Subgroups — C₃×#10589803 #13153207

Order 1728.

636 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#126	C₂	1	1	yes	maximal, characteristic
2	C₃×#63452	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#63451	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63451	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#63451	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#63450	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#63449	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#63441	C₂	1	1	yes	maximal, characteristic
9	C₃×#63441	C₂	1	1	yes	maximal, characteristic
10	C₃×#63441	C₂	1	1	yes	maximal, characteristic
11	C₃×#63440	C₂	1	1	yes	maximal, characteristic
12	C₃×#63440	C₂	1	1	yes	maximal, characteristic
13	C₃×#63439	C₂	1	1	yes	maximal, characteristic
14	C₃×#63432	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₄×Dic₁₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5701	—	3	1	no	maximal
17	#10589803	C₃	1	1	yes	maximal, characteristic, direct product factor
18	C₂²×C₃×Dic₉	C₂²	1	1	yes	characteristic
19	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic
20	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic
21	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
25	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
28	C₃×#3676	C₂²	1	1	yes	characteristic
29	C₃×#3676	C₂²	1	1	yes	characteristic
30	C₃×#3676	C₂²	1	1	yes	characteristic
31	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
32	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
33	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
34	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
35	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
36	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
37	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
38	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
39	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
40	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
41	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
42	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
43	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
44	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
45	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
46	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
47	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic
48	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
49	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
50	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
51	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
52	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
53	C₃²×#126	D₃	1	1	yes	characteristic
54	C₃×#890	—	3	1	no	—
55	C₃×#889	—	3	1	no	—
56	C₃×#889	—	3	1	no	—
57	C₃×#889	—	3	1	no	—
58	C₃×#888	—	3	1	no	—
59	C₃×#887	—	3	1	no	—
60	C₃×#879	—	3	1	no	—
61	C₃×#879	—	3	1	no	—
62	C₃×#879	—	3	1	no	—
63	C₃×#878	—	3	1	no	—
64	C₃×#878	—	3	1	no	—
65	C₃×#877	—	3	1	no	—
66	C₃×#870	—	3	1	no	—
67	C₃×C₄×Dic₆	—	3	1	no	—
68	C₉×#126	—	2	1	no	—
69	C₉×#126	C₂×C₃	1	1	yes	characteristic
