Finite Group Databasebeta

← #13048655

Subgroups — #13048655

Order 1296.

660 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 106 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⋊D9C212yesmaximal, complemented
2C4×C3⋊(C3⋊D9)C211yesmaximal, characteristic, complemented
3C3×C4⋊(C3⋊D9)C211yesmaximal, characteristic, complemented
4C3×C9×D12C211yesmaximal, characteristic, complemented
5#10619879C212yesmaximal, complemented
6#89026—31nomaximal
7D4×C3⋊D9—31nomaximal
8#88646—33nomaximal
9C2×C3⋊(C3⋊D9)C2211yescharacteristic
10C2×C3×C3⋊D9C2212yescomplemented
11C2×C3×D3×C9C2212yescomplemented
12D3×C3⋊D9—24no—
13C32×C4×C9C2211yescharacteristic, complemented
14C3⋊(C3⋊Dic9)C2211yescharacteristic, complemented
15C2×D3×C3⋊D3—32no—
16C4×C3⋊(C3⋊D3)—31no—
17C3×C4⋊(C3⋊D3)—31no—
18C32×D12D311yescharacteristic
19#6290—32no—
20C22×C3⋊D9—32no—
21C2×D3×D9—36no—
22C3×D4×C9—31no—
23#6233—32no—
24C4⋊(C3⋊D9)D311yescharacteristic, complemented
25C4×C3⋊D9—31no—
26C4×C3⋊D9—33no—
27C4×C3⋊D9—63no—
28C4×C3⋊D9—61no—
29C9×D12D313yescomplemented
30C3×D36—33no—
31#6194—36no—
32C2×C32×C9C2311yescharacteristic
33C3⋊(C3⋊D9)D412yescomplemented
34C3×C3⋊D9—22no—
35C3×D3×C9—22no—
36D4×C3⋊D3—91no—
37#3802—93no—
38#3802—91no—
39D4×D9—93no—
40C2×C3⋊(C3⋊D3)—31no—
41C2×C3×C3⋊D3—32no—
42C2×C32×D3C2×D312yes—
43D3×C3⋊D3—64no—
44C33×C4C2×D311yescharacteristic
45C3⋊(C3⋊Dic3)—31no—
46C22×C3×C9—32no—
47C2×C3⋊D9—31no—
48C2×C3⋊D9—33no—
49C2×C3⋊D9—64no—
50C2×C3⋊D9—63no—
51C2×C3⋊D9—61no—
52C2×C3⋊D9C2×D312yescomplemented
53C2×D3×C9C2×D316yescomplemented
54C2×C3×D9—36no—
55D3×D9—612no—
56C3×C4×C9—21no—
57C3×C4×C9—23no—
58C3×C4×C9C2×D313yescomplemented
59C3×C4×C9C2×D311yescharacteristic, complemented
60C3⋊Dic9—31no—
61C3⋊Dic9—33no—
62C3⋊Dic9—63no—
63C3⋊Dic9—61no—
64C32×C9C2×D411yescharacteristic, complemented, Sylow
65C22×C3⋊D3—92no—
66C2×D32—96no—
67C2×D32—92no—
68C32×D4—31no—
69#638—92no—
70C4⋊(C3⋊D3)—31no—
71C4×C3⋊D3—91no—
72C4×C3⋊D3—93no—
73C4×C3⋊D3—91no—
74C4×C3⋊D3—181no—
75C4×C3⋊D3—183no—
76C3×D12—93no—
77C3×D12—91no—
78C3×D12D913yescomplemented
79C3×D12C3⋊D311yescharacteristic
80#625—96no—
81#625—92no—
82C22×D9—96no—
83D4×C9—33no—
84#611—96no—
85D36—33no—
86C4×D9—93no—
87C4×D9—183no—
88C2×C33C22×D311yescharacteristic
89C3⋊(C3⋊D3)—32no—
90C3×C3⋊D3—62no—
91C32×D3—22no—
92C2×C3×C9—21no—
93C2×C3×C9—23no—
94C2×C3×C9—62no—
95C2×C3×C9C22×D313yes—
96C2×C3×C9C22×D311yescharacteristic
97C3⋊D9—22no—
98C3⋊D9—32no—
99C3⋊D9—36no—
100C3⋊D9—66no—
101C3⋊D9—62no—
102D3×C9—26no—
103C3×D9—66no—
104D3×D4—271no—
105D3×D4—273no—
106D3×D4—271no—
107C22×C32—32no—
108C2×C3⋊D3—32no—
109C2×C3⋊D3—91no—
110C2×C3⋊D3—93no—
111C2×C3⋊D3—91no—
112C2×C3⋊D3—181no—
113C2×C3⋊D3—183no—
114C2×C3⋊D3—184no—
115C2×C3×D3—96no—
116C2×C3×D3—92no—
117C2×C3×D3C2×D916yescomplemented
118C2×C3×D3C2×C3⋊D312yes—
119D32—184no—
120D32—1812no—
121C32×C4—23no—
122C32×C4—21no—
123C32×C4C2×D913yescomplemented
124C32×C4D3211yescharacteristic
125C32×C4C2×C3⋊D311yescharacteristic
126C3⋊Dic3—91no—
127C3⋊Dic3—93no—
128C3⋊Dic3—91no—
129C3⋊Dic3—181no—
130C3⋊Dic3—183no—
131C22×C9—36no—
132C2×D9—36no—
133C2×D9—93no—
134C2×D9—183no—
135C2×D9—1812no—
136C4×C9—23no—
137C4×C9D3213yescomplemented
138Dic9—93no—
139Dic9—183no—
140C33D3×D411yescharacteristic
141C3×C9—21no—
142C3×C9—23no—
143C3×C9D3×D413yescomplemented
