Finite Group Databasebeta

← C3×D3×S4 #89098

Subgroups — C3×D3×S4 #89098

Order 432.

163 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 163 conjugacy classes of subgroups — too many to draw. Only its 26 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×D3×A4C211yesmaximal, characteristic, complemented
2C3×C3⋊S4C211yesmaximal, characteristic, complemented
3C32×S4C211yesmaximal, characteristic, complemented
4C2×C3×S4—31nomaximal
5D3×S4C311yesmaximal, characteristic, direct product factor
6C3×D3×D4—31nomaximal
7C32×A4C2211yescharacteristic, complemented
8C3×D32—41nomaximal
9C22×C3×D3—31no—
10C22×C3×D3D311yescharacteristic, complemented
11C2×C3×A4—31no—
12D3×A4—21no—
13D3×A4C2×C311yescharacteristic, complemented
14C3⋊S4C2×C311yescharacteristic, complemented
15C3×S4—21no—
16C3×S4—31no—
17C3×S4—61no—
18C3×S4D311yescharacteristic, direct product factor
19C3×S4C2×C311yescharacteristic, complemented
20C32×D4—31no—
21C3×#67—31no—
22C3×#67—31no—
23C3×D12—31no—
24C3×C4×D3—31no—
25C3×C3⋊D3—41no—
26C32×D3—41no—
27C32×D3—41no—
28C2×S4—31no—
29C2×C3×D4—91no—
30D3×D4—31no—
31C22×C32—31no—
32C22×C32C2×D311yescharacteristic, complemented
33C2×C3×D3—31no—
34C2×C3×D3—31no—
35C2×C3×D3—31no—
36C2×C3×D3—61no—
37C2×C3×D3—61no—
38C2×C3×D3—121no—
39C3×A4—21no—
40C3×A4—21no—
41C3×A4—21no—
42C3×A4—41no—
43C3×A4C2×D311yescharacteristic, complemented
44C3×A4C22×C311yescharacteristic, complemented
45D32—41no—
46C32×C4—31no—
47C3×Dic3—31no—
48C33—41noSylow
49C23×C3—31no—
50C23×C3—91no—
51C22×D3—31no—
52C22×D3C3×D311yescharacteristic, complemented
53C2×A4—31no—
54C2×A4—61no—
55S4—31no—
56S4—61no—
57S4C3×D311yescharacteristic, direct product factor
58C3×D4—31no—
59C3×D4—31no—
60C3×D4—61no—
61C3×D4—91no—
62C3×D4—91no—
63C3×D4—91no—
64C2×C3×C4—91no—
65#67—31no—
66#67—31no—
67D12—31no—
68C4×D3—31no—
69C2×C32—31no—
70C2×C32—61no—
71C2×C32—121no—
72C3⋊D3—41no—
73C3×D3—31no—
74C3×D3—41no—
75C3×D3—41no—
76C3×D3—41no—
77C3×D3—61no—
78C3×D3—81no—
79C3×D3—81no—
80C3×D3—121no—
81C3×D3—241no—
82C3×D3S411yescharacteristic, direct product factor
83C2×D4—91noSylow
84C22×C3—21no—
85C22×C3—31no—
86C22×C3—31no—
87C22×C3—61no—
88C22×C3—91no—
89C22×C3—91no—
90C22×C3—91no—
91C22×C3—181no—
92C22×C3—181no—
93C22×C3D3211yescharacteristic, complemented
94C22×C3C2×C3×D311yescharacteristic, complemented
95C2×D3—31no—
96C2×D3—31no—
97C2×D3—31no—
98C2×D3—61no—
99C2×D3—61no—
100C2×D3—121no—
101A4—21no—
102A4—21no—
103A4—41no—
104A4C2×C3×D311yescharacteristic, complemented
105C3×C4—31no—
106C3×C4—31no—
107C3×C4—61no—
108C3×C4—91no—
109Dic3—31no—
110C32—41no—
111C32—41no—
112C32—81no—
113C32—81no—
114C32—81no—
115C32—161no—
116C32C2×S411yescharacteristic, complemented
117C23—31no—
118C23—91no—
119D4—31no—
120D4—91no—
121D4—91no—
122D4—91no—
123C2×C4—91no—
124C2×C3—31no—
125C2×C3—31no—
126C2×C3—31no—
127C2×C3—61no—
128C2×C3—61no—
129C2×C3—61no—
130C2×C3—91no—
131C2×C3—121no—
132C2×C3—121no—
133C2×C3—181no—
134C2×C3—241no—
135D3—31no—
136D3—41no—
137D3—61no—
138D3—121no—
139D3—241no—
140D3C3×S411yescharacteristic, direct product factor
141C22—31no—
142C22—91no—
143C22—91no—
144C22—91no—
145C22—181no—
146C22—181no—
147C22C3×D3211yescharacteristic, complemented
148C4—31no—
149C4—91no—
150C3—21no—
151C3—41no—
152C3—81no—
153C3—81no—
154C3—161no—
155C3D3×S411yescharacteristic, direct product factor
156C3C2×C3×S411yescharacteristic, complemented
157C2—31no—
158C2—31no—
159C2—61no—
160C2—91no—
161C2—181no—
subgroupG/H
center, hypercenterC3D3×S4
commutator, cosocle, hypocenterC3×A4C22×C3
FrattiniC1G
Fitting, socleC22×C32C2×D3
LCSG ▷ C3×A4
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×D3×A4C2semidirect
2. C3×C3⋊S4C2semidirect
3. C32×S4C2semidirect
5. D3×S4C3direct (N × H)
7. C32×A4C22semidirect
10. C22×C3×D3D3semidirect
13. D3×A4C2×C3semidirect
14. C3⋊S4C2×C3semidirect
18. C3×S4D3direct (N × H)
19. C3×S4C2×C3semidirect
32. C22×C32C2×D3semidirect
43. C3×A4C2×D3semidirect
44. C3×A4C22×C3semidirect
52. C22×D3C3×D3semidirect
57. S4C3×D3direct (N × H)
82. C3×D3S4direct (N × H)
93. C22×C3D32semidirect
94. C22×C3C2×C3×D3semidirect
104. A4C2×C3×D3semidirect
116. C32C2×S4semidirect
140. D3C3×S4direct (N × H)
147. C22C3×D32semidirect
155. C3D3×S4direct (N × H)
156. C3C2×C3×S4semidirect

Maximal subgroups

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

subgroupindex
C3×D3×A42
C3×C3⋊S42
C32×S42
C2×C3×S43
D3×S43
C3×D3×D43
C3×D324