Finite Group Databasebeta

← #10590183

Subgroups — #10590183

Order 576.

158 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 34 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#64286C211yesmaximal, characteristic
2#64283C211yesmaximal, characteristic
3C2×#3743C211yesmaximal, characteristic
4C2×C4×C3⋊D3C2211yescharacteristic
5C22⋊#157C412yes—
6#3792C412yescomplemented
7C4⋊#157—21no—
8C4×#157—21no—
9#3788—21no—
10#3787—21no—
11C2×C32×C8C411yescharacteristic, complemented
12C2×C3⋊(C3⋊C8)C411yescharacteristic, complemented
13#3743—21no—
14#3743—21no—
15C2×ΓL(1,𝔽25)—62no—
16C22×C3⋊D3C2×C411yescharacteristic
17C2×#157—22no—
18C2×C32×C4C2×C411yescharacteristic
19C2×C3⋊Dic3C2×C411yescharacteristic
20C4×C3⋊D3D411yescharacteristic
21C4×C3⋊D3D411yescharacteristic
22C4×C3⋊D3D411yescharacteristic
23C4×C3⋊D3Q811yescharacteristic
24#622—22no—
25C32×C8—21no—
26C3⋊(C3⋊C8)—21no—
27#344—91nomaximal, Sylow
28C2×C4×D3—62no—
29C2×C3×C8—22no—
30C2×C3⋊C8—62no—
31ΓL(1,𝔽25)—64no—
32ΓL(1,𝔽25)—64no—
33C22×C32C4211yescharacteristic
34C2×C3⋊D3—41no—
35C2×C3⋊D3C22⋊C411yescharacteristic
36C2×C3⋊D3C4⋊C411yescharacteristic
37#157—42no—
38C32×C4C22⋊C411yescharacteristic
39C32×C4C4⋊C411yescharacteristic
40C3⋊Dic3C22⋊C411yescharacteristic
41C3⋊Dic3C4⋊C411yescharacteristic
42C2×M16—91no—
43C2×M16—91no—
44#117—91no—
45C22×D3—62no—
46C2×C3×C4—22no—
47C2×Dic3—62no—
48C4×D3—62no—
49C4×D3—62no—
50C4×D3—62no—
51C4×D3—62no—
52C3×C8—24no—
53C3⋊C8—64no—
54C2×C32—21no—
55C2×C32#9511yescharacteristic
56C3⋊D3—21no—
57C3⋊D3—21no—
58C22×C4—91no—
59M16—92no—
60M16—181no—
61M16—181no—
62M16—181no—
63C2×C8—91no—
64C2×C8—181no—
65C2×C8#15711yescharacteristic, complemented
66C4⋊C4—181no—
67C22⋊C4—92no—
68C42—181no—
69C22×C3—22no—
70C2×D3—62no—
71C2×D3—62no—
72C2×D3—124no—
73C3×C4—22no—
74C3×C4—22no—
75Dic3—62no—
76Dic3—62no—
77C32#34411yescharacteristic, complemented, Sylow
78C23—91no—
79C2×C4—91no—
80C2×C4—91no—
81C2×C4—91no—
82C2×C4—91no—
83C2×C4—91no—
84C2×C4—182no—
85C2×C4C2×#15711yescharacteristic
86C8—21no—
87C8—182no—
88C8—181no—
89C2×C3—24no—
90C2×C3—22no—
91D3—122no—
92D3—122no—
93C22—91no—
94C22—91no—
95C22—361no—
96C22C4×#15711yescharacteristic
97C4—91no—
98C4—91no—
99C4—362no—
100C4C4⋊#15711yescharacteristic
101C4C22⋊#15711yescharacteristic
102C3—22no—
103C2—21no—
104C2—181no—
105C2—181no—
106C2#6378111yescharacteristic
subgroupG/H
centerC4C22⋊#157
commutatorC22×C32C42
FrattiniC2×C4C2×#157
FittingC2×C32×C8C4
socleC2×C32#95
prime radicalC22×C3⋊D3C2×C4
cosocleC2×C4×C3⋊D3C22
hypercenterC2×C8#157
hypocenterC32#344
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
6. #3792C4semidirect
11. C2×C32×C8C4semidirect
12. C2×C3⋊(C3⋊C8)C4semidirect
65. C2×C8#157semidirect
77. C32#344semidirect

Maximal subgroups

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

subgroupindex
#642862
#642832
C2×#37432
#3449