Subgroups — C₉×#5681 #13153085

Order 1728.

784 conjugacy classes of subgroups.

The subgroup lattice has 508 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, complemented
2	C₉×#947	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#940	C₂	1	1	yes	maximal, characteristic
5	D₄×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#886	C₂	1	2	yes	maximal, complemented
7	C₉×#885	C₂	1	2	yes	maximal, complemented
8	C₉×#883	C₂	1	2	yes	maximal, complemented
9	C₉×#67⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₄×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₉×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5681	C₃	1	1	yes	maximal, characteristic
13	C₉×#559	—	3	1	no	maximal
14	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
16	C₂×C₉×#67	C₂²	1	2	yes	—
17	C₂×C₉×#67	C₂²	1	2	yes	—
18	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
19	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
21	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
22	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
25	C₉×#217	C₂²	1	2	yes	—
26	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
27	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
28	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
29	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
30	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
31	C₉×C₄⋊Dic₃	C₂²	1	2	yes	—
32	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
33	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
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×#124	C₂×C₃	1	1	yes	characteristic
38	C₃×#947	C₂×C₃	1	1	yes	characteristic
39	C₃×Q₈×Dic₃	C₂×C₃	1	1	yes	characteristic
40	C₃×#940	C₂×C₃	1	1	yes	characteristic
41	C₃×D₄×Dic₃	C₂×C₃	1	1	yes	characteristic
42	C₃×#886	C₂×C₃	1	2	yes	—
43	C₃×#885	C₂×C₃	1	2	yes	—
44	C₃×#883	C₂×C₃	1	2	yes	—
45	C₃×#67⋊C₄	C₂×C₃	1	2	yes	—
46	C₃×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
47	C₃×C₄×Dic₆	C₂×C₃	1	1	yes	characteristic
48	C₉×#127	—	3	1	no	—
49	C₉×#124	—	2	1	no	—
50	C₉×#124	—	3	1	no	—
51	C₉×#124	—	3	2	no	—
52	C₉×#124	D₃	1	1	yes	characteristic, complemented
53	C₉×#123	—	3	2	no	—
54	C₉×#123	—	3	2	no	—
55	C₄×Q₈×C₉	—	3	1	no	—
56	C₄×Q₈×C₉	—	3	1	no	—
57	C₄×D₄×C₉	—	3	1	no	—
58	C₄×D₄×C₉	—	3	2	no	—
59	C₄×D₄×C₉	—	3	1	no	—
60	C₂³×C₃×C₉	C₂³	1	2	yes	—
61	C₂²×D₃×C₉	C₂³	1	2	yes	—
62	C₃×Q₈×C₉	—	2	2	no	—
63	C₃×D₄×C₉	—	2	2	no	—
64	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
67	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
68	C₉×#67	—	2	4	no	—
69	C₉×#67	—	4	2	no	—
70	C₂×C₉×Dic₃	—	4	2	no	—
71	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
72	C₂×C₉×Dic₃	C₂³	1	2	yes	—
73	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
74	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
75	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
76	C₉×D₁₂	—	2	2	no	—
77	C₄×D₃×C₉	—	4	2	no	—
78	C₉×Dic₆	—	2	2	no	—
79	C₃×#559	—	3	1	no	—
80	#5681	C₉	1	1	yes	characteristic, direct product factor
