Subgroups — C₂²×C₃×C₄×C₇×C₈×C₉ #72201481

Order 24192.

7600 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄²×C₇×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₃×C₇×C₈×C₉	C₂	1	2	yes	maximal
3	C₂×C₃×C₄×C₇×C₈×C₉	C₂	1	12	yes	maximal, direct product factor
4	C₂²×C₃²×C₄×C₇×C₈	C₃	1	1	yes	maximal, characteristic
5	C₂²×C₄×C₇×C₈×C₉	C₃	1	3	yes	maximal, direct product factor
6	C₂³×C₃×C₄×C₇×C₉	C₄	1	2	yes	—
7	C₂³×C₃×C₄×C₇×C₉	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₄²×C₇×C₉	C₄	1	6	yes	—
9	C₂×C₃×C₄²×C₇×C₉	C₂²	1	6	yes	—
10	C₂²×C₃×C₇×C₈×C₉	C₄	1	16	yes	direct product factor
11	C₂²×C₃×C₇×C₈×C₉	C₂²	1	12	yes	—
12	C₃×C₄×C₇×C₈×C₉	C₂²	1	16	yes	direct product factor
13	C₂²×C₃²×C₄²×C₇	C₂×C₃	1	1	yes	characteristic
14	C₂²×C₄²×C₇×C₉	C₂×C₃	1	3	yes	—
15	C₂³×C₃²×C₇×C₈	C₂×C₃	1	2	yes	—
16	C₂³×C₇×C₈×C₉	C₂×C₃	1	6	yes	—
17	C₂×C₃²×C₄×C₇×C₈	C₂×C₃	1	12	yes	—
18	C₂×C₄×C₇×C₈×C₉	C₂×C₃	1	36	yes	direct product factor
19	C₂²×C₃×C₄×C₈×C₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂⁴×C₃×C₇×C₉	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₃×C₄×C₇×C₉	C₈	1	16	yes	direct product factor
22	C₂²×C₃×C₄×C₇×C₉	C₂×C₄	1	3	yes	—
23	C₂²×C₃×C₄×C₇×C₉	C₂×C₄	1	8	yes	—
24	C₂²×C₃×C₄×C₇×C₉	C₂×C₄	1	12	yes	—
25	C₂²×C₃×C₄×C₇×C₉	C₂³	1	3	yes	—
26	C₃×C₄²×C₇×C₉	C₂×C₄	1	12	yes	—
27	C₃×C₄²×C₇×C₉	C₂³	1	4	yes	—
28	C₂×C₃×C₇×C₈×C₉	C₂×C₄	1	48	yes	direct product factor
29	C₂×C₃×C₇×C₈×C₉	C₂³	1	8	yes	—
30	C₂²×C₃×C₄×C₇×C₈	C₉	1	3	yes	direct product factor
31	C₂²×C₃×C₄×C₇×C₈	C₃²	1	1	yes	characteristic
32	C₂³×C₃²×C₄×C₇	C₃×C₄	1	2	yes	—
33	C₂³×C₃²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic
34	C₂³×C₄×C₇×C₉	C₃×C₄	1	6	yes	—
35	C₂³×C₄×C₇×C₉	C₂²×C₃	1	3	yes	—
36	C₂×C₄²×C₇×C₉	C₃×C₄	1	18	yes	—
37	C₂×C₄²×C₇×C₉	C₂²×C₃	1	18	yes	—
38	C₂×C₃²×C₄²×C₇	C₃×C₄	1	6	yes	—
39	C₂×C₃²×C₄²×C₇	C₂²×C₃	1	6	yes	—
40	C₂²×C₃²×C₇×C₈	C₃×C₄	1	16	yes	—
41	C₂²×C₃²×C₇×C₈	C₂²×C₃	1	12	yes	—
42	C₂²×C₇×C₈×C₉	C₃×C₄	1	48	yes	direct product factor
43	C₂²×C₇×C₈×C₉	C₂²×C₃	1	36	yes	—
44	C₃²×C₄×C₇×C₈	C₂²×C₃	1	16	yes	—
45	C₄×C₇×C₈×C₉	C₂²×C₃	1	48	yes	direct product factor
46	C₂³×C₃×C₈×C₉	C₂×C₇	1	2	yes	—
47	C₂²×C₃×C₄²×C₉	C₂×C₇	1	1	yes	characteristic
48	C₂×C₃×C₄×C₈×C₉	C₂×C₇	1	12	yes	direct product factor
49	C₂³×C₃×C₇×C₉	C₄²	1	4	yes	—
50	C₂³×C₃×C₇×C₉	C₂×C₈	1	8	yes	—
51	C₂³×C₃×C₇×C₉	C₂²×C₄	1	3	yes	—
52	C₂×C₃×C₄×C₇×C₉	C₄²	1	12	yes	—
53	C₂×C₃×C₄×C₇×C₉	C₂×C₈	1	48	yes	direct product factor
54	C₂×C₃×C₄×C₇×C₉	C₂²×C₄	1	3	yes	—
55	C₂×C₃×C₄×C₇×C₉	C₂²×C₄	1	8	yes	—
56	C₂×C₃×C₄×C₇×C₉	C₂²×C₄	1	12	yes	—
57	C₂×C₃×C₄×C₇×C₉	C₂⁴	1	1	yes	characteristic
58	C₃×C₇×C₈×C₉	C₂²×C₄	1	16	yes	direct product factor
59	C₂³×C₃×C₇×C₈	C₂×C₉	1	6	yes	—
60	C₂³×C₃×C₇×C₈	C₂×C₃²	1	2	yes	—
61	C₂²×C₃×C₄²×C₇	C₂×C₉	1	3	yes	—
62	C₂²×C₃×C₄²×C₇	C₂×C₃²	1	1	yes	characteristic
63	C₂×C₃×C₄×C₇×C₈	C₂×C₉	1	36	yes	direct product factor
64	C₂×C₃×C₄×C₇×C₈	C₂×C₃²	1	12	yes	—
65	C₂²×C₃²×C₄×C₈	C₃×C₇	1	1	yes	characteristic
66	C₂²×C₄×C₈×C₉	C₃×C₇	1	3	yes	direct product factor
67	C₂⁴×C₃²×C₇	C₂×C₃×C₄	1	1	yes	characteristic
68	C₂²×C₃²×C₄×C₇	C₃×C₈	1	16	yes	—
69	C₂²×C₃²×C₄×C₇	C₂×C₃×C₄	1	3	yes	—
70	C₂²×C₃²×C₄×C₇	C₂×C₃×C₄	1	8	yes	—
