Finite Group Databasebeta

← A4⋊#4183 #14518100

Subgroups — A4⋊#4183 #14518100

Order 1944.

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

normal subgroups only

This group has 474 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×AΣL(1,𝔽27)C211yesmaximal, characteristic, complemented
2C3×C3⋊(C3⋊S4)—31nomaximal
3A4⋊AGL(1,ℤ/9)—32nomaximal
4A4⋊((C3⋊D3)⋊C3)—31nomaximal
5#10619762—32nomaximal
6#66366⋊C2—34nomaximal
7#10619757—32nomaximal
8#10619679—31nomaximal
9C3⋊#4183—41nomaximal
10C33×A4D311yescharacteristic, complemented
11A4×3−1+2D312yescomplemented
12A4×H(3,𝔽3)D311yescharacteristic, complemented
13C22×AΣL(1,𝔽27)D311yescharacteristic, complemented
14C2×#4183—31no—
15#66368D312yescomplemented
16#66366D314yescomplemented
17#66363D312yescomplemented
18#66330—31no—
19C3×AΣL(1,𝔽27)—41noSylow
20C3⋊(C3⋊S4)—31no—
21C3⋊(C3⋊S4)—31no—
22C3×C3⋊S4—99no—
23C3×C3⋊S4—91no—
24C3×C3⋊S4—92no—
25C3×#638—91no—
26C9⋊S4—32no—
27(C3⋊S4)⋊C3—92no—
28((C22⋊C9)⋊C2)⋊C3—94no—
29#611⋊C3—92no—
30#638⋊C3—91no—
31C3×C3⋊(C3⋊D3)—121no—
32C3⋊AGL(1,ℤ/9)—122no—
33C3⋊((C3⋊D3)⋊C3)—121no—
34C2×AΣL(1,𝔽27)—31no—
35#4183—61no—
36#4183—122no—
37#4183—124no—
38#4183—122no—
39C22×C33C3⋊D311yescharacteristic, complemented
40C2×C3×C3⋊D3—91no—
41C32×A4—31no—
42C32×A4—39no—
43C32×A4—31no—
44C32×A4—61no—
45C32×A4C3⋊D311yescharacteristic
46C32×A4C3⋊D312yescomplemented
47C3×C3⋊Dic3—91no—
48C22×3−1+2C3⋊D312yescomplemented
49C22×H(3,𝔽3)C3⋊D311yescharacteristic, complemented
50C2×AGL(1,ℤ/9)—92no—
51C2×(C3⋊D3)⋊C3—91no—
52C22⋊H(3,𝔽3)—61no—
53C22⋊H(3,𝔽3)C3⋊D312yescomplemented
54#1094C3⋊D314yescomplemented
55C9⋊A4—62no—
56C9×A4—32no—
573−1+2⋊C4—92no—
58(C3⋊Dic3)⋊C3—91no—
59C34—41no—
60C3×3−1+2—42no—
61C3×H(3,𝔽3)—41no—
62AΣL(1,𝔽27)—42no—
63AΣL(1,𝔽27)—44no—
64AΣL(1,𝔽27)—42no—
65AΣL(1,𝔽27)S411yescharacteristic, complemented
66C3⋊S4—99no—
67C3⋊S4—92no—
68C3⋊S4—91no—
69C3⋊S4—92no—
70C3⋊S4—273no—
71C3×S4—276no—
72C3×S4—273no—
73#638—91no—
74#638—91no—
75C3×#67—273no—
76C3×#67—271no—
77(C22⋊C9)⋊C2—94no—
78#611—92no—
79C2×C33—31no—
80C3⋊(C3⋊D3)—121no—
81C3⋊(C3⋊D3)—121no—
82C3×C3⋊D3—181no—
83C3×C3⋊D3—362no—
84C3×C3⋊D3—361no—
85C3×C3⋊D3—369no—
86C2×3−1+2—32no—
87C2×H(3,𝔽3)—31no—
88C3⋊D9—122no—
89AGL(1,ℤ/9)—182no—
90AGL(1,ℤ/9)—364no—
91(C3⋊D3)⋊C3—181no—
92(C3⋊D3)⋊C3—362no—
93C22×C32—31no—
94C22×C32—33no—
95C22×C32—31no—
96C22×C32C3⋊(C3⋊D3)11yescharacteristic
97C2×C3⋊D3—91no—
98C2×C3⋊D3—91no—
99C2×C3×D3—271no—
100C2×C3×D3—273no—
101C3×A4—21no—
102C3×A4—32no—
103C3×A4—39no—
104C3×A4—36no—
105C3×A4—33no—
106C3×A4—32no—
107C3×A4—69no—
108C3×A4—93no—
109C3×A4#27211yescharacteristic
110C3⋊Dic3—91no—
111C3⋊Dic3—91no—
112C3×Dic3—271no—
113C3×Dic3—273no—
114C22×C9—32no—
115C2×D9—92no—
116C22⋊C9—34no—
117Dic9—92no—
118C33—41no—
119C33—42no—
120C33—121no—
121C33—121no—
122C33—129no—
123C33—241no—
124C33C3⋊S411yescharacteristic, complemented
1253−1+2—44no—
1263−1+2—242no—
1273−1+2C3⋊S412yescomplemented
128H(3,𝔽3)—42no—
129H(3,𝔽3)—241no—
130H(3,𝔽3)C3⋊S411yescharacteristic, complemented
131C3×C9—122no—
132S4—276no—
133S4—273no—
134S4—812no—
135C3×D4—811no—
136#67—273no—
137#67—271no—
138#67—811no—
139C2×C32—31no—
140C2×C32—91no—
141C2×C32—91no—
142C2×C32—93no—
143C3⋊D3—181no—
144C3⋊D3—181no—
145C3⋊D3—362no—
146C3⋊D3—361no—
147C3⋊D3—369no—
148C3⋊D3—362no—
149C3⋊D3—1083no—
150C3×D3—543no—
151C3×D3—541no—
152C3×D3—1083no—
153C3×D3—1086no—
154C2×C9—92no—
155D9—182no—
156D9—364no—
157C22×C3—33no—
158C22×C3—31no—
159C22×C3—91no—
160C22×C3—811no—
161C22×C3C3⋊#27211yescharacteristic
162C2×D3—271no—
163C2×D3—273no—
164C2×D3—811no—
165A4—36no—
166A4—61no—
167A4—92no—
168A4#418313yescomplemented
169C3×C4—811no—
170Dic3—271no—
171Dic3—273no—
172Dic3—811no—
173C32—33no—
174C32—31no—
175C32—31no—
176C32—41no—
177C32—81no—
178C32—129no—
179C32—123no—
180C32—126no—
181C32—122no—
182C32—122no—
183C32—249no—
184C32—363no—
185C32C3⋊(C3⋊S4)11yescharacteristic
186C9—32no—
187C9—124no—
188D4—811noSylow
189C2×C3—31no—
190C2×C3—93no—
191C2×C3—91no—
192C2×C3—271no—
193C2×C3—1621no—
194D3—543no—
195D3—541no—
196D3—3242no—
197D3—1083no—
198D3—1086no—
199D3—1621no—
200C22—811no—
201C22C3⋊#418311yescharacteristic, complemented
202C4—811no—
203C3—33no—
204C3—31no—
205C3—43no—
206C3—91no—
207C3—126no—
208C3—241no—
209C3—362no—
210C3A4⋊#27211yescharacteristic
211C2—31no—
212C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterA4×AΣL(1,𝔽27)C2
FrattiniC32C3⋊(C3⋊S4)
FittingC22×AΣL(1,𝔽27)D3
socleC22×C3C3⋊#272
LCSG ▷ A4×AΣL(1,𝔽27)
UCSC1

