Finite Group Databasebeta

← C9×#2184 #11766905

Subgroups — C9×#2184 #11766905

Order 1152.

399 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 399 conjugacy classes of subgroups — too many to draw. Only its 108 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×C9×D8C211yesmaximal, characteristic, complemented
2C2×C9×D16C212yesmaximal, complemented
3C9×#466C211yesmaximal, characteristic, complemented
4C9×#357C212yesmaximal, complemented
5C9×C22⋊C16C211yesmaximal, characteristic, complemented
6C3×#2184C311yesmaximal, characteristic
7C22×D4×C9—21no—
8C2×C9×D8—24no—
9C2×C9×D8—21no—
10C2×C9×D8C2212yes—
11C2×C9×D8C2211yescharacteristic, complemented
12C22×C8×C9C2211yescharacteristic
13C9×#121—21no—
14C9×D16—24no—
15C2×C9×C16C2212yescomplemented
16C9×#107C2211yescharacteristic, complemented
17C9×#102—21no—
18C22×C3×D8C2×C311yescharacteristic
19C2×C3×D16C2×C312yes—
20C3×#466C2×C311yescharacteristic
21C3×#357C2×C312yes—
22C3×C22⋊C16C2×C311yescharacteristic
23C24×C9—41no—
24C2×D4×C9—24no—
25C2×D4×C9—22no—
26C2×D4×C9—21no—
27C2×D4×C9—42no—
28C2×D4×C9—41no—
29C2×D4×C9—41no—
30C22×C4×C9D411yescharacteristic
31C9×D8—24no—
32C9×D8—22no—
33C9×D8—22no—
34C9×D8D414yescomplemented
35C2×C8×C9—22no—
36C2×C8×C9D411yescharacteristic
37C2×C8×C9C2311yescharacteristic
38C9×C4⋊C4—21no—
39C9×C22⋊C4—41no—
40C9×C16—22no—
41#2184C911yescharacteristic, direct product factor, Sylow
42C22×C3×D4—21no—
43C2×C3×D8—24no—
44C2×C3×D8—21no—
45C2×C3×D8C22×C312yes—
46C2×C3×D8C22×C311yescharacteristic
47C22×C3×C8C22×C311yescharacteristic
48C3×#121—21no—
49C3×D16—24no—
50C2×C3×C16C22×C312yes—
51C3×#107C22×C311yescharacteristic
52C3×#102—21no—
53C23×C9—44no—
54C23×C9—42no—
55C23×C9—41no—
56C23×C9—82no—
57C23×C9—82no—
58C23×C9D811yescharacteristic
59D4×C9—24no—
60D4×C9—44no—
61D4×C9—41no—
62D4×C9—42no—
63D4×C9—41no—
64D4×C9—82no—
65C2×C4×C9—21no—
66C2×C4×C9—21no—
67C2×C4×C9—41no—
68C2×C4×C9D811yescharacteristic
69C2×C4×C9C2×D411yescharacteristic
70C8×C9—21no—
71C8×C9C2×D412yes—
72C22×D8C2×C911yescharacteristic, complemented
73C2×D16C2×C912yescomplemented
74#466C2×C911yescharacteristic, complemented
75#357C2×C912yescomplemented
76C22⋊C16C2×C911yescharacteristic, complemented
77C24×C3—41no—
78C2×C3×D4—24no—
79C2×C3×D4—22no—
80C2×C3×D4—21no—
81C2×C3×D4—42no—
82C2×C3×D4—41no—
83C2×C3×D4—41no—
84C22×C3×C4C3×D411yescharacteristic
85C3×D8—24no—
86C3×D8—22no—
87C3×D8—22no—
88C3×D8C3×D414yes—
89C2×C3×C8—22no—
90C2×C3×C8C3×D411yescharacteristic
91C2×C3×C8C23×C311yescharacteristic
92C3×C4⋊C4—21no—
93C3×C22⋊C4—41no—
94C3×C16—22no—
95C22×C9—21no—
96C22×C9—21no—
97C22×C9—44no—
98C22×C9—88no—
99C22×C9—82no—
100C22×C9—82no—
101C22×C9—81no—
102C22×C9—81no—
103C22×C9—81no—
104C22×C9D1612yescomplemented
105C22×C9C2×D811yescharacteristic
106C4×C9—21no—
107C4×C9—81no—
108C4×C9#12011yescharacteristic
109C4×C9AGL(1,ℤ/8)11yescharacteristic
110C22×D4—21no—
111C2×D8—24no—
112C2×D8—21no—
113C2×D8C22×C912yes—
114C2×D8C22×C911yescharacteristic, complemented
115C22×C8C22×C911yescharacteristic
116#121—21no—
117D16—24no—
118C2×C16C22×C912yescomplemented
119#107C22×C911yescharacteristic, complemented
120#102—21no—
