Subgroups — C₉×#4706 #13141512

Order 1728.

412 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₃×C₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic
4	C₃×C₉×#97	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4706	C₃	1	1	yes	maximal, characteristic
9	C₉×#435	—	3	1	no	maximal
10	C₂×C₉×D₁₂	C₄	1	1	yes	characteristic
11	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic
15	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
16	C₉×(C₂×D₃)⋊C₄	C₄	1	1	yes	characteristic
17	C₉×(C₂×D₃)⋊C₄	C₄	1	1	yes	characteristic
18	C₉×C₄⋊Dic₃	C₄	1	1	yes	characteristic
19	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₉×ΓL(1,𝔽₂₅)	—	2	2	no	—
22	D₃×C₈×C₉	—	2	2	no	—
23	C₂×C₃×ΓL(1,𝔽₂₅)	C₂×C₃	1	1	yes	characteristic
24	C₂×C₃×D₃×C₈	C₂×C₃	1	1	yes	characteristic
25	C₃×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
26	C₃²×#97	C₂×C₃	1	1	yes	characteristic
27	C₃×(C₂×D₃)⋊C₈	C₂×C₃	1	1	yes	characteristic
28	C₃×(C₂×D₃)⋊C₈	C₂×C₃	1	1	yes	characteristic
29	C₃×C₄⋊(C₃⋊C₈)	C₂×C₃	1	1	yes	characteristic
30	C₂×C₉×M₁₆	—	3	1	no	—
31	C₂²×C₈×C₉	—	3	1	no	—
32	C₄×D₄×C₉	—	3	1	no	—
33	C₉×C₄⋊C₈	—	3	1	no	—
34	C₉×C₂²⋊C₈	—	3	1	no	—
35	C₉×C₂²⋊C₈	—	3	1	no	—
36	C₉×#97	—	2	1	no	—
37	C₉×#97	D₃	1	1	yes	characteristic, complemented
38	C₂²×D₃×C₉	C₂×C₄	1	1	yes	characteristic
39	C₂²×D₃×C₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₃×C₄×C₉	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃×C₄×C₉	C₂×C₄	1	1	yes	characteristic
42	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
43	C₂×C₉×Dic₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₉×Dic₃	C₂×C₄	1	1	yes	characteristic
45	C₉×D₁₂	—	2	2	no	—
46	C₄×D₃×C₉	—	2	1	no	—
47	C₄×D₃×C₉	—	2	1	no	—
48	C₄×D₃×C₉	—	2	1	no	—
49	C₄×D₃×C₉	—	2	1	no	—
50	C₃×C₈×C₉	—	2	1	no	—
51	C₃×C₈×C₉	D₄	1	2	yes	complemented
52	C₉×C₃⋊C₈	—	2	1	no	—
53	C₉×C₃⋊C₈	—	2	1	no	—
54	C₃×#435	—	3	1	no	—
55	#4706	C₉	1	1	yes	characteristic, direct product factor
56	C₂×C₃×D₁₂	C₃×C₄	1	1	yes	characteristic
57	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
58	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
59	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
60	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
61	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
62	C₃×(C₂×D₃)⋊C₄	C₃×C₄	1	1	yes	characteristic
63	C₃×(C₂×D₃)⋊C₄	C₃×C₄	1	1	yes	characteristic
64	C₃×C₄⋊Dic₃	C₃×C₄	1	1	yes	characteristic
65	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
66	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
67	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
68	C₃×D₃×C₈	—	2	2	no	—
69	C₂×D₄×C₉	—	3	1	no	—
70	C₂²×C₄×C₉	—	3	1	no	—
71	C₂²×C₄×C₉	—	3	1	no	—
72	C₉×M₁₆	—	6	2	no	—
