Subgroups — C₃×#10589773 #13153078

Order 1728.

712 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#124	C₂	1	1	yes	maximal, characteristic
2	C₃×Q₈×Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#63506	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63498	C₂	1	1	yes	maximal, characteristic
5	C₃×D₄×Dic₉	C₂	1	1	yes	maximal, characteristic
6	C₃×#63441	C₂	1	2	yes	maximal, complemented
7	C₃×#63441	C₂	1	2	yes	maximal, complemented
8	C₃×#63440	C₂	1	2	yes	maximal, complemented
9	C₃×#63439	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×Dic₁₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×Dic₁₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5671	—	3	1	no	maximal
13	#10589773	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
16	C₂²×C₃×Dic₉	C₂²	1	2	yes	—
17	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic
18	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic
19	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
22	C₃×#3676	C₂²	1	2	yes	—
23	C₃×#3676	C₂²	1	2	yes	—
24	C₃×#3676	C₂²	1	2	yes	—
25	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
26	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
27	C₃×C₄⋊Dic₉	C₂²	1	2	yes	—
28	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
29	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
30	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
31	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
32	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
33	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
34	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
35	C₃×C₄×Dic₉	C₂²	1	2	yes	—
36	C₃×C₄×Dic₉	C₂²	1	2	yes	—
37	C₃²×#124	D₃	1	1	yes	characteristic
38	C₃×Q₈×Dic₃	—	3	1	no	—
39	C₃×#944	—	3	1	no	—
40	C₃×#936	—	3	1	no	—
41	C₃×D₄×Dic₃	—	3	1	no	—
42	C₃×#879	—	3	2	no	—
43	C₃×#879	—	3	2	no	—
44	C₃×#878	—	3	2	no	—
45	C₃×#877	—	3	2	no	—
46	C₃×C₄×Dic₆	—	3	1	no	—
47	C₃×C₄×Dic₆	—	3	1	no	—
48	C₉×#124	—	2	1	no	—
49	C₉×#124	C₂×C₃	1	1	yes	characteristic
50	Q₈×Dic₉	C₂×C₃	1	1	yes	characteristic, complemented
51	#63506	C₂×C₃	1	1	yes	characteristic, complemented
52	#63498	C₂×C₃	1	1	yes	characteristic
53	D₄×Dic₉	C₂×C₃	1	1	yes	characteristic
54	#63441	C₂×C₃	1	2	yes	complemented
55	#63441	C₂×C₃	1	2	yes	complemented
56	#63440	C₂×C₃	1	2	yes	complemented
57	#63439	C₂×C₃	1	2	yes	complemented
58	C₄×Dic₁₈	C₂×C₃	1	1	yes	characteristic, complemented
59	C₄×Dic₁₈	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂³×C₃×C₉	C₂³	1	2	yes	—
61	C₃×Q₈×C₉	—	2	2	no	—
62	C₃×D₄×C₉	—	2	2	no	—
63	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
66	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
