Subgroups — C₉×#4821 #13141973

Order 1728.

506 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×C₉×#41	C₂	1	1	yes	maximal, characteristic
2	D₃×C₉×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#872	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₉×#104	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#837	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#825	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#805	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4821	C₃	1	1	yes	maximal, characteristic
9	C₉×#421	—	3	1	no	maximal
10	C₃×C₉×#41	C₂²	1	1	yes	characteristic
11	C₉×#239	C₄	1	1	yes	characteristic, complemented
12	D₃×Q₈×C₉	C₄	1	1	yes	characteristic, complemented
13	C₉×#237	—	2	1	no	—
14	C₉×#237	C₄	1	1	yes	characteristic, complemented
15	D₃×D₄×C₉	—	2	1	no	—
16	D₃×D₄×C₉	C₄	1	1	yes	characteristic, complemented
17	C₉×#235	—	2	1	no	—
18	C₉×#235	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₃×C₉	—	2	1	no	—
20	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
21	C₃×C₉×M₁₆	C₂²	1	1	yes	characteristic, complemented
22	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic, complemented
23	C₉×(C₂×D₃)⋊C₄	—	2	1	no	—
24	C₉×Dic₃⋊C₄	—	2	1	no	—
25	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
26	C₉×#208	C₂²	1	1	yes	characteristic, complemented
27	C₉×ΓL(1,𝔽₂₅)	—	2	1	no	—
28	D₃×C₈×C₉	—	2	1	no	—
29	C₃×D₃×#41	C₂×C₃	1	1	yes	characteristic
30	C₃×D₃×M₁₆	C₂×C₃	1	1	yes	characteristic
31	C₃×#872	C₂×C₃	1	1	yes	characteristic
32	C₂×C₉×#41	—	3	1	no	—
33	C₃²×#104	C₂×C₃	1	1	yes	characteristic
34	C₃×#837	C₂×C₃	1	1	yes	characteristic
35	C₃×#825	C₂×C₃	1	1	yes	characteristic
36	C₃×#805	C₂×C₃	1	1	yes	characteristic
37	C₂×C₉×M₁₆	—	3	1	no	—
38	C₉×#117	—	3	1	no	—
39	C₉×#104	—	2	1	no	—
40	C₉×#104	—	3	1	no	—
41	C₉×#104	—	3	1	no	—
42	C₉×#104	—	3	1	no	—
43	C₉×#104	D₃	1	1	yes	characteristic, complemented
44	C₂²×D₃×C₉	—	2	1	no	—
45	C₂²×D₃×C₉	D₄	1	1	yes	characteristic
46	C₃×Q₈×C₉	C₂×C₄	1	1	yes	characteristic
47	C₃×D₄×C₉	—	2	1	no	—
48	C₃×D₄×C₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃×C₄×C₉	—	2	1	no	—
50	C₂×C₃×C₄×C₉	—	2	1	no	—
51	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
52	C₉×#67	—	2	1	no	—
53	C₉×#67	—	2	1	no	—
54	C₉×#67	—	2	1	no	—
55	C₂×C₉×Dic₃	—	2	1	no	—
56	C₂×C₉×Dic₃	—	2	1	no	—
57	C₂×C₉×Dic₃	D₄	1	1	yes	characteristic
58	C₉×D₁₂	—	2	1	no	—
59	C₉×D₁₂	C₂×C₄	1	1	yes	characteristic
60	C₄×D₃×C₉	—	2	1	no	—
61	C₄×D₃×C₉	—	2	1	no	—
62	C₄×D₃×C₉	—	2	1	no	—