73	C₂×C₈×C₉	—	2	1	no	—
74	C₂×C₈×C₉	—	2	1	no	—
75	C₂×C₈×C₉	—	3	1	no	—
76	C₂×C₈×C₉	—	3	1	no	—
77	C₂×C₈×C₉	—	6	2	no	—
78	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic
79	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic
80	C₉×C₄⋊C₄	—	3	1	no	—
81	C₉×C₂²⋊C₄	—	3	1	no	—
82	C₉×C₂²⋊C₄	—	3	1	no	—
83	C₄²×C₉	—	2	1	no	—
84	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
85	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
86	C₂×D₃×C₉	—	2	1	no	—
87	C₂×D₃×C₉	—	2	1	no	—
88	C₂×D₃×C₉	—	2	1	no	—
89	C₂×D₃×C₉	—	2	1	no	—
90	C₂×D₃×C₉	—	2	1	no	—
91	C₂×D₃×C₉	M₁₆	1	2	yes	complemented
92	C₃×C₄×C₉	—	2	1	no	—
93	C₃×C₄×C₉	—	2	1	no	—
94	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
95	C₃×C₄×C₉	#41	1	1	yes	characteristic
96	C₉×Dic₃	—	2	1	no	—
97	C₉×Dic₃	—	2	1	no	—
98	C₂×C₃×M₁₆	—	3	1	no	—
99	C₂²×C₃×C₈	—	3	1	no	—
100	C₃×C₄×D₄	—	3	1	no	—
101	C₂×ΓL(1,𝔽₂₅)	C₂×C₉	1	1	yes	characteristic, complemented
102	C₂×D₃×C₈	C₂×C₉	1	1	yes	characteristic, complemented
103	C₄×D₁₂	C₂×C₉	1	1	yes	characteristic
104	C₃×C₄⋊C₈	—	3	1	no	—
105	C₃×C₂²⋊C₈	—	3	1	no	—
106	C₃×C₂²⋊C₈	—	3	1	no	—
107	C₃×#97	—	2	1	no	—
108	C₃×#97	C₂×C₉	1	1	yes	characteristic, complemented
109	C₃×#97	C₃×D₃	1	1	yes	characteristic
110	(C₂×D₃)⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
111	(C₂×D₃)⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
112	C₄⋊(C₃⋊C₈)	C₂×C₉	1	1	yes	characteristic, complemented
113	C₂²×C₃×D₃	C₂×C₃×C₄	1	1	yes	characteristic
114	C₂²×C₃×D₃	C₂×C₃×C₄	1	1	yes	characteristic
115	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
116	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
117	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
118	C₂×C₃×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
119	C₂×C₃×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
120	C₃×D₁₂	—	2	2	no	—
121	C₃×C₄×D₃	—	2	1	no	—
122	C₃×C₄×D₃	—	2	1	no	—
123	C₃×C₄×D₃	—	2	1	no	—
124	C₃×C₄×D₃	—	2	1	no	—
125	C₂³×C₉	—	3	1	no	—
126	C₂³×C₉	—	3	1	no	—
127	C₃²×C₈	—	2	1	no	—
128	C₃²×C₈	C₃×D₄	1	2	yes	—
129	C₃×C₃⋊C₈	—	2	1	no	—
130	C₃×C₃⋊C₈	—	2	1	no	—
131	D₄×C₉	—	6	2	no	—
132	C₂×C₄×C₉	—	2	1	no	—
133	C₂×C₄×C₉	—	2	1	no	—
134	C₂×C₄×C₉	—	2	1	no	—
135	C₂×C₄×C₉	—	3	1	no	—
136	C₂×C₄×C₉	—	3	1	no	—
137	C₂×C₄×C₉	—	6	1	no	—
138	C₂×C₄×C₉	—	6	1	no	—
139	C₂×C₄×C₉	—	6	1	no	—
140	C₂×C₄×C₉	—	6	1	no	—
141	C₂×C₄×C₉	C₄×D₃	1	1	yes	characteristic
142	C₂×C₄×C₉	C₄×D₃	1	1	yes	characteristic
143	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
144	C₈×C₉	—	2	2	no	—
145	C₈×C₉	—	2	1	no	—
146	C₈×C₉	—	2	2	no	—
147	C₈×C₉	—	6	1	no	—
148	C₈×C₉	—	6	1	no	—
149	C₈×C₉	D₁₂	1	2	yes	complemented
150	#435	—	3	1	no	Sylow
151	C₂×C₃×C₉	C₄×D₄	1	1	yes	characteristic
