Subgroups — C₉×#5603 #13152806

Order 1728.

742 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#121	C₂	1	1	yes	maximal, characteristic
2	C₉×#936	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#936	C₂	1	2	yes	maximal, complemented
4	C₉×#935	C₂	1	2	yes	maximal, complemented
5	D₄×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#926	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#924	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#888	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#887	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#879	C₂	1	2	yes	maximal, complemented
11	C₉×#878	C₂	1	2	yes	maximal, complemented
12	C₃×#5603	C₃	1	1	yes	maximal, characteristic
13	C₉×#542	—	3	1	no	maximal
14	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₃×D₄×C₉	C₂²	1	2	yes	—
16	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
17	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
18	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
19	C₂×C₉×Dic₆	C₂²	1	2	yes	—
20	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₉×#217	C₂²	1	2	yes	—
23	C₉×#217	C₂²	1	1	yes	characteristic
24	C₉×#217	C₂²	1	1	yes	characteristic
25	C₉×#217	C₂²	1	2	yes	—
26	C₉×#217	C₂²	1	2	yes	—
27	C₉×#217	C₂²	1	2	yes	—
28	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
29	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
30	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
31	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
32	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
33	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
34	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
35	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
36	C₄×C₉×Dic₃	C₂²	1	2	yes	—
37	C₃²×#121	C₂×C₃	1	1	yes	characteristic
38	C₃×#936	C₂×C₃	1	2	yes	—
39	C₃×#936	C₂×C₃	1	1	yes	characteristic
40	C₃×#935	C₂×C₃	1	2	yes	—
41	C₃×D₄×Dic₃	C₂×C₃	1	1	yes	characteristic
42	C₃×#926	C₂×C₃	1	1	yes	characteristic
43	C₃×#924	C₂×C₃	1	1	yes	characteristic
44	C₃×#888	C₂×C₃	1	1	yes	characteristic
45	C₃×#887	C₂×C₃	1	1	yes	characteristic
46	C₃×#879	C₂×C₃	1	2	yes	—
47	C₃×#878	C₂×C₃	1	2	yes	—
48	C₉×C₄⋊Q₈	—	3	1	no	—
49	C₉×#126	—	3	2	no	—
50	C₉×#124	—	3	1	no	—
51	C₉×#124	—	3	2	no	—
52	C₉×#123	—	3	2	no	—
53	C₉×C₂²⋊Q₈	—	3	1	no	—
54	C₉×C₂²⋊Q₈	—	3	2	no	—
55	C₉×#121	—	2	1	no	—
56	C₉×#121	D₃	1	1	yes	characteristic
57	C₄×Q₈×C₉	—	3	1	no	—
58	C₄×D₄×C₉	—	3	1	no	—
59	C₉×#117	—	3	1	no	—
60	C₂³×C₃×C₉	C₂³	1	2	yes	—
61	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
62	C₃×D₄×C₉	—	2	2	no	—
63	C₃×D₄×C₉	—	4	2	no	—
64	C₂×C₃×C₄×C₉	—	2	2	no	—
65	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
66	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
68	C₂×C₉×Dic₃	—	4	2	no	—
69	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
70	C₂×C₉×Dic₃	C₂³	1	2	yes	—
71	C₂×C₉×Dic₃	C₂³	1	2	yes	—
72	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
73	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
