Finite Group Databasebeta

← C9×#2060 #11766781

Subgroups — C9×#2060 #11766781

Order 1152.

369 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 369 conjugacy classes of subgroups — too many to draw. Only its 138 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×#544C211yesmaximal, characteristic
2C9×#428C212yesmaximal
3C9×#384C211yesmaximal, characteristic
4C9×#343C211yesmaximal, characteristic
5C9×#339C212yesmaximal
6C3×#2060C311yesmaximal, characteristic
7C2×C9×M16C2212yes—
8C9×C4⋊Q8—22no—
9C9×#125—22no—
10C9×C22⋊Q8—22no—
11C9×#117C2212yes—
12C2×C9×C4⋊C4—22no—
13C2×C9×C4⋊C4C2211yescharacteristic
14C2×C9×C4⋊C4C2211yescharacteristic
15C2×C42×C9C2211yescharacteristic
16C9×#107—22no—
17C9×#106—22no—
18C3×#544C2×C311yescharacteristic
19C3×#428C2×C312yes—
20C3×#384C2×C311yescharacteristic
21C3×#343C2×C311yescharacteristic
22C3×#339C2×C312yes—
23C2×Q8×C9—22no—
24C22×C4×C9—21no—
25C22×C4×C9—21no—
26C22×C4×C9D412yes—
27C22×C4×C9C2311yescharacteristic
28C9×M16—22no—
29C9×M16Q814yescomplemented
30C2×C8×C9—22no—
31C9×C4⋊C4—22no—
32C9×C4⋊C4—24no—
33C9×C4⋊C4—22no—
34C9×C4⋊C4—22no—
35C9×C4⋊C4—44no—
36C9×C4⋊C4D412yes—
37C9×C4⋊C4D412yes—
38C9×C22⋊C4—22no—
39C42×C9—22no—
40C42×C9—21no—
41C42×C9Q812yescomplemented
42#2060C911yescharacteristic, direct product factor, Sylow
43C2×C3×M16C22×C312yes—
44C3×C4⋊Q8—22no—
45C3×#125—22no—
46C3×C22⋊Q8—22no—
47C3×#117C22×C312yes—
48C2×C3×C4⋊C4—22no—
49C2×C3×C4⋊C4C22×C311yescharacteristic
50C2×C3×C4⋊C4C22×C311yescharacteristic
51C2×C3×C42C22×C311yescharacteristic
52C3×#107—22no—
53C3×#106—22no—
54C23×C9C2×D411yescharacteristic
55Q8×C9—82no—
56C2×C4×C9—22no—
57C2×C4×C9—22no—
58C2×C4×C9—22no—
59C2×C4×C9—22no—
60C2×C4×C9—22no—
61C2×C4×C9—22no—
62C2×C4×C9—42no—
63C2×C4×C9—42no—
64C2×C4×C9—41no—
65C2×C4×C9C2×D412yes—
66C2×C4×C9C2×Q812yes—
67C2×C4×C9C2×Q811yescharacteristic
68C2×C4×C9#4111yescharacteristic
69C8×C9—24no—
70#544C2×C911yescharacteristic
71#428C2×C912yes—
72#384C2×C911yescharacteristic
73#343C2×C911yescharacteristic
74#339C2×C912yes—
75C2×C3×Q8—22no—
76C22×C3×C4—21no—
77C22×C3×C4—21no—
78C22×C3×C4C3×D412yes—
79C22×C3×C4C23×C311yescharacteristic
80C3×M16—22no—
81C3×M16C3×Q814yes—
82C2×C3×C8—22no—
83C3×C4⋊C4—22no—
84C3×C4⋊C4—24no—
85C3×C4⋊C4—22no—
86C3×C4⋊C4—22no—
87C3×C4⋊C4—44no—
88C3×C4⋊C4C3×D412yes—
89C3×C4⋊C4C3×D412yes—
90C3×C22⋊C4—22no—
91C3×C42—22no—
92C3×C42—21no—
93C3×C42C3×Q812yes—
94C22×C9—21no—
95C22×C9—21no—
96C22×C9#12011yescharacteristic
97C22×C9C22⋊Q811yescharacteristic
98C22×C9C4⋊Q811yescharacteristic
99C4×C9—24no—
100C4×C9—42no—
101C4×C9—42no—
102C4×C9—42no—
103C4×C9—81no—
104C4×C9C22⋊Q812yes—
105C4×C9C4⋊Q812yes—