121C23×C3—44no—
122C23×C3—42no—
123C23×C3—41no—
124C23×C3—82no—
125C23×C3—82no—
126C23×C3C3×D811yescharacteristic
127C3×D4—24no—
128C3×D4—44no—
129C3×D4—41no—
130C3×D4—42no—
131C3×D4—41no—
132C3×D4—82no—
133C2×C3×C4—21no—
134C2×C3×C4—21no—
135C2×C3×C4—41no—
136C2×C3×C4C3×D811yescharacteristic
137C2×C3×C4C2×C3×D411yescharacteristic
138C3×C8—21no—
139C3×C8C2×C3×D412yes—
140C2×C9—22no—
141C2×C9—84no—
142C2×C9—161no—
143C2×C9#44711yescharacteristic
144C2×C9C2×D1611yescharacteristic
145C2×C9#50911yescharacteristic
146C24—41no—
147C2×D4—24no—
148C2×D4—22no—
149C2×D4—21no—
150C2×D4—42no—
151C2×D4—41no—
152C2×D4—41no—
153C22×C4D4×C911yescharacteristic
154D8—24no—
155D8—22no—
156D8—22no—
157D8D4×C914yescomplemented
158C2×C8—22no—
159C2×C8D4×C911yescharacteristic
160C2×C8C23×C911yescharacteristic
161C4⋊C4—21no—
162C22⋊C4—41no—
163C16—22no—
164C22×C3—21no—
165C22×C3—21no—
166C22×C3—44no—
167C22×C3—88no—
168C22×C3—82no—
169C22×C3—82no—
170C22×C3—81no—
171C22×C3—81no—
172C22×C3—81no—
173C22×C3C3×D1612yes—
174C22×C3C2×C3×D811yescharacteristic
175C3×C4—21no—
176C3×C4—81no—
177C3×C4C3×#12011yescharacteristic
178C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
179C9#218411yescharacteristic, direct product factor, Sylow
180C23—44no—
181C23—42no—
182C23—41no—
183C23—82no—
184C23—82no—
185C23C9×D811yescharacteristic
186D4—24no—
187D4—44no—
188D4—41no—
189D4—42no—
190D4—41no—
191D4—82no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—41no—
195C2×C4C9×D811yescharacteristic
196C2×C4C2×D4×C911yescharacteristic
197C8—21no—
198C8C2×D4×C912yes—
199C2×C3—22no—
200C2×C3—84no—
201C2×C3—161no—
202C2×C3C3×#44711yescharacteristic
203C2×C3C2×C3×D1611yescharacteristic
204C2×C3C3×#50911yescharacteristic
205C22—21no—
206C22—21no—
207C22—44no—
208C22—88no—
209C22—82no—
210C22—82no—
211C22—81no—
212C22—81no—
213C22—81no—
214C22C9×D1612yescomplemented
215C22C2×C9×D811yescharacteristic
216C4—21no—
217C4—81no—
218C4C9×#12011yescharacteristic
219C4C9×AGL(1,ℤ/8)11yescharacteristic
220C3C3×#218411yescharacteristic
221C2—22no—
222C2—84no—
223C2—161no—
224C2C9×#44711yescharacteristic
225C2C2×C9×D1611yescharacteristic
226C2C9×#50911yescharacteristic
subgroupG/H
centerC22×C9C2×D8
commutatorC2×C8C23×C9
Frattini, cosocleC2×C3×C8C23×C3
socleC22×C3C2×C3×D8
prime radicalC3×#2184C3
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C9 ◁ C22×C4×C9 ◁ C22×C8×C9 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C9×D8C2semidirect
2. C2×C9×D16C2semidirect
3. C9×#466C2semidirect
4. C9×#357C2semidirect
5. C9×C22⋊C16C2semidirect
11. C2×C9×D8C22semidirect
15. C2×C9×C16C22semidirect
16. C9×#107C22semidirect
34. C9×D8D4semidirect
41. #2184C9direct (N × H)
72. C22×D8C2×C9semidirect
73. C2×D16C2×C9semidirect
74. #466C2×C9semidirect
75. #357C2×C9semidirect
76. C22⋊C16C2×C9semidirect
104. C22×C9D16semidirect
114. C2×D8C22×C9semidirect
118. C2×C16C22×C9semidirect
119. #107C22×C9semidirect
157. D8D4×C9semidirect
179. C9#2184direct (N × H)
214. C22C9×D16semidirect

Maximal subgroups

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

subgroupindex
C22×C9×D82
C2×C9×D162
C9×#4662
C9×#3572
C9×C22⋊C162
C3×#21843