C4—91no—
108C2×C4—91no—
109C2×C4—181no—
110C2×C4C2×D3211yescharacteristic
111C8—34no—
112C2×C3—21no—
113C2×C3—21no—
114C2×C3—21no—
115C2×C3#88812yes—
116C2×C3#91412yes—
117C2×C3#91512yes—
118C22#381111yescharacteristic
119C4—41no—
120C4—122no—
121C4—181no—
122C4—181no—
123C4—361no—
124C4D3×Dic612yes—
125C3—21no—
126C3#485612yescomplemented
127C2#6384011yescharacteristic
128C2#6393111yescharacteristic
129C2#6394111yescharacteristic
subgroupG/H
centerC22#3811
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
FittingC32×C4⋊C4C22
socle, prime radicalC22×C32C2×D4
hypercenterC4⋊C4D32
hypocenterC32#501
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
31. C3×C3⋊C8Q8semidirect
75. C3⋊C8Dic6semidirect
103. C32#501semidirect
126. C3#4856semidirect

Maximal subgroups

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

subgroupindex
#640992
#639192
C3×#8082
#635752
#635552
#48563