Subgroups — C₂³×C₄×C₈²×C₉ #72196233

Order 18432.

323256 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄²×C₈×C₉	C₂	1	3	yes	maximal
2	C₂⁴×C₈²×C₉	C₂	1	4	yes	maximal
3	C₂²×C₄×C₈²×C₉	C₂	1	56	yes	maximal, direct product factor
4	C₂³×C₃×C₄×C₈²	C₃	1	1	yes	maximal, characteristic
5	C₂³×C₄³×C₉	C₂²	1	1	yes	characteristic
6	C₂⁴×C₄×C₈×C₉	C₄	1	12	yes	—
7	C₂⁴×C₄×C₈×C₉	C₂²	1	6	yes	—
8	C₂²×C₄²×C₈×C₉	C₄	1	84	yes	—
9	C₂²×C₄²×C₈×C₉	C₂²	1	84	yes	—
10	C₂³×C₈²×C₉	C₄	1	128	yes	direct product factor
11	C₂³×C₈²×C₉	C₂²	1	112	yes	—
12	C₂×C₄×C₈²×C₉	C₂²	1	448	yes	direct product factor
13	C₂³×C₃×C₄²×C₈	C₂×C₃	1	3	yes	—
14	C₂⁴×C₃×C₈²	C₂×C₃	1	4	yes	—
15	C₂²×C₃×C₄×C₈²	C₂×C₃	1	56	yes	—
16	C₂⁴×C₄²×C₉	C₂×C₄	1	6	yes	—
17	C₂⁴×C₄²×C₉	C₂³	1	1	yes	characteristic
18	C₂²×C₄³×C₉	C₂×C₄	1	42	yes	—
19	C₂²×C₄³×C₉	C₂³	1	14	yes	—
20	C₂⁵×C₈×C₉	C₂×C₄	1	12	yes	—
21	C₂³×C₄×C₈×C₉	C₈	1	384	yes	direct product factor
22	C₂³×C₄×C₈×C₉	C₂×C₄	1	336	yes	—
23	C₂³×C₄×C₈×C₉	C₂×C₄	1	84	yes	—
24	C₂³×C₄×C₈×C₉	C₂×C₄	1	192	yes	—
25	C₂³×C₄×C₈×C₉	C₂³	1	84	yes	—
26	C₂×C₄²×C₈×C₉	C₂×C₄	1	1008	yes	—
27	C₂×C₄²×C₈×C₉	C₂³	1	336	yes	—
28	C₂²×C₈²×C₉	C₂×C₄	1	1792	yes	direct product factor
29	C₂²×C₈²×C₉	C₂³	1	448	yes	—
30	C₄×C₈²×C₉	C₂³	1	512	yes	direct product factor
31	C₂³×C₄×C₈²	C₉	1	1	yes	characteristic, direct product factor, Sylow
32	C₂³×C₃×C₄³	C₂²×C₃	1	1	yes	characteristic
33	C₂⁴×C₃×C₄×C₈	C₃×C₄	1	12	yes	—
34	C₂⁴×C₃×C₄×C₈	C₂²×C₃	1	6	yes	—
35	C₂²×C₃×C₄²×C₈	C₃×C₄	1	84	yes	—
36	C₂²×C₃×C₄²×C₈	C₂²×C₃	1	84	yes	—
37	C₂³×C₃×C₈²	C₃×C₄	1	128	yes	—
38	C₂³×C₃×C₈²	C₂²×C₃	1	112	yes	—
39	C₂×C₃×C₄×C₈²	C₂²×C₃	1	448	yes	—
40	C₂³×C₄²×C₈	C₂×C₉	1	3	yes	—
41	C₂²×C₄×C₈²	C₂×C₉	1	56	yes	direct product factor
42	C₂⁴×C₈²	C₂×C₉	1	4	yes	—
43	C₂⁵×C₄×C₉	C₄²	1	4	yes	—
44	C₂⁵×C₄×C₉	C₂²×C₄	1	3	yes	—
45	C₂⁴×C₈×C₉	C₄²	1	192	yes	—
46	C₂⁴×C₈×C₉	C₂×C₈	1	384	yes	—
47	C₂⁴×C₈×C₉	C₂²×C₄	1	168	yes	—
48	C₂³×C₄²×C₉	C₄²	1	84	yes	—
49	C₂³×C₄²×C₉	C₂×C₈	1	192	yes	—
50	C₂³×C₄²×C₉	C₂²×C₄	1	21	yes	—
51	C₂³×C₄²×C₉	C₂²×C₄	1	32	yes	—
52	C₂³×C₄²×C₉	C₂²×C₄	1	84	yes	—
53	C₂³×C₄²×C₉	C₂⁴	1	7	yes	—
54	C₂²×C₄×C₈×C₉	C₄²	1	1344	yes	—
55	C₂²×C₄×C₈×C₉	C₂×C₈	1	5376	yes	direct product factor
56	C₂²×C₄×C₈×C₉	C₂²×C₄	1	1344	yes	—
57	C₂²×C₄×C₈×C₉	C₂²×C₄	1	1344	yes	—
58	C₂²×C₄×C₈×C₉	C₂²×C₄	1	504	yes	—
59	C₂²×C₄×C₈×C₉	C₂⁴	1	168	yes	—
60	C₂×C₄³×C₉	C₄²	1	168	yes	—
61	C₂×C₄³×C₉	C₂²×C₄	1	252	yes	—
62	C₂×C₄³×C₉	C₂⁴	1	28	yes	—
63	C₄²×C₈×C₉	C₂²×C₄	1	1344	yes	—
64	C₄²×C₈×C₉	C₂⁴	1	192	yes	—
65	C₂×C₈²×C₉	C₂²×C₄	1	3584	yes	direct product factor
