Finite Group Databasebeta

← C9×#2040 #11766761

Subgroups — C9×#2040 #11766761

Order 1152.

435 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 435 conjugacy classes of subgroups — too many to draw. Only its 126 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
1C9×#537C211yesmaximal, characteristic
2C2×C9×#104C212yesmaximal, complemented
3C9×#417C212yesmaximal, complemented
4C9×#382C211yesmaximal, characteristic, complemented
5C9×#343C211yesmaximal, characteristic, complemented
6C3×#2040C311yesmaximal, characteristic
7C2×C9×#41C2212yes—
8C2×C9×M16C2212yes—
9C9×C22⋊Q8—22no—
10C9×#121—22no—
11C9×#121—22no—
12C2×C9×C4⋊C4C2211yescharacteristic
13C2×C9×C4⋊C4C2211yescharacteristic
14C2×C42×C9C2211yescharacteristic
15C9×#104—24no—
16C9×#103—22no—
17C9×#102—22no—
18C9×#95—22no—
19C3×#537C2×C311yescharacteristic
20C2×C3×#104C2×C312yes—
21C3×#417C2×C312yes—
22C3×#382C2×C311yescharacteristic
23C3×#343C2×C311yescharacteristic
24C9×#41—22no—
25C9×#41—22no—
26C9×#41—22no—
27C9×#41—22no—
28C2×Q8×C9D412yes—
29C2×D4×C9—22no—
30C2×D4×C9—22no—
31C2×D4×C9D412yes—
32C22×C4×C9—21no—
33C22×C4×C9—22no—
34C22×C4×C9—21no—
35C22×C4×C9D412yes—
36C22×C4×C9C2311yescharacteristic
37C9×M16—22no—
38C9×M16—22no—
39C2×C8×C9—22no—
40C9×C4⋊C4—22no—
41C9×C4⋊C4—22no—
42C9×C4⋊C4—22no—
43C9×C22⋊C4—24no—
44C42×C9—21no—
45C42×C9D412yescomplemented
46#2040C911yescharacteristic, direct product factor, Sylow
47C2×C3×#41C22×C312yes—
48C2×C3×M16C22×C312yes—
49C3×C22⋊Q8—22no—
50C3×#121—22no—
51C3×#121—22no—
52C2×C3×C4⋊C4C22×C311yescharacteristic
53C2×C3×C4⋊C4C22×C311yescharacteristic
54C2×C3×C42C22×C311yescharacteristic
55C3×#104—24no—
56C3×#103—22no—
57C3×#102—22no—
58C3×#95—22no—
59C23×C9—22no—
60C23×C9C2×D411yescharacteristic
61Q8×C9—22no—
62Q8×C9—22no—
63D4×C9—22no—
64D4×C9—22no—
65D4×C9—42no—
66D4×C9—42no—
67D4×C9—82no—
68C2×C4×C9—22no—
69C2×C4×C9—22no—
70C2×C4×C9—22no—
71C2×C4×C9—41no—
72C2×C4×C9—41no—
73C2×C4×C9—42no—
74C2×C4×C9—42no—
75C2×C4×C9—42no—
76C2×C4×C9—42no—
77C2×C4×C9—41no—
78C2×C4×C9C2×D411yescharacteristic
79C2×C4×C9C2×D412yes—
80C2×C4×C9#4112yes—
81C2×C4×C9#4111yescharacteristic
82C8×C9—42no—
83#537C2×C911yescharacteristic
84C2×#104C2×C912yescomplemented
85#417C2×C912yescomplemented
86#382C2×C911yescharacteristic, complemented
87#343C2×C911yescharacteristic, complemented
88C3×#41—22no—
89C3×#41—22no—
90C3×#41—22no—
91C3×#41—22no—
92C2×C3×Q8C3×D412yes—
93C2×C3×D4—22no—
94C2×C3×D4—22no—
95C2×C3×D4C3×D412yes—
96C22×C3×C4—21no—
97C22×C3×C4—22no—
98C22×C3×C4—21no—
99C22×C3×C4C3×D412yes—
100C22×C3×C4C23×C311yescharacteristic
101C3×M16—22no—
102C3×M16—22no—
103C2×C3×C8—22no—
104C3×C4⋊C4—22no—
105C3×C4⋊C4—22no—
106C3×C4⋊C4—22no—
107C3×C22⋊C4—24no—
108C3×C42—21no—
109C3×C42C3×D412yes—
110C22×C9—21no—
111C22×C9—21no—
112C22×C9—42no—
113C22×C9—42no—
114C22×C9—42no—
115C22×C9#12011yescharacteristic
116C22×C9#12111yescharacteristic
117C22×C9#12411yescharacteristic
118C4×C9—42no—
119C4×C9—42no—
120C4×C9—42no—
121C4×C9—81no—
122C4×C9#12112yes—
123C4×C9#12312yes—
124C2×#41C22×C912yes—
125C2×M16C22×C912yes—
126C22⋊Q8—22no—
127#121—22no—
128#121—22no—
