Finite Group Databasebeta

← #71252

Subgroups — #71252

Order 384.

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

normal subgroups only

This group has 172 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
1C3⋊#564C211yesmaximal, characteristic
2C3×#491C211yesmaximal, characteristic
3#5081C212yesmaximal
4#4543C211yesmaximal, characteristic
5#4465C212yesmaximal
6#1663—31nomaximal, Sylow
7C3×C4⋊Q8C2211yescharacteristic
8C3×#125C2211yescharacteristic
9#890—22no—
10#889—22no—
11#889—22no—
12#870C2212yes—
13C3×#103—22no—
14C3×#97C2211yescharacteristic
15#808—22no—
16#807—22no—
17#803C2212yes—
18#564—31no—
19#501—32no—
20#491D311yescharacteristic
21#330—31no—
22#330—32no—
23C2×C3×Q8—21no—
24C2×C3×C8—21no—
25C3×C4⋊C4—22no—
26C3×C4⋊C4—22no—
27C3×C4⋊C4D412yes—
28C3×C42C2311yescharacteristic
29C4⋊Dic3—22no—
30C4⋊Dic3D412yes—
31C4⋊Dic3D412yes—
32Dic3⋊C4—22no—
33Dic3⋊C4—22no—
34Dic3⋊C4—22no—
35Dic3⋊C4—22no—
36C4×Dic3—22no—
37C2×C3⋊C8—22no—
38C4⋊Q8C2×D311yescharacteristic
39#125—32no—
40#125—62no—
41#125—62no—
42#125—62no—
43#125C2×D311yescharacteristic
44#107—62no—
45#106—62no—
46#103—22no—
47#97—32no—
48#97C2×D311yescharacteristic
49C3×Q8—42no—
50C2×C3×C4—22no—
51C2×C3×C4—41no—
52C2×C3×C4C2×D412yes—
53C2×C3×C4C2×D411yescharacteristic
54C2×Dic3—22no—
55C2×Dic3—22no—
56C3×C8—41no—
57C3⋊C8—24no—
58C2×Q8—21no—
59C2×C8—21no—
60C2×C8—62no—
61C4⋊C4—22no—
62C4⋊C4—22no—
63C4⋊C4—32no—
64C4⋊C4—32no—
65C4⋊C4—62no—
66C4⋊C4—62no—
67C4⋊C4—62no—
68C4⋊C4—62no—
69C4⋊C4—62no—
70C4⋊C4#6712yes—
71C42—62no—
72C42C22×D311yescharacteristic
73C22×C3#12011yescharacteristic
74C3×C4—21no—
75C3×C4—22no—
76C3×C4—42no—
77C3×C4—81no—
78Dic3—42no—
79Dic3—42no—
80Q8—42no—
81C2×C4—22no—
82C2×C4—41no—
83C2×C4—62no—
84C2×C4—62no—
85C2×C4D3×D412yes—
86C2×C4C2×#6711yescharacteristic
87C8—41no—
88C8—64no—
89C2×C3#45411yescharacteristic
90C2×C3#45612yes—
91C22#93711yescharacteristic
92C4—22no—
93C4—21no—
94C4—42no—
95C4—81no—
96C4—122no—
97C4—122no—
98C3#166311yescharacteristic, complemented, Sylow
99C2#506211yescharacteristic
100C2#520512yes—
subgroupG/H
centerC22#937
commutator, cosocleC3×C42C23
FrattiniC42C22×D3
FittingC3×#491C2
socle, prime radicalC22×C3#120
hypercenter#491D3
hypocenterC3#1663
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
98. C3#1663semidirect

Maximal subgroups

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

subgroupindex
C3⋊#5642
C3×#4912
#50812
#45432
#44652
#16633