Finite Group Databasebeta

← C9×#937 #11721629

Subgroups — C9×#937 #11721629

Order 864.

444 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 111 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
1C23×D3×C9C211yesmaximal, characteristic, complemented
2C2×C3×D4×C9C211yesmaximal, characteristic, complemented
3C2×C9×#67C212yesmaximal, complemented
4C9×#217C211yesmaximal, characteristic, complemented
5C9×(C2×D3)⋊C4C212yesmaximal, complemented
6C3×#937C311yesmaximal, characteristic
7C9×#120—31nomaximal
8C23×C3×C9C2211yescharacteristic
9C23×C3×C9C2211yescharacteristic, complemented
10C22×D3×C9—22no—
11C22×D3×C9—24no—
12C22×D3×C9C2212yes—
13C3×D4×C9—22no—
14C2×C3×C4×C9C2211yescharacteristic, complemented
15C9×#67—24no—
16C2×C9×Dic3C2212yescomplemented
17C23×C3×D3C2×C311yescharacteristic
18C2×C32×D4C2×C311yescharacteristic
19C2×C3×#67C2×C312yes—
20C24×C9—31no—
21C3×#217C2×C311yescharacteristic
22C3×(C2×D3)⋊C4C2×C312yes—
23C2×D4×C9—21no—
24C2×D4×C9—32no—
25C2×D4×C9D311yescharacteristic, complemented
26C9×C22⋊C4—31no—
27C9×C22⋊C4—32no—
28C22×C3×C9—22no—
29C22×C3×C9—21no—
30C22×C3×C9—22no—
31C22×C3×C9D412yescomplemented
32C22×C3×C9C2311yescharacteristic
33C2×D3×C9—28no—
34C2×D3×C9—22no—
35C2×D3×C9—22no—
36C2×D3×C9D414yescomplemented
37C3×C4×C9—21no—
38C9×Dic3—22no—
39C3×#120—31no—
40#937C911yescharacteristic, direct product factor
41C23×C32C22×C311yescharacteristic
42C23×C32C22×C311yescharacteristic
43C22×C3×D3—22no—
44C22×C3×D3—24no—
45C22×C3×D3C22×C312yes—
46C32×D4—22no—
47C2×C32×C4C22×C311yescharacteristic
48C3×#67—24no—
49C2×C3×Dic3C22×C312yes—
50C23×C9—21no—
51C23×C9—21no—
52C23×C9—32no—
53C23×C9—64no—
54C23×C9—62no—
55C23×C9C2×D311yescharacteristic
56C23×C9C2×D311yescharacteristic, complemented
57D4×C9—24no—
58D4×C9—22no—
59D4×C9—64no—
60C2×C4×C9—21no—
61C2×C4×C9—32no—
62C2×C4×C9C2×D311yescharacteristic, complemented
63C2×C3×C9—22no—
64C2×C3×C9—41no—
65C2×C3×C9C2×D412yes—
66C2×C3×C9C2×D411yescharacteristic
67D3×C9—24no—
68C24×C3—31no—
69C23×D3C2×C911yescharacteristic, complemented
70C2×C3×D4—21no—
71C2×C3×D4—32no—
72C2×C3×D4C2×C911yescharacteristic, complemented
73C2×C3×D4C3×D311yescharacteristic
74C2×#67C2×C912yescomplemented
75C3×C22⋊C4—31no—
76C3×C22⋊C4—32no—
77#217C2×C911yescharacteristic, complemented
78(C2×D3)⋊C4C2×C912yescomplemented
79C22×C32—21no—
80C22×C32—22no—
81C22×C32—22no—
82C22×C32C3×D412yes—
83C22×C32C23×C311yescharacteristic
84C2×C3×D3—28no—
85C2×C3×D3—22no—
86C2×C3×D3—22no—
87C2×C3×D3C3×D414yes—
88C32×C4—21no—
89C3×Dic3—22no—
90C22×C9—22no—
91C22×C9—22no—
92C22×C9—22no—
93C22×C9—21no—
94C22×C9—22no—
95C22×C9—21no—
96C22×C9—34no—
97C22×C9—42no—
98C22×C9—42no—
99C22×C9—68no—
100C22×C9—62no—
101C22×C9—62no—
102C22×C9#6712yescomplemented
103C22×C9C22×D311yescharacteristic
104C4×C9—22no—
105C4×C9—21no—
106C4×C9—62no—
107#120—31noSylow
108C3×C9#12011yescharacteristic, complemented, Sylow
109C23×C3—21no—
110C23×C3—21no—
111C23×C3—32no—
112C23×C3—64no—
113C23×C3—62no—
114C23×C3C22×C911yescharacteristic
115C23×C3C22×C911yescharacteristic, complemented
116C23×C3C2×C3×D311yescharacteristic
117C23×C3C2×C3×D311yescharacteristic
118C22×D3—22no—
119C22×D3—24no—
120C22×D3C22×C912yes—
121C3×D4—24no—
122C3×D4—22no—
123C3×D4—22no—
124C3×D4—64no—
125C2×C3×C4—21no—
126C2×C3×C4—32no—
127C2×C3×C4C22×C911yescharacteristic, complemented
128C2×C3×C4C2×C3×D311yescharacteristic
129#67—24no—
130C2×Dic3C22×C912yescomplemented
131C2×C32—22no—
132C2×C32—41no—
133C2×C32C2×C3×D412yes—
134C2×C32C2×C3×D411yescharacteristic
135C3×D3—24no—
136C2×C9—22no—
137C2×C9—22no—
138C2×C9—21no—
139C2×C9—42no—
140C2×C9—42no—
141C2×C9—41no—
142C2×C9—64no—
143C2×C9D3×D412yes—
144C2×C9C2×#6711yescharacteristic
145C24—31no—
146C2×D4—32no—
147C2×D4D3×C911yescharacteristic, complemented
148C22⋊C4—31no—
149C22⋊C4—32no—
150C22×C3—22no—
151C22×C3—22no—
152C22×C3—22no—
153C22×C3—22no—
154C22×C3—21no—
155C22×C3—22no—
156C22×C3—21no—
157C22×C3—22no—
158C22×C3—21no—
159C22×C3—34no—
160C22×C3—42no—
161C22×C3—42no—
162C22×C3—68no—
163C22×C3—62no—
164C22×C3—62no—
165C22×C3D4×C912yescomplemented
166C22×C3C23×C911yescharacteristic
167C22×C3C3×#6712yes—
168C22×C3C22×C3×D311yescharacteristic
169C2×D3—28no—
170C2×D3—22no—
171C2×D3—22no—
172C2×D3D4×C914yescomplemented
173C3×C4—22no—
174C3×C4—21no—
175C3×C4—21no—
176C3×C4—62no—
177Dic3—22no—
178C32C3×#12011yescharacteristic
179C9—21no—
180C9#93711yescharacteristic, direct product factor
181C23—32no—
182C23—64no—
183C23—62no—
184C23C2×D3×C911yescharacteristic
185C23C2×D3×C911yescharacteristic, complemented
186D4—22no—
187D4—64no—
188C2×C4—32no—
189C2×C4C2×D3×C911yescharacteristic, complemented
190C2×C3—22no—
191C2×C3—22no—
192C2×C3—22no—
193C2×C3—21no—
194C2×C3—42no—
195C2×C3—42no—
196C2×C3—41no—
197C2×C3—41no—
198C2×C3—64no—
199C2×C3C2×D4×C912yes—
200C2×C3C2×D4×C911yescharacteristic
201C2×C3C3×D3×D412yes—
202C2×C3C2×C3×#6711yescharacteristic
203D3—24no—
204C22—22no—
205C22—22no—
206C22—21no—
207C22—34no—
208C22—68no—
209C22—62no—
210C22—62no—
211C22C9×#6712yescomplemented
212C22C22×D3×C911yescharacteristic
213C4—21no—
214C4—62no—
215C3—21no—
216C3C9×#12011yescharacteristic, complemented
217C3C3×#93711yescharacteristic
218C2—22no—
219C2—41no—
220C2—64no—
221C2D3×D4×C912yes—
222C2C2×C9×#6711yescharacteristic
subgroupG/H
centerC22×C9C22×D3
commutatorC22×C3C23×C9
FrattiniC22×C3C22×C3×D3
FittingC2×C3×D4×C9C2
socle, cosocleC22×C32C23×C3
prime radicalC3×#937C3
hypercenterC2×D4×C9D3
hypocenterC3C9×#120
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C9 ◁ C2×D4×C9

