Subgroups — C₉×#5822 #13153691

Order 1728.

950 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₉×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#951	C₂	1	2	yes	maximal, complemented
4	C₉×#950	C₂	1	4	yes	maximal, complemented
5	C₉×#949	C₂	1	2	yes	maximal, complemented
6	C₉×#942	C₂	1	2	yes	maximal, complemented
7	C₉×#932	C₂	1	2	yes	maximal, complemented
8	C₂×C₉×#208	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#5822	C₃	1	1	yes	maximal, characteristic
10	C₉×#575	—	3	1	no	maximal
11	C₃×C₉×#41	—	2	1	no	—
12	C₃×C₉×#41	—	2	1	no	—
13	C₃×C₉×#41	C₂²	1	2	yes	—
14	C₃×C₉×#41	C₂²	1	2	yes	complemented
15	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃×D₄×C₉	—	2	1	no	—
17	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₃×C₄×C₉	—	2	1	no	—
19	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
20	C₂×C₉×#67	—	2	1	no	—
21	C₉×#235	—	2	1	no	—
22	C₉×#235	—	2	1	no	—
23	C₉×#235	C₂²	1	2	yes	—
24	C₉×#235	C₂²	1	2	yes	complemented
25	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₄×D₃×C₉	—	2	1	no	—
27	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic, complemented
28	C₉×#216	C₂²	1	4	yes	complemented
29	C₉×#215	C₂²	1	4	yes	complemented
30	C₉×#214	C₂²	1	4	yes	complemented
31	C₉×#213	C₂²	1	4	yes	complemented
32	C₉×#208	C₂²	1	2	yes	complemented
33	C₉×#208	C₂²	1	2	yes	complemented
34	C₂×C₉×C₃⋊C₈	C₂²	1	2	yes	complemented
35	C₂×C₃²×#41	C₂×C₃	1	1	yes	characteristic
36	C₂×C₃×#235	C₂×C₃	1	1	yes	characteristic
37	C₃×#951	C₂×C₃	1	2	yes	—
38	C₃×#950	C₂×C₃	1	4	yes	—
39	C₃×#949	C₂×C₃	1	2	yes	—
40	C₃×#942	C₂×C₃	1	2	yes	—
41	C₃×#932	C₂×C₃	1	2	yes	—
42	C₂×C₃×#208	C₂×C₃	1	1	yes	characteristic
43	C₂×C₉×#41	—	2	1	no	—
44	C₂×C₉×#41	—	3	1	no	—
45	C₂×C₉×#41	D₃	1	1	yes	characteristic, complemented
46	C₉×#137	—	3	2	no	—
47	C₉×#137	—	3	2	no	—
48	C₉×AGL(1,ℤ/8)	—	3	2	no	—
49	C₉×AGL(1,ℤ/8)	—	3	2	no	—
50	C₉×#135	—	3	4	no	—
51	C₂×C₉×M₁₆	—	3	1	no	—
52	C₂³×C₃×C₉	—	2	1	no	—
53	C₂³×C₃×C₉	D₄	1	1	yes	characteristic
54	C₂²×D₃×C₉	—	2	1	no	—
55	C₃×Q₈×C₉	—	2	1	no	—
56	C₃×Q₈×C₉	C₂³	1	2	yes	—
57	C₃×D₄×C₉	—	2	2	no	—
58	C₃×D₄×C₉	—	2	2	no	—
59	C₃×D₄×C₉	—	2	1	no	—
60	C₃×D₄×C₉	C₂³	1	2	yes	—
61	C₂×C₃×C₄×C₉	—	2	1	no	—
62	C₂×C₃×C₄×C₉	—	2	2	no	—
63	C₂×C₃×C₄×C₉	—	2	2	no	—
64	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
65	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
66	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
67	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
68	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
