Finite Group Databasebeta

← C23×D9×C3⋊D3 #72276107

Subgroups — C23×D9×C3⋊D3 #72276107

Order 2592.

7804 conjugacy classes of subgroups; only the 1003 normal subgroups are shown.

normal subgroups only

This group has 7804 conjugacy classes of subgroups — too many to draw. Only its 1003 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×C3⋊(C3⋊D9)C211yesmaximal, characteristic, complemented
2C23×C9×C3⋊D3C211yesmaximal, characteristic, complemented
3C23×C32×D9C211yesmaximal, characteristic, complemented
4C22×D9×C3⋊D3C2128yesmaximal, direct product factor
5C23×D3×C3⋊D3—31nomaximal
6C23×D3×D9—34nomaximal
7C23×C32×C9C2211yescharacteristic, complemented
8C22×C3⋊(C3⋊D9)C22114yescomplemented
9C22×C9×C3⋊D3C22114yescomplemented
10C22×C32×D9C22114yescomplemented
11C2×D9×C3⋊D3C221112yesdirect product factor
12C23×C3⋊(C3⋊D3)—31no—
13C23×C3×C3⋊D3D311yescharacteristic
14C23×C32×D3—31no—
15C22×D3×C3⋊D3—328no—
16C23×C3⋊D9—34no—
17C23×C3⋊D9—64no—
18C23×D3×C9—34no—
19C23×C3×D9D314yescomplemented
20C22×D3×D9—3112no—
21C22×C32×C9C2317yescomplemented
22C2×C3⋊(C3⋊D9)C23128yescomplemented
23C2×C9×C3⋊D3C23128yescomplemented
24C2×C32×D9C23128yescomplemented
25D9×C3⋊D3C23164yesdirect product factor
26C24×C3⋊D3—91no—
27C23×D32—94no—
28C24×D9—91no—
29C23×C33C2×D311yescharacteristic
30C22×C3⋊(C3⋊D3)—314no—
31C22×C3×C3⋊D3C2×D3114yes—
32C22×C32×D3—314no—
33C2×D3×C3⋊D3—3112no—
34C23×C3×C9—24no—
35C23×C3×C9C2×D314yescomplemented
36C22×C3⋊D9—356no—
37C22×C3⋊D9—656no—
38C22×D3×C9—356no—
39C22×C3×D9C2×D3156yescomplemented
40C2×D3×D9—3448no—
41C2×C32×C9C2417yescomplemented
42C3⋊(C3⋊D9)C2418yescomplemented
43C9×C3⋊D3C2418yescomplemented
44C32×D9C2418yescomplemented
45C24×C32—91no—
46C23×C3⋊D3—91no—
47C23×C3⋊D3—94no—
48C23×C3⋊D3—928no—
49C23×C3⋊D3—184no—
50C23×C3⋊D3D911yescharacteristic, direct product factor
51C23×C3×D3—34no—
52C23×C3×D3—34no—
53C22×D32—9112no—
54C24×C9—91no—
55C23×D9—91no—
56C23×D9—928no—
57C23×D9—184no—
58C23×D9C3⋊D311yescharacteristic, direct product factor
59C22×C33C22×D317yes—
60C2×C3⋊(C3⋊D3)—328no—
61C2×C3×C3⋊D3C22×D3128yes—
62C2×C32×D3—328no—
63D3×C3⋊D3—364no—
64C22×C3×C9—228no—
65C22×C3×C9C22×D3128yescomplemented
66C2×C3⋊D9—3112no—
67C2×C3⋊D9—6112no—
68C2×D3×C9—3112no—
69C2×C3×D9C22×D31112yescomplemented
70D3×D9—3256no—
71C24×D3—271no—
72C24×D3—274no—
73C32×C9C2511yescharacteristic, complemented, Sylow
74C23×C32—24no—
75C23×C32—914no—
76C23×C32C2×D911yescharacteristic, complemented
77C23×C32D3214yes—
78C22×C3⋊D3—914no—
79C22×C3⋊D3—9112no—
80C22×C3⋊D3—956no—
81C22×C3⋊D3—1856no—
82C22×C3⋊D3C2×D9114yesdirect product factor
83C22×C3×D3—356no—
84C22×C3×D3—356no—
85C2×D32—9448no—
86C23×C9—24no—
87C23×C9—914no—
88C23×C9C2×C3⋊D311yescharacteristic, complemented
89C22×D9—914no—
90C22×D9—9112no—
91C22×D9—1856no—
92C22×D9C2×C3⋊D3114yesdirect product factor
93C2×C33C23×D317yes—
94C3⋊(C3⋊D3)—38no—
95C3×C3⋊D3C23×D318yes—
96C32×D3—38no—
97C2×C3×C9—228no—
98C2×C3×C9C23×D3128yescomplemented
99C3⋊D9—332no—
100C3⋊D9—632no—
101D3×C9—332no—
102C3×D9C23×D3132yescomplemented
103C24×C3—94no—
104C24×C3—91no—
105C23×D3—34no—
106C23×D3—31no—
107C23×D3—2728no—
108C23×D3—27112no—
109C23×D3—274no—
110C23×D3—271no—
111C23×D3—544no—
112C22×C32—228no—
113C22×C32—928no—
114C22×C32C22×D917yescomplemented
115C22×C32C2×D32128yes—
116C2×C3⋊D3—928no—
117C2×C3⋊D3—964no—
118C2×C3⋊D3—9112no—
119C2×C3⋊D3—18112no—
120C2×C3⋊D3C22×D9128yesdirect product factor
121C2×C3×D3—3112no—
122C2×C3×D3—3112no—
123D32—9256no—
124C22×C9—228no—
125C22×C9—928no—
126C22×C9C22×C3⋊D317yescomplemented
127C2×D9—928no—
128C2×D9—964no—