74	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
75	C₉×Dic₆	—	2	2	no	—
76	C₉×Dic₆	—	4	2	no	—
77	C₃×#542	—	3	1	no	—
78	#5603	C₉	1	1	yes	characteristic, direct product factor
79	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	—
81	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
82	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
83	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₃×Dic₆	C₂²×C₃	1	2	yes	—
85	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
87	C₃×#217	C₂²×C₃	1	2	yes	—
88	C₃×#217	C₂²×C₃	1	2	yes	—
89	C₃×#217	C₂²×C₃	1	2	yes	—
90	C₃×#217	C₂²×C₃	1	2	yes	—
91	C₃×#217	C₂²×C₃	1	1	yes	characteristic
92	C₃×#217	C₂²×C₃	1	1	yes	characteristic
93	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
94	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
95	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
96	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
97	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
98	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
99	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
100	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
101	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
102	C₂×Q₈×C₉	—	3	1	no	—
103	C₂×Q₈×C₉	—	3	2	no	—
104	C₂×D₄×C₉	—	2	1	no	—
105	C₂×D₄×C₉	—	2	2	no	—
106	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
107	C₂×D₄×C₉	C₂×D₃	1	2	yes	—
108	C₂²×C₄×C₉	—	2	1	no	—
109	C₂²×C₄×C₉	—	3	2	no	—
110	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
111	C₉×C₄⋊C₄	—	2	1	no	—
112	C₉×C₄⋊C₄	—	3	1	no	—
113	C₉×C₄⋊C₄	—	3	1	no	—
114	C₉×C₄⋊C₄	—	3	1	no	—
115	C₉×C₄⋊C₄	—	3	2	no	—
116	C₉×C₄⋊C₄	—	3	2	no	—
117	C₉×C₄⋊C₄	—	3	2	no	—
118	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
119	C₉×C₂²⋊C₄	—	2	2	no	—
120	C₉×C₂²⋊C₄	—	3	1	no	—
121	C₉×C₂²⋊C₄	—	3	1	no	—
122	C₉×C₂²⋊C₄	—	3	2	no	—
123	C₉×C₂²⋊C₄	—	3	2	no	—
124	C₉×C₂²⋊C₄	—	3	2	no	—
125	C₉×C₂²⋊C₄	—	3	2	no	—
126	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
127	C₄²×C₉	—	3	1	no	—
128	C₄²×C₉	—	3	1	no	—
129	C₄²×C₉	—	3	2	no	—
130	C₂²×C₃×C₉	—	2	1	no	—
131	C₂²×C₃×C₉	—	2	2	no	—
132	C₂²×C₃×C₉	—	2	1	no	—
133	C₂²×C₃×C₉	—	2	2	no	—
134	C₂²×C₃×C₉	—	2	1	no	—
135	C₂²×C₃×C₉	—	2	2	no	—
136	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
137	C₃×C₄×C₉	—	2	1	no	—
138	C₃×C₄×C₉	—	2	2	no	—
139	C₃×C₄×C₉	#41	1	2	yes	—
140	C₉×Dic₃	—	2	2	no	—
141	C₉×Dic₃	—	2	1	no	—
142	C₉×Dic₃	—	2	2	no	—
143	C₉×Dic₃	—	2	1	no	—
144	C₉×Dic₃	—	2	1	no	—
145	C₉×Dic₃	—	2	1	no	—
146	C₃×C₄⋊Q₈	—	3	1	no	—
147	C₃×#126	—	3	2	no	—
148	C₃×#124	—	3	1	no	—
149	C₃×#124	—	3	2	no	—
150	C₃×#123	—	3	2	no	—
151	C₃×C₂²⋊Q₈	—	3	1	no	—
152	C₃×C₂²⋊Q₈	—	3	2	no	—
153	C₃×#121	—	2	1	no	—
154	C₃×#121	C₂×C₉	1	1	yes	characteristic
155	C₃×#121	C₃×D₃	1	1	yes	characteristic
156	C₃×C₄×Q₈	—	3	1	no	—
157	C₃×C₄×D₄	—	3	1	no	—
158	C₃×#117	—	3	1	no	—
159	#936	C₂×C₉	1	2	yes	complemented
160	#936	C₂×C₉	1	1	yes	characteristic, complemented
161	#935	C₂×C₉	1	2	yes	complemented