67	C₂×C₃×Dic₉	—	2	4	no	—
68	C₂×C₃×Dic₉	C₂³	1	2	yes	—
69	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
70	C₂×C₃×Dic₉	C₂³	1	2	yes	—
71	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
72	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
73	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
74	C₃×Dic₁₈	—	2	2	no	—
75	C₃×Dic₁₈	—	2	2	no	—
76	C₃×#556	—	9	1	no	—
77	#5671	—	3	1	no	—
78	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
79	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
80	C₂²×C₃×Dic₃	—	3	2	no	—
81	C₂×C₃×Dic₆	—	3	1	no	—
82	C₂×C₃×Dic₆	—	3	1	no	—
83	C₃²×C₂²⋊C₄	C₂×D₃	1	2	yes	—
84	C₃²×C₂²⋊C₄	C₂×D₃	1	2	yes	—
85	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
86	C₃×#217	—	3	2	no	—
87	C₃×#217	—	3	2	no	—
88	C₃×#217	—	3	2	no	—
89	C₃×C₄⋊Dic₃	—	3	2	no	—
90	C₃×C₄⋊Dic₃	—	3	1	no	—
91	C₃×C₄⋊Dic₃	—	3	1	no	—
92	C₃×Dic₃⋊C₄	—	3	1	no	—
93	C₃×Dic₃⋊C₄	—	3	2	no	—
94	C₃×Dic₃⋊C₄	—	3	2	no	—
95	C₃×Dic₃⋊C₄	—	3	2	no	—
96	C₃×Dic₃⋊C₄	—	3	1	no	—
97	C₃×C₄×Dic₃	—	3	2	no	—
98	C₃×C₄×Dic₃	—	3	2	no	—
99	C₃×C₄×Dic₃	—	3	1	no	—
100	C₃×C₄×Dic₃	—	3	1	no	—
101	C₂×Q₈×C₉	—	2	1	no	—
102	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic
103	C₂×D₄×C₉	—	2	1	no	—
104	C₂×D₄×C₉	C₂²×C₃	1	1	yes	characteristic
105	C₂²×Dic₉	C₂²×C₃	1	2	yes	—
106	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
107	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
108	C₉×C₂²⋊C₄	—	2	2	no	—
109	C₉×C₂²⋊C₄	—	2	2	no	—
110	C₉×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
111	C₉×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
112	C₄²×C₉	—	2	1	no	—
113	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
114	#3676	C₂²×C₃	1	2	yes	—
115	#3676	C₂²×C₃	1	2	yes	—
116	#3676	C₂²×C₃	1	2	yes	—
117	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
118	C₄⋊Dic₉	C₂²×C₃	1	2	yes	—
119	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
120	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
121	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
122	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
123	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
124	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
126	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
127	C₄×Dic₉	C₂²×C₃	1	2	yes	—
128	C₄×Dic₉	C₂²×C₃	1	2	yes	—
129	C₂²×C₃×C₉	—	2	2	no	—
130	C₂²×C₃×C₉	—	2	2	no	—
131	C₂²×C₃×C₉	—	2	2	no	—
132	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
133	C₃×C₄×C₉	—	2	1	no	—
134	C₃×C₄×C₉	—	2	2	no	—
135	C₃×C₄×C₉	—	2	1	no	—
136	C₃×C₄×C₉	#41	1	2	yes	—
137	C₃×Dic₉	—	2	2	no	—
138	C₃×Dic₉	—	2	1	no	—
139	C₃×Dic₉	—	2	2	no	—
140	C₃×Dic₉	—	2	1	no	—
141	C₃×Dic₉	—	2	1	no	—
142	C₃×Dic₉	#41	1	2	yes	—
