Subgroups — C₂⁴×C₃×C₈²×C₉ #72204708

Order 27648.

340690 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃×C₄×C₈×C₉	C₂	1	3	yes	maximal
2	C₂³×C₃×C₈²×C₉	C₂	1	60	yes	maximal, direct product factor
3	C₂⁴×C₈²×C₉	C₃	1	3	yes	maximal, direct product factor
4	C₂⁴×C₃²×C₈²	C₃	1	1	yes	maximal, characteristic
5	C₂⁴×C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
6	C₂⁵×C₃×C₈×C₉	C₄	1	6	yes	—
7	C₂³×C₃×C₄×C₈×C₉	C₄	1	90	yes	—
8	C₂³×C₃×C₄×C₈×C₉	C₂²	1	90	yes	—
9	C₂²×C₃×C₈²×C₉	C₂²	1	560	yes	direct product factor
10	C₂⁴×C₃²×C₄×C₈	C₂×C₃	1	3	yes	—
11	C₂⁴×C₄×C₈×C₉	C₂×C₃	1	9	yes	—
12	C₂³×C₃²×C₈²	C₂×C₃	1	60	yes	—
13	C₂³×C₈²×C₉	C₂×C₃	1	180	yes	direct product factor
14	C₂⁵×C₃×C₄×C₉	C₂×C₄	1	3	yes	—
15	C₂³×C₃×C₄²×C₉	C₂×C₄	1	45	yes	—
16	C₂³×C₃×C₄²×C₉	C₂³	1	15	yes	—
17	C₂⁴×C₃×C₈×C₉	C₈	1	192	yes	direct product factor
18	C₂⁴×C₃×C₈×C₉	C₂×C₄	1	180	yes	—
19	C₂²×C₃×C₄×C₈×C₉	C₂×C₄	1	1260	yes	—
20	C₂²×C₃×C₄×C₈×C₉	C₂³	1	420	yes	—
21	C₂×C₃×C₈²×C₉	C₂³	1	960	yes	direct product factor
22	C₂⁴×C₃×C₈²	C₉	1	3	yes	direct product factor
23	C₂⁴×C₃×C₈²	C₃²	1	1	yes	characteristic
24	C₂⁴×C₄²×C₉	C₂²×C₃	1	3	yes	—
25	C₂⁴×C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
26	C₂⁵×C₃²×C₈	C₃×C₄	1	6	yes	—
27	C₂⁵×C₈×C₉	C₃×C₄	1	18	yes	—
28	C₂³×C₃²×C₄×C₈	C₃×C₄	1	90	yes	—
29	C₂³×C₃²×C₄×C₈	C₂²×C₃	1	90	yes	—
30	C₂³×C₄×C₈×C₉	C₃×C₄	1	270	yes	—
31	C₂³×C₄×C₈×C₉	C₂²×C₃	1	270	yes	—
32	C₂²×C₈²×C₉	C₂²×C₃	1	1680	yes	direct product factor
33	C₂²×C₃²×C₈²	C₂²×C₃	1	560	yes	—
34	C₂⁴×C₃×C₄×C₈	C₂×C₉	1	9	yes	—
35	C₂⁴×C₃×C₄×C₈	C₂×C₃²	1	3	yes	—
36	C₂³×C₃×C₈²	C₂×C₉	1	180	yes	direct product factor
37	C₂³×C₃×C₈²	C₂×C₃²	1	60	yes	—
38	C₂⁴×C₈²	C₃×C₉	1	1	yes	characteristic, direct product factor, Sylow
39	C₂⁶×C₃×C₉	C₄²	1	1	yes	characteristic
40	C₂⁴×C₃×C₄×C₉	C₄²	1	45	yes	—
41	C₂⁴×C₃×C₄×C₉	C₂×C₈	1	96	yes	—
42	C₂⁴×C₃×C₄×C₉	C₂²×C₄	1	45	yes	—
43	C₂³×C₃×C₈×C₉	C₂×C₈	1	2880	yes	direct product factor
44	C₂³×C₃×C₈×C₉	C₂²×C₄	1	840	yes	—
45	C₂²×C₃×C₄²×C₉	C₄²	1	210	yes	—
46	C₂²×C₃×C₄²×C₉	C₂²×C₄	1	315	yes	—
47	C₂²×C₃×C₄²×C₉	C₂⁴	1	35	yes	—
48	C₂×C₃×C₄×C₈×C₉	C₂²×C₄	1	2520	yes	—
49	C₂×C₃×C₄×C₈×C₉	C₂⁴	1	360	yes	—
50	C₃×C₈²×C₉	C₂⁴	1	256	yes	direct product factor
51	C₂⁵×C₃²×C₄	C₂×C₃×C₄	1	3	yes	—
52	C₂⁴×C₃²×C₈	C₃×C₈	1	192	yes	—
53	C₂⁴×C₃²×C₈	C₂×C₃×C₄	1	180	yes	—
54	C₂³×C₃²×C₄²	C₂×C₃×C₄	1	45	yes	—
55	C₂³×C₃²×C₄²	C₂³×C₃	1	15	yes	—
