Subgroups — C₂×C₉×#806 #13142477

Order 1728.

762 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×#67	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×#217	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#806	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₃×#806	C₃	1	1	yes	maximal, characteristic
6	C₂×C₉×#99	—	3	1	no	maximal
7	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic
8	C₂³×D₃×C₉	C₄	1	1	yes	characteristic, complemented
9	C₂²×C₃×C₄×C₉	—	2	1	no	—
10	C₂×C₉×#67	—	2	1	no	—
11	C₂×C₉×#67	—	2	1	no	—
12	C₂×C₉×#67	—	2	1	no	—
13	C₂×C₉×#67	—	2	1	no	—
14	C₂×C₉×#67	C₄	1	2	yes	complemented
15	C₂×C₉×#67	C₂²	1	2	yes	—
16	C₂²×C₉×Dic₃	—	2	1	no	—
17	C₂²×C₉×Dic₃	C₄	1	1	yes	characteristic, complemented
18	C₃×C₉×C₂²⋊C₄	—	2	1	no	—
19	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	complemented
20	C₉×#217	—	2	1	no	—
21	C₉×#217	C₂²	1	2	yes	complemented
22	C₂²×C₃×#67	C₂×C₃	1	1	yes	characteristic
23	C₂×C₃²×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
24	C₂×C₃×#217	C₂×C₃	1	1	yes	characteristic
25	C₂²×D₄×C₉	—	3	1	no	—
26	C₃×#806	C₂×C₃	1	4	yes	—
27	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
28	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
29	C₂×C₉×C₂²⋊C₄	D₃	1	1	yes	characteristic, complemented
30	C₉×#99	—	3	4	no	—
31	C₂³×C₃×C₉	—	4	2	no	—
32	C₂³×C₃×C₉	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₃×C₉	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₃×C₉	D₄	1	1	yes	characteristic
35	C₂³×C₃×C₉	D₄	1	1	yes	characteristic
36	C₂³×C₃×C₉	D₄	1	1	yes	characteristic
37	C₂³×C₃×C₉	D₄	1	1	yes	characteristic
38	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
39	C₂²×D₃×C₉	—	2	1	no	—
40	C₂²×D₃×C₉	—	2	1	no	—
41	C₂²×D₃×C₉	—	4	2	no	—
42	C₂²×D₃×C₉	C₂×C₄	1	2	yes	complemented
43	C₂×C₃×C₄×C₉	—	2	2	no	—
44	C₂×C₃×C₄×C₉	—	4	2	no	—
45	C₉×#67	—	2	2	no	—
46	C₉×#67	—	2	2	no	—
47	C₉×#67	—	2	2	no	—
48	C₉×#67	—	2	2	no	—
49	C₂×C₉×Dic₃	—	2	1	no	—
50	C₂×C₉×Dic₃	—	2	1	no	—
51	C₂×C₉×Dic₃	—	2	2	no	—
52	C₂×C₉×Dic₃	—	4	2	no	—
53	C₂×C₉×Dic₃	C₂×C₄	1	2	yes	complemented
54	C₂×C₃×#99	—	3	1	no	—
55	C₂×#806	C₉	1	1	yes	characteristic, direct product factor
