Finite Group Databasebeta

← #13049503

Subgroups — #13049503

Order 1296.

1348 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 1348 conjugacy classes of subgroups — too many to draw. Only its 104 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×D3×C3⋊(C3⋊D3)C212yesmaximal, complemented
2#10620156C211yesmaximal, characteristic, complemented
3#10620150C211yesmaximal, characteristic, complemented
4C3×#6291C212yesmaximal, complemented
5C32×#625C211yesmaximal, characteristic, complemented
6#89039—32nomaximal
7#88954—34nomaximal
8C2×C3⋊(C3⋊(C3⋊D3))C2211yescharacteristic
9C2×C3×C3⋊(C3⋊D3)C2212yescomplemented
10C2×C33×D3C2212yescomplemented
11D3×C3⋊(C3⋊D3)—24no—
12C32×C3⋊Dic3C2211yescharacteristic, complemented
13C32×C3⋊Dic3C2211yescharacteristic, complemented
14C22×C3⋊(C3⋊D3)—32no—
15C2×D3×C3⋊D3—32no—
16C2×D3×C3⋊D3—38no—
17C2×D3×C3⋊D3—68no—
18C3×#638—32no—
19C32×#67—32no—
20#6295—34no—
21#6292—32no—
22#6291D312yescomplemented
23#6289—32no—
24#6289—34no—
25#6289—61no—
26C3×#626—38no—
27C3×#625D314yescomplemented
28C2×C34C2311yescharacteristic
29C3⋊(C3⋊(C3⋊D3))D412yescomplemented
30C3×C3⋊(C3⋊D3)—22no—
31C33×D3—22no—
32D4×C3⋊D3—91no—
33#3811—98no—
34#3802—91no—
35C22×C33—32no—
36C2×C3⋊(C3⋊D3)—32no—
37C2×C3⋊(C3⋊D3)—34no—
38C2×C3⋊(C3⋊D3)—64no—
39C2×C3⋊(C3⋊D3)—61no—
40C2×C3⋊(C3⋊D3)—68no—
41C2×C3⋊(C3⋊D3)—124no—
42C2×C3⋊(C3⋊D3)C2×D312yescomplemented
43C2×C3×C3⋊D3—32no—
44C2×C3×C3⋊D3—38no—
45C2×C3×C3⋊D3—68no—
46C2×C32×D3—28no—
47C2×C32×D3C2×D318yescomplemented
48C2×C32×D3C2×D312yescomplemented
49D3×C3⋊D3—64no—
50D3×C3⋊D3—616no—
51D3×C3⋊D3—632no—
52C3×C3⋊Dic3—21no—
53C3×C3⋊Dic3C2×D312yescomplemented
54C3×C3⋊Dic3C2×D314yescomplemented
55C32×Dic3—32no—
56C32×Dic3—34no—
57C32×Dic3—61no—
58C34C2×D411yescharacteristic, complemented, Sylow
59C22×C3⋊D3—92no—
60C22×C3⋊D3—98no—
61C22×C3⋊D3—188no—
62C2×D32—98no—
63C2×D32—92no—
64C2×D32—188no—
65C32×D4—91no—
66#638—32no—
67C4⋊(C3⋊D3)—91no—
68C4×C3⋊D3—91no—
69C4×C3⋊D3—91no—
70C3×#67—38no—
71C3×#67—98no—
72C3×D12—92no—
73#626—38no—
74#626—98no—
75#625—91no—
76#625C3⋊D311yescharacteristic, complemented
77#624—98no—
78#624—184no—
79C2×C33—21no—
80C2×C33—28no—
81C2×C33—44no—
82C2×C33—62no—
83C2×C33C22×D312yes—
84C2×C33C22×D314yes—
85C3⋊(C3⋊D3)—22no—
86C3⋊(C3⋊D3)—34no—
87C3⋊(C3⋊D3)—38no—
88C3⋊(C3⋊D3)—616no—
89C3⋊(C3⋊D3)—62no—
90C3⋊(C3⋊D3)—128no—
91C3×C3⋊D3—616no—
92C3×C3⋊D3—68no—
93C3×C3⋊D3—62no—
94C32×D3—216no—
95C32×D3—28no—
96C32×D3—22no—
97D3×D4—272no—
98D3×D4—274no—
99C22×C32—32no—
100C22×C32—38no—
101C22×C32—68no—
102C2×C3⋊D3—32no—
103C2×C3⋊D3—38no—
104C2×C3⋊D3—68no—
105C2×C3⋊D3—91no—
106C2×C3⋊D3—98no—
107C2×C3⋊D3—91no—
108C2×C3⋊D3—188no—
109C2×C3⋊D3—188no—
110C2×C3⋊D3—184no—
111C2×C3⋊D3—184no—
112C2×C3⋊D3—1816no—
113C2×C3⋊D3—1832no—
114C2×C3⋊D3—364no—
115C2×C3⋊D3—364no—
116C2×C3⋊D3—3612no—
117C2×C3×D3—28no—
118C2×C3×D3—98no—
119C2×C3×D3—92no—
120C2×C3×D3—188no—
121C2×C3×D3D3218yescomplemented
122C2×C3×D3C2×C3⋊D312yescomplemented
123D32—1816no—
124D32—184no—
125D32—1832no—
126C32×C4—91no—
127C32×C4—91no—
128C3⋊Dic3D3211yescharacteristic, complemented
129C3⋊Dic3C2×C3⋊D311yescharacteristic, complemented
130C3×Dic3—38no—
131C3×Dic3—38no—
132C3×Dic3—64no—
133C3×Dic3—64no—