56	C₂²×C₃²×C₄×C₈	C₂×C₃×C₄	1	1260	yes	—
57	C₂²×C₃²×C₄×C₈	C₂³×C₃	1	420	yes	—
58	C₂×C₃²×C₈²	C₂³×C₃	1	960	yes	—
59	C₂⁵×C₄×C₉	C₂×C₃×C₄	1	9	yes	—
60	C₂⁴×C₈×C₉	C₃×C₈	1	576	yes	direct product factor
61	C₂⁴×C₈×C₉	C₂×C₃×C₄	1	540	yes	—
62	C₂³×C₄²×C₉	C₂×C₃×C₄	1	135	yes	—
63	C₂³×C₄²×C₉	C₂³×C₃	1	45	yes	—
64	C₂²×C₄×C₈×C₉	C₂×C₃×C₄	1	3780	yes	—
65	C₂²×C₄×C₈×C₉	C₂³×C₃	1	1260	yes	—
66	C₂×C₈²×C₉	C₂³×C₃	1	2880	yes	direct product factor
67	C₂⁵×C₃×C₉	C₄×C₈	1	48	yes	—
68	C₂⁵×C₃×C₉	C₂×C₄²	1	15	yes	—
69	C₂³×C₃×C₄×C₉	C₄×C₈	1	720	yes	—
70	C₂³×C₃×C₄×C₉	C₂×C₄²	1	315	yes	—
71	C₂³×C₃×C₄×C₉	C₂²×C₈	1	720	yes	—
72	C₂³×C₃×C₄×C₉	C₂³×C₄	1	105	yes	—
73	C₂²×C₃×C₈×C₉	C₂²×C₈	1	6720	yes	direct product factor
74	C₂²×C₃×C₈×C₉	C₂³×C₄	1	720	yes	—
75	C₂×C₃×C₄²×C₉	C₂×C₄²	1	630	yes	—
76	C₂×C₃×C₄²×C₉	C₂³×C₄	1	315	yes	—
77	C₂×C₃×C₄²×C₉	C₂⁵	1	15	yes	—
78	C₃×C₄×C₈×C₉	C₂³×C₄	1	720	yes	—
79	C₃×C₄×C₈×C₉	C₂⁵	1	48	yes	—
80	C₂⁵×C₃×C₈	C₄×C₉	1	18	yes	—
81	C₂⁵×C₃×C₈	C₃²×C₄	1	6	yes	—
82	C₂⁴×C₃×C₄²	C₂²×C₉	1	3	yes	—
83	C₂⁴×C₃×C₄²	C₂²×C₃²	1	1	yes	characteristic
84	C₂³×C₃×C₄×C₈	C₄×C₉	1	270	yes	—
85	C₂³×C₃×C₄×C₈	C₂²×C₉	1	270	yes	—
86	C₂³×C₃×C₄×C₈	C₃²×C₄	1	90	yes	—
87	C₂³×C₃×C₄×C₈	C₂²×C₃²	1	90	yes	—
88	C₂²×C₃×C₈²	C₂²×C₉	1	1680	yes	direct product factor
89	C₂²×C₃×C₈²	C₂²×C₃²	1	560	yes	—
90	C₂⁶×C₃²	C₃×C₄²	1	1	yes	characteristic
91	C₂⁴×C₃²×C₄	C₃×C₄²	1	45	yes	—
92	C₂⁴×C₃²×C₄	C₂×C₃×C₈	1	96	yes	—
93	C₂⁴×C₃²×C₄	C₂²×C₃×C₄	1	45	yes	—
94	C₂⁶×C₉	C₃×C₄²	1	3	yes	—
95	C₂³×C₃²×C₈	C₂×C₃×C₈	1	2880	yes	—
96	C₂³×C₃²×C₈	C₂²×C₃×C₄	1	840	yes	—
97	C₂²×C₃²×C₄²	C₃×C₄²	1	210	yes	—
98	C₂²×C₃²×C₄²	C₂²×C₃×C₄	1	315	yes	—
99	C₂²×C₃²×C₄²	C₂⁴×C₃	1	35	yes	—
100	C₂⁴×C₄×C₉	C₃×C₄²	1	135	yes	—
101	C₂⁴×C₄×C₉	C₂×C₃×C₈	1	288	yes	—
102	C₂⁴×C₄×C₉	C₂²×C₃×C₄	1	135	yes	—
103	C₂×C₃²×C₄×C₈	C₂²×C₃×C₄	1	2520	yes	—
104	C₂×C₃²×C₄×C₈	C₂⁴×C₃	1	360	yes	—
105	C₂³×C₈×C₉	C₂×C₃×C₈	1	8640	yes	direct product factor
106	C₂³×C₈×C₉	C₂²×C₃×C₄	1	2520	yes	—
107	C₂²×C₄²×C₉	C₃×C₄²	1	630	yes	—
108	C₂²×C₄²×C₉	C₂²×C₃×C₄	1	945	yes	—
109	C₂²×C₄²×C₉	C₂⁴×C₃	1	105	yes	—
110	C₃²×C₈²	C₂⁴×C₃	1	256	yes	—
111	C₂×C₄×C₈×C₉	C₂²×C₃×C₄	1	7560	yes	—
112	C₂×C₄×C₈×C₉	C₂⁴×C₃	1	1080	yes	—
113	C₈²×C₉	C₂⁴×C₃	1	768	yes	direct product factor
114	C₂⁴×C₄×C₈	C₂×C₃×C₉	1	3	yes	—
115	C₂³×C₈²	C₂×C₃×C₉	1	60	yes	direct product factor
116	C₂⁴×C₃×C₉	C₈²	1	256	yes	direct product factor