56	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
57	C₂³×C₃×D₃	C₃×C₄	1	1	yes	characteristic
58	C₂²×C₃²×C₄	—	2	1	no	—
59	C₂×C₃×#67	—	2	1	no	—
60	C₂×C₃×#67	—	2	1	no	—
61	C₂×C₃×#67	—	2	1	no	—
62	C₂×C₃×#67	—	2	1	no	—
63	C₂×C₃×#67	C₃×C₄	1	2	yes	—
64	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
65	C₂²×C₃×Dic₃	—	2	1	no	—
66	C₂²×C₃×Dic₃	C₃×C₄	1	1	yes	characteristic
67	C₂⁴×C₉	—	2	1	no	—
68	C₂⁴×C₉	—	3	1	no	—
69	C₂⁴×C₉	C₂×D₃	1	1	yes	characteristic
70	C₃²×C₂²⋊C₄	—	2	1	no	—
71	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
72	C₃×#217	—	2	1	no	—
73	C₃×#217	C₂²×C₃	1	2	yes	—
74	C₂×D₄×C₉	—	3	2	no	—
75	C₂×D₄×C₉	—	3	2	no	—
76	C₂×D₄×C₉	—	6	1	no	—
77	C₂×D₄×C₉	—	6	1	no	—
78	C₂×D₄×C₉	—	6	1	no	—
79	C₂×D₄×C₉	—	6	1	no	—
80	C₂²×C₄×C₉	—	2	2	no	—
81	C₂²×C₄×C₉	—	2	1	no	—
82	C₂²×C₄×C₉	—	3	1	no	—
83	C₂²×C₄×C₉	—	6	1	no	—
84	C₉×C₂²⋊C₄	—	2	2	no	—
85	C₉×C₂²⋊C₄	—	2	2	no	—
86	C₉×C₂²⋊C₄	—	2	1	no	—
87	C₉×C₂²⋊C₄	—	3	2	no	—
88	C₉×C₂²⋊C₄	—	6	1	no	—
89	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
90	C₂²×C₃×C₉	—	2	2	no	—
91	C₂²×C₃×C₉	—	2	2	no	—
92	C₂²×C₃×C₉	—	2	2	no	—
93	C₂²×C₃×C₉	—	4	1	no	—
94	C₂²×C₃×C₉	—	4	1	no	—
95	C₂²×C₃×C₉	—	4	1	no	—
96	C₂²×C₃×C₉	—	4	1	no	—
97	C₂²×C₃×C₉	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×C₃×C₉	C₂²⋊C₄	1	1	yes	characteristic
99	C₂²×C₃×C₉	C₂²⋊C₄	1	1	yes	characteristic
100	C₂²×C₃×C₉	C₂²⋊C₄	1	1	yes	characteristic
101	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
104	C₂×D₃×C₉	—	2	2	no	—
105	C₂×D₃×C₉	—	4	2	no	—
106	C₂×D₃×C₉	—	4	2	no	—
107	C₂×D₃×C₉	—	4	2	no	—
108	C₃×C₄×C₉	—	4	2	no	—
109	C₉×Dic₃	—	2	2	no	—
110	C₉×Dic₃	—	4	2	no	—
111	C₂²×C₃×D₄	—	3	1	no	—
112	C₂²×#67	C₂×C₉	1	1	yes	characteristic
113	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
115	C₂×C₃×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
116	C₂×C₃×C₂²⋊C₄	C₃×D₃	1	1	yes	characteristic
117	C₂×#217	C₂×C₉	1	1	yes	characteristic, complemented
118	C₃×#99	—	3	4	no	—
119	#806	C₂×C₉	1	4	yes	direct product factor
120	C₂³×C₃²	—	4	2	no	—
121	C₂³×C₃²	C₂×C₃×C₄	1	1	yes	characteristic
122	C₂³×C₃²	C₂×C₃×C₄	1	1	yes	characteristic
123	C₂³×C₃²	C₃×D₄	1	1	yes	characteristic
124	C₂³×C₃²	C₃×D₄	1	1	yes	characteristic
