Finite Group Databasebeta

← C2×D3×S4 #64380

Subgroups — C2×D3×S4 #64380

Order 288.

272 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 35 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
1C2×D3×A4C211yesmaximal, characteristic, complemented
2C2×C3⋊S4C211yesmaximal, characteristic, complemented
3C2×C3×S4C211yesmaximal, characteristic, complemented
4D3×S4C214yesmaximal, direct product factor
5C22×S4—31nomaximal
6C2×D3×D4—31nomaximal
7C2×C3×A4C2211yescharacteristic, complemented
8C2×D32—41nomaximal
9D3×A4C2212yescomplemented
10C3⋊S4C2212yescomplemented
11C3×S4C2212yescomplemented
12C23×D3—31no—
13C23×D3D311yescharacteristic, complemented
14C22×A4—31no—
15C2×S4—31no—
16C2×S4—34no—
17C2×S4—61no—
18C2×S4D311yescharacteristic, direct product factor
19C2×C3×D4—31no—
20C2×#67—31no—
21C2×#67—31no—
22D3×D4—34no—
23D3×D4—34no—
24C2×D12—31no—
25C2×C4×D3—31no—
26C2×C3⋊D3—41no—
27C2×C3×D3—41no—
28C2×C3×D3—41no—
29C3×A4C2311yescharacteristic, complemented
30D32—44no—
31C22×D4—91noSylow
32C23×C3—31no—
33C23×C3C2×D311yescharacteristic, complemented
34C22×D3—31no—
35C22×D3—31no—
36C22×D3—32no—
37C22×D3—31no—
38C22×D3—34no—
39C22×D3—61no—
40C22×D3—62no—
41C22×D3—61no—
42C22×D3—121no—
43C22×D3C2×D312yescomplemented
44C2×A4—21no—
45C2×A4—32no—
46C2×A4C2×D311yescharacteristic, complemented
47S4—32no—
48S4—62no—
49S4C2×D312yesdirect product factor
50C3×D4—32no—
51C3×D4—32no—
52C2×C3×C4—31no—
53#67—34no—
54#67—32no—
55#67—32no—
56C2×Dic3—31no—
57D12—34no—
58C4×D3—34no—
59C2×C32—41no—
60C3⋊D3—42no—
61C3×D3—42no—
62C3×D3—42no—
63C24—31no—
64C24—91no—
65C2×D4—31no—
66C2×D4—91no—
67C2×D4—94no—
68C2×D4—94no—
69C2×D4—91no—
70C2×D4—91no—
71C22×C4—91no—
72C22×C3—31no—
73C22×C3—31no—
74C22×C3—32no—
75C22×C3—61no—
76C22×C3—61no—
77C22×C3—121no—
78C22×C3C22×D311yescharacteristic, complemented
79C2×D3—31no—
80C2×D3—32no—
81C2×D3—32no—
82C2×D3—32no—
83C2×D3—32no—
84C2×D3—41no—
85C2×D3—61no—
86C2×D3—64no—
87C2×D3—61no—
88C2×D3—61no—
89C2×D3—64no—
90C2×D3—124no—
91C2×D3—121no—
92C2×D3—241no—
93C2×D3S411yescharacteristic, direct product factor
94A4—21no—
95A4C22×D311yescharacteristic, complemented
96C3×C4—32no—
97Dic3—32no—
98C32—41noSylow
99C23—31no—
100C23—32no—
101C23—91no—
102C23—92no—
103C23—91no—
104C23—91no—
105C23—94no—
106C23—181no—
107C23—182no—
108C23—181no—
109C23D3211yescharacteristic, complemented
110D4—32no—
111D4—32no—
112D4—94no—
113D4—92no—
114D4—94no—
115D4—92no—
116C2×C4—31no—
117C2×C4—94no—
118C2×C4—91no—
119C2×C3—31no—
120C2×C3—31no—
121C2×C3—41no—
122C2×C3—62no—
123C2×C3—81no—
124C2×C3—122no—
125C2×C3C2×S411yescharacteristic, complemented
126D3—32no—
127D3—42no—
128D3—62no—
129D3—122no—
130D3—242no—
131D3C2×S412yesdirect product factor
132C22—31no—
133C22—31no—
134C22—31no—
135C22—32no—
136C22—61no—
137C22—61no—
138C22—92no—
139C22—92no—
140C22—92no—
141C22—92no—
142C22—91no—
143C22—184no—
144C22—181no—
145C22—181no—
146C22—184no—
147C22—181no—
148C22C2×D3211yescharacteristic, complemented
149C4—32no—
150C4—92no—
151C3—41no—
152C3—81no—
153C3C22×S411yescharacteristic, complemented
154C2—31no—
155C2—31no—
156C2—32no—
157C2—62no—
158C2—92no—
159C2—182no—
160C2D3×S411yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2D3×S4
commutator, cosocle, hypocenterC3×A4C23
FrattiniC1G
Fitting, socleC23×C3C2×D3
LCSG ▷ C3×A4
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×D3×A4C2semidirect
2. C2×C3⋊S4C2semidirect
3. C2×C3×S4C2semidirect
4. D3×S4C2direct (N × H)
7. C2×C3×A4C22semidirect
9. D3×A4C22semidirect
10. C3⋊S4C22semidirect
11. C3×S4C22semidirect
13. C23×D3D3semidirect
18. C2×S4D3direct (N × H)
29. C3×A4C23semidirect
33. C23×C3C2×D3semidirect
43. C22×D3C2×D3semidirect
46. C2×A4C2×D3semidirect
49. S4C2×D3direct (N × H)
78. C22×C3C22×D3semidirect
93. C2×D3S4direct (N × H)
95. A4C22×D3semidirect
109. C23D32semidirect
125. C2×C3C2×S4semidirect
131. D3C2×S4direct (N × H)
148. C22C2×D32semidirect
153. C3C22×S4semidirect
160. C2D3×S4direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D3×A42
C2×C3⋊S42
C2×C3×S42
D3×S42
C22×S43
C2×D3×D43
C2×D324