Finite Group Databasebeta

← A42×C3⋊D3 #72220502

Subgroups — A42×C3⋊D3 #72220502

Order 2592.

1132 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 1132 conjugacy classes of subgroups — too many to draw. Only its 77 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
1C32×A42C211yesmaximal, characteristic, complemented
2C3⋊D3×C22⋊A4C312yesmaximal, complemented
3C22×A4×C3⋊D3C312yesmaximal, complemented
4D3×A42—34nomaximal
5C3×A4×C3⋊D3—42nomaximal
6C32×C22⋊A4C2×C312yescomplemented
7C22×C32×A4C2×C312yescomplemented
8C2×A4×C3⋊D3—32no—
9C2×A4×C3⋊D3—32no—
10C3×A42—28no—
11C3×A42—28no—
12C3×A42D314yescomplemented
13C33×A4—42no—
14C24×C3⋊D3C3211yescharacteristic, complemented
15D3×C22⋊A4—38no—
16C22×D3×A4—38no—
17C2×A42—91no—
18C22×C3×C3⋊D3—42no—
19C2×C32×A4—32no—
20A4×C3⋊D3—32no—
21A4×C3⋊D3—44no—
22A4×C3⋊D3—122no—
23A4×C3⋊D3A412yesdirect product factor
24C3×D3×A4—128no—
25C32×C3⋊D3—161no—
26C24×C32C2×C3211yescharacteristic, complemented
27C23×C3⋊D3—32no—
28C23×C3⋊D3—32no—
29C23×C3⋊D3—91no—
30C23×C3⋊D3—91no—
31C3×C22⋊A4—28no—
32C3×C22⋊A4C3×D318yescomplemented
33C22×C3×A4—28no—
34C22×C3×A4C3×D318yescomplemented
35C2×D3×A4—98no—
36C2×D3×A4—98no—
37A42—224no—
38A42—28no—
39A42—28no—
40A42C3⋊D311yescharacteristic, direct product factor
41C22×C33—42no—
42C2×C3×C3⋊D3—122no—
43C2×C3×C3⋊D3—122no—
44C32×A4—44no—
45C32×A4—48no—
46C32×A4—816no—
47C32×A4—88no—
48C32×A4—88no—
49C32×A4—122no—
50C32×A4C2×A412yescomplemented
51C24×D3—34no—
52C2×C22⋊A4—92no—
53C23×A4—92no—
54C34—161noSylow
55C23×C32—32no—
56C23×C32—91no—
57C22×C3⋊D3—32no—
58C22×C3⋊D3—32no—
59C22×C3⋊D3—91no—
60C22×C3⋊D3—92no—
61C22×C3⋊D3—92no—
62C22×C3⋊D3—92no—
63C22×C3⋊D3—92no—
64C22×C3⋊D3—94no—
65C22×C3⋊D3—91no—
66C22×C3⋊D3C3×A412yescomplemented
67C22×C3×D3—128no—
68C2×C3×A4—38no—
69C2×C3×A4—68no—
70C2×C3×A4—362no—
71D3×A4—38no—
72D3×A4—98no—
73D3×A4—1216no—
74D3×A4—368no—
75C2×C33—122no—
76C3×C3⋊D3—42no—
77C3×C3⋊D3—122no—
78C3×C3⋊D3—162no—
79C32×D3—484no—
80C24×C3C32×D314yescomplemented
81C23×D3—98no—
82C23×D3—98no—
83C23×D3—274no—
84C23×D3—274no—
85C22⋊A4—28no—
86C22⋊A4C3×C3⋊D312yescomplemented
87C22×A4—28no—
88C22×A4—272no—
89C22×A4—272no—
90C22×A4C3×C3⋊D312yescomplemented
91C22×C32—32no—
92C22×C32—48no—
93C22×C32—88no—
94C22×C32—91no—
95C22×C32—92no—
96C22×C32C2×C3×A412yescomplemented
97C2×C3⋊D3—32no—
98C2×C3⋊D3—32no—
99C2×C3⋊D3—91no—
100C2×C3⋊D3—92no—
101C2×C3⋊D3—94no—
102C2×C3⋊D3—91no—
103C2×C3⋊D3—92no—
104C2×C3⋊D3—92no—
105C2×C3×D3—368no—
106C2×C3×D3—368no—
107C3×A4—28no—
108C3×A4—42no—
109C3×A4—416no—
110C3×A4—816no—
111C3×A4—88no—
112C3×A4—848no—
113C3×A4—816no—
114C3×A4—88no—
115C3×A4—128no—
116C3×A4—248no—
117C3×A4D3×A418yescomplemented
118C25—91noSylow
119C33—42no—
120C33—164no—
121C33—162no—
122C33—328no—
123C33—328no—
124C23×C3—38no—
125C23×C3—94no—
126C23×C3—362no—
127C22×D3—38no—
128C22×D3—98no—
129C22×D3—98no—
130C22×D3—274no—
131C22×D3—278no—
132C22×D3—278no—
133C22×D3—278no—
134C22×D3—278no—
135C22×D3—2716no—
136C22×D3—274no—
137C2×A4—32no—
138C2×A4—68no—
139C2×A4—92no—
140C2×A4—272no—
141C2×A4—364no—
142C2×A4—1082no—
143C2×C32—32no—
144C2×C32—91no—
145C2×C32—128no—
146C2×C32—248no—
147C2×C32—1441no—
148C3⋊D3—32no—
149C3⋊D3—91no—
150C3⋊D3A4211yescharacteristic, direct product factor
151C3×D3—128no—
152C3×D3—368no—
153C3×D3—488no—
154C24—272no—
155C24—272no—
156C24—811no—
157C24—811no—
158C24C32×C3⋊D311yescharacteristic, complemented
159C22×C3—38no—
160C22×C3—42no—
161C22×C3—88no—
162C22×C3—94no—
163C22×C3—98no—
164C22×C3—1082no—
165C22×C3—1082no—
166C22×C3C3×D3×A418yescomplemented
167C2×D3—98no—
168C2×D3—98no—
169C2×D3—274no—
170C2×D3—274no—
171C2×D3—278no—
172C2×D3—2716no—
173C2×D3—278no—
174C2×D3—278no—
175A4—28no—
176A4—44no—
177A4—816no—
178A4—122no—
179A4—248no—
180A4A4×C3⋊D312yesdirect product factor
181C32—48no—
182C32—88no—
183C32—161no—
184C32—168no—
185C32—328no—
186C32—328no—
187C32—3224no—
188C32—328no—
189C32C2×A4211yescharacteristic, complemented
190C23—32no—
191C23—91no—
192C23—92no—
193C23—272no—
194C23—272no—
195C23—812no—
196C23—811no—
197C23—812no—
198C23—812no—
199C23—812no—
200C23—811no—
201C23—814no—
202C2×C3—38no—
203C2×C3—94no—
204C2×C3—122no—
205C2×C3—248no—
206C2×C3—362no—
207C2×C3—1082no—
208C2×C3—1442no—
209D3—34no—
210D3—98no—
211D3—274no—
212C22—32no—
213C22—91no—
214C22—92no—
215C22—272no—
216C22—272no—
217C22—812no—
218C22—812no—
219C22—811no—
220C22—811no—
221C22—814no—
222C22—812no—
223C22C3×A4×C3⋊D312yescomplemented
224C3—42no—
225C3—88no—
226C3—162no—
227C3—328no—
228C3D3×A4214yescomplemented
229C2—32no—
230C2—91no—
231C2—91no—
232C2—272no—
233C2—811no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC24×C32C2×C32
LCSG ▷ C24×C32
UCSC1