125	C₂³×C₃²	C₃×D₄	1	1	yes	characteristic
126	C₂³×C₃²	C₃×D₄	1	1	yes	characteristic
127	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
128	C₂²×C₃×D₃	—	2	1	no	—
129	C₂²×C₃×D₃	—	2	1	no	—
130	C₂²×C₃×D₃	—	4	2	no	—
131	C₂²×C₃×D₃	C₂×C₃×C₄	1	2	yes	—
132	C₂×C₃²×C₄	—	2	2	no	—
133	C₂×C₃²×C₄	—	4	2	no	—
134	C₃×#67	—	2	2	no	—
135	C₃×#67	—	2	2	no	—
136	C₃×#67	—	2	2	no	—
137	C₃×#67	—	2	2	no	—
138	C₂×C₃×Dic₃	—	2	1	no	—
139	C₂×C₃×Dic₃	—	2	1	no	—
140	C₂×C₃×Dic₃	—	2	2	no	—
141	C₂×C₃×Dic₃	—	4	2	no	—
142	C₂×C₃×Dic₃	C₂×C₃×C₄	1	2	yes	—
143	C₂³×C₉	—	2	1	no	—
144	C₂³×C₉	—	2	1	no	—
145	C₂³×C₉	—	2	1	no	—
146	C₂³×C₉	—	2	1	no	—
147	C₂³×C₉	—	2	1	no	—
148	C₂³×C₉	—	2	1	no	—
149	C₂³×C₉	—	2	1	no	—
150	C₂³×C₉	—	3	2	no	—
151	C₂³×C₉	—	4	2	no	—
152	C₂³×C₉	—	4	4	no	—
153	C₂³×C₉	—	6	1	no	—
154	C₂³×C₉	—	6	1	no	—
155	C₂³×C₉	—	12	2	no	—
156	C₂³×C₉	C₄×D₃	1	1	yes	characteristic
157	C₂³×C₉	C₄×D₃	1	1	yes	characteristic
158	C₂³×C₉	D₁₂	1	1	yes	characteristic
159	C₂³×C₉	D₁₂	1	1	yes	characteristic
160	C₂³×C₉	#67	1	1	yes	characteristic
161	C₂³×C₉	#67	1	1	yes	characteristic
162	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
163	D₄×C₉	—	6	2	no	—
164	D₄×C₉	—	6	2	no	—
165	D₄×C₉	—	6	2	no	—
166	D₄×C₉	—	6	2	no	—
167	C₂×C₄×C₉	—	2	4	no	—
168	C₂×C₄×C₉	—	2	2	no	—
169	C₂×C₄×C₉	—	3	2	no	—
170	C₂×C₄×C₉	—	4	4	no	—
171	C₂×C₄×C₉	—	4	2	no	—
172	C₂×C₄×C₉	—	6	1	no	—
173	C₂×C₄×C₉	—	6	1	no	—
174	C₂×C₄×C₉	—	6	2	no	—
175	C₂×C₄×C₉	—	12	2	no	—
176	C₂×#99	—	3	1	no	Sylow
177	C₂×C₃×C₉	—	2	1	no	—
178	C₂×C₃×C₉	—	2	1	no	—
179	C₂×C₃×C₉	—	2	1	no	—
180	C₂×C₃×C₉	—	2	1	no	—
181	C₂×C₃×C₉	—	2	1	no	—
182	C₂×C₃×C₉	—	2	1	no	—
183	C₂×C₃×C₉	#99	1	2	yes	complemented
184	C₂×C₃×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	D₃×C₉	—	4	2	no	—
186	C₂⁴×C₃	—	2	1	no	—
187	C₂⁴×C₃	—	3	1	no	—
188	C₂⁴×C₃	C₂²×C₉	1	1	yes	characteristic
189	C₂⁴×C₃	C₂×C₃×D₃	1	1	yes	characteristic
190	C₂³×D₃	C₄×C₉	1	1	yes	characteristic, complemented
191	C₂×C₃×D₄	—	3	2	no	—
192	C₂×C₃×D₄	—	3	2	no	—
193	C₂×C₃×D₄	—	6	1	no	—
194	C₂×C₃×D₄	—	6	1	no	—
195	C₂×C₃×D₄	—	6	1	no	—
196	C₂×C₃×D₄	—	6	1	no	—
197	C₂²×C₃×C₄	—	2	2	no	—
198	C₂²×C₃×C₄	—	2	1	no	—
199	C₂²×C₃×C₄	—	2	1	no	—
200	C₂²×C₃×C₄	—	3	1	no	—
201	C₂²×C₃×C₄	—	6	1	no	—