144C3×C9D3×D411yescharacteristic, complemented
145C22×D3—272no—
146C22×D3—276no—
147C22×D3—272no—
148C3×D4—33no—
149C3×D4—31no—
150C3×D4—271no—
151#67—272no—
152#67—276no—
153#67—272no—
154D12—93no—
155D12—91no—
156D12C3⋊D911yescharacteristic, complemented
157C4×D3—273no—
158C4×D3—271no—
159C4×D3—271no—
160C4×D3—543no—
161C4×D3—541no—
162C2×C32—23no—
163C2×C32—21no—
164C2×C32—62no—
165C2×C32C22×D913yes—
166C2×C32C2×D3211yescharacteristic
167C2×C32C22×C3⋊D311yescharacteristic
168C3⋊D3—62no—
169C3⋊D3—92no—
170C3⋊D3—96no—
171C3⋊D3—92no—
172C3⋊D3—182no—
173C3⋊D3—186no—
174C3×D3—26no—
175C3×D3—22no—
176C3×D3—186no—
177C3×D3—182no—
178C2×C9—23no—
179C2×C9—66no—
180C2×C9C2×D3213yes—
181D9—66no—
182D9—96no—
183D9—186no—
184C2×D4—811noSylow
185C22×C3—36no—
186C22×C3—32no—
187C22×C3—272no—
188C2×D3—96no—
189C2×D3—92no—
190C2×D3—273no—
191C2×D3—271no—
192C2×D3—271no—
193C2×D3—543no—
194C2×D3—541no—
195C2×D3—544no—
196C2×D3—544no—
197C2×D3—5412no—
198C2×D3C2×C3⋊D912yescomplemented
199C3×C4—23no—
200C3×C4—21no—
201C3×C4D3×D913yescomplemented
202C3×C4C2×C3⋊D911yescharacteristic, complemented
203C3×C4D3×C3⋊D311yescharacteristic
204Dic3—273no—
205Dic3—271no—
206Dic3—271no—
207Dic3—543no—
208Dic3—541no—
209C32—23no—
210C32—21no—
211C32D4×D913yescomplemented
212C32#380211yescharacteristic
213C32D4×C3⋊D311yescharacteristic
214C9—23no—
215C9#380213yescomplemented
216C23—812no—
217D4—31no—
218D4—271no—
219D4—812no—
220C2×C4—811no—
221C2×C3—23no—
222C2×C3—21no—
223C2×C3—66no—
224C2×C3—62no—
225C2×C3—542no—
226C2×C3C2×D3×D913yes—
227C2×C3C22×C3⋊D911yescharacteristic
228C2×C3C2×D3×C3⋊D311yescharacteristic
229D3—22no—
230D3—186no—
231D3—182no—
232D3—276no—
233D3—272no—
234D3—272no—
235D3—546no—
236D3—542no—
237C22—32no—
238C22—272no—
239C22—811no—
240C22—1624no—
241C4—811no—
242C4D3×C3⋊D911yescharacteristic, complemented
243C3—23no—
244C3—21no—
245C3#8864613yescomplemented
246C3D4×C3⋊D911yescharacteristic, complemented
247C3#8902611yescharacteristic
248C2—62no—
249C2—542no—
250C2—812no—
251C2C2×D3×C3⋊D911yescharacteristic
subgroupG/H
centerC2C2×D3×C3⋊D9
commutator, cosocleC2×C32×C9C23
FrattiniC2×C3C2×D3×C3⋊D3
FittingC32×C4×C9C22
socleC2×C33C22×D3
hypercenterC4D3×C3⋊D9
hypocenterC32×C9C2×D4
LCSG ▷ C2×C32×C9 ▷ C32×C9
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C2×D3×C3⋊D9C2semidirect
2. C4×C3⋊(C3⋊D9)C2semidirect
3. C3×C4⋊(C3⋊D9)C2semidirect
4. C3×C9×D12C2semidirect
5. #10619879C2semidirect
10. C2×C3×C3⋊D9C22semidirect
11. C2×C3×D3×C9C22semidirect
13. C32×C4×C9C22semidirect
14. C3⋊(C3⋊Dic9)C22semidirect
24. C4⋊(C3⋊D9)D3semidirect
29. C9×D12D3semidirect
33. C3⋊(C3⋊D9)D4semidirect
52. C2×C3⋊D9C2×D3semidirect
53. C2×D3×C9C2×D3semidirect
58. C3×C4×C9C2×D3semidirect
59. C3×C4×C9C2×D3semidirect
64. C32×C9C2×D4semidirect
78. C3×D12D9semidirect
117. C2×C3×D3C2×D9semidirect
123. C32×C4C2×D9semidirect
137. C4×C9D32semidirect
143. C3×C9D3×D4semidirect
144. C3×C9D3×D4semidirect
156. D12C3⋊D9semidirect
198. C2×D3C2×C3⋊D9semidirect
201. C3×C4D3×D9semidirect
202. C3×C4C2×C3⋊D9semidirect
211. C32D4×D9semidirect
215. C9#3802semidirect
242. C4D3×C3⋊D9semidirect
245. C3#88646semidirect
246. C3D4×C3⋊D9semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C3⋊D92
C4×C3⋊(C3⋊D9)2
C3×C4⋊(C3⋊D9)2
C3×C9×D122
#106198792
#890263
D4×C3⋊D93
#886463