Subgroups — C₉×#5832 #13153705

Order 1728.

1094 conjugacy classes of subgroups.

The subgroup lattice has 468 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×#947	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#944	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#940	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#939	C₂	1	4	yes	maximal, complemented
7	C₉×#936	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₉×#67	C₂	1	4	yes	maximal, complemented
9	C₂×C₄×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#5832	C₃	1	1	yes	maximal, characteristic
11	C₉×#532	—	3	1	no	maximal
12	C₃×C₉×#41	—	2	4	no	—
13	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
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	2	yes	—
17	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
18	C₂×C₉×#67	C₂²	1	2	yes	—
19	C₂×C₉×#67	C₂²	1	4	yes	—
20	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
21	C₉×#235	—	2	4	no	—
22	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
24	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
25	C₉×#217	C₂²	1	4	yes	—
26	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
27	C₉×Dic₃⋊C₄	C₂²	1	4	yes	—
28	C₄×C₉×Dic₃	C₂²	1	2	yes	—
29	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
30	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
31	C₂×C₃²×#41	C₂×C₃	1	1	yes	characteristic
32	C₂×C₃×#235	C₂×C₃	1	1	yes	characteristic
33	C₃×#947	C₂×C₃	1	1	yes	characteristic
34	C₃×#944	C₂×C₃	1	1	yes	characteristic
35	C₃×#940	C₂×C₃	1	1	yes	characteristic
36	C₃×#939	C₂×C₃	1	4	yes	—
37	C₃×#936	C₂×C₃	1	1	yes	characteristic
38	C₃×C₄×#67	C₂×C₃	1	4	yes	—
39	C₂×C₃×C₄×Dic₃	C₂×C₃	1	1	yes	characteristic
40	C₂×C₉×#41	—	2	1	no	—
41	C₂×C₉×#41	—	3	1	no	—
42	C₂×C₉×#41	D₃	1	1	yes	characteristic, complemented
43	C₉×C₄⋊Q₈	—	3	1	no	—
44	C₉×#127	—	3	1	no	—
45	C₉×#124	—	3	1	no	—
46	C₉×#124	—	3	1	no	—
47	C₉×#121	—	3	4	no	—
48	C₄×D₄×C₉	—	3	4	no	—
49	C₂×C₄²×C₉	—	3	1	no	—
50	C₂³×C₃×C₉	C₂³	1	2	yes	—
51	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
52	C₂²×D₃×C₉	C₂³	1	2	yes	—
53	C₃×Q₈×C₉	—	2	2	no	—
54	C₃×D₄×C₉	—	2	4	no	—
55	C₃×D₄×C₉	—	2	2	no	—
56	C₂×C₃×C₄×C₉	—	2	4	no	—
57	C₂×C₃×C₄×C₉	D₄	1	4	yes	complemented
58	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
59	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
60	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
61	C₉×#67	—	2	4	no	—
62	C₉×#67	—	2	8	no	—
63	C₂×C₉×Dic₃	—	2	4	no	—
64	C₂×C₉×Dic₃	C₂³	1	2	yes	—
65	C₂×C₉×Dic₃	C₂³	1	2	yes	—
66	C₂×C₉×Dic₃	C₂³	1	2	yes	—
67	C₉×D₁₂	—	2	2	no	—
68	C₄×D₃×C₉	—	2	4	no	—
69	C₉×Dic₆	—	2	2	no	—
70	C₃×#532	—	3	1	no	—
71	#5832	C₉	1	1	yes	characteristic, direct product factor
72	C₃²×#41	—	2	4	no	—
73	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	—
