Finite Group Databasebeta

← C32×#3811 #13049621

Subgroups — C32×#3811 #13049621

Order 1296.

1140 conjugacy classes of subgroups; only the 204 normal subgroups are shown.

normal subgroups only

This group has 1140 conjugacy classes of subgroups — too many to draw. Only its 204 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×C32×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C32×D32C211yesmaximal, characteristic, complemented
3C33×#67C212yesmaximal, complemented
4C32×#626C212yesmaximal, complemented
5C32×#624C211yesmaximal, characteristic, complemented
6C32×D3×D4—32nomaximal
7C3×#3811C314yesmaximal, direct product factor
8C22×C34C2211yescharacteristic, complemented
9C2×C32×C3⋊D3—22no—
10C2×C32×C3⋊D3C2211yescharacteristic
11C2×C32×C3⋊D3C2211yescharacteristic, complemented
12C2×C33×D3C2212yescomplemented
13C32×D32—22no—
14C33×Dic3C2212yescomplemented
15C22×C3×C3⋊D3C2×C314yescomplemented
16C22×C32×D3—32no—
17C22×C32×D3—32no—
18C22×C32×D3—61no—
19C2×C3×D32C2×C314yescomplemented
20C33×D4—32no—
21C32×#67—28no—
22C32×#67—32no—
23C32×#67D312yescomplemented
24C32×#67C2×C318yescomplemented
25C32×D12—32no—
26C32×C4×D3—32no—
27C3×#626C2×C318yescomplemented
28C3×#624C2×C314yescomplemented
29C2×C34—21no—
30C2×C34C2311yescharacteristic
31C32×C3⋊D3—21no—
32C32×C3⋊D3D412yescomplemented
33C33×D3—22no—
34C2×C32×D4—91no—
35C3×D3×D4—38no—
36#3811C3211yescharacteristic, direct product factor
37C22×C33—21no—
38C22×C33—28no—
39C22×C33—32no—
40C22×C33—44no—
41C22×C33C2×D312yescomplemented
42C22×C33C22×C314yescomplemented
43C2×C3×C3⋊D3—28no—
44C2×C3×C3⋊D3C22×C314yes—
45C2×C3×C3⋊D3C22×C314yescomplemented
46C2×C32×D3—28no—
47C2×C32×D3—32no—
48C2×C32×D3—32no—
49C2×C32×D3—64no—
50C2×C32×D3—64no—
51C2×C32×D3—61no—
52C2×C32×D3—61no—
53C2×C32×D3—64no—
54C2×C32×D3C2×D312yescomplemented
55C2×C32×D3C22×C318yescomplemented
56C3×D32—28no—
57C33×C4—32no—
58C32×Dic3—28no—
59C32×Dic3C2×D312yescomplemented
60C32×Dic3C22×C318yescomplemented
61C34C2×D411yescharacteristic, complemented, Sylow
62C23×C32—91no—
63C23×C32—91no—
64C22×C3⋊D3C2×C3211yescharacteristic, complemented
65C22×C3×D3—38no—
66C22×C3×D3—38no—
67C22×C3×D3—64no—
68C2×D32C2×C3211yescharacteristic, complemented
69C32×D4—32no—
70C32×D4—38no—
71C32×D4—68no—
72C32×D4—92no—
73C2×C32×C4—91no—
74C3×#67—28no—
75C3×#67—38no—
76C3×#67C3×D318yescomplemented
77C3×#67C2×C3212yescomplemented
78C3×D12—38no—
79C3×C4×D3—38no—
80#626C2×C3212yescomplemented
81#624C2×C3211yescharacteristic, complemented
82C2×C33—22no—
83C2×C33—22no—
84C2×C33—24no—
85C2×C33—21no—
86C2×C33—28no—
87C2×C33—44no—
88C2×C33—48no—
89C2×C33—48no—
90C2×C33—62no—
91C2×C33C22×D312yes—
92C2×C33C23×C314yes—
93C3×C3⋊D3—24no—
94C3×C3⋊D3C3×D418yescomplemented
95C32×D3—22no—
96C32×D3—28no—
97C32×D3—34no—
98C32×D3—48no—
99C32×D3—62no—
100C32×D3—62no—
101C32×D3—62no—
102C2×C3×D4—94no—
103D3×D4—32no—
104C22×C32—28no—
105C22×C32—24no—
106C22×C32—28no—
107C22×C32—32no—
108C22×C32—38no—
109C22×C32—44no—
110C22×C32—412no—
111C22×C32—44no—
112C22×C32—68no—
113C22×C32—91no—
114C22×C32—91no—
115C22×C32—182no—
116C22×C32—182no—
117C22×C32D3211yescharacteristic, complemented