81	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
84	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
85	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
86	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
88	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
89	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
90	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
91	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
92	C₃×#217	C₂²×C₃	1	2	yes	—
93	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
94	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
95	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
96	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
97	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
98	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
99	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
100	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
101	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
102	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
103	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
104	C₂×Q₈×C₉	—	2	1	no	—
105	C₂×Q₈×C₉	—	3	1	no	—
106	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
107	C₂×D₄×C₉	—	2	1	no	—
108	C₂×D₄×C₉	—	3	2	no	—
109	C₂×D₄×C₉	—	3	2	no	—
110	C₂×D₄×C₉	—	3	1	no	—
111	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
112	C₂²×C₄×C₉	—	3	2	no	—
113	C₂²×C₄×C₉	—	3	2	no	—
114	C₉×C₄⋊C₄	—	3	1	no	—
115	C₉×C₄⋊C₄	—	3	1	no	—
116	C₉×C₄⋊C₄	—	3	1	no	—
117	C₉×C₄⋊C₄	—	3	2	no	—
118	C₉×C₄⋊C₄	—	3	1	no	—
119	C₉×C₂²⋊C₄	—	2	2	no	—
120	C₉×C₂²⋊C₄	—	2	2	no	—
121	C₉×C₂²⋊C₄	—	3	2	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	C₂×D₃	1	2	yes	—
126	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
127	C₄²×C₉	—	2	1	no	—
128	C₄²×C₉	—	3	2	no	—
129	C₄²×C₉	—	3	1	no	—
130	C₄²×C₉	—	3	1	no	—
131	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
132	C₂²×C₃×C₉	—	2	2	no	—
133	C₂²×C₃×C₉	—	2	2	no	—
134	C₂²×C₃×C₉	—	2	2	no	—
135	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
136	C₂×D₃×C₉	—	2	2	no	—
137	C₂×D₃×C₉	—	2	2	no	—
138	C₂×D₃×C₉	—	2	2	no	—
139	C₃×C₄×C₉	—	2	1	no	—
140	C₃×C₄×C₉	—	2	2	no	—
141	C₃×C₄×C₉	—	2	1	no	—
142	C₃×C₄×C₉	#41	1	2	yes	—
143	C₉×Dic₃	—	2	1	no	—
144	C₉×Dic₃	—	2	2	no	—
145	C₉×Dic₃	—	2	1	no	—
146	C₉×Dic₃	—	2	1	no	—
147	C₉×Dic₃	#41	1	2	yes	—
148	C₃×#127	—	3	1	no	—
149	C₃×#124	—	2	1	no	—
150	C₃×#124	—	3	1	no	—
151	C₃×#124	—	3	2	no	—
152	C₃×#124	C₂×C₉	1	1	yes	characteristic, complemented
153	C₃×#124	C₃×D₃	1	1	yes	characteristic
154	C₃×#123	—	3	2	no	—
155	C₃×#123	—	3	2	no	—
156	C₃×C₄×Q₈	—	3	1	no	—
157	C₃×C₄×Q₈	—	3	1	no	—
158	C₃×C₄×D₄	—	3	1	no	—
159	C₃×C₄×D₄	—	3	2	no	—
160	C₃×C₄×D₄	—	3	1	no	—
161	#947	C₂×C₉	1	1	yes	characteristic, complemented
162	Q₈×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
163	#940	C₂×C₉	1	1	yes	characteristic
164	D₄×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
165	#886	C₂×C₉	1	2	yes	complemented
166	#885	C₂×C₉	1	2	yes	complemented
167	#883	C₂×C₉	1	2	yes	complemented
