Finite Group Databasebeta

← A4⋊#4177 #14518031

Subgroups — A4⋊#4177 #14518031

Order 1944.

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

normal subgroups only

This group has 224 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
1A4×#731C211yesmaximal, characteristic, complemented
2C3⋊(C9⋊S4)C311yesmaximal, characteristic, complemented
3A4⋊((C3⋊D3)⋊C3)—31nomaximal
4#10619744—32nomaximal
5#10619646—31nomaximal
6C3⋊#4177—41nomaximal
7A4×3−1+2—21no—
8A4×H(3,𝔽3)D311yescharacteristic
9C3×C9×A4C2×C311yescharacteristic, complemented
10C22×#731D311yescharacteristic, complemented
11C2×#4177—31no—
12#66365—22no—
13#66361D312yescomplemented
14#66357—21no—
15#66324—31no—
16C3×#731—41noSylow
17C3⋊(C3⋊S4)—31no—
18C3×C3⋊S4—91no—
19C3⋊((C22⋊C9)⋊C2)—32no—
20C9⋊S4—91no—
21C9⋊S4—92no—
22(C3⋊S4)⋊C3—92no—
23#6233—31no—
24#638⋊C3—91no—
25C3⋊(C3⋊D9)—41no—
26C3⋊((C3⋊D3)⋊C3)—121no—
27C2×#731—31no—
28#4177—61no—
29#4177—122no—
30C32×A4—31no—
31C32×A4C3×D311yescharacteristic
32C22×3−1+2—21no—
33C22×H(3,𝔽3)C3⋊D311yescharacteristic
34C22×C3×C9C3×D311yescharacteristic, complemented
35C2×C3⋊D9—31no—
36C2×(C3⋊D3)⋊C3—91no—
37C22⋊H(3,𝔽3)—21no—
38C22⋊H(3,𝔽3)—32no—
39#1094—22no—
40C3×C22⋊C9C3×D312yescomplemented
41C9⋊A4—62no—
42C9×A4—32no—
43C9×A4—31no—
44C9×A4—61no—
45C3⋊Dic9—31no—
46(C3⋊Dic3)⋊C3—91no—
47C3×3−1+2—81no—
48C3×H(3,𝔽3)—41no—
49C32×C9—41no—
50#731—42no—
51#731—82no—
52#731—81no—
53#731S411yescharacteristic, complemented
54C3⋊S4—91no—
55C3⋊S4—92no—
56C3⋊S4—273no—
57C3×S4—273no—
58#638—91no—
59C3×#67—271no—
60(C22⋊C9)⋊C2—272no—
61#611—271no—
62C3⋊(C3⋊D3)—121no—
63C3×C3⋊D3—361no—
64C2×3−1+2—61no—
65C2×H(3,𝔽3)—31no—
66C2×C3×C9—31no—
67C3⋊D9—61no—
68C3⋊D9—122no—
69C3⋊D9—362no—
70C3⋊D9—361no—
71(C3⋊D3)⋊C3—181no—
72(C3⋊D3)⋊C3—362no—
73C22×C32—31no—
74C22×C32C3×C3⋊D311yescharacteristic
75C2×C3⋊D3—91no—
76C2×C3×D3—271no—
77C3×A4—33no—
78C3×A4—61no—
79C3×A4—93no—
80C3×A4(C3⋊D3)⋊C312yes—
81C3×A4(C3⋊D3)⋊C311yescharacteristic
82C3⋊Dic3—91no—
83C3×Dic3—271no—
84C22×C9—31no—
85C22×C9—61no—
86C2×D9—271no—
87C22⋊C9—32no—
88C22⋊C9—62no—
89Dic9—271no—
90C33—41no—
91C33—121no—
923−1+2—21no—
933−1+2—82no—
943−1+2—242no—
95H(3,𝔽3)—81no—
96H(3,𝔽3)—122no—
97H(3,𝔽3)C3⋊S411yescharacteristic
98C3×C9—42no—
99C3×C9—121no—
100C3×C9—122no—
101C3×C9—241no—
102C3×C9C3×S411yescharacteristic, complemented
103S4—273no—
104S4—812no—
105C3×D4—811no—
106#67—271no—
107#67—811no—
108C2×C32—31no—
109C2×C32—91no—
110C3⋊D3—181no—
111C3⋊D3—362no—
112C3⋊D3—361no—
113C3⋊D3—1083no—
114C3×D3—541no—
115C3×D3—1083no—
116C2×C9—91no—
117C2×C9—181no—
118D9—541no—
119D9—1082no—
120C22×C3—31no—
121C22×C3—91no—
122C22×C3—811no—
123C22×C3C3⋊((C3⋊D3)⋊C3)11yescharacteristic
124C2×D3—271no—
125C2×D3—811no—
126A4—32no—
127A4—181no—
128A4#417713yescomplemented
129C3×C4—811no—
130Dic3—271no—
131Dic3—811no—
132C32—31no—
133C32—41no—
134C32—42no—
135C32—123no—
136C32—241no—
137C32—363no—
138C32C3×C3⋊S411yescharacteristic
139C9—31no—
140C9—61no—
141C9—122no—
142C9—242no—
143D4—811noSylow
144C2×C3—31no—
145C2×C3—91no—
146C2×C3—271no—
147C2×C3—1621no—
148D3—541no—
149D3—3242no—
150D3—1083no—
151D3—1621no—
152C22—811no—
153C22C3⋊#417711yescharacteristic, complemented
154C4—811no—
155C3—31no—
156C3—43no—
157C3—91no—
158C3—122no—
159C3—721no—
160C3A4⋊((C3⋊D3)⋊C3)11yescharacteristic
161C2—31no—
162C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC3×C9×A4C2×C3
FrattiniC32C3×C3⋊S4
FittingC22×#731D3
socleC22×C3C3⋊((C3⋊D3)⋊C3)
LCSG ▷ C3×C9×A4
UCSC1

Complements

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

NH ≅ G/Ntype
1. A4×#731C2semidirect
2. C3⋊(C9⋊S4)C3semidirect
9. C3×C9×A4C2×C3semidirect
10. C22×#731D3semidirect
13. #66361D3semidirect
34. C22×C3×C9C3×D3semidirect
40. C3×C22⋊C9C3×D3semidirect
53. #731S4semidirect
102. C3×C9C3×S4semidirect
128. A4#4177semidirect
153. C22C3⋊#4177semidirect

Maximal subgroups

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

subgroupindex
A4×#7312
C3⋊(C9⋊S4)3
A4⋊((C3⋊D3)⋊C3)3
#106197443
#106196463
C3⋊#41774