117	C₂⁴×C₃×C₉	C₂×C₄×C₈	1	360	yes	—
118	C₂⁴×C₃×C₉	C₂²×C₄²	1	35	yes	—
119	C₂²×C₃×C₄×C₉	C₂×C₄×C₈	1	2520	yes	—
120	C₂²×C₃×C₄×C₉	C₂²×C₄²	1	315	yes	—
121	C₂²×C₃×C₄×C₉	C₂³×C₈	1	840	yes	—
122	C₂²×C₃×C₄×C₉	C₂⁴×C₄	1	45	yes	—
123	C₂×C₃×C₈×C₉	C₂³×C₈	1	2880	yes	direct product factor
124	C₂×C₃×C₈×C₉	C₂⁴×C₄	1	96	yes	—
125	C₃×C₄²×C₉	C₂²×C₄²	1	210	yes	—
126	C₃×C₄²×C₉	C₂⁴×C₄	1	45	yes	—
127	C₃×C₄²×C₉	C₂⁶	1	1	yes	characteristic
128	C₂⁵×C₃×C₄	C₂×C₄×C₉	1	9	yes	—
129	C₂⁵×C₃×C₄	C₂×C₃²×C₄	1	3	yes	—
130	C₂⁴×C₃×C₈	C₈×C₉	1	576	yes	direct product factor
131	C₂⁴×C₃×C₈	C₂×C₄×C₉	1	540	yes	—
132	C₂⁴×C₃×C₈	C₃²×C₈	1	192	yes	—
133	C₂⁴×C₃×C₈	C₂×C₃²×C₄	1	180	yes	—
134	C₂³×C₃×C₄²	C₂×C₄×C₉	1	135	yes	—
135	C₂³×C₃×C₄²	C₂³×C₉	1	45	yes	—
136	C₂³×C₃×C₄²	C₂×C₃²×C₄	1	45	yes	—
137	C₂³×C₃×C₄²	C₂³×C₃²	1	15	yes	—
138	C₂²×C₃×C₄×C₈	C₂×C₄×C₉	1	3780	yes	—
139	C₂²×C₃×C₄×C₈	C₂³×C₉	1	1260	yes	—
140	C₂²×C₃×C₄×C₈	C₂×C₃²×C₄	1	1260	yes	—
141	C₂²×C₃×C₄×C₈	C₂³×C₃²	1	420	yes	—
142	C₂×C₃×C₈²	C₂³×C₉	1	2880	yes	direct product factor
143	C₂×C₃×C₈²	C₂³×C₃²	1	960	yes	—
144	C₂⁵×C₃²	C₃×C₄×C₈	1	48	yes	—
145	C₂⁵×C₃²	C₂×C₃×C₄²	1	15	yes	—
146	C₂³×C₃²×C₄	C₃×C₄×C₈	1	720	yes	—
147	C₂³×C₃²×C₄	C₂×C₃×C₄²	1	315	yes	—
148	C₂³×C₃²×C₄	C₂²×C₃×C₈	1	720	yes	—
149	C₂³×C₃²×C₄	C₂³×C₃×C₄	1	105	yes	—
150	C₂⁵×C₉	C₃×C₄×C₈	1	144	yes	—
151	C₂⁵×C₉	C₂×C₃×C₄²	1	45	yes	—
152	C₂²×C₃²×C₈	C₂²×C₃×C₈	1	6720	yes	—
153	C₂²×C₃²×C₈	C₂³×C₃×C₄	1	720	yes	—
154	C₂×C₃²×C₄²	C₂×C₃×C₄²	1	630	yes	—
155	C₂×C₃²×C₄²	C₂³×C₃×C₄	1	315	yes	—
156	C₂×C₃²×C₄²	C₂⁵×C₃	1	15	yes	—
157	C₂³×C₄×C₉	C₃×C₄×C₈	1	2160	yes	—
158	C₂³×C₄×C₉	C₂×C₃×C₄²	1	945	yes	—
159	C₂³×C₄×C₉	C₂²×C₃×C₈	1	2160	yes	—
160	C₂³×C₄×C₉	C₂³×C₃×C₄	1	315	yes	—
161	C₃²×C₄×C₈	C₂³×C₃×C₄	1	720	yes	—
162	C₃²×C₄×C₈	C₂⁵×C₃	1	48	yes	—
163	C₂²×C₈×C₉	C₂²×C₃×C₈	1	20160	yes	direct product factor
164	C₂²×C₈×C₉	C₂³×C₃×C₄	1	2160	yes	—
165	C₂×C₄²×C₉	C₂×C₃×C₄²	1	1890	yes	—
166	C₂×C₄²×C₉	C₂³×C₃×C₄	1	945	yes	—
167	C₂×C₄²×C₉	C₂⁵×C₃	1	45	yes	—
168	C₄×C₈×C₉	C₂³×C₃×C₄	1	2160	yes	—
169	C₄×C₈×C₉	C₂⁵×C₃	1	144	yes	—
170	C₂⁵×C₈	C₃×C₄×C₉	1	6	yes	—
171	C₂⁴×C₄²	C₂²×C₃×C₉	1	1	yes	characteristic
172	C₂³×C₄×C₈	C₃×C₄×C₉	1	90	yes	—
173	C₂³×C₄×C₈	C₂²×C₃×C₉	1	90	yes	—
174	C₂²×C₈²	C₂²×C₃×C₉	1	560	yes	direct product factor
175	C₂³×C₃×C₉	C₂×C₈²	1	960	yes	direct product factor
176	C₂³×C₃×C₉	C₂²×C₄×C₈	1	420	yes	—
177	C₂³×C₃×C₉	C₂³×C₄²	1	15	yes	—
