Finite Group Databasebeta

← C9×#2218 #11766939

Subgroups — C9×#2218 #11766939

Order 1152.

255 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 255 conjugacy classes of subgroups — too many to draw. Only its 96 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
1C2×C9×D16C211yesmaximal, characteristic, complemented
2C2×C9×M32C211yesmaximal, characteristic, complemented
3C9×#466C212yesmaximal, complemented
4C9×#367C211yesmaximal, characteristic, complemented
5C9×#357C212yesmaximal, complemented
6C3×#2218C311yesmaximal, characteristic
7C2×C9×D8C2212yes—
8C22×C8×C9C2211yescharacteristic
9C9×#121—22no—
10C9×D16—22no—
11C9×M32—22no—
12C2×C9×C16C2211yescharacteristic
13C2×C9×C16C2211yescharacteristic
14C9×#107C2212yes—
15C9×#102—22no—
16C2×C3×D16C2×C311yescharacteristic
17C2×C3×M32C2×C311yescharacteristic
18C3×#466C2×C312yes—
19C3×#367C2×C311yescharacteristic
20C3×#357C2×C312yes—
21C2×D4×C9—22no—
22C2×D4×C9—42no—
23C22×C4×C9D411yescharacteristic
24C9×D8—22no—
25C9×D8—22no—
26C2×C8×C9—21no—
27C2×C8×C9—21no—
28C2×C8×C9D411yescharacteristic
29C2×C8×C9C2311yescharacteristic
30C9×C4⋊C4—22no—
31C9×C22⋊C4—42no—
32C9×C16—21no—
33C9×C16D412yescomplemented
34#2218C911yescharacteristic, direct product factor, Sylow
35C2×C3×D8C22×C312yes—
36C22×C3×C8C22×C311yescharacteristic
37C3×#121—22no—
38C3×D16—22no—
39C3×M32—22no—
40C2×C3×C16C22×C311yescharacteristic
41C2×C3×C16C22×C311yescharacteristic
42C3×#107C22×C312yes—
43C3×#102—22no—
44C23×C9—42no—
45C23×C9D811yescharacteristic
46D4×C9—42no—
47D4×C9—42no—
48D4×C9—84no—
49C2×C4×C9—21no—
50C2×C4×C9—21no—
51C2×C4×C9—42no—
52C2×C4×C9D811yescharacteristic
53C2×C4×C9C2×D411yescharacteristic
54C8×C9—21no—
55C8×C9C2×D411yescharacteristic
56C8×C9#4111yescharacteristic
57C2×D16C2×C911yescharacteristic, complemented
58C2×M32C2×C911yescharacteristic, complemented
59#466C2×C912yescomplemented
60#367C2×C911yescharacteristic, complemented
61#357C2×C912yescomplemented
62C2×C3×D4—22no—
63C2×C3×D4—42no—
64C22×C3×C4C3×D411yescharacteristic
65C3×D8—22no—
66C3×D8—22no—
67C2×C3×C8—21no—
68C2×C3×C8—21no—
69C2×C3×C8C3×D411yescharacteristic
70C2×C3×C8C23×C311yescharacteristic
71C3×C4⋊C4—22no—
72C3×C22⋊C4—42no—
73C3×C16—21no—
74C3×C16C3×D412yes—
75C22×C9—21no—
76C22×C9—22no—
77C22×C9—82no—
78C22×C9—82no—
79C22×C9—82no—
80C22×C9C2×D811yescharacteristic
81C4×C9—21no—
82C4×C9—82no—
83C4×C9#12111yescharacteristic
84C4×C9#13511yescharacteristic
85C2×D8C22×C912yes—
86C22×C8C22×C911yescharacteristic
87#121—22no—
88D16—22no—
89M32—22no—
90C2×C16C22×C911yescharacteristic
91C2×C16C22×C911yescharacteristic
92#107C22×C912yes—
93#102—22no—
94C23×C3—42no—
95C23×C3C3×D811yescharacteristic
96C3×D4—42no—
97C3×D4—42no—
98C3×D4—84no—
99C2×C3×C4—21no—
100C2×C3×C4—21no—
101C2×C3×C4—42no—
102C2×C3×C4C3×D811yescharacteristic
103C2×C3×C4C2×C3×D411yescharacteristic
104C3×C8—21no—
105C3×C8C2×C3×D411yescharacteristic
106C3×C8C3×#4111yescharacteristic
107C2×C9—41no—
108C2×C9—162no—
109C2×C9#46611yescharacteristic
110C2×C9#50912yes—
111C2×D4—22no—
112C2×D4—42no—
113C22×C4D4×C911yescharacteristic
114D8—22no—
115D8—22no—
116C2×C8—21no—
117C2×C8—21no—
118C2×C8D4×C911yescharacteristic
119C2×C8C23×C911yescharacteristic
120C4⋊C4—22no—
121C22⋊C4—42no—
122C16—21no—
123C16D4×C912yescomplemented
124C22×C3—22no—
125C22×C3—21no—
126C22×C3—82no—
127C22×C3—82no—
128C22×C3—82no—
129C22×C3C2×C3×D811yescharacteristic
130C3×C4—21no—
131C3×C4—82no—
132C3×C4C3×#12111yescharacteristic
133C3×C4C3×#13511yescharacteristic
134C9#221811yescharacteristic, direct product factor, Sylow
135C23—42no—
136C23C9×D811yescharacteristic
137D4—42no—
138D4—42no—
139D4—84no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—42no—
143C2×C4C9×D811yescharacteristic
144C2×C4C2×D4×C911yescharacteristic
145C8—21no—
146C8C2×D4×C911yescharacteristic
147C8C9×#4111yescharacteristic
148C2×C3—41no—
149C2×C3—162no—
150C2×C3C3×#46611yescharacteristic
151C2×C3C3×#50912yes—
152C22—21no—
153C22—22no—
154C22—82no—
155C22—82no—
156C22—82no—
157C22C2×C9×D811yescharacteristic
158C4—21no—
159C4—82no—
160C4C9×#12111yescharacteristic
161C4C9×#13511yescharacteristic
162C3C3×#221811yescharacteristic
163C2—41no—
164C2—162no—
165C2C9×#46611yescharacteristic
166C2C9×#50912yes—
subgroupG/H
centerC22×C9C2×D8
commutatorC2×C8C23×C9
Frattini, cosocleC2×C3×C8C23×C3
socleC22×C3C2×C3×D8
prime radicalC3×#2218C3
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. C2×C9×D16C2semidirect
2. C2×C9×M32C2semidirect
3. C9×#466C2semidirect
4. C9×#367C2semidirect
5. C9×#357C2semidirect
33. C9×C16D4semidirect
34. #2218C9direct (N × H)
57. C2×D16C2×C9semidirect
58. C2×M32C2×C9semidirect
59. #466C2×C9semidirect
60. #367C2×C9semidirect
61. #357C2×C9semidirect
123. C16D4×C9semidirect
134. C9#2218direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C9×D162
C2×C9×M322
C9×#4662
C9×#3672
C9×#3572
C3×#22183