Finite Group Databasebeta

← S4×C32⋊C9 #14517954

Subgroups — S4×C32⋊C9 #14517954

Order 1944.

351 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 351 conjugacy classes of subgroups — too many to draw. Only its 56 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
1A4×C32⋊C9C211yesmaximal, characteristic, complemented
2C33×S4C311yesmaximal, characteristic
3C3×C9×S4C313yesmaximal, complemented
4D4×C32⋊C9—31nomaximal
5D3×C32⋊C9—41nomaximal
6C33×A4C2×C311yescharacteristic
7C3×C9×A4C2×C313yescomplemented
8C22×C32⋊C9—31no—
9C22×C32⋊C9D311yescharacteristic, complemented
10C32⋊(C22⋊C9)—21no—
11(C3×A4)⋊C9—23no—
12C4×C32⋊C9—31no—
13C3×C32⋊C9—41noSylow
14C32×S4—31no—
15C32×S4—32no—
16C32×S4C913yescomplemented
17C32×S4C3211yescharacteristic
18C33×D4—31no—
19C9×S4—33no—
20C3×D4×C9—33no—
21C33×D3—41no—
22C3×D3×C9—43no—
23C2×C32⋊C9—31no—
24C2×C32⋊C9—61no—
25C22×C33—31no—
26C22×C33C3×D311yescharacteristic
27C32×A4—23no—
28C32×A4—21no—
29C32×A4—31no—
30C32×A4—32no—
31C32×A4—61no—
32C32×A4—62no—
33C32×A4C2×C913yescomplemented
34C32×A4C2×C3211yescharacteristic
35C33×C4—31no—
36C22×C3×C9—33no—
37C22×C3×C9C3×D313yescomplemented
38C3×C22⋊C9—23no—
39C9×A4—33no—
40C9×A4—63no—
41C3×C4×C9—33no—
42C34—41no—
43C32×C9—43no—
44C32⋊C9—81no—
45C32⋊C9—83no—
46C32⋊C9S411yescharacteristic, direct product factor
47C3×S4—33no—
48C3×S4C3×C911yescharacteristic
49C3×S4H(3,𝔽3)11yescharacteristic
50C3×S43−1+212yes—
51C32×D4—31no—
52C32×D4—33no—
53C32×D4—91no—
54C32×D4—92no—
55D4×C9—93no—
56C2×C33—31no—
57C2×C33—61no—
58C32×D3—41no—
59C32×D3—43no—
60C32×D3—121no—
61C32×D3—122no—
62C2×C3×C9—33no—
63C2×C3×C9—63no—
64D3×C9—123no—
65C22×C32—31no—
66C22×C32—31no—
67C22×C32—32no—
68C22×C32—33no—
69C22×C32—91no—
70C22×C32—92no—
71C22×C32D3×C913yescomplemented
72C22×C32C32×D311yescharacteristic
73C3×A4—21no—
74C3×A4—21no—
75C3×A4—22no—
76C3×A4—23no—
77C3×A4—33no—
78C3×A4—63no—
79C3×A4—66no—
80C3×A4—63no—
81C3×A4—61no—
82C3×A4—62no—
83C3×A4C2×C3×C911yescharacteristic
84C3×A4C2×H(3,𝔽3)11yescharacteristic
85C3×A4C2×3−1+212yes—
86C32×C4—31no—
87C32×C4—33no—
88C32×C4—91no—
89C32×C4—92no—
90C22×C9—33no—
91C22×C9—93no—
92C22⋊C9—63no—
93C4×C9—93no—
94C33—41no—
95C33—43no—
96C33—83no—
97C33—81no—
98C33—121no—
99C33—122no—
100C33—241no—
101C33—242no—
102C33C3×S411yescharacteristic
103C3×C9—83no—
104C3×C9—123no—
105C3×C9—243no—
106C3×C9C3×S413yescomplemented
107S4C32⋊C911yescharacteristic, direct product factor
108C3×D4—31no—
109C3×D4—31no—
110C3×D4—32no—
111C3×D4—93no—
112C2×C32—31no—
113C2×C32—33no—
114C2×C32—61no—
115C2×C32—63no—
116C2×C32—91no—
117C2×C32—92no—
118C2×C32—181no—
119C2×C32—182no—
120C3×D3—41no—
121C3×D3—41no—
122C3×D3—42no—
123C3×D3—123no—
124C2×C9—93no—
125C2×C9—183no—
126C22×C3—31no—
127C22×C3—31no—
128C22×C3—32no—
129C22×C3—33no—
130C22×C3—93no—
131C22×C3C3×D3×C911yescharacteristic
132C22×C3D3×H(3,𝔽3)11yescharacteristic
133C22×C3D3×3−1+212yes—
134A4—21no—
135A4—21no—
136A4—22no—
137A4—63no—
138A4C2×C32⋊C911yescharacteristic, complemented
139C3×C4—31no—
140C3×C4—31no—
141C3×C4—32no—
142C3×C4—93no—
143C32—31no—
144C32—32no—
145C32—41no—
146C32—41no—
147C32—42no—
148C32—81no—
149C32—81no—
150C32—82no—
151C32—83no—
152C32—123no—
153C32—243no—
154C32—243no—
155C32—246no—
156C32—241no—
157C32—242no—
158C32C9×S413yescomplemented
159C32C32×S411yescharacteristic
160C9—33no—
161C9—243no—
162D4—31noSylow
163C2×C3—31no—
164C2×C3—31no—
165C2×C3—32no—
166C2×C3—61no—
167C2×C3—61no—
168C2×C3—62no—
169C2×C3—93no—
170C2×C3—183no—
171D3—41no—
172C22—31no—
173C22D3×C32⋊C911yescharacteristic, complemented
174C4—31no—
175C3—33no—
176C3—41no—
177C3—81no—
178C3—81no—
179C3—82no—
180C3—243no—
181C3C3×C9×S411yescharacteristic
182C3S4×H(3,𝔽3)11yescharacteristic
183C3S4×3−1+212yes—
184C2—31no—
185C2—61no—
subgroupG/H
center, FrattiniC32C32×S4
commutatorC3×A4C2×C3×C9
FittingC22×C32⋊C9D3
socleC22×C32C32×D3
prime radicalC33×S4C3
cosocleC32×A4C2×C32
hypercenterC32⋊C9S4
hypocenterA4C2×C32⋊C9
LCSG ▷ C3×A4 ▷ A4
UCSC1 ◁ C32 ◁ C32⋊C9

Complements

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

NH ≅ G/Ntype
1. A4×C32⋊C9C2semidirect
3. C3×C9×S4C3semidirect
7. C3×C9×A4C2×C3semidirect
9. C22×C32⋊C9D3semidirect
16. C32×S4C9semidirect
33. C32×A4C2×C9semidirect
37. C22×C3×C9C3×D3semidirect
46. C32⋊C9S4direct (N × H)
71. C22×C32D3×C9semidirect
106. C3×C9C3×S4semidirect
107. S4C32⋊C9direct (N × H)
138. A4C2×C32⋊C9semidirect
158. C32C9×S4semidirect
173. C22D3×C32⋊C9semidirect

Maximal subgroups

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

subgroupindex
A4×C32⋊C92
C33×S43
C3×C9×S43
D4×C32⋊C93
D3×C32⋊C94