70	#63452	C₂×C₃	1	1	yes	characteristic, complemented
71	#63451	C₂×C₃	1	1	yes	characteristic, complemented
72	#63451	C₂×C₃	1	1	yes	characteristic, complemented
73	#63451	C₂×C₃	1	1	yes	characteristic, complemented
74	#63450	C₂×C₃	1	1	yes	characteristic, complemented
75	#63449	C₂×C₃	1	1	yes	characteristic, complemented
76	#63441	C₂×C₃	1	1	yes	characteristic
77	#63441	C₂×C₃	1	1	yes	characteristic
78	#63441	C₂×C₃	1	1	yes	characteristic
79	#63440	C₂×C₃	1	1	yes	characteristic
80	#63440	C₂×C₃	1	1	yes	characteristic
81	#63439	C₂×C₃	1	1	yes	characteristic
82	#63432	C₂×C₃	1	1	yes	characteristic, complemented
83	C₄×Dic₁₈	C₂×C₃	1	1	yes	characteristic, complemented
84	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
85	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
87	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
88	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
89	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
90	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
91	C₂×C₃×Dic₉	—	2	2	no	—
92	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
93	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
94	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
95	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
96	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
97	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
98	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
99	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
100	C₃×Dic₁₈	—	2	2	no	—
101	C₃×Dic₁₈	—	2	2	no	—
102	C₃×#541	—	9	1	no	—
103	#5701	—	3	1	no	—
104	C₂²×C₃×Dic₃	—	3	1	no	—
105	C₂×C₃×Dic₆	—	3	1	no	—
106	C₂×C₃×Dic₆	—	3	1	no	—
107	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
108	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
109	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
110	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
111	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
112	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
113	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
114	C₃×#217	—	3	1	no	—
115	C₃×#217	—	3	1	no	—
116	C₃×#217	—	3	1	no	—
117	C₃×C₄⋊Dic₃	—	3	1	no	—
118	C₃×C₄⋊Dic₃	—	3	1	no	—
119	C₃×C₄⋊Dic₃	—	3	1	no	—
120	C₃×C₄⋊Dic₃	—	3	1	no	—
121	C₃×C₄⋊Dic₃	—	3	1	no	—
122	C₃×Dic₃⋊C₄	—	3	1	no	—
123	C₃×Dic₃⋊C₄	—	3	1	no	—
124	C₃×Dic₃⋊C₄	—	3	1	no	—
125	C₃×Dic₃⋊C₄	—	3	1	no	—
126	C₃×Dic₃⋊C₄	—	3	1	no	—
127	C₃×Dic₃⋊C₄	—	3	1	no	—
128	C₃×Dic₃⋊C₄	—	3	1	no	—
129	C₃×Dic₃⋊C₄	—	3	1	no	—
130	C₃×Dic₃⋊C₄	—	3	1	no	—
131	C₃×Dic₃⋊C₄	—	3	1	no	—
132	C₃×Dic₃⋊C₄	—	3	1	no	—
133	C₃×Dic₃⋊C₄	—	3	1	no	—
134	C₃×C₄×Dic₃	—	3	1	no	—
135	C₃×C₄×Dic₃	—	3	1	no	—
136	C₃×C₄×Dic₃	—	3	1	no	—
137	C₃×C₄×Dic₃	—	3	1	no	—
138	C₃×C₄×Dic₃	—	3	1	no	—
139	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic
140	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
141	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
142	C₉×C₄⋊C₄	—	2	1	no	—
143	C₉×C₄⋊C₄	—	2	1	no	—
144	C₉×C₄⋊C₄	—	2	1	no	—
145	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
146	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
