Subgroups — C₉×#2403 #11767124

Order 1152.

2346 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₄×C₉	C₂	1	2	yes	maximal, complemented
2	C₂×C₉×#120	C₂	1	4	yes	maximal, complemented
3	C₉×#392	C₂	1	4	yes	maximal, complemented
4	C₉×#386	C₂	1	4	yes	maximal, complemented
5	C₉×#379	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2403	C₃	1	1	yes	maximal, characteristic
7	C₂⁵×C₉	C₂²	1	1	yes	characteristic
8	C₂⁵×C₉	C₂²	1	2	yes	complemented
9	C₂²×D₄×C₉	—	2	8	no	—
10	C₂²×D₄×C₉	—	2	16	no	—
11	C₂²×D₄×C₉	C₂²	1	4	yes	—
12	C₂²×D₄×C₉	C₂²	1	4	yes	complemented
13	C₂²×D₄×C₉	C₂²	1	4	yes	complemented
14	C₂³×C₄×C₉	C₂²	1	2	yes	complemented
15	C₉×#120	—	2	16	no	—
16	C₂×C₉×C₂²⋊C₄	C₂²	1	4	yes	complemented
17	C₂×C₉×C₂²⋊C₄	C₂²	1	8	yes	complemented
18	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	complemented
19	C₉×#95	C₂²	1	4	yes	complemented
20	C₂³×C₃×D₄	C₂×C₃	1	2	yes	—
21	C₂×C₃×#120	C₂×C₃	1	4	yes	—
22	C₃×#392	C₂×C₃	1	4	yes	—
23	C₃×#386	C₂×C₃	1	4	yes	—
24	C₃×#379	C₂×C₃	1	1	yes	characteristic
25	C₂⁴×C₉	—	2	8	no	—
26	C₂⁴×C₉	—	2	4	no	—
27	C₂⁴×C₉	—	2	8	no	—
28	C₂⁴×C₉	—	2	8	no	—
29	C₂⁴×C₉	—	4	2	no	—
30	C₂⁴×C₉	—	4	4	no	—
31	C₂⁴×C₉	D₄	1	4	yes	complemented
32	C₂⁴×C₉	C₂³	1	1	yes	characteristic
33	C₂⁴×C₉	C₂³	1	4	yes	—
34	C₂⁴×C₉	C₂³	1	2	yes	—
35	C₂×D₄×C₉	—	2	64	no	—
36	C₂×D₄×C₉	—	2	8	no	—
37	C₂×D₄×C₉	—	2	8	no	—
38	C₂×D₄×C₉	—	2	8	no	—
39	C₂×D₄×C₉	—	2	8	no	—
40	C₂×D₄×C₉	—	2	16	no	—
41	C₂×D₄×C₉	—	2	8	no	—
42	C₂×D₄×C₉	—	4	4	no	—
43	C₂×D₄×C₉	D₄	1	16	yes	complemented
44	C₂²×C₄×C₉	—	2	4	no	—
45	C₂²×C₄×C₉	—	2	8	no	—
46	C₂²×C₄×C₉	C₂³	1	4	yes	—
47	C₂²×C₄×C₉	C₂³	1	4	yes	—
48	C₉×C₂²⋊C₄	—	2	8	no	—
49	C₉×C₂²⋊C₄	—	2	16	no	—
50	C₉×C₂²⋊C₄	—	4	2	no	—
51	#2403	C₉	1	1	yes	characteristic, direct product factor, Sylow
52	C₂⁵×C₃	C₂²×C₃	1	1	yes	characteristic
53	C₂⁵×C₃	C₂²×C₃	1	2	yes	—
54	C₂²×C₃×D₄	—	2	8	no	—
55	C₂²×C₃×D₄	—	2	16	no	—
56	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
57	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
58	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
59	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
60	C₃×#120	—	2	16	no	—
61	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
62	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
63	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
64	C₃×#95	C₂²×C₃	1	4	yes	—
65	C₂³×C₉	—	2	4	no	—
66	C₂³×C₉	—	2	4	no	—
67	C₂³×C₉	—	2	16	no	—
68	C₂³×C₉	—	2	16	no	—
69	C₂³×C₉	—	2	8	no	—
70	C₂³×C₉	—	2	4	no	—
71	C₂³×C₉	—	2	4	no	—
72	C₂³×C₉	—	2	4	no	—
73	C₂³×C₉	—	2	2	no	—
74	C₂³×C₉	—	2	8	no	—
75	C₂³×C₉	—	4	4	no	—
76	C₂³×C₉	—	4	16	no	—
77	C₂³×C₉	—	4	32	no	—
78	C₂³×C₉	—	4	8	no	—
79	C₂³×C₉	—	4	8	no	—
80	C₂³×C₉	C₂×D₄	1	2	yes	—
81	C₂³×C₉	C₂×D₄	1	8	yes	—
82	C₂³×C₉	C₂×D₄	1	4	yes	—
83	C₂³×C₉	C₂×D₄	1	8	yes	complemented
84	C₂³×C₉	C₂⁴	1	1	yes	characteristic
85	D₄×C₉	—	2	32	no	—
86	D₄×C₉	—	2	32	no	—
87	D₄×C₉	—	4	16	no	—
88	C₂×C₄×C₉	—	2	16	no	—
