Finite Group Databasebeta

← C9×#2192 #11766913

Subgroups — C9×#2192 #11766913

Order 1152.

330 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 96 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×#576C211yesmaximal, characteristic, complemented
2C9×#509C211yesmaximal, characteristic, complemented
3C2×C9×D16C211yesmaximal, characteristic, complemented
4C9×#472C211yesmaximal, characteristic, complemented
5C9×#361C211yesmaximal, characteristic, complemented
6C9×#359C211yesmaximal, characteristic, complemented
7C9×#350C211yesmaximal, characteristic, complemented
8C3×#2192C311yesmaximal, characteristic
9C9×H(5,𝔽2)—21no—
10C9×AGL(1,ℤ/8)—22no—
11C9×AGL(1,ℤ/8)—21no—
12C9×AGL(1,ℤ/8)—21no—
13C9×#135—21no—
14C9×#135C2211yescharacteristic
15C2×C9×D8—21no—
16C2×C9×D8C2211yescharacteristic
17C2×C9×D8C2211yescharacteristic, complemented
18C9×#131C2211yescharacteristic
19C9×SD32—21no—
20C9×D16—22no—
21C9×D16—21no—
22C9×M32C2211yescharacteristic, complemented
23C2×C9×C16C2211yescharacteristic, complemented
24C9×#108C2211yescharacteristic, complemented
25C9×#100—21no—
26C3×#576C2×C311yescharacteristic
27C3×#509C2×C311yescharacteristic
28C2×C3×D16C2×C311yescharacteristic
29C3×#472C2×C311yescharacteristic
30C3×#361C2×C311yescharacteristic
31C3×#359C2×C311yescharacteristic
32C3×#350C2×C311yescharacteristic
33C9×#41—22no—
34C9×#41—21no—
35C9×#41—41no—
36C9×#41D411yescharacteristic
37C2×D4×C9—22no—
38C2×D4×C9—21no—
39C2×D4×C9—21no—
40C2×D4×C9—42no—
41C2×D4×C9—41no—
42C9×Q16D411yescharacteristic
43C9×SD16—22no—
44C9×SD16—21no—
45C9×SD16—41no—
46C9×D8—22no—
47C9×D8—21no—
48C9×D8—21no—
49C9×D8—21no—
50C9×D8—41no—
51C9×D8D411yescharacteristic
52C9×D8D412yes—
53C9×M16—21no—
54C9×M16—21no—
55C9×M16D411yescharacteristic
56C2×C8×C9—21no—
57C2×C8×C9C2311yescharacteristic
58C9×C16—21no—
59C9×C16—21no—
60#2192C911yescharacteristic, direct product factor, Sylow
61C3×H(5,𝔽2)—21no—
62C3×AGL(1,ℤ/8)—22no—
63C3×AGL(1,ℤ/8)—21no—
64C3×AGL(1,ℤ/8)—21no—
65C3×#135—21no—
66C3×#135C22×C311yescharacteristic
67C2×C3×D8—21no—
68C2×C3×D8C22×C311yescharacteristic
69C2×C3×D8C22×C311yescharacteristic
70C3×#131C22×C311yescharacteristic
71C3×SD32—21no—
72C3×D16—22no—
73C3×D16—21no—
74C3×M32C22×C311yescharacteristic
75C2×C3×C16C22×C311yescharacteristic
76C3×#108C22×C311yescharacteristic
77C3×#100—21no—
78C23×C9—42no—
79C23×C9—41no—
80C23×C9—41no—
81Q8×C9—21no—
82Q8×C9D811yescharacteristic
83D4×C9—21no—
84D4×C9—21no—
85D4×C9—22no—
86D4×C9—42no—
87D4×C9—42no—
88D4×C9—41no—
89D4×C9—41no—
90D4×C9—41no—
91D4×C9—41no—
92D4×C9D811yescharacteristic
93C2×C4×C9—21no—
94C2×C4×C9—42no—
95C2×C4×C9—41no—
96C2×C4×C9C2×D411yescharacteristic
97C8×C9—21no—
98C8×C9—41no—
99C8×C9C2×D411yescharacteristic
100C8×C9C2×D411yescharacteristic
101#576C2×C911yescharacteristic, complemented
102#509C2×C911yescharacteristic, complemented
103C2×D16C2×C911yescharacteristic, complemented
104#472C2×C911yescharacteristic, complemented
105#361C2×C911yescharacteristic, complemented
106#359C2×C911yescharacteristic, complemented
107#350C2×C911yescharacteristic, complemented
108C3×#41—22no—
109C3×#41—21no—
110C3×#41—41no—
111C3×#41C3×D411yescharacteristic
112C2×C3×D4—22no—
113C2×C3×D4—21no—
114C2×C3×D4—21no—
115C2×C3×D4—42no—
116C2×C3×D4—41no—
117C3×Q16C3×D411yescharacteristic
118C3×SD16—22no—
119C3×SD16—21no—
120C3×SD16—41no—
121C3×D8—22no—
122C3×D8—21no—
123C3×D8—21no—
124C3×D8—21no—
125C3×D8—41no—
126C3×D8C3×D411yescharacteristic
127C3×D8C3×D412yes—
128C3×M16—21no—
129C3×M16—21no—
130C3×M16C3×D411yescharacteristic
131C2×C3×C8—21no—
132C2×C3×C8C23×C311yescharacteristic
133C3×C16—21no—
134C3×C16—21no—
135C22×C9—21no—
136C22×C9—42no—
137C22×C9—41no—
138C22×C9—81no—
139C22×C9—161no—
140C22×C9—161no—
141C22×C9—162no—
142C22×C9AGL(1,ℤ/8)11yescharacteristic
143C4×C9—21no—
144C4×C9—41no—
