Subgroups — C₂×C₃×C₈×C₅₁₂ #72201821

Order 24576.

988 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₈×C₂₅₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₅₁₂	C₂	1	2	yes	maximal
3	C₃×C₈×C₅₁₂	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₈×C₅₁₂	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂×C₃×C₈×C₁₂₈	C₄	1	1	yes	characteristic
6	C₂×C₃×C₄×C₂₅₆	C₄	1	1	yes	characteristic
7	C₂×C₃×C₄×C₂₅₆	C₂²	1	1	yes	characteristic
8	C₃×C₈×C₂₅₆	C₄	1	2	yes	—
9	C₃×C₈×C₂₅₆	C₂²	1	2	yes	—
10	C₂²×C₃×C₅₁₂	C₄	1	4	yes	—
11	C₃×C₄×C₅₁₂	C₄	1	4	yes	—
12	C₃×C₄×C₅₁₂	C₂²	1	4	yes	—
13	C₂×C₈×C₂₅₆	C₂×C₃	1	1	yes	characteristic
14	C₂×C₄×C₅₁₂	C₂×C₃	1	2	yes	—
15	C₈×C₅₁₂	C₂×C₃	1	4	yes	direct product factor
16	C₂×C₃×C₈×C₆₄	C₈	1	1	yes	characteristic
17	C₂×C₃×C₄×C₁₂₈	C₈	1	1	yes	characteristic
18	C₂×C₃×C₄×C₁₂₈	C₂×C₄	1	1	yes	characteristic
19	C₃×C₈×C₁₂₈	C₈	1	2	yes	—
20	C₃×C₈×C₁₂₈	C₂×C₄	1	2	yes	—
21	C₂²×C₃×C₂₅₆	C₈	1	2	yes	—
22	C₂²×C₃×C₂₅₆	C₂×C₄	1	2	yes	—
23	C₃×C₄×C₂₅₆	C₈	1	2	yes	—
24	C₃×C₄×C₂₅₆	C₂×C₄	1	1	yes	characteristic
25	C₃×C₄×C₂₅₆	C₂×C₄	1	2	yes	—
26	C₃×C₄×C₂₅₆	C₂×C₄	1	2	yes	—
27	C₃×C₄×C₂₅₆	C₂³	1	1	yes	characteristic
28	C₂×C₃×C₅₁₂	C₈	1	16	yes	direct product factor
29	C₂×C₃×C₅₁₂	C₂×C₄	1	8	yes	—
30	C₂×C₈×C₁₂₈	C₃×C₄	1	1	yes	characteristic
31	C₂×C₄×C₂₅₆	C₃×C₄	1	1	yes	characteristic
32	C₂×C₄×C₂₅₆	C₂²×C₃	1	1	yes	characteristic
33	C₈×C₂₅₆	C₃×C₄	1	2	yes	—
34	C₈×C₂₅₆	C₂²×C₃	1	2	yes	—
35	C₂²×C₅₁₂	C₃×C₄	1	4	yes	—
36	C₄×C₅₁₂	C₃×C₄	1	4	yes	—
37	C₄×C₅₁₂	C₂²×C₃	1	4	yes	—
38	C₂×C₃×C₈×C₃₂	C₁₆	1	1	yes	characteristic
39	C₂×C₃×C₄×C₆₄	C₁₆	1	1	yes	characteristic
40	C₂×C₃×C₄×C₆₄	C₂×C₈	1	1	yes	characteristic
41	C₂²×C₃×C₁₂₈	C₁₆	1	2	yes	—
42	C₂²×C₃×C₁₂₈	C₄²	1	1	yes	characteristic
43	C₂²×C₃×C₁₂₈	C₂×C₈	1	1	yes	characteristic
44	C₃×C₈×C₆₄	C₁₆	1	2	yes	—
45	C₃×C₈×C₆₄	C₂×C₈	1	2	yes	—
46	C₃×C₄×C₁₂₈	C₁₆	1	2	yes	—
47	C₃×C₄×C₁₂₈	C₄²	1	1	yes	characteristic
48	C₃×C₄×C₁₂₈	C₂×C₈	1	1	yes	characteristic
49	C₃×C₄×C₁₂₈	C₂×C₈	1	1	yes	characteristic
50	C₃×C₄×C₁₂₈	C₂×C₈	1	2	yes	—
51	C₃×C₄×C₁₂₈	C₂²×C₄	1	1	yes	characteristic
52	C₂×C₃×C₂₅₆	C₁₆	1	8	yes	—
53	C₂×C₃×C₂₅₆	C₄²	1	2	yes	—
54	C₂×C₃×C₂₅₆	C₂×C₈	1	4	yes	—