202	C₂×#67	—	2	1	no	—
203	C₂×#67	—	2	1	no	—
204	C₂×#67	—	2	1	no	—
205	C₂×#67	—	2	1	no	—
206	C₂×#67	C₄×C₉	1	2	yes	complemented
207	C₂×#67	C₂²×C₉	1	2	yes	—
208	C₂²×Dic₃	—	2	1	no	—
209	C₂²×Dic₃	C₄×C₉	1	1	yes	characteristic, complemented
210	C₃×C₂²⋊C₄	—	2	2	no	—
211	C₃×C₂²⋊C₄	—	2	1	no	—
212	C₃×C₂²⋊C₄	—	2	1	no	—
213	C₃×C₂²⋊C₄	—	2	2	no	—
214	C₃×C₂²⋊C₄	—	3	2	no	—
215	C₃×C₂²⋊C₄	—	6	1	no	—
216	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	complemented
217	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
218	#217	—	2	1	no	—
219	#217	C₂²×C₉	1	2	yes	complemented
220	C₂²×C₃²	—	2	2	no	—
221	C₂²×C₃²	—	2	2	no	—
222	C₂²×C₃²	—	2	2	no	—
223	C₂²×C₃²	—	4	1	no	—
224	C₂²×C₃²	—	4	1	no	—
225	C₂²×C₃²	—	4	1	no	—
226	C₂²×C₃²	—	4	1	no	—
227	C₂²×C₃²	C₃×C₂²⋊C₄	1	1	yes	characteristic
228	C₂²×C₃²	C₃×C₂²⋊C₄	1	1	yes	characteristic
229	C₂²×C₃²	C₃×C₂²⋊C₄	1	1	yes	characteristic
230	C₂²×C₃²	C₃×C₂²⋊C₄	1	1	yes	characteristic
231	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
232	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
233	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
234	C₂×C₃×D₃	—	2	2	no	—
235	C₂×C₃×D₃	—	4	2	no	—
236	C₂×C₃×D₃	—	4	2	no	—
237	C₂×C₃×D₃	—	4	2	no	—
238	C₃²×C₄	—	4	2	no	—
239	C₃×Dic₃	—	2	2	no	—
240	C₃×Dic₃	—	4	2	no	—
241	C₂²×C₉	—	2	4	no	—
242	C₂²×C₉	—	2	2	no	—
243	C₂²×C₉	—	2	2	no	—
244	C₂²×C₉	—	2	2	no	—
245	C₂²×C₉	—	2	1	no	—
246	C₂²×C₉	—	2	1	no	—
247	C₂²×C₉	—	2	1	no	—
248	C₂²×C₉	—	2	1	no	—
249	C₂²×C₉	—	2	1	no	—
250	C₂²×C₉	—	2	1	no	—
251	C₂²×C₉	—	2	1	no	—
252	C₂²×C₉	—	4	2	no	—
253	C₂²×C₉	—	4	2	no	—
254	C₂²×C₉	—	4	1	no	—
255	C₂²×C₉	—	4	1	no	—
256	C₂²×C₉	—	4	1	no	—
257	C₂²×C₉	—	4	1	no	—
258	C₂²×C₉	—	4	2	no	—
259	C₂²×C₉	—	4	2	no	—
260	C₂²×C₉	—	4	2	no	—
261	C₂²×C₉	—	4	2	no	—
262	C₂²×C₉	—	6	2	no	—
263	C₂²×C₉	—	12	2	no	—
264	C₂²×C₉	—	12	2	no	—
265	C₂²×C₉	—	12	2	no	—
266	C₂²×C₉	(C₂×D₃)⋊C₄	1	1	yes	characteristic
267	C₂²×C₉	(C₂×D₃)⋊C₄	1	1	yes	characteristic
268	C₂²×C₉	(C₂×D₃)⋊C₄	1	1	yes	characteristic
269	C₂²×C₉	(C₂×D₃)⋊C₄	1	1	yes	characteristic
270	C₂²×C₉	C₂×C₄×D₃	1	1	yes	characteristic
271	C₂²×C₉	C₂×D₁₂	1	1	yes	characteristic
272	C₂²×C₉	C₂×#67	1	1	yes	characteristic
273	C₄×C₉	—	4	4	no	—