70	C₉×#67	—	2	2	no	—
71	C₉×#67	—	2	2	no	—
72	C₂×C₉×Dic₃	—	2	1	no	—
73	C₉×D₁₂	—	2	1	no	—
74	C₉×D₁₂	C₂³	1	2	yes	—
75	C₄×D₃×C₉	—	2	2	no	—
76	C₄×D₃×C₉	—	2	2	no	—
77	C₉×Dic₆	—	2	1	no	—
78	C₉×Dic₆	C₂³	1	2	yes	—
79	C₉×C₃⋊C₈	C₂³	1	4	yes	—
80	C₃×#575	—	3	1	no	—
81	#5822	C₉	1	1	yes	characteristic, direct product factor
82	C₃²×#41	—	2	1	no	—
83	C₃²×#41	—	2	1	no	—
84	C₃²×#41	C₂²×C₃	1	2	yes	—
85	C₃²×#41	C₂²×C₃	1	2	yes	—
86	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₃²×D₄	—	2	1	no	—
88	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
89	C₂²×C₃²×C₄	—	2	1	no	—
90	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₃×#67	—	2	1	no	—
92	C₃×#235	—	2	1	no	—
93	C₃×#235	—	2	1	no	—
94	C₃×#235	C₂²×C₃	1	2	yes	—
95	C₃×#235	C₂²×C₃	1	2	yes	—
96	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
97	C₂×C₃×C₄×D₃	—	2	1	no	—
98	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
99	C₃×#216	C₂²×C₃	1	4	yes	—
100	C₃×#215	C₂²×C₃	1	4	yes	—
101	C₃×#214	C₂²×C₃	1	4	yes	—
102	C₃×#213	C₂²×C₃	1	4	yes	—
103	C₃×#208	C₂²×C₃	1	2	yes	—
104	C₃×#208	C₂²×C₃	1	2	yes	—
105	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	2	yes	—
106	C₉×#41	—	2	2	no	—
107	C₉×#41	—	2	2	no	—
108	C₉×#41	—	2	2	no	—
109	C₉×#41	—	2	2	no	—
110	C₉×#41	—	2	1	no	—
111	C₉×#41	—	2	1	no	—
112	C₉×#41	—	3	2	no	—
113	C₉×#41	—	3	2	no	—
114	C₉×#41	—	6	1	no	—
115	C₉×#41	—	6	1	no	—
116	C₉×#41	C₂×D₃	1	2	yes	—
117	C₉×#41	C₂×D₃	1	2	yes	complemented
118	C₂×Q₈×C₉	—	2	1	no	—
119	C₂×Q₈×C₉	—	3	1	no	—
120	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic, complemented
121	C₂×D₄×C₉	—	2	2	no	—
122	C₂×D₄×C₉	—	2	1	no	—
123	C₂×D₄×C₉	—	2	1	no	—
124	C₂×D₄×C₉	—	3	1	no	—
125	C₂×D₄×C₉	—	6	1	no	—
126	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic, complemented
127	C₂²×C₄×C₉	—	2	2	no	—
128	C₂²×C₄×C₉	—	2	1	no	—
129	C₂²×C₄×C₉	—	2	1	no	—
130	C₂²×C₄×C₉	—	6	1	no	—
131	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
132	C₉×Q₁₆	—	3	4	no	—
133	C₉×SD₁₆	—	3	4	no	—
134	C₉×SD₁₆	—	3	4	no	—
135	C₉×D₈	—	3	4	no	—
136	C₉×M₁₆	—	3	2	no	—
137	C₉×M₁₆	—	3	2	no	—
138	C₂×C₈×C₉	—	3	2	no	—
139	C₂²×C₃×C₉	—	2	2	no	—
140	C₂²×C₃×C₉	—	4	1	no	—
141	C₂²×C₃×C₉	—	4	2	no	—
142	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
145	C₂×D₃×C₉	—	2	2	no	—
146	C₂×D₃×C₉	—	4	2	no	—
147	C₃×C₄×C₉	—	2	2	no	—
148	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
149	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
150	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
