Finite Group Databasebeta

← A4×#4207 #14519260

Subgroups — A4×#4207 #14519260

Order 1944.

441 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 441 conjugacy classes of subgroups — too many to draw. Only its 59 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×#737C211yesmaximal, characteristic, complemented
2C22×#4207C311yesmaximal, characteristic, complemented
3A4×C3⋊D9C311yesmaximal, characteristic, complemented
4#10620070C312yesmaximal, complemented
5A4×AGL(1,ℤ/9)—32nomaximal
6A4×(C3⋊D3)⋊C3—31nomaximal
7C3×A4×D9—31nomaximal
8C3×#4207—41nomaximal
9C22×#737C2×C311yescharacteristic, complemented
10C2×#4207—31no—
11C2×#4207—31no—
12#66440—22no—
13#66440—22no—
14#66440—24no—
15A4×3−1+2—21no—
16A4×3−1+2—22no—
17A4×3−1+2D312yescomplemented
18A4×H(3,𝔽3)D311yescharacteristic
19#66437—21no—
20#66436—21no—
21#66436—22no—
22#66436C2×C312yescomplemented
23C3×C9×A4—21no—
24C3×C9×A4D311yescharacteristic, complemented
25C3×C9×A4C2×C311yescharacteristic, complemented
26C3×#737—41noSylow
27A4×C3⋊D3—31no—
28C3×D3×A4—91no—
29C22×C3⋊D9C3211yescharacteristic, complemented
30C22×AGL(1,ℤ/9)—32no—
31C22×(C3⋊D3)⋊C3—31no—
32C22×C3×D9—31no—
33(C3⋊D3)⋊A4—32no—
34A4×D9—31no—
35A4×D9—32no—
36A4×D9—32no—
37D9⋊A4—34no—
38C2×#737—31no—
39#4207—31no—
40#4207—42no—
41#4207A411yescharacteristic, direct product factor
42C3×C3⋊D9—41no—
43C3×AGL(1,ℤ/9)—122no—
44C3×(C3⋊D3)⋊C3—121no—
45C32×D9—121no—
46C32×A4—21no—
47C32×A4C3×D311yescharacteristic
48C32×A4C3⋊D311yescharacteristic
49C22×3−1+2—21no—
50C22×3−1+2—22no—
51C22×3−1+2C3×D312yescomplemented
52C22×H(3,𝔽3)C3×D311yescharacteristic
53C22×C3×C9—21no—
54C22×C3×C9C3×D311yescharacteristic, complemented
55C22×C3×C9C2×C3211yescharacteristic, complemented
56C2×C3⋊D9—31no—
57C2×C3⋊D9—31no—
58C2×AGL(1,ℤ/9)—92no—
59C2×AGL(1,ℤ/9)—92no—
60C2×(C3⋊D3)⋊C3—91no—
61C2×(C3⋊D3)⋊C3—91no—
62C2×C3×D9—91no—
63C2×C3×D9—91no—
64C22⋊H(3,𝔽3)—21no—
65C22⋊H(3,𝔽3)—22no—
66C22⋊H(3,𝔽3)C3×D312yes—
67#1094—24no—
68#1094—22no—
69#1094—22no—
70C3×C22⋊C9—22no—
71C3×C22⋊C9—21no—
72C3×C22⋊C9—21no—
73C9⋊A4—22no—
74C9⋊A4—24no—
75C9⋊A4—24no—
76C9⋊A4—24no—
77C9⋊A4—24no—
78C9⋊A4—24no—
79C9⋊A4C3×D314yescomplemented
80C9×A4—24no—
81C9×A4—22no—
82C9×A4—21no—
83C9×A4—22no—
84C9×A4—22no—
85C9×A4—21no—
86C9×A4—22no—
87C9×A4C3×D311yescharacteristic
88C9×A4C3×D312yes—
89C9×A4C3×D312yescomplemented
90#737—42no—
91#737—82no—
92#737—82no—
93#737—84no—
94#737—82no—
95#737—81no—
96#737—81no—
97#737C2×A411yescharacteristic, complemented
98C3×3−1+2—42no—
99C3×3−1+2—82no—
100C3×3−1+2—81no—
101C3×H(3,𝔽3)—41no—
102C32×C9—41no—
103C32×C9—41no—
104C32×C9—81no—
105C22×C3⋊D3—31no—
106C22×C3×D3—91no—
107C2×C3×A4—271no—
108D3×A4—92no—
109D3×A4—91no—
110D3×A4—271no—
111C22×D9—32no—
112C22×D9—31no—
113C3×C3⋊D3—121no—
114C32×D3—361no—
115C2×3−1+2—32no—
116C2×3−1+2—62no—
117C2×3−1+2—61no—
118C2×H(3,𝔽3)—31no—
119C2×C3×C9—31no—
120C2×C3×C9—31no—
121C2×C3×C9—61no—
122C3⋊D9—31no—
123C3⋊D9C3×A411yescharacteristic, complemented
124AGL(1,ℤ/9)—32no—
125AGL(1,ℤ/9)—92no—
126AGL(1,ℤ/9)—124no—
127(C3⋊D3)⋊C3—31no—
128(C3⋊D3)⋊C3—91no—
129(C3⋊D3)⋊C3—122no—
130C3×D9—31no—
131C3×D9—91no—
132C3×D9—121no—
133C3×D9—122no—
134C3×D9—122no—
135C22×C32—21no—
136C22×C32C32×D311yescharacteristic
137C22×C32C3×C3⋊D311yescharacteristic
138C2×C3⋊D3—91no—
139C2×C3⋊D3—91no—
140C2×C3×D3—271no—
141C2×C3×D3—271no—
142C3×A4—21no—
143C3×A4—22no—
144C3×A4—31no—
145C3×A4—31no—
146C3×A4—61no—
147C3×A4—62no—
148C3×A4—61no—
149C3×A4—61no—
150C3×A4C3×C3⋊D311yescharacteristic
151C3×A4C3×C3⋊D312yes—
152C22×C9—22no—
153C22×C9—21no—
154C22×C9C32×D311yescharacteristic
155C22×C9C32×D312yes—
156C2×D9—91no—
157C2×D9—92no—
158C2×D9—91no—
159C2×D9—92no—
160C22⋊C9—21no—
161C22⋊C9—24no—
162C22⋊C9—22no—
163C22⋊C9—22no—
164C33—41no—
165C33—41no—
166C33—81no—
1673−1+2—21no—
1683−1+2—22no—
1693−1+2—44no—
1703−1+2—84no—
1713−1+2—84no—
1723−1+2—84no—
1733−1+2—84no—
1743−1+2—82no—
1753−1+2—84no—
1763−1+2—82no—
1773−1+2—82no—
1783−1+2—84no—
1793−1+2D3×A412yescomplemented
180H(3,𝔽3)—42no—
181H(3,𝔽3)—82no—
182H(3,𝔽3)—81no—
183H(3,𝔽3)D3×A411yescharacteristic
184C3×C9—21no—
185C3×C9—41no—
186C3×C9—42no—
187C3×C9—42no—
188C3×C9—81no—
189C3×C9—82no—
190C3×C9—82no—
191C3×C9—84no—
192C3×C9—82no—
193C3×C9—81no—
194C3×C9—81no—
195C3×C9—82no—
196C3×C9—81no—
197C3×C9—82no—
198C3×C9D3×A411yescharacteristic, complemented
199C3×C9C2×C3×A411yescharacteristic, complemented
200C23×C3—271no—
201C22×D3—91no—
202C22×D3—271no—
203C2×A4—272no—
204C2×A4—271no—
205C2×C32—31no—
206C2×C32—31no—
207C2×C32—61no—
208C2×C32—1081no—
209C3⋊D3—31no—
210C3⋊D3—91no—
211C3×D3—91no—
212C3×D3—271no—
213C3×D3—361no—
214C3×D3—362no—
215C3×D3—1081no—
216C2×C9—31no—
217C2×C9—32no—
218C2×C9—61no—
219C2×C9—62no—
220D9—31no—
221D9—32no—
222D9—91no—
223D9—92no—
224C22×C3—31no—
225C22×C3—31no—
226C22×C3—61no—
227C22×C3—811no—
228C22×C3—811no—
229C22×C3C32×C3⋊D311yescharacteristic
230C2×D3—271no—
231C2×D3—271no—
232C2×D3—811no—
233C2×D3—811no—
234A4—21no—
235A4—32no—
236A4—61no—
237A4—62no—
238A4#420711yescharacteristic, direct product factor
239C32—21no—
240C32—41no—
241C32—42no—
242C32—82no—
243C32—81no—
244C32—121no—
245C32—121no—
246C32—241no—
247C32—241no—
248C32—241no—
249C32—242no—
250C32C3×D3×A411yescharacteristic
251C32A4×C3⋊D311yescharacteristic
252C9—22no—
253C9—21no—
254C9—81no—
255C9—82no—
256C9—82no—
257C9—84no—
258C9C3×D3×A411yescharacteristic
259C9C3×D3×A412yes—
260C23—271noSylow
261C2×C3—31no—
262C2×C3—91no—
263C2×C3—91no—
264C2×C3—181no—
265C2×C3—271no—
266C2×C3—811no—
267C2×C3—1081no—
268C2×C3—1082no—
269D3—91no—
270D3—271no—
271D3—271no—
272D3—811no—
273C22—811no—
274C22—811no—
275C22C3×#420711yescharacteristic, complemented
276C3—31no—
277C3—31no—
278C3—41no—
279C3—61no—
280C3—81no—
281C3—122no—
282C3—241no—
283C3—242no—
284C3C3×A4×C3⋊D311yescharacteristic
285C2—31no—
286C2—271no—
287C2—811no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC22×C3×C9C2×C32
FrattiniC3C3×A4×C3⋊D3
FittingC22×#737C2×C3
socleC22×C3C32×C3⋊D3
LCSG ▷ C22×C3×C9
UCSC1