274	C₄×C₉	—	4	2	no	—
275	C₄×C₉	—	6	2	no	—
276	C₄×C₉	—	12	2	no	—
277	C₂²×D₄	—	3	1	no	—
278	C₂×C₂²⋊C₄	—	3	1	no	—
279	C₂×C₂²⋊C₄	D₃×C₉	1	1	yes	characteristic, complemented
280	#99	—	3	4	no	—
281	C₃×C₉	C₂×#99	1	1	yes	characteristic, complemented, Sylow
282	C₂³×C₃	—	2	1	no	—
283	C₂³×C₃	—	2	1	no	—
284	C₂³×C₃	—	2	1	no	—
285	C₂³×C₃	—	2	1	no	—
286	C₂³×C₃	—	2	1	no	—
287	C₂³×C₃	—	2	1	no	—
288	C₂³×C₃	—	2	1	no	—
289	C₂³×C₃	—	3	2	no	—
290	C₂³×C₃	—	4	2	no	—
291	C₂³×C₃	—	4	2	no	—
292	C₂³×C₃	—	4	4	no	—
293	C₂³×C₃	—	6	1	no	—
294	C₂³×C₃	—	6	1	no	—
295	C₂³×C₃	—	12	2	no	—
296	C₂³×C₃	C₂×C₄×C₉	1	1	yes	characteristic
297	C₂³×C₃	C₂×C₄×C₉	1	1	yes	characteristic
298	C₂³×C₃	D₄×C₉	1	1	yes	characteristic
299	C₂³×C₃	D₄×C₉	1	1	yes	characteristic
300	C₂³×C₃	D₄×C₉	1	1	yes	characteristic
301	C₂³×C₃	D₄×C₉	1	1	yes	characteristic
302	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
303	C₂³×C₃	C₃×C₄×D₃	1	1	yes	characteristic
304	C₂³×C₃	C₃×C₄×D₃	1	1	yes	characteristic
305	C₂³×C₃	C₃×D₁₂	1	1	yes	characteristic
306	C₂³×C₃	C₃×D₁₂	1	1	yes	characteristic
307	C₂³×C₃	C₃×#67	1	1	yes	characteristic
308	C₂³×C₃	C₃×#67	1	1	yes	characteristic
309	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
310	C₂²×D₃	—	2	1	no	—
311	C₂²×D₃	—	2	1	no	—
312	C₂²×D₃	—	4	2	no	—
313	C₂²×D₃	C₂×C₄×C₉	1	2	yes	complemented
314	C₃×D₄	—	6	2	no	—
315	C₃×D₄	—	6	2	no	—
316	C₃×D₄	—	6	2	no	—
317	C₃×D₄	—	6	2	no	—
318	C₂×C₃×C₄	—	2	4	no	—
319	C₂×C₃×C₄	—	2	2	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	3	2	no	—
322	C₂×C₃×C₄	—	4	2	no	—
323	C₂×C₃×C₄	—	4	4	no	—
324	C₂×C₃×C₄	—	4	2	no	—
325	C₂×C₃×C₄	—	6	1	no	—
326	C₂×C₃×C₄	—	6	1	no	—
327	C₂×C₃×C₄	—	6	2	no	—
328	C₂×C₃×C₄	—	12	2	no	—
329	#67	—	2	2	no	—
330	#67	—	2	2	no	—
331	#67	—	2	2	no	—
332	#67	—	2	2	no	—
333	C₂×Dic₃	—	2	1	no	—
334	C₂×Dic₃	—	2	1	no	—
335	C₂×Dic₃	—	2	2	no	—
336	C₂×Dic₃	—	4	2	no	—
337	C₂×Dic₃	C₂×C₄×C₉	1	2	yes	complemented
338	C₂×C₃²	—	2	1	no	—
339	C₂×C₃²	—	2	1	no	—
340	C₂×C₃²	—	2	1	no	—
341	C₂×C₃²	—	2	1	no	—
342	C₂×C₃²	—	2	1	no	—
343	C₂×C₃²	—	2	1	no	—
344	C₂×C₃²	C₃×#99	1	2	yes	—
345	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
346	C₃×D₃	—	4	2	no	—
347	C₂×C₉	—	2	2	no	—
348	C₂×C₉	—	2	2	no	—