151	C₃×C₄×C₉	C₂⁴	1	1	yes	characteristic
152	C₉×Dic₃	—	2	2	no	—
153	C₂×C₃×#41	—	2	1	no	—
154	C₂×C₃×#41	—	3	1	no	—
155	C₂×C₃×#41	C₂×C₉	1	1	yes	characteristic, complemented
156	C₂×C₃×#41	C₃×D₃	1	1	yes	characteristic
157	C₂×#235	C₂×C₉	1	1	yes	characteristic, complemented
158	C₃×#137	—	3	2	no	—
159	C₃×#137	—	3	2	no	—
160	C₃×AGL(1,ℤ/8)	—	3	2	no	—
161	C₃×AGL(1,ℤ/8)	—	3	2	no	—
162	C₃×#135	—	3	4	no	—
163	C₂×C₃×M₁₆	—	3	1	no	—
164	#951	C₂×C₉	1	2	yes	complemented
165	#950	C₂×C₉	1	4	yes	complemented
166	#949	C₂×C₉	1	2	yes	complemented
167	#942	C₂×C₉	1	2	yes	complemented
168	#932	C₂×C₉	1	2	yes	complemented
169	C₂×#208	C₂×C₉	1	1	yes	characteristic, complemented
170	C₂³×C₃²	—	2	1	no	—
171	C₂³×C₃²	C₃×D₄	1	1	yes	characteristic
172	C₂²×C₃×D₃	—	2	1	no	—
173	C₃²×Q₈	—	2	1	no	—
174	C₃²×Q₈	C₂³×C₃	1	2	yes	—
175	C₃²×D₄	—	2	2	no	—
176	C₃²×D₄	—	2	2	no	—
177	C₃²×D₄	—	2	1	no	—
178	C₃²×D₄	C₂³×C₃	1	2	yes	—
179	C₂×C₃²×C₄	—	2	1	no	—
180	C₂×C₃²×C₄	—	2	2	no	—
181	C₂×C₃²×C₄	—	2	2	no	—
182	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
183	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
184	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
185	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
186	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
187	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
188	C₃×#67	—	2	2	no	—
189	C₃×#67	—	2	2	no	—
190	C₂×C₃×Dic₃	—	2	1	no	—
191	C₃×D₁₂	—	2	1	no	—
192	C₃×D₁₂	C₂³×C₃	1	2	yes	—
193	C₃×C₄×D₃	—	2	2	no	—
194	C₃×C₄×D₃	—	2	2	no	—
195	C₃×Dic₆	—	2	1	no	—
196	C₃×Dic₆	C₂³×C₃	1	2	yes	—
197	C₂³×C₉	—	2	2	no	—
198	C₂³×C₉	—	2	1	no	—
199	C₂³×C₉	—	2	1	no	—
200	C₂³×C₉	—	6	1	no	—
201	C₂³×C₉	#67	1	1	yes	characteristic
202	C₃×C₃⋊C₈	C₂³×C₃	1	4	yes	—
203	Q₈×C₉	—	2	2	no	—
204	Q₈×C₉	—	2	1	no	—
205	Q₈×C₉	—	2	2	no	—
206	Q₈×C₉	—	3	2	no	—
207	Q₈×C₉	—	6	1	no	—
208	Q₈×C₉	C₂²×D₃	1	2	yes	—
209	D₄×C₉	—	2	4	no	—
210	D₄×C₉	—	2	4	no	—
211	D₄×C₉	—	2	2	no	—
212	D₄×C₉	—	2	2	no	—
213	D₄×C₉	—	2	2	no	—
214	D₄×C₉	—	2	1	no	—
215	D₄×C₉	—	2	2	no	—
216	D₄×C₉	—	3	2	no	—
217	D₄×C₉	—	6	2	no	—
218	D₄×C₉	—	6	2	no	—
219	D₄×C₉	—	6	1	no	—
220	D₄×C₉	C₂²×D₃	1	2	yes	—
221	C₂×C₄×C₉	—	2	2	no	—
222	C₂×C₄×C₉	—	2	4	no	—
223	C₂×C₄×C₉	—	2	4	no	—
224	C₂×C₄×C₉	—	2	1	no	—
225	C₂×C₄×C₉	—	2	2	no	—
226	C₂×C₄×C₉	—	2	2	no	—
227	C₂×C₄×C₉	—	2	1	no	—
228	C₂×C₄×C₉	—	2	1	no	—
229	C₂×C₄×C₉	—	2	1	no	—
230	C₂×C₄×C₉	—	2	1	no	—
231	C₂×C₄×C₉	—	2	1	no	—
232	C₂×C₄×C₉	—	2	1	no	—
233	C₂×C₄×C₉	—	6	1	no	—
234	C₂×C₄×C₉	—	6	2	no	—
235	C₂×C₄×C₉	—	6	2	no	—