89	C₂×C₄×C₉	—	2	4	no	—
90	C₂×C₄×C₉	—	2	4	no	—
91	C₂×C₄×C₉	—	2	8	no	—
92	C₂×C₄×C₉	—	2	4	no	—
93	C₂×C₄×C₉	C₂×D₄	1	8	yes	complemented
94	C₂³×D₄	C₂×C₉	1	2	yes	complemented
95	C₂×#120	C₂×C₉	1	4	yes	complemented
96	#392	C₂×C₉	1	4	yes	complemented
97	#386	C₂×C₉	1	4	yes	complemented
98	#379	C₂×C₉	1	1	yes	characteristic, complemented
99	C₂⁴×C₃	—	2	8	no	—
100	C₂⁴×C₃	—	2	4	no	—
101	C₂⁴×C₃	—	2	8	no	—
102	C₂⁴×C₃	—	2	8	no	—
103	C₂⁴×C₃	—	4	2	no	—
104	C₂⁴×C₃	—	4	4	no	—
105	C₂⁴×C₃	C₃×D₄	1	4	yes	—
106	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
107	C₂⁴×C₃	C₂³×C₃	1	4	yes	—
108	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
109	C₂×C₃×D₄	—	2	64	no	—
110	C₂×C₃×D₄	—	2	8	no	—
111	C₂×C₃×D₄	—	2	8	no	—
112	C₂×C₃×D₄	—	2	8	no	—
113	C₂×C₃×D₄	—	2	8	no	—
114	C₂×C₃×D₄	—	2	16	no	—
115	C₂×C₃×D₄	—	2	8	no	—
116	C₂×C₃×D₄	—	4	4	no	—
117	C₂×C₃×D₄	C₃×D₄	1	16	yes	—
118	C₂²×C₃×C₄	—	2	4	no	—
119	C₂²×C₃×C₄	—	2	8	no	—
120	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
121	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
122	C₃×C₂²⋊C₄	—	2	8	no	—
123	C₃×C₂²⋊C₄	—	2	16	no	—
124	C₃×C₂²⋊C₄	—	4	2	no	—
125	C₂²×C₉	—	2	4	no	—
126	C₂²×C₉	—	2	4	no	—
127	C₂²×C₉	—	2	16	no	—
128	C₂²×C₉	—	2	4	no	—
129	C₂²×C₉	—	2	8	no	—
130	C₂²×C₉	—	2	2	no	—
131	C₂²×C₉	—	2	16	no	—
132	C₂²×C₉	—	4	16	no	—
133	C₂²×C₉	—	4	32	no	—
134	C₂²×C₉	—	4	4	no	—
135	C₂²×C₉	—	4	4	no	—
136	C₂²×C₉	—	4	8	no	—
137	C₂²×C₉	—	4	4	no	—
138	C₂²×C₉	#120	1	8	yes	complemented
139	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
140	C₂²×C₉	C₂²×D₄	1	4	yes	—
141	C₂²×C₉	H(5,𝔽₂)	1	2	yes	—
142	C₄×C₉	—	2	8	no	—
143	C₄×C₉	—	4	4	no	—
144	C₂⁵	C₂²×C₉	1	1	yes	characteristic
145	C₂⁵	C₂²×C₉	1	2	yes	complemented
146	C₂²×D₄	—	2	8	no	—
147	C₂²×D₄	—	2	16	no	—
148	C₂²×D₄	C₂²×C₉	1	4	yes	—
149	C₂²×D₄	C₂²×C₉	1	4	yes	complemented
150	C₂²×D₄	C₂²×C₉	1	4	yes	complemented
151	C₂³×C₄	C₂²×C₉	1	2	yes	complemented
152	#120	—	2	16	no	—
153	C₂×C₂²⋊C₄	C₂²×C₉	1	4	yes	complemented
154	C₂×C₂²⋊C₄	C₂²×C₉	1	8	yes	complemented
155	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	complemented
156	#95	C₂²×C₉	1	4	yes	complemented
157	C₂³×C₃	—	2	4	no	—
158	C₂³×C₃	—	2	4	no	—
159	C₂³×C₃	—	2	16	no	—
160	C₂³×C₃	—	2	16	no	—
161	C₂³×C₃	—	2	8	no	—
162	C₂³×C₃	—	2	4	no	—
163	C₂³×C₃	—	2	4	no	—
164	C₂³×C₃	—	2	4	no	—
165	C₂³×C₃	—	2	2	no	—
166	C₂³×C₃	—	2	8	no	—
167	C₂³×C₃	—	4	4	no	—
168	C₂³×C₃	—	4	16	no	—
169	C₂³×C₃	—	4	32	no	—
170	C₂³×C₃	—	4	8	no	—
171	C₂³×C₃	—	4	8	no	—
172	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
173	C₂³×C₃	C₂×C₃×D₄	1	8	yes	—
174	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
175	C₂³×C₃	C₂×C₃×D₄	1	8	yes	—
176	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
177	C₃×D₄	—	2	32	no	—
178	C₃×D₄	—	2	32	no	—
179	C₃×D₄	—	4	16	no	—
180	C₂×C₃×C₄	—	2	16	no	—
181	C₂×C₃×C₄	—	2	4	no	—
182	C₂×C₃×C₄	—	2	4	no	—
183	C₂×C₃×C₄	—	2	8	no	—
184	C₂×C₃×C₄	—	2	4	no	—
