Finite Group Databasebeta

← C9×#2061 #11766782

Subgroups — C9×#2061 #11766782

Order 1152.

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

normal subgroups only

This group has 345 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×#382C211yesmaximal, characteristic
4C9×#343C211yesmaximal, characteristic
5C9×#339C212yesmaximal
6C3×#2061C311yesmaximal, characteristic
7C2×C9×M16C2212yes—
8C9×C4⋊Q8—22no—
9C9×#125—22no—
10C9×C22⋊Q8—22no—
11C9×#117C2212yes—
12C2×C9×C4⋊C4C2211yescharacteristic
13C2×C9×C4⋊C4C2211yescharacteristic
14C2×C42×C9C2211yescharacteristic
15C9×#107—22no—
16C9×#106—22no—
17C9×#95—22no—
18C3×#544C2×C311yescharacteristic
19C3×#428C2×C312yes—
20C3×#382C2×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⋊C4D412yes—
36C9×C4⋊C4D412yes—
37C9×C22⋊C4—22no—
38C42×C9—22no—
39C42×C9—21no—
40C42×C9Q812yescomplemented
41#2061C911yescharacteristic, direct product factor, Sylow
42C2×C3×M16C22×C312yes—
43C3×C4⋊Q8—22no—
44C3×#125—22no—
45C3×C22⋊Q8—22no—
46C3×#117C22×C312yes—
47C2×C3×C4⋊C4C22×C311yescharacteristic
48C2×C3×C4⋊C4C22×C311yescharacteristic
49C2×C3×C42C22×C311yescharacteristic
50C3×#107—22no—
51C3×#106—22no—
52C3×#95—22no—
53C23×C9C2×D411yescharacteristic
54Q8×C9—82no—
55C2×C4×C9—22no—
56C2×C4×C9—22no—
57C2×C4×C9—22no—
58C2×C4×C9—22no—
59C2×C4×C9—41no—
60C2×C4×C9—41no—
61C2×C4×C9—42no—
62C2×C4×C9—42no—
63C2×C4×C9—41no—
64C2×C4×C9C2×D412yes—
65C2×C4×C9C2×Q812yes—
66C2×C4×C9C2×Q811yescharacteristic
67C2×C4×C9#4111yescharacteristic
68C8×C9—24no—
69#544C2×C911yescharacteristic
70#428C2×C912yes—
71#382C2×C911yescharacteristic
72#343C2×C911yescharacteristic
73#339C2×C912yes—
74C2×C3×Q8—22no—
75C22×C3×C4—21no—
76C22×C3×C4—21no—
77C22×C3×C4C3×D412yes—
78C22×C3×C4C23×C311yescharacteristic
79C3×M16—22no—
80C3×M16C3×Q814yes—
81C2×C3×C8—22no—
82C3×C4⋊C4—22no—
83C3×C4⋊C4—24no—
84C3×C4⋊C4—22no—
85C3×C4⋊C4—22no—
86C3×C4⋊C4C3×D412yes—
87C3×C4⋊C4C3×D412yes—
88C3×C22⋊C4—22no—
89C3×C42—22no—
90C3×C42—21no—
91C3×C42C3×Q812yes—
92C22×C9—21no—
93C22×C9—21no—
94C22×C9#12011yescharacteristic
95C22×C9C22⋊Q811yescharacteristic
96C22×C9C4⋊Q811yescharacteristic
97C4×C9—42no—
98C4×C9—42no—
99C4×C9—42no—
100C4×C9—42no—
101C4×C9—81no—
102C4×C9C22⋊Q812yes—
103C4×C9C4⋊Q812yes—
104C2×M16C22×C912yes—
105C4⋊Q8—22no—
106#125—22no—
107C22⋊Q8—22no—
108#117C22×C912yes—
109C2×C4⋊C4C22×C911yescharacteristic
110C2×C4⋊C4C22×C911yescharacteristic
111C2×C42C22×C911yescharacteristic
112#107—22no—
113#106—22no—
114#95—22no—
115C23×C3C2×C3×D411yescharacteristic
116C3×Q8—82no—
117C2×C3×C4—22no—
118C2×C3×C4—22no—
119C2×C3×C4—22no—
120C2×C3×C4—22no—
121C2×C3×C4—41no—
122C2×C3×C4—41no—
123C2×C3×C4—42no—
124C2×C3×C4—42no—
125C2×C3×C4—41no—
126C2×C3×C4C2×C3×D412yes—
127C2×C3×C4C2×C3×Q812yes—
128C2×C3×C4C2×C3×Q811yescharacteristic
129C2×C3×C4C3×#4111yescharacteristic
130C3×C8—24no—
131C2×C9—21no—
132C2×C9—21no—
133C2×C9#39511yescharacteristic
134C2×C9#45411yescharacteristic
135C2×C9#45511yescharacteristic
136C2×Q8—22no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4D4×C912yes—
140C22×C4C23×C911yescharacteristic
141M16—22no—
142M16Q8×C914yescomplemented
143C2×C8—22no—
144C4⋊C4—22no—
145C4⋊C4—24no—
146C4⋊C4—22no—
147C4⋊C4—22no—
148C4⋊C4D4×C912yes—
149C4⋊C4D4×C912yes—
150C22⋊C4—22no—
151C42—22no—
152C42—21no—
153C42Q8×C912yescomplemented
154C22×C3—21no—
155C22×C3—21no—
156C22×C3C3×#12011yescharacteristic
157C22×C3C3×C22⋊Q811yescharacteristic
158C22×C3C3×C4⋊Q811yescharacteristic
159C3×C4—42no—
160C3×C4—42no—
161C3×C4—42no—
162C3×C4—42no—
163C3×C4—81no—
164C3×C4C3×C22⋊Q812yes—
165C3×C4C3×C4⋊Q812yes—
166C9#206111yescharacteristic, direct product factor, Sylow
167C23C2×D4×C911yescharacteristic
168Q8—82no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—41no—
178C2×C4C2×D4×C912yes—
179C2×C4C2×Q8×C912yes—
180C2×C4C2×Q8×C911yescharacteristic
181C2×C4C9×#4111yescharacteristic
182C8—24no—
183C2×C3—21no—
184C2×C3—21no—
185C2×C3C3×#39511yescharacteristic
186C2×C3C3×#45411yescharacteristic
187C2×C3C3×#45511yescharacteristic
188C22—21no—
189C22—21no—
190C22C9×#12011yescharacteristic
191C22C9×C22⋊Q811yescharacteristic
192C22C9×C4⋊Q811yescharacteristic
193C4—42no—
194C4—42no—
195C4—42no—
196C4—42no—
197C4—81no—
198C4C9×C22⋊Q812yes—
199C4C9×C4⋊Q812yes—
200C3C3×#206111yescharacteristic
201C2—21no—
202C2—21no—
203C2C9×#39511yescharacteristic
204C2C9×#45411yescharacteristic
205C2C9×#45511yescharacteristic
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
40. C42×C9Q8semidirect
41. #2061C9direct (N × H)
142. M16Q8×C9semidirect
153. C42Q8×C9semidirect
166. C9#2061direct (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×#3822
C9×#3432
C9×#3392
C3×#20613