152	C₂×C₃×C₉	C₂×M₁₆	1	1	yes	characteristic
153	C₂×C₃×C₉	#131	1	1	yes	characteristic
154	D₃×C₉	—	2	2	no	—
155	D₃×C₉	—	4	1	no	—
156	C₂×C₃×D₄	—	3	1	no	—
157	C₂²×C₃×C₄	—	3	1	no	—
158	C₂²×C₃×C₄	—	3	1	no	—
159	C₂×D₁₂	C₄×C₉	1	1	yes	characteristic
160	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
161	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
162	C₃×M₁₆	—	6	2	no	—
163	C₂×C₃×C₈	—	2	1	no	—
164	C₂×C₃×C₈	—	2	1	no	—
165	C₂×C₃×C₈	—	3	1	no	—
166	C₂×C₃×C₈	—	3	1	no	—
167	C₂×C₃×C₈	—	6	2	no	—
168	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic
169	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic
170	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
171	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
172	C₃×C₄⋊C₄	—	3	1	no	—
173	C₃×C₂²⋊C₄	—	3	1	no	—
174	C₃×C₂²⋊C₄	—	3	1	no	—
175	C₃×C₄²	—	2	1	no	—
176	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
177	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
178	(C₂×D₃)⋊C₄	C₄×C₉	1	1	yes	characteristic
179	(C₂×D₃)⋊C₄	C₄×C₉	1	1	yes	characteristic
180	C₄⋊Dic₃	C₄×C₉	1	1	yes	characteristic
181	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
182	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
183	ΓL(1,𝔽₂₅)	—	2	2	no	—
184	D₃×C₈	—	2	2	no	—
185	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
186	C₂×C₃×D₃	—	2	1	no	—
187	C₂×C₃×D₃	—	2	1	no	—
188	C₂×C₃×D₃	—	2	1	no	—
189	C₂×C₃×D₃	—	2	1	no	—
190	C₂×C₃×D₃	—	2	1	no	—
191	C₂×C₃×D₃	C₃×M₁₆	1	2	yes	—
192	C₃²×C₄	—	2	1	no	—
193	C₃²×C₄	—	2	1	no	—
194	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
195	C₃²×C₄	C₃×#41	1	1	yes	characteristic
196	C₃×Dic₃	—	2	1	no	—
197	C₃×Dic₃	—	2	1	no	—
198	C₂²×C₉	—	2	1	no	—
199	C₂²×C₉	—	3	2	no	—
200	C₂²×C₉	—	6	1	no	—
201	C₂²×C₉	—	6	1	no	—
202	C₂²×C₉	—	6	1	no	—
203	C₂²×C₉	—	6	1	no	—
204	C₂²×C₉	—	6	1	no	—
205	C₂²×C₉	C₂×C₄×D₃	1	1	yes	characteristic
206	C₄×C₉	—	2	1	no	—
207	C₄×C₉	—	2	1	no	—
208	C₄×C₉	—	2	1	no	—
209	C₄×C₉	—	2	1	no	—
210	C₄×C₉	—	4	1	no	—
211	C₄×C₉	—	4	1	no	—
212	C₄×C₉	—	6	1	no	—
213	C₄×C₉	—	6	1	no	—
214	C₄×C₉	C₂×D₁₂	1	1	yes	characteristic
215	C₄×C₉	#235	1	1	yes	characteristic
216	C₂×M₁₆	—	3	1	no	—
217	C₂²×C₈	—	3	1	no	—
218	C₄×D₄	—	3	1	no	—
219	C₄⋊C₈	—	3	1	no	—
220	C₂²⋊C₈	—	3	1	no	—
221	C₂²⋊C₈	—	3	1	no	—
222	#97	D₃×C₉	1	1	yes	characteristic, complemented
223	C₃×C₉	#435	1	1	yes	characteristic, complemented, Sylow
224	C₂³×C₃	—	3	1	no	—
225	C₂³×C₃	—	3	1	no	—
226	C₂²×D₃	C₂×C₄×C₉	1	1	yes	characteristic
227	C₂²×D₃	C₂×C₄×C₉	1	1	yes	characteristic
228	C₃×D₄	—	6	2	no	—
229	C₂×C₃×C₄	—	2	1	no	—
230	C₂×C₃×C₄	—	2	1	no	—
231	C₂×C₃×C₄	—	2	1	no	—
232	C₂×C₃×C₄	—	3	1	no	—
233	C₂×C₃×C₄	—	3	1	no	—
234	C₂×C₃×C₄	—	6	1	no	—
235	C₂×C₃×C₄	—	6	1	no	—