145C4×C9#12011yescharacteristic
146C4×C9C2×D811yescharacteristic
147H(5,𝔽2)—21no—
148AGL(1,ℤ/8)—22no—
149AGL(1,ℤ/8)—21no—
150AGL(1,ℤ/8)—21no—
151#135—21no—
152#135C22×C911yescharacteristic
153C2×D8—21no—
154C2×D8C22×C911yescharacteristic
155C2×D8C22×C911yescharacteristic, complemented
156#131C22×C911yescharacteristic
157SD32—21no—
158D16—22no—
159D16—21no—
160M32C22×C911yescharacteristic, complemented
161C2×C16C22×C911yescharacteristic, complemented
162#108C22×C911yescharacteristic, complemented
163#100—21no—
164C23×C3—42no—
165C23×C3—41no—
166C23×C3—41no—
167C3×Q8—21no—
168C3×Q8C3×D811yescharacteristic
169C3×D4—21no—
170C3×D4—21no—
171C3×D4—22no—
172C3×D4—42no—
173C3×D4—42no—
174C3×D4—41no—
175C3×D4—41no—
176C3×D4—41no—
177C3×D4—41no—
178C3×D4C3×D811yescharacteristic
179C2×C3×C4—21no—
180C2×C3×C4—42no—
181C2×C3×C4—41no—
182C2×C3×C4C2×C3×D411yescharacteristic
183C3×C8—21no—
184C3×C8—41no—
185C3×C8C2×C3×D411yescharacteristic
186C3×C8C2×C3×D411yescharacteristic
187C2×C9—21no—
188C2×C9—41no—
189C2×C9—82no—
190C2×C9—81no—
191C2×C9—161no—
192C2×C9#44711yescharacteristic
193#41—22no—
194#41—21no—
195#41—41no—
196#41D4×C911yescharacteristic
197C2×D4—22no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—42no—
201C2×D4—41no—
202Q16D4×C911yescharacteristic
203SD16—22no—
204SD16—21no—
205SD16—41no—
206D8—22no—
207D8—21no—
208D8—21no—
209D8—21no—
210D8—41no—
211D8D4×C911yescharacteristic
212D8D4×C912yes—
213M16—21no—
214M16—21no—
215M16D4×C911yescharacteristic
216C2×C8—21no—
217C2×C8C23×C911yescharacteristic
218C16—21no—
219C16—21no—
220C22×C3—21no—
221C22×C3—42no—
222C22×C3—41no—
223C22×C3—81no—
224C22×C3—161no—
225C22×C3—161no—
226C22×C3—162no—
227C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
228C3×C4—21no—
229C3×C4—41no—
230C3×C4C3×#12011yescharacteristic
231C3×C4C2×C3×D811yescharacteristic
232C9#219211yescharacteristic, direct product factor, Sylow
233C23—42no—
234C23—41no—
235C23—41no—
236Q8—21no—
237Q8C9×D811yescharacteristic
238D4—21no—
239D4—21no—
240D4—22no—
241D4—42no—
242D4—42no—
243D4—41no—
244D4—41no—
245D4—41no—
246D4—41no—
247D4C9×D811yescharacteristic
248C2×C4—21no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4C2×D4×C911yescharacteristic
252C8—21no—
253C8—41no—
254C8C2×D4×C911yescharacteristic
255C8C2×D4×C911yescharacteristic
256C2×C3—21no—
257C2×C3—41no—
258C2×C3—82no—
259C2×C3—81no—
260C2×C3—161no—
261C2×C3C3×#44711yescharacteristic
262C22—21no—
263C22—42no—
264C22—41no—
265C22—81no—
266C22—161no—
267C22—161no—
268C22—162no—
269C22C9×AGL(1,ℤ/8)11yescharacteristic
270C4—21no—
271C4—41no—
272C4C9×#12011yescharacteristic
273C4C2×C9×D811yescharacteristic
274C3C3×#219211yescharacteristic
275C2—21no—
276C2—41no—
277C2—82no—
278C2—81no—
279C2—161no—
280C2C9×#44711yescharacteristic
subgroupG/H
centerC2×C9#447
commutatorC2×C8C23×C9
Frattini, cosocleC2×C3×C8C23×C3
socleC2×C3C3×#447
prime radicalC3×#2192C3
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C9 ◁ C2×C4×C9 ◁ C9×#131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C9×#576C2semidirect
2. C9×#509C2semidirect
3. C2×C9×D16C2semidirect
4. C9×#472C2semidirect
5. C9×#361C2semidirect
6. C9×#359C2semidirect
7. C9×#350C2semidirect
17. C2×C9×D8C22semidirect
22. C9×M32C22semidirect
23. C2×C9×C16C22semidirect
24. C9×#108C22semidirect
60. #2192C9direct (N × H)
101. #576C2×C9semidirect
102. #509C2×C9semidirect
103. C2×D16C2×C9semidirect
104. #472C2×C9semidirect
105. #361C2×C9semidirect
106. #359C2×C9semidirect
107. #350C2×C9semidirect
155. C2×D8C22×C9semidirect
160. M32C22×C9semidirect
161. C2×C16C22×C9semidirect
162. #108C22×C9semidirect
232. C9#2192direct (N × H)

Maximal subgroups

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

subgroupindex
C9×#5762
C9×#5092
C2×C9×D162
C9×#4722
C9×#3612
C9×#3592
C9×#3502
C3×#21923