Finite Group Databasebeta

← #10592556

Subgroups — #10592556

Order 576.

270 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 87 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#64099C211yesmaximal, characteristic
2#64096C211yesmaximal, characteristic
3C32×#106C211yesmaximal, characteristic
4#63643C211yesmaximal, characteristic
5#63641C211yesmaximal, characteristic
6#63637C211yesmaximal, characteristic
7#63634C211yesmaximal, characteristic
8#4857—34nomaximal
9C2×#634C2211yescharacteristic
10C2×C32×C8C2211yescharacteristic
11C32×C4⋊C4C2211yescharacteristic
12C32×C4⋊C4C2211yescharacteristic
13C4⋊(C3⋊Dic3)—21no—
14C4⋊(C3⋊Dic3)C2211yescharacteristic
15#3750—21no—
16#3750—21no—
17C4×C3⋊Dic3—21no—
18C4×C3⋊Dic3C2211yescharacteristic
19C2×C3⋊(C3⋊C8)C2211yescharacteristic
20#890—34no—
21#887—34no—
22C3×#106D314yes—
23#816—34no—
24Dic3⋊C8—34no—
25#810—34no—
26#807—34no—
27C2×C32×C4—21no—
28C2×C32×C4—21no—
29C2×C32×C4C2311yescharacteristic
30C2×C3⋊Dic3—21no—
31C2×C3⋊Dic3—21no—
32C2×C3⋊Dic3D411yescharacteristic
33C2×C3⋊Dic3D411yescharacteristic
34#634—21no—
35#634Q812yes—
36C32×C8—21no—
37C3⋊(C3⋊C8)—21no—
38#479—91noSylow
39C2×Dic6—34no—
40C2×C3×C8C2×D314yes—
41C3×C4⋊C4C2×D314yes—
42C3×C4⋊C4C2×D314yes—
43C4⋊Dic3—34no—
44C4⋊Dic3—64no—
45Dic3⋊C4—64no—
46Dic3⋊C4—64no—
47C4×Dic3—34no—
48C4×Dic3—64no—
49C2×C3⋊C8—34no—
50C22×C32C2×D411yescharacteristic
51C32×C4—41no—
52C32×C4—41no—
53C32×C4C2×Q811yescharacteristic
54C32×C4#4111yescharacteristic
55C3⋊Dic3—22no—
56C3⋊Dic3—21no—
57C3⋊Dic3—21no—
58C3⋊Dic3—41no—
59#125—91no—
60C4×Q8—91no—
61#107—91no—
62#106C3⋊D311yescharacteristic
63C4⋊C8—91no—
64#103—91no—
65#103—91no—
66C2×C3×C4—24no—
67C2×C3×C4—24no—
68C2×C3×C4C22×D314yes—
69C2×Dic3—34no—
70C2×Dic3—34no—
71C2×Dic3—64no—
72C2×Dic3—64no—
73Dic6—38no—
74Dic6—64no—
75C3×C8—24no—
76C3⋊C8—64no—
77C2×C32C22⋊Q811yescharacteristic
78C2×C32#13511yescharacteristic
79C2×C32#13711yescharacteristic
80C2×Q8—91no—
81C2×C8—91no—
82C2×C8C2×C3⋊D311yescharacteristic
83C4⋊C4—91no—
84C4⋊C4—181no—
85C4⋊C4—181no—
86C4⋊C4—181no—
87C4⋊C4C2×C3⋊D311yescharacteristic
88C4⋊C4C2×C3⋊D311yescharacteristic
89C42—91no—
90C42—181no—
91C22×C3D3×D414yes—
92C3×C4—44no—
93C3×C4—44no—
94C3×C4#23514yes—
95C3×C4D3×Q814yes—
96Dic3—68no—
97Dic3—64no—
98Dic3—64no—
99Dic3—124no—
100C32#47911yescharacteristic, complemented, Sylow
101Q8—92no—
102Q8—181no—
103C2×C4—21no—
104C2×C4—21no—
105C2×C4—91no—
106C2×C4—91no—
107C2×C4—181no—
108C2×C4—181no—
109C2×C4C22×C3⋊D311yescharacteristic
110C8—21no—
111C8—181no—
112C2×C3#89614yes—
113C2×C3#91514yes—
114C2×C3#91614yes—
115C22D4×C3⋊D311yescharacteristic
116C4—41no—
117C4—41no—
118C4—182no—
119C4—181no—
120C4—181no—
121C4—361no—
122C4#382811yescharacteristic
123C4Q8×C3⋊D311yescharacteristic
124C3#485714yescomplemented
125C2#6410511yescharacteristic
126C2#6412411yescharacteristic
127C2#6412511yescharacteristic
subgroupG/H
centerC22D4×C3⋊D3
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C22×C3⋊D3
FittingC32×#106C2
socle, prime radicalC22×C32C2×D4
hypercenter#106C3⋊D3
hypocenterC32#479
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
100. C32#479semidirect
124. C3#4857semidirect

Maximal subgroups

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

subgroupindex
#640992
#640962
C32×#1062
#636432
#636412
#636372
#636342
#48573