Finite Group Databasebeta

← #10593330

Subgroups — #10593330

Order 576.

170 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 45 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#64283C211yesmaximal, characteristic
2C2×#3712C211yesmaximal, characteristic
3#63818C211yesmaximal, characteristic
4#63733C214yesmaximal, complemented
5C2×C4×C3⋊D3C2211yescharacteristic
6#3792C412yes—
7#3788C412yes—
8#3787C2212yes—
9C3×#208—21no—
10C2×C3×C3⋊C8—21no—
11#3712—21no—
12#3712C2212yes—
13#3712C2212yes—
14#3710—21no—
15D3×M16—61no—
16C2×ΓL(1,𝔽25)—61no—
17C22×C3⋊D3Q811yescharacteristic
18C2×C32×C4D411yescharacteristic
19C2×C3⋊Dic3C2×C411yescharacteristic
20C4×C3⋊D3C2×C411yescharacteristic
21C4×C3⋊D3D411yescharacteristic
22C4×C3⋊D3Q811yescharacteristic
23C4×C3⋊D3C2311yescharacteristic
24#622C2×C414yes—
25C3×C3⋊C8—22no—
26C3×C3⋊C8—22no—
27#430—91nomaximal, Sylow
28C2×C4×D3—61no—
29C2×C4×D3—61no—
30C3×M16—61no—
31C2×C3×C8—61no—
32#208—21no—
33C2×C3⋊C8—21no—
34ΓL(1,𝔽25)—62no—
35ΓL(1,𝔽25)—62no—
36ΓL(1,𝔽25)—62no—
37D3×C8—62no—
38C22×C32C4⋊C411yescharacteristic
39C2×C3⋊D3—41no—
40C2×C3⋊D3C4⋊C411yescharacteristic
41C2×C3⋊D3C2×Q811yescharacteristic
42C32×C4C4⋊C411yescharacteristic
43C32×C4C2×D411yescharacteristic
44C3⋊Dic3C4⋊C411yescharacteristic
45C3⋊Dic3C22×C411yescharacteristic
46C2×M16—91no—
47C2×M16—91no—
48C2×M16—91no—
49#108—94no—
50C22×D3—61no—
51C22×D3—61no—
52C2×C3×C4—21no—
53C2×C3×C4—21no—
54C2×Dic3—61no—
55C2×Dic3—61no—
56C4×D3—61no—
57C4×D3—61no—
58C4×D3—61no—
59C4×D3—61no—
60C4×D3—61no—
61C4×D3—61no—
62C4×D3—61no—
63C4×D3—61no—
64C3×C8—62no—
65C3×C8—62no—
66C3⋊C8—22no—
67C3⋊C8—22no—
68C2×C32—21no—
69C2×C32C2×C4⋊C411yescharacteristic
70C3⋊D3—21no—
71C3⋊D3—21no—
72C22×C4—91no—
73M16—61no—
74M16—92no—
75M16—92no—
76M16—92no—
77M16—92no—
78M16—181no—
79C2×C8—61no—
80C2×C8—92no—
81C2×C8—181no—
82C22×C3—21no—
83C22×C3—21no—
84C2×D3—61no—
85C2×D3—61no—
86C2×D3—61no—
87C2×D3—61no—
88C2×D3—122no—
89C2×D3—122no—
90C3×C4—21no—
91C3×C4—21no—
92C3×C4—21no—
93C3×C4—21no—
94Dic3—61no—
95Dic3—61no—
96Dic3—61no—
97Dic3—61no—
98C32#43011yescharacteristic, complemented, Sylow
99C23—91no—
100C2×C4—91no—
101C2×C4—91no—
102C2×C4—91no—
103C2×C4—91no—
104C2×C4—91no—
105C2×C4GO+(4,𝔽2)11yescharacteristic
106C8—62no—
107C8—62no—
108C8—94no—
109C2×C3—22no—
110C2×C3—21no—
111C2×C3—21no—
112C2×C3—41no—
113D3—62no—
114D3—121no—
115D3—121no—
116D3—121no—
117C22—91no—
118C22—91no—
119C22—361no—
120C22#377311yescharacteristic
121C4—91no—
122C4—91no—
123C4#377311yescharacteristic
124C4C2×GO+(4,𝔽2)11yescharacteristic
125C3—21no—
126C3—21no—
127C2—21no—
128C2—181no—
129C2—181no—
130C2C2×#377311yescharacteristic
subgroupG/H
center, FrattiniC4C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C22×C4
FittingC2×C32×C4D4
socleC2×C32C2×C4⋊C4
prime radicalC22×C3⋊D3Q8
cosocleC4×C3⋊D3C23
hypercenterC2×C4GO+(4,𝔽2)
hypocenterC32#430
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
4. #63733C2semidirect
98. C32#430semidirect

Maximal subgroups

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

subgroupindex
#642832
C2×#37122
#638182
#637332
#4309