147	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
148	C₉×C₂²⋊C₄	—	2	1	no	—
149	C₉×C₂²⋊C₄	—	2	1	no	—
150	C₉×C₂²⋊C₄	—	2	1	no	—
151	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
152	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
153	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
154	C₄²×C₉	—	2	1	no	—
155	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
156	#3676	C₂²×C₃	1	1	yes	characteristic
157	#3676	C₂²×C₃	1	1	yes	characteristic
158	#3676	C₂²×C₃	1	1	yes	characteristic
159	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
160	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
161	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
162	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
163	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
164	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
165	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
166	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
167	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
168	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
169	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
170	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
171	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
172	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
173	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
174	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
175	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
176	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
177	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
178	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
179	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
180	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
181	C₂²×C₃×C₉	—	2	1	no	—
182	C₂²×C₃×C₉	—	2	1	no	—
183	C₂²×C₃×C₉	—	2	1	no	—
184	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
185	C₃×C₄×C₉	—	2	1	no	—
186	C₃×C₄×C₉	—	2	1	no	—
187	C₃×C₄×C₉	—	2	1	no	—
188	C₃×C₄×C₉	—	2	1	no	—
189	C₃×C₄×C₉	—	2	1	no	—
190	C₃×C₄×C₉	—	2	1	no	—
191	C₃×Dic₉	—	2	1	no	—
192	C₃×Dic₉	—	2	1	no	—
193	C₃×Dic₉	—	2	1	no	—
194	C₃×Dic₉	—	2	1	no	—
195	C₃×Dic₉	—	2	1	no	—
196	C₃×Dic₉	—	2	1	no	—
197	C₃×Dic₉	—	2	1	no	—
198	C₃×Dic₉	#41	1	2	yes	—
199	C₃×C₄⋊Q₈	—	9	1	no	—
200	C₃×#126	—	2	1	no	—
201	C₃×#126	—	9	1	no	—
202	C₃×#126	—	9	1	no	—
203	C₃×#126	—	9	1	no	—
204	C₃×#126	D₉	1	1	yes	characteristic
205	C₃×#126	C₃×D₃	1	1	yes	characteristic
206	C₃×#125	—	9	1	no	—
207	C₃×#125	—	9	1	no	—
208	C₃×#125	—	9	1	no	—
209	C₃×#125	—	9	1	no	—
210	C₃×#125	—	9	1	no	—
211	C₃×C₂²⋊Q₈	—	9	1	no	—
212	C₃×C₂²⋊Q₈	—	9	1	no	—
213	C₃×C₄×Q₈	—	9	1	no	—
214	C₃×C₄×Q₈	—	9	1	no	—
215	C₃×#117	—	9	1	no	—
216	#890	—	3	1	no	—
217	#889	—	3	1	no	—
218	#889	—	3	1	no	—
219	#889	—	3	1	no	—
220	#888	—	3	1	no	—
221	#887	—	3	1	no	—
222	#879	—	3	1	no	—
223	#879	—	3	1	no	—
224	#879	—	3	1	no	—
225	#878	—	3	1	no	—
226	#878	—	3	1	no	—
227	#877	—	3	1	no	—
228	#870	—	3	1	no	—
229	C₄×Dic₆	—	3	1	no	—
230	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
231	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