66	C₂×C₈²×C₉	C₂⁴	1	256	yes	—
67	C₂⁵×C₃×C₈	C₂×C₃×C₄	1	12	yes	—
68	C₂⁴×C₃×C₄²	C₂×C₃×C₄	1	6	yes	—
69	C₂⁴×C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
70	C₂³×C₃×C₄×C₈	C₃×C₈	1	384	yes	—
71	C₂³×C₃×C₄×C₈	C₂×C₃×C₄	1	336	yes	—
72	C₂³×C₃×C₄×C₈	C₂×C₃×C₄	1	84	yes	—
73	C₂³×C₃×C₄×C₈	C₂×C₃×C₄	1	192	yes	—
74	C₂³×C₃×C₄×C₈	C₂³×C₃	1	84	yes	—
75	C₂²×C₃×C₄³	C₂×C₃×C₄	1	42	yes	—
76	C₂²×C₃×C₄³	C₂³×C₃	1	14	yes	—
77	C₂×C₃×C₄²×C₈	C₂×C₃×C₄	1	1008	yes	—
78	C₂×C₃×C₄²×C₈	C₂³×C₃	1	336	yes	—
79	C₂²×C₃×C₈²	C₂×C₃×C₄	1	1792	yes	—
80	C₂²×C₃×C₈²	C₂³×C₃	1	448	yes	—
81	C₃×C₄×C₈²	C₂³×C₃	1	512	yes	—
82	C₂⁶×C₉	C₂×C₄²	1	1	yes	characteristic
83	C₂⁴×C₄×C₉	C₄×C₈	1	192	yes	—
84	C₂⁴×C₄×C₉	C₂×C₄²	1	21	yes	—
85	C₂⁴×C₄×C₉	C₂×C₄²	1	48	yes	—
86	C₂⁴×C₄×C₉	C₂×C₄²	1	56	yes	—
87	C₂⁴×C₄×C₉	C₂²×C₈	1	96	yes	—
88	C₂⁴×C₄×C₉	C₂³×C₄	1	21	yes	—
89	C₂³×C₈×C₉	C₄×C₈	1	3072	yes	direct product factor
90	C₂³×C₈×C₉	C₂×C₄²	1	1344	yes	—
91	C₂³×C₈×C₉	C₂²×C₈	1	2688	yes	—
92	C₂³×C₈×C₉	C₂³×C₄	1	336	yes	—
93	C₂²×C₄²×C₉	C₄×C₈	1	1344	yes	—
94	C₂²×C₄²×C₉	C₂×C₄²	1	42	yes	—
95	C₂²×C₄²×C₉	C₂×C₄²	1	336	yes	—
96	C₂²×C₄²×C₉	C₂×C₄²	1	504	yes	—
97	C₂²×C₄²×C₉	C₂²×C₈	1	1344	yes	—
98	C₂²×C₄²×C₉	C₂³×C₄	1	63	yes	—
99	C₂²×C₄²×C₉	C₂³×C₄	1	112	yes	—
100	C₂²×C₄²×C₉	C₂³×C₄	1	168	yes	—
101	C₂²×C₄²×C₉	C₂⁵	1	7	yes	—
102	C₂×C₄×C₈×C₉	C₂×C₄²	1	4032	yes	—
103	C₂×C₄×C₈×C₉	C₂²×C₈	1	10752	yes	direct product factor
104	C₂×C₄×C₈×C₉	C₂³×C₄	1	768	yes	—
105	C₂×C₄×C₈×C₉	C₂³×C₄	1	1344	yes	—
106	C₂×C₄×C₈×C₉	C₂³×C₄	1	336	yes	—
107	C₂×C₄×C₈×C₉	C₂⁵	1	48	yes	—
108	C₄³×C₉	C₂×C₄²	1	336	yes	—
109	C₄³×C₉	C₂³×C₄	1	168	yes	—
110	C₄³×C₉	C₂⁵	1	8	yes	—
111	C₈²×C₉	C₂³×C₄	1	1024	yes	direct product factor
112	C₂⁴×C₄×C₈	C₄×C₉	1	12	yes	—
113	C₂⁴×C₄×C₈	C₂²×C₉	1	6	yes	—
114	C₂³×C₄³	C₂²×C₉	1	1	yes	characteristic
115	C₂²×C₄²×C₈	C₄×C₉	1	84	yes	—
116	C₂²×C₄²×C₈	C₂²×C₉	1	84	yes	—
117	C₂³×C₈²	C₄×C₉	1	128	yes	direct product factor
118	C₂³×C₈²	C₂²×C₉	1	112	yes	—
119	C₂×C₄×C₈²	C₂²×C₉	1	448	yes	direct product factor
120	C₂⁵×C₃×C₄	C₃×C₄²	1	4	yes	—
121	C₂⁵×C₃×C₄	C₂²×C₃×C₄	1	3	yes	—
122	C₂⁴×C₃×C₈	C₃×C₄²	1	192	yes	—
123	C₂⁴×C₃×C₈	C₂×C₃×C₈	1	384	yes	—
124	C₂⁴×C₃×C₈	C₂²×C₃×C₄	1	168	yes	—
125	C₂³×C₃×C₄²	C₃×C₄²	1	84	yes	—
126	C₂³×C₃×C₄²	C₂×C₃×C₈	1	192	yes	—
127	C₂³×C₃×C₄²	C₂²×C₃×C₄	1	21	yes	—
128	C₂³×C₃×C₄²	C₂²×C₃×C₄	1	32	yes	—
129	C₂³×C₃×C₄²	C₂²×C₃×C₄	1	84	yes	—
130	C₂³×C₃×C₄²	C₂⁴×C₃	1	7	yes	—
131	C₂²×C₃×C₄×C₈	C₃×C₄²	1	1344	yes	—
132	C₂²×C₃×C₄×C₈	C₂×C₃×C₈	1	5376	yes	—
133	C₂²×C₃×C₄×C₈	C₂²×C₃×C₄	1	1344	yes	—