63	C₄×D₃×C₉	C₂×C₄	1	1	yes	characteristic
64	C₄×D₃×C₉	C₂×C₄	1	1	yes	characteristic
65	C₄×D₃×C₉	D₄	1	1	yes	characteristic
66	C₄×D₃×C₉	D₄	1	1	yes	characteristic
67	C₉×Dic₆	—	2	1	no	—
68	C₉×Dic₆	C₂×C₄	1	1	yes	characteristic
69	C₃×C₈×C₉	—	2	1	no	—
70	C₉×C₃⋊C₈	—	2	1	no	—
71	C₃×#421	—	3	1	no	—
72	#4821	C₉	1	1	yes	characteristic, direct product factor
73	C₃²×#41	C₂²×C₃	1	1	yes	characteristic
74	C₃×#239	C₃×C₄	1	1	yes	characteristic
75	C₃×D₃×Q₈	C₃×C₄	1	1	yes	characteristic
76	C₃×#237	—	2	1	no	—
77	C₃×#237	C₃×C₄	1	1	yes	characteristic
78	C₃×D₃×D₄	—	2	1	no	—
79	C₃×D₃×D₄	C₃×C₄	1	1	yes	characteristic
80	C₃×#235	—	2	1	no	—
81	C₃×#235	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₃×C₄×D₃	—	2	1	no	—
83	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
84	C₃²×M₁₆	C₂²×C₃	1	1	yes	characteristic
85	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
86	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
87	C₃×Dic₃⋊C₄	—	2	1	no	—
88	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
89	C₃×#208	C₂²×C₃	1	1	yes	characteristic
90	C₃×ΓL(1,𝔽₂₅)	—	2	1	no	—
91	C₃×D₃×C₈	—	2	1	no	—
92	C₉×#41	—	2	1	no	—
93	C₉×#41	—	3	1	no	—
94	C₉×#41	—	3	1	no	—
95	C₉×#41	—	3	1	no	—
96	C₉×#41	—	6	1	no	—
97	C₉×#41	—	6	1	no	—
98	C₉×#41	C₂×D₃	1	1	yes	characteristic
99	C₂×Q₈×C₉	—	3	1	no	—
100	C₂×D₄×C₉	—	3	1	no	—
101	C₂×D₄×C₉	—	6	1	no	—
102	C₂²×C₄×C₉	—	3	1	no	—
103	C₂²×C₄×C₉	—	6	1	no	—
104	C₉×M₁₆	—	2	1	no	—
105	C₉×M₁₆	—	3	1	no	—
106	C₉×M₁₆	—	6	1	no	—
107	C₉×M₁₆	C₂×D₃	1	1	yes	characteristic, complemented
108	C₂×C₈×C₉	—	6	1	no	—
109	C₉×C₄⋊C₄	—	6	1	no	—
110	C₉×C₂²⋊C₄	—	6	1	no	—
111	C₄²×C₉	—	2	1	no	—
112	C₄²×C₉	—	3	1	no	—
113	C₄²×C₉	C₂×D₃	1	1	yes	characteristic, complemented
114	C₂²×C₃×C₉	—	2	1	no	—
115	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
116	C₂×D₃×C₉	—	2	1	no	—
117	C₂×D₃×C₉	—	4	1	no	—
118	C₂×D₃×C₉	—	4	2	no	—
119	C₂×D₃×C₉	C₂²⋊C₄	1	1	yes	characteristic
120	C₂×D₃×C₉	C₂²⋊C₄	1	1	yes	characteristic
121	C₃×C₄×C₉	—	2	1	no	—
122	C₃×C₄×C₉	—	4	1	no	—
123	C₃×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
124	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
125	C₉×Dic₃	—	2	1	no	—
126	C₉×Dic₃	—	4	1	no	—
127	C₉×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
128	C₉×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
129	C₂×C₃×#41	—	3	1	no	—
130	D₃×#41	C₂×C₉	1	1	yes	characteristic
131	C₂×C₃×M₁₆	—	3	1	no	—
132	C₃×#117	—	3	1	no	—
133	D₃×M₁₆	C₂×C₉	1	1	yes	characteristic, complemented
134	#872	C₂×C₉	1	1	yes	characteristic, complemented