71	C₂²×C₃²×C₄×C₇	C₂×C₃×C₄	1	12	yes	—
72	C₂²×C₃²×C₄×C₇	C₂³×C₃	1	3	yes	—
73	C₂⁴×C₇×C₉	C₂×C₃×C₄	1	3	yes	—
74	C₂×C₃²×C₇×C₈	C₂×C₃×C₄	1	48	yes	—
75	C₂×C₃²×C₇×C₈	C₂³×C₃	1	8	yes	—
76	C₃²×C₄²×C₇	C₂×C₃×C₄	1	12	yes	—
77	C₃²×C₄²×C₇	C₂³×C₃	1	4	yes	—
78	C₂²×C₄×C₇×C₉	C₃×C₈	1	48	yes	direct product factor
79	C₂²×C₄×C₇×C₉	C₂×C₃×C₄	1	9	yes	—
80	C₂²×C₄×C₇×C₉	C₂×C₃×C₄	1	24	yes	—
81	C₂²×C₄×C₇×C₉	C₂×C₃×C₄	1	36	yes	—
82	C₂²×C₄×C₇×C₉	C₂³×C₃	1	9	yes	—
83	C₂×C₇×C₈×C₉	C₂×C₃×C₄	1	144	yes	direct product factor
84	C₂×C₇×C₈×C₉	C₂³×C₃	1	24	yes	—
85	C₄²×C₇×C₉	C₂×C₃×C₄	1	36	yes	—
86	C₄²×C₇×C₉	C₂³×C₃	1	12	yes	—
87	C₂²×C₄×C₇×C₈	C₃×C₉	1	1	yes	characteristic, direct product factor, Hall
88	C₂³×C₃×C₄×C₉	C₄×C₇	1	2	yes	—
89	C₂³×C₃×C₄×C₉	C₂²×C₇	1	1	yes	characteristic
90	C₂²×C₃×C₈×C₉	C₄×C₇	1	16	yes	direct product factor
91	C₂²×C₃×C₈×C₉	C₂²×C₇	1	12	yes	—
92	C₂×C₃×C₄²×C₉	C₄×C₇	1	6	yes	—
93	C₂×C₃×C₄²×C₉	C₂²×C₇	1	6	yes	—
94	C₃×C₄×C₈×C₉	C₂²×C₇	1	16	yes	direct product factor
95	C₂²×C₃×C₇×C₉	C₄×C₈	1	16	yes	direct product factor
96	C₂²×C₃×C₇×C₉	C₂×C₄²	1	6	yes	—
97	C₂²×C₃×C₇×C₉	C₂²×C₈	1	12	yes	—
98	C₂²×C₃×C₇×C₉	C₂³×C₄	1	1	yes	characteristic
99	C₃×C₄×C₇×C₉	C₂×C₄²	1	6	yes	—
100	C₃×C₄×C₇×C₉	C₂²×C₈	1	16	yes	direct product factor
101	C₃×C₄×C₇×C₉	C₂³×C₄	1	2	yes	—
102	C₂³×C₃×C₄×C₇	C₄×C₉	1	6	yes	—
103	C₂³×C₃×C₄×C₇	C₂²×C₉	1	3	yes	—
104	C₂³×C₃×C₄×C₇	C₃²×C₄	1	2	yes	—
105	C₂³×C₃×C₄×C₇	C₂²×C₃²	1	1	yes	characteristic
106	C₂²×C₃×C₇×C₈	C₄×C₉	1	48	yes	direct product factor
107	C₂²×C₃×C₇×C₈	C₂²×C₉	1	36	yes	—
108	C₂²×C₃×C₇×C₈	C₃²×C₄	1	16	yes	—
109	C₂²×C₃×C₇×C₈	C₂²×C₃²	1	12	yes	—
110	C₂×C₃×C₄²×C₇	C₄×C₉	1	18	yes	—
111	C₂×C₃×C₄²×C₇	C₂²×C₉	1	18	yes	—
112	C₂×C₃×C₄²×C₇	C₃²×C₄	1	6	yes	—
113	C₂×C₃×C₄²×C₇	C₂²×C₃²	1	6	yes	—
114	C₃×C₄×C₇×C₈	C₂²×C₉	1	48	yes	direct product factor
115	C₃×C₄×C₇×C₈	C₂²×C₃²	1	16	yes	—
116	C₂³×C₃²×C₈	C₂×C₃×C₇	1	2	yes	—
117	C₂²×C₃²×C₄²	C₂×C₃×C₇	1	1	yes	characteristic
118	C₂×C₃²×C₄×C₈	C₂×C₃×C₇	1	12	yes	—
119	C₂³×C₈×C₉	C₂×C₃×C₇	1	6	yes	—
120	C₂²×C₄²×C₉	C₂×C₃×C₇	1	3	yes	—
121	C₂×C₄×C₈×C₉	C₂×C₃×C₇	1	36	yes	direct product factor
122	C₂³×C₃²×C₇	C₃×C₄²	1	4	yes	—
123	C₂³×C₃²×C₇	C₂×C₃×C₈	1	8	yes	—
124	C₂³×C₃²×C₇	C₂²×C₃×C₄	1	3	yes	—
125	C₂×C₃²×C₄×C₇	C₃×C₄²	1	12	yes	—
126	C₂×C₃²×C₄×C₇	C₂×C₃×C₈	1	48	yes	—
127	C₂×C₃²×C₄×C₇	C₂²×C₃×C₄	1	3	yes	—
128	C₂×C₃²×C₄×C₇	C₂²×C₃×C₄	1	8	yes	—
129	C₂×C₃²×C₄×C₇	C₂²×C₃×C₄	1	12	yes	—
130	C₂×C₃²×C₄×C₇	C₂⁴×C₃	1	1	yes	characteristic
131	C₂³×C₇×C₉	C₃×C₄²	1	12	yes	—
132	C₂³×C₇×C₉	C₂×C₃×C₈	1	24	yes	—
133	C₂³×C₇×C₉	C₂²×C₃×C₄	1	9	yes	—
134	C₃²×C₇×C₈	C₂²×C₃×C₄	1	16	yes	—
135	C₂×C₄×C₇×C₉	C₃×C₄²	1	36	yes	—
136	C₂×C₄×C₇×C₉	C₂×C₃×C₈	1	144	yes	direct product factor
137	C₂×C₄×C₇×C₉	C₂²×C₃×C₄	1	9	yes	—
138	C₂×C₄×C₇×C₉	C₂²×C₃×C₄	1	24	yes	—
139	C₂×C₄×C₇×C₉	C₂²×C₃×C₄	1	36	yes	—
140	C₂×C₄×C₇×C₉	C₂⁴×C₃	1	3	yes	—
141	C₇×C₈×C₉	C₂²×C₃×C₄	1	48	yes	direct product factor
142	C₂³×C₇×C₈	C₂×C₃×C₉	1	2	yes	—
143	C₂²×C₄²×C₇	C₂×C₃×C₉	1	1	yes	characteristic
144	C₂×C₄×C₇×C₈	C₂×C₃×C₉	1	12	yes	direct product factor
145	C₂⁴×C₃×C₉	C₂×C₄×C₇	1	1	yes	characteristic
146	C₂²×C₃×C₄×C₉	C₇×C₈	1	16	yes	direct product factor
147	C₂²×C₃×C₄×C₉	C₂×C₄×C₇	1	3	yes	—
