Finite Group Databasebeta

← C9×#2213 #11766934

Subgroups — C9×#2213 #11766934

Order 1152.

255 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 255 conjugacy classes of subgroups — too many to draw. Only its 90 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×#509C212yesmaximal, complemented
2C9×#493C211yesmaximal, characteristic, complemented
3C9×#443C211yesmaximal, characteristic, complemented
4C9×#364C211yesmaximal, characteristic, complemented
5C9×#361C212yesmaximal, complemented
6C3×#2213C311yesmaximal, characteristic
7C9×#135C2211yescharacteristic
8C2×C9×D8—21no—
9C2×C9×D8C2212yes—
10C9×#131—21no—
11C9×#127—21no—
12C9×SD32—22no—
13C9×D16—22no—
14C9×M32C2212yes—
15C9×#108C2211yescharacteristic
16C9×#104—21no—
17C4×C8×C9C2211yescharacteristic
18C3×#509C2×C312yes—
19C3×#493C2×C311yescharacteristic
20C3×#443C2×C311yescharacteristic
21C3×#364C2×C311yescharacteristic
22C3×#361C2×C312yes—
23C9×#41—21no—
24C2×D4×C9—22no—
25C2×D4×C9—42no—
26C9×Q16D411yescharacteristic, complemented
27C9×SD16—21no—
28C9×D8—22no—
29C9×D8—22no—
30C9×D8—41no—
31C9×D8—41no—
32C9×D8D411yescharacteristic, complemented
33C9×M16—21no—
34C9×M16—41no—
35C2×C8×C9—41no—
36C2×C8×C9D411yescharacteristic
37C2×C8×C9C2311yescharacteristic
38C42×C9D411yescharacteristic
39C9×C16—22no—
40#2213C911yescharacteristic, direct product factor, Sylow
41C3×#135C22×C311yescharacteristic
42C2×C3×D8—21no—
43C2×C3×D8C22×C312yes—
44C3×#131—21no—
45C3×#127—21no—
46C3×SD32—22no—
47C3×D16—22no—
48C3×M32C22×C312yes—
49C3×#108C22×C311yescharacteristic
50C3×#104—21no—
51C3×C4×C8C22×C311yescharacteristic
52C23×C9—42no—
53Q8×C9—21no—
54D4×C9—21no—
55D4×C9—41no—
56D4×C9—42no—
57D4×C9—42no—
58D4×C9—84no—
59C2×C4×C9—21no—
60C2×C4×C9—41no—
61C2×C4×C9C2×D411yescharacteristic
62C8×C9—41no—
63C8×C9D811yescharacteristic
64C8×C9D811yescharacteristic
65C8×C9C2×D411yescharacteristic
66C8×C9#4111yescharacteristic
67#509C2×C912yescomplemented
68#493C2×C911yescharacteristic, complemented
69#443C2×C911yescharacteristic, complemented
70#364C2×C911yescharacteristic, complemented
71#361C2×C912yescomplemented
72C3×#41—21no—
73C2×C3×D4—22no—
74C2×C3×D4—42no—
75C3×Q16C3×D411yescharacteristic
76C3×SD16—21no—
77C3×D8—22no—
78C3×D8—22no—
79C3×D8—41no—
80C3×D8—41no—
81C3×D8C3×D411yescharacteristic
82C3×M16—21no—
83C3×M16—41no—
84C2×C3×C8—41no—
85C2×C3×C8C3×D411yescharacteristic
86C2×C3×C8C23×C311yescharacteristic
87C3×C42C3×D411yescharacteristic
88C3×C16—22no—
89C22×C9—41no—
90C22×C9—84no—
91C22×C9—82no—
92C22×C9AGL(1,ℤ/8)11yescharacteristic
93C4×C9—22no—
94C4×C9—41no—
95C4×C9#12111yescharacteristic
96C4×C9C2×D811yescharacteristic
97#135C22×C911yescharacteristic
98C2×D8—21no—
99C2×D8C22×C912yes—
100#131—21no—
101#127—21no—
102SD32—22no—
103D16—22no—
104M32C22×C912yes—
105#108C22×C911yescharacteristic
106#104—21no—
107C4×C8C22×C911yescharacteristic
108C23×C3—42no—
109C3×Q8—21no—
110C3×D4—21no—
111C3×D4—41no—
112C3×D4—42no—
113C3×D4—42no—
114C3×D4—84no—
115C2×C3×C4—21no—
116C2×C3×C4—41no—
117C2×C3×C4C2×C3×D411yescharacteristic
118C3×C8—41no—
119C3×C8C3×D811yescharacteristic
120C3×C8C3×D811yescharacteristic
121C3×C8C2×C3×D411yescharacteristic
122C3×C8C3×#4111yescharacteristic
123C2×C9—21no—
124C2×C9—81no—
125C2×C9—162no—
126C2×C9#45911yescharacteristic
127#41—21no—
128C2×D4—22no—
129C2×D4—42no—
130Q16D4×C911yescharacteristic, complemented
131SD16—21no—
132D8—22no—
133D8—22no—
134D8—41no—
135D8—41no—
136D8D4×C911yescharacteristic, complemented
137M16—21no—
138M16—41no—
139C2×C8—41no—
140C2×C8D4×C911yescharacteristic
141C2×C8C23×C911yescharacteristic
142C42D4×C911yescharacteristic
143C16—22no—
144C22×C3—41no—
145C22×C3—84no—
146C22×C3—82no—
147C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
148C3×C4—22no—
149C3×C4—41no—
150C3×C4C3×#12111yescharacteristic
151C3×C4C2×C3×D811yescharacteristic
152C9#221311yescharacteristic, direct product factor, Sylow
153C23—42no—
154Q8—21no—
155D4—21no—
156D4—41no—
157D4—42no—
158D4—42no—
159D4—84no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4C2×D4×C911yescharacteristic
163C8—41no—
164C8C9×D811yescharacteristic
165C8C9×D811yescharacteristic
166C8C2×D4×C911yescharacteristic
167C8C9×#4111yescharacteristic
168C2×C3—21no—
169C2×C3—81no—
170C2×C3—162no—
171C2×C3C3×#45911yescharacteristic
172C22—41no—
173C22—84no—
174C22—82no—
175C22C9×AGL(1,ℤ/8)11yescharacteristic
176C4—22no—
177C4—41no—
178C4C9×#12111yescharacteristic
179C4C2×C9×D811yescharacteristic
180C3C3×#221311yescharacteristic
181C2—21no—
182C2—81no—
183C2—162no—
184C2C9×#45911yescharacteristic
subgroupG/H
centerC2×C9#459
commutatorC2×C8C23×C9
Frattini, cosocleC2×C3×C8C23×C3
socleC2×C3C3×#459
prime radicalC3×#2213C3
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C9 ◁ C2×C4×C9 ◁ C4×C8×C9 ◁ G

Complements

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

NH ≅ G/Ntype
1. C9×#509C2semidirect
2. C9×#493C2semidirect
3. C9×#443C2semidirect
4. C9×#364C2semidirect
5. C9×#361C2semidirect
26. C9×Q16D4semidirect
32. C9×D8D4semidirect
40. #2213C9direct (N × H)
67. #509C2×C9semidirect
68. #493C2×C9semidirect
69. #443C2×C9semidirect
70. #364C2×C9semidirect
71. #361C2×C9semidirect
130. Q16D4×C9semidirect
136. D8D4×C9semidirect
152. C9#2213direct (N × H)

Maximal subgroups

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

subgroupindex
C9×#5092
C9×#4932
C9×#4432
C9×#3642
C9×#3612
C3×#22133