Finite Group Databasebeta

← C9×#2185 #11766906

Subgroups — C9×#2185 #11766906

Order 1152.

339 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 339 conjugacy classes of subgroups — too many to draw. Only its 108 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
1C22×C9×Q16C211yesmaximal, characteristic, complemented
2C2×C9×SD32C212yesmaximal, complemented
3C9×#466C211yesmaximal, characteristic
4C9×#358C212yesmaximal, complemented
5C9×C22⋊C16C211yesmaximal, characteristic, complemented
6C3×#2185C311yesmaximal, characteristic
7C22×Q8×C9—21no—
8C2×C9×Q16—24no—
9C2×C9×Q16—21no—
10C2×C9×Q16C2212yes—
11C2×C9×D8C2211yescharacteristic
12C22×C8×C9C2211yescharacteristic
13C9×#121—21no—
14C9×SD32—24no—
15C2×C9×C16C2212yes—
16C9×#107C2211yescharacteristic
17C9×#102—21no—
18C22×C3×Q16C2×C311yescharacteristic
19C2×C3×SD32C2×C312yes—
20C3×#466C2×C311yescharacteristic
21C3×#358C2×C312yes—
22C3×C22⋊C16C2×C311yescharacteristic
23C2×Q8×C9—24no—
24C2×Q8×C9—22no—
25C2×Q8×C9—42no—
26C2×Q8×C9—41no—
27C2×D4×C9—21no—
28C2×D4×C9—41no—
29C22×C4×C9—41no—
30C22×C4×C9D411yescharacteristic
31C9×Q16—24no—
32C9×Q16—22no—
33C9×Q16D414yescomplemented
34C9×D8—22no—
35C2×C8×C9—22no—
36C2×C8×C9D411yescharacteristic
37C2×C8×C9C2311yescharacteristic
38C9×C4⋊C4—21no—
39C9×C22⋊C4—41no—
40C9×C16—22no—
41#2185C911yescharacteristic, direct product factor, Sylow
42C22×C3×Q8—21no—
43C2×C3×Q16—24no—
44C2×C3×Q16—21no—
45C2×C3×Q16C22×C312yes—
46C2×C3×D8C22×C311yescharacteristic
47C22×C3×C8C22×C311yescharacteristic
48C3×#121—21no—
49C3×SD32—24no—
50C2×C3×C16C22×C312yes—
51C3×#107C22×C311yescharacteristic
52C3×#102—21no—
53C23×C9—41no—
54C23×C9D811yescharacteristic
55Q8×C9—24no—
56Q8×C9—44no—
57Q8×C9—42no—
58D4×C9—41no—
59D4×C9—41no—
60D4×C9—82no—
61C2×C4×C9—21no—
62C2×C4×C9—21no—
63C2×C4×C9—44no—
64C2×C4×C9—42no—
65C2×C4×C9—41no—
66C2×C4×C9D811yescharacteristic
67C2×C4×C9C2×D411yescharacteristic
68C8×C9—21no—
69C8×C9C2×D412yes—
70C22×Q16C2×C911yescharacteristic, complemented
71C2×SD32C2×C912yescomplemented
72#466C2×C911yescharacteristic
73#358C2×C912yescomplemented
74C22⋊C16C2×C911yescharacteristic, complemented
75C2×C3×Q8—24no—
76C2×C3×Q8—22no—
77C2×C3×Q8—42no—
78C2×C3×Q8—41no—
79C2×C3×D4—21no—
80C2×C3×D4—41no—
81C22×C3×C4—41no—
82C22×C3×C4C3×D411yescharacteristic
83C3×Q16—24no—
84C3×Q16—22no—
85C3×Q16C3×D414yes—
86C3×D8—22no—
87C2×C3×C8—22no—
88C2×C3×C8C3×D411yescharacteristic
89C2×C3×C8C23×C311yescharacteristic
90C3×C4⋊C4—21no—
91C3×C22⋊C4—41no—
92C3×C16—22no—
93C22×C9—21no—
94C22×C9—21no—
95C22×C9—81no—
96C22×C9—81no—
97C22×C9—81no—
98C22×C9SD3212yescomplemented
99C22×C9C2×D811yescharacteristic
100C4×C9—21no—
101C4×C9—44no—
102C4×C9—81no—
103C4×C9#12011yescharacteristic
104C4×C9AGL(1,ℤ/8)11yescharacteristic
105C22×Q8—21no—
106C2×Q16—24no—
107C2×Q16—21no—
108C2×Q16C22×C912yes—
109C2×D8C22×C911yescharacteristic
110C22×C8C22×C911yescharacteristic