148	C₂²×C₃×C₄×C₉	C₂×C₄×C₇	1	8	yes	—
149	C₂²×C₃×C₄×C₉	C₂×C₄×C₇	1	12	yes	—
150	C₂²×C₃×C₄×C₉	C₂³×C₇	1	3	yes	—
151	C₂×C₃×C₈×C₉	C₂×C₄×C₇	1	48	yes	direct product factor
152	C₂×C₃×C₈×C₉	C₂³×C₇	1	8	yes	—
153	C₃×C₄²×C₉	C₂×C₄×C₇	1	12	yes	—
154	C₃×C₄²×C₉	C₂³×C₇	1	4	yes	—
155	C₂²×C₃×C₄×C₈	C₇×C₉	1	3	yes	direct product factor
156	C₂²×C₃×C₄×C₈	C₃²×C₇	1	1	yes	characteristic
157	C₂×C₃×C₇×C₉	C₂×C₄×C₈	1	12	yes	direct product factor
158	C₂×C₃×C₇×C₉	C₂²×C₄²	1	1	yes	characteristic
159	C₂×C₃×C₇×C₉	C₂³×C₈	1	2	yes	—
160	C₂⁴×C₃×C₇	C₂×C₄×C₉	1	3	yes	—
161	C₂⁴×C₃×C₇	C₂×C₃²×C₄	1	1	yes	characteristic
162	C₂²×C₃×C₄×C₇	C₈×C₉	1	48	yes	direct product factor
163	C₂²×C₃×C₄×C₇	C₂×C₄×C₉	1	9	yes	—
164	C₂²×C₃×C₄×C₇	C₂×C₄×C₉	1	24	yes	—
165	C₂²×C₃×C₄×C₇	C₂×C₄×C₉	1	36	yes	—
166	C₂²×C₃×C₄×C₇	C₃²×C₈	1	16	yes	—
167	C₂²×C₃×C₄×C₇	C₂³×C₉	1	9	yes	—
168	C₂²×C₃×C₄×C₇	C₂×C₃²×C₄	1	3	yes	—
169	C₂²×C₃×C₄×C₇	C₂×C₃²×C₄	1	8	yes	—
170	C₂²×C₃×C₄×C₇	C₂×C₃²×C₄	1	12	yes	—
171	C₂²×C₃×C₄×C₇	C₂³×C₃²	1	3	yes	—
172	C₂×C₃×C₇×C₈	C₂×C₄×C₉	1	144	yes	direct product factor
173	C₂×C₃×C₇×C₈	C₂³×C₉	1	24	yes	—
174	C₂×C₃×C₇×C₈	C₂×C₃²×C₄	1	48	yes	—
175	C₂×C₃×C₇×C₈	C₂³×C₃²	1	8	yes	—
176	C₃×C₄²×C₇	C₂×C₄×C₉	1	36	yes	—
177	C₃×C₄²×C₇	C₂³×C₉	1	12	yes	—
178	C₃×C₄²×C₇	C₂×C₃²×C₄	1	12	yes	—
179	C₃×C₄²×C₇	C₂³×C₃²	1	4	yes	—
180	C₂³×C₃²×C₄	C₃×C₄×C₇	1	2	yes	—
181	C₂³×C₃²×C₄	C₂²×C₃×C₇	1	1	yes	characteristic
182	C₂²×C₃²×C₈	C₃×C₄×C₇	1	16	yes	—
183	C₂²×C₃²×C₈	C₂²×C₃×C₇	1	12	yes	—
184	C₂×C₃²×C₄²	C₃×C₄×C₇	1	6	yes	—
185	C₂×C₃²×C₄²	C₂²×C₃×C₇	1	6	yes	—
186	C₂³×C₄×C₉	C₃×C₄×C₇	1	6	yes	—
187	C₂³×C₄×C₉	C₂²×C₃×C₇	1	3	yes	—
188	C₃²×C₄×C₈	C₂²×C₃×C₇	1	16	yes	—
189	C₂²×C₈×C₉	C₃×C₄×C₇	1	48	yes	direct product factor
190	C₂²×C₈×C₉	C₂²×C₃×C₇	1	36	yes	—
191	C₂×C₄²×C₉	C₃×C₄×C₇	1	18	yes	—
192	C₂×C₄²×C₉	C₂²×C₃×C₇	1	18	yes	—
193	C₄×C₈×C₉	C₂²×C₃×C₇	1	48	yes	direct product factor
194	C₂²×C₃²×C₇	C₃×C₄×C₈	1	16	yes	—
195	C₂²×C₃²×C₇	C₂×C₃×C₄²	1	6	yes	—
196	C₂²×C₃²×C₇	C₂²×C₃×C₈	1	12	yes	—
197	C₂²×C₃²×C₇	C₂³×C₃×C₄	1	1	yes	characteristic
198	C₃²×C₄×C₇	C₂×C₃×C₄²	1	6	yes	—
199	C₃²×C₄×C₇	C₂²×C₃×C₈	1	16	yes	—
200	C₃²×C₄×C₇	C₂³×C₃×C₄	1	2	yes	—
201	C₂²×C₇×C₉	C₃×C₄×C₈	1	48	yes	direct product factor
202	C₂²×C₇×C₉	C₂×C₃×C₄²	1	18	yes	—
203	C₂²×C₇×C₉	C₂²×C₃×C₈	1	36	yes	—
204	C₂²×C₇×C₉	C₂³×C₃×C₄	1	3	yes	—
205	C₄×C₇×C₉	C₂×C₃×C₄²	1	18	yes	—
206	C₄×C₇×C₉	C₂²×C₃×C₈	1	48	yes	direct product factor
207	C₄×C₇×C₉	C₂³×C₃×C₄	1	6	yes	—
208	C₂³×C₄×C₇	C₃×C₄×C₉	1	2	yes	—
209	C₂³×C₄×C₇	C₂²×C₃×C₉	1	1	yes	characteristic
210	C₂²×C₇×C₈	C₃×C₄×C₉	1	16	yes	direct product factor
211	C₂²×C₇×C₈	C₂²×C₃×C₉	1	12	yes	—
212	C₂×C₄²×C₇	C₃×C₄×C₉	1	6	yes	—
213	C₂×C₄²×C₇	C₂²×C₃×C₉	1	6	yes	—
214	C₄×C₇×C₈	C₂²×C₃×C₉	1	16	yes	direct product factor
215	C₂³×C₃×C₉	C₄²×C₇	1	4	yes	—
216	C₂³×C₃×C₉	C₂×C₇×C₈	1	8	yes	—
217	C₂³×C₃×C₉	C₂²×C₄×C₇	1	3	yes	—
218	C₂×C₃×C₄×C₉	C₄²×C₇	1	12	yes	—
219	C₂×C₃×C₄×C₉	C₂×C₇×C₈	1	48	yes	direct product factor
220	C₂×C₃×C₄×C₉	C₂²×C₄×C₇	1	3	yes	—
221	C₂×C₃×C₄×C₉	C₂²×C₄×C₇	1	8	yes	—
222	C₂×C₃×C₄×C₉	C₂²×C₄×C₇	1	12	yes	—
223	C₂×C₃×C₄×C₉	C₂⁴×C₇	1	1	yes	characteristic
224	C₃×C₈×C₉	C₂²×C₄×C₇	1	16	yes	direct product factor
225	C₂³×C₃×C₈	C₂×C₇×C₉	1	6	yes	—
