Finite Group Databasebeta

← #13048744

Subgroups — #13048744

Order 1296.

424 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 66 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×#66431C212yesmaximal, complemented
2C9×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3C3×C4⋊(C3⋊D9)C211yesmaximal, characteristic, complemented
4C3×C4×C3⋊D9C211yesmaximal, characteristic, complemented
5#10619899C212yesmaximal, complemented
6C4⋊#1113—31nomaximal
7#88646—31nomaximal
8D9×D12—31nomaximal
9C2×C9×C3⋊D3C2212yescomplemented
10C2×C3×C3⋊D9C2211yescharacteristic
11C2×C3×C3⋊D9C2212yescomplemented
12#66431—24no—
13C32×C4×C9C2211yescharacteristic, complemented
14C3×C3⋊Dic9C2211yescharacteristic, complemented
15C2×#1113—32no—
16C3×C4⋊(C3⋊D3)—31no—
17C3×C4⋊(C3⋊D3)D311yescharacteristic
18C3×C4×C3⋊D3—31no—
19#6295—32no—
20C2×D3×D9—32no—
21C2×D3×D9—32no—
22C4⋊(C3⋊D9)D311yescharacteristic, complemented
23C4×C3⋊D9D311yescharacteristic, complemented
24C9×D12—31no—
25C9×D12—31no—
26C9×D12—61no—
27C3×D36—31no—
28C3×D36—61no—
29C3×C4×D9—31no—
30C3×C4×D9—61no—
31#6195—32no—
32#6194—32no—
33C2×C32×C9C2311yescharacteristic
34C9×C3⋊D3—22no—
35C3×C3⋊D9—22no—
36C3×C3⋊D9D412yescomplemented
37#3802—91no—
38D3×D12—91no—
39D3×D12—91no—
40D4×D9—91no—
41C2×C3×C3⋊D3—31no—
42C2×C3×C3⋊D3—32no—
43C2×C3×C3⋊D3C2×D312yes—
44#1113—64no—
45C33×C4C2×D311yescharacteristic
46C3×C3⋊Dic3—31no—
47C2×C3⋊D9C2×D311yescharacteristic
48C2×C3⋊D9C2×D312yescomplemented
49C2×D3×C9—32no—
50C2×D3×C9—32no—
51C2×D3×C9—62no—
52C2×C3×D9—31no—
53C2×C3×D9—32no—
54C2×C3×D9—61no—
55C2×C3×D9—62no—
56D3×D9—64no—
57D3×D9—64no—
58C3×C4×C9—21no—
59C3×C4×C9—21no—
60C3×C4×C9—21no—
61C3×C4×C9—41no—
62C3×C4×C9C2×D311yescharacteristic, complemented
63C3×C4×C9C2×D311yescharacteristic, complemented
64C3⋊Dic9C2×D311yescharacteristic, complemented
65C3×Dic9—31no—
66C3×Dic9—61no—
67C32×C9C2×D411yescharacteristic, complemented, Sylow
68C2×D32—92no—
69C2×D32—92no—
70C2×D32—92no—
71C4⋊(C3⋊D3)—31no—
72C4⋊(C3⋊D3)D911yescharacteristic, complemented
73C4×C3⋊D3—31no—
74C3×D12—31no—
75C3×D12—31no—
76C3×D12—61no—
77C3×D12—91no—
78C3×D12—91no—
79C3×D12—181no—
80C3×C4×D3—91no—
81C3×C4×D3—91no—
82C3×C4×D3—181no—
83#626—92no—
84#626—92no—
85#625—92no—
86C22×D9—92no—
87D4×C9—91no—
88#611—92no—
89D36—31no—
90D36—61no—
91C4×D9—31no—
92C4×D9—61no—
93C2×C33C22×D311yescharacteristic
94C3×C3⋊D3—22no—
95C3×C3⋊D3—32no—
96C3×C3⋊D3—62no—
97C2×C3×C9—21no—
98C2×C3×C9—21no—
99C2×C3×C9—21no—
100C2×C3×C9—41no—
101C2×C3×C9C22×D311yescharacteristic
102C2×C3×C9C22×D311yescharacteristic
103C3⋊D9—22no—
104C3⋊D9D1212yescomplemented
105D3×C9—62no—
106D3×C9—62no—
107D3×C9—122no—
108C3×D9—32no—
109C3×D9—62no—
110C3×D9—62no—
111C3×D9—122no—
112D3×D4—271no—
113D3×D4—271no—
114C2×D12—271no—
115C2×C3⋊D3—31no—
116C2×C3⋊D3—32no—
117C2×C3⋊D3C2×D912yescomplemented
118C2×C3×D3—32no—
119C2×C3×D3—32no—
120C2×C3×D3—62no—
121C2×C3×D3—91no—
122C2×C3×D3—91no—
123C2×C3×D3—92no—
124C2×C3×D3—92no—
125C2×C3×D3—181no—
126C2×C3×D3—182no—
127D32—184no—
128D32—184no—
129D32—184no—
130C32×C4—21no—
131C32×C4—21no—
132C32×C4—21no—
133C32×C4—41no—
134C32×C4C2×D911yescharacteristic, complemented
135C32×C4D3211yescharacteristic
136C32×C4D3211yescharacteristic
137C3⋊Dic3—31no—
138C3×Dic3—91no—
139C3×Dic3—91no—
140C3×Dic3—181no—
141C22×C9—92no—
142C2×D9—31no—
143C2×D9—32no—
144C2×D9—61no—
145C2×D9—62no—
146C2×D9—184no—
147C4×C9—21no—
148C4×C9—21no—
149C4×C9—41no—
150C4×C9D3211yescharacteristic, complemented
151Dic9—31no—
152Dic9—61no—
153C33D3×D411yescharacteristic
154C3×C9—21no—
155C3×C9—21no—
156C3×C9—21no—
157C3×C9—41no—