232	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
233	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
234	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
235	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
236	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
237	C₂×C₃×Dic₃	—	3	1	no	—
238	C₂×C₃×Dic₃	—	3	1	no	—
239	C₂×C₃×Dic₃	—	3	1	no	—
240	C₂×C₃×Dic₃	—	3	1	no	—
241	C₂×C₃×Dic₃	—	3	1	no	—
242	C₂×C₃×Dic₃	—	3	1	no	—
243	C₂×C₃×Dic₃	—	3	1	no	—
244	C₂×C₃×Dic₃	—	3	1	no	—
245	C₂×C₃×Dic₃	—	6	2	no	—
246	C₃×Dic₆	—	6	2	no	—
247	C₃×Dic₆	—	6	2	no	—
248	C₂³×C₉	—	2	1	no	—
249	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
250	C₂×C₄×C₉	—	2	1	no	—
251	C₂×C₄×C₉	—	2	1	no	—
252	C₂×C₄×C₉	—	2	1	no	—
253	C₂×C₄×C₉	—	2	1	no	—
254	C₂×C₄×C₉	—	2	1	no	—
255	C₂×C₄×C₉	—	2	1	no	—
256	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
257	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
258	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
259	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
260	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
261	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
262	C₂×Dic₉	—	2	2	no	—
263	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
264	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
265	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
266	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
267	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
268	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
269	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
270	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
271	Dic₁₈	—	2	2	no	—
272	Dic₁₈	—	2	2	no	—
273	#541	—	9	1	no	Sylow
274	C₂×C₃×C₉	—	4	1	no	—
275	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
276	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
277	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
278	C₂×C₃×Q₈	—	9	1	no	—
279	C₂×C₃×Q₈	—	9	1	no	—
280	C₂²×C₃×C₄	—	9	1	no	—
281	C₂²×Dic₃	—	3	1	no	—
282	C₂×Dic₆	—	3	1	no	—
283	C₂×Dic₆	—	3	1	no	—
284	C₃×C₄⋊C₄	—	2	1	no	—
285	C₃×C₄⋊C₄	—	2	1	no	—
286	C₃×C₄⋊C₄	—	2	1	no	—
287	C₃×C₄⋊C₄	—	9	1	no	—
288	C₃×C₄⋊C₄	—	9	1	no	—
289	C₃×C₄⋊C₄	—	9	1	no	—
290	C₃×C₄⋊C₄	—	9	1	no	—
291	C₃×C₄⋊C₄	—	9	1	no	—
292	C₃×C₄⋊C₄	—	9	1	no	—
293	C₃×C₄⋊C₄	—	9	1	no	—
294	C₃×C₄⋊C₄	—	9	1	no	—
295	C₃×C₄⋊C₄	—	9	1	no	—
296	C₃×C₄⋊C₄	—	9	1	no	—
297	C₃×C₄⋊C₄	—	9	1	no	—
298	C₃×C₄⋊C₄	—	9	1	no	—
299	C₃×C₄⋊C₄	—	9	1	no	—
300	C₃×C₄⋊C₄	—	9	1	no	—
301	C₃×C₄⋊C₄	—	9	1	no	—
302	C₃×C₄⋊C₄	—	9	1	no	—
303	C₃×C₄⋊C₄	—	9	1	no	—
304	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
305	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
306	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
307	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
308	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
309	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
310	C₃×C₂²⋊C₄	—	2	1	no	—
311	C₃×C₂²⋊C₄	—	2	1	no	—
312	C₃×C₂²⋊C₄	—	2	1	no	—
313	C₃×C₂²⋊C₄	—	9	1	no	—
314	C₃×C₂²⋊C₄	—	9	1	no	—
315	C₃×C₂²⋊C₄	—	9	1	no	—
316	C₃×C₂²⋊C₄	C₂×D₉	1	1	yes	characteristic
