Finite Group Databasebeta

← C2×D4×C22⋊C9 #10593113

Subgroups — C2×D4×C22⋊C9 #10593113

Order 576.

580 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C23×C22⋊C9C212yesmaximal, complemented
2D4×C22⋊C9C214yesmaximal, direct product factor
3C2×C4×C22⋊C9C211yesmaximal, characteristic, complemented
4C23×C3×D4C311yesmaximal, characteristic
5C22×C22⋊C9—24no—
6C22×C22⋊C9C2211yescharacteristic
7C22×C22⋊C9C2214yescomplemented
8C2×D4×C9—41nomaximal
9C4×C22⋊C9C2212yescomplemented
10C25×C3C2×C312yes—
11C22×C3×D4—31no—
12C22×C3×D4—31no—
13C22×C3×D4—32no—
14C22×C3×D4—34no—
15C22×C3×D4C2×C314yes—
16C23×C3×C4C2×C311yescharacteristic
17C23×C9—42no—
18C2×C22⋊C9—24no—
19C2×C22⋊C9D412yesdirect product factor
20C2×C22⋊C9C2311yescharacteristic
21D4×C9—44no—
22C2×C4×C9—41no—
23C23×D4C911yescharacteristic, complemented, Sylow
24C24×C3—24no—
25C24×C3—34no—
26C24×C3—32no—
27C24×C3—32no—
28C24×C3—64no—
29C24×C3C22×C311yescharacteristic
30C24×C3C22×C314yes—
31C2×C3×D4—38no—
32C2×C3×D4—32no—
33C2×C3×D4—34no—
34C2×C3×D4—32no—
35C2×C3×D4—34no—
36C2×C3×D4—34no—
37C2×C3×D4—34no—
38C2×C3×D4—38no—
39C2×C3×D4—31no—
40C2×C3×D4A411yescharacteristic
41C22×C3×C4—31no—
42C22×C3×C4—31no—
43C22×C3×C4—32no—
44C22×C3×C4C22×C312yes—
45C22×C9—44no—
46C22×C9—41no—
47C22×C9—84no—
48C22⋊C9C2×D411yescharacteristic, direct product factor
49C4×C9—42no—
50C25C2×C912yescomplemented
51C22×D4—31no—
52C22×D4—31no—
53C22×D4—32no—
54C22×D4—34no—
55C22×D4C2×C914yescomplemented
56C23×C4C2×C911yescharacteristic, complemented
57C23×C3—24no—
58C23×C3—31no—
59C23×C3—32no—
60C23×C3—31no—
61C23×C3—34no—
62C23×C3—34no—
63C23×C3—34no—
64C23×C3—34no—
65C23×C3—32no—
66C23×C3—64no—
67C23×C3—64no—
68C23×C3—64no—
69C23×C3—68no—
70C23×C3—64no—
71C23×C3—64no—
72C23×C3—68no—
73C23×C3C3×D412yes—
74C23×C3C2×A412yes—
75C23×C3C23×C311yescharacteristic
76C3×D4—38no—
77C3×D4—38no—
78C3×D4—34no—
79C3×D4C2×A414yes—
80C2×C3×C4—32no—
81C2×C3×C4—31no—
82C2×C3×C4—32no—
83C2×C3×C4—32no—
84C2×C3×C4—32no—
85C2×C3×C4C2×A411yescharacteristic
86C2×C9—42no—
87C2×C9—41no—
88C2×C9—84no—
89C24—24no—
90C24—34no—
91C24—32no—
92C24—32no—
93C24—64no—
94C24C22×C911yescharacteristic
95C24C22×C914yescomplemented
96C2×D4—38no—
97C2×D4—32no—
98C2×D4—34no—
99C2×D4—32no—
100C2×D4—34no—
101C2×D4—34no—
102C2×D4—34no—
103C2×D4—38no—
104C2×D4—31no—
105C2×D4C22⋊C911yescharacteristic, direct product factor
106C22×C4—31no—
107C22×C4—31no—
108C22×C4—32no—
109C22×C4C22×C912yescomplemented
110C22×C3—24no—
111C22×C3—32no—
112C22×C3—31no—