226	C₂³×C₃×C₈	C₂×C₃²×C₇	1	2	yes	—
227	C₂²×C₃×C₄²	C₂×C₇×C₉	1	3	yes	—
228	C₂²×C₃×C₄²	C₂×C₃²×C₇	1	1	yes	characteristic
229	C₂×C₃×C₄×C₈	C₂×C₇×C₉	1	36	yes	direct product factor
230	C₂×C₃×C₄×C₈	C₂×C₃²×C₇	1	12	yes	—
231	C₃×C₇×C₉	C₂²×C₄×C₈	1	1	yes	characteristic, direct product factor, Hall
232	C₂³×C₃×C₇	C₄²×C₉	1	12	yes	—
233	C₂³×C₃×C₇	C₂×C₈×C₉	1	24	yes	—
234	C₂³×C₃×C₇	C₂²×C₄×C₉	1	9	yes	—
235	C₂³×C₃×C₇	C₃²×C₄²	1	4	yes	—
236	C₂³×C₃×C₇	C₂×C₃²×C₈	1	8	yes	—
237	C₂³×C₃×C₇	C₂²×C₃²×C₄	1	3	yes	—
238	C₂×C₃×C₄×C₇	C₄²×C₉	1	36	yes	—
239	C₂×C₃×C₄×C₇	C₂×C₈×C₉	1	144	yes	direct product factor
240	C₂×C₃×C₄×C₇	C₂²×C₄×C₉	1	9	yes	—
241	C₂×C₃×C₄×C₇	C₂²×C₄×C₉	1	24	yes	—
242	C₂×C₃×C₄×C₇	C₂²×C₄×C₉	1	36	yes	—
243	C₂×C₃×C₄×C₇	C₃²×C₄²	1	12	yes	—
244	C₂×C₃×C₄×C₇	C₂×C₃²×C₈	1	48	yes	—
245	C₂×C₃×C₄×C₇	C₂⁴×C₉	1	3	yes	—
246	C₂×C₃×C₄×C₇	C₂²×C₃²×C₄	1	3	yes	—
247	C₂×C₃×C₄×C₇	C₂²×C₃²×C₄	1	8	yes	—
248	C₂×C₃×C₄×C₇	C₂²×C₃²×C₄	1	12	yes	—
249	C₂×C₃×C₄×C₇	C₂⁴×C₃²	1	1	yes	characteristic
250	C₃×C₇×C₈	C₂²×C₄×C₉	1	48	yes	direct product factor
251	C₃×C₇×C₈	C₂²×C₃²×C₄	1	16	yes	—
252	C₂⁴×C₃²	C₂×C₃×C₄×C₇	1	1	yes	characteristic
253	C₂²×C₃²×C₄	C₃×C₇×C₈	1	16	yes	—
254	C₂²×C₃²×C₄	C₂×C₃×C₄×C₇	1	3	yes	—
255	C₂²×C₃²×C₄	C₂×C₃×C₄×C₇	1	8	yes	—
256	C₂²×C₃²×C₄	C₂×C₃×C₄×C₇	1	12	yes	—
257	C₂²×C₃²×C₄	C₂³×C₃×C₇	1	3	yes	—
258	C₂⁴×C₉	C₂×C₃×C₄×C₇	1	3	yes	—
259	C₂×C₃²×C₈	C₂×C₃×C₄×C₇	1	48	yes	—
260	C₂×C₃²×C₈	C₂³×C₃×C₇	1	8	yes	—
261	C₃²×C₄²	C₂×C₃×C₄×C₇	1	12	yes	—
262	C₃²×C₄²	C₂³×C₃×C₇	1	4	yes	—
263	C₂²×C₄×C₉	C₃×C₇×C₈	1	48	yes	direct product factor
264	C₂²×C₄×C₉	C₂×C₃×C₄×C₇	1	9	yes	—
265	C₂²×C₄×C₉	C₂×C₃×C₄×C₇	1	24	yes	—
266	C₂²×C₄×C₉	C₂×C₃×C₄×C₇	1	36	yes	—
267	C₂²×C₄×C₉	C₂³×C₃×C₇	1	9	yes	—
268	C₂×C₈×C₉	C₂×C₃×C₄×C₇	1	144	yes	direct product factor
269	C₂×C₈×C₉	C₂³×C₃×C₇	1	24	yes	—
270	C₄²×C₉	C₂×C₃×C₄×C₇	1	36	yes	—
271	C₄²×C₉	C₂³×C₃×C₇	1	12	yes	—
272	C₂²×C₄×C₈	C₃×C₇×C₉	1	1	yes	characteristic, direct product factor, Sylow
273	C₂×C₃²×C₇	C₂×C₃×C₄×C₈	1	12	yes	—
274	C₂×C₃²×C₇	C₂²×C₃×C₄²	1	1	yes	characteristic
275	C₂×C₃²×C₇	C₂³×C₃×C₈	1	2	yes	—
276	C₂×C₇×C₉	C₂×C₃×C₄×C₈	1	36	yes	direct product factor
277	C₂×C₇×C₉	C₂²×C₃×C₄²	1	3	yes	—
278	C₂×C₇×C₉	C₂³×C₃×C₈	1	6	yes	—
279	C₂⁴×C₇	C₂×C₃×C₄×C₉	1	1	yes	characteristic
280	C₂²×C₄×C₇	C₃×C₈×C₉	1	16	yes	direct product factor
281	C₂²×C₄×C₇	C₂×C₃×C₄×C₉	1	3	yes	—
282	C₂²×C₄×C₇	C₂×C₃×C₄×C₉	1	8	yes	—
283	C₂²×C₄×C₇	C₂×C₃×C₄×C₉	1	12	yes	—
284	C₂²×C₄×C₇	C₂³×C₃×C₉	1	3	yes	—
285	C₂×C₇×C₈	C₂×C₃×C₄×C₉	1	48	yes	direct product factor
286	C₂×C₇×C₈	C₂³×C₃×C₉	1	8	yes	—
287	C₄²×C₇	C₂×C₃×C₄×C₉	1	12	yes	—
288	C₄²×C₇	C₂³×C₃×C₉	1	4	yes	—
289	C₂²×C₃×C₉	C₄×C₇×C₈	1	16	yes	direct product factor
290	C₂²×C₃×C₉	C₂×C₄²×C₇	1	6	yes	—
291	C₂²×C₃×C₉	C₂²×C₇×C₈	1	12	yes	—
292	C₂²×C₃×C₉	C₂³×C₄×C₇	1	1	yes	characteristic
293	C₃×C₄×C₉	C₂×C₄²×C₇	1	6	yes	—
294	C₃×C₄×C₉	C₂²×C₇×C₈	1	16	yes	direct product factor
295	C₃×C₄×C₉	C₂³×C₄×C₇	1	2	yes	—
296	C₂³×C₃×C₄	C₄×C₇×C₉	1	6	yes	—
297	C₂³×C₃×C₄	C₂²×C₇×C₉	1	3	yes	—
298	C₂³×C₃×C₄	C₃²×C₄×C₇	1	2	yes	—
299	C₂³×C₃×C₄	C₂²×C₃²×C₇	1	1	yes	characteristic
300	C₂²×C₃×C₈	C₄×C₇×C₉	1	48	yes	direct product factor
301	C₂²×C₃×C₈	C₂²×C₇×C₉	1	36	yes	—