134	C₂²×C₃×C₄×C₈	C₂²×C₃×C₄	1	1344	yes	—
135	C₂²×C₃×C₄×C₈	C₂²×C₃×C₄	1	504	yes	—
136	C₂²×C₃×C₄×C₈	C₂⁴×C₃	1	168	yes	—
137	C₂×C₃×C₄³	C₃×C₄²	1	168	yes	—
138	C₂×C₃×C₄³	C₂²×C₃×C₄	1	252	yes	—
139	C₂×C₃×C₄³	C₂⁴×C₃	1	28	yes	—
140	C₃×C₄²×C₈	C₂²×C₃×C₄	1	1344	yes	—
141	C₃×C₄²×C₈	C₂⁴×C₃	1	192	yes	—
142	C₂×C₃×C₈²	C₂²×C₃×C₄	1	3584	yes	—
143	C₂×C₃×C₈²	C₂⁴×C₃	1	256	yes	—
144	C₂⁵×C₉	C₄³	1	8	yes	—
145	C₂⁵×C₉	C₂×C₄×C₈	1	48	yes	—
146	C₂⁵×C₉	C₂²×C₄²	1	7	yes	—
147	C₂³×C₄×C₉	C₈²	1	1024	yes	direct product factor
148	C₂³×C₄×C₉	C₄³	1	168	yes	—
149	C₂³×C₄×C₉	C₂×C₄×C₈	1	768	yes	—
150	C₂³×C₄×C₉	C₂×C₄×C₈	1	1344	yes	—
151	C₂³×C₄×C₉	C₂×C₄×C₈	1	336	yes	—
152	C₂³×C₄×C₉	C₂²×C₄²	1	63	yes	—
153	C₂³×C₄×C₉	C₂²×C₄²	1	112	yes	—
154	C₂³×C₄×C₉	C₂²×C₄²	1	168	yes	—
155	C₂³×C₄×C₉	C₂³×C₈	1	336	yes	—
156	C₂³×C₄×C₉	C₂⁴×C₄	1	21	yes	—
157	C₂²×C₈×C₉	C₂×C₄×C₈	1	10752	yes	direct product factor
158	C₂²×C₈×C₉	C₂²×C₄²	1	1344	yes	—
159	C₂²×C₈×C₉	C₂³×C₈	1	2688	yes	—
160	C₂²×C₈×C₉	C₂⁴×C₄	1	96	yes	—
161	C₂×C₄²×C₉	C₄³	1	336	yes	—
162	C₂×C₄²×C₉	C₂×C₄×C₈	1	4032	yes	—
163	C₂×C₄²×C₉	C₂²×C₄²	1	42	yes	—
164	C₂×C₄²×C₉	C₂²×C₄²	1	336	yes	—
165	C₂×C₄²×C₉	C₂²×C₄²	1	504	yes	—
166	C₂×C₄²×C₉	C₂³×C₈	1	1344	yes	—
167	C₂×C₄²×C₉	C₂⁴×C₄	1	21	yes	—
168	C₂×C₄²×C₉	C₂⁴×C₄	1	48	yes	—
169	C₂×C₄²×C₉	C₂⁴×C₄	1	56	yes	—
170	C₂×C₄²×C₉	C₂⁶	1	1	yes	characteristic
171	C₄×C₈×C₉	C₂²×C₄²	1	1344	yes	—
172	C₄×C₈×C₉	C₂³×C₈	1	3072	yes	direct product factor
173	C₄×C₈×C₉	C₂⁴×C₄	1	192	yes	—
174	C₂⁵×C₈	C₂×C₄×C₉	1	12	yes	—
175	C₂⁴×C₄²	C₂×C₄×C₉	1	6	yes	—
176	C₂⁴×C₄²	C₂³×C₉	1	1	yes	characteristic
177	C₂³×C₄×C₈	C₈×C₉	1	384	yes	direct product factor
178	C₂³×C₄×C₈	C₂×C₄×C₉	1	336	yes	—
179	C₂³×C₄×C₈	C₂×C₄×C₉	1	84	yes	—
180	C₂³×C₄×C₈	C₂×C₄×C₉	1	192	yes	—
181	C₂³×C₄×C₈	C₂³×C₉	1	84	yes	—
182	C₂²×C₄³	C₂×C₄×C₉	1	42	yes	—
183	C₂²×C₄³	C₂³×C₉	1	14	yes	—
184	C₂×C₄²×C₈	C₂×C₄×C₉	1	1008	yes	—
185	C₂×C₄²×C₈	C₂³×C₉	1	336	yes	—
186	C₂²×C₈²	C₂×C₄×C₉	1	1792	yes	direct product factor
187	C₂²×C₈²	C₂³×C₉	1	448	yes	—
188	C₄×C₈²	C₂³×C₉	1	512	yes	direct product factor
189	C₂⁶×C₃	C₂×C₃×C₄²	1	1	yes	characteristic
190	C₂⁴×C₃×C₄	C₃×C₄×C₈	1	192	yes	—
191	C₂⁴×C₃×C₄	C₂×C₃×C₄²	1	21	yes	—
192	C₂⁴×C₃×C₄	C₂×C₃×C₄²	1	48	yes	—
193	C₂⁴×C₃×C₄	C₂×C₃×C₄²	1	56	yes	—
194	C₂⁴×C₃×C₄	C₂²×C₃×C₈	1	96	yes	—
195	C₂⁴×C₃×C₄	C₂³×C₃×C₄	1	21	yes	—
196	C₂³×C₃×C₈	C₃×C₄×C₈	1	3072	yes	—
197	C₂³×C₃×C₈	C₂×C₃×C₄²	1	1344	yes	—
198	C₂³×C₃×C₈	C₂²×C₃×C₈	1	2688	yes	—
199	C₂³×C₃×C₈	C₂³×C₃×C₄	1	336	yes	—
200	C₂²×C₃×C₄²	C₃×C₄×C₈	1	1344	yes	—
201	C₂²×C₃×C₄²	C₂×C₃×C₄²	1	42	yes	—
