Finite Group Databasebeta

← #10590568

Subgroups — #10590568

Order 576.

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

normal subgroups only

This group has 208 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
2#63873C211yesmaximal, characteristic
3C3×#810C212yesmaximal
4#63566C212yesmaximal
5#63555C211yesmaximal, characteristic
6#4797—32nomaximal
7C2×C3×Dic6C2212yes—
8C32×C4⋊C4C2211yescharacteristic
9C4⋊(C3⋊Dic3)—21no—
10C4⋊(C3⋊Dic3)C2211yescharacteristic
11#3750—21no—
12C4×C3⋊Dic3C2211yescharacteristic
13C2×C3×C3⋊C8C2212yes—
14#3724—21no—
15#3724—21no—
16#944—32no—
17#890—32no—
18#890—61no—
19C3×#103—32no—
20#835—32no—
21#816—32no—
22#815—32no—
23#810D312yes—
24C2×C32×C4—21no—
25C2×C32×C4C2311yescharacteristic
26C2×C3⋊Dic3—21no—
27C2×C3⋊Dic3D411yescharacteristic
28C2×C3⋊Dic3D411yescharacteristic
29C2×C3×Dic3—22no—
30C3×Dic6—22no—
31C3×Dic6—22no—
32C3×C3⋊C8—22no—
33#491—91noSylow
34C2×C3×Q8—32no—
35C2×Dic6C2×D312yes—
36C2×C3×C8—32no—
37C3×C4⋊C4—21no—
38C3×C4⋊C4C2×D312yes—
39C4⋊Dic3—32no—
40C4⋊Dic3—61no—
41C4⋊Dic3—62no—
42C4⋊Dic3—62no—
43Dic3⋊C4—62no—
44Dic3⋊C4—62no—
45Dic3⋊C4—62no—
46Dic3⋊C4—62no—
47C4×Dic3—32no—
48C4×Dic3—61no—
49C2×C3⋊C8C2×D312yes—
50C22×C32C2×D411yescharacteristic
51C32×C4—41no—
52C32×C4#4112yes—
53C3⋊Dic3—21no—
54C3⋊Dic3—21no—
55C3⋊Dic3—41no—
56C3×Dic3—42no—
57C4⋊Q8—91no—
58#125—91no—
59#103—32no—
60#103—92no—
61#97—91no—
62C3×Q8—62no—
63C3×Q8—62no—
64C2×C3×C4—22no—
65C2×C3×C4—22no—
66C2×C3×C4—21no—
67C2×C3×C4—62no—
68C2×C3×C4C22×D312yes—
69C2×Dic3—22no—
70C2×Dic3—32no—
71C2×Dic3—32no—
72C2×Dic3—61no—
73C2×Dic3—61no—
74C2×Dic3—62no—
75C2×Dic3—62no—
76Dic6—22no—
77Dic6—22no—
78C3×C8—62no—
79C3⋊C8—22no—
80C2×C32#12411yescharacteristic
81C2×C32#13711yescharacteristic
82C2×C32#13711yescharacteristic
83C2×Q8—32no—
84C2×C8—32no—
85C4⋊C4—91no—
86C4⋊C4—181no—
87C4⋊C4—181no—
88C4⋊C4—181no—
89C4⋊C4—181no—
90C4⋊C4D3211yescharacteristic
91C42—91no—
92C22×C3—21no—
93C22×C3D3×D412yes—
94C3×C4—22no—
95C3×C4—42no—
96C3×C4—42no—
97C3×C4—122no—
98C3×C4#23512yes—
99C3×C4#23712yes—
100Dic3—42no—
101Dic3—62no—
102Dic3—62no—
103Dic3—121no—
104Dic3—121no—
105Dic3—122no—
106Dic3—122no—
107C32#49111yescharacteristic, complemented, Sylow
108Q8—62no—
109Q8—62no—
110C2×C4—21no—
111C2×C4—62no—
112C2×C4—91no—
113C2×C4—91no—
114C2×C4—181no—
115C2×C4C2×D3211yescharacteristic
116C8—62no—
117C2×C3—21no—
118C2×C3—21no—
119C2×C3—21no—
120C2×C3#88512yes—
121C2×C3#91512yes—
122C2×C3#91812yes—
123C22#381111yescharacteristic
124C4—41no—
125C4—122no—
126C4—181no—
127C4—181no—
128C4—361no—
129C4#379512yes—
130C3—21no—
131C3#479712yescomplemented
132C2#6391311yescharacteristic
133C2#6393111yescharacteristic
134C2#6394511yescharacteristic
subgroupG/H
centerC22#3811
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
FittingC32×C4⋊C4C22
socle, prime radicalC22×C32C2×D4
hypercenterC4⋊C4D32
hypocenterC32#491
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
107. C32#491semidirect
131. C3#4797semidirect

Maximal subgroups

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

subgroupindex
#640992
#638732
C3×#8102
#635662
#635552
#47973