Finite Group Databasebeta

← #10590554

Subgroups — #10590554

Order 576.

248 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 58 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, complemented
2#63914C211yesmaximal, characteristic
3C3×#809C212yesmaximal, complemented
4#63563C212yesmaximal, complemented
5#63555C211yesmaximal, characteristic, complemented
6#4764—32nomaximal
7C2×C3×D12C2212yes—
8C2×#625—21no—
9C2×#625—21no—
10C32×C4⋊C4C2211yescharacteristic
11C4⋊(C3⋊Dic3)—21no—
12C4⋊(C3⋊Dic3)C2211yescharacteristic
13#3750—21no—
14C4×C3⋊Dic3C2211yescharacteristic
15C2×C3×C3⋊C8C2212yes—
16#940—32no—
17#890—32no—
18#890—61no—
19C3×#102—32no—
20#832—32no—
21#821—32no—
22#815—32no—
23#809D312yescomplemented
24C22×C3×D3—22no—
25C2×C32×C4—21no—
26C2×C32×C4C2311yescharacteristic
27C2×C3⋊Dic3—21no—
28C2×C3⋊Dic3D411yescharacteristic
29C2×C3⋊Dic3D411yescharacteristic
30C3×D12—22no—
31C3×D12—22no—
32#625—42no—
33#625—42no—
34C3×C3⋊C8—22no—
35#490—91noSylow
36C2×C3×D4—32no—
37C2×#67—62no—
38C2×#67—62no—
39C2×D12C2×D312yes—
40C2×C3×C8—32no—
41C3×C4⋊C4—21no—
42C3×C4⋊C4C2×D312yes—
43C4⋊Dic3—32no—
44C4⋊Dic3—61no—
45C4⋊Dic3—62no—
46C4⋊Dic3—62no—
47Dic3⋊C4—62no—
48Dic3⋊C4—62no—
49C4×Dic3—32no—
50C4×Dic3—61no—
51C2×C3⋊C8C2×D312yes—
52C22×C32C2×D411yescharacteristic
53C2×C3×D3—42no—
54C2×C3×D3—42no—
55C2×C3×D3—42no—
56C32×C4—41no—
57C32×C4#4112yes—
58C3⋊Dic3—21no—
59C3⋊Dic3—21no—
60C3⋊Dic3—41no—
61#127—91no—
62#125—91no—
63#102—32no—
64#102—92no—
65#97—91no—
66C23×C3—62no—
67C22×D3—22no—
68C3×D4—62no—
69C3×D4—62no—
70C2×C3×C4—22no—
71C2×C3×C4—22no—
72C2×C3×C4—21no—
73C2×C3×C4C22×D312yes—
74#67—124no—
75#67—124no—
76C2×Dic3—32no—
77C2×Dic3—32no—
78C2×Dic3—61no—
79C2×Dic3—61no—
80C2×Dic3—62no—
81C2×Dic3—62no—
82D12—22no—
83D12—22no—
84C3×C8—62no—
85C3⋊C8—22no—
86C2×C32#12411yescharacteristic
87C2×C32AGL(1,ℤ/8)11yescharacteristic
88C2×C32AGL(1,ℤ/8)11yescharacteristic
89C3×D3—82no—
90C2×D4—32no—
91C2×D4—181no—
92C2×D4—181no—
93C2×C8—32no—
94C4⋊C4—91no—
95C4⋊C4—181no—
96C4⋊C4—181no—
97C4⋊C4D3211yescharacteristic
98C42—91no—
99C22×C3—21no—
100C22×C3—122no—
101C22×C3—122no—
102C22×C3—122no—
103C22×C3D3×D412yes—
104C2×D3—42no—
105C2×D3—42no—
106C2×D3—42no—
107C3×C4—22no—
108C3×C4—42no—
109C3×C4—42no—
110C3×C4#23512yes—
111C3×C4#23712yes—
112Dic3—62no—
113Dic3—62no—
114Dic3—121no—
115Dic3—121no—
116Dic3—122no—
117Dic3—122no—
118C32#49011yescharacteristic, complemented, Sylow
119C23—62no—
120D4—62no—
121D4—62no—
122D4—362no—
123D4—362no—
124C2×C4—21no—
125C2×C4—91no—
126C2×C4—91no—
127C2×C4—181no—
128C2×C4C2×D3211yescharacteristic
129C8—62no—
130C2×C3—21no—
131C2×C3—21no—
132C2×C3—21no—
133C2×C3—242no—
134C2×C3#88512yes—
135C2×C3#91112yes—
136C2×C3#91412yes—
137D3—82no—
138C22—122no—
139C22—122no—
140C22—122no—
141C22#381111yescharacteristic
142C4—41no—
143C4—181no—
144C4—181no—
145C4—361no—
146C4#379512yes—
147C3—21no—
148C3#476412yescomplemented
149C2—242no—
150C2#6391311yescharacteristic
151C2#6392711yescharacteristic
152C2#6394111yescharacteristic
subgroupG/H
centerC22#3811
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
FittingC32×C4⋊C4C22
socleC22×C32C2×D4
prime radical#63914C2
hypercenterC4⋊C4D32
hypocenterC32#490
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
1. #64099C2semidirect
3. C3×#809C2semidirect
4. #63563C2semidirect
5. #63555C2semidirect
23. #809D3semidirect
118. C32#490semidirect
148. C3#4764semidirect

Maximal subgroups

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

subgroupindex
#640992
#639142
C3×#8092
#635632
#635552
#47643