Finite Group Databasebeta

← #10592496

Subgroups — #10592496

Order 576.

270 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 85 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#64099C211yesmaximal, characteristic
3C32×#103C211yesmaximal, characteristic
4#63662C211yesmaximal, characteristic
5#63643C211yesmaximal, characteristic
6#63642C211yesmaximal, characteristic
7#63637C211yesmaximal, characteristic
8#4797—34nomaximal
9C2×C32×Q8C2211yescharacteristic
10C2×#634C2211yescharacteristic
11C2×C32×C8C2211yescharacteristic
12C32×C4⋊C4C2211yescharacteristic
13C4⋊(C3⋊Dic3)—21no—
14C4⋊(C3⋊Dic3)C2211yescharacteristic
15#3750—21no—
16#3750—21no—
17#3750—21no—
18C4×C3⋊Dic3C2211yescharacteristic
19C2×C3⋊(C3⋊C8)C2211yescharacteristic
20#944—34no—
21#890—34no—
22C3×#103D314yes—
23#835—34no—
24#816—34no—
25#815—34no—
26#810—34no—
27C32×Q8—21no—
28C32×Q8—21no—
29C2×C32×C4—21no—
30C2×C32×C4—21no—
31C2×C32×C4C2311yescharacteristic
32C2×C3⋊Dic3—21no—
33C2×C3⋊Dic3—21no—
34C2×C3⋊Dic3D411yescharacteristic
35C2×C3⋊Dic3D411yescharacteristic
36#634—21no—
37#634—21no—
38C32×C8—21no—
39C3⋊(C3⋊C8)—21no—
40#491—91noSylow
41C2×C3×Q8C2×D314yes—
42C2×Dic6—34no—
43C2×C3×C8C2×D314yes—
44C3×C4⋊C4C2×D314yes—
45C4⋊Dic3—34no—
46C4⋊Dic3—64no—
47Dic3⋊C4—64no—
48Dic3⋊C4—64no—
49Dic3⋊C4—64no—
50C4×Dic3—34no—
51C2×C3⋊C8—34no—
52C22×C32C2×D411yescharacteristic
53C32×C4—41no—
54C32×C4—41no—
55C32×C4#4111yescharacteristic
56C32×C4#4111yescharacteristic
57C3⋊Dic3—21no—
58C3⋊Dic3—21no—
59C3⋊Dic3—41no—
60C3⋊Dic3—41no—
61C4⋊Q8—91no—
62#125—91no—
63#103—91no—
64#103—91no—
65#103—91no—
66#103C3⋊D311yescharacteristic
67#97—91no—
68C3×Q8—24no—
69C3×Q8—24no—
70C2×C3×C4—24no—
71C2×C3×C4—24no—
72C2×C3×C4C22×D314yes—
73C2×Dic3—34no—
74C2×Dic3—34no—
75C2×Dic3—64no—
76C2×Dic3—64no—
77Dic6—64no—
78Dic6—64no—
79C3×C8—24no—
80C3⋊C8—64no—
81C2×C32#12411yescharacteristic
82C2×C32#13711yescharacteristic
83C2×C32#13711yescharacteristic
84C2×Q8—91no—
85C2×Q8C2×C3⋊D311yescharacteristic
86C2×C8—91no—
87C2×C8C2×C3⋊D311yescharacteristic
88C4⋊C4—91no—
89C4⋊C4—181no—
90C4⋊C4—181no—
91C4⋊C4—181no—
92C4⋊C4—181no—
93C4⋊C4C2×C3⋊D311yescharacteristic
94C42—91no—
95C22×C3D3×D414yes—
96C3×C4—44no—
97C3×C4—44no—
98C3×C4#23514yes—
99C3×C4#23714yes—
100Dic3—64no—
101Dic3—64no—
102Dic3—124no—
103Dic3—124no—
104C32#49111yescharacteristic, complemented, Sylow
105Q8—21no—
106Q8—21no—
107Q8—181no—
108Q8—181no—
109C2×C4—21no—
110C2×C4—21no—
111C2×C4—91no—
112C2×C4—91no—
113C2×C4—181no—
114C2×C4—181no—
115C2×C4C22×C3⋊D311yescharacteristic
116C8—21no—
117C8—181no—
118C2×C3#88514yes—
119C2×C3#91514yes—
120C2×C3#91814yes—
121C22D4×C3⋊D311yescharacteristic
122C4—41no—
123C4—41no—
124C4—181no—
125C4—181no—
126C4—361no—
127C4—361no—
128C4#382811yescharacteristic
129C4#383011yescharacteristic
130C3#479714yescomplemented
131C2#6409411yescharacteristic
132C2#6412411yescharacteristic
133C2#6412711yescharacteristic
subgroupG/H
centerC22D4×C3⋊D3
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C22×C3⋊D3
FittingC32×#103C2
socle, prime radicalC22×C32C2×D4
hypercenter#103C3⋊D3
hypocenterC32#491
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
104. C32#491semidirect
130. C3#4797semidirect

Maximal subgroups

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

subgroupindex
#641532
#640992
C32×#1032
#636622
#636432
#636422
#636372
#47973