Finite Group Databasebeta

← C22×C3×D3×D9 #13049312

Subgroups — C22×C3×D3×D9 #13049312

Order 1296.

1000 conjugacy classes of subgroups; only the 250 normal subgroups are shown.

normal subgroups only

This group has 1000 conjugacy classes of subgroups — too many to draw. Only its 250 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
1C22×C3×C3⋊D9C211yesmaximal, characteristic, complemented
2C22×C3×D3×C9C211yesmaximal, characteristic, complemented
3C22×C32×D9C211yesmaximal, characteristic, complemented
4C2×C3×D3×D9C2112yesmaximal, direct product factor
5C22×C3×D32—31nomaximal
6C23×C3×D9—31nomaximal
7C22×D3×D9C311yesmaximal, characteristic, direct product factor
8C22×C32×C9C2211yescharacteristic, complemented
9C2×C3×C3⋊D9C2216yescomplemented
10C2×C3×D3×C9C2216yescomplemented
11C2×C32×D9C2216yescomplemented
12C3×D3×D9C22116yesdirect product factor
13C22×C3×C3⋊D3—31no—
14C22×C32×D3—31no—
15C22×C32×D3D311yescharacteristic
16C2×C3×D32—312no—
17C23×C3×C9—31no—
18C22×C3⋊D9C2×C311yescharacteristic, complemented
19C22×D3×C9—21no—
20C22×D3×C9C2×C311yescharacteristic, complemented
21C22×C3×D9—21no—
22C22×C3×D9—31no—
23C22×C3×D9—312no—
24C22×C3×D9—61no—
25C22×C3×D9D311yescharacteristic, direct product factor
26C22×C3×D9C2×C311yescharacteristic, complemented
27C2×D3×D9C2×C3112yesdirect product factor
28C2×C32×C9C2313yescomplemented
29C3×C3⋊D9C2314yescomplemented
30C3×D3×C9C2314yescomplemented
31C32×D9C2314yescomplemented
32C23×C3×D3—91no—
33C23×C3×D3—91no—
34C22×D32—31no—
35C23×D9—31no—
36C22×C33C2×D311yescharacteristic
37C2×C3×C3⋊D3—36no—
38C2×C32×D3—36no—
39C2×C32×D3C2×D316yes—
40C3×D32—316no—
41C22×C3×C9—21no—
42C22×C3×C9—21no—
43C22×C3×C9—21no—
44C22×C3×C9—36no—
45C22×C3×C9—41no—
46C22×C3×C9C2×D311yescharacteristic, complemented
47C22×C3×C9C22×C311yescharacteristic, complemented
48C2×C3⋊D9C22×C316yescomplemented
49C2×D3×C9—26no—
50C2×D3×C9C22×C316yescomplemented
51C2×C3×D9—26no—
52C2×C3×D9—36no—
53C2×C3×D9—316no—
54C2×C3×D9—66no—
55C2×C3×D9C2×D316yesdirect product factor
56C2×C3×D9C22×C316yescomplemented
57D3×D9C22×C3116yesdirect product factor
58C32×C9C2411yescharacteristic, complemented, Sylow
59C23×C32—31no—
60C23×C32—91no—
61C22×C3⋊D3—31no—
62C22×C3×D3—21no—
63C22×C3×D3—31no—
64C22×C3×D3—31no—
65C22×C3×D3—61no—
66C22×C3×D3—912no—
67C22×C3×D3—91no—
68C22×C3×D3—91no—
69C22×C3×D3—912no—
70C22×C3×D3—181no—
71C22×C3×D3D911yescharacteristic, direct product factor
72C22×C3×D3C3×D311yescharacteristic
73C2×D32—312no—
74C23×C9—31no—
75C23×C9—61no—
76C22×D9—31no—
77C22×D9—312no—
78C22×D9—61no—
79C22×D9C3×D311yescharacteristic, direct product factor
80C2×C33C22×D313yes—
81C3×C3⋊D3—34no—
82C32×D3—34no—
83C32×D3C22×D314yes—
84C2×C3×C9—23no—
85C2×C3×C9—23no—
86C2×C3×C9—23no—
87C2×C3×C9—34no—
88C2×C3×C9—43no—
89C2×C3×C9C22×D313yescomplemented