143	C₃×C₄⋊Q₈	—	9	1	no	—
144	C₃×#126	—	9	2	no	—
145	C₃×#126	—	9	2	no	—
146	C₃×#124	—	2	1	no	—
147	C₃×#124	—	9	1	no	—
148	C₃×#124	D₉	1	1	yes	characteristic
149	C₃×#124	C₃×D₃	1	1	yes	characteristic
150	C₃×C₂²⋊Q₈	—	9	2	no	—
151	C₃×C₄×Q₈	—	9	1	no	—
152	C₃×C₄×Q₈	—	9	1	no	—
153	C₃×C₄×Q₈	—	9	1	no	—
154	C₃×C₄×D₄	—	9	1	no	—
155	C₃×#117	—	9	2	no	—
156	Q₈×Dic₃	—	3	1	no	—
157	#944	—	3	1	no	—
158	#936	—	3	1	no	—
159	D₄×Dic₃	—	3	1	no	—
160	#879	—	3	2	no	—
161	#879	—	3	2	no	—
162	#878	—	3	2	no	—
163	#877	—	3	2	no	—
164	C₄×Dic₆	—	3	1	no	—
165	C₄×Dic₆	—	3	1	no	—
166	C₂³×C₃²	C₂²×D₃	1	2	yes	—
167	C₃²×Q₈	—	2	2	no	—
168	C₃²×D₄	—	2	2	no	—
169	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
170	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
171	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
172	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
173	C₂×C₃×Dic₃	—	3	1	no	—
174	C₂×C₃×Dic₃	—	3	1	no	—
175	C₂×C₃×Dic₃	—	3	2	no	—
176	C₂×C₃×Dic₃	—	3	1	no	—
177	C₂×C₃×Dic₃	—	3	2	no	—
178	C₂×C₃×Dic₃	—	3	1	no	—
179	C₂×C₃×Dic₃	—	6	4	no	—
180	C₃×Dic₆	—	6	2	no	—
181	C₃×Dic₆	—	6	2	no	—
182	C₂³×C₉	—	2	2	no	—
183	C₂³×C₉	C₂³×C₃	1	2	yes	—
184	Q₈×C₉	—	2	2	no	—
185	Q₈×C₉	—	4	2	no	—
186	D₄×C₉	—	2	2	no	—
187	D₄×C₉	—	4	2	no	—
188	C₂×C₄×C₉	—	2	1	no	—
189	C₂×C₄×C₉	—	2	1	no	—
190	C₂×C₄×C₉	—	2	1	no	—
191	C₂×C₄×C₉	—	2	2	no	—
192	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
193	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
194	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
195	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
196	C₂×Dic₉	—	2	4	no	—
197	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
198	C₂×Dic₉	C₂³×C₃	1	2	yes	—
199	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
200	C₂×Dic₉	C₂³×C₃	1	2	yes	—
201	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
202	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
203	Dic₁₈	—	2	2	no	—
204	Dic₁₈	—	2	2	no	—
205	#556	—	9	1	no	Sylow
206	C₂×C₃×C₉	—	4	2	no	—
207	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
208	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
209	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
210	C₂×C₃×Q₈	—	2	1	no	—
211	C₂×C₃×Q₈	—	9	1	no	—
212	C₂×C₃×Q₈	—	9	1	no	—
213	C₂×C₃×Q₈	C₂×D₉	1	1	yes	characteristic
214	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
215	C₂×C₃×D₄	—	2	1	no	—
216	C₂×C₃×D₄	C₂×D₉	1	1	yes	characteristic
217	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
218	C₂²×C₃×C₄	—	9	2	no	—
219	C₂²×Dic₃	—	3	2	no	—
220	C₂×Dic₆	—	3	1	no	—
221	C₂×Dic₆	—	3	1	no	—
222	C₃×C₄⋊C₄	—	9	1	no	—
223	C₃×C₄⋊C₄	—	9	2	no	—
224	C₃×C₄⋊C₄	—	9	2	no	—
225	C₃×C₄⋊C₄	—	9	1	no	—
226	C₃×C₄⋊C₄	—	9	2	no	—