236	C₂×C₃×C₄	—	6	1	no	—
237	C₂×C₃×C₄	—	6	1	no	—
238	C₂×C₃×C₄	C₂×C₄×C₉	1	1	yes	characteristic
239	C₂×C₃×C₄	C₂×C₄×C₉	1	1	yes	characteristic
240	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
241	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
242	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
243	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
244	C₂×Dic₃	C₂×C₄×C₉	1	1	yes	characteristic
245	C₂×Dic₃	C₂×C₄×C₉	1	1	yes	characteristic
246	D₁₂	—	2	2	no	—
247	C₄×D₃	—	2	1	no	—
248	C₄×D₃	—	2	1	no	—
249	C₄×D₃	—	2	1	no	—
250	C₄×D₃	—	2	1	no	—
251	C₃×C₈	—	2	2	no	—
252	C₃×C₈	—	2	1	no	—
253	C₃×C₈	—	2	1	no	—
254	C₃×C₈	—	2	2	no	—
255	C₃×C₈	—	6	1	no	—
256	C₃×C₈	—	6	1	no	—
257	C₃×C₈	D₄×C₉	1	2	yes	complemented
258	C₃×C₈	C₃×D₁₂	1	2	yes	—
259	C₃⋊C₈	—	2	1	no	—
260	C₃⋊C₈	—	2	1	no	—
261	C₂×C₃²	C₃×C₄×D₄	1	1	yes	characteristic
262	C₂×C₃²	C₂×C₃×M₁₆	1	1	yes	characteristic
263	C₂×C₃²	C₃×#131	1	1	yes	characteristic
264	C₃×D₃	—	2	2	no	—
265	C₃×D₃	—	4	1	no	—
266	C₂×C₉	—	2	1	no	—
267	C₂×C₉	—	2	1	no	—
268	C₂×C₉	—	2	1	no	—
269	C₂×C₉	—	6	2	no	—
270	C₂×C₉	—	12	1	no	—
271	C₂×C₉	C₄×D₁₂	1	1	yes	characteristic
272	C₂×C₉	D₃×M₁₆	1	1	yes	characteristic
273	C₂×C₉	#907	1	1	yes	characteristic
274	C₂×D₄	—	3	1	no	—
275	C₂²×C₄	—	3	1	no	—
276	C₂²×C₄	—	3	1	no	—
277	M₁₆	—	6	2	no	—
278	C₂×C₈	—	3	1	no	—
279	C₂×C₈	—	3	1	no	—
280	C₂×C₈	—	6	2	no	—
281	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic
282	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic
283	C₄⋊C₄	—	3	1	no	—
284	C₂²⋊C₄	—	3	1	no	—
285	C₂²⋊C₄	—	3	1	no	—
286	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
287	C₂²×C₃	—	2	1	no	—
288	C₂²×C₃	—	3	2	no	—
289	C₂²×C₃	—	6	1	no	—
290	C₂²×C₃	—	6	1	no	—
291	C₂²×C₃	—	6	1	no	—
292	C₂²×C₃	—	6	1	no	—
293	C₂²×C₃	—	6	1	no	—
294	C₂²×C₃	C₂²×C₄×C₉	1	1	yes	characteristic
295	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
296	C₂×D₃	—	2	1	no	—
297	C₂×D₃	—	2	1	no	—
298	C₂×D₃	—	2	1	no	—
299	C₂×D₃	—	2	1	no	—
300	C₂×D₃	—	2	1	no	—
301	C₂×D₃	C₉×M₁₆	1	2	yes	complemented
302	C₃×C₄	—	2	1	no	—
303	C₃×C₄	—	2	1	no	—
304	C₃×C₄	—	2	1	no	—
305	C₃×C₄	—	2	1	no	—
306	C₃×C₄	—	2	1	no	—
307	C₃×C₄	—	2	1	no	—
308	C₃×C₄	—	4	1	no	—
309	C₃×C₄	—	4	1	no	—
310	C₃×C₄	—	6	1	no	—
311	C₃×C₄	—	6	1	no	—
312	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
313	C₃×C₄	C₉×#41	1	1	yes	characteristic
314	C₃×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
315	C₃×C₄	C₃×#235	1	1	yes	characteristic
316	Dic₃	—	2	1	no	—
317	Dic₃	—	2	1	no	—
318	C₃²	C₃×#435	1	1	yes	characteristic
319	C₉	—	2	1	no	—
320	C₉	#4706	1	1	yes	characteristic, direct product factor
321	C₂³	—	3	1	no	—
322	C₂³	—	3	1	no	—
323	D₄	—	6	2	no	—
324	C₂×C₄	—	3	1	no	—