202	C₂²×C₃×C₄²	C₂×C₃×C₄²	1	336	yes	—
203	C₂²×C₃×C₄²	C₂×C₃×C₄²	1	504	yes	—
204	C₂²×C₃×C₄²	C₂²×C₃×C₈	1	1344	yes	—
205	C₂²×C₃×C₄²	C₂³×C₃×C₄	1	63	yes	—
206	C₂²×C₃×C₄²	C₂³×C₃×C₄	1	112	yes	—
207	C₂²×C₃×C₄²	C₂³×C₃×C₄	1	168	yes	—
208	C₂²×C₃×C₄²	C₂⁵×C₃	1	7	yes	—
209	C₂×C₃×C₄×C₈	C₂×C₃×C₄²	1	4032	yes	—
210	C₂×C₃×C₄×C₈	C₂²×C₃×C₈	1	10752	yes	—
211	C₂×C₃×C₄×C₈	C₂³×C₃×C₄	1	768	yes	—
212	C₂×C₃×C₄×C₈	C₂³×C₃×C₄	1	1344	yes	—
213	C₂×C₃×C₄×C₈	C₂³×C₃×C₄	1	336	yes	—
214	C₂×C₃×C₄×C₈	C₂⁵×C₃	1	48	yes	—
215	C₃×C₄³	C₂×C₃×C₄²	1	336	yes	—
216	C₃×C₄³	C₂³×C₃×C₄	1	168	yes	—
217	C₃×C₄³	C₂⁵×C₃	1	8	yes	—
218	C₃×C₈²	C₂³×C₃×C₄	1	1024	yes	—
219	C₂⁴×C₉	C₂×C₈²	1	256	yes	—
220	C₂⁴×C₉	C₄²×C₈	1	192	yes	—
221	C₂⁴×C₉	C₂×C₄³	1	28	yes	—
222	C₂⁴×C₉	C₂²×C₄×C₈	1	168	yes	—
223	C₂⁴×C₉	C₂³×C₄²	1	7	yes	—
224	C₂²×C₄×C₉	C₂×C₈²	1	3584	yes	direct product factor
225	C₂²×C₄×C₉	C₄²×C₈	1	1344	yes	—
226	C₂²×C₄×C₉	C₂×C₄³	1	252	yes	—
227	C₂²×C₄×C₉	C₂²×C₄×C₈	1	1344	yes	—
228	C₂²×C₄×C₉	C₂²×C₄×C₈	1	1344	yes	—
229	C₂²×C₄×C₉	C₂²×C₄×C₈	1	504	yes	—
230	C₂²×C₄×C₉	C₂³×C₄²	1	21	yes	—
231	C₂²×C₄×C₉	C₂³×C₄²	1	32	yes	—
232	C₂²×C₄×C₉	C₂³×C₄²	1	84	yes	—
233	C₂²×C₄×C₉	C₂⁴×C₈	1	168	yes	—
234	C₂²×C₄×C₉	C₂⁵×C₄	1	3	yes	—
235	C₂×C₈×C₉	C₂²×C₄×C₈	1	5376	yes	direct product factor
236	C₂×C₈×C₉	C₂³×C₄²	1	192	yes	—
237	C₂×C₈×C₉	C₂⁴×C₈	1	384	yes	—
238	C₄²×C₉	C₂×C₄³	1	168	yes	—
239	C₄²×C₉	C₂²×C₄×C₈	1	1344	yes	—
240	C₄²×C₉	C₂³×C₄²	1	84	yes	—
241	C₄²×C₉	C₂⁴×C₈	1	192	yes	—
242	C₄²×C₉	C₂⁵×C₄	1	4	yes	—
243	C₂⁵×C₄	C₄²×C₉	1	4	yes	—
244	C₂⁵×C₄	C₂²×C₄×C₉	1	3	yes	—
245	C₂⁴×C₈	C₄²×C₉	1	192	yes	—
246	C₂⁴×C₈	C₂×C₈×C₉	1	384	yes	—
247	C₂⁴×C₈	C₂²×C₄×C₉	1	168	yes	—
248	C₂³×C₄²	C₄²×C₉	1	84	yes	—
249	C₂³×C₄²	C₂×C₈×C₉	1	192	yes	—
250	C₂³×C₄²	C₂²×C₄×C₉	1	21	yes	—
251	C₂³×C₄²	C₂²×C₄×C₉	1	32	yes	—
252	C₂³×C₄²	C₂²×C₄×C₉	1	84	yes	—
253	C₂³×C₄²	C₂⁴×C₉	1	7	yes	—
254	C₂²×C₄×C₈	C₄²×C₉	1	1344	yes	—
255	C₂²×C₄×C₈	C₂×C₈×C₉	1	5376	yes	direct product factor
256	C₂²×C₄×C₈	C₂²×C₄×C₉	1	1344	yes	—
257	C₂²×C₄×C₈	C₂²×C₄×C₉	1	1344	yes	—
258	C₂²×C₄×C₈	C₂²×C₄×C₉	1	504	yes	—
259	C₂²×C₄×C₈	C₂⁴×C₉	1	168	yes	—
260	C₂×C₄³	C₄²×C₉	1	168	yes	—
261	C₂×C₄³	C₂²×C₄×C₉	1	252	yes	—
262	C₂×C₄³	C₂⁴×C₉	1	28	yes	—
263	C₄²×C₈	C₂²×C₄×C₉	1	1344	yes	—
264	C₄²×C₈	C₂⁴×C₉	1	192	yes	—
265	C₂×C₈²	C₂²×C₄×C₉	1	3584	yes	direct product factor
266	C₂×C₈²	C₂⁴×C₉	1	256	yes	—
267	C₂⁵×C₃	C₃×C₄³	1	8	yes	—
268	C₂⁵×C₃	C₂×C₃×C₄×C₈	1	48	yes	—
269	C₂⁵×C₃	C₂²×C₃×C₄²	1	7	yes	—
270	C₂³×C₃×C₄	C₃×C₈²	1	1024	yes	—
271	C₂³×C₃×C₄	C₃×C₄³	1	168	yes	—