Complements

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

NH ≅ G/Ntype
1. C23×D3×C9C2semidirect
2. C2×C3×D4×C9C2semidirect
3. C2×C9×#67C2semidirect
4. C9×#217C2semidirect
5. C9×(C2×D3)⋊C4C2semidirect
9. C23×C3×C9C22semidirect
14. C2×C3×C4×C9C22semidirect
16. C2×C9×Dic3C22semidirect
25. C2×D4×C9D3semidirect
31. C22×C3×C9D4semidirect
36. C2×D3×C9D4semidirect
40. #937C9direct (N × H)
56. C23×C9C2×D3semidirect
62. C2×C4×C9C2×D3semidirect
69. C23×D3C2×C9semidirect
72. C2×C3×D4C2×C9semidirect
74. C2×#67C2×C9semidirect
77. #217C2×C9semidirect
78. (C2×D3)⋊C4C2×C9semidirect
102. C22×C9#67semidirect
108. C3×C9#120semidirect
115. C23×C3C22×C9semidirect
127. C2×C3×C4C22×C9semidirect
130. C2×Dic3C22×C9semidirect
147. C2×D4D3×C9semidirect
165. C22×C3D4×C9semidirect
172. C2×D3D4×C9semidirect
180. C9#937direct (N × H)
185. C23C2×D3×C9semidirect
189. C2×C4C2×D3×C9semidirect
211. C22C9×#67semidirect
216. C3C9×#120semidirect

Maximal subgroups

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

subgroupindex
C23×D3×C92
C2×C3×D4×C92
C2×C9×#672
C9×#2172
C9×(C2×D3)⋊C42
C3×#9373
C9×#1203