135	C₃×#104	—	2	1	no	—
136	C₃×#104	—	3	1	no	—
137	C₃×#104	—	3	1	no	—
138	C₃×#104	—	3	1	no	—
139	C₃×#104	C₂×C₉	1	1	yes	characteristic, complemented
140	C₃×#104	C₃×D₃	1	1	yes	characteristic
141	#837	C₂×C₉	1	1	yes	characteristic, complemented
142	#825	C₂×C₉	1	1	yes	characteristic, complemented
143	#805	C₂×C₉	1	1	yes	characteristic, complemented
144	C₂²×C₃×D₃	—	2	1	no	—
145	C₂²×C₃×D₃	C₃×D₄	1	1	yes	characteristic
146	C₃²×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
147	C₃²×D₄	—	2	1	no	—
148	C₃²×D₄	C₂×C₃×C₄	1	1	yes	characteristic
149	C₂×C₃²×C₄	—	2	1	no	—
150	C₂×C₃²×C₄	—	2	1	no	—
151	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
152	C₃×#67	—	2	1	no	—
153	C₃×#67	—	2	1	no	—
154	C₃×#67	—	2	1	no	—
155	C₂×C₃×Dic₃	—	2	1	no	—
156	C₂×C₃×Dic₃	—	2	1	no	—
157	C₂×C₃×Dic₃	C₃×D₄	1	1	yes	characteristic
158	C₃×D₁₂	—	2	1	no	—
159	C₃×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
160	C₃×C₄×D₃	—	2	1	no	—
161	C₃×C₄×D₃	—	2	1	no	—
162	C₃×C₄×D₃	—	2	1	no	—
163	C₃×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
164	C₃×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
165	C₃×C₄×D₃	C₃×D₄	1	1	yes	characteristic
166	C₃×C₄×D₃	C₃×D₄	1	1	yes	characteristic
167	C₃×Dic₆	—	2	1	no	—
168	C₃×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
169	C₂³×C₉	—	3	1	no	—
170	C₂³×C₉	—	6	1	no	—
171	C₃²×C₈	—	2	1	no	—
172	C₃×C₃⋊C₈	—	2	1	no	—
173	Q₈×C₉	—	2	1	no	—
174	Q₈×C₉	—	3	1	no	—
175	Q₈×C₉	—	6	1	no	—
176	Q₈×C₉	C₄×D₃	1	1	yes	characteristic
177	D₄×C₉	—	2	1	no	—
178	D₄×C₉	—	2	1	no	—
179	D₄×C₉	—	3	1	no	—
180	D₄×C₉	—	4	1	no	—
181	D₄×C₉	—	6	1	no	—
182	D₄×C₉	—	6	1	no	—
183	D₄×C₉	—	6	1	no	—
184	D₄×C₉	—	6	1	no	—
185	D₄×C₉	C₄×D₃	1	1	yes	characteristic
186	C₂×C₄×C₉	—	2	1	no	—
187	C₂×C₄×C₉	—	2	1	no	—
188	C₂×C₄×C₉	—	2	1	no	—
189	C₂×C₄×C₉	—	3	1	no	—
190	C₂×C₄×C₉	—	3	1	no	—
191	C₂×C₄×C₉	—	3	1	no	—
192	C₂×C₄×C₉	—	3	1	no	—
193	C₂×C₄×C₉	—	3	1	no	—
194	C₂×C₄×C₉	—	4	1	no	—
195	C₂×C₄×C₉	—	4	1	no	—
196	C₂×C₄×C₉	—	6	1	no	—
197	C₂×C₄×C₉	—	6	1	no	—
198	C₂×C₄×C₉	—	6	1	no	—
199	C₂×C₄×C₉	—	6	1	no	—
200	C₂×C₄×C₉	—	6	1	no	—
201	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
202	C₈×C₉	—	2	1	no	—
203	C₈×C₉	—	4	1	no	—
204	C₈×C₉	—	6	1	no	—
205	#421	—	3	1	no	Sylow
206	C₂×C₃×C₉	—	2	1	no	—
207	C₂×C₃×C₉	—	4	1	no	—
208	C₂×C₃×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	D₃×C₉	—	2	1	no	—
210	D₃×C₉	—	2	1	no	—
211	D₃×C₉	—	4	1	no	—
212	C₃×#41	—	2	1	no	—
213	C₃×#41	—	3	1	no	—
214	C₃×#41	—	3	1	no	—
215	C₃×#41	—	3	1	no	—