76	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
77	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₃×#67	C₂²×C₃	1	4	yes	—
79	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
80	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
81	C₃×#235	—	2	4	no	—
82	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
84	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
85	C₃×#217	C₂²×C₃	1	4	yes	—
86	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
87	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
88	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
89	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
90	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
91	C₉×#41	—	2	8	no	—
92	C₉×#41	—	2	4	no	—
93	C₉×#41	—	6	4	no	—
94	C₂×Q₈×C₉	—	2	1	no	—
95	C₂×Q₈×C₉	—	3	1	no	—
96	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
97	C₂×D₄×C₉	—	2	2	no	—
98	C₂×D₄×C₉	—	2	1	no	—
99	C₂×D₄×C₉	—	3	4	no	—
100	C₂×D₄×C₉	—	3	2	no	—
101	C₂×D₄×C₉	—	3	1	no	—
102	C₂×D₄×C₉	C₂×D₃	1	2	yes	—
103	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
104	C₂²×C₄×C₉	—	2	2	no	—
105	C₂²×C₄×C₉	—	2	1	no	—
106	C₂²×C₄×C₉	—	3	2	no	—
107	C₂²×C₄×C₉	—	3	2	no	—
108	C₂²×C₄×C₉	C₂×D₃	1	2	yes	—
109	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
110	C₉×C₄⋊C₄	—	3	4	no	—
111	C₉×C₂²⋊C₄	—	3	4	no	—
112	C₉×C₂²⋊C₄	—	3	4	no	—
113	C₄²×C₉	—	3	1	no	—
114	C₄²×C₉	—	3	1	no	—
115	C₄²×C₉	—	3	2	no	—
116	C₂²×C₃×C₉	—	2	2	no	—
117	C₂²×C₃×C₉	—	2	2	no	—
118	C₂²×C₃×C₉	—	2	4	no	—
119	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
120	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
121	C₂×D₃×C₉	—	2	2	no	—
122	C₂×D₃×C₉	—	2	4	no	—
123	C₃×C₄×C₉	—	2	2	no	—
124	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
125	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
126	C₉×Dic₃	—	2	2	no	—
127	C₉×Dic₃	—	2	2	no	—
128	C₉×Dic₃	#41	1	4	yes	complemented
129	C₂×C₃×#41	—	2	1	no	—
130	C₂×C₃×#41	—	3	1	no	—
131	C₂×C₃×#41	C₂×C₉	1	1	yes	characteristic, complemented
132	C₂×C₃×#41	C₃×D₃	1	1	yes	characteristic
133	C₂×#235	C₂×C₉	1	1	yes	characteristic, complemented
134	C₃×C₄⋊Q₈	—	3	1	no	—
135	C₃×#127	—	3	1	no	—
136	C₃×#124	—	3	1	no	—
137	C₃×#124	—	3	1	no	—
138	C₃×#121	—	3	4	no	—
139	C₃×C₄×D₄	—	3	4	no	—
140	C₂×C₃×C₄²	—	3	1	no	—
141	#947	C₂×C₉	1	1	yes	characteristic, complemented
142	#944	C₂×C₉	1	1	yes	characteristic, complemented
143	#940	C₂×C₉	1	1	yes	characteristic, complemented
144	#939	C₂×C₉	1	4	yes	complemented
145	#936	C₂×C₉	1	1	yes	characteristic, complemented
146	C₄×#67	C₂×C₉	1	4	yes	complemented
147	C₂×C₄×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
148	C₂³×C₃²	C₂³×C₃	1	2	yes	—
149	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
