Finite Group Databasebeta

← C2×D3×C9×A4 #13049292

Subgroups — C2×D3×C9×A4 #13049292

Order 1296.

382 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 91 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×C3×C9×A4C211yesmaximal, characteristic, complemented
2D3×C9×A4C212yesmaximal, direct product factor
3C2×C3×D3×A4C311yesmaximal, characteristic
4C23×D3×C9C311yesmaximal, characteristic, complemented
5C22×C9×A4—31nomaximal
6C2×D3×C22⋊C9C312yesmaximal, complemented
7C2×C3×D3×C9—41nomaximal
8C3×C9×A4C2211yescharacteristic, complemented
9C2×C32×A4C2×C311yescharacteristic
10C3×D3×A4C2×C312yes—
11C23×C3×C9C2×C311yescharacteristic, complemented
12C22×D3×C9—31no—
13C22×D3×C9—31no—
14C22×D3×C9—32no—
15C22×D3×C9C2×C312yescomplemented
16C2×C3×C22⋊C9C2×C312yescomplemented
17C2×C9×A4—21no—
18C2×C9×A4—21no—
19C2×C9×A4—22no—
20C2×C9×A4—32no—
21C2×C9×A4D311yescharacteristic, direct product factor
22D3×C22⋊C9C2×C314yescomplemented
23C2×C32×C9—41no—
24C3×D3×C9—42no—
25C23×C3×D3C3211yescharacteristic
26C22×C3×A4—31no—
27C2×D3×A4C913yesdirect product factor
28C24×C9—31no—
29C22×C22⋊C9—32no—
30C2×C32×D3—41no—
31C32×A4C22×C311yescharacteristic
32C22×C3×C9—31no—
33C22×C3×C9—31no—
34C22×C3×C9—121no—
35C22×C3×C9C22×C311yescharacteristic, complemented
36C2×D3×C9—32no—
37C2×D3×C9—31no—
38C2×D3×C9—32no—
39C2×D3×C9—32no—
40C2×D3×C9—32no—
41C2×D3×C9—42no—
42C2×D3×C9A411yescharacteristic, direct product factor
43C3×C22⋊C9C22×C312yescomplemented
44C9×A4—21no—
45C9×A4—21no—
46C9×A4—22no—
47C9×A4C2×D311yescharacteristic, direct product factor
48C32×C9—41noSylow
49C23×C32C2×C3211yescharacteristic
50C22×C3×D3—31no—
51C22×C3×D3—31no—
52C22×C3×D3—32no—
53C22×C3×D3C2×C3212yes—
54C2×C3×A4—21no—
55C2×C3×A4—23no—
56C2×C3×A4—32no—
57C2×C3×A4C2×C913yescomplemented
58C2×C3×A4C3×D311yescharacteristic
59D3×A4C2×C916yesdirect product factor
60C23×C9—21no—
61C23×C9—32no—
62C23×C9—91no—
63C23×C9—92no—
64C23×C9—91no—
65C23×C9C3×D311yescharacteristic, complemented
66C2×C22⋊C9—22no—
67C2×C22⋊C9—34no—
68C2×C22⋊C9C3×D312yescomplemented
69C2×C33—41no—
70C32×D3—42no—
71C2×C3×C9—31no—
72C2×C3×C9—31no—
73C2×C3×C9—41no—
74C2×C3×C9—42no—
75C2×C3×C9—82no—
76C2×C3×C9—81no—
77C2×C3×C9—81no—
78C2×C3×C9—122no—
79C2×C3×C9C2×A411yescharacteristic, complemented
80D3×C9—32no—
81D3×C9—44no—
82D3×C9C2×A412yesdirect product factor
83C24×C3—31no—
84C23×D3C3×C911yescharacteristic, complemented
85C22×A4—33no—
86C22×C32—31no—
87C22×C32—31no—
88C22×C32—121no—
89C22×C32C22×C3211yescharacteristic
90C2×C3×D3—32no—
91C2×C3×D3—31no—
92C2×C3×D3—32no—
93C2×C3×D3—32no—
94C2×C3×D3—32no—
95C2×C3×D3—43no—
96C2×C3×D3C3×A411yescharacteristic
97C3×A4—21no—
98C3×A4—23no—
99C3×A4C22×C913yescomplemented
100C3×A4C2×C3×D311yescharacteristic
101C22×C9—21no—
102C22×C9—31no—
103C22×C9—31no—
104C22×C9—31no—
105C22×C9—61no—
106C22×C9—61no—
107C22×C9—92no—
108C22×C9—92no—
109C22×C9—92no—
110C22×C9—92no—
111C22×C9—91no—
112C22×C9—122no—
113C22×C9C2×C3×D311yescharacteristic, complemented
114C22⋊C9—22no—
115C22⋊C9C2×C3×D312yescomplemented
116C33—41no—
117C3×C9—41no—
118C3×C9—42no—
119C3×C9—82no—
120C3×C9—81no—
121C3×C9—81no—
122C3×C9C22×A411yescharacteristic, complemented
123C23×C3—21no—
124C23×C3—32no—
125C23×C3—91no—
126C23×C3—92no—
127C23×C3—91no—
128C23×C3C2×C3×C911yescharacteristic, complemented
129C23×C3C32×D311yescharacteristic
130C22×D3—31no—
131C22×D3—31no—
132C22×D3—32no—
133C22×D3C2×C3×C912yescomplemented
134C2×A4—23no—
135C2×A4—36no—
136C2×A4D3×C913yesdirect product factor
137C2×C32—31no—
138C2×C32—31no—
139C2×C32—41no—
140C2×C32—43no—
141C2×C32—83no—
142C2×C32—81no—
143C2×C32—122no—
144C2×C32C2×C3×A411yescharacteristic
145C3×D3—32no—
146C3×D3—46no—
147C3×D3C2×C3×A412yes—
148C2×C9—21no—
149C2×C9—32no—
150C2×C9—31no—
151C2×C9—31no—
152C2×C9—42no—
153C2×C9—61no—
154C2×C9—61no—
155C2×C9—82no—
156C2×C9—92no—
157C2×C9—124no—
158C2×C9D3×A411yescharacteristic, direct product factor
159C24—31noSylow
160C22×C3—21no—
161C22×C3—31no—
162C22×C3—31no—
163C22×C3—31no—
164C22×C3—31no—
165C22×C3—31no—
166C22×C3—61no—
167C22×C3—61no—
168C22×C3—92no—
169C22×C3—92no—
170C22×C3—92no—
171C22×C3—92no—
172C22×C3—91no—
173C22×C3—123no—
174C22×C3C22×C3×C911yescharacteristic, complemented
175C22×C3C2×C32×D311yescharacteristic
176C2×D3—32no—
177C2×D3—31no—
178C2×D3—32no—
179C2×D3—32no—
180C2×D3—32no—
181C2×D3C9×A411yescharacteristic, direct product factor
182A4—23no—
183A4C2×D3×C913yesdirect product factor
184C32—41no—
185C32—43no—
186C32—83no—
187C32—81no—
188C32C22×C3×A411yescharacteristic
189C9—21no—
190C9—42no—
191C9—82no—
192C9C2×D3×A411yescharacteristic, direct product factor
193C23—32no—
194C23—91no—
195C23—92no—
196C23—91no—
197C23C3×D3×C911yescharacteristic, complemented
198C2×C3—21no—
199C2×C3—31no—
200C2×C3—31no—
201C2×C3—32no—
202C2×C3—31no—
203C2×C3—31no—
204C2×C3—43no—
205C2×C3—61no—
206C2×C3—61no—
207C2×C3—83no—
208C2×C3—92no—
209C2×C3—126no—
210C2×C3C2×C9×A411yescharacteristic, complemented
211C2×C3C3×D3×A411yescharacteristic
212D3—32no—
213D3C2×C9×A412yesdirect product factor
214C22—31no—
215C22—31no—
216C22—31no—
217C22—92no—
218C22—92no—
219C22—92no—
220C22—92no—
221C22—91no—
222C22C2×C3×D3×C911yescharacteristic, complemented
223C3—21no—
224C3—43no—
225C3—83no—
226C3C22×C9×A411yescharacteristic, complemented
227C3C2×C3×D3×A411yescharacteristic
228C2—31no—
229C2—31no—
230C2—32no—
231C2—92no—
232C2D3×C9×A411yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C9D3×A4
commutator, hypocenterC22×C3C22×C3×C9
FrattiniC3C2×C3×D3×A4
FittingC23×C3×C9C2×C3
socleC23×C32C2×C32
prime radicalC2×C3×D3×A4C3
cosocleC22×C32C22×C32
LCSG ▷ C22×C3
UCSC1 ◁ C2×C9

