Finite Group Databasebeta

← C2×D32×C8 #10594664

Subgroups — C2×D32×C8 #10594664

Order 576.

714 conjugacy classes of subgroups; only the 256 normal subgroups are shown.

normal subgroups only

This group has 714 conjugacy classes of subgroups — too many to draw. Only its 256 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×C4×D32C211yesmaximal, characteristic
2C2×C8×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×C3×D3×C8C212yesmaximal, complemented
4C2×#3710C211yesmaximal, characteristic, complemented
5C2×D3×C3⋊C8C212yesmaximal, complemented
6D32×C8C218yesmaximal, direct product factor
7C22×D3×C8—32nomaximal
8C22×D32C411yescharacteristic
9C2×C4×C3⋊D3C2211yescharacteristic
10C2×C3×C4×D3C2212yes—
11C2×#624C411yescharacteristic
12C2×D3×Dic3C412yes—
13C4×D32C414yes—
14C4×D32C2214yes—
15C2×C32×C8C2211yescharacteristic, complemented
16C2×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
17C8×C3⋊D3C2214yescomplemented
18C2×C3×C3⋊C8C2212yescomplemented
19C3×D3×C8C2218yescomplemented
20#3710C2214yescomplemented
21D3×C3⋊C8C2218yescomplemented
22C22×C4×D3—32no—
23C22×C3×C8—32no—
24C22×C3⋊C8—32no—
25C2×D3×C8—32no—
26C2×D3×C8—32no—
27C2×D3×C8—32no—
28C2×D3×C8—316no—
29C2×D3×C8—61no—
30C2×D3×C8D312yesdirect product factor
31C22×C3⋊D3C2×C411yescharacteristic
32C22×C3×D3C2×C412yes—
33C2×D32C818yesdirect product factor
34C2×D32C2×C414yes—
35C2×C32×C4C2311yescharacteristic
36C2×C3⋊Dic3C2×C411yescharacteristic
37C4×C3⋊D3C2×C412yes—
38C4×C3⋊D3C2312yes—
39C2×C3×Dic3C2×C412yes—
40C3×C4×D3C2×C414yes—
41C3×C4×D3C2314yes—
42#624C2×C414yes—
43D3×Dic3C2×C418yes—
44C32×C8C2312yescomplemented
45C3⋊(C3⋊C8)C2312yescomplemented
46C3×C3⋊C8C2314yescomplemented
47C23×C8—91noSylow
48C23×D3—32no—
49C22×C3×C4—32no—
50C22×Dic3—32no—
51C2×C4×D3—32no—
52C2×C4×D3—32no—
53C2×C4×D3—32no—
54C2×C4×D3—38no—
55C2×C4×D3—38no—
56C2×C4×D3—61no—
57C2×C4×D3C2×D312yes—
58C2×C3×C8—21no—
59C2×C3×C8—32no—
60C2×C3×C8—38no—
61C2×C3×C8C2×D312yescomplemented
62C2×C3⋊C8—32no—
63C2×C3⋊C8—38no—
64C2×C3⋊C8—61no—
65C2×C3⋊C8C2×D312yescomplemented
66D3×C8—38no—
67D3×C8—38no—
68D3×C8—38no—
69D3×C8—64no—
70D3×C8C2×D318yesdirect product factor
71C22×C32C22×C411yescharacteristic
72C2×C3⋊D3C2×C814yescomplemented
73C2×C3⋊D3C22×C412yes—
74C2×C3×D3C2×C818yescomplemented
75C2×C3×D3C22×C414yes—
76D32C2×C8116yesdirect product factor
77C32×C4C22×C411yescharacteristic
78C32×C4C2411yescharacteristic
79C3⋊Dic3C22×C412yes—
80C3×Dic3C22×C414yes—
81C23×C4—91no—
82C22×C8—32no—
83C22×C8—91no—
84C22×C8—98no—
85C22×C8—92no—
86C22×C8—91no—
87C23×C3—32no—
88C22×D3—32no—
89C22×D3—316no—
90C22×D3—38no—
91C22×D3—61no—
92C22×D3C4×D312yes—
93C2×C3×C4—21no—
94C2×C3×C4—32no—
95C2×C3×C4—34no—
96C2×C3×C4—34no—
97C2×C3×C4C22×D312yes—
98C2×Dic3—32no—
99C2×Dic3—38no—
100C2×Dic3—61no—
101C2×Dic3C4×D312yes—
102C4×D3—38no—
103C4×D3—34no—
104C4×D3—34no—
105C4×D3—38no—
106C4×D3—62no—
107C4×D3—62no—
108C4×D3C4×D314yes—
109C4×D3C22×D314yes—
110C3×C8—22no—
111C3×C8—34no—
112C3×C8C22×D314yescomplemented