118C22×C32C2×C3×D318yescomplemented
119C22×C32C22×C3211yescharacteristic, complemented
120C2×C3⋊D3—22no—
121C2×C3⋊D3C22×C3211yescharacteristic
122C2×C3⋊D3C22×C3211yescharacteristic, complemented
123C2×C3×D3—28no—
124C2×C3×D3—38no—
125C2×C3×D3—38no—
126C2×C3×D3—64no—
127C2×C3×D3—64no—
128C2×C3×D3—616no—
129C2×C3×D3—616no—
130C2×C3×D3—616no—
131C2×C3×D3C2×C3×D318yescomplemented
132C2×C3×D3C22×C3212yescomplemented
133D32—22no—
134C32×C4—32no—
135C32×C4—38no—
136C32×C4—68no—
137C3×Dic3—28no—
138C3×Dic3C2×C3×D318yescomplemented
139C3×Dic3C22×C3212yescomplemented
140C33—21no—
141C33—28no—
142C33—44no—
143C33D3×D412yescomplemented
144C33C2×C3×D414yescomplemented
145C23×C3—94no—
146C23×C3—94no—
147C22×D3—32no—
148C22×D3—32no—
149C22×D3—61no—
150C3×D4—38no—
151C3×D4—32no—
152C3×D4—68no—
153C3×D4—98no—
154C2×C3×C4—94no—
155#67—32no—
156#67C32×D312yescomplemented
157D12—32no—
158C4×D3—32no—
159C2×C32—21no—
160C2×C32—21no—
161C2×C32—28no—
162C2×C32—28no—
163C2×C32—28no—
164C2×C32—24no—
165C2×C32—28no—
166C2×C32—44no—
167C2×C32—412no—
168C2×C32—48no—
169C2×C32—48no—
170C2×C32—48no—
171C2×C32—48no—
172C2×C32—424no—
173C2×C32—44no—
174C2×C32—62no—
175C2×C32—68no—
176C2×C32—92no—
177C2×C32—128no—
178C2×C32—181no—
179C2×C32C2×D3211yescharacteristic
180C2×C32C22×C3×D318yes—
181C2×C32C23×C3211yescharacteristic
182C3⋊D3—21no—
183C3⋊D3C32×D412yescomplemented
184C3×D3—28no—
185C3×D3—22no—
186C3×D3—316no—
187C3×D3—48no—
188C3×D3—68no—
189C3×D3—68no—
190C3×D3—68no—
191C2×D4—91noSylow
192C22×C3—21no—
193C22×C3—28no—
194C22×C3—38no—
195C22×C3—32no—
196C22×C3—44no—
197C22×C3—68no—
198C22×C3—94no—
199C22×C3—94no—
200C22×C3—188no—
201C22×C3—188no—
202C22×C3C3×D3214yescomplemented
203C22×C3C2×C32×D312yescomplemented
204C2×D3—32no—
205C2×D3—32no—
206C2×D3—61no—
207C2×D3—61no—
208C2×D3—64no—
209C2×D3—64no—
210C2×D3—64no—
211C2×D3C2×C32×D312yescomplemented
212C3×C4—38no—
213C3×C4—32no—
214C3×C4—68no—
215Dic3C2×C32×D312yescomplemented
216C32—28no—
217C32—24no—
218C32—28no—
219C32—44no—
220C32—412no—
221C32—44no—
222C32#381111yescharacteristic, direct product factor
223C32C3×D3×D418yescomplemented
224C32C2×C32×D411yescharacteristic, complemented
225C23—91no—
226C23—91no—
227D4—32no—
228D4—92no—
229C2×C4—91no—
230C2×C3—22no—
231C2×C3—24no—
232C2×C3—22no—
233C2×C3—28no—
234C2×C3—21no—
235C2×C3—48no—
236C2×C3—48no—
237C2×C3—44no—
238C2×C3—68no—
239C2×C3—62no—
240C2×C3—98no—
241C2×C3—128no—
242C2×C3—184no—
243C2×C3C2×C3×D3214yes—
244C2×C3C22×C32×D312yes—
245D3—22no—
246D3—34no—
247D3—62no—
248D3—62no—
249D3—62no—
250C22—32no—
251C22—91no—
252C22—91no—
253C22—182no—
254C22—182no—
255C22C32×D3211yescharacteristic, complemented
256C4—32no—
257C3—21no—
258C3—28no—
259C3—44no—
260C3C3×#381114yesdirect product factor
261C3C32×D3×D412yescomplemented
262C2—21no—
263C2—62no—
264C2—92no—
265C2—181no—
266C2C2×C32×D3211yescharacteristic
subgroupG/H
centerC2×C32C2×D32
commutator, cosocleC2×C32C23×C32
FrattiniC2C2×C32×D32
FittingC22×C34C22
socleC2×C34C23
hypercenterC22×C32D32
hypocenterC32C2×C32×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C32 ◁ C22×C32