150	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
151	C₃²×Q₈	—	2	2	no	—
152	C₃²×D₄	—	2	4	no	—
153	C₃²×D₄	—	2	2	no	—
154	C₂×C₃²×C₄	—	2	4	no	—
155	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
156	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
157	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
158	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
159	C₃×#67	—	2	4	no	—
160	C₃×#67	—	2	8	no	—
161	C₂×C₃×Dic₃	—	2	4	no	—
162	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
163	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
164	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
165	C₃×D₁₂	—	2	2	no	—
166	C₃×C₄×D₃	—	2	4	no	—
167	C₃×Dic₆	—	2	2	no	—
168	C₂³×C₉	—	2	2	no	—
169	C₂³×C₉	—	2	1	no	—
170	C₂³×C₉	—	3	2	no	—
171	C₂³×C₉	C₂²×D₃	1	2	yes	—
172	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
173	Q₈×C₉	—	2	4	no	—
174	Q₈×C₉	—	2	2	no	—
175	Q₈×C₉	—	6	2	no	—
176	D₄×C₉	—	2	8	no	—
177	D₄×C₉	—	2	4	no	—
178	D₄×C₉	—	2	4	no	—
179	D₄×C₉	—	2	2	no	—
180	D₄×C₉	—	6	8	no	—
181	D₄×C₉	—	6	4	no	—
182	D₄×C₉	—	6	2	no	—
183	C₂×C₄×C₉	—	2	8	no	—
184	C₂×C₄×C₉	—	2	4	no	—
185	C₂×C₄×C₉	—	2	4	no	—
186	C₂×C₄×C₉	—	2	1	no	—
187	C₂×C₄×C₉	—	2	2	no	—
188	C₂×C₄×C₉	—	2	1	no	—
189	C₂×C₄×C₉	—	3	2	no	—
190	C₂×C₄×C₉	—	3	2	no	—
191	C₂×C₄×C₉	—	3	2	no	—
192	C₂×C₄×C₉	—	6	4	no	—
193	C₂×C₄×C₉	—	6	4	no	—
194	C₂×C₄×C₉	#67	1	4	yes	complemented
195	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
196	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
197	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
198	#532	—	3	1	no	Sylow
199	C₂×C₃×C₉	—	2	2	no	—
200	C₂×C₃×C₉	—	4	2	no	—
201	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₃×C₉	C₂×#41	1	2	yes	—
203	D₃×C₉	—	4	2	no	—
204	C₃×#41	—	2	8	no	—
205	C₃×#41	—	2	4	no	—
206	C₃×#41	—	2	4	no	—
207	C₃×#41	—	6	4	no	—
208	C₂×C₃×Q₈	—	2	1	no	—
209	C₂×C₃×Q₈	—	3	1	no	—
210	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
211	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
212	C₂×C₃×D₄	—	2	2	no	—
213	C₂×C₃×D₄	—	2	1	no	—
214	C₂×C₃×D₄	—	3	4	no	—
215	C₂×C₃×D₄	—	3	2	no	—
216	C₂×C₃×D₄	—	3	1	no	—
217	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
218	C₂×C₃×D₄	C₂²×C₉	1	2	yes	—
219	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
220	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
221	C₂²×C₃×C₄	—	2	2	no	—
222	C₂²×C₃×C₄	—	2	1	no	—
223	C₂²×C₃×C₄	—	3	2	no	—
224	C₂²×C₃×C₄	—	3	2	no	—
225	C₂²×C₃×C₄	C₂²×C₉	1	2	yes	—
226	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
227	C₂²×C₃×C₄	C₂×C₃×D₃	1	2	yes	—
228	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
229	C₂×#67	C₂²×C₉	1	4	yes	—
230	C₂×#67	C₂²×C₉	1	2	yes	—
231	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
232	#235	—	2	4	no	—