317	C₃×C₂²⋊C₄	C₂×D₉	1	1	yes	characteristic
318	C₃×C₂²⋊C₄	C₂×D₉	1	1	yes	characteristic
319	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
320	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
321	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
322	C₃×C₄²	—	2	1	no	—
323	C₃×C₄²	—	9	1	no	—
324	C₃×C₄²	—	9	1	no	—
325	C₃×C₄²	—	9	1	no	—
326	C₃×C₄²	—	9	1	no	—
327	C₃×C₄²	—	9	1	no	—
328	C₃×C₄²	C₂×D₉	1	1	yes	characteristic
329	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
330	#217	—	3	1	no	—
331	#217	—	3	1	no	—
332	#217	—	3	1	no	—
333	C₄⋊Dic₃	—	3	1	no	—
334	C₄⋊Dic₃	—	3	1	no	—
335	C₄⋊Dic₃	—	3	1	no	—
336	C₄⋊Dic₃	—	3	1	no	—
337	C₄⋊Dic₃	—	3	1	no	—
338	Dic₃⋊C₄	—	3	1	no	—
339	Dic₃⋊C₄	—	3	1	no	—
340	Dic₃⋊C₄	—	3	1	no	—
341	Dic₃⋊C₄	—	3	1	no	—
342	Dic₃⋊C₄	—	3	1	no	—
343	Dic₃⋊C₄	—	3	1	no	—
344	Dic₃⋊C₄	—	3	1	no	—
345	Dic₃⋊C₄	—	3	1	no	—
346	Dic₃⋊C₄	—	3	1	no	—
347	Dic₃⋊C₄	—	3	1	no	—
348	Dic₃⋊C₄	—	3	1	no	—
349	Dic₃⋊C₄	—	3	1	no	—
350	C₄×Dic₃	—	3	1	no	—
351	C₄×Dic₃	—	3	1	no	—
352	C₄×Dic₃	—	3	1	no	—
353	C₄×Dic₃	—	3	1	no	—
354	C₄×Dic₃	—	3	1	no	—
355	C₂²×C₃²	—	2	1	no	—
356	C₂²×C₃²	—	2	1	no	—
357	C₂²×C₃²	—	2	1	no	—
358	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
359	C₃²×C₄	—	2	1	no	—
360	C₃²×C₄	—	2	1	no	—
361	C₃²×C₄	—	2	1	no	—
362	C₃²×C₄	—	2	1	no	—
363	C₃²×C₄	—	2	1	no	—
364	C₃²×C₄	—	2	1	no	—
365	C₃×Dic₃	—	3	2	no	—
366	C₃×Dic₃	—	6	1	no	—
367	C₃×Dic₃	—	6	1	no	—
368	C₃×Dic₃	—	6	1	no	—
369	C₃×Dic₃	—	6	1	no	—
370	C₃×Dic₃	—	6	1	no	—
371	C₃×Dic₃	—	6	1	no	—
372	C₃×Dic₃	—	6	1	no	—
373	C₂²×C₉	—	2	1	no	—
374	C₂²×C₉	—	2	1	no	—
375	C₂²×C₉	—	2	1	no	—
376	C₂²×C₉	—	2	1	no	—
377	C₂²×C₉	—	4	1	no	—
378	C₂²×C₉	—	4	1	no	—
379	C₂²×C₉	—	4	1	no	—
380	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
381	C₄×C₉	—	2	1	no	—
382	C₄×C₉	—	2	1	no	—
383	C₄×C₉	—	2	1	no	—
384	C₄×C₉	—	2	1	no	—
385	C₄×C₉	—	2	1	no	—
386	C₄×C₉	—	2	1	no	—
387	C₄×C₉	—	4	1	no	—
388	C₄×C₉	—	4	1	no	—
389	C₄×C₉	—	4	1	no	—
390	C₄×C₉	—	4	1	no	—
391	C₄×C₉	—	4	1	no	—
392	C₄×C₉	—	4	1	no	—
393	Dic₉	—	2	1	no	—
394	Dic₉	—	2	1	no	—
395	Dic₉	—	2	1	no	—
396	Dic₉	—	2	1	no	—
397	Dic₉	—	2	1	no	—
398	Dic₉	—	2	1	no	—
399	Dic₉	—	2	1	no	—
400	Dic₉	C₃×#41	1	2	yes	—
401	C₄⋊Q₈	—	9	1	no	—
402	#126	—	9	1	no	—
403	#126	—	9	1	no	—
404	#126	—	9	1	no	—
405	#126	C₃×D₉	1	1	yes	characteristic
406	#125	—	9	1	no	—
407	#125	—	9	1	no	—
408	#125	—	9	1	no	—
409	#125	—	9	1	no	—
410	#125	—	9	1	no	—
411	C₂²⋊Q₈	—	9	1	no	—
412	C₂²⋊Q₈	—	9	1	no	—
413	C₄×Q₈	—	9	1	no	—
414	C₄×Q₈	—	9	1	no	—
415	#117	—	9	1	no	—
416	C₃×C₉	#541	1	1	yes	characteristic, complemented, Sylow
417	C₂³×C₃	—	2	1	no	—
418	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
419	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
420	C₃×Q₈	—	18	2	no	—
421	C₃×Q₈	—	18	2	no	—
422	C₂×C₃×C₄	—	2	1	no	—
423	C₂×C₃×C₄	—	2	1	no	—
424	C₂×C₃×C₄	—	2	1	no	—
425	C₂×C₃×C₄	—	2	1	no	—
426	C₂×C₃×C₄	—	2	1	no	—
427	C₂×C₃×C₄	—	2	1	no	—
428	C₂×C₃×C₄	—	9	1	no	—
429	C₂×C₃×C₄	—	9	1	no	—
430	C₂×C₃×C₄	—	9	1	no	—
431	C₂×C₃×C₄	—	9	1	no	—
432	C₂×C₃×C₄	—	9	1	no	—
433	C₂×C₃×C₄	—	9	1	no	—
434	C₂×C₃×C₄	—	9	1	no	—
435	C₂×C₃×C₄	—	9	1	no	—
436	C₂×C₃×C₄	—	18	2	no	—