162	D₄×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
163	#926	C₂×C₉	1	1	yes	characteristic, complemented
164	#924	C₂×C₉	1	1	yes	characteristic, complemented
165	#888	C₂×C₉	1	1	yes	characteristic, complemented
166	#887	C₂×C₉	1	1	yes	characteristic, complemented
167	#879	C₂×C₉	1	2	yes	complemented
168	#878	C₂×C₉	1	2	yes	complemented
169	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
170	C₂³×C₃²	C₂³×C₃	1	2	yes	—
171	C₃²×D₄	—	2	2	no	—
172	C₃²×D₄	—	4	2	no	—
173	C₂×C₃²×C₄	—	2	2	no	—
174	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
175	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
176	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
177	C₂×C₃×Dic₃	—	4	2	no	—
178	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
179	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
180	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
181	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
182	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
183	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
184	C₃×Dic₆	—	2	2	no	—
185	C₃×Dic₆	—	4	2	no	—
186	C₂³×C₉	—	2	1	no	—
187	C₂³×C₉	—	2	2	no	—
188	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
189	C₂³×C₉	C₂²×D₃	1	2	yes	—
190	Q₈×C₉	—	6	2	no	—
191	Q₈×C₉	—	12	2	no	—
192	D₄×C₉	—	2	2	no	—
193	D₄×C₉	—	4	2	no	—
194	D₄×C₉	—	4	2	no	—
195	D₄×C₉	—	4	4	no	—
196	C₂×C₄×C₉	—	2	2	no	—
197	C₂×C₄×C₉	—	2	1	no	—
198	C₂×C₄×C₉	—	2	1	no	—
199	C₂×C₄×C₉	—	2	2	no	—
200	C₂×C₄×C₉	—	3	1	no	—
201	C₂×C₄×C₉	—	3	1	no	—
202	C₂×C₄×C₉	—	3	2	no	—
203	C₂×C₄×C₉	—	3	1	no	—
204	C₂×C₄×C₉	—	3	1	no	—
205	C₂×C₄×C₉	—	3	2	no	—
206	C₂×C₄×C₉	—	4	2	no	—
207	C₂×C₄×C₉	—	12	2	no	—
208	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
209	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
210	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
211	#542	—	3	1	no	Sylow
212	C₂×C₃×C₉	—	4	1	no	—
213	C₂×C₃×C₉	—	4	2	no	—
214	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
215	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
216	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
217	C₂×C₃×Q₈	—	3	1	no	—
218	C₂×C₃×Q₈	—	3	2	no	—
219	C₂×C₃×D₄	—	2	1	no	—
220	C₂×C₃×D₄	—	2	2	no	—
221	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
222	C₂×C₃×D₄	C₂²×C₉	1	2	yes	—
223	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
224	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
225	C₂²×C₃×C₄	—	2	1	no	—
226	C₂²×C₃×C₄	—	3	2	no	—
227	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
228	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
229	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
230	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
231	C₂×Dic₆	C₂²×C₉	1	2	yes	—
232	C₃×C₄⋊C₄	—	2	1	no	—
233	C₃×C₄⋊C₄	—	3	2	no	—
234	C₃×C₄⋊C₄	—	3	2	no	—
235	C₃×C₄⋊C₄	—	3	2	no	—
236	C₃×C₄⋊C₄	—	3	1	no	—
237	C₃×C₄⋊C₄	—	3	1	no	—
238	C₃×C₄⋊C₄	—	3	1	no	—
239	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
240	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