129C2×D9—18112no—
130C2×D9C22×C3⋊D3128yesdirect product factor
131C25—811noSylow
132C33C24×D311yescharacteristic
133C3×C9—24no—
134C3×C9C24×D314yescomplemented
135C23×C3—24no—
136C23×C3—956no—
137C23×C3—914no—
138C23×C3D3×D914yescomplemented
139C23×C3D3×C3⋊D311yescharacteristic
140C22×D3—356no—
141C22×D3—314no—
142C22×D3—27112no—
143C22×D3—27448no—
144C22×D3—2756no—
145C22×D3—2714no—
146C22×D3—5456no—
147C2×C32—228no—
148C2×C32—98no—
149C2×C32C23×D917yescomplemented
150C2×C32C22×D32128yes—
151C3⋊D3—98no—
152C3⋊D3—932no—
153C3⋊D3—1832no—
154C3⋊D3C23×D918yesdirect product factor
155C3×D3—332no—
156C3×D3—332no—
157C2×C9—228no—
158C2×C9—98no—
159C2×C9C23×C3⋊D317yescomplemented
160D9—98no—
161D9—1832no—
162D9C23×C3⋊D318yesdirect product factor
163C24—91no—
164C24—91no—
165C24—8128no—
166C24—811no—
167C22×C3—228no—
168C22×C3—928no—
169C22×C3—9112no—
170C22×C3C2×D3×D9128yescomplemented
171C22×C3C2×D3×C3⋊D317yes—
172C2×D3—328no—
173C2×D3—3112no—
174C2×D3—2764no—
175C2×D3—27256no—
176C2×D3—2728no—
177C2×D3—27112no—
178C2×D3—54112no—
179C32—24no—
180C32C24×D911yescharacteristic, complemented
181C32C23×D3214yes—
182C9—24no—
183C9C24×C3⋊D311yescharacteristic, complemented
184C23—914no—
185C23—914no—
186C23—81112no—
187C23—8114no—
188C23D9×C3⋊D311yescharacteristic, direct product factor
189C2×C3—228no—
190C2×C3—932no—
191C2×C3—98no—
192C2×C3C22×D3×D9128yescomplemented
193C2×C3C22×D3×C3⋊D317yes—
194D3—332no—
195D3—38no—
196D3—2732no—
197D3—278no—
198D3—5432no—
199C22—928no—
200C22—928no—
201C22—8164no—
202C22—8128no—
203C22C2×D9×C3⋊D317yesdirect product factor
204C3—24no—
205C3C23×D3×D914yescomplemented
206C3C23×D3×C3⋊D311yescharacteristic
207C2—98no—
208C2—98no—
209C2—818no—
210C2C22×D9×C3⋊D317yesdirect product factor
subgroupG/H
center, hypercenterC23D9×C3⋊D3
commutator, cosocle, hypocenterC32×C9C25
FrattiniC3C23×D3×C3⋊D3
FittingC23×C32×C9C22
socleC23×C33C2×D3
LCSG ▷ C32×C9
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C23×C3⋊(C3⋊D9)C2semidirect
2. C23×C9×C3⋊D3C2semidirect
3. C23×C32×D9C2semidirect
4. C22×D9×C3⋊D3C2direct (N × H)
7. C23×C32×C9C22semidirect
8. C22×C3⋊(C3⋊D9)C22semidirect
9. C22×C9×C3⋊D3C22semidirect
10. C22×C32×D9C22semidirect
11. C2×D9×C3⋊D3C22direct (N × H)
19. C23×C3×D9D3semidirect
21. C22×C32×C9C23semidirect
22. C2×C3⋊(C3⋊D9)C23semidirect
23. C2×C9×C3⋊D3C23semidirect
24. C2×C32×D9C23semidirect
25. D9×C3⋊D3C23direct (N × H)
35. C23×C3×C9C2×D3semidirect
39. C22×C3×D9C2×D3semidirect
41. C2×C32×C9C24semidirect
42. C3⋊(C3⋊D9)C24semidirect
43. C9×C3⋊D3C24semidirect
44. C32×D9C24semidirect
50. C23×C3⋊D3D9direct (N × H)
58. C23×D9C3⋊D3direct (N × H)
65. C22×C3×C9C22×D3semidirect
69. C2×C3×D9C22×D3semidirect
73. C32×C9C25semidirect
76. C23×C32C2×D9semidirect
82. C22×C3⋊D3C2×D9direct (N × H)
88. C23×C9C2×C3⋊D3semidirect
92. C22×D9C2×C3⋊D3direct (N × H)
98. C2×C3×C9C23×D3semidirect
102. C3×D9C23×D3semidirect
114. C22×C32C22×D9semidirect
120. C2×C3⋊D3C22×D9direct (N × H)
126. C22×C9C22×C3⋊D3semidirect
130. C2×D9C22×C3⋊D3direct (N × H)
134. C3×C9C24×D3semidirect
138. C23×C3D3×D9semidirect
149. C2×C32C23×D9semidirect
154. C3⋊D3C23×D9direct (N × H)
159. C2×C9C23×C3⋊D3semidirect
162. D9C23×C3⋊D3direct (N × H)
170. C22×C3C2×D3×D9semidirect
180. C32C24×D9semidirect
183. C9C24×C3⋊D3semidirect
188. C23D9×C3⋊D3direct (N × H)
192. C2×C3C22×D3×D9semidirect
203. C22C2×D9×C3⋊D3direct (N × H)
205. C3C23×D3×D9semidirect
210. C2C22×D9×C3⋊D3direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3⋊(C3⋊D9)2
C23×C9×C3⋊D32
C23×C32×D92
C22×D9×C3⋊D32
C23×D3×C3⋊D33
C23×D3×D93