Complements

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

NH ≅ G/Ntype
1. C32×A42C2semidirect
2. C3⋊D3×C22⋊A4C3semidirect
3. C22×A4×C3⋊D3C3semidirect
6. C32×C22⋊A4C2×C3semidirect
7. C22×C32×A4C2×C3semidirect
12. C3×A42D3semidirect
14. C24×C3⋊D3C32semidirect
23. A4×C3⋊D3A4direct (N × H)
26. C24×C32C2×C32semidirect
32. C3×C22⋊A4C3×D3semidirect
34. C22×C3×A4C3×D3semidirect
40. A42C3⋊D3direct (N × H)
50. C32×A4C2×A4semidirect
66. C22×C3⋊D3C3×A4semidirect
80. C24×C3C32×D3semidirect
86. C22⋊A4C3×C3⋊D3semidirect
90. C22×A4C3×C3⋊D3semidirect
96. C22×C32C2×C3×A4semidirect
117. C3×A4D3×A4semidirect
150. C3⋊D3A42direct (N × H)
158. C24C32×C3⋊D3semidirect
166. C22×C3C3×D3×A4semidirect
180. A4A4×C3⋊D3direct (N × H)
189. C32C2×A42semidirect
223. C22C3×A4×C3⋊D3semidirect
228. C3D3×A42semidirect

Maximal subgroups

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

subgroupindex
C32×A422
C3⋊D3×C22⋊A43
C22×A4×C3⋊D33
D3×A423
C3×A4×C3⋊D34