349	C₂×C₉	—	2	1	no	—
350	C₂×C₉	—	2	1	no	—
351	C₂×C₉	—	2	1	no	—
352	C₂×C₉	—	2	1	no	—
353	C₂×C₉	—	2	1	no	—
354	C₂×C₉	—	2	1	no	—
355	C₂×C₉	—	2	1	no	—
356	C₂×C₉	—	2	2	no	—
357	C₂×C₉	—	4	1	no	—
358	C₂×C₉	—	4	1	no	—
359	C₂×C₉	—	4	1	no	—
360	C₂×C₉	—	4	1	no	—
361	C₂×C₉	—	12	2	no	—
362	C₂×C₉	#806	1	2	yes	direct product factor
363	C₂×C₉	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
364	C₂⁴	—	3	1	no	—
365	C₂⁴	C₂×D₃×C₉	1	1	yes	characteristic
366	C₂×D₄	—	3	2	no	—
367	C₂×D₄	—	3	2	no	—
368	C₂×D₄	—	6	1	no	—
369	C₂×D₄	—	6	1	no	—
370	C₂×D₄	—	6	1	no	—
371	C₂×D₄	—	6	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	3	1	no	—
374	C₂²×C₄	—	6	1	no	—
375	C₂²⋊C₄	—	2	1	no	—
376	C₂²⋊C₄	—	3	2	no	—
377	C₂²⋊C₄	—	6	1	no	—
378	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	complemented
379	C₂²×C₃	—	2	4	no	—
380	C₂²×C₃	—	2	2	no	—
381	C₂²×C₃	—	2	2	no	—
382	C₂²×C₃	—	2	2	no	—
383	C₂²×C₃	—	2	2	no	—
384	C₂²×C₃	—	2	2	no	—
385	C₂²×C₃	—	2	2	no	—
386	C₂²×C₃	—	2	1	no	—
387	C₂²×C₃	—	2	1	no	—
388	C₂²×C₃	—	2	1	no	—
389	C₂²×C₃	—	2	1	no	—
390	C₂²×C₃	—	2	1	no	—
391	C₂²×C₃	—	2	1	no	—
392	C₂²×C₃	—	2	1	no	—
393	C₂²×C₃	—	4	2	no	—
394	C₂²×C₃	—	4	2	no	—
395	C₂²×C₃	—	4	1	no	—
396	C₂²×C₃	—	4	1	no	—
397	C₂²×C₃	—	4	1	no	—
398	C₂²×C₃	—	4	1	no	—
399	C₂²×C₃	—	4	1	no	—
400	C₂²×C₃	—	4	1	no	—
401	C₂²×C₃	—	4	1	no	—
402	C₂²×C₃	—	4	1	no	—
403	C₂²×C₃	—	4	2	no	—
404	C₂²×C₃	—	4	2	no	—
405	C₂²×C₃	—	4	2	no	—
406	C₂²×C₃	—	4	2	no	—
407	C₂²×C₃	—	6	2	no	—
408	C₂²×C₃	—	12	2	no	—
409	C₂²×C₃	—	12	2	no	—
410	C₂²×C₃	—	12	2	no	—
411	C₂²×C₃	C₉×C₂²⋊C₄	1	1	yes	characteristic
412	C₂²×C₃	C₉×C₂²⋊C₄	1	1	yes	characteristic
413	C₂²×C₃	C₉×C₂²⋊C₄	1	1	yes	characteristic
414	C₂²×C₃	C₉×C₂²⋊C₄	1	1	yes	characteristic
415	C₂²×C₃	C₂²×C₄×C₉	1	1	yes	characteristic
416	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
417	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
418	C₂²×C₃	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
419	C₂²×C₃	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
420	C₂²×C₃	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
421	C₂²×C₃	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
422	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