236	C₂×C₄×C₉	#67	1	1	yes	characteristic
237	C₂×C₄×C₉	#67	1	1	yes	characteristic
238	C₂×C₄×C₉	#67	1	1	yes	characteristic
239	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
240	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
241	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
242	C₈×C₉	—	3	4	no	—
243	#575	—	3	1	no	Sylow
244	C₂×C₃×C₉	—	2	1	no	—
245	C₂×C₃×C₉	—	2	1	no	—
246	C₂×C₃×C₉	—	2	1	no	—
247	C₂×C₃×C₉	—	4	2	no	—
248	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
249	D₃×C₉	—	4	2	no	—
250	C₃×#41	—	2	2	no	—
251	C₃×#41	—	2	2	no	—
252	C₃×#41	—	2	1	no	—
253	C₃×#41	—	2	1	no	—
254	C₃×#41	—	2	1	no	—
255	C₃×#41	—	2	1	no	—
256	C₃×#41	—	2	2	no	—
257	C₃×#41	—	2	2	no	—
258	C₃×#41	—	3	2	no	—
259	C₃×#41	—	3	2	no	—
260	C₃×#41	—	6	1	no	—
261	C₃×#41	—	6	1	no	—
262	C₃×#41	C₂²×C₉	1	2	yes	—
263	C₃×#41	C₂²×C₉	1	2	yes	complemented
264	C₃×#41	C₂×C₃×D₃	1	2	yes	—
265	C₃×#41	C₂×C₃×D₃	1	2	yes	—
266	C₂×C₃×Q₈	—	2	1	no	—
267	C₂×C₃×Q₈	—	3	1	no	—
268	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
269	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
270	C₂×C₃×D₄	—	2	2	no	—
271	C₂×C₃×D₄	—	2	1	no	—
272	C₂×C₃×D₄	—	2	1	no	—
273	C₂×C₃×D₄	—	2	1	no	—
274	C₂×C₃×D₄	—	3	1	no	—
275	C₂×C₃×D₄	—	6	1	no	—
276	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic, complemented
277	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
278	C₂²×C₃×C₄	—	2	2	no	—
279	C₂²×C₃×C₄	—	2	1	no	—
280	C₂²×C₃×C₄	—	2	1	no	—
281	C₂²×C₃×C₄	—	2	1	no	—
282	C₂²×C₃×C₄	—	6	1	no	—
283	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
284	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
285	C₂×#67	—	2	1	no	—
286	#235	—	2	1	no	—
287	#235	—	2	1	no	—
288	#235	C₂²×C₉	1	2	yes	—
289	#235	C₂²×C₉	1	2	yes	complemented
290	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic, complemented
291	C₂×C₄×D₃	—	2	1	no	—
292	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic, complemented
293	C₃×Q₁₆	—	3	4	no	—
294	C₃×SD₁₆	—	3	4	no	—
295	C₃×SD₁₆	—	3	4	no	—
296	C₃×D₈	—	3	4	no	—
297	C₃×M₁₆	—	3	2	no	—
298	C₃×M₁₆	—	3	2	no	—
299	C₂×C₃×C₈	—	3	2	no	—
300	#216	C₂²×C₉	1	4	yes	complemented
301	#215	C₂²×C₉	1	4	yes	complemented
302	#214	C₂²×C₉	1	4	yes	complemented
303	#213	C₂²×C₉	1	4	yes	complemented
304	#208	C₂²×C₉	1	2	yes	complemented
305	#208	C₂²×C₉	1	2	yes	complemented
306	C₂×C₃⋊C₈	C₂²×C₉	1	2	yes	complemented
307	C₂²×C₃²	—	2	2	no	—
308	C₂²×C₃²	—	4	1	no	—
309	C₂²×C₃²	—	4	2	no	—
310	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
