Finite Group Databasebeta

← C9×#2201 #11766922

Subgroups — C9×#2201 #11766922

Order 1152.

339 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 339 conjugacy classes of subgroups — too many to draw. Only its 84 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×#563C211yesmaximal, characteristic, complemented
2C9×#458C212yesmaximal
3C9×#455C211yesmaximal, characteristic
4C9×#354C211yesmaximal, characteristic, complemented
5C9×#352C212yesmaximal, complemented
6C3×#2201C311yesmaximal, characteristic
7C9×H(5,𝔽2)C2211yescharacteristic
8C9×#137—21no—
9C9×C4⋊Q8—21no—
10C9×#126—22no—
11C9×#125—21no—
12C9×#124C2211yescharacteristic
13C9×#123—22no—
14C9×#123C2212yes—
15C9×C22⋊Q8—22no—
16C9×#104—21no—
17C9×#100C2211yescharacteristic
18C9×#99—22no—
19C9×#99C2212yes—
20C3×#563C2×C311yescharacteristic
21C3×#458C2×C312yes—
22C3×#455C2×C311yescharacteristic
23C3×#354C2×C311yescharacteristic
24C3×#352C2×C312yes—
25C9×#41—21no—
26C9×#41—41no—
27C2×Q8×C9—21no—
28C2×Q8×C9D411yescharacteristic
29C2×D4×C9—22no—
30C2×D4×C9—41no—
31C2×D4×C9C2311yescharacteristic
32C22×C4×C9D412yes—
33C9×Q16—41no—
34C9×SD16—41no—
35C9×M16—21no—
36C9×C4⋊C4—21no—
37C9×C4⋊C4—22no—
38C9×C4⋊C4—22no—
39C9×C4⋊C4—21no—
40C9×C4⋊C4—22no—
41C9×C4⋊C4—42no—
42C9×C22⋊C4—22no—
43C9×C22⋊C4—22no—
44C9×C22⋊C4—22no—
45C9×C22⋊C4—42no—
46C9×C22⋊C4D412yes—
47C42×C9—21no—
48C42×C9D411yescharacteristic
49#2201C911yescharacteristic, direct product factor, Sylow
50C3×H(5,𝔽2)C22×C311yescharacteristic
51C3×#137—21no—
52C3×C4⋊Q8—21no—
53C3×#126—22no—
54C3×#125—21no—
55C3×#124C22×C311yescharacteristic
56C3×#123—22no—
57C3×#123C22×C312yes—
58C3×C22⋊Q8—22no—
59C3×#104—21no—
60C3×#100C22×C311yescharacteristic
61C3×#99—22no—
62C3×#99C22×C312yes—
63C23×C9—22no—
64C23×C9C2×D412yes—
65Q8×C9—21no—
66Q8×C9—41no—
67Q8×C9—81no—
68D4×C9—21no—
69D4×C9—41no—
70D4×C9—42no—
71D4×C9—41no—
72C2×C4×C9—22no—
73C2×C4×C9—21no—
74C2×C4×C9—22no—
75C2×C4×C9—21no—
76C2×C4×C9—22no—
77C2×C4×C9—41no—
78C2×C4×C9—42no—
79C2×C4×C9—42no—
80C2×C4×C9C2×D411yescharacteristic
81C8×C9—41no—
82#563C2×C911yescharacteristic, complemented
83#458C2×C912yes—
84#455C2×C911yescharacteristic
85#354C2×C911yescharacteristic, complemented
86#352C2×C912yescomplemented
87C3×#41—21no—
88C3×#41—41no—
89C2×C3×Q8—21no—
90C2×C3×Q8C3×D411yescharacteristic
91C2×C3×D4—22no—
92C2×C3×D4—41no—
93C2×C3×D4C23×C311yescharacteristic
94C22×C3×C4C3×D412yes—
95C3×Q16—41no—
96C3×SD16—41no—
97C3×M16—21no—
98C3×C4⋊C4—21no—
99C3×C4⋊C4—22no—
100C3×C4⋊C4—22no—
101C3×C4⋊C4—21no—
102C3×C4⋊C4—22no—
103C3×C4⋊C4—42no—
104C3×C22⋊C4—22no—
105C3×C22⋊C4—22no—
106C3×C22⋊C4—22no—
107C3×C22⋊C4—42no—
108C3×C22⋊C4C3×D412yes—
109C3×C42—21no—
110C3×C42C3×D411yescharacteristic
111C22×C9—22no—
112C22×C9—42no—
113C22×C9—41no—
