Finite Group Databasebeta

← #71304

Subgroups — #71304

Order 384.

218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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#5734C211yesmaximal, characteristic
2C3×#494C211yesmaximal, characteristic, complemented
3#5084C212yesmaximal, complemented
4#4546C211yesmaximal, characteristic, complemented
5#4459C212yesmaximal, complemented
6#1634—31nomaximal, Sylow
7C2×C3×Q16—22no—
8C3×C4⋊Q8C2211yescharacteristic
9C3×C4⋊Q8C2211yescharacteristic
10#947—22no—
11#895—22no—
12#892—22no—
13C4×D12C2212yes—
14C3×C4×C8C2211yescharacteristic
15#809—22no—
16#808—22no—
17C4⋊(C3⋊C8)C2212yes—
18#555—31no—
19#494D311yescharacteristic, complemented
20#476—32no—
21#333—31no—
22D4⋊C8—32no—
23C2×C3×Q8—21no—
24C2×C3×Q8D412yes—
25C2×D12—22no—
26C2×D12D412yes—
27C2×C4×D3—22no—
28C3×Q16—44no—
29C2×C3×C8—21no—
30C3×C4⋊C4—22no—
31C3×C4⋊C4—22no—
32C3×C42C2311yescharacteristic
33(C2×D3)⋊C4—24no—
34(C2×D3)⋊C4—22no—
35C4⋊Dic3D412yes—
36C4×Dic3—22no—
37C2×C3⋊C8—22no—
38C2×Q16—22no—
39C4⋊Q8C2×D311yescharacteristic
40C4⋊Q8C2×D311yescharacteristic
41#124—62no—
42#121—62no—
43C4×D4—32no—
44#117—62no—
45#106—62no—
46C4⋊C8—32no—
47#102—62no—
48C4×C8C2×D311yescharacteristic
49C22×D3—22no—
50C3×Q8—42no—
51C3×Q8—42no—
52C2×C3×C4—22no—
53C2×C3×C4—41no—
54C2×C3×C4C2×D412yes—
55C2×C3×C4C2×D411yescharacteristic
56C2×Dic3—22no—
57D12—22no—
58D12—22no—
59D12—82no—
60C4×D3—42no—
61C4×D3—42no—
62C3×C8—22no—
63C3⋊C8—42no—
64C2×Q8—21no—
65C2×Q8#6712yes—
66C2×D4—32no—
67C2×D4—62no—
68C22×C4—62no—
69Q16—44no—
70C2×C8—21no—
71C2×C8—62no—
72C4⋊C4—22no—
73C4⋊C4—22no—
74C4⋊C4—32no—
75C22⋊C4—64no—
76C22⋊C4—62no—
77C42—62no—
78C42C22×D311yescharacteristic
79C22×C3#12011yescharacteristic
80C2×D3—42no—
81C2×D3—42no—
82C2×D3—42no—
83C3×C4—21no—
84C3×C4—42no—
85C3×C4—81no—
86C3×C4#13512yes—
87C3×C4#13712yes—
88Dic3—42no—
89C23—62no—
90Q8—42no—
91Q8—42no—
92D4—62no—
93D4—62no—
94D4—242no—
95C2×C4—22no—
96C2×C4—41no—
97C2×C4—62no—
98C2×C4—122no—
99C2×C4—122no—
100C2×C4D3×D412yes—
101C2×C4C2×#6711yescharacteristic
102C8—22no—
103C8—122no—
104C2×C3#45212yes—
105C2×C3#45311yescharacteristic
106D3—82no—
107C22—122no—
108C22—122no—
109C22—122no—
110C22#93711yescharacteristic
111C4—21no—
112C4—42no—
113C4—81no—
114C4—122no—
115C4#91812yes—
116C4#91912yes—
117C3#163411yescharacteristic, complemented, Sylow
118C2—242no—
119C2#507711yescharacteristic
120C2#518712yes—
subgroupG/H
centerC22#937
commutator, cosocleC3×C42C23
FrattiniC42C22×D3
FittingC3×#494C2
socleC22×C3#120
prime radical#5734C2
hypercenter#494D3
hypocenterC3#1634
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
2. C3×#494C2semidirect
3. #5084C2semidirect
4. #4546C2semidirect
5. #4459C2semidirect
19. #494D3semidirect
117. C3#1634semidirect

Maximal subgroups

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

subgroupindex
#57342
C3×#4942
#50842
#45462
#44592
#16343