Finite Group Databasebeta

← C22×D3×D8 #87169

Subgroups — C22×D3×D8 #87169

Order 384.

1976 conjugacy classes of subgroups; only the 565 normal subgroups are shown.

normal subgroups only

This group has 1976 conjugacy classes of subgroups — too many to draw. Only its 565 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
1C22×D3×D4C212yesmaximal, complemented
2C22×C3×D8C211yesmaximal, characteristic, complemented
3C22×#213C212yesmaximal, complemented
4C2×D3×D8C2124yesmaximal, direct product factor
5C22×D24C211yesmaximal, characteristic, complemented
6C22×D3×C8C211yesmaximal, characteristic, complemented
7C23×D8—31nomaximal, Sylow
8C24×D3—22no—
9C22×C3×D4C2212yescomplemented
10C22×#67—22no—
11C2×D3×D4—212no—
12C2×D3×D4C22124yescomplemented
13C22×D12C2212yescomplemented
14C22×C4×D3C2211yescharacteristic
15C2×C3×D8C22112yescomplemented
16C22×C3×C8C2211yescharacteristic, complemented
17C2×#213C22124yescomplemented
18C22×C3⋊C8C2211yescharacteristic, complemented
19D3×D8C22164yesdirect product factor
20C2×D24C22112yescomplemented
21C2×D3×C8C22112yescomplemented
22C23×D4—32no—
23C22×D8—32no—
24C22×D8—324no—
25C22×D8—31no—
26C22×D8D311yescharacteristic, direct product factor
27C23×C8—31no—
28C24×C3—22no—
29C23×D3—22no—
30C23×D3—224no—
31C23×D3—416no—
32C23×D3D411yescharacteristic
33C2×C3×D4—26no—
34C2×C3×D4C23112yescomplemented
35C22×C3×C4C2311yescharacteristic
36C2×#67—224no—
37C22×Dic3D411yescharacteristic
38D3×D4—248no—
39D3×D4C23132yescomplemented
40C2×D12—26no—
41C2×D12C23112yescomplemented
42C2×C4×D3D416yes—
43C2×C4×D3C2316yes—
44C3×D8C23116yescomplemented
45C2×C3×C8C2316yescomplemented
46#213C23132yescomplemented
47C2×C3⋊C8C2316yescomplemented
48D24C23116yescomplemented
49D3×C8C23116yescomplemented
50C25—62no—
51C22×D4—324no—
52C22×D4—32no—
53C22×D4—612no—
54C22×D4—62no—
55C22×D4C2×D312yescomplemented
56C23×C4—31no—
57C2×D8—324no—
58C2×D8—364no—
59C2×D8—312no—
60C2×D8C2×D3112yesdirect product factor
61C22×C8—31no—
62C22×C8—312no—
63C22×C8C2×D311yescharacteristic, complemented
64C23×C3—212no—
65C23×C3—48no—
66C23×C3C2×D411yescharacteristic
67C22×D3—212no—
68C22×D3—232no—
69C22×D3—48no—
70C22×D3—496no—
71C22×D3D818yesdirect product factor
72C22×D3C2×D416yes—
73C3×D4—212no—
74C3×D4C2418yescomplemented
75C2×C3×C4C2×D413yes—
76C2×C3×C4C2413yes—
77#67—232no—
78C2×Dic3C2×D416yes—
79D12—212no—
80D12C2418yescomplemented
81C4×D3C2×D4112yes—
82C4×D3C2414yes—
83C3×C8C2414yescomplemented
84C3⋊C8C2414yescomplemented
85C24—22no—
86C24—31no—
87C24—624no—
88C24—62no—
89C24—1216no—
90C2×D4—26no—
91C2×D4—332no—
92C2×D4—312no—
93C2×D4—648no—
94C2×D4—624no—
95C2×D4—66no—
96C2×D4C22×D3112yescomplemented
97C22×C4—31no—
98C22×C4—36no—
99C22×C4—36no—
100C22×C4C22×D311yescharacteristic
101D8—332no—