233	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
234	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
235	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
236	C₃×C₄⋊C₄	—	3	4	no	—
237	C₃×C₂²⋊C₄	—	3	4	no	—
238	C₃×C₂²⋊C₄	—	3	4	no	—
239	C₃×C₄²	—	3	2	no	—
240	C₃×C₄²	—	3	1	no	—
241	C₃×C₄²	—	3	1	no	—
242	#217	C₂²×C₉	1	4	yes	—
243	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	—
244	Dic₃⋊C₄	C₂²×C₉	1	4	yes	—
245	C₄×Dic₃	C₂²×C₉	1	2	yes	—
246	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
247	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
248	C₂²×C₃²	—	2	2	no	—
249	C₂²×C₃²	—	2	2	no	—
250	C₂²×C₃²	—	2	4	no	—
251	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
252	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
253	C₂×C₃×D₃	—	2	2	no	—
254	C₂×C₃×D₃	—	2	4	no	—
255	C₃²×C₄	—	2	2	no	—
256	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
257	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
258	C₃×Dic₃	—	2	2	no	—
259	C₃×Dic₃	—	2	2	no	—
260	C₃×Dic₃	C₃×#41	1	4	yes	—
261	C₂²×C₉	—	2	2	no	—
262	C₂²×C₉	—	2	4	no	—
263	C₂²×C₉	—	2	4	no	—
264	C₂²×C₉	—	2	2	no	—
265	C₂²×C₉	—	2	1	no	—
266	C₂²×C₉	—	2	2	no	—
267	C₂²×C₉	—	4	2	no	—
268	C₂²×C₉	—	4	4	no	—
269	C₂²×C₉	—	6	4	no	—
270	C₂²×C₉	—	6	2	no	—
271	C₂²×C₉	C₂×#67	1	2	yes	—
272	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
273	C₄×C₉	—	2	4	no	—
274	C₄×C₉	—	2	2	no	—
275	C₄×C₉	—	2	2	no	—
276	C₄×C₉	—	2	2	no	—
277	C₄×C₉	—	3	4	no	—
278	C₄×C₉	—	6	2	no	—
279	C₄×C₉	—	6	2	no	—
280	C₄×C₉	C₂×#67	1	2	yes	—
281	C₄×C₉	C₂×#67	1	2	yes	—
282	C₂×#41	—	3	1	no	—
283	C₂×#41	D₃×C₉	1	1	yes	characteristic, complemented
284	C₄⋊Q₈	—	3	1	no	—
285	#127	—	3	1	no	—
286	#124	—	3	1	no	—
287	#124	—	3	1	no	—
288	#121	—	3	4	no	—
289	C₄×D₄	—	3	4	no	—
290	C₂×C₄²	—	3	1	no	—
291	C₃×C₉	#532	1	1	yes	characteristic, complemented, Sylow
292	C₂³×C₃	—	2	2	no	—
293	C₂³×C₃	—	2	1	no	—
294	C₂³×C₃	—	3	2	no	—
295	C₂³×C₃	C₂³×C₉	1	2	yes	—
296	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
297	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
298	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
299	C₂²×D₃	C₂³×C₉	1	2	yes	—
300	C₃×Q₈	—	2	4	no	—
301	C₃×Q₈	—	2	2	no	—
302	C₃×Q₈	—	2	2	no	—
303	C₃×Q₈	—	6	2	no	—
304	C₃×D₄	—	2	8	no	—
305	C₃×D₄	—	2	4	no	—
306	C₃×D₄	—	2	4	no	—
307	C₃×D₄	—	2	4	no	—
308	C₃×D₄	—	2	2	no	—
309	C₃×D₄	—	2	2	no	—
310	C₃×D₄	—	6	8	no	—
311	C₃×D₄	—	6	4	no	—
312	C₃×D₄	—	6	2	no	—
313	C₂×C₃×C₄	—	2	8	no	—
314	C₂×C₃×C₄	—	2	4	no	—
315	C₂×C₃×C₄	—	2	4	no	—
316	C₂×C₃×C₄	—	2	4	no	—
317	C₂×C₃×C₄	—	2	1	no	—
318	C₂×C₃×C₄	—	2	2	no	—
319	C₂×C₃×C₄	—	2	1	no	—
320	C₂×C₃×C₄	—	3	2	no	—
321	C₂×C₃×C₄	—	3	2	no	—
322	C₂×C₃×C₄	—	3	2	no	—
323	C₂×C₃×C₄	—	6	4	no	—
324	C₂×C₃×C₄	—	6	4	no	—
325	C₂×C₃×C₄	D₄×C₉	1	4	yes	complemented