272	C₂³×C₃×C₄	C₂×C₃×C₄×C₈	1	768	yes	—
273	C₂³×C₃×C₄	C₂×C₃×C₄×C₈	1	1344	yes	—
274	C₂³×C₃×C₄	C₂×C₃×C₄×C₈	1	336	yes	—
275	C₂³×C₃×C₄	C₂²×C₃×C₄²	1	63	yes	—
276	C₂³×C₃×C₄	C₂²×C₃×C₄²	1	112	yes	—
277	C₂³×C₃×C₄	C₂²×C₃×C₄²	1	168	yes	—
278	C₂³×C₃×C₄	C₂³×C₃×C₈	1	336	yes	—
279	C₂³×C₃×C₄	C₂⁴×C₃×C₄	1	21	yes	—
280	C₂²×C₃×C₈	C₂×C₃×C₄×C₈	1	10752	yes	—
281	C₂²×C₃×C₈	C₂²×C₃×C₄²	1	1344	yes	—
282	C₂²×C₃×C₈	C₂³×C₃×C₈	1	2688	yes	—
283	C₂²×C₃×C₈	C₂⁴×C₃×C₄	1	96	yes	—
284	C₂×C₃×C₄²	C₃×C₄³	1	336	yes	—
285	C₂×C₃×C₄²	C₂×C₃×C₄×C₈	1	4032	yes	—
286	C₂×C₃×C₄²	C₂²×C₃×C₄²	1	42	yes	—
287	C₂×C₃×C₄²	C₂²×C₃×C₄²	1	336	yes	—
288	C₂×C₃×C₄²	C₂²×C₃×C₄²	1	504	yes	—
289	C₂×C₃×C₄²	C₂³×C₃×C₈	1	1344	yes	—
290	C₂×C₃×C₄²	C₂⁴×C₃×C₄	1	21	yes	—
291	C₂×C₃×C₄²	C₂⁴×C₃×C₄	1	48	yes	—
292	C₂×C₃×C₄²	C₂⁴×C₃×C₄	1	56	yes	—
293	C₂×C₃×C₄²	C₂⁶×C₃	1	1	yes	characteristic
294	C₃×C₄×C₈	C₂²×C₃×C₄²	1	1344	yes	—
295	C₃×C₄×C₈	C₂³×C₃×C₈	1	3072	yes	—
296	C₃×C₄×C₈	C₂⁴×C₃×C₄	1	192	yes	—
297	C₂³×C₉	C₄×C₈²	1	512	yes	direct product factor
298	C₂³×C₉	C₂²×C₈²	1	448	yes	—
299	C₂³×C₉	C₂×C₄²×C₈	1	336	yes	—
300	C₂³×C₉	C₂²×C₄³	1	14	yes	—
301	C₂³×C₉	C₂³×C₄×C₈	1	84	yes	—
302	C₂³×C₉	C₂⁴×C₄²	1	1	yes	characteristic
303	C₂×C₄×C₉	C₂²×C₈²	1	1792	yes	direct product factor
304	C₂×C₄×C₉	C₂×C₄²×C₈	1	1008	yes	—
305	C₂×C₄×C₉	C₂²×C₄³	1	42	yes	—
306	C₂×C₄×C₉	C₂³×C₄×C₈	1	336	yes	—
307	C₂×C₄×C₉	C₂³×C₄×C₈	1	84	yes	—
308	C₂×C₄×C₉	C₂³×C₄×C₈	1	192	yes	—
309	C₂×C₄×C₉	C₂⁴×C₄²	1	6	yes	—
310	C₂×C₄×C₉	C₂⁵×C₈	1	12	yes	—
311	C₈×C₉	C₂³×C₄×C₈	1	384	yes	direct product factor
312	C₂⁶	C₂×C₄²×C₉	1	1	yes	characteristic
313	C₂⁴×C₄	C₄×C₈×C₉	1	192	yes	—
314	C₂⁴×C₄	C₂×C₄²×C₉	1	21	yes	—
315	C₂⁴×C₄	C₂×C₄²×C₉	1	48	yes	—
316	C₂⁴×C₄	C₂×C₄²×C₉	1	56	yes	—
317	C₂⁴×C₄	C₂²×C₈×C₉	1	96	yes	—
318	C₂⁴×C₄	C₂³×C₄×C₉	1	21	yes	—
319	C₂³×C₈	C₄×C₈×C₉	1	3072	yes	direct product factor
320	C₂³×C₈	C₂×C₄²×C₉	1	1344	yes	—
321	C₂³×C₈	C₂²×C₈×C₉	1	2688	yes	—
322	C₂³×C₈	C₂³×C₄×C₉	1	336	yes	—
323	C₂²×C₄²	C₄×C₈×C₉	1	1344	yes	—
324	C₂²×C₄²	C₂×C₄²×C₉	1	42	yes	—
325	C₂²×C₄²	C₂×C₄²×C₉	1	336	yes	—
326	C₂²×C₄²	C₂×C₄²×C₉	1	504	yes	—
327	C₂²×C₄²	C₂²×C₈×C₉	1	1344	yes	—
328	C₂²×C₄²	C₂³×C₄×C₉	1	63	yes	—
329	C₂²×C₄²	C₂³×C₄×C₉	1	112	yes	—
330	C₂²×C₄²	C₂³×C₄×C₉	1	168	yes	—
331	C₂²×C₄²	C₂⁵×C₉	1	7	yes	—
332	C₂×C₄×C₈	C₂×C₄²×C₉	1	4032	yes	—
333	C₂×C₄×C₈	C₂²×C₈×C₉	1	10752	yes	direct product factor
334	C₂×C₄×C₈	C₂³×C₄×C₉	1	768	yes	—
335	C₂×C₄×C₈	C₂³×C₄×C₉	1	1344	yes	—
336	C₂×C₄×C₈	C₂³×C₄×C₉	1	336	yes	—
337	C₂×C₄×C₈	C₂⁵×C₉	1	48	yes	—
338	C₄³	C₂×C₄²×C₉	1	336	yes	—