302	C₂²×C₃×C₈	C₃²×C₄×C₇	1	16	yes	—
303	C₂²×C₃×C₈	C₂²×C₃²×C₇	1	12	yes	—
304	C₂×C₃×C₄²	C₄×C₇×C₉	1	18	yes	—
305	C₂×C₃×C₄²	C₂²×C₇×C₉	1	18	yes	—
306	C₂×C₃×C₄²	C₃²×C₄×C₇	1	6	yes	—
307	C₂×C₃×C₄²	C₂²×C₃²×C₇	1	6	yes	—
308	C₃×C₄×C₈	C₂²×C₇×C₉	1	48	yes	direct product factor
309	C₃×C₄×C₈	C₂²×C₃²×C₇	1	16	yes	—
310	C₂²×C₃×C₇	C₄×C₈×C₉	1	48	yes	direct product factor
311	C₂²×C₃×C₇	C₂×C₄²×C₉	1	18	yes	—
312	C₂²×C₃×C₇	C₂²×C₈×C₉	1	36	yes	—
313	C₂²×C₃×C₇	C₃²×C₄×C₈	1	16	yes	—
314	C₂²×C₃×C₇	C₂³×C₄×C₉	1	3	yes	—
315	C₂²×C₃×C₇	C₂×C₃²×C₄²	1	6	yes	—
316	C₂²×C₃×C₇	C₂²×C₃²×C₈	1	12	yes	—
317	C₂²×C₃×C₇	C₂³×C₃²×C₄	1	1	yes	characteristic
318	C₃×C₄×C₇	C₂×C₄²×C₉	1	18	yes	—
319	C₃×C₄×C₇	C₂²×C₈×C₉	1	48	yes	direct product factor
320	C₃×C₄×C₇	C₂³×C₄×C₉	1	6	yes	—
321	C₃×C₄×C₇	C₂×C₃²×C₄²	1	6	yes	—
322	C₃×C₄×C₇	C₂²×C₃²×C₈	1	16	yes	—
323	C₃×C₄×C₇	C₂³×C₃²×C₄	1	2	yes	—
324	C₂³×C₃²	C₃×C₄²×C₇	1	4	yes	—
325	C₂³×C₃²	C₂×C₃×C₇×C₈	1	8	yes	—
326	C₂³×C₃²	C₂²×C₃×C₄×C₇	1	3	yes	—
327	C₂×C₃²×C₄	C₃×C₄²×C₇	1	12	yes	—
328	C₂×C₃²×C₄	C₂×C₃×C₇×C₈	1	48	yes	—
329	C₂×C₃²×C₄	C₂²×C₃×C₄×C₇	1	3	yes	—
330	C₂×C₃²×C₄	C₂²×C₃×C₄×C₇	1	8	yes	—
331	C₂×C₃²×C₄	C₂²×C₃×C₄×C₇	1	12	yes	—
332	C₂×C₃²×C₄	C₂⁴×C₃×C₇	1	1	yes	characteristic
333	C₂³×C₉	C₃×C₄²×C₇	1	12	yes	—
334	C₂³×C₉	C₂×C₃×C₇×C₈	1	24	yes	—
335	C₂³×C₉	C₂²×C₃×C₄×C₇	1	9	yes	—
336	C₃²×C₈	C₂²×C₃×C₄×C₇	1	16	yes	—
337	C₂×C₄×C₉	C₃×C₄²×C₇	1	36	yes	—
338	C₂×C₄×C₉	C₂×C₃×C₇×C₈	1	144	yes	direct product factor
339	C₂×C₄×C₉	C₂²×C₃×C₄×C₇	1	9	yes	—
340	C₂×C₄×C₉	C₂²×C₃×C₄×C₇	1	24	yes	—
341	C₂×C₄×C₉	C₂²×C₃×C₄×C₇	1	36	yes	—
342	C₂×C₄×C₉	C₂⁴×C₃×C₇	1	3	yes	—
343	C₈×C₉	C₂²×C₃×C₄×C₇	1	48	yes	direct product factor
344	C₂³×C₈	C₂×C₃×C₇×C₉	1	2	yes	—
345	C₂²×C₄²	C₂×C₃×C₇×C₉	1	1	yes	characteristic
346	C₂×C₄×C₈	C₂×C₃×C₇×C₉	1	12	yes	direct product factor
347	C₃²×C₇	C₂²×C₃×C₄×C₈	1	1	yes	characteristic
348	C₇×C₉	C₂²×C₃×C₄×C₈	1	3	yes	direct product factor
349	C₂³×C₇	C₃×C₄²×C₉	1	4	yes	—
350	C₂³×C₇	C₂×C₃×C₈×C₉	1	8	yes	—
351	C₂³×C₇	C₂²×C₃×C₄×C₉	1	3	yes	—
352	C₂×C₄×C₇	C₃×C₄²×C₉	1	12	yes	—
353	C₂×C₄×C₇	C₂×C₃×C₈×C₉	1	48	yes	direct product factor
354	C₂×C₄×C₇	C₂²×C₃×C₄×C₉	1	3	yes	—
355	C₂×C₄×C₇	C₂²×C₃×C₄×C₉	1	8	yes	—
356	C₂×C₄×C₇	C₂²×C₃×C₄×C₉	1	12	yes	—
357	C₂×C₄×C₇	C₂⁴×C₃×C₉	1	1	yes	characteristic
358	C₇×C₈	C₂²×C₃×C₄×C₉	1	16	yes	direct product factor
359	C₂×C₃×C₉	C₂×C₄×C₇×C₈	1	12	yes	direct product factor
360	C₂×C₃×C₉	C₂²×C₄²×C₇	1	1	yes	characteristic
361	C₂×C₃×C₉	C₂³×C₇×C₈	1	2	yes	—
362	C₂⁴×C₃	C₂×C₄×C₇×C₉	1	3	yes	—
363	C₂⁴×C₃	C₂×C₃²×C₄×C₇	1	1	yes	characteristic
364	C₂²×C₃×C₄	C₇×C₈×C₉	1	48	yes	direct product factor
365	C₂²×C₃×C₄	C₂×C₄×C₇×C₉	1	9	yes	—
366	C₂²×C₃×C₄	C₂×C₄×C₇×C₉	1	24	yes	—
367	C₂²×C₃×C₄	C₂×C₄×C₇×C₉	1	36	yes	—
368	C₂²×C₃×C₄	C₃²×C₇×C₈	1	16	yes	—
369	C₂²×C₃×C₄	C₂³×C₇×C₉	1	9	yes	—
370	C₂²×C₃×C₄	C₂×C₃²×C₄×C₇	1	3	yes	—
371	C₂²×C₃×C₄	C₂×C₃²×C₄×C₇	1	8	yes	—
372	C₂²×C₃×C₄	C₂×C₃²×C₄×C₇	1	12	yes	—
373	C₂²×C₃×C₄	C₂³×C₃²×C₇	1	3	yes	—
374	C₂×C₃×C₈	C₂×C₄×C₇×C₉	1	144	yes	direct product factor
375	C₂×C₃×C₈	C₂³×C₇×C₉	1	24	yes	—
376	C₂×C₃×C₈	C₂×C₃²×C₄×C₇	1	48	yes	—
377	C₂×C₃×C₈	C₂³×C₃²×C₇	1	8	yes	—
378	C₃×C₄²	C₂×C₄×C₇×C₉	1	36	yes	—
379	C₃×C₄²	C₂³×C₇×C₉	1	12	yes	—