326	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
327	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
328	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
329	C₂×C₃×C₄	C₃×#67	1	4	yes	—
330	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
331	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
332	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
333	#67	—	2	4	no	—
334	#67	—	2	8	no	—
335	C₂×Dic₃	—	2	4	no	—
336	C₂×Dic₃	C₂³×C₉	1	2	yes	—
337	C₂×Dic₃	C₂³×C₉	1	2	yes	—
338	C₂×Dic₃	C₂³×C₉	1	2	yes	—
339	D₁₂	—	2	2	no	—
340	C₄×D₃	—	2	4	no	—
341	Dic₆	—	2	2	no	—
342	C₂×C₃²	—	2	2	no	—
343	C₂×C₃²	—	4	2	no	—
344	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
345	C₂×C₃²	C₂×C₃×#41	1	2	yes	—
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	—	4	2	no	—
351	C₂×C₉	—	4	4	no	—
352	C₂×C₉	—	4	2	no	—
353	C₂×C₉	—	12	2	no	—
354	C₂×C₉	D₃×#41	1	2	yes	—
355	C₂×C₉	C₂²×#67	1	1	yes	characteristic
356	#41	—	2	4	no	—
357	#41	—	6	4	no	—
358	C₂×Q₈	—	3	1	no	—
359	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
360	C₂×D₄	—	3	4	no	—
361	C₂×D₄	—	3	2	no	—
362	C₂×D₄	—	3	1	no	—
363	C₂×D₄	C₂×D₃×C₉	1	2	yes	—
364	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
365	C₂²×C₄	—	3	2	no	—
366	C₂²×C₄	—	3	2	no	—
367	C₂²×C₄	C₂×D₃×C₉	1	2	yes	—
368	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
369	C₄⋊C₄	—	3	4	no	—
370	C₂²⋊C₄	—	3	4	no	—
371	C₂²⋊C₄	—	3	4	no	—
372	C₄²	—	3	2	no	—
373	C₄²	—	3	1	no	—
374	C₄²	—	3	1	no	—
375	C₂²×C₃	—	2	2	no	—
376	C₂²×C₃	—	2	2	no	—
377	C₂²×C₃	—	2	4	no	—
378	C₂²×C₃	—	2	4	no	—
379	C₂²×C₃	—	2	2	no	—
380	C₂²×C₃	—	2	2	no	—
381	C₂²×C₃	—	2	4	no	—
382	C₂²×C₃	—	2	1	no	—
383	C₂²×C₃	—	2	2	no	—
384	C₂²×C₃	—	4	2	no	—
385	C₂²×C₃	—	4	4	no	—
386	C₂²×C₃	—	6	4	no	—
387	C₂²×C₃	—	6	2	no	—
388	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
389	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
390	C₂²×C₃	C₂×C₃×#67	1	2	yes	—
391	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
392	C₂×D₃	—	2	2	no	—
393	C₂×D₃	—	2	4	no	—
394	C₃×C₄	—	2	4	no	—
395	C₃×C₄	—	2	2	no	—
396	C₃×C₄	—	2	2	no	—
397	C₃×C₄	—	2	2	no	—
398	C₃×C₄	—	2	2	no	—
399	C₃×C₄	—	3	4	no	—
400	C₃×C₄	—	6	2	no	—
401	C₃×C₄	—	6	2	no	—
402	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
403	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
404	C₃×C₄	C₂×C₃×#67	1	2	yes	—
405	C₃×C₄	C₂×C₃×#67	1	2	yes	—
406	Dic₃	—	2	2	no	—
407	Dic₃	—	2	2	no	—
408	Dic₃	C₉×#41	1	4	yes	complemented
409	C₃²	C₃×#532	1	1	yes	characteristic
410	C₉	—	2	1	no	—
411	C₉	#5832	1	1	yes	characteristic, direct product factor
412	C₂³	—	3	2	no	—
413	C₂³	C₂²×D₃×C₉	1	2	yes	—
414	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
415	Q₈	—	2	2	no	—
416	Q₈	—	6	2	no	—
417	D₄	—	2	4	no	—
418	D₄	—	2	2	no	—