437	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
438	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
439	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
440	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
441	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
442	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
443	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
444	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
445	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
446	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
447	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
448	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
449	C₂×Dic₃	—	3	1	no	—
450	C₂×Dic₃	—	3	1	no	—
451	C₂×Dic₃	—	3	1	no	—
452	C₂×Dic₃	—	3	1	no	—
453	C₂×Dic₃	—	3	1	no	—
454	C₂×Dic₃	—	3	1	no	—
455	C₂×Dic₃	—	3	1	no	—
456	C₂×Dic₃	—	3	1	no	—
457	C₂×Dic₃	—	6	2	no	—
458	Dic₆	—	6	2	no	—
459	Dic₆	—	6	2	no	—
460	C₂×C₃²	—	4	1	no	—
461	C₂×C₃²	D₃×#41	1	1	yes	characteristic
462	C₂×C₃²	#1010	1	1	yes	characteristic
463	C₂×C₃²	#1010	1	1	yes	characteristic
464	C₂×C₉	—	2	1	no	—
465	C₂×C₉	—	2	1	no	—
466	C₂×C₉	—	2	1	no	—
467	C₂×C₉	—	4	1	no	—
468	C₂×C₉	—	8	1	no	—
469	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
470	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
471	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
472	C₂×Q₈	—	9	1	no	—
473	C₂×Q₈	—	9	1	no	—
474	C₂²×C₄	—	9	1	no	—
475	C₄⋊C₄	—	9	1	no	—
476	C₄⋊C₄	—	9	1	no	—
477	C₄⋊C₄	—	9	1	no	—
478	C₄⋊C₄	—	9	1	no	—
479	C₄⋊C₄	—	9	1	no	—
480	C₄⋊C₄	—	9	1	no	—
481	C₄⋊C₄	—	9	1	no	—
482	C₄⋊C₄	—	9	1	no	—
483	C₄⋊C₄	—	9	1	no	—
484	C₄⋊C₄	—	9	1	no	—
485	C₄⋊C₄	—	9	1	no	—
486	C₄⋊C₄	—	9	1	no	—
487	C₄⋊C₄	—	9	1	no	—
488	C₄⋊C₄	—	9	1	no	—
489	C₄⋊C₄	—	9	1	no	—
490	C₄⋊C₄	—	9	1	no	—
491	C₄⋊C₄	—	9	1	no	—
492	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
493	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
494	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
495	C₂²⋊C₄	—	9	1	no	—
496	C₂²⋊C₄	—	9	1	no	—
497	C₂²⋊C₄	—	9	1	no	—
498	C₂²⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
499	C₂²⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
500	C₂²⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
501	C₄²	—	9	1	no	—
502	C₄²	—	9	1	no	—
503	C₄²	—	9	1	no	—
504	C₄²	—	9	1	no	—
505	C₄²	—	9	1	no	—
506	C₄²	C₂×C₃×D₉	1	1	yes	characteristic
507	C₂²×C₃	—	2	1	no	—
508	C₂²×C₃	—	2	1	no	—
509	C₂²×C₃	—	2	1	no	—
510	C₂²×C₃	—	2	1	no	—
511	C₂²×C₃	—	2	1	no	—
512	C₂²×C₃	—	2	1	no	—
513	C₂²×C₃	—	2	1	no	—
514	C₂²×C₃	—	4	1	no	—
515	C₂²×C₃	—	4	1	no	—
516	C₂²×C₃	—	4	1	no	—
517	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
518	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
519	C₃×C₄	—	2	1	no	—
520	C₃×C₄	—	2	1	no	—
521	C₃×C₄	—	2	1	no	—
522	C₃×C₄	—	2	1	no	—
523	C₃×C₄	—	2	1	no	—
524	C₃×C₄	—	2	1	no	—
525	C₃×C₄	—	2	1	no	—
526	C₃×C₄	—	2	1	no	—
527	C₃×C₄	—	2	1	no	—
528	C₃×C₄	—	2	1	no	—
529	C₃×C₄	—	2	1	no	—
530	C₃×C₄	—	2	1	no	—
531	C₃×C₄	—	4	1	no	—
532	C₃×C₄	—	4	1	no	—
533	C₃×C₄	—	4	1	no	—
534	C₃×C₄	—	4	1	no	—
535	C₃×C₄	—	4	1	no	—
536	C₃×C₄	—	4	1	no	—
537	C₃×C₄	—	9	2	no	—
538	C₃×C₄	—	18	1	no	—