55	C₂×C₃×C₂₅₆	C₂×C₈	1	8	yes	—
56	C₂×C₃×C₂₅₆	C₂²×C₄	1	2	yes	—
57	C₃×C₅₁₂	C₂×C₈	1	16	yes	direct product factor
58	C₂×C₈×C₆₄	C₃×C₈	1	1	yes	characteristic
59	C₂×C₄×C₁₂₈	C₃×C₈	1	1	yes	characteristic
60	C₂×C₄×C₁₂₈	C₂×C₃×C₄	1	1	yes	characteristic
61	C₈×C₁₂₈	C₃×C₈	1	2	yes	—
62	C₈×C₁₂₈	C₂×C₃×C₄	1	2	yes	—
63	C₂²×C₂₅₆	C₃×C₈	1	2	yes	—
64	C₂²×C₂₅₆	C₂×C₃×C₄	1	2	yes	—
65	C₄×C₂₅₆	C₃×C₈	1	2	yes	—
66	C₄×C₂₅₆	C₂×C₃×C₄	1	1	yes	characteristic
67	C₄×C₂₅₆	C₂×C₃×C₄	1	2	yes	—
68	C₄×C₂₅₆	C₂×C₃×C₄	1	2	yes	—
69	C₄×C₂₅₆	C₂³×C₃	1	1	yes	characteristic
70	C₂×C₅₁₂	C₃×C₈	1	16	yes	direct product factor
71	C₂×C₅₁₂	C₂×C₃×C₄	1	8	yes	—
72	C₂²×C₃×C₆₄	C₃₂	1	2	yes	—
73	C₂²×C₃×C₆₄	C₄×C₈	1	1	yes	characteristic
74	C₂²×C₃×C₆₄	C₂×C₁₆	1	1	yes	characteristic
75	C₂×C₃×C₄×C₃₂	C₃₂	1	1	yes	characteristic
76	C₂×C₃×C₄×C₃₂	C₂×C₁₆	1	1	yes	characteristic
77	C₂×C₃×C₈×C₁₆	C₃₂	1	1	yes	characteristic
78	C₂×C₃×C₁₂₈	C₃₂	1	8	yes	—
79	C₂×C₃×C₁₂₈	C₄×C₈	1	1	yes	characteristic
80	C₂×C₃×C₁₂₈	C₄×C₈	1	1	yes	characteristic
81	C₂×C₃×C₁₂₈	C₄×C₈	1	4	yes	—
82	C₂×C₃×C₁₂₈	C₂×C₁₆	1	4	yes	—
83	C₂×C₃×C₁₂₈	C₂×C₁₆	1	4	yes	—
84	C₂×C₃×C₁₂₈	C₂×C₄²	1	1	yes	characteristic
85	C₂×C₃×C₁₂₈	C₂²×C₈	1	1	yes	characteristic
86	C₃×C₄×C₆₄	C₃₂	1	2	yes	—
87	C₃×C₄×C₆₄	C₄×C₈	1	1	yes	characteristic
88	C₃×C₄×C₆₄	C₂×C₁₆	1	1	yes	characteristic
89	C₃×C₄×C₆₄	C₂×C₁₆	1	1	yes	characteristic
90	C₃×C₄×C₆₄	C₂×C₁₆	1	2	yes	—
91	C₃×C₄×C₆₄	C₂²×C₈	1	1	yes	characteristic
92	C₃×C₈×C₃₂	C₃₂	1	2	yes	—
93	C₃×C₈×C₃₂	C₂×C₁₆	1	2	yes	—
94	C₃×C₂₅₆	C₄×C₈	1	4	yes	—
95	C₃×C₂₅₆	C₂×C₁₆	1	8	yes	—
96	C₃×C₂₅₆	C₂²×C₈	1	4	yes	—
97	C₂²×C₁₂₈	C₃×C₁₆	1	2	yes	—
98	C₂²×C₁₂₈	C₃×C₄²	1	1	yes	characteristic
99	C₂²×C₁₂₈	C₂×C₃×C₈	1	1	yes	characteristic
100	C₂×C₄×C₆₄	C₃×C₁₆	1	1	yes	characteristic
101	C₂×C₄×C₆₄	C₂×C₃×C₈	1	1	yes	characteristic
102	C₂×C₈×C₃₂	C₃×C₁₆	1	1	yes	characteristic
103	C₂×C₂₅₆	C₃×C₁₆	1	8	yes	—
104	C₂×C₂₅₆	C₃×C₄²	1	2	yes	—
105	C₂×C₂₅₆	C₂×C₃×C₈	1	4	yes	—
106	C₂×C₂₅₆	C₂×C₃×C₈	1	8	yes	—
107	C₂×C₂₅₆	C₂²×C₃×C₄	1	2	yes	—
108	C₄×C₁₂₈	C₃×C₁₆	1	2	yes	—
109	C₄×C₁₂₈	C₃×C₄²	1	1	yes	characteristic
110	C₄×C₁₂₈	C₂×C₃×C₈	1	1	yes	characteristic
111	C₄×C₁₂₈	C₂×C₃×C₈	1	1	yes	characteristic