Complements

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

NH ≅ G/Ntype
1. A4×AΣL(1,𝔽27)C2semidirect
10. C33×A4D3semidirect
11. A4×3−1+2D3semidirect
12. A4×H(3,𝔽3)D3semidirect
13. C22×AΣL(1,𝔽27)D3semidirect
15. #66368D3semidirect
16. #66366D3semidirect
17. #66363D3semidirect
39. C22×C33C3⋊D3semidirect
46. C32×A4C3⋊D3semidirect
48. C22×3−1+2C3⋊D3semidirect
49. C22×H(3,𝔽3)C3⋊D3semidirect
53. C22⋊H(3,𝔽3)C3⋊D3semidirect
54. #1094C3⋊D3semidirect
65. AΣL(1,𝔽27)S4semidirect
124. C33C3⋊S4semidirect
127. 3−1+2C3⋊S4semidirect
130. H(3,𝔽3)C3⋊S4semidirect
168. A4#4183semidirect
201. C22C3⋊#4183semidirect

Maximal subgroups

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

subgroupindex
A4×AΣL(1,𝔽27)2
C3×C3⋊(C3⋊S4)3
A4⋊AGL(1,ℤ/9)3
A4⋊((C3⋊D3)⋊C3)3
#106197623
#66366⋊C23
#106197573
#106196793
C3⋊#41834