158C3×C9C2×D1211yescharacteristic, complemented
159C3×C9D3×D411yescharacteristic, complemented
160C22×D3—272no—
161C22×D3—272no—
162C22×D3—272no—
163C3×D4—91no—
164C3×D4—271no—
165C2×C3×C4—271no—
166#67—272no—
167#67—272no—
168D12—31no—
169D12—31no—
170D12—61no—
171D12—91no—
172D12—91no—
173D12—181no—
174D12—272no—
175C4×D3—91no—
176C4×D3—91no—
177C4×D3—181no—
178C2×C32—21no—
179C2×C32—21no—
180C2×C32—21no—
181C2×C32—41no—
182C2×C32C22×D911yescharacteristic
183C2×C32C2×D3211yescharacteristic
184C2×C32C2×D3211yescharacteristic
185C3⋊D3—22no—
186C3⋊D3—32no—
187C3⋊D3—62no—
188C3×D3—62no—
189C3×D3—62no—
190C3×D3—92no—
191C3×D3—92no—
192C3×D3—122no—
193C3×D3—182no—
194C3×D3—182no—
195C3×D3—182no—
196C3×D3—362no—
197C2×C9—21no—
198C2×C9—21no—
199C2×C9—41no—
200C2×C9—182no—
201C2×C9C2×D3211yescharacteristic
202D9—32no—
203D9—62no—
204D9—62no—
205D9—122no—
206C2×D4—811noSylow
207C22×C3—92no—
208C22×C3—271no—
209C22×C3—272no—
210C2×D3—32no—
211C2×D3—32no—
212C2×D3—62no—
213C2×D3—91no—
214C2×D3—91no—
215C2×D3—92no—
216C2×D3—92no—
217C2×D3—181no—
218C2×D3—182no—
219C2×D3—544no—
220C2×D3—544no—
221C2×D3—544no—
222C3×C4—21no—
223C3×C4—21no—
224C3×C4—21no—
225C3×C4—41no—
226C3×C4—271no—
227C3×C4D3×D911yescharacteristic, complemented
228C3×C4D3×D911yescharacteristic, complemented
229C3×C4#111311yescharacteristic
230Dic3—91no—
231Dic3—91no—
232Dic3—181no—
233C32—21no—
234C32—21no—
235C32—21no—
236C32—41no—
237C32D4×D911yescharacteristic, complemented
238C32D3×D1211yescharacteristic
239C32#380211yescharacteristic
240C9—21no—
241C9—21no—
242C9—41no—
243C9D3×D1211yescharacteristic, complemented
244C23—812no—
245D4—91no—
246D4—271no—
247D4—812no—
248C2×C4—271no—
249C2×C3—21no—
250C2×C3—21no—
251C2×C3—21no—
252C2×C3—41no—
253C2×C3—182no—
254C2×C3—272no—
255C2×C3—542no—
256C2×C3C2×D3×D911yescharacteristic
257C2×C3C2×D3×D911yescharacteristic
258C2×C3C2×#111311yescharacteristic
259D3—62no—
260D3—62no—
261D3—92no—
262D3—92no—
263D3—122no—
264D3—182no—
265D3—182no—
266D3—182no—
267D3—362no—
268C22—92no—
269C22—271no—
270C22—272no—
271C22—1624no—
272C4—271no—
273C4#6643111yescharacteristic, complemented
274C3—21no—
275C3—21no—
276C3—21no—
277C3—41no—
278C3D9×D1211yescharacteristic, complemented
279C3#8864611yescharacteristic, complemented
280C3C4⋊#111311yescharacteristic
281C2—182no—
282C2—272no—
283C2—542no—
284C2C2×#6643111yescharacteristic
subgroupG/H
centerC2C2×#66431
commutator, cosocleC2×C32×C9C23
FrattiniC2×C3C2×#1113
FittingC32×C4×C9C22
socleC2×C33C22×D3
hypercenterC4#66431
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×#66431C2semidirect
2. C9×C4⋊(C3⋊D3)C2semidirect
3. C3×C4⋊(C3⋊D9)C2semidirect
4. C3×C4×C3⋊D9C2semidirect
5. #10619899C2semidirect
9. C2×C9×C3⋊D3C22semidirect
11. C2×C3×C3⋊D9C22semidirect
13. C32×C4×C9C22semidirect
14. C3×C3⋊Dic9C22semidirect
22. C4⋊(C3⋊D9)D3semidirect
23. C4×C3⋊D9D3semidirect
36. C3×C3⋊D9D4semidirect
48. C2×C3⋊D9C2×D3semidirect
62. C3×C4×C9C2×D3semidirect
63. C3×C4×C9C2×D3semidirect
64. C3⋊Dic9C2×D3semidirect
67. C32×C9C2×D4semidirect
72. C4⋊(C3⋊D3)D9semidirect
104. C3⋊D9D12semidirect
117. C2×C3⋊D3C2×D9semidirect
134. C32×C4C2×D9semidirect
150. C4×C9D32semidirect
158. C3×C9C2×D12semidirect
159. C3×C9D3×D4semidirect
227. C3×C4D3×D9semidirect
228. C3×C4D3×D9semidirect
237. C32D4×D9semidirect
243. C9D3×D12semidirect
273. C4#66431semidirect
278. C3D9×D12semidirect
279. C3#88646semidirect

Maximal subgroups

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

subgroupindex
C2×#664312
C9×C4⋊(C3⋊D3)2
C3×C4⋊(C3⋊D9)2
C3×C4×C3⋊D92
#106198992
C4⋊#11133
#886463
D9×D123