Complements

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

NH ≅ G/Ntype
1. C2×C3×C9×A4C2semidirect
2. D3×C9×A4C2direct (N × H)
4. C23×D3×C9C3semidirect
6. C2×D3×C22⋊C9C3semidirect
8. C3×C9×A4C22semidirect
11. C23×C3×C9C2×C3semidirect
15. C22×D3×C9C2×C3semidirect
16. C2×C3×C22⋊C9C2×C3semidirect
21. C2×C9×A4D3direct (N × H)
22. D3×C22⋊C9C2×C3semidirect
27. C2×D3×A4C9direct (N × H)
35. C22×C3×C9C22×C3semidirect
42. C2×D3×C9A4direct (N × H)
43. C3×C22⋊C9C22×C3semidirect
47. C9×A4C2×D3direct (N × H)
57. C2×C3×A4C2×C9semidirect
59. D3×A4C2×C9direct (N × H)
65. C23×C9C3×D3semidirect
68. C2×C22⋊C9C3×D3semidirect
79. C2×C3×C9C2×A4semidirect
82. D3×C9C2×A4direct (N × H)
84. C23×D3C3×C9semidirect
99. C3×A4C22×C9semidirect
113. C22×C9C2×C3×D3semidirect
115. C22⋊C9C2×C3×D3semidirect
122. C3×C9C22×A4semidirect
128. C23×C3C2×C3×C9semidirect
133. C22×D3C2×C3×C9semidirect
136. C2×A4D3×C9direct (N × H)
158. C2×C9D3×A4direct (N × H)
174. C22×C3C22×C3×C9semidirect
181. C2×D3C9×A4direct (N × H)
183. A4C2×D3×C9direct (N × H)
192. C9C2×D3×A4direct (N × H)
197. C23C3×D3×C9semidirect
210. C2×C3C2×C9×A4semidirect
213. D3C2×C9×A4direct (N × H)
222. C22C2×C3×D3×C9semidirect
226. C3C22×C9×A4semidirect
232. C2D3×C9×A4direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C9×A42
D3×C9×A42
C2×C3×D3×A43
C23×D3×C93
C22×C9×A43
C2×D3×C22⋊C93
C2×C3×D3×C94