380	C₃×C₄²	C₂×C₃²×C₄×C₇	1	12	yes	—
381	C₃×C₄²	C₂³×C₃²×C₇	1	4	yes	—
382	C₂×C₃×C₇	C₂×C₄×C₈×C₉	1	36	yes	direct product factor
383	C₂×C₃×C₇	C₂²×C₄²×C₉	1	3	yes	—
384	C₂×C₃×C₇	C₂³×C₈×C₉	1	6	yes	—
385	C₂×C₃×C₇	C₂×C₃²×C₄×C₈	1	12	yes	—
386	C₂×C₃×C₇	C₂²×C₃²×C₄²	1	1	yes	characteristic
387	C₂×C₃×C₇	C₂³×C₃²×C₈	1	2	yes	—
388	C₂²×C₃²	C₃×C₄×C₇×C₈	1	16	yes	—
389	C₂²×C₃²	C₂×C₃×C₄²×C₇	1	6	yes	—
390	C₂²×C₃²	C₂²×C₃×C₇×C₈	1	12	yes	—
391	C₂²×C₃²	C₂³×C₃×C₄×C₇	1	1	yes	characteristic
392	C₃²×C₄	C₂×C₃×C₄²×C₇	1	6	yes	—
393	C₃²×C₄	C₂²×C₃×C₇×C₈	1	16	yes	—
394	C₃²×C₄	C₂³×C₃×C₄×C₇	1	2	yes	—
395	C₂²×C₉	C₃×C₄×C₇×C₈	1	48	yes	direct product factor
396	C₂²×C₉	C₂×C₃×C₄²×C₇	1	18	yes	—
397	C₂²×C₉	C₂²×C₃×C₇×C₈	1	36	yes	—
398	C₂²×C₉	C₂³×C₃×C₄×C₇	1	3	yes	—
399	C₄×C₉	C₂×C₃×C₄²×C₇	1	18	yes	—
400	C₄×C₉	C₂²×C₃×C₇×C₈	1	48	yes	direct product factor
401	C₄×C₉	C₂³×C₃×C₄×C₇	1	6	yes	—
402	C₂³×C₄	C₃×C₄×C₇×C₉	1	2	yes	—
403	C₂³×C₄	C₂²×C₃×C₇×C₉	1	1	yes	characteristic
404	C₂²×C₈	C₃×C₄×C₇×C₉	1	16	yes	direct product factor
405	C₂²×C₈	C₂²×C₃×C₇×C₉	1	12	yes	—
406	C₂×C₄²	C₃×C₄×C₇×C₉	1	6	yes	—
407	C₂×C₄²	C₂²×C₃×C₇×C₉	1	6	yes	—
408	C₄×C₈	C₂²×C₃×C₇×C₉	1	16	yes	direct product factor
409	C₂²×C₇	C₃×C₄×C₈×C₉	1	16	yes	direct product factor
410	C₂²×C₇	C₂×C₃×C₄²×C₉	1	6	yes	—
411	C₂²×C₇	C₂²×C₃×C₈×C₉	1	12	yes	—
412	C₂²×C₇	C₂³×C₃×C₄×C₉	1	1	yes	characteristic
413	C₄×C₇	C₂×C₃×C₄²×C₉	1	6	yes	—
414	C₄×C₇	C₂²×C₃×C₈×C₉	1	16	yes	direct product factor
415	C₄×C₇	C₂³×C₃×C₄×C₉	1	2	yes	—
416	C₃×C₉	C₂²×C₄×C₇×C₈	1	1	yes	characteristic, direct product factor, Sylow
417	C₂³×C₃	C₄²×C₇×C₉	1	12	yes	—
418	C₂³×C₃	C₂×C₇×C₈×C₉	1	24	yes	—
419	C₂³×C₃	C₂²×C₄×C₇×C₉	1	9	yes	—
420	C₂³×C₃	C₃²×C₄²×C₇	1	4	yes	—
421	C₂³×C₃	C₂×C₃²×C₇×C₈	1	8	yes	—
422	C₂³×C₃	C₂²×C₃²×C₄×C₇	1	3	yes	—
423	C₂×C₃×C₄	C₄²×C₇×C₉	1	36	yes	—
424	C₂×C₃×C₄	C₂×C₇×C₈×C₉	1	144	yes	direct product factor
425	C₂×C₃×C₄	C₂²×C₄×C₇×C₉	1	9	yes	—
426	C₂×C₃×C₄	C₂²×C₄×C₇×C₉	1	24	yes	—
427	C₂×C₃×C₄	C₂²×C₄×C₇×C₉	1	36	yes	—
428	C₂×C₃×C₄	C₃²×C₄²×C₇	1	12	yes	—
429	C₂×C₃×C₄	C₂×C₃²×C₇×C₈	1	48	yes	—
430	C₂×C₃×C₄	C₂⁴×C₇×C₉	1	3	yes	—
431	C₂×C₃×C₄	C₂²×C₃²×C₄×C₇	1	3	yes	—
432	C₂×C₃×C₄	C₂²×C₃²×C₄×C₇	1	8	yes	—
433	C₂×C₃×C₄	C₂²×C₃²×C₄×C₇	1	12	yes	—
434	C₂×C₃×C₄	C₂⁴×C₃²×C₇	1	1	yes	characteristic
435	C₃×C₈	C₂²×C₄×C₇×C₉	1	48	yes	direct product factor
436	C₃×C₈	C₂²×C₃²×C₄×C₇	1	16	yes	—
437	C₃×C₇	C₂²×C₄×C₈×C₉	1	3	yes	direct product factor
438	C₃×C₇	C₂²×C₃²×C₄×C₈	1	1	yes	characteristic
439	C₂×C₃²	C₂×C₃×C₄×C₇×C₈	1	12	yes	—
440	C₂×C₃²	C₂²×C₃×C₄²×C₇	1	1	yes	characteristic
441	C₂×C₃²	C₂³×C₃×C₇×C₈	1	2	yes	—
442	C₂×C₉	C₂×C₃×C₄×C₇×C₈	1	36	yes	direct product factor
443	C₂×C₉	C₂²×C₃×C₄²×C₇	1	3	yes	—
444	C₂×C₉	C₂³×C₃×C₇×C₈	1	6	yes	—
445	C₂⁴	C₂×C₃×C₄×C₇×C₉	1	1	yes	characteristic
446	C₂²×C₄	C₃×C₇×C₈×C₉	1	16	yes	direct product factor
447	C₂²×C₄	C₂×C₃×C₄×C₇×C₉	1	3	yes	—
448	C₂²×C₄	C₂×C₃×C₄×C₇×C₉	1	8	yes	—
449	C₂²×C₄	C₂×C₃×C₄×C₇×C₉	1	12	yes	—
450	C₂²×C₄	C₂³×C₃×C₇×C₉	1	3	yes	—
451	C₂×C₈	C₂×C₃×C₄×C₇×C₉	1	48	yes	direct product factor
452	C₂×C₈	C₂³×C₃×C₇×C₉	1	8	yes	—
453	C₄²	C₂×C₃×C₄×C₇×C₉	1	12	yes	—
454	C₄²	C₂³×C₃×C₇×C₉	1	4	yes	—
455	C₂×C₇	C₂×C₃×C₄×C₈×C₉	1	12	yes	direct product factor