113C22×C3—32no—
114C22×C3—32no—
115C22×C3—32no—
116C22×C3—31no—
117C22×C3—31no—
118C22×C3—34no—
119C22×C3—64no—
120C22×C3—68no—
121C22×C3—64no—
122C22×C3—64no—
123C22×C3—64no—
124C22×C3—68no—
125C22×C3—64no—
126C22×C3C2×C3×D411yescharacteristic
127C22×C3C22×A414yes—
128C22×C3C22×A411yescharacteristic
129C3×C4—32no—
130C3×C4C22×A412yes—
131C9—41noSylow
132C23—24no—
133C23—31no—
134C23—32no—
135C23—31no—
136C23—34no—
137C23—34no—
138C23—32no—
139C23—34no—
140C23—34no—
141C23—64no—
142C23—64no—
143C23—64no—
144C23—68no—
145C23—64no—
146C23—64no—
147C23—68no—
148C23D4×C912yescomplemented
149C23C2×C22⋊C912yescomplemented
150C23C23×C911yescharacteristic
151D4—38no—
152D4—38no—
153D4—34no—
154D4C2×C22⋊C914yesdirect product factor
155C2×C4—32no—
156C2×C4—31no—
157C2×C4—32no—
158C2×C4—32no—
159C2×C4—32no—
160C2×C4C2×C22⋊C911yescharacteristic, complemented
161C2×C3—24no—
162C2×C3—32no—
163C2×C3—31no—
164C2×C3—31no—
165C2×C3—64no—
166C2×C3D4×A412yes—
167C2×C3C23×A411yescharacteristic
168C22—24no—
169C22—32no—
170C22—31no—
171C22—32no—
172C22—31no—
173C22—31no—
174C22—32no—
175C22—32no—
176C22—34no—
177C22—64no—
178C22—64no—
179C22—68no—
180C22—64no—
181C22—64no—
182C22—68no—
183C22—64no—
184C22C2×D4×C911yescharacteristic, complemented
185C22C22×C22⋊C911yescharacteristic
186C22C22×C22⋊C914yescomplemented
187C4—32no—
188C4C22×C22⋊C912yescomplemented
189C3C2×D4×A411yescharacteristic
190C2—24no—
191C2—31no—
192C2—32no—
193C2—31no—
194C2—64no—
195C2D4×C22⋊C912yesdirect product factor
196C2C23×C22⋊C911yescharacteristic
subgroupG/H
centerC22×C3C22×A4
commutatorC23C23×C9
FrattiniC2×C3C23×A4
Fitting, prime radicalC23×C3×D4C3
socleC24×C3C22×C3
cosocleC23×C3C23×C3
hypercenterC2×C3×D4A4
hypocenterC22C2×D4×C9
LCSG ▷ C23 ▷ C22
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊C9C2semidirect
2. D4×C22⋊C9C2direct (N × H)
3. C2×C4×C22⋊C9C2semidirect
7. C22×C22⋊C9C22semidirect
9. C4×C22⋊C9C22semidirect
19. C2×C22⋊C9D4direct (N × H)
23. C23×D4C9semidirect
48. C22⋊C9C2×D4direct (N × H)
50. C25C2×C9semidirect
55. C22×D4C2×C9semidirect
56. C23×C4C2×C9semidirect
95. C24C22×C9semidirect
105. C2×D4C22⋊C9direct (N × H)
109. C22×C4C22×C9semidirect
148. C23D4×C9semidirect
149. C23C2×C22⋊C9semidirect
154. D4C2×C22⋊C9direct (N × H)
160. C2×C4C2×C22⋊C9semidirect
184. C22C2×D4×C9semidirect
186. C22C22×C22⋊C9semidirect
188. C4C22×C22⋊C9semidirect
195. C2D4×C22⋊C9direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊C92
D4×C22⋊C92
C2×C4×C22⋊C92
C23×C3×D43
C2×D4×C94