178	C₂×C₃×C₄×C₉	C₂²×C₄×C₈	1	1260	yes	—
179	C₂×C₃×C₄×C₉	C₂³×C₄²	1	45	yes	—
180	C₂×C₃×C₄×C₉	C₂⁴×C₈	1	180	yes	—
181	C₂×C₃×C₄×C₉	C₂⁵×C₄	1	3	yes	—
182	C₃×C₈×C₉	C₂⁴×C₈	1	192	yes	direct product factor
183	C₂⁶×C₃	C₄²×C₉	1	3	yes	—
184	C₂⁶×C₃	C₃²×C₄²	1	1	yes	characteristic
185	C₂⁴×C₃×C₄	C₄²×C₉	1	135	yes	—
186	C₂⁴×C₃×C₄	C₂×C₈×C₉	1	288	yes	—
187	C₂⁴×C₃×C₄	C₂²×C₄×C₉	1	135	yes	—
188	C₂⁴×C₃×C₄	C₃²×C₄²	1	45	yes	—
189	C₂⁴×C₃×C₄	C₂×C₃²×C₈	1	96	yes	—
190	C₂⁴×C₃×C₄	C₂²×C₃²×C₄	1	45	yes	—
191	C₂³×C₃×C₈	C₂×C₈×C₉	1	8640	yes	direct product factor
192	C₂³×C₃×C₈	C₂²×C₄×C₉	1	2520	yes	—
193	C₂³×C₃×C₈	C₂×C₃²×C₈	1	2880	yes	—
194	C₂³×C₃×C₈	C₂²×C₃²×C₄	1	840	yes	—
195	C₂²×C₃×C₄²	C₄²×C₉	1	630	yes	—
196	C₂²×C₃×C₄²	C₂²×C₄×C₉	1	945	yes	—
197	C₂²×C₃×C₄²	C₃²×C₄²	1	210	yes	—
198	C₂²×C₃×C₄²	C₂⁴×C₉	1	105	yes	—
199	C₂²×C₃×C₄²	C₂²×C₃²×C₄	1	315	yes	—
200	C₂²×C₃×C₄²	C₂⁴×C₃²	1	35	yes	—
201	C₂×C₃×C₄×C₈	C₂²×C₄×C₉	1	7560	yes	—
202	C₂×C₃×C₄×C₈	C₂⁴×C₉	1	1080	yes	—
203	C₂×C₃×C₄×C₈	C₂²×C₃²×C₄	1	2520	yes	—
204	C₂×C₃×C₄×C₈	C₂⁴×C₃²	1	360	yes	—
205	C₃×C₈²	C₂⁴×C₉	1	768	yes	direct product factor
206	C₃×C₈²	C₂⁴×C₃²	1	256	yes	—
207	C₂⁴×C₃²	C₃×C₈²	1	256	yes	—
208	C₂⁴×C₃²	C₂×C₃×C₄×C₈	1	360	yes	—
209	C₂⁴×C₃²	C₂²×C₃×C₄²	1	35	yes	—
210	C₂²×C₃²×C₄	C₂×C₃×C₄×C₈	1	2520	yes	—
211	C₂²×C₃²×C₄	C₂²×C₃×C₄²	1	315	yes	—
212	C₂²×C₃²×C₄	C₂³×C₃×C₈	1	840	yes	—
213	C₂²×C₃²×C₄	C₂⁴×C₃×C₄	1	45	yes	—
214	C₂⁴×C₉	C₃×C₈²	1	768	yes	direct product factor
215	C₂⁴×C₉	C₂×C₃×C₄×C₈	1	1080	yes	—
216	C₂⁴×C₉	C₂²×C₃×C₄²	1	105	yes	—
217	C₂×C₃²×C₈	C₂³×C₃×C₈	1	2880	yes	—
218	C₂×C₃²×C₈	C₂⁴×C₃×C₄	1	96	yes	—
219	C₃²×C₄²	C₂²×C₃×C₄²	1	210	yes	—
220	C₃²×C₄²	C₂⁴×C₃×C₄	1	45	yes	—
221	C₃²×C₄²	C₂⁶×C₃	1	1	yes	characteristic
222	C₂²×C₄×C₉	C₂×C₃×C₄×C₈	1	7560	yes	—
223	C₂²×C₄×C₉	C₂²×C₃×C₄²	1	945	yes	—
224	C₂²×C₄×C₉	C₂³×C₃×C₈	1	2520	yes	—
225	C₂²×C₄×C₉	C₂⁴×C₃×C₄	1	135	yes	—
226	C₂×C₈×C₉	C₂³×C₃×C₈	1	8640	yes	direct product factor
227	C₂×C₈×C₉	C₂⁴×C₃×C₄	1	288	yes	—
228	C₄²×C₉	C₂²×C₃×C₄²	1	630	yes	—
229	C₄²×C₉	C₂⁴×C₃×C₄	1	135	yes	—
230	C₄²×C₉	C₂⁶×C₃	1	3	yes	—
231	C₂⁵×C₄	C₂×C₃×C₄×C₉	1	3	yes	—
232	C₂⁴×C₈	C₃×C₈×C₉	1	192	yes	direct product factor
233	C₂⁴×C₈	C₂×C₃×C₄×C₉	1	180	yes	—
234	C₂³×C₄²	C₂×C₃×C₄×C₉	1	45	yes	—
235	C₂³×C₄²	C₂³×C₃×C₉	1	15	yes	—
236	C₂²×C₄×C₈	C₂×C₃×C₄×C₉	1	1260	yes	—
237	C₂²×C₄×C₈	C₂³×C₃×C₉	1	420	yes	—
238	C₂×C₈²	C₂³×C₃×C₉	1	960	yes	direct product factor