129C2×C4⋊C4C22×C911yescharacteristic
130C2×C4⋊C4C22×C911yescharacteristic
131C2×C42C22×C911yescharacteristic
132#104—24no—
133#103—22no—
134#102—22no—
135#95—22no—
136C23×C3—22no—
137C23×C3C2×C3×D411yescharacteristic
138C3×Q8—22no—
139C3×Q8—22no—
140C3×D4—22no—
141C3×D4—22no—
142C3×D4—42no—
143C3×D4—42no—
144C3×D4—82no—
145C2×C3×C4—22no—
146C2×C3×C4—22no—
147C2×C3×C4—22no—
148C2×C3×C4—41no—
149C2×C3×C4—41no—
150C2×C3×C4—42no—
151C2×C3×C4—42no—
152C2×C3×C4—42no—
153C2×C3×C4—42no—
154C2×C3×C4—41no—
155C2×C3×C4C2×C3×D411yescharacteristic
156C2×C3×C4C2×C3×D412yes—
157C2×C3×C4C3×#4112yes—
158C2×C3×C4C3×#4111yescharacteristic
159C3×C8—42no—
160C2×C9—21no—
161C2×C9—21no—
162C2×C9—82no—
163C2×C9#39411yescharacteristic
164C2×C9#45411yescharacteristic
165C2×C9#45511yescharacteristic
166#41—22no—
167#41—22no—
168#41—22no—
169#41—22no—
170C2×Q8D4×C912yes—
171C2×D4—22no—
172C2×D4—22no—
173C2×D4D4×C912yes—
174C22×C4—21no—
175C22×C4—22no—
176C22×C4—21no—
177C22×C4D4×C912yes—
178C22×C4C23×C911yescharacteristic
179M16—22no—
180M16—22no—
181C2×C8—22no—
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C22⋊C4—24no—
186C42—21no—
187C42D4×C912yescomplemented
188C22×C3—21no—
189C22×C3—21no—
190C22×C3—42no—
191C22×C3—42no—
192C22×C3—42no—
193C22×C3C3×#12011yescharacteristic
194C22×C3C3×#12111yescharacteristic
195C22×C3C3×#12411yescharacteristic
196C3×C4—42no—
197C3×C4—42no—
198C3×C4—42no—
199C3×C4—81no—
200C3×C4C3×#12112yes—
201C3×C4C3×#12312yes—
202C9#204011yescharacteristic, direct product factor, Sylow
203C23—22no—
204C23C2×D4×C911yescharacteristic
205Q8—22no—
206Q8—22no—
207D4—22no—
208D4—22no—
209D4—42no—
210D4—42no—
211D4—82no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—41no—
222C2×C4C2×D4×C911yescharacteristic
223C2×C4C2×D4×C912yes—
224C2×C4C9×#4112yes—
225C2×C4C9×#4111yescharacteristic
226C8—42no—
227C2×C3—21no—
228C2×C3—21no—
229C2×C3—82no—
230C2×C3C3×#39411yescharacteristic
231C2×C3C3×#45411yescharacteristic
232C2×C3C3×#45511yescharacteristic
233C22—21no—
234C22—21no—
235C22—42no—
236C22—42no—
237C22—42no—
238C22C9×#12011yescharacteristic
239C22C9×#12111yescharacteristic
240C22C9×#12411yescharacteristic
241C4—42no—
242C4—42no—
243C4—42no—
244C4—81no—
245C4C9×#12112yes—
246C4C9×#12312yes—
247C3C3×#204011yescharacteristic
248C2—21no—
249C2—21no—
250C2—82no—
251C2C9×#39411yescharacteristic
252C2C9×#45411yescharacteristic
253C2C9×#45511yescharacteristic
subgroupG/H
centerC22×C9#120
commutatorC22×C4C23×C9
Frattini, cosocleC22×C3×C4C23×C3
socleC22×C3C3×#120
prime radicalC3×#537C2×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C9 ◁ C22×C4×C9 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C9×#104C2semidirect
3. C9×#417C2semidirect
4. C9×#382C2semidirect
5. C9×#343C2semidirect
45. C42×C9D4semidirect
46. #2040C9direct (N × H)
84. C2×#104C2×C9semidirect
85. #417C2×C9semidirect
86. #382C2×C9semidirect
87. #343C2×C9semidirect
187. C42D4×C9semidirect
202. C9#2040direct (N × H)

Maximal subgroups

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

subgroupindex
C9×#5372
C2×C9×#1042
C9×#4172
C9×#3822
C9×#3432
C3×#20403