311	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
312	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
313	C₂×C₃×D₃	—	2	2	no	—
314	C₂×C₃×D₃	—	4	2	no	—
315	C₃²×C₄	—	2	2	no	—
316	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
317	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
318	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
319	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
320	C₃×Dic₃	—	2	2	no	—
321	C₂²×C₉	—	2	4	no	—
322	C₂²×C₉	—	2	2	no	—
323	C₂²×C₉	—	2	1	no	—
324	C₂²×C₉	—	2	1	no	—
325	C₂²×C₉	—	2	1	no	—
326	C₂²×C₉	—	4	1	no	—
327	C₂²×C₉	—	4	2	no	—
328	C₂²×C₉	—	4	4	no	—
329	C₂²×C₉	—	4	2	no	—
330	C₂²×C₉	—	6	2	no	—
331	C₂²×C₉	—	12	2	no	—
332	C₂²×C₉	C₂×#67	1	1	yes	characteristic
333	C₂²×C₉	C₂×#67	1	1	yes	characteristic
334	C₂²×C₉	C₂×#67	1	1	yes	characteristic
335	C₄×C₉	—	2	4	no	—
336	C₄×C₉	—	2	2	no	—
337	C₄×C₉	—	2	1	no	—
338	C₄×C₉	—	2	1	no	—
339	C₄×C₉	—	2	1	no	—
340	C₄×C₉	—	2	1	no	—
341	C₄×C₉	—	6	2	no	—
342	C₄×C₉	C₂×#67	1	1	yes	characteristic
343	C₄×C₉	C₂×#67	1	1	yes	characteristic
344	C₄×C₉	C₂×#67	1	1	yes	characteristic
345	C₄×C₉	C₂³×D₃	1	1	yes	characteristic
346	C₂×#41	—	3	1	no	—
347	C₂×#41	D₃×C₉	1	1	yes	characteristic, complemented
348	#137	—	3	2	no	—
349	#137	—	3	2	no	—
350	AGL(1,ℤ/8)	—	3	2	no	—
351	AGL(1,ℤ/8)	—	3	2	no	—
352	#135	—	3	4	no	—
353	C₂×M₁₆	—	3	1	no	—
354	C₃×C₉	#575	1	1	yes	characteristic, complemented, Sylow
355	C₂³×C₃	—	2	2	no	—
356	C₂³×C₃	—	2	1	no	—
357	C₂³×C₃	—	2	1	no	—
358	C₂³×C₃	—	2	1	no	—
359	C₂³×C₃	—	6	1	no	—
360	C₂³×C₃	D₄×C₉	1	1	yes	characteristic
361	C₂³×C₃	C₃×#67	1	1	yes	characteristic
362	C₂²×D₃	—	2	1	no	—
363	C₃×Q₈	—	2	2	no	—
364	C₃×Q₈	—	2	1	no	—
365	C₃×Q₈	—	2	1	no	—
366	C₃×Q₈	—	2	2	no	—
367	C₃×Q₈	—	3	2	no	—
368	C₃×Q₈	—	6	1	no	—
369	C₃×Q₈	C₂³×C₉	1	2	yes	—
370	C₃×Q₈	C₂²×C₃×D₃	1	2	yes	—
371	C₃×D₄	—	2	4	no	—
372	C₃×D₄	—	2	4	no	—
373	C₃×D₄	—	2	2	no	—
374	C₃×D₄	—	2	2	no	—
375	C₃×D₄	—	2	2	no	—
376	C₃×D₄	—	2	2	no	—
377	C₃×D₄	—	2	2	no	—
378	C₃×D₄	—	2	1	no	—
379	C₃×D₄	—	2	1	no	—
380	C₃×D₄	—	2	2	no	—
381	C₃×D₄	—	3	2	no	—
382	C₃×D₄	—	6	2	no	—
383	C₃×D₄	—	6	2	no	—
384	C₃×D₄	—	6	1	no	—
385	C₃×D₄	C₂³×C₉	1	2	yes	—
386	C₃×D₄	C₂²×C₃×D₃	1	2	yes	—
387	C₂×C₃×C₄	—	2	2	no	—
388	C₂×C₃×C₄	—	2	4	no	—
389	C₂×C₃×C₄	—	2	4	no	—
390	C₂×C₃×C₄	—	2	1	no	—
391	C₂×C₃×C₄	—	2	1	no	—
392	C₂×C₃×C₄	—	2	2	no	—
393	C₂×C₃×C₄	—	2	2	no	—
394	C₂×C₃×C₄	—	2	2	no	—
395	C₂×C₃×C₄	—	2	2	no	—
396	C₂×C₃×C₄	—	2	1	no	—
397	C₂×C₃×C₄	—	2	1	no	—
398	C₂×C₃×C₄	—	2	1	no	—
399	C₂×C₃×C₄	—	2	1	no	—
400	C₂×C₃×C₄	—	2	1	no	—
