Finite Group Databasebeta

← D9×#638 #13048708

Subgroups — D9×#638 #13048708

Order 1296.

614 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 101 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×C32×D9C211yesmaximal, characteristic, complemented
2C2×D9×C3⋊D3C211yesmaximal, characteristic, complemented
3#10619992C211yesmaximal, characteristic, complemented
4C9×#638C211yesmaximal, characteristic, complemented
5#10619877C211yesmaximal, characteristic, complemented
6#10619873C211yesmaximal, characteristic, complemented
7D9×C3⋊Dic3C211yesmaximal, characteristic, complemented
8D3×#638—31nomaximal
9D9×#67—34nomaximal
10C22×C32×C9C2211yescharacteristic, complemented
11C2×C3⋊(C3⋊D9)C2211yescharacteristic, complemented
12C2×C9×C3⋊D3C2211yescharacteristic, complemented
13C2×C32×D9—22no—
14C2×C32×D9C2211yescharacteristic
15C2×C32×D9C2211yescharacteristic, complemented
16D9×C3⋊D3—22no—
17C3⋊(C3⋊Dic9)C2211yescharacteristic, complemented
18C9×C3⋊Dic3C2211yescharacteristic, complemented
19C22×C32×D3—31no—
20C2×D3×C3⋊D3—31no—
21#6312—31no—
22C3×#638D311yescharacteristic
23#6291—31no—
24#6290—31no—
25D3×C3⋊Dic3—31no—
26C22×C3×D9D314yescomplemented
27C2×D3×D9—34no—
28#6233—34no—
29#6233—64no—
30C9×#67—34no—
31#6194—34no—
32#6192—34no—
33Dic3×D9—34no—
34C2×C32×C9—21no—
35C2×C32×C9C2311yescharacteristic
36C3⋊(C3⋊D9)—21no—
37C9×C3⋊D3—21no—
38C32×D9—21no—
39C32×D9D412yescomplemented
40C2×#638—91no—
41D3×#67—94no—
42D4×D9—91no—
43C22×C33C2×D311yescharacteristic
44C2×C3⋊(C3⋊D3)—31no—
45C2×C3×C3⋊D3C2×D311yescharacteristic
46C2×C32×D3—31no—
47C2×C32×D3—31no—
48C2×C32×D3—62no—
49D3×C3⋊D3—62no—
50C3⋊(C3⋊Dic3)—31no—
51C3×C3⋊Dic3C2×D311yescharacteristic
52C22×C3×C9—24no—
53C22×C3×C9C2×D314yescomplemented
54C2×C3⋊D9—34no—
55C2×C3⋊D9—64no—
56C2×D3×C9—34no—
57C2×C3×D9—28no—
58C2×C3×D9C2×D314yes—
59C2×C3×D9C2×D314yescomplemented
60D3×D9—68no—
61C3⋊Dic9—34no—
62C3⋊Dic9—64no—
63C9×Dic3—34no—
64C32×C9C2×D411yescharacteristic, complemented, Sylow
65C23×C32—91no—
66C22×C3⋊D3—91no—
67C22×C3×D3—34no—
68C2×D32—94no—
69#638—91no—
70#638—91no—
71#638—91no—
72#638—94no—
73#638—184no—
74#638D911yescharacteristic, direct product factor
75C2×C3⋊Dic3—91no—
76C3×#67—34no—
77#626—94no—
78#625—94no—
79D3×Dic3—94no—
80C22×D9—91no—
81C22×D9C3⋊D311yescharacteristic, complemented
82D4×C9—91no—
83#611—91no—
84#611—91no—
85#611—184no—
86D36—91no—
87C4×D9—91no—
88C2×C33—21no—
89C2×C33C22×D311yescharacteristic
90C3⋊(C3⋊D3)—61no—
91C3×C3⋊D3—21no—
92C32×D3—32no—
93C32×D3—61no—
94C2×C3×C9—24no—
95C2×C3×C9—24no—
96C2×C3×C9—44no—
97C2×C3×C9C22×D314yes—
98C3⋊D9—64no—
99C3⋊D9—124no—
100D3×C9—64no—
101C3×D9—24no—
102C3×D9#6718yescomplemented
103C2×#67—274no—
104D3×D4—271no—
105C22×C32—24no—
106C22×C32—91no—
107C22×C32—91no—
108C22×C32—182no—
109C22×C32C2×D911yescharacteristic, complemented
110C22×C32D3214yes—
111C2×C3⋊D3—91no—
112C2×C3⋊D3—94no—
113C2×C3⋊D3—184no—
114C2×C3⋊D3—182no—
115C2×C3⋊D3C2×D911yescharacteristic, complemented
116C2×C3×D3—34no—
117C2×C3×D3—34no—
118C2×C3×D3—34no—
119C2×C3×D3—68no—
120D32—188no—
121C3⋊Dic3—91no—
122C3⋊Dic3—94no—
123C3⋊Dic3—184no—
124C3⋊Dic3C2×D911yescharacteristic, complemented
125C3×Dic3—34no—
126C22×C9—24no—
127C22×C9—91no—
128C22×C9C2×C3⋊D311yescharacteristic, complemented
129C2×D9—22no—
130C2×D9—91no—
131C2×D9—184no—
132C2×D9—182no—
133C2×D9C2×C3⋊D311yescharacteristic