168	#67⋊C₄	C₂×C₉	1	2	yes	complemented
169	C₄×D₁₂	C₂×C₉	1	1	yes	characteristic, complemented
170	C₄×Dic₆	C₂×C₉	1	1	yes	characteristic, complemented
171	C₂³×C₃²	C₂³×C₃	1	2	yes	—
172	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
173	C₃²×Q₈	—	2	2	no	—
174	C₃²×D₄	—	2	2	no	—
175	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
176	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
177	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
178	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
179	C₃×#67	—	2	4	no	—
180	C₃×#67	—	4	2	no	—
181	C₂×C₃×Dic₃	—	4	2	no	—
182	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
183	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
184	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
185	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
186	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
187	C₃×D₁₂	—	2	2	no	—
188	C₃×C₄×D₃	—	4	2	no	—
189	C₃×Dic₆	—	2	2	no	—
190	C₂³×C₉	—	2	2	no	—
191	C₂³×C₉	—	3	2	no	—
192	C₂³×C₉	C₂²×D₃	1	2	yes	—
193	Q₈×C₉	—	2	2	no	—
194	Q₈×C₉	—	4	2	no	—
195	Q₈×C₉	—	6	2	no	—
196	D₄×C₉	—	2	2	no	—
197	D₄×C₉	—	4	2	no	—
198	D₄×C₉	—	6	4	no	—
199	D₄×C₉	—	6	2	no	—
200	D₄×C₉	—	12	2	no	—
201	C₂×C₄×C₉	—	2	1	no	—
202	C₂×C₄×C₉	—	2	1	no	—
203	C₂×C₄×C₉	—	2	1	no	—
204	C₂×C₄×C₉	—	2	2	no	—
205	C₂×C₄×C₉	—	3	1	no	—
206	C₂×C₄×C₉	—	3	1	no	—
207	C₂×C₄×C₉	—	3	2	no	—
208	C₂×C₄×C₉	—	3	1	no	—
209	C₂×C₄×C₉	—	3	1	no	—
210	C₂×C₄×C₉	—	12	2	no	—
211	C₂×C₄×C₉	—	12	2	no	—
212	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
213	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
214	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
215	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
216	#559	—	3	1	no	Sylow
217	C₂×C₃×C₉	—	4	2	no	—
218	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
219	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
220	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
221	D₃×C₉	—	4	2	no	—
222	C₂×C₃×Q₈	—	2	1	no	—
223	C₂×C₃×Q₈	—	3	1	no	—
224	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
225	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
226	C₂×C₃×D₄	—	2	1	no	—
227	C₂×C₃×D₄	—	3	2	no	—
228	C₂×C₃×D₄	—	3	2	no	—
229	C₂×C₃×D₄	—	3	1	no	—
230	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
231	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
232	C₂²×C₃×C₄	—	3	2	no	—
233	C₂²×C₃×C₄	—	3	2	no	—
234	C₂×#67	C₂²×C₉	1	2	yes	—
235	C₂×#67	C₂²×C₉	1	2	yes	—
236	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
237	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
238	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
239	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
240	C₃×C₄⋊C₄	—	3	1	no	—
241	C₃×C₄⋊C₄	—	3	1	no	—
242	C₃×C₄⋊C₄	—	3	1	no	—
243	C₃×C₄⋊C₄	—	3	2	no	—
244	C₃×C₄⋊C₄	—	3	1	no	—
245	C₃×C₂²⋊C₄	—	2	2	no	—
246	C₃×C₂²⋊C₄	—	2	2	no	—
247	C₃×C₂²⋊C₄	—	3	2	no	—
248	C₃×C₂²⋊C₄	—	3	2	no	—
249	C₃×C₂²⋊C₄	—	3	2	no	—
250	C₃×C₂²⋊C₄	—	3	2	no	—
251	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