239	C₂²×C₃×C₉	C₂²×C₈²	1	560	yes	direct product factor
240	C₂²×C₃×C₉	C₂³×C₄×C₈	1	90	yes	—
241	C₂²×C₃×C₉	C₂⁴×C₄²	1	1	yes	characteristic
242	C₃×C₄×C₉	C₂³×C₄×C₈	1	90	yes	—
243	C₃×C₄×C₉	C₂⁵×C₈	1	6	yes	—
244	C₂⁵×C₃	C₄×C₈×C₉	1	144	yes	—
245	C₂⁵×C₃	C₂×C₄²×C₉	1	45	yes	—
246	C₂⁵×C₃	C₃²×C₄×C₈	1	48	yes	—
247	C₂⁵×C₃	C₂×C₃²×C₄²	1	15	yes	—
248	C₂³×C₃×C₄	C₄×C₈×C₉	1	2160	yes	—
249	C₂³×C₃×C₄	C₂×C₄²×C₉	1	945	yes	—
250	C₂³×C₃×C₄	C₂²×C₈×C₉	1	2160	yes	—
251	C₂³×C₃×C₄	C₃²×C₄×C₈	1	720	yes	—
252	C₂³×C₃×C₄	C₂³×C₄×C₉	1	315	yes	—
253	C₂³×C₃×C₄	C₂×C₃²×C₄²	1	315	yes	—
254	C₂³×C₃×C₄	C₂²×C₃²×C₈	1	720	yes	—
255	C₂³×C₃×C₄	C₂³×C₃²×C₄	1	105	yes	—
256	C₂²×C₃×C₈	C₂²×C₈×C₉	1	20160	yes	direct product factor
257	C₂²×C₃×C₈	C₂³×C₄×C₉	1	2160	yes	—
258	C₂²×C₃×C₈	C₂²×C₃²×C₈	1	6720	yes	—
259	C₂²×C₃×C₈	C₂³×C₃²×C₄	1	720	yes	—
260	C₂×C₃×C₄²	C₂×C₄²×C₉	1	1890	yes	—
261	C₂×C₃×C₄²	C₂³×C₄×C₉	1	945	yes	—
262	C₂×C₃×C₄²	C₂×C₃²×C₄²	1	630	yes	—
263	C₂×C₃×C₄²	C₂⁵×C₉	1	45	yes	—
264	C₂×C₃×C₄²	C₂³×C₃²×C₄	1	315	yes	—
265	C₂×C₃×C₄²	C₂⁵×C₃²	1	15	yes	—
266	C₃×C₄×C₈	C₂³×C₄×C₉	1	2160	yes	—
267	C₃×C₄×C₈	C₂⁵×C₉	1	144	yes	—
268	C₃×C₄×C₈	C₂³×C₃²×C₄	1	720	yes	—
269	C₃×C₄×C₈	C₂⁵×C₃²	1	48	yes	—
270	C₂³×C₃²	C₂×C₃×C₈²	1	960	yes	—
271	C₂³×C₃²	C₂²×C₃×C₄×C₈	1	420	yes	—
272	C₂³×C₃²	C₂³×C₃×C₄²	1	15	yes	—
273	C₂×C₃²×C₄	C₂²×C₃×C₄×C₈	1	1260	yes	—
274	C₂×C₃²×C₄	C₂³×C₃×C₄²	1	45	yes	—
275	C₂×C₃²×C₄	C₂⁴×C₃×C₈	1	180	yes	—
276	C₂×C₃²×C₄	C₂⁵×C₃×C₄	1	3	yes	—
277	C₂³×C₉	C₂×C₃×C₈²	1	2880	yes	direct product factor
278	C₂³×C₉	C₂²×C₃×C₄×C₈	1	1260	yes	—
279	C₂³×C₉	C₂³×C₃×C₄²	1	45	yes	—
280	C₃²×C₈	C₂⁴×C₃×C₈	1	192	yes	—
281	C₂×C₄×C₉	C₂²×C₃×C₄×C₈	1	3780	yes	—
282	C₂×C₄×C₉	C₂³×C₃×C₄²	1	135	yes	—
283	C₂×C₄×C₉	C₂⁴×C₃×C₈	1	540	yes	—
284	C₂×C₄×C₉	C₂⁵×C₃×C₄	1	9	yes	—
285	C₈×C₉	C₂⁴×C₃×C₈	1	576	yes	direct product factor
286	C₂⁶	C₃×C₄²×C₉	1	1	yes	characteristic
287	C₂⁴×C₄	C₃×C₄²×C₉	1	45	yes	—
288	C₂⁴×C₄	C₂×C₃×C₈×C₉	1	96	yes	—
289	C₂⁴×C₄	C₂²×C₃×C₄×C₉	1	45	yes	—
290	C₂³×C₈	C₂×C₃×C₈×C₉	1	2880	yes	direct product factor
291	C₂³×C₈	C₂²×C₃×C₄×C₉	1	840	yes	—
292	C₂²×C₄²	C₃×C₄²×C₉	1	210	yes	—
293	C₂²×C₄²	C₂²×C₃×C₄×C₉	1	315	yes	—
294	C₂²×C₄²	C₂⁴×C₃×C₉	1	35	yes	—
295	C₂×C₄×C₈	C₂²×C₃×C₄×C₉	1	2520	yes	—
296	C₂×C₄×C₈	C₂⁴×C₃×C₉	1	360	yes	—
297	C₈²	C₂⁴×C₃×C₉	1	256	yes	direct product factor
298	C₂×C₃×C₉	C₂³×C₈²	1	60	yes	direct product factor