456	C₂×C₇	C₂²×C₃×C₄²×C₉	1	1	yes	characteristic
457	C₂×C₇	C₂³×C₃×C₈×C₉	1	2	yes	—
458	C₂²×C₃	C₄×C₇×C₈×C₉	1	48	yes	direct product factor
459	C₂²×C₃	C₃²×C₄×C₇×C₈	1	16	yes	—
460	C₂²×C₃	C₂²×C₇×C₈×C₉	1	36	yes	—
461	C₂²×C₃	C₂²×C₃²×C₇×C₈	1	12	yes	—
462	C₂²×C₃	C₂×C₃²×C₄²×C₇	1	6	yes	—
463	C₂²×C₃	C₂×C₄²×C₇×C₉	1	18	yes	—
464	C₂²×C₃	C₂³×C₄×C₇×C₉	1	3	yes	—
465	C₂²×C₃	C₂³×C₃²×C₄×C₇	1	1	yes	characteristic
466	C₃×C₄	C₂²×C₇×C₈×C₉	1	48	yes	direct product factor
467	C₃×C₄	C₂²×C₃²×C₇×C₈	1	16	yes	—
468	C₃×C₄	C₂×C₃²×C₄²×C₇	1	6	yes	—
469	C₃×C₄	C₂×C₄²×C₇×C₉	1	18	yes	—
470	C₃×C₄	C₂³×C₄×C₇×C₉	1	6	yes	—
471	C₃×C₄	C₂³×C₃²×C₄×C₇	1	2	yes	—
472	C₃²	C₂²×C₃×C₄×C₇×C₈	1	1	yes	characteristic
473	C₉	C₂²×C₃×C₄×C₇×C₈	1	3	yes	direct product factor
474	C₂³	C₂×C₃×C₇×C₈×C₉	1	8	yes	—
475	C₂³	C₃×C₄²×C₇×C₉	1	4	yes	—
476	C₂³	C₂²×C₃×C₄×C₇×C₉	1	3	yes	—
477	C₂×C₄	C₂×C₃×C₇×C₈×C₉	1	48	yes	direct product factor
478	C₂×C₄	C₃×C₄²×C₇×C₉	1	12	yes	—
479	C₂×C₄	C₂²×C₃×C₄×C₇×C₉	1	3	yes	—
480	C₂×C₄	C₂²×C₃×C₄×C₇×C₉	1	8	yes	—
481	C₂×C₄	C₂²×C₃×C₄×C₇×C₉	1	12	yes	—
482	C₂×C₄	C₂⁴×C₃×C₇×C₉	1	1	yes	characteristic
483	C₈	C₂²×C₃×C₄×C₇×C₉	1	16	yes	direct product factor
484	C₇	C₂²×C₃×C₄×C₈×C₉	1	1	yes	characteristic, direct product factor, Sylow
485	C₂×C₃	C₂×C₄×C₇×C₈×C₉	1	36	yes	direct product factor
486	C₂×C₃	C₂×C₃²×C₄×C₇×C₈	1	12	yes	—
487	C₂×C₃	C₂³×C₇×C₈×C₉	1	6	yes	—
488	C₂×C₃	C₂³×C₃²×C₇×C₈	1	2	yes	—
489	C₂×C₃	C₂²×C₄²×C₇×C₉	1	3	yes	—
490	C₂×C₃	C₂²×C₃²×C₄²×C₇	1	1	yes	characteristic
491	C₂²	C₃×C₄×C₇×C₈×C₉	1	16	yes	direct product factor
492	C₂²	C₂²×C₃×C₇×C₈×C₉	1	12	yes	—
493	C₂²	C₂×C₃×C₄²×C₇×C₉	1	6	yes	—
494	C₂²	C₂³×C₃×C₄×C₇×C₉	1	1	yes	characteristic
495	C₄	C₂²×C₃×C₇×C₈×C₉	1	16	yes	direct product factor
496	C₄	C₂×C₃×C₄²×C₇×C₉	1	6	yes	—
497	C₄	C₂³×C₃×C₄×C₇×C₉	1	2	yes	—
498	C₃	C₂²×C₄×C₇×C₈×C₉	1	3	yes	direct product factor
499	C₃	C₂²×C₃²×C₄×C₇×C₈	1	1	yes	characteristic
500	C₂	C₂×C₃×C₄×C₇×C₈×C₉	1	12	yes	direct product factor
501	C₂	C₂³×C₃×C₇×C₈×C₉	1	2	yes	—
502	C₂	C₂²×C₃×C₄²×C₇×C₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃²×C₇
socle, prime radical	C₂⁴×C₃²×C₇	C₂×C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₃×C₄×C₇×C₈×C₉	C₂	direct (N × H)
5. C₂²×C₄×C₇×C₈×C₉	C₃	direct (N × H)
10. C₂²×C₃×C₇×C₈×C₉	C₄	direct (N × H)
12. C₃×C₄×C₇×C₈×C₉	C₂²	direct (N × H)
18. C₂×C₄×C₇×C₈×C₉	C₂×C₃	direct (N × H)
19. C₂²×C₃×C₄×C₈×C₉	C₇	direct (N × H)
21. C₂²×C₃×C₄×C₇×C₉	C₈	direct (N × H)
28. C₂×C₃×C₇×C₈×C₉	C₂×C₄	direct (N × H)
30. C₂²×C₃×C₄×C₇×C₈	C₉	direct (N × H)
42. C₂²×C₇×C₈×C₉	C₃×C₄	direct (N × H)
45. C₄×C₇×C₈×C₉	C₂²×C₃	direct (N × H)
48. C₂×C₃×C₄×C₈×C₉	C₂×C₇	direct (N × H)
53. C₂×C₃×C₄×C₇×C₉	C₂×C₈	direct (N × H)
58. C₃×C₇×C₈×C₉	C₂²×C₄	direct (N × H)
63. C₂×C₃×C₄×C₇×C₈	C₂×C₉	direct (N × H)
66. C₂²×C₄×C₈×C₉	C₃×C₇	direct (N × H)
78. C₂²×C₄×C₇×C₉	C₃×C₈	direct (N × H)
83. C₂×C₇×C₈×C₉	C₂×C₃×C₄	direct (N × H)
87. C₂²×C₄×C₇×C₈	C₃×C₉	direct (N × H)
90. C₂²×C₃×C₈×C₉	C₄×C₇	direct (N × H)
94. C₃×C₄×C₈×C₉	C₂²×C₇	direct (N × H)
95. C₂²×C₃×C₇×C₉	C₄×C₈	direct (N × H)
100. C₃×C₄×C₇×C₉	C₂²×C₈	direct (N × H)
106. C₂²×C₃×C₇×C₈	C₄×C₉	direct (N × H)