134C2×D9C2×C3⋊D311yescharacteristic, complemented
135C4×C9—91no—
136Dic9—91no—
137Dic9—184no—
138C33D3×D411yescharacteristic
139C3×C9—24no—
140C3×C9C2×#6714yescomplemented
141C23×C3—94no—
142C22×D3—31no—
143C22×D3—271no—
144C22×D3—274no—
145C3×D4—91no—
146#67—34no—
147#67—274no—
148#67—271no—
149#67—274no—
150#67—274no—
151#67—271no—
152#67—544no—
153C2×Dic3—274no—
154D12—271no—
155C4×D3—271no—
156C2×C32—21no—
157C2×C32—24no—
158C2×C32—24no—
159C2×C32—44no—
160C2×C32—92no—
161C2×C32—181no—
162C2×C32C22×D911yescharacteristic
163C2×C32C2×D3214yes—
164C3⋊D3—21no—
165C3⋊D3—181no—
166C3⋊D3—184no—
167C3⋊D3—364no—
168C3×D3—38no—
169C3×D3—64no—
170C3×D3—64no—
171C2×C9—21no—
172C2×C9—24no—
173C2×C9—44no—
174C2×C9—181no—
175C2×C9C22×C3⋊D311yescharacteristic
176D9—21no—
177D9—181no—
178D9—364no—
179D9#63812yesdirect product factor
180C2×D4—811noSylow
181C22×C3—24no—
182C22×C3—94no—
183C22×C3—94no—
184C22×C3—91no—
185C22×C3—188no—
186C22×C3D3×D914yescomplemented
187C22×C3D3×C3⋊D311yescharacteristic
188C2×D3—31no—
189C2×D3—34no—
190C2×D3—31no—
191C2×D3—62no—
192C2×D3—274no—
193C2×D3—271no—
194C2×D3—544no—
195C2×D3—542no—
196C2×D3—548no—
197C3×C4—91no—
198Dic3—34no—
199Dic3—274no—
200Dic3—271no—
201Dic3—544no—
202C32—24no—
203C32D4×D911yescharacteristic, complemented
204C32D3×#6714yes—
205C9—24no—
206C9C2×#63811yescharacteristic, complemented
207C23—91no—
208C23—811no—
209D4—91no—
210D4—811no—
211D4—811no—
212D4—811no—
213C2×C4—811no—
214C2×C3—24no—
215C2×C3—21no—
216C2×C3—24no—
217C2×C3—44no—
218C2×C3—98no—
219C2×C3—184no—
220C2×C3—181no—
221C2×C3C2×D3×D914yes—
222C2×C3C2×D3×C3⋊D311yescharacteristic
223D3—32no—
224D3—64no—
225D3—61no—
226D3—544no—
227D3—541no—
228D3—1084no—
229C22—91no—
230C22—91no—
231C22—91no—
232C22—182no—
233C22—811no—
234C22—1622no—
235C22D9×C3⋊D311yescharacteristic, complemented
236C4—91no—
237C4—811no—
238C3—24no—
239C3D9×#6714yescomplemented
240C3D3×#63811yescharacteristic
241C2—21no—
242C2—92no—
243C2—181no—
244C2—181no—
245C2—1621no—
246C2C2×D9×C3⋊D311yescharacteristic
subgroupG/H
centerC2C2×D9×C3⋊D3
commutator, cosocleC2×C32×C9C23
FrattiniC2×C3C2×D3×C3⋊D3
FittingC22×C32×C9C22
socleC2×C33C22×D3
hypercenterC22D9×C3⋊D3
hypocenterC32×C9C2×D4
LCSG ▷ C2×C32×C9 ▷ C32×C9
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C32×D9C2semidirect
2. C2×D9×C3⋊D3C2semidirect
3. #10619992C2semidirect
4. C9×#638C2semidirect
5. #10619877C2semidirect
6. #10619873C2semidirect
7. D9×C3⋊Dic3C2semidirect
10. C22×C32×C9C22semidirect
11. C2×C3⋊(C3⋊D9)C22semidirect
12. C2×C9×C3⋊D3C22semidirect
15. C2×C32×D9C22semidirect
17. C3⋊(C3⋊Dic9)C22semidirect
18. C9×C3⋊Dic3C22semidirect
26. C22×C3×D9D3semidirect
39. C32×D9D4semidirect
53. C22×C3×C9C2×D3semidirect
59. C2×C3×D9C2×D3semidirect
64. C32×C9C2×D4semidirect
74. #638D9direct (N × H)
81. C22×D9C3⋊D3semidirect
102. C3×D9#67semidirect
109. C22×C32C2×D9semidirect
115. C2×C3⋊D3C2×D9semidirect
124. C3⋊Dic3C2×D9semidirect
128. C22×C9C2×C3⋊D3semidirect
134. C2×D9C2×C3⋊D3semidirect
140. C3×C9C2×#67semidirect
179. D9#638direct (N × H)
186. C22×C3D3×D9semidirect
203. C32D4×D9semidirect
206. C9C2×#638semidirect
235. C22D9×C3⋊D3semidirect
239. C3D9×#67semidirect

Maximal subgroups

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

subgroupindex
C22×C32×D92
C2×D9×C3⋊D32
#106199922
C9×#6382
#106198772
#106198732
D9×C3⋊Dic32
D3×#6383
D9×#673