134C33—21no—
135C33—28no—
136C33—44no—
137C33D3×D412yescomplemented
138C33D3×D414yescomplemented
139C22×D3—272no—
140C22×D3—278no—
141C22×D3—272no—
142C22×D3—548no—
143C3×D4—94no—
144C3×D4—272no—
145#67—32no—
146#67—98no—
147#67—272no—
148D12—92no—
149D12—274no—
150C4×D3—272no—
151C4×D3—274no—
152C4×D3—541no—
153C2×C32—28no—
154C2×C32—24no—
155C2×C32—28no—
156C2×C32—44no—
157C2×C32—412no—
158C2×C32—44no—
159C2×C32—616no—
160C2×C32—62no—
161C2×C32—68no—
162C2×C32C2×D3218yes—
163C2×C32C2×D3211yescharacteristic
164C2×C32C22×C3⋊D311yescharacteristic
165C3⋊D3—616no—
166C3⋊D3—62no—
167C3⋊D3—68no—
168C3⋊D3—92no—
169C3⋊D3—916no—
170C3⋊D3—92no—
171C3⋊D3—1816no—
172C3⋊D3—1816no—
173C3⋊D3—188no—
174C3⋊D3—368no—
175C3⋊D3—368no—
176C3⋊D3—3624no—
177C3×D3—216no—
178C3×D3—28no—
179C3×D3—22no—
180C3×D3—1816no—
181C3×D3—188no—
182C3×D3—182no—
183C2×D4—811noSylow
184C22×C3—38no—
185C22×C3—32no—
186C22×C3—68no—
187C22×C3—272no—
188C2×D3—98no—
189C2×D3—92no—
190C2×D3—188no—
191C2×D3—274no—
192C2×D3—272no—
193C2×D3—541no—
194C2×D3—548no—
195C2×D3—544no—
196C2×D3—5416no—
197C2×D3—544no—
198C2×D3—5432no—
199C2×D3—1084no—
200C2×D3D3×C3⋊D312yescomplemented
201C3×C4—94no—
202C3×C4—92no—
203C3×C4—181no—
204Dic3—34no—
205Dic3—32no—
206Dic3—61no—
207C32—28no—
208C32—24no—
209C32—28no—
210C32—44no—
211C32—412no—
212C32—44no—
213C32#380211yescharacteristic, complemented
214C32#381118yescomplemented
215C32D4×C3⋊D311yescharacteristic, complemented
216C23—812no—
217D4—91no—
218D4—272no—
219D4—811no—
220C2×C4—811no—
221C2×C3—21no—
222C2×C3—28no—
223C2×C3—44no—
224C2×C3—616no—
225C2×C3—68no—
226C2×C3—62no—
227C2×C3—542no—
228C2×C3D3314yes—
229C2×C3C2×D3×C3⋊D312yes—
230D3—22no—
231D3—1816no—
232D3—188no—
233D3—182no—
234D3—278no—
235D3—274no—
236D3—5416no—
237D3—542no—
238D3—1088no—
239C22—32no—
240C22—272no—
241C22—811no—
242C22—1624no—
243C4—91no—
244C4—91no—
245C3—28no—
246C3—21no—
247C3—44no—
248C3#8895414yescomplemented
249C3#8903912yescomplemented
250C2—62no—
251C2—542no—
252C2—812no—
253C2D32×C3⋊D311yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D32×C3⋊D3
commutator, Fitting, socle, cosocleC2×C34C23
hypocenterC34C2×D4
LCSG ▷ C2×C34 ▷ C34
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×D3×C3⋊(C3⋊D3)C2semidirect
2. #10620156C2semidirect
3. #10620150C2semidirect
4. C3×#6291C2semidirect
5. C32×#625C2semidirect
9. C2×C3×C3⋊(C3⋊D3)C22semidirect
10. C2×C33×D3C22semidirect
12. C32×C3⋊Dic3C22semidirect
13. C32×C3⋊Dic3C22semidirect
22. #6291D3semidirect
27. C3×#625D3semidirect
29. C3⋊(C3⋊(C3⋊D3))D4semidirect
42. C2×C3⋊(C3⋊D3)C2×D3semidirect
47. C2×C32×D3C2×D3semidirect
48. C2×C32×D3C2×D3semidirect
53. C3×C3⋊Dic3C2×D3semidirect
54. C3×C3⋊Dic3C2×D3semidirect
58. C34C2×D4semidirect
76. #625C3⋊D3semidirect
121. C2×C3×D3D32semidirect
122. C2×C3×D3C2×C3⋊D3semidirect
128. C3⋊Dic3D32semidirect
129. C3⋊Dic3C2×C3⋊D3semidirect
137. C33D3×D4semidirect
138. C33D3×D4semidirect
200. C2×D3D3×C3⋊D3semidirect
213. C32#3802semidirect
214. C32#3811semidirect
215. C32D4×C3⋊D3semidirect
248. C3#88954semidirect
249. C3#89039semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C3⋊(C3⋊D3)2
#106201562
#106201502
C3×#62912
C32×#6252
#890393
#889543