114C22×C9—82no—
115C22×C9#12011yescharacteristic
116C4×C9—21no—
117C4×C9—42no—
118C4×C9—41no—
119C4×C9—41no—
120C4×C9—42no—
121C4×C9—41no—
122C4×C9—82no—
123H(5,𝔽2)C22×C911yescharacteristic
124#137—21no—
125C4⋊Q8—21no—
126#126—22no—
127#125—21no—
128#124C22×C911yescharacteristic
129#123—22no—
130#123C22×C912yes—
131C22⋊Q8—22no—
132#104—21no—
133#100C22×C911yescharacteristic
134#99—22no—
135#99C22×C912yes—
136C23×C3—22no—
137C23×C3C2×C3×D412yes—
138C3×Q8—21no—
139C3×Q8—41no—
140C3×Q8—81no—
141C3×D4—21no—
142C3×D4—41no—
143C3×D4—42no—
144C3×D4—41no—
145C2×C3×C4—22no—
146C2×C3×C4—21no—
147C2×C3×C4—22no—
148C2×C3×C4—21no—
149C2×C3×C4—22no—
150C2×C3×C4—41no—
151C2×C3×C4—42no—
152C2×C3×C4—42no—
153C2×C3×C4C2×C3×D411yescharacteristic
154C3×C8—41no—
155C2×C9—21no—
156C2×C9—42no—
157C2×C9—81no—
158C2×C9B(4,𝔽2)11yescharacteristic
159#41—21no—
160#41—41no—
161C2×Q8—21no—
162C2×Q8D4×C911yescharacteristic
163C2×D4—22no—
164C2×D4—41no—
165C2×D4C23×C911yescharacteristic
166C22×C4D4×C912yes—
167Q16—41no—
168SD16—41no—
169M16—21no—
170C4⋊C4—21no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—21no—
174C4⋊C4—22no—
175C4⋊C4—42no—
176C22⋊C4—22no—
177C22⋊C4—22no—
178C22⋊C4—22no—
179C22⋊C4—42no—
180C22⋊C4D4×C912yes—
181C42—21no—
182C42D4×C911yescharacteristic
183C22×C3—22no—
184C22×C3—42no—
185C22×C3—41no—
186C22×C3—82no—
187C22×C3C3×#12011yescharacteristic
188C3×C4—21no—
189C3×C4—42no—
190C3×C4—41no—
191C3×C4—41no—
192C3×C4—42no—
193C3×C4—41no—
194C3×C4—82no—
195C9#220111yescharacteristic, direct product factor, Sylow
196C23—22no—
197C23C2×D4×C912yes—
198Q8—21no—
199Q8—41no—
200Q8—81no—
201D4—21no—
202D4—41no—
203D4—42no—
204D4—41no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4C2×D4×C911yescharacteristic
214C8—41no—
215C2×C3—21no—
216C2×C3—42no—
217C2×C3—81no—
218C2×C3C3×B(4,𝔽2)11yescharacteristic
219C22—22no—
220C22—42no—
221C22—41no—
222C22—82no—
223C22C9×#12011yescharacteristic
224C4—21no—
225C4—42no—
226C4—41no—
227C4—41no—
228C4—42no—
229C4—41no—
230C4—82no—
231C3C3×#220111yescharacteristic
232C2—21no—
233C2—42no—
234C2—81no—
235C2C9×B(4,𝔽2)11yescharacteristic
subgroupG/H
centerC2×C9B(4,𝔽2)
commutatorC2×D4C23×C9
Frattini, cosocleC2×C3×D4C23×C3
socleC2×C3C3×B(4,𝔽2)
prime radicalC3×H(5,𝔽2)C22×C3
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C9 ◁ C22×C9 ◁ C2×D4×C9 ◁ G

Complements

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

NH ≅ G/Ntype
1. C9×#563C2semidirect
4. C9×#354C2semidirect
5. C9×#352C2semidirect
49. #2201C9direct (N × H)
82. #563C2×C9semidirect
85. #354C2×C9semidirect
86. #352C2×C9semidirect
195. C9#2201direct (N × H)

Maximal subgroups

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

subgroupindex
C9×#5632
C9×#4582
C9×#4552
C9×#3542
C9×#3522
C3×#22013