185	C₂×C₃×C₄	C₂×C₃×D₄	1	8	yes	—
186	C₂×C₉	—	2	8	no	—
187	C₂×C₉	—	4	2	no	—
188	C₂×C₉	—	4	8	no	—
189	C₂×C₉	C₂×#120	1	2	yes	—
190	C₂×C₉	#534	1	1	yes	characteristic
191	C₂×C₉	D₄²	1	4	yes	—
192	C₂⁴	—	2	8	no	—
193	C₂⁴	—	2	4	no	—
194	C₂⁴	—	2	8	no	—
195	C₂⁴	—	2	8	no	—
196	C₂⁴	—	4	2	no	—
197	C₂⁴	—	4	4	no	—
198	C₂⁴	D₄×C₉	1	4	yes	complemented
199	C₂⁴	C₂³×C₉	1	1	yes	characteristic
200	C₂⁴	C₂³×C₉	1	4	yes	—
201	C₂⁴	C₂³×C₉	1	2	yes	—
202	C₂×D₄	—	2	64	no	—
203	C₂×D₄	—	2	8	no	—
204	C₂×D₄	—	2	8	no	—
205	C₂×D₄	—	2	8	no	—
206	C₂×D₄	—	2	8	no	—
207	C₂×D₄	—	2	16	no	—
208	C₂×D₄	—	2	8	no	—
209	C₂×D₄	—	4	4	no	—
210	C₂×D₄	D₄×C₉	1	16	yes	complemented
211	C₂²×C₄	—	2	4	no	—
212	C₂²×C₄	—	2	8	no	—
213	C₂²×C₄	C₂³×C₉	1	4	yes	—
214	C₂²×C₄	C₂³×C₉	1	4	yes	—
215	C₂²⋊C₄	—	2	8	no	—
216	C₂²⋊C₄	—	2	16	no	—
217	C₂²⋊C₄	—	4	2	no	—
218	C₂²×C₃	—	2	4	no	—
219	C₂²×C₃	—	2	4	no	—
220	C₂²×C₃	—	2	16	no	—
221	C₂²×C₃	—	2	4	no	—
222	C₂²×C₃	—	2	8	no	—
223	C₂²×C₃	—	2	2	no	—
224	C₂²×C₃	—	2	16	no	—
225	C₂²×C₃	—	4	16	no	—
226	C₂²×C₃	—	4	32	no	—
227	C₂²×C₃	—	4	4	no	—
228	C₂²×C₃	—	4	4	no	—
229	C₂²×C₃	—	4	8	no	—
230	C₂²×C₃	—	4	4	no	—
231	C₂²×C₃	C₃×#120	1	8	yes	—
232	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
233	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
234	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	—
235	C₃×C₄	—	2	8	no	—
236	C₃×C₄	—	4	4	no	—
237	C₉	#2403	1	1	yes	characteristic, direct product factor, Sylow
238	C₂³	—	2	4	no	—
239	C₂³	—	2	4	no	—
240	C₂³	—	2	16	no	—
241	C₂³	—	2	16	no	—
242	C₂³	—	2	8	no	—
243	C₂³	—	2	4	no	—
244	C₂³	—	2	4	no	—
245	C₂³	—	2	4	no	—
246	C₂³	—	2	2	no	—
247	C₂³	—	2	8	no	—
248	C₂³	—	4	4	no	—
249	C₂³	—	4	16	no	—
250	C₂³	—	4	32	no	—
251	C₂³	—	4	8	no	—
252	C₂³	—	4	8	no	—
253	C₂³	C₂×D₄×C₉	1	2	yes	—
254	C₂³	C₂×D₄×C₉	1	8	yes	—
255	C₂³	C₂×D₄×C₉	1	4	yes	—
256	C₂³	C₂×D₄×C₉	1	8	yes	complemented
257	C₂³	C₂⁴×C₉	1	1	yes	characteristic
258	D₄	—	2	32	no	—
259	D₄	—	2	32	no	—
260	D₄	—	4	16	no	—
261	C₂×C₄	—	2	16	no	—
262	C₂×C₄	—	2	4	no	—
263	C₂×C₄	—	2	4	no	—
264	C₂×C₄	—	2	8	no	—
265	C₂×C₄	—	2	4	no	—
266	C₂×C₄	C₂×D₄×C₉	1	8	yes	complemented
267	C₂×C₃	—	2	8	no	—
268	C₂×C₃	—	4	2	no	—
269	C₂×C₃	—	4	8	no	—
270	C₂×C₃	C₂×C₃×#120	1	2	yes	—
271	C₂×C₃	C₃×#534	1	1	yes	characteristic
272	C₂×C₃	C₃×D₄²	1	4	yes	—
273	C₂²	—	2	4	no	—
274	C₂²	—	2	4	no	—
275	C₂²	—	2	16	no	—
276	C₂²	—	2	4	no	—
277	C₂²	—	2	8	no	—
278	C₂²	—	2	2	no	—
279	C₂²	—	2	16	no	—
280	C₂²	—	4	16	no	—
281	C₂²	—	4	32	no	—
282	C₂²	—	4	4	no	—
283	C₂²	—	4	4	no	—
284	C₂²	—	4	8	no	—
285	C₂²	—	4	4	no	—
286	C₂²	C₉×#120	1	8	yes	complemented
287	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
288	C₂²	C₂²×D₄×C₉	1	4	yes	—
289	C₂²	C₉×H(5,𝔽₂)	1	2	yes	—
290	C₄	—	2	8	no	—
291	C₄	—	4	4	no	—
292	C₃	C₃×#2403	1	1	yes	characteristic
293	C₂	—	2	8	no	—
294	C₂	—	4	2	no	—
295	C₂	—	4	8	no	—
296	C₂	C₂×C₉×#120	1	2	yes	—
297	C₂	C₉×#534	1	1	yes	characteristic
298	C₂	D₄²×C₉	1	4	yes	—