241	C₃×C₂²⋊C₄	—	2	2	no	—
242	C₃×C₂²⋊C₄	—	3	1	no	—
243	C₃×C₂²⋊C₄	—	3	1	no	—
244	C₃×C₂²⋊C₄	—	3	2	no	—
245	C₃×C₂²⋊C₄	—	3	2	no	—
246	C₃×C₂²⋊C₄	—	3	2	no	—
247	C₃×C₂²⋊C₄	—	3	2	no	—
248	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
249	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
250	C₃×C₄²	—	3	1	no	—
251	C₃×C₄²	—	3	1	no	—
252	C₃×C₄²	—	3	2	no	—
253	#217	C₂²×C₉	1	2	yes	—
254	#217	C₂²×C₉	1	2	yes	—
255	#217	C₂²×C₉	1	2	yes	—
256	#217	C₂²×C₉	1	2	yes	—
257	#217	C₂²×C₉	1	1	yes	characteristic
258	#217	C₂²×C₉	1	1	yes	characteristic
259	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
260	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
261	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
262	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
263	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
264	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
265	C₄×Dic₃	C₂²×C₉	1	2	yes	—
266	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
267	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
268	C₂²×C₃²	—	2	1	no	—
269	C₂²×C₃²	—	2	1	no	—
270	C₂²×C₃²	—	2	2	no	—
271	C₂²×C₃²	—	2	2	no	—
272	C₂²×C₃²	—	2	1	no	—
273	C₂²×C₃²	—	2	2	no	—
274	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
275	C₃²×C₄	—	2	1	no	—
276	C₃²×C₄	—	2	2	no	—
277	C₃²×C₄	C₃×#41	1	2	yes	—
278	C₃×Dic₃	—	2	2	no	—
279	C₃×Dic₃	—	2	1	no	—
280	C₃×Dic₃	—	2	2	no	—
281	C₃×Dic₃	—	2	1	no	—
282	C₃×Dic₃	—	2	1	no	—
283	C₃×Dic₃	—	2	1	no	—
284	C₂²×C₉	—	2	2	no	—
285	C₂²×C₉	—	2	1	no	—
286	C₂²×C₉	—	2	2	no	—
287	C₂²×C₉	—	2	2	no	—
288	C₂²×C₉	—	2	1	no	—
289	C₂²×C₉	—	2	1	no	—
290	C₂²×C₉	—	2	2	no	—
291	C₂²×C₉	—	2	1	no	—
292	C₂²×C₉	—	4	1	no	—
293	C₂²×C₉	—	4	1	no	—
294	C₂²×C₉	—	4	2	no	—
295	C₂²×C₉	—	4	2	no	—
296	C₂²×C₉	—	4	2	no	—
297	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
298	C₄×C₉	—	2	1	no	—
299	C₄×C₉	—	2	2	no	—
300	C₄×C₉	—	2	2	no	—
301	C₄×C₉	—	4	1	no	—
302	C₄×C₉	—	4	2	no	—
303	C₄×C₉	—	6	2	no	—
304	C₄×C₉	—	6	1	no	—
305	C₄×C₉	—	6	2	no	—
306	C₄×C₉	—	6	1	no	—
307	C₄×C₉	—	6	1	no	—
308	C₄×C₉	—	6	1	no	—
309	C₄×C₉	#237	1	2	yes	—
310	C₄⋊Q₈	—	3	1	no	—
311	#126	—	3	2	no	—
312	#124	—	3	1	no	—
313	#124	—	3	2	no	—
314	#123	—	3	2	no	—
315	C₂²⋊Q₈	—	3	1	no	—
316	C₂²⋊Q₈	—	3	2	no	—
317	#121	D₃×C₉	1	1	yes	characteristic
318	C₄×Q₈	—	3	1	no	—
319	C₄×D₄	—	3	1	no	—
320	#117	—	3	1	no	—
321	C₃×C₉	#542	1	1	yes	characteristic, complemented, Sylow
322	C₂³×C₃	—	2	1	no	—
323	C₂³×C₃	—	2	2	no	—
324	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
325	C₂³×C₃	C₂³×C₉	1	2	yes	—
326	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
327	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
328	C₃×Q₈	—	6	2	no	—
329	C₃×Q₈	—	12	2	no	—
330	C₃×D₄	—	2	2	no	—
331	C₃×D₄	—	2	2	no	—
332	C₃×D₄	—	4	2	no	—
333	C₃×D₄	—	4	2	no	—
334	C₃×D₄	—	4	2	no	—
335	C₃×D₄	—	4	4	no	—
336	C₂×C₃×C₄	—	2	2	no	—
337	C₂×C₃×C₄	—	2	2	no	—
338	C₂×C₃×C₄	—	2	1	no	—
339	C₂×C₃×C₄	—	2	1	no	—
340	C₂×C₃×C₄	—	2	2	no	—
341	C₂×C₃×C₄	—	3	1	no	—
342	C₂×C₃×C₄	—	3	1	no	—