114. C₃×C₄×C₇×C₈	C₂²×C₉	direct (N × H)
121. C₂×C₄×C₈×C₉	C₂×C₃×C₇	direct (N × H)
136. C₂×C₄×C₇×C₉	C₂×C₃×C₈	direct (N × H)
141. C₇×C₈×C₉	C₂²×C₃×C₄	direct (N × H)
144. C₂×C₄×C₇×C₈	C₂×C₃×C₉	direct (N × H)
146. C₂²×C₃×C₄×C₉	C₇×C₈	direct (N × H)
151. C₂×C₃×C₈×C₉	C₂×C₄×C₇	direct (N × H)
155. C₂²×C₃×C₄×C₈	C₇×C₉	direct (N × H)
157. C₂×C₃×C₇×C₉	C₂×C₄×C₈	direct (N × H)
162. C₂²×C₃×C₄×C₇	C₈×C₉	direct (N × H)
172. C₂×C₃×C₇×C₈	C₂×C₄×C₉	direct (N × H)
189. C₂²×C₈×C₉	C₃×C₄×C₇	direct (N × H)
193. C₄×C₈×C₉	C₂²×C₃×C₇	direct (N × H)
201. C₂²×C₇×C₉	C₃×C₄×C₈	direct (N × H)
206. C₄×C₇×C₉	C₂²×C₃×C₈	direct (N × H)
210. C₂²×C₇×C₈	C₃×C₄×C₉	direct (N × H)
214. C₄×C₇×C₈	C₂²×C₃×C₉	direct (N × H)
219. C₂×C₃×C₄×C₉	C₂×C₇×C₈	direct (N × H)
224. C₃×C₈×C₉	C₂²×C₄×C₇	direct (N × H)
229. C₂×C₃×C₄×C₈	C₂×C₇×C₉	direct (N × H)
231. C₃×C₇×C₉	C₂²×C₄×C₈	direct (N × H)
239. C₂×C₃×C₄×C₇	C₂×C₈×C₉	direct (N × H)
250. C₃×C₇×C₈	C₂²×C₄×C₉	direct (N × H)
263. C₂²×C₄×C₉	C₃×C₇×C₈	direct (N × H)
268. C₂×C₈×C₉	C₂×C₃×C₄×C₇	direct (N × H)
272. C₂²×C₄×C₈	C₃×C₇×C₉	direct (N × H)
276. C₂×C₇×C₉	C₂×C₃×C₄×C₈	direct (N × H)
280. C₂²×C₄×C₇	C₃×C₈×C₉	direct (N × H)
285. C₂×C₇×C₈	C₂×C₃×C₄×C₉	direct (N × H)
289. C₂²×C₃×C₉	C₄×C₇×C₈	direct (N × H)
294. C₃×C₄×C₉	C₂²×C₇×C₈	direct (N × H)
300. C₂²×C₃×C₈	C₄×C₇×C₉	direct (N × H)
308. C₃×C₄×C₈	C₂²×C₇×C₉	direct (N × H)
310. C₂²×C₃×C₇	C₄×C₈×C₉	direct (N × H)
319. C₃×C₄×C₇	C₂²×C₈×C₉	direct (N × H)
338. C₂×C₄×C₉	C₂×C₃×C₇×C₈	direct (N × H)
343. C₈×C₉	C₂²×C₃×C₄×C₇	direct (N × H)
346. C₂×C₄×C₈	C₂×C₃×C₇×C₉	direct (N × H)
348. C₇×C₉	C₂²×C₃×C₄×C₈	direct (N × H)
353. C₂×C₄×C₇	C₂×C₃×C₈×C₉	direct (N × H)
358. C₇×C₈	C₂²×C₃×C₄×C₉	direct (N × H)
359. C₂×C₃×C₉	C₂×C₄×C₇×C₈	direct (N × H)
364. C₂²×C₃×C₄	C₇×C₈×C₉	direct (N × H)
374. C₂×C₃×C₈	C₂×C₄×C₇×C₉	direct (N × H)
382. C₂×C₃×C₇	C₂×C₄×C₈×C₉	direct (N × H)
395. C₂²×C₉	C₃×C₄×C₇×C₈	direct (N × H)
400. C₄×C₉	C₂²×C₃×C₇×C₈	direct (N × H)
404. C₂²×C₈	C₃×C₄×C₇×C₉	direct (N × H)
408. C₄×C₈	C₂²×C₃×C₇×C₉	direct (N × H)
409. C₂²×C₇	C₃×C₄×C₈×C₉	direct (N × H)
414. C₄×C₇	C₂²×C₃×C₈×C₉	direct (N × H)
416. C₃×C₉	C₂²×C₄×C₇×C₈	direct (N × H)
424. C₂×C₃×C₄	C₂×C₇×C₈×C₉	direct (N × H)
435. C₃×C₈	C₂²×C₄×C₇×C₉	direct (N × H)
437. C₃×C₇	C₂²×C₄×C₈×C₉	direct (N × H)
442. C₂×C₉	C₂×C₃×C₄×C₇×C₈	direct (N × H)
446. C₂²×C₄	C₃×C₇×C₈×C₉	direct (N × H)
451. C₂×C₈	C₂×C₃×C₄×C₇×C₉	direct (N × H)
455. C₂×C₇	C₂×C₃×C₄×C₈×C₉	direct (N × H)
458. C₂²×C₃	C₄×C₇×C₈×C₉	direct (N × H)
466. C₃×C₄	C₂²×C₇×C₈×C₉	direct (N × H)
473. C₉	C₂²×C₃×C₄×C₇×C₈	direct (N × H)
477. C₂×C₄	C₂×C₃×C₇×C₈×C₉	direct (N × H)
483. C₈	C₂²×C₃×C₄×C₇×C₉	direct (N × H)
484. C₇	C₂²×C₃×C₄×C₈×C₉	direct (N × H)
485. C₂×C₃	C₂×C₄×C₇×C₈×C₉	direct (N × H)
491. C₂²	C₃×C₄×C₇×C₈×C₉	direct (N × H)
495. C₄	C₂²×C₃×C₇×C₈×C₉	direct (N × H)
498. C₃	C₂²×C₄×C₇×C₈×C₉	direct (N × H)
500. C₂	C₂×C₃×C₄×C₇×C₈×C₉	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×C₃×C₄²×C₇×C₉	2
C₂³×C₃×C₇×C₈×C₉	2
C₂×C₃×C₄×C₇×C₈×C₉	2
C₂²×C₃²×C₄×C₇×C₈	3
C₂²×C₄×C₇×C₈×C₉	3
C₂²×C₃×C₄×C₈×C₉	7

Subgroups — C22×C3×C4×C7×C8×C9 #72201481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×C₄×C₇×C₈×C₉ #72201481