90C2×C3×C9C23×C313yescomplemented
91C3⋊D9C23×C314yescomplemented
92D3×C9—24no—
93D3×C9C23×C314yescomplemented
94C3×D9—24no—
95C3×D9—34no—
96C3×D9—64no—
97C3×D9C22×D314yesdirect product factor
98C3×D9C23×C314yescomplemented
99C24×C3—271no—
100C23×D3—91no—
101C23×D3—91no—
102C22×C32—21no—
103C22×C32—21no—
104C22×C32—21no—
105C22×C32—36no—
106C22×C32—41no—
107C22×C32—96no—
108C22×C32C2×D911yescharacteristic, complemented
109C22×C32D3211yescharacteristic
110C22×C32C2×C3×D311yescharacteristic
111C2×C3⋊D3—36no—
112C2×C3×D3—26no—
113C2×C3×D3—36no—
114C2×C3×D3—36no—
115C2×C3×D3—66no—
116C2×C3×D3—916no—
117C2×C3×D3—96no—
118C2×C3×D3—96no—
119C2×C3×D3—916no—
120C2×C3×D3—186no—
121C2×C3×D3C2×D916yesdirect product factor
122C2×C3×D3C2×C3×D316yes—
123D32—316no—
124C22×C9—21no—
125C22×C9—21no—
126C22×C9—36no—
127C22×C9—41no—
128C22×C9—66no—
129C22×C9C2×C3×D311yescharacteristic, complemented
130C2×D9—36no—
131C2×D9—316no—
132C2×D9—66no—
133C2×D9C2×C3×D316yesdirect product factor
134C33C23×D311yescharacteristic
135C3×C9—21no—
136C3×C9—21no—
137C3×C9—21no—
138C3×C9—41no—
139C3×C9C23×D311yescharacteristic, complemented
140C3×C9C24×C311yescharacteristic, complemented
141C23×C3—31no—
142C23×C3—31no—
143C23×C3—61no—
144C23×C3—91no—
145C23×C3—91no—
146C23×C3—181no—
147C23×C3—2712no—
148C23×C3—271no—
149C22×D3—31no—
150C22×D3—912no—
151C22×D3—91no—
152C22×D3—91no—
153C22×D3—912no—
154C22×D3—181no—
155C22×D3C3×D911yescharacteristic, direct product factor
156C2×C32—23no—
157C2×C32—23no—
158C2×C32—23no—
159C2×C32—34no—
160C2×C32—43no—
161C2×C32—94no—
162C2×C32C22×D913yescomplemented
163C2×C32C2×D3213yes—
164C2×C32C22×C3×D313yes—
165C3⋊D3—34no—
166C3×D3—24no—
167C3×D3—34no—
168C3×D3—34no—
169C3×D3—64no—
170C3×D3—94no—
171C3×D3—94no—
172C3×D3—184no—
173C3×D3C22×D914yesdirect product factor
174C3×D3C22×C3×D314yes—
175C2×C9—23no—
176C2×C9—23no—
177C2×C9—34no—
178C2×C9—43no—
179C2×C9—64no—
180C2×C9C22×C3×D313yescomplemented
181D9—34no—
182D9—64no—
183D9C22×C3×D314yesdirect product factor
184C24—271noSylow
185C22×C3—21no—
186C22×C3—21no—
187C22×C3—21no—
188C22×C3—36no—
189C22×C3—36no—
190C22×C3—41no—
191C22×C3—66no—
192C22×C3—96no—
193C22×C3—96no—
194C22×C3—186no—
195C22×C3—2716no—
196C22×C3—276no—
197C22×C3D3×D911yescharacteristic, direct product factor
198C22×C3C2×C3×D911yescharacteristic, complemented
199C22×C3C3×D3211yescharacteristic
200C2×D3—36no—
201C2×D3—916no—
202C2×D3—96no—
203C2×D3—96no—
204C2×D3—916no—
205C2×D3—186no—
206C2×D3C2×C3×D916yesdirect product factor
207C32—21no—
208C32—21no—
209C32—21no—
210C32—41no—
211C32C23×D911yescharacteristic, complemented
212C32C22×D3211yescharacteristic
213C32C23×C3×D311yescharacteristic
214C9—21no—
215C9—21no—
216C9—41no—
217C9C23×C3×D311yescharacteristic, complemented
218C23—31no—
219C23—91no—
220C23—2712no—