252	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
253	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
254	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
255	C₃×C₄²	—	2	1	no	—
256	C₃×C₄²	—	3	2	no	—
257	C₃×C₄²	—	3	1	no	—
258	C₃×C₄²	—	3	1	no	—
259	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
260	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
261	#217	C₂²×C₉	1	2	yes	—
262	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
263	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
264	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
265	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
266	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
267	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
268	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
269	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
270	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
271	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
272	C₄×Dic₃	C₂²×C₉	1	2	yes	—
273	C₂²×C₃²	—	2	2	no	—
274	C₂²×C₃²	—	2	2	no	—
275	C₂²×C₃²	—	2	2	no	—
276	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
277	C₂×C₃×D₃	—	2	2	no	—
278	C₂×C₃×D₃	—	2	2	no	—
279	C₂×C₃×D₃	—	2	2	no	—
280	C₃²×C₄	—	2	1	no	—
281	C₃²×C₄	—	2	2	no	—
282	C₃²×C₄	—	2	1	no	—
283	C₃²×C₄	C₃×#41	1	2	yes	—
284	C₃×Dic₃	—	2	1	no	—
285	C₃×Dic₃	—	2	2	no	—
286	C₃×Dic₃	—	2	1	no	—
287	C₃×Dic₃	—	2	1	no	—
288	C₃×Dic₃	C₃×#41	1	2	yes	—
289	C₂²×C₉	—	2	2	no	—
290	C₂²×C₉	—	2	2	no	—
291	C₂²×C₉	—	2	2	no	—
292	C₂²×C₉	—	2	1	no	—
293	C₂²×C₉	—	4	2	no	—
294	C₂²×C₉	—	4	2	no	—
295	C₂²×C₉	—	4	2	no	—
296	C₂²×C₉	—	6	2	no	—
297	C₂²×C₉	—	6	2	no	—
298	C₂²×C₉	—	6	2	no	—
299	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
300	C₄×C₉	—	2	2	no	—
301	C₄×C₉	—	2	1	no	—
302	C₄×C₉	—	2	1	no	—
303	C₄×C₉	—	2	2	no	—
304	C₄×C₉	—	3	2	no	—
305	C₄×C₉	—	4	1	no	—
306	C₄×C₉	—	4	1	no	—
307	C₄×C₉	—	4	2	no	—
308	C₄×C₉	—	6	1	no	—
309	C₄×C₉	—	6	2	no	—
310	C₄×C₉	—	6	1	no	—
311	C₄×C₉	—	6	1	no	—
312	C₄×C₉	#237	1	2	yes	—
313	#127	—	3	1	no	—
314	#124	—	3	1	no	—
315	#124	—	3	2	no	—
316	#124	D₃×C₉	1	1	yes	characteristic, complemented
317	#123	—	3	2	no	—
318	#123	—	3	2	no	—
319	C₄×Q₈	—	3	1	no	—
320	C₄×Q₈	—	3	1	no	—
321	C₄×D₄	—	3	1	no	—
322	C₄×D₄	—	3	2	no	—
323	C₄×D₄	—	3	1	no	—
324	C₃×C₉	#559	1	1	yes	characteristic, complemented, Sylow
325	C₂³×C₃	—	2	2	no	—
326	C₂³×C₃	—	3	2	no	—
327	C₂³×C₃	C₂³×C₉	1	2	yes	—
328	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
329	C₂²×D₃	C₂³×C₉	1	2	yes	—
330	C₃×Q₈	—	2	2	no	—
331	C₃×Q₈	—	2	2	no	—
332	C₃×Q₈	—	4	2	no	—
333	C₃×Q₈	—	6	2	no	—
334	C₃×D₄	—	2	2	no	—
335	C₃×D₄	—	2	2	no	—
336	C₃×D₄	—	4	2	no	—
337	C₃×D₄	—	6	4	no	—
338	C₃×D₄	—	6	2	no	—
339	C₃×D₄	—	12	2	no	—
340	C₂×C₃×C₄	—	2	1	no	—
341	C₂×C₃×C₄	—	2	1	no	—
342	C₂×C₃×C₄	—	2	1	no	—
343	C₂×C₃×C₄	—	2	2	no	—
344	C₂×C₃×C₄	—	3	1	no	—
345	C₂×C₃×C₄	—	3	1	no	—
346	C₂×C₃×C₄	—	3	1	no	—
347	C₂×C₃×C₄	—	3	2	no	—
348	C₂×C₃×C₄	—	3	1	no	—
349	C₂×C₃×C₄	—	12	2	no	—
350	C₂×C₃×C₄	—	12	2	no	—