325	C₂×C₄	—	3	1	no	—
326	C₂×C₄	—	6	1	no	—
327	C₂×C₄	—	6	1	no	—
328	C₂×C₄	—	6	1	no	—
329	C₂×C₄	—	6	1	no	—
330	C₂×C₄	C₄×D₃×C₉	1	1	yes	characteristic
331	C₂×C₄	C₄×D₃×C₉	1	1	yes	characteristic
332	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
333	C₈	—	2	1	no	—
334	C₈	—	6	1	no	—
335	C₈	—	6	1	no	—
336	C₈	C₉×D₁₂	1	2	yes	complemented
337	C₂×C₃	—	2	1	no	—
338	C₂×C₃	—	2	1	no	—
339	C₂×C₃	—	2	1	no	—
340	C₂×C₃	—	6	2	no	—
341	C₂×C₃	—	12	1	no	—
342	C₂×C₃	C₄×D₄×C₉	1	1	yes	characteristic
343	C₂×C₃	C₂×C₉×M₁₆	1	1	yes	characteristic
344	C₂×C₃	C₉×#131	1	1	yes	characteristic
345	C₂×C₃	C₃×C₄×D₁₂	1	1	yes	characteristic
346	C₂×C₃	C₃×D₃×M₁₆	1	1	yes	characteristic
347	C₂×C₃	C₃×#907	1	1	yes	characteristic
348	D₃	—	2	2	no	—
349	D₃	—	4	1	no	—
350	C₂²	—	3	2	no	—
351	C₂²	—	6	1	no	—
352	C₂²	—	6	1	no	—
353	C₂²	—	6	1	no	—
354	C₂²	—	6	1	no	—
355	C₂²	—	6	1	no	—
356	C₂²	C₂×C₄×D₃×C₉	1	1	yes	characteristic
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	6	1	no	—
360	C₄	—	6	1	no	—
361	C₄	C₂×C₉×D₁₂	1	1	yes	characteristic
362	C₄	C₉×#235	1	1	yes	characteristic
363	C₃	—	2	1	no	—
364	C₃	C₉×#435	1	1	yes	characteristic, complemented
365	C₃	C₃×#4706	1	1	yes	characteristic
366	C₂	—	6	2	no	—
367	C₂	—	12	1	no	—
368	C₂	C₄×C₉×D₁₂	1	1	yes	characteristic
369	C₂	D₃×C₉×M₁₆	1	1	yes	characteristic
370	C₂	C₉×#907	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₉	C₂²×D₃
commutator	C₂²×C₃	C₂²×C₄×C₉
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₃×C₉×#97	C₂
socle	C₂²×C₃²	C₂²×C₃×C₄
prime radical	C₂×C₃×D₁₂	C₃×C₄
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₉×#97	D₃
hypocenter	C₃	C₉×#435
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₉ ◁ C₉×#97

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×ΓL(1,𝔽₂₅)	C₂	semidirect
2. C₂×D₃×C₈×C₉	C₂	semidirect
4. C₃×C₉×#97	C₂	semidirect
5. C₉×(C₂×D₃)⋊C₈	C₂	semidirect
6. C₉×(C₂×D₃)⋊C₈	C₂	semidirect
7. C₉×C₄⋊(C₃⋊C₈)	C₂	semidirect
37. C₉×#97	D₃	semidirect
51. C₃×C₈×C₉	D₄	semidirect
55. #4706	C₉	direct (N × H)
91. C₂×D₃×C₉	M₁₆	semidirect
101. C₂×ΓL(1,𝔽₂₅)	C₂×C₉	semidirect
102. C₂×D₃×C₈	C₂×C₉	semidirect
108. C₃×#97	C₂×C₉	semidirect
110. (C₂×D₃)⋊C₈	C₂×C₉	semidirect
111. (C₂×D₃)⋊C₈	C₂×C₉	semidirect
112. C₄⋊(C₃⋊C₈)	C₂×C₉	semidirect
149. C₈×C₉	D₁₂	semidirect
222. #97	D₃×C₉	semidirect
223. C₃×C₉	#435	semidirect
257. C₃×C₈	D₄×C₉	semidirect
301. C₂×D₃	C₉×M₁₆	semidirect
320. C₉	#4706	direct (N × H)
336. C₈	C₉×D₁₂	semidirect
364. C₃	C₉×#435	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×ΓL(1,𝔽₂₅)	2
C₂×D₃×C₈×C₉	2
C₄×C₉×D₁₂	2
C₃×C₉×#97	2
C₉×(C₂×D₃)⋊C₈	2
C₉×C₄⋊(C₃⋊C₈)	2
C₃×#4706	3
C₉×#435	3

Subgroups — C9×#4706 #13141512

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#4706 #13141512