Finite Group Databasebeta

← D16×C22⋊C9 #11919625

Subgroups — D16×C22⋊C9 #11919625

Order 1152.

212 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 40 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
1D8×C22⋊C9C212yesmaximal, complemented
2C16×C22⋊C9C211yesmaximal, characteristic, complemented
3C22×C3×D16C311yesmaximal, characteristic
4D4×C22⋊C9—22no—
5C8×C22⋊C9C2211yescharacteristic
6C9×D16—41nomaximal
7C22×C3×D8C2×C312yes—
8C2×C3×D16—31no—
9C2×C3×D16—31no—
10C2×C3×D16—32no—
11C22×C3×C16C2×C311yescharacteristic
12C22×C22⋊C9—42no—
13C4×C22⋊C9D411yescharacteristic
14C9×D8—42no—
15C9×C16—41no—
16C22×D16C911yescharacteristic, complemented, Sylow
17C22×C3×D4—22no—
18C2×C3×D8—32no—
19C2×C3×D8—32no—
20C2×C3×D8—62no—
21C22×C3×C8C22×C311yescharacteristic
22C3×D16—32no—
23C3×D16—32no—
24C3×D16—31no—
25C3×D16A411yescharacteristic
26C2×C3×C16—31no—
27C2×C3×C16—31no—
28C2×C22⋊C9—82no—
29C2×C22⋊C9D811yescharacteristic
30D4×C9—82no—
31C8×C9—41no—
32C22×D8C2×C912yescomplemented
33C2×D16—31no—
34C2×D16—31no—
35C2×D16—32no—
36C22×C16C2×C911yescharacteristic, complemented
37C24×C3—42no—
38C2×C3×D4—62no—
39C2×C3×D4—62no—
40C2×C3×D4—122no—
41C22×C3×C4C3×D411yescharacteristic
42C3×D8—32no—
43C3×D8—62no—
44C3×D8—62no—
45C3×D8C2×A412yes—
46C2×C3×C8—31no—
47C2×C3×C8—31no—
48C3×C16—31no—
49C3×C16C2×A411yescharacteristic
50C22×C9—162no—
51C22⋊C9D1611yescharacteristic, direct product factor
52C4×C9—41no—
53C22×D4—22no—
54C2×D8—32no—
55C2×D8—32no—
56C2×D8—62no—
57C22×C8C22×C911yescharacteristic
58D16—32no—
59D16—32no—
60D16—31no—
61D16C22⋊C911yescharacteristic, direct product factor
62C2×C16—31no—
63C2×C16—31no—
64C23×C3—82no—
65C23×C3—122no—
66C23×C3—122no—
67C23×C3—242no—
68C23×C3C3×D811yescharacteristic
69C3×D4—22no—
70C3×D4—62no—
71C3×D4—122no—
72C3×D4—122no—
73C2×C3×C4—31no—
74C2×C3×C4—31no—
75C3×C8—31no—
76C3×C8C22×A411yescharacteristic
77C2×C9—41no—
78C2×C9—322no—
79C24—42no—
80C2×D4—62no—
81C2×D4—62no—
82C2×D4—122no—
83C22×C4D4×C911yescharacteristic
84D8—32no—
85D8—62no—
86D8—62no—
87D8C2×C22⋊C912yescomplemented
88C2×C8—31no—
89C2×C8—31no—
90C16—31no—
91C16C2×C22⋊C911yescharacteristic, complemented
92C22×C3—31no—
93C22×C3—31no—
94C22×C3—42no—
95C22×C3—122no—
96C22×C3—242no—
97C22×C3—242no—
98C22×C3—242no—
99C22×C3—242no—
100C22×C3C3×D1611yescharacteristic
101C3×C4—31no—
102C3×C4D4×A411yescharacteristic
103C9—41noSylow
104C23—82no—
105C23—122no—
106C23—122no—
107C23—242no—
108C23C9×D811yescharacteristic
109D4—22no—
110D4—62no—
111D4—122no—
112D4—122no—
113C2×C4—31no—
114C2×C4—31no—
115C8—31no—
116C8C22×C22⋊C911yescharacteristic
117C2×C3—31no—
118C2×C3—31no—
119C2×C3—82no—
120C2×C3—242no—
121C2×C3A4×D811yescharacteristic
122C22—31no—
123C22—31no—
124C22—42no—
125C22—122no—
126C22—242no—
127C22—242no—
128C22—242no—
129C22—242no—
130C22C9×D1611yescharacteristic, complemented
131C4—31no—
132C4D4×C22⋊C911yescharacteristic
133C3A4×D1611yescharacteristic
134C2—31no—
135C2—31no—
136C2—82no—
137C2—242no—
138C2D8×C22⋊C911yescharacteristic
subgroupG/H
centerC2×C3A4×D8
commutatorC22×C8C22×C9
FrattiniC3×C8C22×A4
Fitting, prime radicalC22×C3×D16C3
socleC23×C3C3×D8
cosocleC22×C3×C8C22×C3
hypercenterC3×D16A4
hypocenterC22C9×D16
LCSG ▷ C22×C8 ▷ C22×C4 ▷ C23 ▷ C22
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8 ◁ C3×D16

Complements

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

NH ≅ G/Ntype
1. D8×C22⋊C9C2semidirect
2. C16×C22⋊C9C2semidirect
16. C22×D16C9semidirect
32. C22×D8C2×C9semidirect
36. C22×C16C2×C9semidirect
51. C22⋊C9D16direct (N × H)
61. D16C22⋊C9direct (N × H)
87. D8C2×C22⋊C9semidirect
91. C16C2×C22⋊C9semidirect
130. C22C9×D16semidirect

Maximal subgroups

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

subgroupindex
D8×C22⋊C92
C16×C22⋊C92
C22×C3×D163
C9×D164