351	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
352	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
353	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
354	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
355	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
356	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
357	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
358	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
359	#67	—	2	4	no	—
360	#67	—	4	2	no	—
361	C₂×Dic₃	—	4	2	no	—
362	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
363	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
364	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
365	C₂×Dic₃	C₂³×C₉	1	2	yes	—
366	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
367	D₁₂	—	2	2	no	—
368	C₄×D₃	—	4	2	no	—
369	Dic₆	—	2	2	no	—
370	C₂×C₃²	—	4	2	no	—
371	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
372	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
373	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
374	C₃×D₃	—	4	2	no	—
375	C₂×C₉	—	2	1	no	—
376	C₂×C₉	—	2	1	no	—
377	C₂×C₉	—	2	1	no	—
378	C₂×C₉	—	4	2	no	—
379	C₂×C₉	—	8	2	no	—
380	C₂×C₉	—	12	2	no	—
381	C₂×C₉	C₂×#237	1	1	yes	characteristic
382	C₂×C₉	D₃×#41	1	1	yes	characteristic
383	C₂×C₉	#1009	1	1	yes	characteristic
384	C₂×Q₈	—	3	1	no	—
385	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
386	C₂×D₄	—	3	2	no	—
387	C₂×D₄	—	3	2	no	—
388	C₂×D₄	—	3	1	no	—
389	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
390	C₂²×C₄	—	3	2	no	—
391	C₂²×C₄	—	3	2	no	—
392	C₄⋊C₄	—	3	1	no	—
393	C₄⋊C₄	—	3	1	no	—
394	C₄⋊C₄	—	3	1	no	—
395	C₄⋊C₄	—	3	2	no	—
396	C₄⋊C₄	—	3	1	no	—
397	C₂²⋊C₄	—	3	2	no	—
398	C₂²⋊C₄	—	3	2	no	—
399	C₂²⋊C₄	—	3	2	no	—
400	C₂²⋊C₄	—	3	2	no	—
401	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
402	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
403	C₄²	—	3	2	no	—
404	C₄²	—	3	1	no	—
405	C₄²	—	3	1	no	—
406	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
407	C₂²×C₃	—	2	2	no	—
408	C₂²×C₃	—	2	2	no	—
409	C₂²×C₃	—	2	2	no	—
410	C₂²×C₃	—	2	2	no	—
411	C₂²×C₃	—	2	2	no	—
412	C₂²×C₃	—	2	2	no	—
413	C₂²×C₃	—	2	1	no	—
414	C₂²×C₃	—	4	2	no	—
415	C₂²×C₃	—	4	2	no	—
416	C₂²×C₃	—	4	2	no	—
417	C₂²×C₃	—	6	2	no	—
418	C₂²×C₃	—	6	2	no	—
419	C₂²×C₃	—	6	2	no	—
420	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
421	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
422	C₂×D₃	—	2	2	no	—
423	C₂×D₃	—	2	2	no	—
424	C₂×D₃	—	2	2	no	—
425	C₃×C₄	—	2	2	no	—
426	C₃×C₄	—	2	1	no	—
427	C₃×C₄	—	2	1	no	—
428	C₃×C₄	—	2	1	no	—
429	C₃×C₄	—	2	2	no	—
430	C₃×C₄	—	2	1	no	—
431	C₃×C₄	—	2	2	no	—
432	C₃×C₄	—	3	2	no	—
433	C₃×C₄	—	4	2	no	—
434	C₃×C₄	—	4	1	no	—
435	C₃×C₄	—	4	1	no	—
436	C₃×C₄	—	6	1	no	—
437	C₃×C₄	—	6	2	no	—
438	C₃×C₄	—	6	1	no	—
439	C₃×C₄	—	6	1	no	—
440	C₃×C₄	C₉×#41	1	2	yes	—
441	C₃×C₄	C₃×#237	1	2	yes	—
442	Dic₃	—	2	1	no	—
443	Dic₃	—	2	2	no	—
444	Dic₃	—	2	1	no	—
445	Dic₃	—	2	1	no	—
446	Dic₃	C₉×#41	1	2	yes	—
447	C₃²	C₃×#559	1	1	yes	characteristic
