Subgroups — C₂×C₄×C₉×#67 #13153543

Order 1728.

1514 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×C₄×C₉	C₂	semidirect
3. C₂²×C₄×D₃×C₉	C₂	semidirect
4. C₂×C₉×#217	C₂	semidirect
5. C₄×C₉×#67	C₂	direct (N × H)
6. C₂×C₉×(C₂×D₃)⋊C₄	C₂	semidirect
7. C₂×C₉×Dic₃⋊C₄	C₂	semidirect
8. C₂×C₄×C₉×Dic₃	C₂	semidirect
16. C₂²×C₃×C₄×C₉	C₂²	semidirect
17. C₂×C₉×#67	C₄	direct (N × H)
23. C₂×C₄×D₃×C₉	C₂²	semidirect
24. C₉×#217	C₂²	semidirect
25. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
26. C₉×Dic₃⋊C₄	C₂²	semidirect
27. C₄×C₉×Dic₃	C₂²	semidirect
39. C₂³×C₄×C₉	D₃	semidirect
47. C₂³×C₃×C₉	C₂×C₄	semidirect
52. C₂²×D₃×C₉	C₂×C₄	semidirect
56. C₂×C₃×C₄×C₉	D₄	semidirect
59. C₉×#67	C₂×C₄	direct (N × H)
62. C₂×C₉×Dic₃	C₂×C₄	semidirect
68. C₂×C₄×#67	C₉	direct (N × H)
103. C₂²×C₄×C₉	C₂×D₃	semidirect
112. C₂²×C₃×C₉	C₂²×C₄	semidirect
119. C₂×D₃×C₉	C₂²×C₄	semidirect
121. C₃×C₄×C₉	C₂×D₄	semidirect
124. C₉×Dic₃	C₂²×C₄	semidirect
128. C₂³×C₃×C₄	C₂×C₉	semidirect
131. C₂²×C₄×D₃	C₂×C₉	semidirect
137. C₂×#217	C₂×C₉	semidirect
138. C₄×#67	C₂×C₉	direct (N × H)
139. C₂×(C₂×D₃)⋊C₄	C₂×C₉	semidirect
140. C₂×Dic₃⋊C₄	C₂×C₉	semidirect
141. C₂×C₄×Dic₃	C₂×C₉	semidirect
175. C₂³×C₉	C₄×D₃	semidirect
193. C₂×C₄×C₉	#67	direct (N × H)
198. C₂×C₃×C₉	C₄×D₄	semidirect
223. C₂²×C₃×C₄	C₂²×C₉	semidirect
227. C₂×#67	C₄×C₉	direct (N × H)
233. C₂×C₄×D₃	C₂²×C₉	semidirect
238. #217	C₂²×C₉	semidirect
239. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
240. Dic₃⋊C₄	C₂²×C₉	semidirect
241. C₄×Dic₃	C₂²×C₉	semidirect
275. C₂²×C₉	C₂×C₄×D₃	semidirect
285. C₄×C₉	C₂×#67	direct (N × H)
288. C₂³×C₄	D₃×C₉	semidirect
294. C₃×C₉	C₂×C₄×D₄	semidirect
308. C₂³×C₃	C₂×C₄×C₉	semidirect
316. C₂²×D₃	C₂×C₄×C₉	semidirect
335. C₂×C₃×C₄	D₄×C₉	semidirect
341. #67	C₂×C₄×C₉	direct (N × H)
344. C₂×Dic₃	C₂×C₄×C₉	semidirect
362. C₂×C₉	C₄×#67	direct (N × H)
378. C₂²×C₄	C₂×D₃×C₉	semidirect
402. C₂²×C₃	C₂²×C₄×C₉	semidirect
414. C₂×D₃	C₂²×C₄×C₉	semidirect
422. C₃×C₄	C₂×D₄×C₉	semidirect
426. Dic₃	C₂²×C₄×C₉	semidirect
429. C₉	C₂×C₄×#67	direct (N × H)
436. C₂³	C₄×D₃×C₉	semidirect
449. C₂×C₄	C₉×#67	direct (N × H)
460. C₂×C₃	C₄×D₄×C₉	semidirect
477. C₂²	C₂×C₄×D₃×C₉	semidirect
485. C₄	C₂×C₉×#67	direct (N × H)
487. C₃	C₂×C₄×D₄×C₉	semidirect
491. C₂	C₄×C₉×#67	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₄×C₉	2
C₂²×C₉×#67	2
C₂²×C₄×D₃×C₉	2
C₂×C₉×#217	2
C₄×C₉×#67	2
C₂×C₉×(C₂×D₃)⋊C₄	2
C₂×C₉×Dic₃⋊C₄	2
C₂×C₄×C₉×Dic₃	2
C₂×C₃×C₄×#67	3
C₂×C₄×D₄×C₉	3

Subgroups — C2×C4×C9×#67 #13153543

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₉×#67 #13153543