102D8—316no—
103D8C22×D3116yesdirect product factor
104C2×C8—36no—
105C2×C8—316no—
106C2×C8C22×D316yescomplemented
107C22×C3—28no—
108C22×C3—424no—
109C22×C3C2×D814yescomplemented
110C22×C3C22×D413yes—
111C2×D3—28no—
112C2×D3—424no—
113C2×D3—464no—
114C2×D3C2×D8124yesdirect product factor
115C2×D3C22×D414yes—
116C3×C4C22×D413yes—
117C3×C4C2511yescharacteristic
118Dic3C22×D414yes—
119C23—212no—
120C23—38no—
121C23—36no—
122C23—48no—
123C23—632no—
124C23—612no—
125C23—1296no—
126C23—128no—
127C23D3×D411yescharacteristic
128D4—212no—
129D4—38no—
130D4—632no—
131D4—612no—
132D4C23×D318yescomplemented
133C2×C4—36no—
134C2×C4—312no—
135C2×C4—34no—
136C2×C4D3×D413yes—
137C2×C4C23×D313yes—
138C8—34no—
139C8C23×D314yescomplemented
140C2×C3—48no—
141C2×C3C22×D816yescomplemented
142C2×C3C23×D411yescharacteristic
143D3—48no—
144D3C22×D818yesdirect product factor
145C22—28no—
146C22—34no—
147C22—324no—
148C22—424no—
149C22—68no—
150C22—1264no—
151C22—1224no—
152C22D3×D814yesdirect product factor
153C22C2×D3×D413yes—
154C4—34no—
155C4C2×D3×D413yes—
156C4C24×D311yescharacteristic
157C3C23×D811yescharacteristic, complemented, Sylow
158C2—38no—
159C2—48no—
160C2—128no—
161C2C2×D3×D816yesdirect product factor
162C2C22×D3×D411yescharacteristic
subgroupG/H
centerC23D3×D4
commutator, cosocleC3×C4C25
FrattiniC4C24×D3
FittingC22×C3×D8C2
socleC23×C3C2×D4
hypercenterC22×D8D3
hypocenterC3C23×D8
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×D3×D4C2semidirect
2. C22×C3×D8C2semidirect
3. C22×#213C2semidirect
4. C2×D3×D8C2direct (N × H)
5. C22×D24C2semidirect
6. C22×D3×C8C2semidirect
9. C22×C3×D4C22semidirect
12. C2×D3×D4C22semidirect
13. C22×D12C22semidirect
15. C2×C3×D8C22semidirect
16. C22×C3×C8C22semidirect
17. C2×#213C22semidirect
18. C22×C3⋊C8C22semidirect
19. D3×D8C22direct (N × H)
20. C2×D24C22semidirect
21. C2×D3×C8C22semidirect
26. C22×D8D3direct (N × H)
34. C2×C3×D4C23semidirect
39. D3×D4C23semidirect
41. C2×D12C23semidirect
44. C3×D8C23semidirect
45. C2×C3×C8C23semidirect
46. #213C23semidirect
47. C2×C3⋊C8C23semidirect
48. D24C23semidirect
49. D3×C8C23semidirect
55. C22×D4C2×D3semidirect
60. C2×D8C2×D3direct (N × H)
63. C22×C8C2×D3semidirect
71. C22×D3D8direct (N × H)
74. C3×D4C24semidirect
80. D12C24semidirect
83. C3×C8C24semidirect
84. C3⋊C8C24semidirect
96. C2×D4C22×D3semidirect
103. D8C22×D3direct (N × H)
106. C2×C8C22×D3semidirect
109. C22×C3C2×D8semidirect
114. C2×D3C2×D8direct (N × H)
132. D4C23×D3semidirect
139. C8C23×D3semidirect
141. C2×C3C22×D8semidirect
144. D3C22×D8direct (N × H)
152. C22D3×D8direct (N × H)
157. C3C23×D8semidirect
161. C2C2×D3×D8direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×D42
C22×C3×D82
C22×#2132
C2×D3×D82
C22×D242
C22×D3×C82
C23×D83