Finite Group Databasebeta

← C2×C3×A4×C3⋊D3 #13049873

Subgroups — C2×C3×A4×C3⋊D3 #13049873

Order 1296.

972 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 972 conjugacy classes of subgroups — too many to draw. Only its 120 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
1C2×C33×A4C211yesmaximal, characteristic, complemented
2C3×A4×C3⋊D3C212yesmaximal, direct product factor
3C23×C3×C3⋊D3C311yesmaximal, characteristic, complemented
4C2×A4×C3⋊D3C313yesmaximal, direct product factor
5C2×C3×D3×A4—34nomaximal
6C2×C32×C3⋊D3—41nomaximal
7C33×A4C2211yescharacteristic, complemented
8C23×C33C2×C311yescharacteristic, complemented
9C22×C3×C3⋊D3—31no—
10C22×C3×C3⋊D3—31no—
11C22×C3×C3⋊D3—32no—
12C22×C3×C3⋊D3C2×C312yescomplemented
13C2×C32×A4—24no—
14C2×C32×A4—212no—
15C2×C32×A4D314yescomplemented
16C2×C32×A4C2×C313yescomplemented
17A4×C3⋊D3C2×C316yesdirect product factor
18C3×D3×A4—38no—
19C2×C34—41no—
20C32×C3⋊D3—42no—
21C23×C3⋊D3C3211yescharacteristic, complemented
22C23×C3×D3—34no—
23C22×C3×A4—91no—
24C2×D3×A4—312no—
25C22×C33—31no—
26C22×C33—31no—
27C22×C33C22×C311yescharacteristic, complemented
28C2×C3×C3⋊D3—32no—
29C2×C3×C3⋊D3—31no—
30C2×C3×C3⋊D3—32no—
31C2×C3×C3⋊D3—32no—
32C2×C3×C3⋊D3—32no—
33C2×C3×C3⋊D3—43no—
34C2×C3×C3⋊D3A411yescharacteristic, direct product factor
35C2×C32×D3—124no—
36C32×A4—24no—
37C32×A4—212no—
38C32×A4C2×D314yescomplemented
39C32×A4C22×C313yescomplemented
40C34—41noSylow
41C23×C32—24no—
42C23×C32C3×D314yescomplemented
43C23×C32C2×C3211yescharacteristic, complemented
44C22×C3⋊D3—31no—
45C22×C3⋊D3—31no—
46C22×C3⋊D3—32no—
47C22×C3⋊D3C2×C3212yescomplemented
48C22×C3×D3—38no—
49C22×C3×D3—94no—
50C22×C3×D3—98no—
51C22×C3×D3—94no—
52C2×C3×A4—224no—
53C2×C3×A4—212no—
54C2×C3×A4—24no—
55C2×C3×A4—212no—
56C2×C3×A4—92no—
57C2×C3×A4C3×D3112yescomplemented
58C2×C3×A4C3⋊D311yescharacteristic, direct product factor
59D3×A4—324no—
60C2×C33—31no—
61C2×C33—31no—
62C2×C33—44no—
63C2×C33—43no—
64C2×C33—812no—
65C2×C33—84no—
66C2×C33C2×A411yescharacteristic, complemented
67C3×C3⋊D3—32no—
68C3×C3⋊D3—46no—
69C3×C3⋊D3C2×A412yesdirect product factor
70C32×D3—128no—
71C24×C3—91no—
72C23×D3—34no—
73C22×A4—93no—
74C22×C32—24no—
75C22×C32—31no—
76C22×C32—31no—
77C22×C32—34no—
78C22×C32—34no—
79C22×C32—64no—
80C22×C32—64no—
81C22×C32—361no—
82C22×C32C2×C3×D314yescomplemented
83C22×C32C22×C3211yescharacteristic, complemented
84C2×C3⋊D3—32no—
85C2×C3⋊D3—31no—
86C2×C3⋊D3—32no—
87C2×C3⋊D3—32no—
88C2×C3⋊D3—32no—
89C2×C3⋊D3C3×A411yescharacteristic, direct product factor
90C2×C3×D3—34no—
91C2×C3×D3—98no—
92C2×C3×D3—98no—
93C2×C3×D3—98no—
94C2×C3×D3—94no—
95C2×C3×D3—98no—
96C2×C3×D3—1212no—
97C3×A4—224no—
98C3×A4—212no—
99C3×A4—24no—
100C3×A4—212no—
101C3×A4C2×C3×D3112yescomplemented
102C3×A4C2×C3⋊D311yescharacteristic, direct product factor
103C33—44no—
104C33—43no—
105C33—812no—
106C33—84no—
107C33C22×A411yescharacteristic, complemented
108C23×C3—24no—
109C23×C3—92no—
110C23×C3—271no—
111C23×C3—272no—
112C23×C3—271no—
113C23×C3C32×D314yescomplemented
114C23×C3C3×C3⋊D311yescharacteristic, complemented
115C22×D3—38no—
116C22×D3—94no—
117C22×D3—98no—
118C22×D3—94no—
119C2×A4—212no—
120C2×A4—96no—
121C2×A4C3×C3⋊D313yesdirect product factor
122C2×C32—24no—
123C2×C32—31no—
124C2×C32—31no—
125C2×C32—34no—
126C2×C32—34no—
127C2×C32—41no—
128C2×C32—412no—
129C2×C32—64no—
130C2×C32—64no—
131C2×C32—812no—