423	C₂²×C₃	C₂×C₃×D₁₂	1	1	yes	characteristic
424	C₂²×C₃	C₂×C₃×#67	1	1	yes	characteristic
425	C₂×D₃	—	2	2	no	—
426	C₂×D₃	—	4	2	no	—
427	C₂×D₃	—	4	2	no	—
428	C₂×D₃	—	4	2	no	—
429	C₃×C₄	—	4	2	no	—
430	C₃×C₄	—	4	4	no	—
431	C₃×C₄	—	4	2	no	—
432	C₃×C₄	—	6	2	no	—
433	C₃×C₄	—	12	2	no	—
434	Dic₃	—	2	2	no	—
435	Dic₃	—	4	2	no	—
436	C₃²	C₂×C₃×#99	1	1	yes	characteristic
437	C₉	—	2	1	no	—
438	C₉	C₂×#806	1	1	yes	characteristic, direct product factor
439	C₂³	—	3	2	no	—
440	C₂³	—	4	2	no	—
441	C₂³	—	6	1	no	—
442	C₂³	—	6	1	no	—
443	C₂³	—	12	2	no	—
444	C₂³	C₄×D₃×C₉	1	1	yes	characteristic
445	C₂³	C₄×D₃×C₉	1	1	yes	characteristic
446	C₂³	C₉×D₁₂	1	1	yes	characteristic
447	C₂³	C₉×D₁₂	1	1	yes	characteristic
448	C₂³	C₉×#67	1	1	yes	characteristic
449	C₂³	C₉×#67	1	1	yes	characteristic
450	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
451	D₄	—	6	2	no	—
452	D₄	—	6	2	no	—
453	D₄	—	6	2	no	—
454	D₄	—	6	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	3	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	6	1	no	—
459	C₂×C₄	—	6	1	no	—
460	C₂×C₄	—	6	2	no	—
461	C₂×C₄	—	12	2	no	—
462	C₂×C₃	—	2	2	no	—
463	C₂×C₃	—	2	2	no	—
464	C₂×C₃	—	2	1	no	—
465	C₂×C₃	—	2	1	no	—
466	C₂×C₃	—	2	1	no	—
467	C₂×C₃	—	2	1	no	—
468	C₂×C₃	—	2	1	no	—
469	C₂×C₃	—	2	1	no	—
470	C₂×C₃	—	2	1	no	—
471	C₂×C₃	—	2	1	no	—
472	C₂×C₃	—	2	1	no	—
473	C₂×C₃	—	2	1	no	—
474	C₂×C₃	—	2	1	no	—
475	C₂×C₃	—	2	1	no	—
476	C₂×C₃	—	2	1	no	—
477	C₂×C₃	—	2	2	no	—
478	C₂×C₃	—	4	1	no	—
479	C₂×C₃	—	4	1	no	—
480	C₂×C₃	—	4	1	no	—
481	C₂×C₃	—	4	1	no	—
482	C₂×C₃	—	12	2	no	—
483	C₂×C₃	C₉×#99	1	2	yes	complemented
484	C₂×C₃	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
485	C₂×C₃	C₃×#806	1	2	yes	—
486	C₂×C₃	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
487	D₃	—	4	2	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	4	1	no	—
492	C₂²	—	4	1	no	—
493	C₂²	—	4	1	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	6	2	no	—
496	C₂²	—	12	2	no	—
497	C₂²	—	12	2	no	—
498	C₂²	—	12	2	no	—
499	C₂²	C₉×(C₂×D₃)⋊C₄	1	1	yes	characteristic
500	C₂²	C₉×(C₂×D₃)⋊C₄	1	1	yes	characteristic
501	C₂²	C₉×(C₂×D₃)⋊C₄	1	1	yes	characteristic