Complements

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

NH ≅ G/Ntype
1. A4×#737C2semidirect
2. C22×#4207C3semidirect
3. A4×C3⋊D9C3semidirect
4. #10620070C3semidirect
9. C22×#737C2×C3semidirect
17. A4×3−1+2D3semidirect
22. #66436C2×C3semidirect
24. C3×C9×A4D3semidirect
25. C3×C9×A4C2×C3semidirect
29. C22×C3⋊D9C32semidirect
41. #4207A4direct (N × H)
51. C22×3−1+2C3×D3semidirect
54. C22×C3×C9C3×D3semidirect
55. C22×C3×C9C2×C32semidirect
79. C9⋊A4C3×D3semidirect
89. C9×A4C3×D3semidirect
97. #737C2×A4semidirect
123. C3⋊D9C3×A4semidirect
179. 3−1+2D3×A4semidirect
198. C3×C9D3×A4semidirect
199. C3×C9C2×C3×A4semidirect
238. A4#4207direct (N × H)
275. C22C3×#4207semidirect

Maximal subgroups

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

subgroupindex
A4×#7372
C22×#42073
A4×C3⋊D93
#106200703
A4×AGL(1,ℤ/9)3
A4×(C3⋊D3)⋊C33
C3×A4×D93
C3×#42074