299	C₂×C₃×C₉	C₂⁴×C₄×C₈	1	3	yes	—
300	C₂⁴×C₃	C₈²×C₉	1	768	yes	direct product factor
301	C₂⁴×C₃	C₂×C₄×C₈×C₉	1	1080	yes	—
302	C₂⁴×C₃	C₃²×C₈²	1	256	yes	—
303	C₂⁴×C₃	C₂²×C₄²×C₉	1	105	yes	—
304	C₂⁴×C₃	C₂×C₃²×C₄×C₈	1	360	yes	—
305	C₂⁴×C₃	C₂²×C₃²×C₄²	1	35	yes	—
306	C₂²×C₃×C₄	C₂×C₄×C₈×C₉	1	7560	yes	—
307	C₂²×C₃×C₄	C₂²×C₄²×C₉	1	945	yes	—
308	C₂²×C₃×C₄	C₂³×C₈×C₉	1	2520	yes	—
309	C₂²×C₃×C₄	C₂×C₃²×C₄×C₈	1	2520	yes	—
310	C₂²×C₃×C₄	C₂⁴×C₄×C₉	1	135	yes	—
311	C₂²×C₃×C₄	C₂²×C₃²×C₄²	1	315	yes	—
312	C₂²×C₃×C₄	C₂³×C₃²×C₈	1	840	yes	—
313	C₂²×C₃×C₄	C₂⁴×C₃²×C₄	1	45	yes	—
314	C₂×C₃×C₈	C₂³×C₈×C₉	1	8640	yes	direct product factor
315	C₂×C₃×C₈	C₂⁴×C₄×C₉	1	288	yes	—
316	C₂×C₃×C₈	C₂³×C₃²×C₈	1	2880	yes	—
317	C₂×C₃×C₈	C₂⁴×C₃²×C₄	1	96	yes	—
318	C₃×C₄²	C₂²×C₄²×C₉	1	630	yes	—
319	C₃×C₄²	C₂⁴×C₄×C₉	1	135	yes	—
320	C₃×C₄²	C₂²×C₃²×C₄²	1	210	yes	—
321	C₃×C₄²	C₂⁶×C₉	1	3	yes	—
322	C₃×C₄²	C₂⁴×C₃²×C₄	1	45	yes	—
323	C₃×C₄²	C₂⁶×C₃²	1	1	yes	characteristic
324	C₂²×C₃²	C₂²×C₃×C₈²	1	560	yes	—
325	C₂²×C₃²	C₂³×C₃×C₄×C₈	1	90	yes	—
326	C₂²×C₃²	C₂⁴×C₃×C₄²	1	1	yes	characteristic
327	C₃²×C₄	C₂³×C₃×C₄×C₈	1	90	yes	—
328	C₃²×C₄	C₂⁵×C₃×C₈	1	6	yes	—
329	C₂²×C₉	C₂²×C₃×C₈²	1	1680	yes	direct product factor
330	C₂²×C₉	C₂³×C₃×C₄×C₈	1	270	yes	—
331	C₂²×C₉	C₂⁴×C₃×C₄²	1	3	yes	—
332	C₄×C₉	C₂³×C₃×C₄×C₈	1	270	yes	—
333	C₄×C₉	C₂⁵×C₃×C₈	1	18	yes	—
334	C₂⁵	C₃×C₄×C₈×C₉	1	48	yes	—
335	C₂⁵	C₂×C₃×C₄²×C₉	1	15	yes	—
336	C₂³×C₄	C₃×C₄×C₈×C₉	1	720	yes	—
337	C₂³×C₄	C₂×C₃×C₄²×C₉	1	315	yes	—
338	C₂³×C₄	C₂²×C₃×C₈×C₉	1	720	yes	—
339	C₂³×C₄	C₂³×C₃×C₄×C₉	1	105	yes	—
340	C₂²×C₈	C₂²×C₃×C₈×C₉	1	6720	yes	direct product factor
341	C₂²×C₈	C₂³×C₃×C₄×C₉	1	720	yes	—
342	C₂×C₄²	C₂×C₃×C₄²×C₉	1	630	yes	—
343	C₂×C₄²	C₂³×C₃×C₄×C₉	1	315	yes	—
344	C₂×C₄²	C₂⁵×C₃×C₉	1	15	yes	—
345	C₄×C₈	C₂³×C₃×C₄×C₉	1	720	yes	—
346	C₄×C₈	C₂⁵×C₃×C₉	1	48	yes	—
347	C₃×C₉	C₂⁴×C₈²	1	1	yes	characteristic, direct product factor, Sylow
348	C₂³×C₃	C₂×C₈²×C₉	1	2880	yes	direct product factor
349	C₂³×C₃	C₂²×C₄×C₈×C₉	1	1260	yes	—
350	C₂³×C₃	C₂³×C₄²×C₉	1	45	yes	—
351	C₂³×C₃	C₂×C₃²×C₈²	1	960	yes	—
352	C₂³×C₃	C₂²×C₃²×C₄×C₈	1	420	yes	—
353	C₂³×C₃	C₂³×C₃²×C₄²	1	15	yes	—
354	C₂×C₃×C₄	C₂²×C₄×C₈×C₉	1	3780	yes	—
355	C₂×C₃×C₄	C₂³×C₄²×C₉	1	135	yes	—
356	C₂×C₃×C₄	C₂⁴×C₈×C₉	1	540	yes	—
357	C₂×C₃×C₄	C₂⁵×C₄×C₉	1	9	yes	—
358	C₂×C₃×C₄	C₂²×C₃²×C₄×C₈	1	1260	yes	—
359	C₂×C₃×C₄	C₂³×C₃²×C₄²	1	45	yes	—