401	C₂×C₃×C₄	—	2	1	no	—
402	C₂×C₃×C₄	—	6	1	no	—
403	C₂×C₃×C₄	—	6	2	no	—
404	C₂×C₃×C₄	—	6	2	no	—
405	C₂×C₃×C₄	D₄×C₉	1	1	yes	characteristic
406	C₂×C₃×C₄	D₄×C₉	1	1	yes	characteristic
407	C₂×C₃×C₄	D₄×C₉	1	1	yes	characteristic
408	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
409	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
410	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
411	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
412	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
413	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
414	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
415	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
416	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
417	#67	—	2	2	no	—
418	#67	—	2	2	no	—
419	C₂×Dic₃	—	2	1	no	—
420	D₁₂	—	2	1	no	—
421	D₁₂	C₂³×C₉	1	2	yes	—
422	C₄×D₃	—	2	2	no	—
423	C₄×D₃	—	2	2	no	—
424	Dic₆	—	2	1	no	—
425	Dic₆	C₂³×C₉	1	2	yes	—
426	C₃×C₈	—	3	4	no	—
427	C₃⋊C₈	C₂³×C₉	1	4	yes	—
428	C₂×C₃²	—	2	1	no	—
429	C₂×C₃²	—	2	1	no	—
430	C₂×C₃²	—	2	1	no	—
431	C₂×C₃²	—	4	2	no	—
432	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
433	C₃×D₃	—	4	2	no	—
434	C₂×C₉	—	2	2	no	—
435	C₂×C₉	—	2	1	no	—
436	C₂×C₉	—	2	1	no	—
437	C₂×C₉	—	2	1	no	—
438	C₂×C₉	—	2	1	no	—
439	C₂×C₉	—	4	1	no	—
440	C₂×C₉	—	4	1	no	—
441	C₂×C₉	—	4	4	no	—
442	C₂×C₉	—	4	2	no	—
443	C₂×C₉	—	12	2	no	—
444	C₂×C₉	C₂²×#67	1	1	yes	characteristic
445	#41	—	2	1	no	—
446	#41	—	2	1	no	—
447	#41	—	3	2	no	—
448	#41	—	3	2	no	—
449	#41	—	6	1	no	—
450	#41	—	6	1	no	—
451	#41	C₂×D₃×C₉	1	2	yes	—
452	#41	C₂×D₃×C₉	1	2	yes	complemented
453	C₂×Q₈	—	3	1	no	—
454	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic, complemented
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	3	1	no	—
457	C₂×D₄	—	6	1	no	—
458	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	6	1	no	—
461	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
462	Q₁₆	—	3	4	no	—
463	SD₁₆	—	3	4	no	—
464	SD₁₆	—	3	4	no	—
465	D₈	—	3	4	no	—
466	M₁₆	—	3	2	no	—
467	M₁₆	—	3	2	no	—
468	C₂×C₈	—	3	2	no	—
469	C₂²×C₃	—	2	4	no	—
470	C₂²×C₃	—	2	2	no	—
471	C₂²×C₃	—	2	2	no	—
472	C₂²×C₃	—	2	1	no	—
473	C₂²×C₃	—	2	1	no	—
474	C₂²×C₃	—	2	1	no	—
475	C₂²×C₃	—	4	1	no	—
476	C₂²×C₃	—	4	1	no	—
477	C₂²×C₃	—	4	2	no	—
478	C₂²×C₃	—	4	2	no	—
479	C₂²×C₃	—	4	4	no	—
480	C₂²×C₃	—	4	2	no	—
481	C₂²×C₃	—	6	2	no	—
482	C₂²×C₃	—	12	2	no	—
483	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
484	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