132C2×C32—824no—
133C2×C32—812no—
134C2×C32—84no—
135C2×C32—362no—
136C2×C32D3×A414yescomplemented
137C2×C32C2×C3×A411yescharacteristic, complemented
138C3⋊D3—32no—
139C3⋊D3C2×C3×A412yesdirect product factor
140C3×D3—38no—
141C3×D3—98no—
142C3×D3—1224no—
143C24—91noSylow
144C22×C3—24no—
145C22×C3—34no—
146C22×C3—31no—
147C22×C3—34no—
148C22×C3—31no—
149C22×C3—64no—
150C22×C3—64no—
151C22×C3—91no—
152C22×C3—272no—
153C22×C3—272no—
154C22×C3—272no—
155C22×C3—272no—
156C22×C3—271no—
157C22×C3—363no—
158C22×C3C2×C32×D314yescomplemented
159C22×C3C2×C3×C3⋊D311yescharacteristic, complemented
160C2×D3—34no—
161C2×D3—98no—
162C2×D3—98no—
163C2×D3—98no—
164C2×D3—94no—
165C2×D3—98no—
166A4—212no—
167A4C2×C3×C3⋊D313yesdirect product factor
168C32—24no—
169C32—41no—
170C32—412no—
171C32—812no—
172C32—824no—
173C32—812no—
174C32—84no—
175C32C2×D3×A414yescomplemented
176C32C22×C3×A411yescharacteristic, complemented
177C23—92no—
178C23—271no—
179C23—272no—
180C23—271no—
181C23C32×C3⋊D311yescharacteristic, complemented
182C2×C3—24no—
183C2×C3—34no—
184C2×C3—34no—
185C2×C3—31no—
186C2×C3—31no—
187C2×C3—43no—
188C2×C3—64no—
189C2×C3—64no—
190C2×C3—812no—
191C2×C3—92no—
192C2×C3—272no—
193C2×C3—366no—
194C2×C3C3×D3×A414yescomplemented
195C2×C3A4×C3⋊D311yescharacteristic, direct product factor
196D3—38no—
197D3—98no—
198C22—31no—
199C22—31no—
200C22—91no—
201C22—272no—
202C22—272no—
203C22—272no—
204C22—272no—
205C22—271no—
206C22C2×C32×C3⋊D311yescharacteristic, complemented
207C3—24no—
208C3—43no—
209C3—812no—
210C3C2×C3×D3×A414yescomplemented
211C3C2×A4×C3⋊D311yescharacteristic, direct product factor
212C2—31no—
213C2—31no—
214C2—92no—
215C2—272no—
216C2C3×A4×C3⋊D311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3A4×C3⋊D3
commutator, cosocle, hypocenterC22×C32C22×C32
FrattiniC1G
Fitting, socleC23×C33C2×C3
LCSG ▷ C22×C32
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C2×C33×A4C2semidirect
2. C3×A4×C3⋊D3C2direct (N × H)
3. C23×C3×C3⋊D3C3semidirect
4. C2×A4×C3⋊D3C3direct (N × H)
7. C33×A4C22semidirect
8. C23×C33C2×C3semidirect
12. C22×C3×C3⋊D3C2×C3semidirect
15. C2×C32×A4D3semidirect
16. C2×C32×A4C2×C3semidirect
17. A4×C3⋊D3C2×C3direct (N × H)
21. C23×C3⋊D3C32semidirect
27. C22×C33C22×C3semidirect
34. C2×C3×C3⋊D3A4direct (N × H)
38. C32×A4C2×D3semidirect
39. C32×A4C22×C3semidirect
42. C23×C32C3×D3semidirect
43. C23×C32C2×C32semidirect
47. C22×C3⋊D3C2×C32semidirect
57. C2×C3×A4C3×D3semidirect
58. C2×C3×A4C3⋊D3direct (N × H)
66. C2×C33C2×A4semidirect
69. C3×C3⋊D3C2×A4direct (N × H)
82. C22×C32C2×C3×D3semidirect
83. C22×C32C22×C32semidirect
89. C2×C3⋊D3C3×A4direct (N × H)
101. C3×A4C2×C3×D3semidirect
102. C3×A4C2×C3⋊D3direct (N × H)
107. C33C22×A4semidirect
113. C23×C3C32×D3semidirect
114. C23×C3C3×C3⋊D3semidirect
121. C2×A4C3×C3⋊D3direct (N × H)
136. C2×C32D3×A4semidirect
137. C2×C32C2×C3×A4semidirect
139. C3⋊D3C2×C3×A4direct (N × H)
158. C22×C3C2×C32×D3semidirect
159. C22×C3C2×C3×C3⋊D3semidirect
167. A4C2×C3×C3⋊D3direct (N × H)
175. C32C2×D3×A4semidirect
176. C32C22×C3×A4semidirect
181. C23C32×C3⋊D3semidirect
194. C2×C3C3×D3×A4semidirect
195. C2×C3A4×C3⋊D3direct (N × H)
206. C22C2×C32×C3⋊D3semidirect
210. C3C2×C3×D3×A4semidirect
211. C3C2×A4×C3⋊D3direct (N × H)
216. C2C3×A4×C3⋊D3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C33×A42
C3×A4×C3⋊D32
C23×C3×C3⋊D33
C2×A4×C3⋊D33
C2×C3×D3×A43
C2×C32×C3⋊D34