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂³	C₂⁴×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₃×#2403	C₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×D₄×C₉	C₂	semidirect
2. C₂×C₉×#120	C₂	semidirect
3. C₉×#392	C₂	semidirect
4. C₉×#386	C₂	semidirect
5. C₉×#379	C₂	semidirect
8. C₂⁵×C₉	C₂²	semidirect
12. C₂²×D₄×C₉	C₂²	semidirect
13. C₂²×D₄×C₉	C₂²	semidirect
14. C₂³×C₄×C₉	C₂²	semidirect
16. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
17. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
18. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
19. C₉×#95	C₂²	semidirect
31. C₂⁴×C₉	D₄	semidirect
43. C₂×D₄×C₉	D₄	semidirect
51. #2403	C₉	direct (N × H)
83. C₂³×C₉	C₂×D₄	semidirect
93. C₂×C₄×C₉	C₂×D₄	semidirect
94. C₂³×D₄	C₂×C₉	semidirect
95. C₂×#120	C₂×C₉	semidirect
96. #392	C₂×C₉	semidirect
97. #386	C₂×C₉	semidirect
98. #379	C₂×C₉	semidirect
138. C₂²×C₉	#120	semidirect
145. C₂⁵	C₂²×C₉	semidirect
149. C₂²×D₄	C₂²×C₉	semidirect
150. C₂²×D₄	C₂²×C₉	semidirect
151. C₂³×C₄	C₂²×C₉	semidirect
153. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
154. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
155. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
156. #95	C₂²×C₉	semidirect
198. C₂⁴	D₄×C₉	semidirect
210. C₂×D₄	D₄×C₉	semidirect
237. C₉	#2403	direct (N × H)
256. C₂³	C₂×D₄×C₉	semidirect
266. C₂×C₄	C₂×D₄×C₉	semidirect
286. C₂²	C₉×#120	semidirect

Maximal subgroups

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

subgroup	index
C₂³×D₄×C₉	2
C₂×C₉×#120	2
C₉×#392	2
C₉×#386	2
C₉×#379	2
C₃×#2403	3

Subgroups — C9×#2403 #11767124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2403 #11767124