502	C₂²	C₉×(C₂×D₃)⋊C₄	1	1	yes	characteristic
503	C₂²	C₂×C₄×D₃×C₉	1	1	yes	characteristic
504	C₂²	C₂×C₉×D₁₂	1	1	yes	characteristic
505	C₂²	C₂×C₉×#67	1	1	yes	characteristic
506	C₄	—	4	2	no	—
507	C₄	—	6	2	no	—
508	C₄	—	12	2	no	—
509	C₃	—	2	1	no	—
510	C₃	C₂×C₉×#99	1	1	yes	characteristic, complemented
511	C₃	C₂×C₃×#806	1	1	yes	characteristic
512	C₂	—	2	1	no	—
513	C₂	—	2	1	no	—
514	C₂	—	2	1	no	—
515	C₂	—	2	1	no	—
516	C₂	—	2	1	no	—
517	C₂	—	2	1	no	—
518	C₂	—	12	2	no	—
519	C₂	C₉×#806	1	2	yes	direct product factor
520	C₂	C₂×C₉×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	(C₂×D₃)⋊C₄
commutator	C₂²×C₃	C₂²×C₄×C₉
Frattini	C₂³×C₃	C₂²×C₃×D₃
Fitting	C₂×C₃×C₉×C₂²⋊C₄	C₂
socle	C₂²×C₃²	C₃×C₂²⋊C₄
prime radical	C₂²×C₃×#67	C₂×C₃
cosocle	C₂³×C₃²	C₂³×C₃
hypercenter	C₂×C₉×C₂²⋊C₄	D₃
hypocenter	C₃	C₂×C₉×#99
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₂⁴×C₉ ◁ C₂×C₉×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₉×C₂²⋊C₄	C₂	semidirect
3. C₂×C₉×#217	C₂	semidirect
4. C₉×#806	C₂	direct (N × H)
8. C₂³×D₃×C₉	C₄	semidirect
14. C₂×C₉×#67	C₄	semidirect
17. C₂²×C₉×Dic₃	C₄	semidirect
19. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
21. C₉×#217	C₂²	semidirect
29. C₂×C₉×C₂²⋊C₄	D₃	semidirect
42. C₂²×D₃×C₉	C₂×C₄	semidirect
53. C₂×C₉×Dic₃	C₂×C₄	semidirect
55. C₂×#806	C₉	direct (N × H)
89. C₉×C₂²⋊C₄	C₂×D₃	semidirect
115. C₂×C₃×C₂²⋊C₄	C₂×C₉	semidirect
117. C₂×#217	C₂×C₉	semidirect
119. #806	C₂×C₉	direct (N × H)
183. C₂×C₃×C₉	#99	semidirect
190. C₂³×D₃	C₄×C₉	semidirect
206. C₂×#67	C₄×C₉	semidirect
209. C₂²×Dic₃	C₄×C₉	semidirect
216. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
219. #217	C₂²×C₉	semidirect
279. C₂×C₂²⋊C₄	D₃×C₉	semidirect
281. C₃×C₉	C₂×#99	semidirect
313. C₂²×D₃	C₂×C₄×C₉	semidirect
337. C₂×Dic₃	C₂×C₄×C₉	semidirect
362. C₂×C₉	#806	direct (N × H)
378. C₂²⋊C₄	C₂×D₃×C₉	semidirect
438. C₉	C₂×#806	direct (N × H)
483. C₂×C₃	C₉×#99	semidirect
510. C₃	C₂×C₉×#99	semidirect
519. C₂	C₉×#806	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₉×#67	2
C₂×C₃×C₉×C₂²⋊C₄	2
C₂×C₉×#217	2
C₉×#806	2
C₂×C₃×#806	3
C₂×C₉×#99	3

Subgroups — C2×C9×#806 #13142477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#806 #13142477