Finite Group Databasebeta

← #10591616

Subgroups — #10591616

Order 576.

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

normal subgroups only

This group has 214 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#64153C211yesmaximal, characteristic
2#63872C211yesmaximal, characteristic
3C3×#835C212yesmaximal
4#63567C212yesmaximal
5#63555C211yesmaximal, characteristic
6#4797—32nomaximal
7C2×C32×Q8C2211yescharacteristic
8C2×#634C2211yescharacteristic
9#3750—22no—
10C4×C3⋊Dic3C2211yescharacteristic
11C3×C4⋊Dic3C2212yes—
12C2×C3×C3⋊C8C2212yes—
13Dic3⋊Dic3—22no—
14#944—32no—
15#944—61no—
16#890—32no—
17C3×#103—32no—
18#835D312yes—
19#816—32no—
20#815—32no—
21#810—32no—
22C32×Q8—22no—
23C2×C32×C4—21no—
24C2×C32×C4C2311yescharacteristic
25C2×C3⋊Dic3—21no—
26C2×C3⋊Dic3D412yes—
27#634—22no—
28C2×C3×Dic3—22no—
29C3×C3⋊C8—22no—
30#491—91noSylow
31C2×C3×Q8—21no—
32C2×C3×Q8C2×D312yes—
33C2×Dic6—32no—
34C2×Dic6—61no—
35C2×C3×C8—32no—
36C3×C4⋊C4—32no—
37C4⋊Dic3—62no—
38C4⋊Dic3C2×D312yes—
39Dic3⋊C4—62no—
40Dic3⋊C4—62no—
41Dic3⋊C4—62no—
42Dic3⋊C4—64no—
43C4×Dic3—32no—
44C4×Dic3—61no—
45C2×C3⋊C8C2×D312yes—
46C22×C32C2×D411yescharacteristic
47C32×C4—41no—
48C32×C4#4112yes—
49C3⋊Dic3—22no—
50C3⋊Dic3—41no—
51C3×Dic3—42no—
52C4⋊Q8—91no—
53#125—91no—
54#103—32no—
55#103—92no—
56#97—91no—
57C3×Q8—22no—
58C3×Q8—22no—
59C3×Q8—42no—
60C2×C3×C4—22no—
61C2×C3×C4—22no—
62C2×C3×C4—21no—
63C2×C3×C4—62no—
64C2×C3×C4C22×D312yes—
65C2×Dic3—22no—
66C2×Dic3—32no—
67C2×Dic3—32no—
68C2×Dic3—62no—
69C2×Dic3—62no—
70C2×Dic3—62no—
71Dic6—62no—
72Dic6—62no—
73Dic6—122no—
74C3×C8—62no—
75C3⋊C8—22no—
76C2×C32#12411yescharacteristic
77C2×C32#13712yes—
78C2×Q8—91no—
79C2×Q8D3211yescharacteristic
80C2×C8—32no—
81C4⋊C4—32no—
82C4⋊C4—182no—
83C4⋊C4—182no—
84C42—91no—
85C22×C3—21no—
86C22×C3D3×D412yes—
87C3×C4—22no—
88C3×C4—42no—
89C3×C4—42no—
90C3×C4—122no—
91C3×C4#23512yes—
92C3×C4#23712yes—
93Dic3—42no—
94Dic3—64no—
95Dic3—62no—
96Dic3—62no—
97Dic3—122no—
98Dic3—122no—
99C32#49111yescharacteristic, complemented, Sylow
100Q8—22no—
101Q8—182no—
102C2×C4—21no—
103C2×C4—62no—
104C2×C4—92no—
105C2×C4—181no—
106C2×C4C2×D3211yescharacteristic
107C8—62no—
108C2×C3—22no—
109C2×C3—21no—
110C2×C3#88512yes—
111C2×C3#91512yes—
112C2×C3#91812yes—
113C22#381111yescharacteristic
114C4—41no—
115C4—122no—
116C4—182no—
117C4—361no—
118C4#380412yes—
119C3—21no—
120C3#479712yescomplemented
121C2#6395112yes—
122C2#6395311yescharacteristic
subgroupG/H
centerC22#3811
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
FittingC2×C32×Q8C22
socle, prime radicalC22×C32C2×D4
hypercenterC2×Q8D32
hypocenterC32#491
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
99. C32#491semidirect
120. C3#4797semidirect

Maximal subgroups

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

subgroupindex
#641532
#638722
C3×#8352
#635672
#635552
#47973