Finite Group Databasebeta

← A4⋊#4184 #14518102

Subgroups — A4⋊#4184 #14518102

Order 1944.

294 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 43 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
2A4⋊AGL(1,ℤ/9)—32nomaximal
3A4⋊((C3⋊D3)⋊C3)—31nomaximal
4C3×C9⋊S4—31nomaximal
5#66365⋊C2—34nomaximal
6#10619756—32nomaximal
7#10619751—32nomaximal
8#10619681—31nomaximal
9C3⋊#4184—41nomaximal
10A4×3−1+2D312yescomplemented
11A4×H(3,𝔽3)D311yescharacteristic
12C3×C9×A4D311yescharacteristic, complemented
13C22×#731D311yescharacteristic, complemented
14C2×#4184—31no—
15#66365D314yescomplemented
16#66361D312yescomplemented
17#66357D312yescomplemented
18#66331—31no—
19C3×#731—41noSylow
20C3⋊(C3⋊S4)—31no—
21C3×C3⋊S4—91no—
22C9⋊S4—31no—
23C9⋊S4—32no—
24(C3⋊S4)⋊C3—92no—
25C3×(C22⋊C9)⋊C2—92no—
26((C22⋊C9)⋊C2)⋊C3—94no—
27#611⋊C3—92no—
28#638⋊C3—91no—
29C3×#611—91no—
30C3⋊AGL(1,ℤ/9)—122no—
31C3⋊((C3⋊D3)⋊C3)—121no—
32C3×C3⋊D9—121no—
33C2×#731—31no—
34#4184—61no—
35#4184—122no—
36#4184—122no—
37#4184—124no—
38C32×A4—31no—
39C32×A4C3⋊D311yescharacteristic
40C22×3−1+2C3⋊D312yescomplemented
41C22×H(3,𝔽3)C3⋊D311yescharacteristic
42C22×C3×C9C3⋊D311yescharacteristic, complemented
43C2×AGL(1,ℤ/9)—92no—
44C2×(C3⋊D3)⋊C3—91no—
45C2×C3×D9—91no—
46C22⋊H(3,𝔽3)—61no—
47C22⋊H(3,𝔽3)C3⋊D312yes—
48#1094C3⋊D314yescomplemented
49C3×C22⋊C9C3⋊D312yescomplemented
50C9⋊A4—62no—
51C9×A4—31no—
52C9×A4—32no—
53C9×A4—61no—
543−1+2⋊C4—92no—
55(C3⋊Dic3)⋊C3—91no—
56C3×Dic9—91no—
57C3×3−1+2—42no—
58C3×H(3,𝔽3)—41no—
59C32×C9—41no—
60#731—44no—
61#731—42no—
62#731—42no—
63#731S411yescharacteristic, complemented
64C3⋊S4—91no—
65C3⋊S4—92no—
66C3⋊S4—273no—
67C3×S4—273no—
68#638—91no—
69C3×#67—271no—
70(C22⋊C9)⋊C2—94no—
71(C22⋊C9)⋊C2—92no—
72#611—91no—
73#611—92no—
74C3⋊(C3⋊D3)—121no—
75C3×C3⋊D3—361no—
76C2×3−1+2—32no—
77C2×H(3,𝔽3)—31no—
78C2×C3×C9—31no—
79C3⋊D9—121no—
80C3⋊D9—122no—
81AGL(1,ℤ/9)—182no—
82AGL(1,ℤ/9)—364no—
83(C3⋊D3)⋊C3—181no—
84(C3⋊D3)⋊C3—362no—
85C3×D9—181no—
86C3×D9—362no—
87C22×C32—31no—
88C22×C32C3⋊(C3⋊D3)11yescharacteristic
89C2×C3⋊D3—91no—
90C2×C3×D3—271no—
91C3×A4—21no—
92C3×A4—33no—
93C3×A4—32no—
94C3×A4—93no—
95C3×A4#27211yescharacteristic
96C3⋊Dic3—91no—
97C3×Dic3—271no—
98C22×C9—31no—
99C22×C9—32no—
100C2×D9—91no—
101C2×D9—92no—
102C22⋊C9—32no—
103C22⋊C9—34no—
104Dic9—91no—
105Dic9—92no—
106C33—41no—
107C33—121no—
1083−1+2—44no—
1093−1+2—242no—
1103−1+2C3⋊S412yescomplemented
111H(3,𝔽3)—42no—
112H(3,𝔽3)—241no—
113H(3,𝔽3)C3⋊S411yescharacteristic
114C3×C9—42no—
115C3×C9—121no—
116C3×C9—122no—
117C3×C9—241no—
118C3×C9C3⋊S411yescharacteristic, complemented
119S4—273no—
120S4—812no—
121C3×D4—811no—
122#67—271no—
123#67—811no—
124C2×C32—31no—
125C2×C32—91no—
126C3⋊D3—181no—
127C3⋊D3—362no—
128C3⋊D3—361no—
129C3⋊D3—1083no—
130C3×D3—541no—
131C3×D3—1083no—
132C2×C9—91no—
133C2×C9—92no—
134D9—181no—
135D9—182no—
136D9—362no—
137D9—364no—
138C22×C3—31no—
139C22×C3—91no—
140C22×C3—811no—
141C22×C3C3⋊#27211yescharacteristic
142C2×D3—271no—
143C2×D3—811no—
144A4—61no—
145A4—92no—
146A4#418413yescomplemented
147C3×C4—811no—
148Dic3—271no—
149Dic3—811no—
150C32—31no—
151C32—41no—
152C32—81no—
153C32—123no—
154C32—122no—
155C32—363no—
156C32C3⋊(C3⋊S4)11yescharacteristic
157C9—31no—
158C9—32no—
159C9—122no—
160C9—124no—
161D4—811noSylow
162C2×C3—31no—
163C2×C3—91no—
164C2×C3—271no—
165C2×C3—1621no—
166D3—541no—
167D3—3242no—
168D3—1083no—
169D3—1621no—
170C22—811no—
171C22C3⋊#418411yescharacteristic, complemented
172C4—811no—
173C3—31no—
174C3—43no—
175C3—91no—
176C3—241no—
177C3—362no—
178C3A4⋊#27211yescharacteristic
179C2—31no—
180C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterA4×#731C2
FrattiniC32C3⋊(C3⋊S4)
FittingC22×#731D3
socleC22×C3C3⋊#272
LCSG ▷ A4×#731
UCSC1

Complements

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

NH ≅ G/Ntype
1. A4×#731C2semidirect
10. A4×3−1+2D3semidirect
12. C3×C9×A4D3semidirect
13. C22×#731D3semidirect
15. #66365D3semidirect
16. #66361D3semidirect
17. #66357D3semidirect
40. C22×3−1+2C3⋊D3semidirect
42. C22×C3×C9C3⋊D3semidirect
48. #1094C3⋊D3semidirect
49. C3×C22⋊C9C3⋊D3semidirect
63. #731S4semidirect
110. 3−1+2C3⋊S4semidirect
118. C3×C9C3⋊S4semidirect
146. A4#4184semidirect
171. C22C3⋊#4184semidirect

Maximal subgroups

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

subgroupindex
A4×#7312
A4⋊AGL(1,ℤ/9)3
A4⋊((C3⋊D3)⋊C3)3
C3×C9⋊S43
#66365⋊C23
#106197563
#106197513
#106196813
C3⋊#41844