539	C₃×C₄	—	18	1	no	—
540	C₃×C₄	—	18	1	no	—
541	C₃×C₄	—	18	1	no	—
542	C₃×C₄	—	18	1	no	—
543	C₃×C₄	—	18	1	no	—
544	C₃×C₄	—	18	1	no	—
545	Dic₃	—	3	2	no	—
546	Dic₃	—	6	1	no	—
547	Dic₃	—	6	1	no	—
548	Dic₃	—	6	1	no	—
549	Dic₃	—	6	1	no	—
550	Dic₃	—	6	1	no	—
551	Dic₃	—	6	1	no	—
552	Dic₃	—	6	1	no	—
553	C₃²	#5701	1	1	yes	characteristic
554	C₉	—	2	1	no	—
555	C₉	C₃×#541	1	1	yes	characteristic, complemented
556	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
557	Q₈	—	18	2	no	—
558	Q₈	—	18	2	no	—
559	C₂×C₄	—	9	1	no	—
560	C₂×C₄	—	9	1	no	—
561	C₂×C₄	—	9	1	no	—
562	C₂×C₄	—	9	1	no	—
563	C₂×C₄	—	9	1	no	—
564	C₂×C₄	—	9	1	no	—
565	C₂×C₄	—	9	1	no	—
566	C₂×C₄	—	9	1	no	—
567	C₂×C₄	—	18	2	no	—
568	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
569	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
570	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
571	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
572	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
573	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
574	C₂×C₃	—	2	1	no	—
575	C₂×C₃	—	2	1	no	—
576	C₂×C₃	—	2	1	no	—
577	C₂×C₃	—	4	1	no	—
578	C₂×C₃	—	4	1	no	—
579	C₂×C₃	—	8	1	no	—
580	C₂×C₃	#41×D₉	1	1	yes	characteristic
581	C₂×C₃	#63716	1	1	yes	characteristic
582	C₂×C₃	#63716	1	1	yes	characteristic
583	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
584	C₂×C₃	C₃×#1010	1	1	yes	characteristic
585	C₂×C₃	C₃×#1010	1	1	yes	characteristic
586	C₂²	—	2	1	no	—
587	C₂²	—	2	1	no	—
588	C₂²	—	2	1	no	—
589	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	1	no	—
596	C₄	—	9	2	no	—
597	C₄	—	18	1	no	—
598	C₄	—	18	1	no	—
599	C₄	—	18	1	no	—
600	C₄	—	18	1	no	—
601	C₄	—	18	1	no	—
602	C₄	—	18	1	no	—
603	C₄	—	18	1	no	—
604	C₃	—	2	1	no	—
605	C₃	#10589803	1	1	yes	characteristic, direct product factor
606	C₃	C₃×#5701	1	1	yes	characteristic
607	C₂	—	4	1	no	—
608	C₂	C₃×#41×D₉	1	1	yes	characteristic
609	C₂	C₃×#63716	1	1	yes	characteristic
610	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×#126	C₂
socle	C₂²×C₃²	C₂³×D₃
prime radical	C₂³×C₃²	C₂²×D₃
hypercenter	C₃×#126	D₉
hypocenter	C₉	C₃×#541
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#126

Complements

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

N	H ≅ G/N	type
2. C₃×#63452	C₂	semidirect
3. C₃×#63451	C₂	semidirect
4. C₃×#63451	C₂	semidirect
5. C₃×#63451	C₂	semidirect
6. C₃×#63450	C₂	semidirect
7. C₃×#63449	C₂	semidirect
14. C₃×#63432	C₂	semidirect
15. C₃×C₄×Dic₁₈	C₂	semidirect
17. #10589803	C₃	direct (N × H)
70. #63452	C₂×C₃	semidirect
71. #63451	C₂×C₃	semidirect
72. #63451	C₂×C₃	semidirect
73. #63451	C₂×C₃	semidirect
74. #63450	C₂×C₃	semidirect
75. #63449	C₂×C₃	semidirect
82. #63432	C₂×C₃	semidirect
83. C₄×Dic₁₈	C₂×C₃	semidirect
416. C₃×C₉	#541	semidirect
555. C₉	C₃×#541	semidirect
605. C₃	#10589803	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×#126	2
C₃×#63452	2
C₃×#63451	2
C₃×#63450	2
C₃×#63449	2
C₃×#63441	2
C₃×#63440	2
C₃×#63439	2
C₃×#63432	2
C₃×C₄×Dic₁₈	2
C₃×#5701	3
#10589803	3

Subgroups — C3×#10589803 #13153207

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589803 #13153207