216	C₃×#41	—	6	1	no	—
217	C₃×#41	—	6	1	no	—
218	C₃×#41	C₂²×C₉	1	1	yes	characteristic
219	C₃×#41	C₂×C₃×D₃	1	1	yes	characteristic
220	C₂×C₃×Q₈	—	3	1	no	—
221	C₂×C₃×D₄	—	3	1	no	—
222	C₂×C₃×D₄	—	6	1	no	—
223	C₂²×C₃×C₄	—	3	1	no	—
224	C₂²×C₃×C₄	—	6	1	no	—
225	#239	C₄×C₉	1	1	yes	characteristic, complemented
226	D₃×Q₈	C₄×C₉	1	1	yes	characteristic, complemented
227	#237	—	2	1	no	—
228	#237	C₄×C₉	1	1	yes	characteristic, complemented
229	D₃×D₄	—	2	1	no	—
230	D₃×D₄	C₄×C₉	1	1	yes	characteristic, complemented
231	#235	—	2	1	no	—
232	#235	C₂²×C₉	1	1	yes	characteristic
233	C₂×C₄×D₃	—	2	1	no	—
234	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
235	C₃×M₁₆	—	2	1	no	—
236	C₃×M₁₆	—	3	1	no	—
237	C₃×M₁₆	—	6	1	no	—
238	C₃×M₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
239	C₃×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
240	C₂×C₃×C₈	—	6	1	no	—
241	C₃×C₄⋊C₄	—	6	1	no	—
242	C₃×C₂²⋊C₄	—	6	1	no	—
243	C₃×C₄²	—	2	1	no	—
244	C₃×C₄²	—	3	1	no	—
245	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic, complemented
246	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
247	(C₂×D₃)⋊C₄	—	2	1	no	—
248	Dic₃⋊C₄	—	2	1	no	—
249	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
250	#208	C₂²×C₉	1	1	yes	characteristic, complemented
251	ΓL(1,𝔽₂₅)	—	2	1	no	—
252	D₃×C₈	—	2	1	no	—
253	C₂²×C₃²	—	2	1	no	—
254	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
255	C₂×C₃×D₃	—	2	1	no	—
256	C₂×C₃×D₃	—	4	1	no	—
257	C₂×C₃×D₃	—	4	2	no	—
258	C₂×C₃×D₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×C₃×D₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
260	C₃²×C₄	—	2	1	no	—
261	C₃²×C₄	—	4	1	no	—
262	C₃²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
263	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
264	C₃×Dic₃	—	2	1	no	—
265	C₃×Dic₃	—	4	1	no	—
266	C₃×Dic₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
267	C₃×Dic₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
268	C₂²×C₉	—	2	1	no	—
269	C₂²×C₉	—	2	1	no	—
270	C₂²×C₉	—	3	1	no	—
271	C₂²×C₉	—	3	1	no	—
272	C₂²×C₉	—	4	1	no	—
273	C₂²×C₉	—	6	1	no	—
274	C₂²×C₉	—	12	1	no	—
275	C₂²×C₉	—	12	2	no	—
276	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
277	C₄×C₉	—	2	1	no	—
278	C₄×C₉	—	2	1	no	—
279	C₄×C₉	—	2	1	no	—
280	C₄×C₉	—	3	1	no	—
281	C₄×C₉	—	3	1	no	—
282	C₄×C₉	—	4	1	no	—
283	C₄×C₉	—	4	1	no	—
284	C₄×C₉	—	4	2	no	—
285	C₄×C₉	—	6	1	no	—
286	C₄×C₉	—	12	1	no	—
287	C₄×C₉	C₂×C₄×D₃	1	1	yes	characteristic
288	C₄×C₉	D₃×D₄	1	1	yes	characteristic