106C2×M16C22×C912yes—
107C4⋊Q8—22no—
108#125—22no—
109C22⋊Q8—22no—
110#117C22×C912yes—
111C2×C4⋊C4—22no—
112C2×C4⋊C4C22×C911yescharacteristic
113C2×C4⋊C4C22×C911yescharacteristic
114C2×C42C22×C911yescharacteristic
115#107—22no—
116#106—22no—
117C23×C3C2×C3×D411yescharacteristic
118C3×Q8—82no—
119C2×C3×C4—22no—
120C2×C3×C4—22no—
121C2×C3×C4—22no—
122C2×C3×C4—22no—
123C2×C3×C4—22no—
124C2×C3×C4—22no—
125C2×C3×C4—42no—
126C2×C3×C4—42no—
127C2×C3×C4—41no—
128C2×C3×C4C2×C3×D412yes—
129C2×C3×C4C2×C3×Q812yes—
130C2×C3×C4C2×C3×Q811yescharacteristic
131C2×C3×C4C3×#4111yescharacteristic
132C3×C8—24no—
133C2×C9—21no—
134C2×C9—21no—
135C2×C9#39511yescharacteristic
136C2×C9#45311yescharacteristic
137C2×C9#45611yescharacteristic
138C2×Q8—22no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4D4×C912yes—
142C22×C4C23×C911yescharacteristic
143M16—22no—
144M16Q8×C914yescomplemented
145C2×C8—22no—
146C4⋊C4—22no—
147C4⋊C4—24no—
148C4⋊C4—22no—
149C4⋊C4—22no—
150C4⋊C4—44no—
151C4⋊C4D4×C912yes—
152C4⋊C4D4×C912yes—
153C22⋊C4—22no—
154C42—22no—
155C42—21no—
156C42Q8×C912yescomplemented
157C22×C3—21no—
158C22×C3—21no—
159C22×C3C3×#12011yescharacteristic
160C22×C3C3×C22⋊Q811yescharacteristic
161C22×C3C3×C4⋊Q811yescharacteristic
162C3×C4—24no—
163C3×C4—42no—
164C3×C4—42no—
165C3×C4—42no—
166C3×C4—81no—
167C3×C4C3×C22⋊Q812yes—
168C3×C4C3×C4⋊Q812yes—
169C9#206011yescharacteristic, direct product factor, Sylow
170C23C2×D4×C911yescharacteristic
171Q8—82no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—41no—
181C2×C4C2×D4×C912yes—
182C2×C4C2×Q8×C912yes—
183C2×C4C2×Q8×C911yescharacteristic
184C2×C4C9×#4111yescharacteristic
185C8—24no—
186C2×C3—21no—
187C2×C3—21no—
188C2×C3C3×#39511yescharacteristic
189C2×C3C3×#45311yescharacteristic
190C2×C3C3×#45611yescharacteristic
191C22—21no—
192C22—21no—
193C22C9×#12011yescharacteristic
194C22C9×C22⋊Q811yescharacteristic
195C22C9×C4⋊Q811yescharacteristic
196C4—24no—
197C4—42no—
198C4—42no—
199C4—42no—
200C4—81no—
201C4C9×C22⋊Q812yes—
202C4C9×C4⋊Q812yes—
203C3C3×#206011yescharacteristic
204C2—21no—
205C2—21no—
206C2C9×#39511yescharacteristic
207C2C9×#45311yescharacteristic
208C2C9×#45611yescharacteristic
subgroupG/H
centerC22×C9#120
commutatorC22×C4C23×C9
Frattini, cosocleC22×C3×C4C23×C3
socleC22×C3C3×#120
prime radicalC23×C3C2×C3×D4
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
29. C9×M16Q8semidirect
41. C42×C9Q8semidirect
42. #2060C9direct (N × H)
144. M16Q8×C9semidirect
156. C42Q8×C9semidirect
169. C9#2060direct (N × H)

Maximal subgroups

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

subgroupindex
C9×#5442
C9×#4282
C9×#3842
C9×#3432
C9×#3392
C3×#20603