Finite Group Databasebeta

← D3×GO+(4,𝔽2) #89094

Subgroups — D3×GO+(4,𝔽2) #89094

Order 432.

192 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 28 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
1D33C212yesmaximal, complemented
2#157⋊D3C211yesmaximal, characteristic, complemented
3D32⋊D3C212yesmaximal, complemented
4C3×GO+(4,𝔽2)C211yesmaximal, characteristic, complemented
5D3×#157C211yesmaximal, characteristic, complemented
6C2×GO+(4,𝔽2)—31nomaximal
7#1113C2212yescomplemented
8D3×C3⋊D3—22no—
9D3×C3⋊D3C2211yescharacteristic
10C3×D32—22no—
11C3×D32C2212yescomplemented
12C3⋊#157C2211yescharacteristic, complemented
13C3×#157C2211yescharacteristic, complemented
14C2×D32—32no—
15C2×D32—62no—
16C2×#157—31no—
17GO+(4,𝔽2)—32no—
18GO+(4,𝔽2)—31no—
19GO+(4,𝔽2)D311yescharacteristic, direct product factor
20C3⋊(C3⋊D3)D411yescharacteristic, complemented
21C3×C3⋊D3—22no—
22C3×C3⋊D3C2311yescharacteristic
23C32×D3—22no—
24C32×D3D411yescharacteristic, complemented
25D3×D4—91nomaximal
26C2×C3⋊D3—31no—
27C2×C3⋊D3—62no—
28C2×C3×D3—62no—
29C2×C3×D3—62no—
30C2×C3×D3—62no—
31D32—22no—
32D32—32no—
33D32—62no—
34D32—62no—
35D32—62no—
36D32—62no—
37D32—122no—
38D32C2×D312yescomplemented
39#157—31no—
40#157C2×D311yescharacteristic, complemented
41C33C2×D411yescharacteristic, complemented, Sylow
42C22×D3—92no—
43C22×D3—182no—
44C3×D4—91no—
45#67—92no—
46D12—91no—
47C4×D3—91no—
48C2×C32—31no—
49C2×C32—62no—
50C3⋊D3—22no—
51C3⋊D3—31no—
52C3⋊D3—62no—
53C3⋊D3—122no—
54C3⋊D3C22×D311yescharacteristic
55C3×D3—22no—
56C3×D3—22no—
57C3×D3—22no—
58C3×D3—42no—
59C3×D3—62no—
60C3×D3—62no—
61C3×D3—62no—
62C3×D3—122no—
63C2×D4—271noSylow
64C22×C3—92no—
65C22×C3—182no—
66C2×D3—62no—
67C2×D3—62no—
68C2×D3—62no—
69C2×D3—92no—
70C2×D3—91no—
71C2×D3—182no—
72C2×D3—182no—
73C2×D3—182no—
74C2×D3—182no—
75C2×D3—182no—
76C2×D3—362no—
77C3×C4—91no—
78Dic3—91no—
79C32—22no—
80C32—42no—
81C32D3×D411yescharacteristic, complemented
82C23—272no—
83D4—91no—
84D4—271no—
85D4—272no—
86C2×C4—271no—
87C2×C3—62no—
88C2×C3—62no—
89C2×C3—62no—
90C2×C3—91no—
91C2×C3—122no—
92C2×C3—182no—
93D3—22no—
94D3—62no—
95D3—62no—
96D3—62no—
97D3—91no—
98D3—122no—
99D3—182no—
100D3—362no—
101D3GO+(4,𝔽2)11yescharacteristic, direct product factor
102C22—92no—
103C22—182no—
104C22—271no—
105C22—272no—
106C22—542no—
107C4—91no—
108C4—271no—
109C3—22no—
110C3—42no—
111C3C2×GO+(4,𝔽2)11yescharacteristic, complemented
112C2—31no—
113C2—62no—
114C2—91no—
115C2—182no—
116C2—271no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, cosocleC3×C3⋊D3C23
Fitting, socle, hypocenterC33C2×D4
LCSG ▷ C3×C3⋊D3 ▷ C33
UCSC1

Complements

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

NH ≅ G/Ntype
1. D33C2semidirect
2. #157⋊D3C2semidirect
3. D32⋊D3C2semidirect
4. C3×GO+(4,𝔽2)C2semidirect
5. D3×#157C2semidirect
7. #1113C22semidirect
11. C3×D32C22semidirect
12. C3⋊#157C22semidirect
13. C3×#157C22semidirect
19. GO+(4,𝔽2)D3direct (N × H)
20. C3⋊(C3⋊D3)D4semidirect
24. C32×D3D4semidirect
38. D32C2×D3semidirect
40. #157C2×D3semidirect
41. C33C2×D4semidirect
81. C32D3×D4semidirect
101. D3GO+(4,𝔽2)direct (N × H)
111. C3C2×GO+(4,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
D332
#157⋊D32
D32⋊D32
C3×GO+(4,𝔽2)2
D3×#1572
C2×GO+(4,𝔽2)3
D3×D49