448	C₉	—	2	1	no	—
449	C₉	#5681	1	1	yes	characteristic, direct product factor
450	C₂³	—	3	2	no	—
451	C₂³	C₂²×D₃×C₉	1	2	yes	—
452	Q₈	—	2	2	no	—
453	Q₈	—	6	2	no	—
454	D₄	—	2	2	no	—
455	D₄	—	6	4	no	—
456	D₄	—	6	2	no	—
457	D₄	—	12	2	no	—
458	C₂×C₄	—	3	1	no	—
459	C₂×C₄	—	3	1	no	—
460	C₂×C₄	—	3	2	no	—
461	C₂×C₄	—	3	1	no	—
462	C₂×C₄	—	3	1	no	—
463	C₂×C₄	—	12	2	no	—
464	C₂×C₄	—	12	2	no	—
465	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
466	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
467	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
468	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
469	C₂×C₃	—	2	1	no	—
470	C₂×C₃	—	2	1	no	—
471	C₂×C₃	—	2	1	no	—
472	C₂×C₃	—	4	2	no	—
473	C₂×C₃	—	4	2	no	—
474	C₂×C₃	—	8	2	no	—
475	C₂×C₃	—	12	2	no	—
476	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
477	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
478	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
479	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
480	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
481	C₂×C₃	C₃×#1009	1	1	yes	characteristic
482	D₃	—	4	2	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	6	2	no	—
487	C₂²	—	6	2	no	—
488	C₂²	—	6	2	no	—
489	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
490	C₄	—	2	2	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	3	2	no	—
494	C₄	—	6	1	no	—
495	C₄	—	6	2	no	—
496	C₄	—	6	1	no	—
497	C₄	—	6	1	no	—
498	C₄	C₉×#237	1	2	yes	—
499	C₃	—	2	1	no	—
500	C₃	C₉×#559	1	1	yes	characteristic, complemented
501	C₃	C₃×#5681	1	1	yes	characteristic
502	C₂	—	4	2	no	—
503	C₂	—	12	2	no	—
504	C₂	C₂×C₉×#237	1	1	yes	characteristic
505	C₂	D₃×C₉×#41	1	1	yes	characteristic
506	C₂	C₉×#1009	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×#124	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#940	C₂×C₃
hypercenter	C₉×#124	D₃
hypocenter	C₃	C₉×#559
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#124

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×#124	C₂	semidirect
2. C₉×#947	C₂	semidirect
3. Q₈×C₉×Dic₃	C₂	semidirect
5. D₄×C₉×Dic₃	C₂	semidirect
6. C₉×#886	C₂	semidirect
7. C₉×#885	C₂	semidirect
8. C₉×#883	C₂	semidirect
9. C₉×#67⋊C₄	C₂	semidirect
10. C₄×C₉×D₁₂	C₂	semidirect
11. C₄×C₉×Dic₆	C₂	semidirect
52. C₉×#124	D₃	semidirect
80. #5681	C₉	direct (N × H)
152. C₃×#124	C₂×C₉	semidirect
161. #947	C₂×C₉	semidirect
162. Q₈×Dic₃	C₂×C₉	semidirect
164. D₄×Dic₃	C₂×C₉	semidirect
165. #886	C₂×C₉	semidirect
166. #885	C₂×C₉	semidirect
167. #883	C₂×C₉	semidirect
168. #67⋊C₄	C₂×C₉	semidirect
169. C₄×D₁₂	C₂×C₉	semidirect
170. C₄×Dic₆	C₂×C₉	semidirect
316. #124	D₃×C₉	semidirect
324. C₃×C₉	#559	semidirect
449. C₉	#5681	direct (N × H)
500. C₃	C₉×#559	semidirect

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
C₉×#947	2
Q₈×C₉×Dic₃	2
C₉×#940	2
D₄×C₉×Dic₃	2
C₉×#886	2
C₉×#885	2
C₉×#883	2
C₉×#67⋊C₄	2
C₄×C₉×D₁₂	2
C₄×C₉×Dic₆	2
C₃×#5681	3
C₉×#559	3

Subgroups — C9×#5681 #13153085

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5681 #13153085