227	C₃×C₄⋊C₄	—	9	1	no	—
228	C₃×C₄⋊C₄	—	9	2	no	—
229	C₃×C₄⋊C₄	—	9	1	no	—
230	C₃×C₂²⋊C₄	—	2	2	no	—
231	C₃×C₂²⋊C₄	—	2	2	no	—
232	C₃×C₂²⋊C₄	—	9	2	no	—
233	C₃×C₂²⋊C₄	—	9	2	no	—
234	C₃×C₂²⋊C₄	—	9	2	no	—
235	C₃×C₂²⋊C₄	C₂×D₉	1	2	yes	—
236	C₃×C₂²⋊C₄	C₂×D₉	1	2	yes	—
237	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
238	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
239	C₃×C₄²	—	2	1	no	—
240	C₃×C₄²	—	9	2	no	—
241	C₃×C₄²	—	9	2	no	—
242	C₃×C₄²	—	9	1	no	—
243	C₃×C₄²	—	9	1	no	—
244	C₃×C₄²	C₂×D₉	1	1	yes	characteristic
245	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
246	#217	—	3	2	no	—
247	#217	—	3	2	no	—
248	#217	—	3	2	no	—
249	C₄⋊Dic₃	—	3	1	no	—
250	C₄⋊Dic₃	—	3	1	no	—
251	C₄⋊Dic₃	—	3	2	no	—
252	Dic₃⋊C₄	—	3	1	no	—
253	Dic₃⋊C₄	—	3	2	no	—
254	Dic₃⋊C₄	—	3	1	no	—
255	Dic₃⋊C₄	—	3	2	no	—
256	Dic₃⋊C₄	—	3	2	no	—
257	C₄×Dic₃	—	3	2	no	—
258	C₄×Dic₃	—	3	1	no	—
259	C₄×Dic₃	—	3	1	no	—
260	C₄×Dic₃	—	3	2	no	—
261	C₂²×C₃²	—	2	2	no	—
262	C₂²×C₃²	—	2	2	no	—
263	C₂²×C₃²	—	2	2	no	—
264	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
265	C₃²×C₄	—	2	2	no	—
266	C₃²×C₄	—	2	1	no	—
267	C₃²×C₄	—	2	1	no	—
268	C₃²×C₄	#237	1	2	yes	—
269	C₃×Dic₃	—	3	2	no	—
270	C₃×Dic₃	—	6	2	no	—
271	C₃×Dic₃	—	6	1	no	—
272	C₃×Dic₃	—	6	2	no	—
273	C₃×Dic₃	—	6	1	no	—
274	C₃×Dic₃	—	6	1	no	—
275	C₂²×C₉	—	2	2	no	—
276	C₂²×C₉	—	2	2	no	—
277	C₂²×C₉	—	2	2	no	—
278	C₂²×C₉	—	2	1	no	—
279	C₂²×C₉	—	4	2	no	—
280	C₂²×C₉	—	4	2	no	—
281	C₂²×C₉	—	4	2	no	—
282	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
283	C₄×C₉	—	2	1	no	—
284	C₄×C₉	—	2	2	no	—
285	C₄×C₉	—	2	1	no	—
286	C₄×C₉	—	2	2	no	—
287	C₄×C₉	—	4	1	no	—
288	C₄×C₉	—	4	1	no	—
289	C₄×C₉	—	4	2	no	—
290	C₄×C₉	C₃×#41	1	2	yes	—
291	Dic₉	—	2	2	no	—
292	Dic₉	—	2	1	no	—
293	Dic₉	—	2	2	no	—
294	Dic₉	—	2	1	no	—
295	Dic₉	—	2	1	no	—
296	Dic₉	C₃×#41	1	2	yes	—
297	C₄⋊Q₈	—	9	1	no	—
298	#126	—	9	2	no	—
299	#126	—	9	2	no	—
300	#124	—	9	1	no	—
301	#124	C₃×D₉	1	1	yes	characteristic
302	C₂²⋊Q₈	—	9	2	no	—
303	C₄×Q₈	—	9	1	no	—
304	C₄×Q₈	—	9	1	no	—
305	C₄×Q₈	—	9	1	no	—
306	C₄×D₄	—	9	1	no	—
307	#117	—	9	2	no	—
308	C₃×C₉	#556	1	1	yes	characteristic, complemented, Sylow
309	C₂³×C₃	—	2	2	no	—
310	C₂³×C₃	C₂²×D₉	1	2	yes	—
311	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
312	C₃×Q₈	—	2	2	no	—
313	C₃×Q₈	—	2	2	no	—
314	C₃×Q₈	—	4	2	no	—
315	C₃×Q₈	—	18	2	no	—
316	C₃×Q₈	—	18	2	no	—
317	C₃×D₄	—	2	2	no	—
318	C₃×D₄	—	2	2	no	—
319	C₃×D₄	—	4	2	no	—
320	C₂×C₃×C₄	—	2	1	no	—
321	C₂×C₃×C₄	—	2	1	no	—
322	C₂×C₃×C₄	—	2	1	no	—
323	C₂×C₃×C₄	—	2	2	no	—
324	C₂×C₃×C₄	—	9	1	no	—
325	C₂×C₃×C₄	—	9	1	no	—
326	C₂×C₃×C₄	—	9	2	no	—
327	C₂×C₃×C₄	—	9	1	no	—
328	C₂×C₃×C₄	—	9	2	no	—
329	C₂×C₃×C₄	—	9	1	no	—