Complements

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

NH ≅ G/Ntype
1. C22×C32×C3⋊D3C2semidirect
2. C2×C32×D32C2semidirect
3. C33×#67C2semidirect
4. C32×#626C2semidirect
5. C32×#624C2semidirect
7. C3×#3811C3direct (N × H)
8. C22×C34C22semidirect
11. C2×C32×C3⋊D3C22semidirect
12. C2×C33×D3C22semidirect
14. C33×Dic3C22semidirect
15. C22×C3×C3⋊D3C2×C3semidirect
19. C2×C3×D32C2×C3semidirect
23. C32×#67D3semidirect
24. C32×#67C2×C3semidirect
27. C3×#626C2×C3semidirect
28. C3×#624C2×C3semidirect
32. C32×C3⋊D3D4semidirect
36. #3811C32direct (N × H)
41. C22×C33C2×D3semidirect
42. C22×C33C22×C3semidirect
45. C2×C3×C3⋊D3C22×C3semidirect
54. C2×C32×D3C2×D3semidirect
55. C2×C32×D3C22×C3semidirect
59. C32×Dic3C2×D3semidirect
60. C32×Dic3C22×C3semidirect
61. C34C2×D4semidirect
64. C22×C3⋊D3C2×C32semidirect
68. C2×D32C2×C32semidirect
76. C3×#67C3×D3semidirect
77. C3×#67C2×C32semidirect
80. #626C2×C32semidirect
81. #624C2×C32semidirect
94. C3×C3⋊D3C3×D4semidirect
117. C22×C32D32semidirect
118. C22×C32C2×C3×D3semidirect
119. C22×C32C22×C32semidirect
122. C2×C3⋊D3C22×C32semidirect
131. C2×C3×D3C2×C3×D3semidirect
132. C2×C3×D3C22×C32semidirect
138. C3×Dic3C2×C3×D3semidirect
139. C3×Dic3C22×C32semidirect
143. C33D3×D4semidirect
144. C33C2×C3×D4semidirect
156. #67C32×D3semidirect
183. C3⋊D3C32×D4semidirect
202. C22×C3C3×D32semidirect
203. C22×C3C2×C32×D3semidirect
211. C2×D3C2×C32×D3semidirect
215. Dic3C2×C32×D3semidirect
222. C32#3811direct (N × H)
223. C32C3×D3×D4semidirect
224. C32C2×C32×D4semidirect
255. C22C32×D32semidirect
260. C3C3×#3811direct (N × H)
261. C3C32×D3×D4semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C3⋊D32
C2×C32×D322
C33×#672
C32×#6262
C32×#6242
C32×D3×D43
C3×#38113