Finite Group Databasebeta

← #10590904

Subgroups — #10590904

Order 576.

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

normal subgroups only

This group has 200 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#63873C211yesmaximal, characteristic
2#63872C211yesmaximal, characteristic
3#63642C211yesmaximal, characteristic
4C3×#816C212yesmaximal
5#63565C212yesmaximal
6#4797—32nomaximal
7C2×C3×Dic6C2212yes—
8C2×C32×C8C2211yescharacteristic
9C4×C3⋊Dic3C2211yescharacteristic
10C2×C3⋊(C3⋊C8)C2211yescharacteristic
11C3×C4⋊Dic3C2212yes—
12#3724—22no—
13Dic3⋊Dic3—22no—
14#944—32no—
15#890—32no—
16C3×#103—32no—
17#835—32no—
18#816D312yes—
19#815—32no—
20#815—61no—
21#810—32no—
22C2×C32×C4C2311yescharacteristic
23C2×C3⋊Dic3D412yes—
24C2×C3×Dic3—22no—
25C2×C3×Dic3—22no—
26C3×Dic6—22no—
27C3×Dic6—22no—
28C32×C8—21no—
29C3⋊(C3⋊C8)—21no—
30#491—91noSylow
31C2×C3×Q8—32no—
32C2×Dic6C2×D312yes—
33C2×C3×C8—21no—
34C2×C3×C8C2×D312yes—
35C3×C4⋊C4—32no—
36C4⋊Dic3—62no—
37C4⋊Dic3C2×D312yes—
38Dic3⋊C4—62no—
39Dic3⋊C4—62no—
40Dic3⋊C4—62no—
41C4×Dic3—32no—
42C4×Dic3—61no—
43C2×C3⋊C8—32no—
44C2×C3⋊C8—61no—
45C22×C32C2×D411yescharacteristic
46C32×C4#4111yescharacteristic
47C32×C4#4111yescharacteristic
48C3⋊Dic3—22no—
49C3×Dic3—42no—
50C3×Dic3—42no—
51C4⋊Q8—91no—
52#125—91no—
53#103—32no—
54#103—92no—
55#97—91no—
56C3×Q8—62no—
57C3×Q8—62no—
58C2×C3×C4—21no—
59C2×C3×C4—62no—
60C2×C3×C4—62no—
61C2×C3×C4C22×D312yes—
62C2×Dic3—22no—
63C2×Dic3—22no—
64C2×Dic3—32no—
65C2×Dic3—32no—
66C2×Dic3—62no—
67Dic6—22no—
68Dic6—22no—
69C3×C8—22no—
70C3×C8—22no—
71C3⋊C8—62no—
72C3⋊C8—62no—
73C2×C32#12411yescharacteristic
74C2×C32#13712yes—
75C2×Q8—32no—
76C2×C8—91no—
77C2×C8D3211yescharacteristic
78C4⋊C4—32no—
79C4⋊C4—182no—
80C4⋊C4—182no—
81C42—91no—
82C22×C3—21no—
83C22×C3D3×D412yes—
84C3×C4—21no—
85C3×C4—21no—
86C3×C4—122no—
87C3×C4—122no—
88C3×C4#23512yes—
89C3×C4#23712yes—
90Dic3—42no—
91Dic3—42no—
92Dic3—62no—
93Dic3—62no—
94Dic3—122no—
95C32#49111yescharacteristic, complemented, Sylow
96Q8—62no—
97Q8—62no—
98C2×C4—62no—
99C2×C4—62no—
100C2×C4—92no—
101C2×C4C2×D3211yescharacteristic
102C8—21no—
103C8—181no—
104C2×C3—22no—
105C2×C3—21no—
106C2×C3#88512yes—
107C2×C3#91512yes—
108C2×C3#91812yes—
109C22#380211yescharacteristic
110C4—122no—
111C4—122no—
112C4—182no—
113C4#379811yescharacteristic
114C4#380511yescharacteristic
115C3—21no—
116C3#479712yescomplemented
117C2#6381112yes—
118C2#6391511yescharacteristic
subgroupG/H
centerC22#3802
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
FittingC2×C32×C8C22
socle, prime radicalC22×C32C2×D4
hypercenterC2×C8D32
hypocenterC32#491
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
95. C32#491semidirect
116. C3#4797semidirect

Maximal subgroups

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

subgroupindex
#638732
#638722
#636422
C3×#8162
#635652
#47973