289	C₂×#41	—	3	1	no	—
290	C₂×M₁₆	—	3	1	no	—
291	#117	—	3	1	no	—
292	#104	—	3	1	no	—
293	#104	—	3	1	no	—
294	#104	—	3	1	no	—
295	#104	D₃×C₉	1	1	yes	characteristic, complemented
296	C₃×C₉	#421	1	1	yes	characteristic, complemented, Sylow
297	C₂³×C₃	—	3	1	no	—
298	C₂³×C₃	—	6	1	no	—
299	C₂²×D₃	—	2	1	no	—
300	C₂²×D₃	D₄×C₉	1	1	yes	characteristic
301	C₃×Q₈	—	2	1	no	—
302	C₃×Q₈	—	3	1	no	—
303	C₃×Q₈	—	6	1	no	—
304	C₃×Q₈	C₂×C₄×C₉	1	1	yes	characteristic
305	C₃×Q₈	C₃×C₄×D₃	1	1	yes	characteristic
306	C₃×D₄	—	2	1	no	—
307	C₃×D₄	—	2	1	no	—
308	C₃×D₄	—	2	1	no	—
309	C₃×D₄	—	3	1	no	—
310	C₃×D₄	—	4	1	no	—
311	C₃×D₄	—	6	1	no	—
312	C₃×D₄	—	6	1	no	—
313	C₃×D₄	—	6	1	no	—
314	C₃×D₄	—	6	1	no	—
315	C₃×D₄	C₂×C₄×C₉	1	1	yes	characteristic
316	C₃×D₄	C₃×C₄×D₃	1	1	yes	characteristic
317	C₂×C₃×C₄	—	2	1	no	—
318	C₂×C₃×C₄	—	2	1	no	—
319	C₂×C₃×C₄	—	2	1	no	—
320	C₂×C₃×C₄	—	2	1	no	—
321	C₂×C₃×C₄	—	2	1	no	—
322	C₂×C₃×C₄	—	3	1	no	—
323	C₂×C₃×C₄	—	3	1	no	—
324	C₂×C₃×C₄	—	3	1	no	—
325	C₂×C₃×C₄	—	3	1	no	—
326	C₂×C₃×C₄	—	3	1	no	—
327	C₂×C₃×C₄	—	4	1	no	—
328	C₂×C₃×C₄	—	4	1	no	—
329	C₂×C₃×C₄	—	6	1	no	—
330	C₂×C₃×C₄	—	6	1	no	—
331	C₂×C₃×C₄	—	6	1	no	—
332	C₂×C₃×C₄	—	6	1	no	—
333	C₂×C₃×C₄	—	6	1	no	—
334	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
335	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
336	#67	—	2	1	no	—
337	#67	—	2	1	no	—
338	#67	—	2	1	no	—
339	C₂×Dic₃	—	2	1	no	—
340	C₂×Dic₃	—	2	1	no	—
341	C₂×Dic₃	D₄×C₉	1	1	yes	characteristic
342	D₁₂	—	2	1	no	—
343	D₁₂	C₂×C₄×C₉	1	1	yes	characteristic
344	C₄×D₃	—	2	1	no	—
345	C₄×D₃	—	2	1	no	—
346	C₄×D₃	—	2	1	no	—
347	C₄×D₃	C₂×C₄×C₉	1	1	yes	characteristic
348	C₄×D₃	C₂×C₄×C₉	1	1	yes	characteristic
349	C₄×D₃	D₄×C₉	1	1	yes	characteristic
350	C₄×D₃	D₄×C₉	1	1	yes	characteristic
351	Dic₆	—	2	1	no	—
352	Dic₆	C₂×C₄×C₉	1	1	yes	characteristic
353	C₃×C₈	—	2	1	no	—
354	C₃×C₈	—	2	1	no	—
355	C₃×C₈	—	4	1	no	—
356	C₃×C₈	—	6	1	no	—
357	C₃⋊C₈	—	2	1	no	—
358	C₂×C₃²	—	2	1	no	—
359	C₂×C₃²	—	4	1	no	—
360	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
361	C₃×D₃	—	2	1	no	—
362	C₃×D₃	—	2	1	no	—
363	C₃×D₃	—	4	1	no	—
364	C₂×C₉	—	2	1	no	—
365	C₂×C₉	—	2	1	no	—
366	C₂×C₉	—	4	1	no	—
367	C₂×C₉	—	4	1	no	—
368	C₂×C₉	—	6	1	no	—
369	C₂×C₉	—	6	1	no	—
370	C₂×C₉	—	8	1	no	—
371	C₂×C₉	—	12	1	no	—
372	C₂×C₉	D₃×C₂²⋊C₄	1	1	yes	characteristic
373	#41	—	3	1	no	—
374	#41	—	3	1	no	—
375	#41	—	3	1	no	—
376	#41	—	6	1	no	—
377	#41	—	6	1	no	—
378	#41	C₂×D₃×C₉	1	1	yes	characteristic
379	C₂×Q₈	—	3	1	no	—
380	C₂×D₄	—	3	1	no	—