339	C₄³	C₂³×C₄×C₉	1	168	yes	—
340	C₄³	C₂⁵×C₉	1	8	yes	—
341	C₈²	C₂³×C₄×C₉	1	1024	yes	direct product factor
342	C₂⁴×C₃	C₂×C₃×C₈²	1	256	yes	—
343	C₂⁴×C₃	C₃×C₄²×C₈	1	192	yes	—
344	C₂⁴×C₃	C₂×C₃×C₄³	1	28	yes	—
345	C₂⁴×C₃	C₂²×C₃×C₄×C₈	1	168	yes	—
346	C₂⁴×C₃	C₂³×C₃×C₄²	1	7	yes	—
347	C₂²×C₃×C₄	C₂×C₃×C₈²	1	3584	yes	—
348	C₂²×C₃×C₄	C₃×C₄²×C₈	1	1344	yes	—
349	C₂²×C₃×C₄	C₂×C₃×C₄³	1	252	yes	—
350	C₂²×C₃×C₄	C₂²×C₃×C₄×C₈	1	1344	yes	—
351	C₂²×C₃×C₄	C₂²×C₃×C₄×C₈	1	1344	yes	—
352	C₂²×C₃×C₄	C₂²×C₃×C₄×C₈	1	504	yes	—
353	C₂²×C₃×C₄	C₂³×C₃×C₄²	1	21	yes	—
354	C₂²×C₃×C₄	C₂³×C₃×C₄²	1	32	yes	—
355	C₂²×C₃×C₄	C₂³×C₃×C₄²	1	84	yes	—
356	C₂²×C₃×C₄	C₂⁴×C₃×C₈	1	168	yes	—
357	C₂²×C₃×C₄	C₂⁵×C₃×C₄	1	3	yes	—
358	C₂×C₃×C₈	C₂²×C₃×C₄×C₈	1	5376	yes	—
359	C₂×C₃×C₈	C₂³×C₃×C₄²	1	192	yes	—
360	C₂×C₃×C₈	C₂⁴×C₃×C₈	1	384	yes	—
361	C₃×C₄²	C₂×C₃×C₄³	1	168	yes	—
362	C₃×C₄²	C₂²×C₃×C₄×C₈	1	1344	yes	—
363	C₃×C₄²	C₂³×C₃×C₄²	1	84	yes	—
364	C₃×C₄²	C₂⁴×C₃×C₈	1	192	yes	—
365	C₃×C₄²	C₂⁵×C₃×C₄	1	4	yes	—
366	C₂²×C₉	C₂×C₄×C₈²	1	448	yes	direct product factor
367	C₂²×C₉	C₂³×C₈²	1	112	yes	—
368	C₂²×C₉	C₂²×C₄²×C₈	1	84	yes	—
369	C₂²×C₉	C₂³×C₄³	1	1	yes	characteristic
370	C₂²×C₉	C₂⁴×C₄×C₈	1	6	yes	—
371	C₄×C₉	C₂³×C₈²	1	128	yes	direct product factor
372	C₄×C₉	C₂²×C₄²×C₈	1	84	yes	—
373	C₄×C₉	C₂⁴×C₄×C₈	1	12	yes	—
374	C₂⁵	C₄³×C₉	1	8	yes	—
375	C₂⁵	C₂×C₄×C₈×C₉	1	48	yes	—
376	C₂⁵	C₂²×C₄²×C₉	1	7	yes	—
377	C₂³×C₄	C₈²×C₉	1	1024	yes	direct product factor
378	C₂³×C₄	C₄³×C₉	1	168	yes	—
379	C₂³×C₄	C₂×C₄×C₈×C₉	1	768	yes	—
380	C₂³×C₄	C₂×C₄×C₈×C₉	1	1344	yes	—
381	C₂³×C₄	C₂×C₄×C₈×C₉	1	336	yes	—
382	C₂³×C₄	C₂²×C₄²×C₉	1	63	yes	—
383	C₂³×C₄	C₂²×C₄²×C₉	1	112	yes	—
384	C₂³×C₄	C₂²×C₄²×C₉	1	168	yes	—
385	C₂³×C₄	C₂³×C₈×C₉	1	336	yes	—
386	C₂³×C₄	C₂⁴×C₄×C₉	1	21	yes	—
387	C₂²×C₈	C₂×C₄×C₈×C₉	1	10752	yes	direct product factor
388	C₂²×C₈	C₂²×C₄²×C₉	1	1344	yes	—
389	C₂²×C₈	C₂³×C₈×C₉	1	2688	yes	—
390	C₂²×C₈	C₂⁴×C₄×C₉	1	96	yes	—
391	C₂×C₄²	C₄³×C₉	1	336	yes	—
392	C₂×C₄²	C₂×C₄×C₈×C₉	1	4032	yes	—
393	C₂×C₄²	C₂²×C₄²×C₉	1	42	yes	—
394	C₂×C₄²	C₂²×C₄²×C₉	1	336	yes	—
395	C₂×C₄²	C₂²×C₄²×C₉	1	504	yes	—
396	C₂×C₄²	C₂³×C₈×C₉	1	1344	yes	—
397	C₂×C₄²	C₂⁴×C₄×C₉	1	21	yes	—
398	C₂×C₄²	C₂⁴×C₄×C₉	1	48	yes	—
399	C₂×C₄²	C₂⁴×C₄×C₉	1	56	yes	—
400	C₂×C₄²	C₂⁶×C₉	1	1	yes	characteristic
401	C₄×C₈	C₂²×C₄²×C₉	1	1344	yes	—
402	C₄×C₈	C₂³×C₈×C₉	1	3072	yes	direct product factor
403	C₄×C₈	C₂⁴×C₄×C₉	1	192	yes	—
404	C₂³×C₃	C₃×C₄×C₈²	1	512	yes	—
405	C₂³×C₃	C₂²×C₃×C₈²	1	448	yes	—
406	C₂³×C₃	C₂×C₃×C₄²×C₈	1	336	yes	—
