Finite Group Databasebeta

← #3830⋊C3 #88714

Subgroups — #3830⋊C3 #88714

Order 432.

156 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 52 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
1D4×H(3,𝔽3)C211yesmaximal, characteristic, complemented
2#638⋊C3C212yesmaximal, complemented
3C2×(C3⋊Dic3)⋊C3C212yesmaximal, complemented
4C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
5#634⋊C3C211yesmaximal, characteristic, complemented
6#3830C311yesmaximal, characteristic, complemented
7C3×#237—31nomaximal
8C22×H(3,𝔽3)C2212yes—
9C2×(C3⋊D3)⋊C3C2211yescharacteristic
10C4×H(3,𝔽3)C2211yescharacteristic
11(C3⋊Dic3)⋊C3C2212yes—
12(C3⋊Dic3)⋊C3C2211yescharacteristic
13C32×D4—21no—
14C32×D4D311yescharacteristic, complemented
15C32×D4C2×C311yescharacteristic, complemented
16#638C2×C312yescomplemented
17C2×C3⋊Dic3C2×C312yescomplemented
18C4×C3⋊D3C2×C311yescharacteristic, complemented
19#634C2×C311yescharacteristic, complemented
20C3×#67—32no—
21C2×C3×Dic3—32no—
22C3×C4×D3—31no—
23C3×Dic6—31no—
24C2×H(3,𝔽3)—22no—
25C2×H(3,𝔽3)C2311yescharacteristic
26(C3⋊D3)⋊C3—21no—
27C3×#41—91no—
28#237—31no—
29#237—91no—
30C22×C32—22no—
31C22×C32C2×D312yes—
32C22×C32C22×C312yes—
33C2×C3⋊D3C22×C311yescharacteristic
34C2×C3×D3—31no—
35C32×C4—21no—
36C32×C4C2×D311yescharacteristic
37C32×C4C22×C311yescharacteristic
38C3⋊Dic3C22×C312yes—
39C3⋊Dic3C22×C311yescharacteristic
40C3×Dic3—32no—
41C3×Dic3—31no—
42H(3,𝔽3)#4111yescharacteristic, complemented, Sylow
43C3×Q8—91no—
44C3×D4—31no—
45C3×D4—31no—
46C3×D4—61no—
47C3×D4—92no—
48C3×D4C3×D311yescharacteristic
49C2×C3×C4—91no—
50C2×C3×C4—92no—
51#67—32no—
52#67—92no—
53C2×Dic3—32no—
54C2×Dic3—92no—
55C4×D3—31no—
56C4×D3—91no—
57Dic6—31no—
58Dic6—91no—
59C2×C32—22no—
60C2×C32—22no—
61C2×C32—21no—
62C2×C32—42no—
63C2×C32C22×D311yescharacteristic
64C2×C32C23×C311yescharacteristic
65C3⋊D3—21no—
66C3×D3—61no—
67#41—91noSylow
68C22×C3—32no—
69C22×C3—32no—
70C22×C3—62no—
71C22×C3—91no—
72C22×C3C2×C3×D312yes—
73C2×D3—31no—
74C2×D3—91no—
75C3×C4—31no—
76C3×C4—31no—
77C3×C4—61no—
78C3×C4—91no—
79C3×C4—92no—
80C3×C4C2×C3×D311yescharacteristic
81Dic3—32no—
82Dic3—31no—
83Dic3—92no—
84Dic3—91no—
85C32—21no—
86C32#23711yescharacteristic, complemented
87C32C3×#4111yescharacteristic, complemented
88Q8—91no—
89D4—92no—
90D4(C3⋊D3)⋊C311yescharacteristic, complemented
91C2×C4—92no—
92C2×C4—91no—
93C2×C3—22no—
94C2×C3—31no—
95C2×C3—31no—
96C2×C3—62no—
97C2×C3—62no—
98C2×C3—61no—
99C2×C3—122no—
100C2×C3—181no—
101C2×C3C22×C3×D311yescharacteristic
102D3—61no—
103D3—181no—
104C22—91no—
105C22C2×(C3⋊D3)⋊C312yes—
106C4—91no—
107C4—92no—
108C4C2×(C3⋊D3)⋊C311yescharacteristic
109C3—31no—
110C3—31no—
111C3—61no—
112C3C3×#23711yescharacteristic
113C2—22no—
114C2—181no—
115C2C22×(C3⋊D3)⋊C311yescharacteristic
subgroupG/H
centerC2C22×(C3⋊D3)⋊C3
commutator, cosocleC2×C32C23×C3
Frattini, socleC2×C3C22×C3×D3
FittingD4×H(3,𝔽3)C2
hypercenterD4(C3⋊D3)⋊C3
hypocenterC32C3×#41
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ D4

Complements

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

NH ≅ G/Ntype
1. D4×H(3,𝔽3)C2semidirect
2. #638⋊C3C2semidirect
3. C2×(C3⋊Dic3)⋊C3C2semidirect
4. C4×(C3⋊D3)⋊C3C2semidirect
5. #634⋊C3C2semidirect
6. #3830C3semidirect
14. C32×D4D3semidirect
15. C32×D4C2×C3semidirect
16. #638C2×C3semidirect
17. C2×C3⋊Dic3C2×C3semidirect
18. C4×C3⋊D3C2×C3semidirect
19. #634C2×C3semidirect
42. H(3,𝔽3)#41semidirect
86. C32#237semidirect
87. C32C3×#41semidirect
90. D4(C3⋊D3)⋊C3semidirect

Maximal subgroups

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

subgroupindex
D4×H(3,𝔽3)2
#638⋊C32
C2×(C3⋊Dic3)⋊C32
C4×(C3⋊D3)⋊C32
#634⋊C32
#38303
C3×#2373