Finite Group Databasebeta

← C9×#3027 #11767748

Subgroups — C9×#3027 #11767748

Order 1152.

1158 conjugacy classes of subgroups; only the 318 normal subgroups are shown.

normal subgroups only

This group has 1158 conjugacy classes of subgroups — too many to draw. Only its 318 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×#585C211yesmaximal, characteristic, complemented
2C9×#535C213yesmaximal, complemented
3C9×B(4,𝔽2)C218yesmaximal, complemented
4C9×#410C213yesmaximal, complemented
5C3×#3027C311yesmaximal, characteristic
6C9×2−1+4—23no—
7C9×H(5,𝔽2)—23no—
8C9×H(5,𝔽2)C2214yes—
9C2×C9×#41—26no—
10C2×C9×#41C2213yes—
11C22×D4×C9C2211yescharacteristic, complemented
12C9×#127—23no—
13C9×#124—23no—
14C9×#121—26no—
15C9×#120C22112yescomplemented
16C9×#117C2213yescomplemented
17C9×#99C22112yescomplemented
18C3×#585C2×C311yescharacteristic
19C3×#535C2×C313yes—
20C3×B(4,𝔽2)C2×C318yes—
21C3×#410C2×C313yes—
22C24×C9C2312yes—
23C9×#41—24no—
24C9×#41—212no—
25C9×#41—26no—
26C9×#41—212no—
27C9×#41—26no—
28C2×Q8×C9—26no—
29C2×Q8×C9D413yescomplemented
30C2×D4×C9—26no—
31C2×D4×C9—212no—
32C2×D4×C9—212no—
33C2×D4×C9—23no—
34C2×D4×C9—23no—
35C2×D4×C9D413yescomplemented
36C2×D4×C9C2316yes—
37C22×C4×C9—24no—
38C22×C4×C9D416yescomplemented
39C22×C4×C9C2311yescharacteristic
40C9×C4⋊C4—23no—
41C9×C22⋊C4—212no—
42C9×C22⋊C4C2316yes—
43C42×C9—23no—
44#3027C911yescharacteristic, direct product factor, Sylow
45C3×2−1+4—23no—
46C3×H(5,𝔽2)—23no—
47C3×H(5,𝔽2)C22×C314yes—
48C2×C3×#41—26no—
49C2×C3×#41C22×C313yes—
50C22×C3×D4C22×C311yescharacteristic
51C3×#127—23no—
52C3×#124—23no—
53C3×#121—26no—
54C3×#120C22×C3112yes—
55C3×#117C22×C313yes—
56C3×#99C22×C3112yes—
57C23×C9—24no—
58C23×C9—26no—
59C23×C9—82no—
60C23×C9C2×D416yes—
61C23×C9C2411yescharacteristic
62Q8×C9—24no—
63Q8×C9—26no—
64D4×C9—212no—
65D4×C9—212no—
66D4×C9—26no—
67D4×C9—41no—
68D4×C9—43no—
69D4×C9—812no—
70C2×C4×C9—212no—
71C2×C4×C9—26no—
72C2×C4×C9—26no—
73C2×C4×C9—26no—
74C2×C4×C9C2×D416yes—
75C2×C4×C9C2×D413yes—
76C2×C4×C9C2×D413yes—
77#585C2×C911yescharacteristic, complemented
78#535C2×C913yescomplemented
79B(4,𝔽2)C2×C918yescomplemented
80#410C2×C913yescomplemented
81C24×C3C23×C312yes—
82C3×#41—24no—
83C3×#41—212no—
84C3×#41—26no—
85C3×#41—212no—
86C3×#41—26no—
87C2×C3×Q8—26no—
88C2×C3×Q8C3×D413yes—
89C2×C3×D4—26no—
90C2×C3×D4—212no—
91C2×C3×D4—212no—
92C2×C3×D4—23no—
93C2×C3×D4—23no—
94C2×C3×D4C3×D413yes—
95C2×C3×D4C23×C316yes—
96C22×C3×C4—24no—
97C22×C3×C4C3×D416yes—
98C22×C3×C4C23×C311yescharacteristic
99C3×C4⋊C4—23no—
100C3×C22⋊C4—212no—
101C3×C22⋊C4C23×C316yes—
102C3×C42—23no—
103C22×C9—26no—
104C22×C9—41no—
105C22×C9—46no—
106C22×C9—412no—
107C22×C9—42no—
108C22×C9—84no—
109C22×C9C22×D413yes—
110C4×C9—26no—
111C4×C9—46no—
112C4×C9#12011yescharacteristic
113C4×C9#12013yes—
1142−1+4—23no—
115H(5,𝔽2)—23no—
116H(5,𝔽2)C22×C914yes—
117C2×#41—26no—
118C2×#41C22×C913yes—
119C22×D4C22×C911yescharacteristic, complemented
120#127—23no—
121#124—23no—
122#121—26no—
