Finite Group Databasebeta

← C3×A4×D16 #11919624

Subgroups — C3×A4×D16 #11919624

Order 1152.

296 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 64 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
1C3×A4×D8C212yesmaximal, complemented
2C3×A4×C16C211yesmaximal, characteristic, complemented
3C22×C3×D16C311yesmaximal, characteristic, complemented
4A4×D16C313yesmaximal, direct product factor
5C3×D4×A4—22no—
6C3×C8×A4C2211yescharacteristic
7C32×D16—41nomaximal
8C22×C3×D8C2×C312yescomplemented
9A4×D8C2×C316yescomplemented
10C2×C3×D16—31no—
11C2×C3×D16—31no—
12C2×C3×D16—32no—
13C22×C3×C16C2×C311yescharacteristic, complemented
14A4×C16C2×C313yescomplemented
15C22×C3×A4—42no—
16C3×C4×A4D411yescharacteristic
17C32×D8—42no—
18C32×C16—41no—
19C22×D16C3211yescharacteristic, complemented, Sylow
20C22×C3×D4—22no—
21D4×A4—26no—
22C2×C3×D8—32no—
23C2×C3×D8—32no—
24C2×C3×D8—62no—
25C22×C3×C8C22×C311yescharacteristic
26C8×A4C22×C313yes—
27C3×D16—32no—
28C3×D16—32no—
29C3×D16—31no—
30C3×D16—43no—
31C3×D16A411yescharacteristic, direct product factor
32C2×C3×C16—31no—
33C2×C3×C16—31no—
34C2×C3×A4—82no—
35C2×C3×A4D811yescharacteristic
36C32×D4—82no—
37C32×C8—41no—
38C22×D8C2×C3212yescomplemented
39C2×D16—31no—
40C2×D16—31no—
41C2×D16—32no—
42C22×C16C2×C3211yescharacteristic, complemented
43C24×C3—42no—
44C22×A4—46no—
45C2×C3×D4—62no—
46C2×C3×D4—62no—
47C2×C3×D4—122no—
48C22×C3×C4C3×D411yescharacteristic
49C4×A4C3×D413yes—
50C3×D8—32no—
51C3×D8—46no—
52C3×D8—62no—
53C3×D8—62no—
54C3×D8C2×A412yescomplemented
55C2×C3×C8—31no—
56C2×C3×C8—31no—
57C3×C16—31no—
58C3×C16—43no—
59C3×C16C2×A411yescharacteristic, complemented
60C22×C32—162no—
61C3×A4D1611yescharacteristic, direct product factor
62C32×C4—41no—
63C22×D4—22no—
64C2×D8—32no—
65C2×D8—32no—
66C2×D8—62no—
67C22×C8C22×C3211yescharacteristic
68D16—32no—
69D16—32no—
70D16—31no—
71D16C3×A411yescharacteristic, direct product factor
72C2×C16—31no—
73C2×C16—31no—
74C23×C3—82no—
75C23×C3—122no—
76C23×C3—122no—
77C23×C3—242no—
78C23×C3C3×D811yescharacteristic
79C2×A4—86no—
80C2×A4C3×D813yes—
81C3×D4—22no—
82C3×D4—62no—
83C3×D4—86no—
84C3×D4—122no—
85C3×D4—122no—
86C2×C3×C4—31no—
87C2×C3×C4—31no—
88C3×C8—31no—
89C3×C8—43no—
90C3×C8C22×A411yescharacteristic
91C2×C32—41no—
92C2×C32—322no—
93C24—42no—
94C2×D4—62no—
95C2×D4—62no—
96C2×D4—122no—
97C22×C4C32×D411yescharacteristic
98D8—32no—
99D8—62no—
100D8—62no—
101D8C2×C3×A412yescomplemented
102C2×C8—31no—
103C2×C8—31no—
104C16—31no—
105C16C2×C3×A411yescharacteristic, complemented
106C22×C3—31no—
107C22×C3—31no—
108C22×C3—42no—
109C22×C3—122no—
110C22×C3—166no—
111C22×C3—242no—
112C22×C3—242no—
113C22×C3—242no—
114C22×C3—242no—
115C22×C3C3×D1611yescharacteristic, complemented
116A4C3×D1613yesdirect product factor
117C3×C4—31no—
118C3×C4—43no—
119C3×C4D4×A411yescharacteristic
120C32—41noSylow
121C23—82no—
122C23—122no—
123C23—122no—
124C23—242no—
125C23C32×D811yescharacteristic
126D4—22no—
127D4—62no—
128D4—122no—
129D4—122no—
130C2×C4—31no—
131C2×C4—31no—
132C8—31no—
133C8C22×C3×A411yescharacteristic
134C2×C3—31no—
135C2×C3—31no—
136C2×C3—43no—
137C2×C3—82no—
138C2×C3—242no—
139C2×C3—326no—
140C2×C3A4×D811yescharacteristic
141C22—31no—
142C22—31no—
143C22—42no—
144C22—122no—
145C22—242no—
146C22—242no—
147C22—242no—
148C22—242no—
149C22C32×D1611yescharacteristic, complemented
150C4—31no—
151C4C3×D4×A411yescharacteristic
152C3—43no—
153C3A4×D1611yescharacteristic, direct product factor
154C2—31no—
155C2—31no—
156C2—82no—
157C2—242no—
158C2C3×A4×D811yescharacteristic
subgroupG/H
centerC2×C3A4×D8
commutator, cosocleC22×C8C22×C32
FrattiniC8C22×C3×A4
FittingC22×C3×D16C3
socleC23×C3C3×D8
hypercenterC3×D16A4
hypocenterC22C32×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. C3×A4×D8C2semidirect
2. C3×A4×C16C2semidirect
3. C22×C3×D16C3semidirect
4. A4×D16C3direct (N × H)
8. C22×C3×D8C2×C3semidirect
9. A4×D8C2×C3semidirect
13. C22×C3×C16C2×C3semidirect
14. A4×C16C2×C3semidirect
19. C22×D16C32semidirect
31. C3×D16A4direct (N × H)
38. C22×D8C2×C32semidirect
42. C22×C16C2×C32semidirect
54. C3×D8C2×A4semidirect
59. C3×C16C2×A4semidirect
61. C3×A4D16direct (N × H)
71. D16C3×A4direct (N × H)
101. D8C2×C3×A4semidirect
105. C16C2×C3×A4semidirect
115. C22×C3C3×D16semidirect
116. A4C3×D16direct (N × H)
149. C22C32×D16semidirect
153. C3A4×D16direct (N × H)

Maximal subgroups

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

subgroupindex
C3×A4×D82
C3×A4×C162
C22×C3×D163
A4×D163
C32×D164