330	C₂×C₃×C₄	—	18	4	no	—
331	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
332	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
333	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
334	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
335	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
336	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
337	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
338	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
339	C₂×Dic₃	—	3	1	no	—
340	C₂×Dic₃	—	3	1	no	—
341	C₂×Dic₃	—	3	2	no	—
342	C₂×Dic₃	—	3	1	no	—
343	C₂×Dic₃	—	3	2	no	—
344	C₂×Dic₃	—	3	1	no	—
345	C₂×Dic₃	—	6	4	no	—
346	Dic₆	—	6	2	no	—
347	Dic₆	—	6	2	no	—
348	C₂×C₃²	—	4	2	no	—
349	C₂×C₃²	C₂×#237	1	1	yes	characteristic
350	C₂×C₃²	D₃×#41	1	1	yes	characteristic
351	C₂×C₃²	#1010	1	1	yes	characteristic
352	C₂×C₉	—	2	1	no	—
353	C₂×C₉	—	2	1	no	—
354	C₂×C₉	—	2	1	no	—
355	C₂×C₉	—	4	2	no	—
356	C₂×C₉	—	8	2	no	—
357	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
358	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
359	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
360	C₂×Q₈	—	9	1	no	—
361	C₂×Q₈	—	9	1	no	—
362	C₂×Q₈	C₂×C₃×D₉	1	1	yes	characteristic
363	C₂×D₄	C₂×C₃×D₉	1	1	yes	characteristic
364	C₂²×C₄	—	9	2	no	—
365	C₄⋊C₄	—	9	1	no	—
366	C₄⋊C₄	—	9	2	no	—
367	C₄⋊C₄	—	9	1	no	—
368	C₄⋊C₄	—	9	2	no	—
369	C₄⋊C₄	—	9	2	no	—
370	C₄⋊C₄	—	9	1	no	—
371	C₄⋊C₄	—	9	1	no	—
372	C₄⋊C₄	—	9	2	no	—
373	C₂²⋊C₄	—	9	2	no	—
374	C₂²⋊C₄	—	9	2	no	—
375	C₂²⋊C₄	—	9	2	no	—
376	C₂²⋊C₄	C₂×C₃×D₉	1	2	yes	—
377	C₂²⋊C₄	C₂×C₃×D₉	1	2	yes	—
378	C₄²	—	9	2	no	—
379	C₄²	—	9	2	no	—
380	C₄²	—	9	1	no	—
381	C₄²	—	9	1	no	—
382	C₄²	C₂×C₃×D₉	1	1	yes	characteristic
383	C₂²×C₃	—	2	2	no	—
384	C₂²×C₃	—	2	2	no	—
385	C₂²×C₃	—	2	2	no	—
386	C₂²×C₃	—	2	2	no	—
387	C₂²×C₃	—	2	2	no	—
388	C₂²×C₃	—	2	2	no	—
389	C₂²×C₃	—	2	1	no	—
390	C₂²×C₃	—	4	2	no	—
391	C₂²×C₃	—	4	2	no	—
392	C₂²×C₃	—	4	2	no	—
393	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
394	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
395	C₃×C₄	—	2	2	no	—
396	C₃×C₄	—	2	1	no	—
397	C₃×C₄	—	2	1	no	—
398	C₃×C₄	—	2	2	no	—
399	C₃×C₄	—	2	1	no	—
400	C₃×C₄	—	2	1	no	—
401	C₃×C₄	—	2	2	no	—
402	C₃×C₄	—	4	2	no	—
403	C₃×C₄	—	4	1	no	—
404	C₃×C₄	—	4	1	no	—
405	C₃×C₄	—	9	2	no	—
406	C₃×C₄	—	18	2	no	—
407	C₃×C₄	—	18	2	no	—
408	C₃×C₄	—	18	1	no	—
409	C₃×C₄	—	18	1	no	—
410	C₃×C₄	—	18	1	no	—
411	C₃×C₄	#3699	1	2	yes	—
412	C₃×C₄	C₃×#237	1	2	yes	—
413	Dic₃	—	3	2	no	—
414	Dic₃	—	6	2	no	—
415	Dic₃	—	6	1	no	—
416	Dic₃	—	6	2	no	—
417	Dic₃	—	6	1	no	—
418	Dic₃	—	6	1	no	—
419	C₃²	#5671	1	1	yes	characteristic
420	C₉	—	2	1	no	—
421	C₉	C₃×#556	1	1	yes	characteristic, complemented