381	C₂×D₄	—	6	1	no	—
382	C₂²×C₄	—	3	1	no	—
383	C₂²×C₄	—	6	1	no	—
384	M₁₆	—	3	1	no	—
385	M₁₆	—	6	1	no	—
386	M₁₆	C₂×D₃×C₉	1	1	yes	characteristic, complemented
387	C₂×C₈	—	6	1	no	—
388	C₄⋊C₄	—	6	1	no	—
389	C₂²⋊C₄	—	6	1	no	—
390	C₄²	—	3	1	no	—
391	C₄²	C₂×D₃×C₉	1	1	yes	characteristic, complemented
392	C₂²×C₃	—	2	1	no	—
393	C₂²×C₃	—	2	1	no	—
394	C₂²×C₃	—	2	1	no	—
395	C₂²×C₃	—	3	1	no	—
396	C₂²×C₃	—	3	1	no	—
397	C₂²×C₃	—	4	1	no	—
398	C₂²×C₃	—	6	1	no	—
399	C₂²×C₃	—	12	1	no	—
400	C₂²×C₃	—	12	2	no	—
401	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
402	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
403	C₂×D₃	—	2	1	no	—
404	C₂×D₃	—	4	1	no	—
405	C₂×D₃	—	4	2	no	—
406	C₂×D₃	C₉×C₂²⋊C₄	1	1	yes	characteristic
407	C₂×D₃	C₉×C₂²⋊C₄	1	1	yes	characteristic
408	C₃×C₄	—	2	1	no	—
409	C₃×C₄	—	2	1	no	—
410	C₃×C₄	—	2	1	no	—
411	C₃×C₄	—	2	1	no	—
412	C₃×C₄	—	3	1	no	—
413	C₃×C₄	—	3	1	no	—
414	C₃×C₄	—	4	1	no	—
415	C₃×C₄	—	4	1	no	—
416	C₃×C₄	—	4	1	no	—
417	C₃×C₄	—	4	2	no	—
418	C₃×C₄	—	6	1	no	—
419	C₃×C₄	—	12	1	no	—
420	C₃×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
421	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
422	C₃×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
423	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
424	Dic₃	—	2	1	no	—
425	Dic₃	—	4	1	no	—
426	Dic₃	C₉×C₂²⋊C₄	1	1	yes	characteristic
427	Dic₃	C₉×C₂²⋊C₄	1	1	yes	characteristic
428	C₃²	C₃×#421	1	1	yes	characteristic
429	C₉	—	2	1	no	—
430	C₉	#4821	1	1	yes	characteristic, direct product factor
431	C₂³	—	3	1	no	—
432	C₂³	—	6	1	no	—
433	Q₈	—	3	1	no	—
434	Q₈	—	6	1	no	—
435	Q₈	C₄×D₃×C₉	1	1	yes	characteristic
436	D₄	—	2	1	no	—
437	D₄	—	3	1	no	—
438	D₄	—	6	1	no	—
439	D₄	—	6	1	no	—
440	D₄	—	6	1	no	—
441	D₄	—	6	1	no	—
442	D₄	C₄×D₃×C₉	1	1	yes	characteristic
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	3	1	no	—
446	C₂×C₄	—	3	1	no	—
447	C₂×C₄	—	3	1	no	—
448	C₂×C₄	—	3	1	no	—
449	C₂×C₄	—	3	1	no	—
450	C₂×C₄	—	6	1	no	—
451	C₂×C₄	—	6	1	no	—
452	C₂×C₄	—	6	1	no	—
453	C₂×C₄	—	6	1	no	—
454	C₂×C₄	—	6	1	no	—
455	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
456	C₈	—	2	1	no	—
457	C₈	—	6	1	no	—
458	C₂×C₃	—	2	1	no	—
459	C₂×C₃	—	2	1	no	—
460	C₂×C₃	—	2	1	no	—
461	C₂×C₃	—	4	1	no	—
462	C₂×C₃	—	4	1	no	—
463	C₂×C₃	—	4	1	no	—
464	C₂×C₃	—	6	1	no	—
465	C₂×C₃	—	6	1	no	—
466	C₂×C₃	—	8	1	no	—
467	C₂×C₃	—	12	1	no	—
468	C₂×C₃	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
469	C₂×C₃	C₃×D₃×C₂²⋊C₄	1	1	yes	characteristic
470	D₃	—	2	1	no	—