360	C₂×C₃×C₄	C₂⁴×C₃²×C₈	1	180	yes	—
361	C₂×C₃×C₄	C₂⁵×C₃²×C₄	1	3	yes	—
362	C₃×C₈	C₂⁴×C₈×C₉	1	576	yes	direct product factor
363	C₃×C₈	C₂⁴×C₃²×C₈	1	192	yes	—
364	C₂×C₃²	C₂³×C₃×C₈²	1	60	yes	—
365	C₂×C₃²	C₂⁴×C₃×C₄×C₈	1	3	yes	—
366	C₂×C₉	C₂³×C₃×C₈²	1	180	yes	direct product factor
367	C₂×C₉	C₂⁴×C₃×C₄×C₈	1	9	yes	—
368	C₂⁴	C₃×C₈²×C₉	1	256	yes	direct product factor
369	C₂⁴	C₂×C₃×C₄×C₈×C₉	1	360	yes	—
370	C₂⁴	C₂²×C₃×C₄²×C₉	1	35	yes	—
371	C₂²×C₄	C₂×C₃×C₄×C₈×C₉	1	2520	yes	—
372	C₂²×C₄	C₂²×C₃×C₄²×C₉	1	315	yes	—
373	C₂²×C₄	C₂³×C₃×C₈×C₉	1	840	yes	—
374	C₂²×C₄	C₂⁴×C₃×C₄×C₉	1	45	yes	—
375	C₂×C₈	C₂³×C₃×C₈×C₉	1	2880	yes	direct product factor
376	C₂×C₈	C₂⁴×C₃×C₄×C₉	1	96	yes	—
377	C₄²	C₂²×C₃×C₄²×C₉	1	210	yes	—
378	C₄²	C₂⁴×C₃×C₄×C₉	1	45	yes	—
379	C₄²	C₂⁶×C₃×C₉	1	1	yes	characteristic
380	C₂²×C₃	C₂²×C₃²×C₈²	1	560	yes	—
381	C₂²×C₃	C₂²×C₈²×C₉	1	1680	yes	direct product factor
382	C₂²×C₃	C₂³×C₄×C₈×C₉	1	270	yes	—
383	C₂²×C₃	C₂³×C₃²×C₄×C₈	1	90	yes	—
384	C₂²×C₃	C₂⁴×C₃²×C₄²	1	1	yes	characteristic
385	C₂²×C₃	C₂⁴×C₄²×C₉	1	3	yes	—
386	C₃×C₄	C₂³×C₄×C₈×C₉	1	270	yes	—
387	C₃×C₄	C₂³×C₃²×C₄×C₈	1	90	yes	—
388	C₃×C₄	C₂⁵×C₈×C₉	1	18	yes	—
389	C₃×C₄	C₂⁵×C₃²×C₈	1	6	yes	—
390	C₃²	C₂⁴×C₃×C₈²	1	1	yes	characteristic
391	C₉	C₂⁴×C₃×C₈²	1	3	yes	direct product factor
392	C₂³	C₂×C₃×C₈²×C₉	1	960	yes	direct product factor
393	C₂³	C₂²×C₃×C₄×C₈×C₉	1	420	yes	—
394	C₂³	C₂³×C₃×C₄²×C₉	1	15	yes	—
395	C₂×C₄	C₂²×C₃×C₄×C₈×C₉	1	1260	yes	—
396	C₂×C₄	C₂⁴×C₃×C₈×C₉	1	180	yes	—
397	C₂×C₄	C₂³×C₃×C₄²×C₉	1	45	yes	—
398	C₂×C₄	C₂⁵×C₃×C₄×C₉	1	3	yes	—
399	C₈	C₂⁴×C₃×C₈×C₉	1	192	yes	direct product factor
400	C₂×C₃	C₂³×C₈²×C₉	1	180	yes	direct product factor
401	C₂×C₃	C₂³×C₃²×C₈²	1	60	yes	—
402	C₂×C₃	C₂⁴×C₄×C₈×C₉	1	9	yes	—
403	C₂×C₃	C₂⁴×C₃²×C₄×C₈	1	3	yes	—
404	C₂²	C₂²×C₃×C₈²×C₉	1	560	yes	direct product factor
405	C₂²	C₂³×C₃×C₄×C₈×C₉	1	90	yes	—
406	C₂²	C₂⁴×C₃×C₄²×C₉	1	1	yes	characteristic
407	C₄	C₂³×C₃×C₄×C₈×C₉	1	90	yes	—
408	C₄	C₂⁵×C₃×C₈×C₉	1	6	yes	—
409	C₃	C₂⁴×C₃²×C₈²	1	1	yes	characteristic
410	C₃	C₂⁴×C₈²×C₉	1	3	yes	direct product factor
411	C₂	C₂³×C₃×C₈²×C₉	1	60	yes	direct product factor
412	C₂	C₂⁴×C₃×C₄×C₈×C₉	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄²	C₂⁶×C₃²
socle, prime radical	C₂⁶×C₃²	C₃×C₄²
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×C₃×C₈²×C₉	C₂	direct (N × H)