221C23—271no—
222C2×C3—23no—
223C2×C3—23no—
224C2×C3—23no—
225C2×C3—34no—
226C2×C3—34no—
227C2×C3—43no—
228C2×C3—64no—
229C2×C3—94no—
230C2×C3—94no—
231C2×C3—184no—
232C2×C3—274no—
233C2×C3C2×D3×D913yesdirect product factor
234C2×C3C22×C3×D913yescomplemented
235C2×C3C2×C3×D3213yes—
236D3—34no—
237D3—94no—
238D3—94no—
239D3—184no—
240D3C22×C3×D914yesdirect product factor
241C22—36no—
242C22—96no—
243C22—2716no—
244C22—276no—
245C22C3×D3×D911yescharacteristic, direct product factor
246C3—21no—
247C3—21no—
248C3—21no—
249C3—41no—
250C3C22×D3×D911yescharacteristic, direct product factor
251C3C23×C3×D911yescharacteristic, complemented
252C3C22×C3×D3211yescharacteristic
253C2—34no—
254C2—94no—
255C2—274no—
256C2C2×C3×D3×D913yesdirect product factor
subgroupG/H
center, hypercenterC22×C3D3×D9
commutator, cosocle, hypocenterC3×C9C24×C3
FrattiniC3C22×C3×D32
FittingC22×C32×C9C22
socleC22×C33C2×D3
LCSG ▷ C3×C9
UCSC1 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C22×C3×C3⋊D9C2semidirect
2. C22×C3×D3×C9C2semidirect
3. C22×C32×D9C2semidirect
4. C2×C3×D3×D9C2direct (N × H)
7. C22×D3×D9C3direct (N × H)
8. C22×C32×C9C22semidirect
9. C2×C3×C3⋊D9C22semidirect
10. C2×C3×D3×C9C22semidirect
11. C2×C32×D9C22semidirect
12. C3×D3×D9C22direct (N × H)
18. C22×C3⋊D9C2×C3semidirect
20. C22×D3×C9C2×C3semidirect
25. C22×C3×D9D3direct (N × H)
26. C22×C3×D9C2×C3semidirect
27. C2×D3×D9C2×C3direct (N × H)
28. C2×C32×C9C23semidirect
29. C3×C3⋊D9C23semidirect
30. C3×D3×C9C23semidirect
31. C32×D9C23semidirect
46. C22×C3×C9C2×D3semidirect
47. C22×C3×C9C22×C3semidirect
48. C2×C3⋊D9C22×C3semidirect
50. C2×D3×C9C22×C3semidirect
55. C2×C3×D9C2×D3direct (N × H)
56. C2×C3×D9C22×C3semidirect
57. D3×D9C22×C3direct (N × H)
58. C32×C9C24semidirect
71. C22×C3×D3D9direct (N × H)
79. C22×D9C3×D3direct (N × H)
89. C2×C3×C9C22×D3semidirect
90. C2×C3×C9C23×C3semidirect
91. C3⋊D9C23×C3semidirect
93. D3×C9C23×C3semidirect
97. C3×D9C22×D3direct (N × H)
98. C3×D9C23×C3semidirect
108. C22×C32C2×D9semidirect
121. C2×C3×D3C2×D9direct (N × H)
129. C22×C9C2×C3×D3semidirect
133. C2×D9C2×C3×D3direct (N × H)
139. C3×C9C23×D3semidirect
140. C3×C9C24×C3semidirect
155. C22×D3C3×D9direct (N × H)
162. C2×C32C22×D9semidirect
173. C3×D3C22×D9direct (N × H)
180. C2×C9C22×C3×D3semidirect
183. D9C22×C3×D3direct (N × H)
197. C22×C3D3×D9direct (N × H)
198. C22×C3C2×C3×D9semidirect
206. C2×D3C2×C3×D9direct (N × H)
211. C32C23×D9semidirect
217. C9C23×C3×D3semidirect
233. C2×C3C2×D3×D9direct (N × H)
234. C2×C3C22×C3×D9semidirect
240. D3C22×C3×D9direct (N × H)
245. C22C3×D3×D9direct (N × H)
250. C3C22×D3×D9direct (N × H)
251. C3C23×C3×D9semidirect
256. C2C2×C3×D3×D9direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C3⋊D92
C22×C3×D3×C92
C22×C32×D92
C2×C3×D3×D92
C22×C3×D323
C23×C3×D93
C22×D3×D93