407	C₂³×C₃	C₂²×C₃×C₄³	1	14	yes	—
408	C₂³×C₃	C₂³×C₃×C₄×C₈	1	84	yes	—
409	C₂³×C₃	C₂⁴×C₃×C₄²	1	1	yes	characteristic
410	C₂×C₃×C₄	C₂²×C₃×C₈²	1	1792	yes	—
411	C₂×C₃×C₄	C₂×C₃×C₄²×C₈	1	1008	yes	—
412	C₂×C₃×C₄	C₂²×C₃×C₄³	1	42	yes	—
413	C₂×C₃×C₄	C₂³×C₃×C₄×C₈	1	336	yes	—
414	C₂×C₃×C₄	C₂³×C₃×C₄×C₈	1	84	yes	—
415	C₂×C₃×C₄	C₂³×C₃×C₄×C₈	1	192	yes	—
416	C₂×C₃×C₄	C₂⁴×C₃×C₄²	1	6	yes	—
417	C₂×C₃×C₄	C₂⁵×C₃×C₈	1	12	yes	—
418	C₃×C₈	C₂³×C₃×C₄×C₈	1	384	yes	—
419	C₂×C₉	C₂⁴×C₈²	1	4	yes	—
420	C₂×C₉	C₂²×C₄×C₈²	1	56	yes	direct product factor
421	C₂×C₉	C₂³×C₄²×C₈	1	3	yes	—
422	C₂⁴	C₂×C₈²×C₉	1	256	yes	—
423	C₂⁴	C₄²×C₈×C₉	1	192	yes	—
424	C₂⁴	C₂×C₄³×C₉	1	28	yes	—
425	C₂⁴	C₂²×C₄×C₈×C₉	1	168	yes	—
426	C₂⁴	C₂³×C₄²×C₉	1	7	yes	—
427	C₂²×C₄	C₂×C₈²×C₉	1	3584	yes	direct product factor
428	C₂²×C₄	C₄²×C₈×C₉	1	1344	yes	—
429	C₂²×C₄	C₂×C₄³×C₉	1	252	yes	—
430	C₂²×C₄	C₂²×C₄×C₈×C₉	1	1344	yes	—
431	C₂²×C₄	C₂²×C₄×C₈×C₉	1	1344	yes	—
432	C₂²×C₄	C₂²×C₄×C₈×C₉	1	504	yes	—
433	C₂²×C₄	C₂³×C₄²×C₉	1	21	yes	—
434	C₂²×C₄	C₂³×C₄²×C₉	1	32	yes	—
435	C₂²×C₄	C₂³×C₄²×C₉	1	84	yes	—
436	C₂²×C₄	C₂⁴×C₈×C₉	1	168	yes	—
437	C₂²×C₄	C₂⁵×C₄×C₉	1	3	yes	—
438	C₂×C₈	C₂²×C₄×C₈×C₉	1	5376	yes	direct product factor
439	C₂×C₈	C₂³×C₄²×C₉	1	192	yes	—
440	C₂×C₈	C₂⁴×C₈×C₉	1	384	yes	—
441	C₄²	C₂×C₄³×C₉	1	168	yes	—
442	C₄²	C₂²×C₄×C₈×C₉	1	1344	yes	—
443	C₄²	C₂³×C₄²×C₉	1	84	yes	—
444	C₄²	C₂⁴×C₈×C₉	1	192	yes	—
445	C₄²	C₂⁵×C₄×C₉	1	4	yes	—
446	C₂²×C₃	C₂×C₃×C₄×C₈²	1	448	yes	—
447	C₂²×C₃	C₂³×C₃×C₈²	1	112	yes	—
448	C₂²×C₃	C₂²×C₃×C₄²×C₈	1	84	yes	—
449	C₂²×C₃	C₂⁴×C₃×C₄×C₈	1	6	yes	—
450	C₂²×C₃	C₂³×C₃×C₄³	1	1	yes	characteristic
451	C₃×C₄	C₂³×C₃×C₈²	1	128	yes	—
452	C₃×C₄	C₂²×C₃×C₄²×C₈	1	84	yes	—
453	C₃×C₄	C₂⁴×C₃×C₄×C₈	1	12	yes	—
454	C₉	C₂³×C₄×C₈²	1	1	yes	characteristic, direct product factor, Sylow
455	C₂³	C₄×C₈²×C₉	1	512	yes	direct product factor
456	C₂³	C₂²×C₈²×C₉	1	448	yes	—
457	C₂³	C₂×C₄²×C₈×C₉	1	336	yes	—
458	C₂³	C₂³×C₄×C₈×C₉	1	84	yes	—
459	C₂³	C₂²×C₄³×C₉	1	14	yes	—
460	C₂³	C₂⁴×C₄²×C₉	1	1	yes	characteristic
461	C₂×C₄	C₂²×C₈²×C₉	1	1792	yes	direct product factor
462	C₂×C₄	C₂×C₄²×C₈×C₉	1	1008	yes	—
463	C₂×C₄	C₂³×C₄×C₈×C₉	1	336	yes	—
464	C₂×C₄	C₂³×C₄×C₈×C₉	1	84	yes	—
465	C₂×C₄	C₂³×C₄×C₈×C₉	1	192	yes	—
466	C₂×C₄	C₂⁵×C₈×C₉	1	12	yes	—
467	C₂×C₄	C₂²×C₄³×C₉	1	42	yes	—
468	C₂×C₄	C₂⁴×C₄²×C₉	1	6	yes	—
469	C₈	C₂³×C₄×C₈×C₉	1	384	yes	direct product factor
470	C₂×C₃	C₂²×C₃×C₄×C₈²	1	56	yes	—
471	C₂×C₃	C₂⁴×C₃×C₈²	1	4	yes	—
472	C₂×C₃	C₂³×C₃×C₄²×C₈	1	3	yes	—
473	C₂²	C₂×C₄×C₈²×C₉	1	448	yes	direct product factor