422	C₂³	C₂²×C₃×D₉	1	2	yes	—
423	Q₈	—	2	2	no	—
424	Q₈	—	18	2	no	—
425	Q₈	—	18	2	no	—
426	D₄	—	2	2	no	—
427	C₂×C₄	—	9	1	no	—
428	C₂×C₄	—	9	1	no	—
429	C₂×C₄	—	9	2	no	—
430	C₂×C₄	—	9	1	no	—
431	C₂×C₄	—	9	2	no	—
432	C₂×C₄	—	9	1	no	—
433	C₂×C₄	—	18	4	no	—
434	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
435	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
436	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
437	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
438	C₂×C₃	—	2	1	no	—
439	C₂×C₃	—	2	1	no	—
440	C₂×C₃	—	2	1	no	—
441	C₂×C₃	—	4	2	no	—
442	C₂×C₃	—	4	2	no	—
443	C₂×C₃	—	8	2	no	—
444	C₂×C₃	C₂×#3699	1	1	yes	characteristic
445	C₂×C₃	#41×D₉	1	1	yes	characteristic
446	C₂×C₃	#63716	1	1	yes	characteristic
447	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
448	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
449	C₂×C₃	C₃×#1010	1	1	yes	characteristic
450	C₂²	—	2	2	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
454	C₄	—	2	2	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	9	2	no	—
458	C₄	—	18	2	no	—
459	C₄	—	18	2	no	—
460	C₄	—	18	1	no	—
461	C₄	—	18	1	no	—
462	C₄	—	18	1	no	—
463	C₄	C₃×#3699	1	2	yes	—
464	C₃	—	2	1	no	—
465	C₃	#10589773	1	1	yes	characteristic, direct product factor
466	C₃	C₃×#5671	1	1	yes	characteristic
467	C₂	—	4	2	no	—
468	C₂	C₂×C₃×#3699	1	1	yes	characteristic
469	C₂	C₃×#41×D₉	1	1	yes	characteristic
470	C₂	C₃×#63716	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₉
commutator, cosocle	C₂²×C₉	C₂⁴×C₃
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#124	C₂
socle	C₂²×C₃²	C₂³×D₃
prime radical	C₂×C₃²×D₄	C₂×D₃
hypercenter	C₃×#124	D₉
hypocenter	C₉	C₃×#556
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#124

Complements

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

N	H ≅ G/N	type
2. C₃×Q₈×Dic₉	C₂	semidirect
3. C₃×#63506	C₂	semidirect
6. C₃×#63441	C₂	semidirect
7. C₃×#63441	C₂	semidirect
8. C₃×#63440	C₂	semidirect
9. C₃×#63439	C₂	semidirect
10. C₃×C₄×Dic₁₈	C₂	semidirect
11. C₃×C₄×Dic₁₈	C₂	semidirect
13. #10589773	C₃	direct (N × H)
50. Q₈×Dic₉	C₂×C₃	semidirect
51. #63506	C₂×C₃	semidirect
54. #63441	C₂×C₃	semidirect
55. #63441	C₂×C₃	semidirect
56. #63440	C₂×C₃	semidirect
57. #63439	C₂×C₃	semidirect
58. C₄×Dic₁₈	C₂×C₃	semidirect
59. C₄×Dic₁₈	C₂×C₃	semidirect
308. C₃×C₉	#556	semidirect
421. C₉	C₃×#556	semidirect
465. C₃	#10589773	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₉×#124	2
C₃×Q₈×Dic₉	2
C₃×#63506	2
C₃×#63498	2
C₃×D₄×Dic₉	2
C₃×#63441	2
C₃×#63440	2
C₃×#63439	2
C₃×C₄×Dic₁₈	2
C₃×#5671	3
#10589773	3

Subgroups — C3×#10589773 #13153078

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589773 #13153078