113C3⋊C8—34no—
114C3⋊C8—62no—
115C3⋊C8C22×D314yescomplemented
116C2×C32C22×C812yescomplemented
117C2×C32C23×C411yescharacteristic
118C3⋊D3C22×C814yescomplemented
119C3×D3C22×C818yescomplemented
120C24—91no—
121C22×C4—32no—
122C22×C4—94no—
123C22×C4—91no—
124C22×C4—94no—
125C22×C4—92no—
126C22×C4—91no—
127C2×C8—32no—
128C2×C8—38no—
129C2×C8—94no—
130C2×C8—98no—
131C2×C8—91no—
132C2×C8—94no—
133C2×C8D3211yescharacteristic, direct product factor
134C22×C3—21no—
135C22×C3—38no—
136C22×C3—34no—
137C22×C3C2×C4×D312yes—
138C2×D3—38no—
139C2×D3—34no—
140C2×D3—332no—
141C2×D3—62no—
142C2×D3—64no—
143C2×D3D3×C818yesdirect product factor
144C2×D3C2×C4×D314yes—
145C3×C4—21no—
146C3×C4—21no—
147C3×C4—34no—
148C3×C4C2×C4×D312yes—
149C3×C4C23×D312yes—
150Dic3—34no—
151Dic3—62no—
152Dic3C2×C4×D314yes—
153C32C23×C811yescharacteristic, complemented, Sylow
154C23—32no—
155C23—94no—
156C23—98no—
157C23—91no—
158C2×C4—32no—
159C2×C4—34no—
160C2×C4—34no—
161C2×C4—94no—
162C2×C4—98no—
163C2×C4—91no—
164C2×C4—92no—
165C2×C4—92no—
166C2×C4C2×D3211yescharacteristic
167C8—34no—
168C8—92no—
169C8C2×D3212yesdirect product factor
170C2×C3—22no—
171C2×C3—21no—
172C2×C3—38no—
173C2×C3C2×D3×C814yescomplemented
174C2×C3C22×C4×D312yes—
175D3—38no—
176D3—64no—
177D3C2×D3×C818yesdirect product factor
178C22—38no—
179C22—34no—
180C22—916no—
181C22—94no—
182C22—92no—
183C22C4×D3211yescharacteristic
184C4—34no—
185C4—92no—
186C4C4×D3211yescharacteristic
187C4C22×D3211yescharacteristic
188C3—21no—
189C3C22×D3×C812yescomplemented
190C2—38no—
191C2—94no—
192C2D32×C812yesdirect product factor
193C2C2×C4×D3211yescharacteristic
subgroupG/H
center, hypercenterC2×C8D32
commutator, hypocenterC32C23×C8
FrattiniC4C22×D32
FittingC2×C32×C8C22
socleC22×C32C22×C4
prime radicalC22×D32C4
cosocleC32×C4C24
LCSG ▷ C32
UCSC1 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C2×C8×C3⋊D3C2semidirect
3. C2×C3×D3×C8C2semidirect
4. C2×#3710C2semidirect
5. C2×D3×C3⋊C8C2semidirect
6. D32×C8C2direct (N × H)
15. C2×C32×C8C22semidirect
16. C2×C3⋊(C3⋊C8)C22semidirect
17. C8×C3⋊D3C22semidirect
18. C2×C3×C3⋊C8C22semidirect
19. C3×D3×C8C22semidirect
20. #3710C22semidirect
21. D3×C3⋊C8C22semidirect
30. C2×D3×C8D3direct (N × H)
33. C2×D32C8direct (N × H)
44. C32×C8C23semidirect
45. C3⋊(C3⋊C8)C23semidirect
46. C3×C3⋊C8C23semidirect
61. C2×C3×C8C2×D3semidirect
65. C2×C3⋊C8C2×D3semidirect
70. D3×C8C2×D3direct (N × H)
72. C2×C3⋊D3C2×C8semidirect
74. C2×C3×D3C2×C8semidirect
76. D32C2×C8direct (N × H)
112. C3×C8C22×D3semidirect
115. C3⋊C8C22×D3semidirect
116. C2×C32C22×C8semidirect
118. C3⋊D3C22×C8semidirect
119. C3×D3C22×C8semidirect
133. C2×C8D32direct (N × H)
143. C2×D3D3×C8direct (N × H)
153. C32C23×C8semidirect
169. C8C2×D32direct (N × H)
173. C2×C3C2×D3×C8semidirect
177. D3C2×D3×C8direct (N × H)
189. C3C22×D3×C8semidirect
192. C2D32×C8direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×D322
C2×C8×C3⋊D32
C2×C3×D3×C82
C2×#37102
C2×D3×C3⋊C82
D32×C82
C22×D3×C83