Finite Group Databasebeta

← C9×#2215 #11766936

Subgroups — C9×#2215 #11766936

Order 1152.

261 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 261 conjugacy classes of subgroups — too many to draw. Only its 102 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
2C22×C9×C16C211yesmaximal, characteristic, complemented
3C9×#466C212yesmaximal, complemented
4C9×#366C211yesmaximal, characteristic, complemented
5C9×#357C212yesmaximal, complemented
6C3×#2215C311yesmaximal, characteristic
7C2×C9×D8C2212yes—
8C22×C8×C9C2211yescharacteristic
9C9×#121—22no—
10C9×D16—22no—
11C2×C9×C16—22no—
12C2×C9×C16C2211yescharacteristic
13C2×C9×C16C2211yescharacteristic
14C9×#107C2212yes—
15C9×#102—22no—
16C2×C3×D16C2×C311yescharacteristic
17C22×C3×C16C2×C311yescharacteristic
18C3×#466C2×C312yes—
19C3×#366C2×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#2215C911yescharacteristic, direct product factor, Sylow
35C2×C3×D8C22×C312yes—
36C22×C3×C8C22×C311yescharacteristic
37C3×#121—22no—
38C3×D16—22no—
39C2×C3×C16—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
58C22×C16C2×C911yescharacteristic, complemented
59#466C2×C912yescomplemented
60#366C2×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—21no—
77C22×C9—82no—
78C22×C9—82no—
79C22×C9—82no—
80C22×C9D1612yescomplemented
81C22×C9C2×D811yescharacteristic
82C4×C9—21no—
83C4×C9—82no—
84C4×C9#12111yescharacteristic
85C4×C9#13511yescharacteristic
86C2×D8C22×C912yes—
87C22×C8C22×C911yescharacteristic
88#121—22no—
89D16—22no—
90C2×C16—22no—
91C2×C16C22×C911yescharacteristic
92C2×C16C22×C911yescharacteristic
93#107C22×C912yes—
94#102—22no—
95C23×C3—42no—
96C23×C3C3×D811yescharacteristic
97C3×D4—42no—
98C3×D4—42no—
99C3×D4—84no—
100C2×C3×C4—21no—
101C2×C3×C4—21no—
102C2×C3×C4—42no—
103C2×C3×C4C3×D811yescharacteristic
104C2×C3×C4C2×C3×D411yescharacteristic
105C3×C8—21no—
106C3×C8C2×C3×D411yescharacteristic
107C3×C8C3×#4111yescharacteristic
108C2×C9—22no—
109C2×C9—162no—
110C2×C9#46611yescharacteristic
111C2×C9C2×D1611yescharacteristic
112C2×C9#50811yescharacteristic
113C2×D4—22no—
114C2×D4—42no—
115C22×C4D4×C911yescharacteristic
116D8—22no—
117D8—22no—
118C2×C8—21no—
119C2×C8—21no—
120C2×C8D4×C911yescharacteristic
121C2×C8C23×C911yescharacteristic
122C4⋊C4—22no—
123C22⋊C4—42no—
124C16—21no—
125C16D4×C912yescomplemented
126C22×C3—21no—
127C22×C3—21no—
128C22×C3—82no—
129C22×C3—82no—
130C22×C3—82no—
131C22×C3C3×D1612yes—
132C22×C3C2×C3×D811yescharacteristic
133C3×C4—21no—
134C3×C4—82no—
135C3×C4C3×#12111yescharacteristic
136C3×C4C3×#13511yescharacteristic
137C9#221511yescharacteristic, direct product factor, Sylow
138C23—42no—
139C23C9×D811yescharacteristic
140D4—42no—
141D4—42no—
142D4—84no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—42no—
146C2×C4C9×D811yescharacteristic
147C2×C4C2×D4×C911yescharacteristic
148C8—21no—
149C8C2×D4×C911yescharacteristic
150C8C9×#4111yescharacteristic
151C2×C3—22no—
152C2×C3—162no—
153C2×C3C3×#46611yescharacteristic
154C2×C3C2×C3×D1611yescharacteristic
155C2×C3C3×#50811yescharacteristic
156C22—21no—
157C22—21no—
158C22—82no—
159C22—82no—
160C22—82no—
161C22C9×D1612yescomplemented
162C22C2×C9×D811yescharacteristic
163C4—21no—
164C4—82no—
165C4C9×#12111yescharacteristic
166C4C9×#13511yescharacteristic
167C3C3×#221511yescharacteristic
168C2—22no—
169C2—162no—
170C2C9×#46611yescharacteristic
171C2C2×C9×D1611yescharacteristic
172C2C9×#50811yescharacteristic
subgroupG/H
centerC22×C9C2×D8
commutatorC2×C8C23×C9
Frattini, cosocleC2×C3×C8C23×C3
socleC22×C3C2×C3×D8
prime radicalC3×#2215C3
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. C22×C9×C16C2semidirect
3. C9×#466C2semidirect
4. C9×#366C2semidirect
5. C9×#357C2semidirect
33. C9×C16D4semidirect
34. #2215C9direct (N × H)
57. C2×D16C2×C9semidirect
58. C22×C16C2×C9semidirect
59. #466C2×C9semidirect
60. #366C2×C9semidirect
61. #357C2×C9semidirect
80. C22×C9D16semidirect
125. C16D4×C9semidirect
137. C9#2215direct (N × H)
161. C22C9×D16semidirect

Maximal subgroups

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

subgroupindex
C2×C9×D162
C22×C9×C162
C9×#4662
C9×#3662
C9×#3572
C3×#22153