471	D₃	—	2	1	no	—
472	D₃	—	4	1	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	3	1	no	—
475	C₂²	—	3	1	no	—
476	C₂²	—	6	1	no	—
477	C₂²	—	12	1	no	—
478	C₂²	—	12	2	no	—
479	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
480	C₄	—	2	1	no	—
481	C₄	—	3	1	no	—
482	C₄	—	3	1	no	—
483	C₄	—	4	1	no	—
484	C₄	—	6	1	no	—
485	C₄	—	12	1	no	—
486	C₄	C₂×C₄×D₃×C₉	1	1	yes	characteristic
487	C₄	D₃×D₄×C₉	1	1	yes	characteristic
488	C₃	—	2	1	no	—
489	C₃	C₉×#421	1	1	yes	characteristic, complemented
490	C₃	C₃×#4821	1	1	yes	characteristic
491	C₂	—	2	1	no	—
492	C₂	—	4	1	no	—
493	C₂	—	6	1	no	—
494	C₂	—	6	1	no	—
495	C₂	—	12	1	no	—
496	C₂	D₃×C₉×C₂²⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₉	D₃×D₄
commutator	C₃×C₄	C₂²×C₄×C₉
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₃×C₉×#104	C₂
socle	C₂×C₃²	C₂×C₃×C₂²⋊C₄
prime radical	C₃×D₃×#41	C₂×C₃
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₉×#104	D₃
hypocenter	C₃	C₉×#421
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₉ ◁ C₂×C₄×C₉ ◁ C₉×#104

Complements

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

N	H ≅ G/N	type
2. D₃×C₉×M₁₆	C₂	semidirect
3. C₉×#872	C₂	semidirect
4. C₃×C₉×#104	C₂	semidirect
5. C₉×#837	C₂	semidirect
6. C₉×#825	C₂	semidirect
7. C₉×#805	C₂	semidirect
11. C₉×#239	C₄	semidirect
12. D₃×Q₈×C₉	C₄	semidirect
14. C₉×#237	C₄	semidirect
16. D₃×D₄×C₉	C₄	semidirect
21. C₃×C₉×M₁₆	C₂²	semidirect
22. C₃×C₄²×C₉	C₂²	semidirect
25. C₄×C₉×Dic₃	C₂²	semidirect
26. C₉×#208	C₂²	semidirect
43. C₉×#104	D₃	semidirect
72. #4821	C₉	direct (N × H)
107. C₉×M₁₆	C₂×D₃	semidirect
113. C₄²×C₉	C₂×D₃	semidirect
133. D₃×M₁₆	C₂×C₉	semidirect
134. #872	C₂×C₉	semidirect
139. C₃×#104	C₂×C₉	semidirect
141. #837	C₂×C₉	semidirect
142. #825	C₂×C₉	semidirect
143. #805	C₂×C₉	semidirect
225. #239	C₄×C₉	semidirect
226. D₃×Q₈	C₄×C₉	semidirect
228. #237	C₄×C₉	semidirect
230. D₃×D₄	C₄×C₉	semidirect
238. C₃×M₁₆	C₂²×C₉	semidirect
245. C₃×C₄²	C₂²×C₉	semidirect
249. C₄×Dic₃	C₂²×C₉	semidirect
250. #208	C₂²×C₉	semidirect
295. #104	D₃×C₉	semidirect
296. C₃×C₉	#421	semidirect
386. M₁₆	C₂×D₃×C₉	semidirect
391. C₄²	C₂×D₃×C₉	semidirect
430. C₉	#4821	direct (N × H)
489. C₃	C₉×#421	semidirect

Maximal subgroups

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

subgroup	index
D₃×C₉×#41	2
D₃×C₉×M₁₆	2
C₉×#872	2
C₃×C₉×#104	2
C₉×#837	2
C₉×#825	2
C₉×#805	2
C₃×#4821	3
C₉×#421	3

Subgroups — C9×#4821 #13141973

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#4821 #13141973