474	C₂²	C₂³×C₈²×C₉	1	112	yes	—
475	C₂²	C₂²×C₄²×C₈×C₉	1	84	yes	—
476	C₂²	C₂⁴×C₄×C₈×C₉	1	6	yes	—
477	C₂²	C₂³×C₄³×C₉	1	1	yes	characteristic
478	C₄	C₂³×C₈²×C₉	1	128	yes	direct product factor
479	C₄	C₂²×C₄²×C₈×C₉	1	84	yes	—
480	C₄	C₂⁴×C₄×C₈×C₉	1	12	yes	—
481	C₃	C₂³×C₃×C₄×C₈²	1	1	yes	characteristic
482	C₂	C₂²×C₄×C₈²×C₉	1	56	yes	direct product factor
483	C₂	C₂⁴×C₈²×C₉	1	4	yes	—
484	C₂	C₂³×C₄²×C₈×C₉	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃×C₄²	C₂⁶×C₃
socle, prime radical	C₂⁶×C₃	C₂×C₃×C₄²
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂²×C₄×C₈²×C₉	C₂	direct (N × H)
10. C₂³×C₈²×C₉	C₄	direct (N × H)
12. C₂×C₄×C₈²×C₉	C₂²	direct (N × H)
21. C₂³×C₄×C₈×C₉	C₈	direct (N × H)
28. C₂²×C₈²×C₉	C₂×C₄	direct (N × H)
30. C₄×C₈²×C₉	C₂³	direct (N × H)
31. C₂³×C₄×C₈²	C₉	direct (N × H)
41. C₂²×C₄×C₈²	C₂×C₉	direct (N × H)
55. C₂²×C₄×C₈×C₉	C₂×C₈	direct (N × H)
65. C₂×C₈²×C₉	C₂²×C₄	direct (N × H)
89. C₂³×C₈×C₉	C₄×C₈	direct (N × H)
103. C₂×C₄×C₈×C₉	C₂²×C₈	direct (N × H)
111. C₈²×C₉	C₂³×C₄	direct (N × H)
117. C₂³×C₈²	C₄×C₉	direct (N × H)
119. C₂×C₄×C₈²	C₂²×C₉	direct (N × H)
147. C₂³×C₄×C₉	C₈²	direct (N × H)
157. C₂²×C₈×C₉	C₂×C₄×C₈	direct (N × H)
172. C₄×C₈×C₉	C₂³×C₈	direct (N × H)
177. C₂³×C₄×C₈	C₈×C₉	direct (N × H)
186. C₂²×C₈²	C₂×C₄×C₉	direct (N × H)
188. C₄×C₈²	C₂³×C₉	direct (N × H)
224. C₂²×C₄×C₉	C₂×C₈²	direct (N × H)
235. C₂×C₈×C₉	C₂²×C₄×C₈	direct (N × H)
255. C₂²×C₄×C₈	C₂×C₈×C₉	direct (N × H)
265. C₂×C₈²	C₂²×C₄×C₉	direct (N × H)
297. C₂³×C₉	C₄×C₈²	direct (N × H)
303. C₂×C₄×C₉	C₂²×C₈²	direct (N × H)
311. C₈×C₉	C₂³×C₄×C₈	direct (N × H)
319. C₂³×C₈	C₄×C₈×C₉	direct (N × H)
333. C₂×C₄×C₈	C₂²×C₈×C₉	direct (N × H)
341. C₈²	C₂³×C₄×C₉	direct (N × H)
366. C₂²×C₉	C₂×C₄×C₈²	direct (N × H)
371. C₄×C₉	C₂³×C₈²	direct (N × H)
377. C₂³×C₄	C₈²×C₉	direct (N × H)
387. C₂²×C₈	C₂×C₄×C₈×C₉	direct (N × H)
402. C₄×C₈	C₂³×C₈×C₉	direct (N × H)
420. C₂×C₉	C₂²×C₄×C₈²	direct (N × H)
427. C₂²×C₄	C₂×C₈²×C₉	direct (N × H)
438. C₂×C₈	C₂²×C₄×C₈×C₉	direct (N × H)
454. C₉	C₂³×C₄×C₈²	direct (N × H)
455. C₂³	C₄×C₈²×C₉	direct (N × H)
461. C₂×C₄	C₂²×C₈²×C₉	direct (N × H)
469. C₈	C₂³×C₄×C₈×C₉	direct (N × H)
473. C₂²	C₂×C₄×C₈²×C₉	direct (N × H)
478. C₄	C₂³×C₈²×C₉	direct (N × H)
482. C₂	C₂²×C₄×C₈²×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
C₂³×C₄²×C₈×C₉	2
C₂⁴×C₈²×C₉	2
C₂²×C₄×C₈²×C₉	2
C₂³×C₃×C₄×C₈²	3

Subgroups — C23×C4×C82×C9 #72196233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₄×C₈²×C₉ #72196233