123#120C22×C9112yescomplemented
124#117C22×C913yescomplemented
125#99C22×C9112yescomplemented
126C23×C3—24no—
127C23×C3—26no—
128C23×C3—82no—
129C23×C3C2×C3×D416yes—
130C23×C3C24×C311yescharacteristic
131C3×Q8—24no—
132C3×Q8—26no—
133C3×D4—212no—
134C3×D4—212no—
135C3×D4—26no—
136C3×D4—41no—
137C3×D4—43no—
138C3×D4—812no—
139C2×C3×C4—212no—
140C2×C3×C4—26no—
141C2×C3×C4—26no—
142C2×C3×C4—26no—
143C2×C3×C4C2×C3×D416yes—
144C2×C3×C4C2×C3×D413yes—
145C2×C3×C4C2×C3×D413yes—
146C2×C9—23no—
147C2×C9—46no—
148C2×C9—82no—
149C2×C9C2×#12011yescharacteristic
150C24C23×C912yes—
151#41—24no—
152#41—212no—
153#41—26no—
154#41—212no—
155#41—26no—
156C2×Q8—26no—
157C2×Q8D4×C913yescomplemented
158C2×D4—26no—
159C2×D4—212no—
160C2×D4—212no—
161C2×D4—23no—
162C2×D4—23no—
163C2×D4D4×C913yescomplemented
164C2×D4C23×C916yes—
165C22×C4—24no—
166C22×C4D4×C916yescomplemented
167C22×C4C23×C911yescharacteristic
168C4⋊C4—23no—
169C22⋊C4—212no—
170C22⋊C4C23×C916yes—
171C42—23no—
172C22×C3—26no—
173C22×C3—41no—
174C22×C3—46no—
175C22×C3—412no—
176C22×C3—42no—
177C22×C3—84no—
178C22×C3C22×C3×D413yes—
179C3×C4—26no—
180C3×C4—46no—
181C3×C4C3×#12011yescharacteristic
182C3×C4C3×#12013yes—
183C9#302711yescharacteristic, direct product factor, Sylow
184C23—24no—
185C23—26no—
186C23—82no—
187C23C2×D4×C916yes—
188C23C24×C911yescharacteristic
189Q8—24no—
190Q8—26no—
191D4—212no—
192D4—212no—
193D4—26no—
194D4—41no—
195D4—43no—
196D4—812no—
197C2×C4—212no—
198C2×C4—26no—
199C2×C4—26no—
200C2×C4—26no—
201C2×C4C2×D4×C916yes—
202C2×C4C2×D4×C913yes—
203C2×C4C2×D4×C913yes—
204C2×C3—23no—
205C2×C3—46no—
206C2×C3—82no—
207C2×C3C2×C3×#12011yescharacteristic
208C22—26no—
209C22—41no—
210C22—46no—
211C22—412no—
212C22—42no—
213C22—84no—
214C22C22×D4×C913yes—
215C4—26no—
216C4—46no—
217C4C9×#12011yescharacteristic
218C4C9×#12013yes—
219C3C3×#302711yescharacteristic
220C2—23no—
221C2—46no—
222C2—82no—
223C2C2×C9×#12011yescharacteristic
subgroupG/H
centerC2×C9C2×#120
commutatorC23C24×C9
Frattini, cosocleC23×C3C24×C3
socleC2×C3C2×C3×#120
prime radicalC3×#3027C3
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C9 ◁ C22×C4×C9 ◁ G

Complements

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

NH ≅ G/Ntype
1. C9×#585C2semidirect
2. C9×#535C2semidirect
3. C9×B(4,𝔽2)C2semidirect
4. C9×#410C2semidirect
11. C22×D4×C9C22semidirect
15. C9×#120C22semidirect
16. C9×#117C22semidirect
17. C9×#99C22semidirect
29. C2×Q8×C9D4semidirect
35. C2×D4×C9D4semidirect
38. C22×C4×C9D4semidirect
44. #3027C9direct (N × H)
77. #585C2×C9semidirect
78. #535C2×C9semidirect
79. B(4,𝔽2)C2×C9semidirect
80. #410C2×C9semidirect
119. C22×D4C22×C9semidirect
123. #120C22×C9semidirect
124. #117C22×C9semidirect
125. #99C22×C9semidirect
157. C2×Q8D4×C9semidirect
163. C2×D4D4×C9semidirect
166. C22×C4D4×C9semidirect
183. C9#3027direct (N × H)

Maximal subgroups

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

subgroupindex
C9×#5852
C9×#5352
C9×B(4,𝔽2)2
C9×#4102
C3×#30273