485	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
486	C₂²×C₃	C₂×C₃×#67	1	1	yes	characteristic
487	C₂²×C₃	C₂×C₃×#67	1	1	yes	characteristic
488	C₂²×C₃	C₂×C₃×#67	1	1	yes	characteristic
489	C₂×D₃	—	2	2	no	—
490	C₂×D₃	—	4	2	no	—
491	C₃×C₄	—	2	4	no	—
492	C₃×C₄	—	2	2	no	—
493	C₃×C₄	—	2	2	no	—
494	C₃×C₄	—	2	1	no	—
495	C₃×C₄	—	2	1	no	—
496	C₃×C₄	—	2	1	no	—
497	C₃×C₄	—	2	1	no	—
498	C₃×C₄	—	6	2	no	—
499	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
500	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
501	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
502	C₃×C₄	C₂⁴×C₉	1	1	yes	characteristic
503	C₃×C₄	C₂×C₃×#67	1	1	yes	characteristic
504	C₃×C₄	C₂×C₃×#67	1	1	yes	characteristic
505	C₃×C₄	C₂×C₃×#67	1	1	yes	characteristic
506	C₃×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
507	Dic₃	—	2	2	no	—
508	C₃²	C₃×#575	1	1	yes	characteristic
509	C₉	—	2	1	no	—
510	C₉	#5822	1	1	yes	characteristic, direct product factor
511	C₂³	—	2	1	no	—
512	C₂³	—	6	1	no	—
513	C₂³	C₉×#67	1	1	yes	characteristic
514	Q₈	—	2	1	no	—
515	Q₈	—	3	2	no	—
516	Q₈	—	6	1	no	—
517	Q₈	C₂²×D₃×C₉	1	2	yes	—
518	D₄	—	2	2	no	—
519	D₄	—	2	2	no	—
520	D₄	—	2	1	no	—
521	D₄	—	3	2	no	—
522	D₄	—	6	2	no	—
523	D₄	—	6	2	no	—
524	D₄	—	6	1	no	—
525	D₄	C₂²×D₃×C₉	1	2	yes	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	6	1	no	—
530	C₂×C₄	—	6	2	no	—
531	C₂×C₄	—	6	2	no	—
532	C₂×C₄	C₉×#67	1	1	yes	characteristic
533	C₂×C₄	C₉×#67	1	1	yes	characteristic
534	C₂×C₄	C₉×#67	1	1	yes	characteristic
535	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
536	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
537	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
538	C₈	—	3	4	no	—
539	C₂×C₃	—	2	2	no	—
540	C₂×C₃	—	2	1	no	—
541	C₂×C₃	—	2	1	no	—
542	C₂×C₃	—	2	1	no	—
543	C₂×C₃	—	2	1	no	—
544	C₂×C₃	—	2	1	no	—
545	C₂×C₃	—	2	1	no	—
546	C₂×C₃	—	2	1	no	—
547	C₂×C₃	—	4	1	no	—
548	C₂×C₃	—	4	1	no	—
549	C₂×C₃	—	4	4	no	—
550	C₂×C₃	—	4	2	no	—
551	C₂×C₃	—	4	2	no	—
552	C₂×C₃	—	12	2	no	—
553	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
554	C₂×C₃	C₂²×C₃×#67	1	1	yes	characteristic
555	D₃	—	4	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	6	2	no	—
560	C₂²	—	12	2	no	—
561	C₂²	C₂×C₉×#67	1	1	yes	characteristic
562	C₂²	C₂×C₉×#67	1	1	yes	characteristic
563	C₂²	C₂×C₉×#67	1	1	yes	characteristic
564	C₄	—	2	2	no	—
565	C₄	—	6	2	no	—
566	C₄	C₂×C₉×#67	1	1	yes	characteristic
567	C₄	C₂×C₉×#67	1	1	yes	characteristic
568	C₄	C₂×C₉×#67	1	1	yes	characteristic