111#121—21no—
112SD32—24no—
113C2×C16C22×C912yes—
114#107C22×C911yescharacteristic
115#102—21no—
116C23×C3—41no—
117C23×C3C3×D811yescharacteristic
118C3×Q8—24no—
119C3×Q8—44no—
120C3×Q8—42no—
121C3×D4—41no—
122C3×D4—41no—
123C3×D4—82no—
124C2×C3×C4—21no—
125C2×C3×C4—21no—
126C2×C3×C4—44no—
127C2×C3×C4—42no—
128C2×C3×C4—41no—
129C2×C3×C4C3×D811yescharacteristic
130C2×C3×C4C2×C3×D411yescharacteristic
131C3×C8—21no—
132C3×C8C2×C3×D412yes—
133C2×C9—22no—
134C2×C9—161no—
135C2×C9#44711yescharacteristic
136C2×C9C2×SD3211yescharacteristic
137C2×C9#51011yescharacteristic
138C2×Q8—24no—
139C2×Q8—22no—
140C2×Q8—42no—
141C2×Q8—41no—
142C2×D4—21no—
143C2×D4—41no—
144C22×C4—41no—
145C22×C4D4×C911yescharacteristic
146Q16—24no—
147Q16—22no—
148Q16D4×C914yescomplemented
149D8—22no—
150C2×C8—22no—
151C2×C8D4×C911yescharacteristic
152C2×C8C23×C911yescharacteristic
153C4⋊C4—21no—
154C22⋊C4—41no—
155C16—22no—
156C22×C3—21no—
157C22×C3—21no—
158C22×C3—81no—
159C22×C3—81no—
160C22×C3—81no—
161C22×C3C3×SD3212yes—
162C22×C3C2×C3×D811yescharacteristic
163C3×C4—21no—
164C3×C4—44no—
165C3×C4—81no—
166C3×C4C3×#12011yescharacteristic
167C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
168C9#218511yescharacteristic, direct product factor, Sylow
169C23—41no—
170C23C9×D811yescharacteristic
171Q8—24no—
172Q8—44no—
173Q8—42no—
174D4—41no—
175D4—41no—
176D4—82no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—44no—
180C2×C4—42no—
181C2×C4—41no—
182C2×C4C9×D811yescharacteristic
183C2×C4C2×D4×C911yescharacteristic
184C8—21no—
185C8C2×D4×C912yes—
186C2×C3—22no—
187C2×C3—161no—
188C2×C3C3×#44711yescharacteristic
189C2×C3C2×C3×SD3211yescharacteristic
190C2×C3C3×#51011yescharacteristic
191C22—21no—
192C22—21no—
193C22—81no—
194C22—81no—
195C22—81no—
196C22C9×SD3212yescomplemented
197C22C2×C9×D811yescharacteristic
198C4—21no—
199C4—44no—
200C4—81no—
201C4C9×#12011yescharacteristic
202C4C9×AGL(1,ℤ/8)11yescharacteristic
203C3C3×#218511yescharacteristic
204C2—22no—
205C2—161no—
206C2C9×#44711yescharacteristic
207C2C2×C9×SD3211yescharacteristic
208C2C9×#51011yescharacteristic
subgroupG/H
centerC22×C9C2×D8
commutatorC2×C8C23×C9
Frattini, cosocleC2×C3×C8C23×C3
socleC22×C3C2×C3×D8
prime radicalC3×#466C2×C3
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C9 ◁ C22×C4×C9 ◁ C22×C8×C9 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C9×Q16C2semidirect
2. C2×C9×SD32C2semidirect
4. C9×#358C2semidirect
5. C9×C22⋊C16C2semidirect
33. C9×Q16D4semidirect
41. #2185C9direct (N × H)
70. C22×Q16C2×C9semidirect
71. C2×SD32C2×C9semidirect
73. #358C2×C9semidirect
74. C22⋊C16C2×C9semidirect
98. C22×C9SD32semidirect
148. Q16D4×C9semidirect
168. C9#2185direct (N × H)
196. C22C9×SD32semidirect

Maximal subgroups

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

subgroupindex
C22×C9×Q162
C2×C9×SD322
C9×#4662
C9×#3582
C9×C22⋊C162
C3×#21853