343	C₂×C₃×C₄	—	3	2	no	—
344	C₂×C₃×C₄	—	3	1	no	—
345	C₂×C₃×C₄	—	3	1	no	—
346	C₂×C₃×C₄	—	3	2	no	—
347	C₂×C₃×C₄	—	4	2	no	—
348	C₂×C₃×C₄	—	12	2	no	—
349	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
350	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
351	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
352	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
353	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
354	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
355	C₂×Dic₃	—	4	2	no	—
356	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
357	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
358	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
359	C₂×Dic₃	C₂³×C₉	1	2	yes	—
360	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
361	C₂×Dic₃	C₂³×C₉	1	2	yes	—
362	Dic₆	—	2	2	no	—
363	Dic₆	—	4	2	no	—
364	C₂×C₃²	—	4	1	no	—
365	C₂×C₃²	—	4	2	no	—
366	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
367	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
368	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
369	C₂×C₉	—	2	1	no	—
370	C₂×C₉	—	2	1	no	—
371	C₂×C₉	—	2	1	no	—
372	C₂×C₉	—	4	2	no	—
373	C₂×C₉	—	4	1	no	—
374	C₂×C₉	—	4	2	no	—
375	C₂×C₉	—	8	2	no	—
376	C₂×C₉	C₂×#237	1	1	yes	characteristic
377	C₂×C₉	#1004	1	1	yes	characteristic
378	C₂×C₉	#1010	1	1	yes	characteristic
379	C₂×Q₈	—	3	1	no	—
380	C₂×Q₈	—	3	2	no	—
381	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
382	C₂×D₄	C₂×D₃×C₉	1	2	yes	—
383	C₂²×C₄	—	3	2	no	—
384	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
385	C₄⋊C₄	—	3	1	no	—
386	C₄⋊C₄	—	3	1	no	—
387	C₄⋊C₄	—	3	1	no	—
388	C₄⋊C₄	—	3	2	no	—
389	C₄⋊C₄	—	3	2	no	—
390	C₄⋊C₄	—	3	2	no	—
391	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
392	C₂²⋊C₄	—	3	1	no	—
393	C₂²⋊C₄	—	3	1	no	—
394	C₂²⋊C₄	—	3	2	no	—
395	C₂²⋊C₄	—	3	2	no	—
396	C₂²⋊C₄	—	3	2	no	—
397	C₂²⋊C₄	—	3	2	no	—
398	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
399	C₄²	—	3	1	no	—
400	C₄²	—	3	1	no	—
401	C₄²	—	3	2	no	—
402	C₂²×C₃	—	2	2	no	—
403	C₂²×C₃	—	2	1	no	—
404	C₂²×C₃	—	2	2	no	—
405	C₂²×C₃	—	2	2	no	—
406	C₂²×C₃	—	2	1	no	—
407	C₂²×C₃	—	2	1	no	—
408	C₂²×C₃	—	2	2	no	—
409	C₂²×C₃	—	2	1	no	—
410	C₂²×C₃	—	2	2	no	—
411	C₂²×C₃	—	2	2	no	—
412	C₂²×C₃	—	2	1	no	—
413	C₂²×C₃	—	2	1	no	—
414	C₂²×C₃	—	2	2	no	—
415	C₂²×C₃	—	2	1	no	—
416	C₂²×C₃	—	4	1	no	—
417	C₂²×C₃	—	4	1	no	—
418	C₂²×C₃	—	4	2	no	—
419	C₂²×C₃	—	4	2	no	—
420	C₂²×C₃	—	4	2	no	—
421	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
422	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
423	C₃×C₄	—	2	1	no	—
424	C₃×C₄	—	2	2	no	—
425	C₃×C₄	—	2	1	no	—
426	C₃×C₄	—	2	2	no	—
427	C₃×C₄	—	2	2	no	—
428	C₃×C₄	—	4	1	no	—
429	C₃×C₄	—	4	2	no	—
430	C₃×C₄	—	6	2	no	—
431	C₃×C₄	—	6	1	no	—
432	C₃×C₄	—	6	2	no	—
433	C₃×C₄	—	6	1	no	—
434	C₃×C₄	—	6	1	no	—
435	C₃×C₄	—	6	1	no	—
436	C₃×C₄	C₉×#41	1	2	yes	—
437	C₃×C₄	C₃×#237	1	2	yes	—
438	Dic₃	—	2	2	no	—
439	Dic₃	—	2	1	no	—
440	Dic₃	—	2	2	no	—
441	Dic₃	—	2	1	no	—
442	Dic₃	—	2	1	no	—