569	C₄	C₂³×D₃×C₉	1	1	yes	characteristic
570	C₃	—	2	1	no	—
571	C₃	C₉×#575	1	1	yes	characteristic, complemented
572	C₃	C₃×#5822	1	1	yes	characteristic
573	C₂	—	2	1	no	—
574	C₂	—	2	1	no	—
575	C₂	—	2	1	no	—
576	C₂	—	4	2	no	—
577	C₂	—	12	2	no	—
578	C₂	C₂²×C₉×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₉	C₂×#67
commutator	C₃×C₄	C₂⁴×C₉
Frattini	C₃×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃×C₉×#41	C₂
socle	C₂×C₃²	C₂²×C₃×D₄
prime radical	C₃×#5822	C₃
cosocle	C₃²×C₄	C₂⁴×C₃
hypercenter	C₂×C₉×#41	D₃
hypocenter	C₃	C₉×#575
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₉ ◁ C₂²×C₄×C₉ ◁ C₂×C₉×#41

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₉×#41	C₂	semidirect
2. C₂×C₉×#235	C₂	semidirect
3. C₉×#951	C₂	semidirect
4. C₉×#950	C₂	semidirect
5. C₉×#949	C₂	semidirect
6. C₉×#942	C₂	semidirect
7. C₉×#932	C₂	semidirect
8. C₂×C₉×#208	C₂	semidirect
14. C₃×C₉×#41	C₂²	semidirect
15. C₂×C₃×Q₈×C₉	C₂²	semidirect
17. C₂×C₃×D₄×C₉	C₂²	semidirect
24. C₉×#235	C₂²	semidirect
25. C₂×C₉×D₁₂	C₂²	semidirect
27. C₂×C₉×Dic₆	C₂²	semidirect
28. C₉×#216	C₂²	semidirect
29. C₉×#215	C₂²	semidirect
30. C₉×#214	C₂²	semidirect
31. C₉×#213	C₂²	semidirect
32. C₉×#208	C₂²	semidirect
33. C₉×#208	C₂²	semidirect
34. C₂×C₉×C₃⋊C₈	C₂²	semidirect
45. C₂×C₉×#41	D₃	semidirect
81. #5822	C₉	direct (N × H)
117. C₉×#41	C₂×D₃	semidirect
120. C₂×Q₈×C₉	C₂×D₃	semidirect
126. C₂×D₄×C₉	C₂×D₃	semidirect
155. C₂×C₃×#41	C₂×C₉	semidirect
157. C₂×#235	C₂×C₉	semidirect
164. #951	C₂×C₉	semidirect
165. #950	C₂×C₉	semidirect
166. #949	C₂×C₉	semidirect
167. #942	C₂×C₉	semidirect
168. #932	C₂×C₉	semidirect
169. C₂×#208	C₂×C₉	semidirect
263. C₃×#41	C₂²×C₉	semidirect
268. C₂×C₃×Q₈	C₂²×C₉	semidirect
276. C₂×C₃×D₄	C₂²×C₉	semidirect
289. #235	C₂²×C₉	semidirect
290. C₂×D₁₂	C₂²×C₉	semidirect
292. C₂×Dic₆	C₂²×C₉	semidirect
300. #216	C₂²×C₉	semidirect
301. #215	C₂²×C₉	semidirect
302. #214	C₂²×C₉	semidirect
303. #213	C₂²×C₉	semidirect
304. #208	C₂²×C₉	semidirect
305. #208	C₂²×C₉	semidirect
306. C₂×C₃⋊C₈	C₂²×C₉	semidirect
347. C₂×#41	D₃×C₉	semidirect
354. C₃×C₉	#575	semidirect
452. #41	C₂×D₃×C₉	semidirect
454. C₂×Q₈	C₂×D₃×C₉	semidirect
458. C₂×D₄	C₂×D₃×C₉	semidirect
510. C₉	#5822	direct (N × H)
571. C₃	C₉×#575	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₉×#41	2
C₂×C₉×#235	2
C₉×#951	2
C₉×#950	2
C₉×#949	2
C₉×#942	2
C₉×#932	2
C₂×C₉×#208	2
C₃×#5822	3
C₉×#575	3

Subgroups — C9×#5822 #13153691

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5822 #13153691