Finite Group Databasebeta

← C9×#2216 #11766937

Subgroups — C9×#2216 #11766937

Order 1152.

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

normal subgroups only

This group has 231 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×Q32C211yesmaximal, characteristic, complemented
2C22×C9×C16C211yesmaximal, characteristic
3C9×#467C212yesmaximal
4C9×#366C211yesmaximal, characteristic, complemented
5C9×#358C212yesmaximal, complemented
6C3×#2216C311yesmaximal, characteristic
7C2×C9×Q16C2212yes—
8C22×C8×C9C2211yescharacteristic
9C9×C22⋊Q8—22no—
10C9×Q32—22no—
11C2×C9×C16—22no—
12C2×C9×C16C2211yescharacteristic
13C2×C9×C16C2211yescharacteristic
14C9×#107C2212yes—
15C9×#103—22no—
16C2×C3×Q32C2×C311yescharacteristic
17C22×C3×C16C2×C311yescharacteristic
18C3×#467C2×C312yes—
19C3×#366C2×C311yescharacteristic
20C3×#358C2×C312yes—
21C2×Q8×C9—22no—
22C22×C4×C9D411yescharacteristic
23C9×Q16—22no—
24C9×Q16—22no—
25C2×C8×C9—21no—
26C2×C8×C9—21no—
27C2×C8×C9D411yescharacteristic
28C2×C8×C9C2311yescharacteristic
29C9×C4⋊C4—22no—
30C9×C4⋊C4—42no—
31C9×C22⋊C4—42no—
32C9×C16—21no—
33C9×C16D412yes—
34#2216C911yescharacteristic, direct product factor, Sylow
35C2×C3×Q16C22×C312yes—
36C22×C3×C8C22×C311yescharacteristic
37C3×C22⋊Q8—22no—
38C3×Q32—22no—
39C2×C3×C16—22no—
40C2×C3×C16C22×C311yescharacteristic
41C2×C3×C16C22×C311yescharacteristic
42C3×#107C22×C312yes—
43C3×#103—22no—
44C23×C9D811yescharacteristic
45Q8×C9—42no—
46Q8×C9—42no—
47C2×C4×C9—21no—
48C2×C4×C9—21no—
49C2×C4×C9—42no—
50C2×C4×C9—42no—
51C2×C4×C9D811yescharacteristic
52C2×C4×C9C2×D411yescharacteristic
53C8×C9—21no—
54C8×C9C2×D411yescharacteristic
55C8×C9#4111yescharacteristic
56C2×Q32C2×C911yescharacteristic, complemented
57C22×C16C2×C911yescharacteristic
58#467C2×C912yes—
59#366C2×C911yescharacteristic, complemented
60#358C2×C912yescomplemented
61C2×C3×Q8—22no—
62C22×C3×C4C3×D411yescharacteristic
63C3×Q16—22no—
64C3×Q16—22no—
65C2×C3×C8—21no—
66C2×C3×C8—21no—
67C2×C3×C8C3×D411yescharacteristic
68C2×C3×C8C23×C311yescharacteristic
69C3×C4⋊C4—22no—
70C3×C4⋊C4—42no—
71C3×C22⋊C4—42no—
72C3×C16—21no—
73C3×C16C3×D412yes—
74C22×C9—21no—
75C22×C9—21no—
76C22×C9Q3212yescomplemented
77C22×C9C2×D811yescharacteristic
78C4×C9—21no—
79C4×C9—82no—
80C4×C9—82no—
81C4×C9#12111yescharacteristic
82C4×C9#13511yescharacteristic
83C2×Q16C22×C912yes—
84C22×C8C22×C911yescharacteristic
85C22⋊Q8—22no—
86Q32—22no—
87C2×C16—22no—
88C2×C16C22×C911yescharacteristic
89C2×C16C22×C911yescharacteristic
90#107C22×C912yes—
91#103—22no—
92C23×C3C3×D811yescharacteristic
93C3×Q8—42no—
94C3×Q8—42no—
95C2×C3×C4—21no—
96C2×C3×C4—21no—
97C2×C3×C4—42no—
98C2×C3×C4—42no—
99C2×C3×C4C3×D811yescharacteristic
100C2×C3×C4C2×C3×D411yescharacteristic
101C3×C8—21no—
102C3×C8C2×C3×D411yescharacteristic
103C3×C8C3×#4111yescharacteristic
104C2×C9—22no—
105C2×C9#46611yescharacteristic
106C2×C9C2×Q3211yescharacteristic
107C2×C9#50811yescharacteristic
108C2×Q8—22no—
109C22×C4D4×C911yescharacteristic
110Q16—22no—
111Q16—22no—
112C2×C8—21no—
113C2×C8—21no—
114C2×C8D4×C911yescharacteristic
115C2×C8C23×C911yescharacteristic
116C4⋊C4—22no—
117C4⋊C4—42no—
118C22⋊C4—42no—
119C16—21no—
120C16D4×C912yes—
121C22×C3—21no—
122C22×C3—21no—
123C22×C3C3×Q3212yes—
124C22×C3C2×C3×D811yescharacteristic
125C3×C4—21no—
126C3×C4—82no—
127C3×C4—82no—
128C3×C4C3×#12111yescharacteristic
129C3×C4C3×#13511yescharacteristic
130C9#221611yescharacteristic, direct product factor, Sylow
131C23C9×D811yescharacteristic
132Q8—42no—
133Q8—42no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—42no—
137C2×C4—42no—
138C2×C4C9×D811yescharacteristic
139C2×C4C2×D4×C911yescharacteristic
140C8—21no—
141C8C2×D4×C911yescharacteristic
142C8C9×#4111yescharacteristic
143C2×C3—22no—
144C2×C3C3×#46611yescharacteristic
145C2×C3C2×C3×Q3211yescharacteristic
146C2×C3C3×#50811yescharacteristic
147C22—21no—
148C22—21no—
149C22C9×Q3212yescomplemented
150C22C2×C9×D811yescharacteristic
151C4—21no—
152C4—82no—
153C4—82no—
154C4C9×#12111yescharacteristic
155C4C9×#13511yescharacteristic
156C3C3×#221611yescharacteristic
157C2—22no—
158C2C9×#46611yescharacteristic
159C2C2×C9×Q3211yescharacteristic
160C2C9×#50811yescharacteristic
subgroupG/H
centerC22×C9C2×D8
commutatorC2×C8C23×C9
Frattini, cosocleC2×C3×C8C23×C3
socleC22×C3C2×C3×D8
prime radicalC23×C3C3×D8
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×Q32C2semidirect
4. C9×#366C2semidirect
5. C9×#358C2semidirect
34. #2216C9direct (N × H)
56. C2×Q32C2×C9semidirect
59. #366C2×C9semidirect
60. #358C2×C9semidirect
76. C22×C9Q32semidirect
130. C9#2216direct (N × H)
149. C22C9×Q32semidirect

Maximal subgroups

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

subgroupindex
C2×C9×Q322
C22×C9×C162
C9×#4672
C9×#3662
C9×#3582
C3×#22163