3. C₂⁴×C₈²×C₉	C₃	direct (N × H)
9. C₂²×C₃×C₈²×C₉	C₂²	direct (N × H)
13. C₂³×C₈²×C₉	C₂×C₃	direct (N × H)
17. C₂⁴×C₃×C₈×C₉	C₈	direct (N × H)
21. C₂×C₃×C₈²×C₉	C₂³	direct (N × H)
22. C₂⁴×C₃×C₈²	C₉	direct (N × H)
32. C₂²×C₈²×C₉	C₂²×C₃	direct (N × H)
36. C₂³×C₃×C₈²	C₂×C₉	direct (N × H)
38. C₂⁴×C₈²	C₃×C₉	direct (N × H)
43. C₂³×C₃×C₈×C₉	C₂×C₈	direct (N × H)
50. C₃×C₈²×C₉	C₂⁴	direct (N × H)
60. C₂⁴×C₈×C₉	C₃×C₈	direct (N × H)
66. C₂×C₈²×C₉	C₂³×C₃	direct (N × H)
73. C₂²×C₃×C₈×C₉	C₂²×C₈	direct (N × H)
88. C₂²×C₃×C₈²	C₂²×C₉	direct (N × H)
105. C₂³×C₈×C₉	C₂×C₃×C₈	direct (N × H)
113. C₈²×C₉	C₂⁴×C₃	direct (N × H)
115. C₂³×C₈²	C₂×C₃×C₉	direct (N × H)
116. C₂⁴×C₃×C₉	C₈²	direct (N × H)
123. C₂×C₃×C₈×C₉	C₂³×C₈	direct (N × H)
130. C₂⁴×C₃×C₈	C₈×C₉	direct (N × H)
142. C₂×C₃×C₈²	C₂³×C₉	direct (N × H)
163. C₂²×C₈×C₉	C₂²×C₃×C₈	direct (N × H)
174. C₂²×C₈²	C₂²×C₃×C₉	direct (N × H)
175. C₂³×C₃×C₉	C₂×C₈²	direct (N × H)
182. C₃×C₈×C₉	C₂⁴×C₈	direct (N × H)
191. C₂³×C₃×C₈	C₂×C₈×C₉	direct (N × H)
205. C₃×C₈²	C₂⁴×C₉	direct (N × H)
214. C₂⁴×C₉	C₃×C₈²	direct (N × H)
226. C₂×C₈×C₉	C₂³×C₃×C₈	direct (N × H)
232. C₂⁴×C₈	C₃×C₈×C₉	direct (N × H)
238. C₂×C₈²	C₂³×C₃×C₉	direct (N × H)
239. C₂²×C₃×C₉	C₂²×C₈²	direct (N × H)
256. C₂²×C₃×C₈	C₂²×C₈×C₉	direct (N × H)
277. C₂³×C₉	C₂×C₃×C₈²	direct (N × H)
285. C₈×C₉	C₂⁴×C₃×C₈	direct (N × H)
290. C₂³×C₈	C₂×C₃×C₈×C₉	direct (N × H)
297. C₈²	C₂⁴×C₃×C₉	direct (N × H)
298. C₂×C₃×C₉	C₂³×C₈²	direct (N × H)
300. C₂⁴×C₃	C₈²×C₉	direct (N × H)
314. C₂×C₃×C₈	C₂³×C₈×C₉	direct (N × H)
329. C₂²×C₉	C₂²×C₃×C₈²	direct (N × H)
340. C₂²×C₈	C₂²×C₃×C₈×C₉	direct (N × H)
347. C₃×C₉	C₂⁴×C₈²	direct (N × H)
348. C₂³×C₃	C₂×C₈²×C₉	direct (N × H)
362. C₃×C₈	C₂⁴×C₈×C₉	direct (N × H)
366. C₂×C₉	C₂³×C₃×C₈²	direct (N × H)
368. C₂⁴	C₃×C₈²×C₉	direct (N × H)
375. C₂×C₈	C₂³×C₃×C₈×C₉	direct (N × H)
381. C₂²×C₃	C₂²×C₈²×C₉	direct (N × H)
391. C₉	C₂⁴×C₃×C₈²	direct (N × H)
392. C₂³	C₂×C₃×C₈²×C₉	direct (N × H)
399. C₈	C₂⁴×C₃×C₈×C₉	direct (N × H)
400. C₂×C₃	C₂³×C₈²×C₉	direct (N × H)
404. C₂²	C₂²×C₃×C₈²×C₉	direct (N × H)
410. C₃	C₂⁴×C₈²×C₉	direct (N × H)
411. C₂	C₂³×C₃×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
C₂⁴×C₃×C₄×C₈×C₉	2
C₂³×C₃×C₈²×C₉	2
C₂⁴×C₈²×C₉	3
C₂⁴×C₃²×C₈²	3

Subgroups — C24×C3×C82×C9 #72204708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₃×C₈²×C₉ #72204708