443	Dic₃	—	2	1	no	—
444	C₃²	C₃×#542	1	1	yes	characteristic
445	C₉	—	2	1	no	—
446	C₉	#5603	1	1	yes	characteristic, direct product factor
447	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
448	C₂³	C₂²×D₃×C₉	1	2	yes	—
449	Q₈	—	6	2	no	—
450	Q₈	—	12	2	no	—
451	D₄	—	2	2	no	—
452	D₄	—	4	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	3	1	no	—
455	C₂×C₄	—	3	1	no	—
456	C₂×C₄	—	3	2	no	—
457	C₂×C₄	—	3	1	no	—
458	C₂×C₄	—	3	1	no	—
459	C₂×C₄	—	3	2	no	—
460	C₂×C₄	—	12	2	no	—
461	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
462	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
463	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
464	C₂×C₃	—	2	1	no	—
465	C₂×C₃	—	2	1	no	—
466	C₂×C₃	—	2	1	no	—
467	C₂×C₃	—	4	2	no	—
468	C₂×C₃	—	4	1	no	—
469	C₂×C₃	—	4	2	no	—
470	C₂×C₃	—	4	1	no	—
471	C₂×C₃	—	4	2	no	—
472	C₂×C₃	—	8	2	no	—
473	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
474	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
475	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
476	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
477	C₂×C₃	C₃×#1004	1	1	yes	characteristic
478	C₂×C₃	C₃×#1010	1	1	yes	characteristic
479	C₂²	—	2	1	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	2	no	—
485	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
486	C₄	—	2	1	no	—
487	C₄	—	2	2	no	—
488	C₄	—	6	2	no	—
489	C₄	—	6	1	no	—
490	C₄	—	6	2	no	—
491	C₄	—	6	1	no	—
492	C₄	—	6	1	no	—
493	C₄	—	6	1	no	—
494	C₄	C₉×#237	1	2	yes	—
495	C₃	—	2	1	no	—
496	C₃	C₉×#542	1	1	yes	characteristic, complemented
497	C₃	C₃×#5603	1	1	yes	characteristic
498	C₂	—	4	1	no	—
499	C₂	—	4	2	no	—
500	C₂	C₂×C₉×#237	1	1	yes	characteristic
501	C₂	C₉×#1004	1	1	yes	characteristic
502	C₂	C₉×#1010	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#121	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃²×#121	C₂×C₃
hypercenter	C₉×#121	D₃
hypocenter	C₃	C₉×#542
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#121

Complements

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

N	H ≅ G/N	type
2. C₉×#936	C₂	semidirect
3. C₉×#936	C₂	semidirect
4. C₉×#935	C₂	semidirect
5. D₄×C₉×Dic₃	C₂	semidirect
6. C₉×#926	C₂	semidirect
7. C₉×#924	C₂	semidirect
8. C₉×#888	C₂	semidirect
9. C₉×#887	C₂	semidirect
10. C₉×#879	C₂	semidirect
11. C₉×#878	C₂	semidirect
78. #5603	C₉	direct (N × H)
159. #936	C₂×C₉	semidirect
160. #936	C₂×C₉	semidirect
161. #935	C₂×C₉	semidirect
162. D₄×Dic₃	C₂×C₉	semidirect
163. #926	C₂×C₉	semidirect
164. #924	C₂×C₉	semidirect
165. #888	C₂×C₉	semidirect
166. #887	C₂×C₉	semidirect
167. #879	C₂×C₉	semidirect
168. #878	C₂×C₉	semidirect
321. C₃×C₉	#542	semidirect
446. C₉	#5603	direct (N × H)
496. C₃	C₉×#542	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×#121	2
C₉×#936	2
C₉×#935	2
D₄×C₉×Dic₃	2
C₉×#926	2
C₉×#924	2
C₉×#888	2
C₉×#887	2
C₉×#879	2
C₉×#878	2
C₃×#5603	3
C₉×#542	3

Subgroups — C9×#5603 #13152806

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5603 #13152806