419	D₄	—	6	8	no	—
420	D₄	—	6	4	no	—
421	D₄	—	6	2	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	3	2	no	—
424	C₂×C₄	—	3	2	no	—
425	C₂×C₄	—	3	2	no	—
426	C₂×C₄	—	6	4	no	—
427	C₂×C₄	—	6	4	no	—
428	C₂×C₄	C₉×#67	1	4	yes	complemented
429	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
430	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
431	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
432	C₂×C₃	—	2	2	no	—
433	C₂×C₃	—	2	2	no	—
434	C₂×C₃	—	2	2	no	—
435	C₂×C₃	—	2	1	no	—
436	C₂×C₃	—	4	2	no	—
437	C₂×C₃	—	4	4	no	—
438	C₂×C₃	—	4	2	no	—
439	C₂×C₃	—	4	2	no	—
440	C₂×C₃	—	12	2	no	—
441	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
442	C₂×C₃	C₂×C₉×#41	1	2	yes	—
443	C₂×C₃	C₃×D₃×#41	1	2	yes	—
444	C₂×C₃	C₂²×C₃×#67	1	1	yes	characteristic
445	D₃	—	4	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	4	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	6	4	no	—
450	C₂²	—	6	2	no	—
451	C₂²	C₂×C₉×#67	1	2	yes	—
452	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
453	C₄	—	2	2	no	—
454	C₄	—	3	4	no	—
455	C₄	—	6	2	no	—
456	C₄	—	6	2	no	—
457	C₄	C₂×C₉×#67	1	2	yes	—
458	C₄	C₂×C₉×#67	1	2	yes	—
459	C₃	—	2	1	no	—
460	C₃	C₉×#532	1	1	yes	characteristic, complemented
461	C₃	C₃×#5832	1	1	yes	characteristic
462	C₂	—	2	2	no	—
463	C₂	—	4	2	no	—
464	C₂	—	12	2	no	—
465	C₂	D₃×C₉×#41	1	2	yes	—
466	C₂	C₂²×C₉×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₉	C₂²×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₂×C₃×C₉×#41	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5832	C₃
hypercenter	C₂×C₉×#41	D₃
hypocenter	C₃	C₉×#532
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×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×#947	C₂	semidirect
4. C₉×#944	C₂	semidirect
5. C₉×#940	C₂	semidirect
6. C₉×#939	C₂	semidirect
7. C₉×#936	C₂	semidirect
8. C₄×C₉×#67	C₂	semidirect
9. C₂×C₄×C₉×Dic₃	C₂	semidirect
42. C₂×C₉×#41	D₃	semidirect
57. C₂×C₃×C₄×C₉	D₄	semidirect
71. #5832	C₉	direct (N × H)
128. C₉×Dic₃	#41	semidirect
131. C₂×C₃×#41	C₂×C₉	semidirect
133. C₂×#235	C₂×C₉	semidirect
141. #947	C₂×C₉	semidirect
142. #944	C₂×C₉	semidirect
143. #940	C₂×C₉	semidirect
144. #939	C₂×C₉	semidirect
145. #936	C₂×C₉	semidirect
146. C₄×#67	C₂×C₉	semidirect
147. C₂×C₄×Dic₃	C₂×C₉	semidirect
194. C₂×C₄×C₉	#67	semidirect
283. C₂×#41	D₃×C₉	semidirect
291. C₃×C₉	#532	semidirect
325. C₂×C₃×C₄	D₄×C₉	semidirect
408. Dic₃	C₉×#41	semidirect
411. C₉	#5832	direct (N × H)
428. C₂×C₄	C₉×#67	semidirect
460. C₃	C₉×#532	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×#947	2
C₉×#944	2
C₉×#940	2
C₉×#939	2
C₉×#936	2
C₄×C₉×#67	2
C₂×C₄×C₉×Dic₃	2
C₃×#5832	3
C₉×#532	3

Subgroups — C9×#5832 #13153705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5832 #13153705