112	C₄×C₁₂₈	C₂×C₃×C₈	1	2	yes	—
113	C₄×C₁₂₈	C₂²×C₃×C₄	1	1	yes	characteristic
114	C₈×C₆₄	C₃×C₁₆	1	2	yes	—
115	C₈×C₆₄	C₂×C₃×C₈	1	2	yes	—
116	C₅₁₂	C₂×C₃×C₈	1	16	yes	direct product factor
117	C₂²×C₃×C₃₂	C₆₄	1	2	yes	—
118	C₂²×C₃×C₃₂	C₄×C₁₆	1	1	yes	characteristic
119	C₂²×C₃×C₃₂	C₂×C₃₂	1	1	yes	characteristic
120	C₂×C₃×C₄×C₁₆	C₆₄	1	1	yes	characteristic
121	C₂×C₃×C₄×C₁₆	C₂×C₃₂	1	1	yes	characteristic
122	C₂×C₃×C₈²	C₆₄	1	1	yes	characteristic
123	C₂×C₃×C₆₄	C₆₄	1	8	yes	—
124	C₂×C₃×C₆₄	C₈²	1	2	yes	—
125	C₂×C₃×C₆₄	C₄×C₁₆	1	1	yes	characteristic
126	C₂×C₃×C₆₄	C₄×C₁₆	1	1	yes	characteristic
127	C₂×C₃×C₆₄	C₄×C₁₆	1	2	yes	—
128	C₂×C₃×C₆₄	C₂×C₃₂	1	4	yes	—
129	C₂×C₃×C₆₄	C₂×C₃₂	1	4	yes	—
130	C₂×C₃×C₆₄	C₂×C₄×C₈	1	1	yes	characteristic
131	C₂×C₃×C₆₄	C₂²×C₁₆	1	1	yes	characteristic
132	C₃×C₄×C₃₂	C₆₄	1	2	yes	—
133	C₃×C₄×C₃₂	C₄×C₁₆	1	1	yes	characteristic
134	C₃×C₄×C₃₂	C₂×C₃₂	1	1	yes	characteristic
135	C₃×C₄×C₃₂	C₂×C₃₂	1	1	yes	characteristic
136	C₃×C₄×C₃₂	C₂×C₃₂	1	2	yes	—
137	C₃×C₄×C₃₂	C₂²×C₁₆	1	1	yes	characteristic
138	C₃×C₈×C₁₆	C₆₄	1	2	yes	—
139	C₃×C₈×C₁₆	C₂×C₃₂	1	2	yes	—
140	C₃×C₁₂₈	C₈²	1	2	yes	—
141	C₃×C₁₂₈	C₄×C₁₆	1	2	yes	—
142	C₃×C₁₂₈	C₂×C₃₂	1	8	yes	—
143	C₃×C₁₂₈	C₂×C₄×C₈	1	2	yes	—
144	C₃×C₁₂₈	C₂²×C₁₆	1	2	yes	—
145	C₂²×C₆₄	C₃×C₃₂	1	2	yes	—
146	C₂²×C₆₄	C₃×C₄×C₈	1	1	yes	characteristic
147	C₂²×C₆₄	C₂×C₃×C₁₆	1	1	yes	characteristic
148	C₂×C₄×C₃₂	C₃×C₃₂	1	1	yes	characteristic
149	C₂×C₄×C₃₂	C₂×C₃×C₁₆	1	1	yes	characteristic
150	C₂×C₈×C₁₆	C₃×C₃₂	1	1	yes	characteristic
151	C₂×C₁₂₈	C₃×C₃₂	1	8	yes	—
152	C₂×C₁₂₈	C₃×C₄×C₈	1	1	yes	characteristic
153	C₂×C₁₂₈	C₃×C₄×C₈	1	1	yes	characteristic
154	C₂×C₁₂₈	C₃×C₄×C₈	1	4	yes	—
155	C₂×C₁₂₈	C₂×C₃×C₁₆	1	4	yes	—
156	C₂×C₁₂₈	C₂×C₃×C₁₆	1	4	yes	—
157	C₂×C₁₂₈	C₂×C₃×C₄²	1	1	yes	characteristic
158	C₂×C₁₂₈	C₂²×C₃×C₈	1	1	yes	characteristic
159	C₄×C₆₄	C₃×C₃₂	1	2	yes	—
160	C₄×C₆₄	C₃×C₄×C₈	1	1	yes	characteristic
161	C₄×C₆₄	C₂×C₃×C₁₆	1	1	yes	characteristic
162	C₄×C₆₄	C₂×C₃×C₁₆	1	1	yes	characteristic
163	C₄×C₆₄	C₂×C₃×C₁₆	1	2	yes	—
164	C₄×C₆₄	C₂²×C₃×C₈	1	1	yes	characteristic
165	C₈×C₃₂	C₃×C₃₂	1	2	yes	—
166	C₈×C₃₂	C₂×C₃×C₁₆	1	2	yes	—
167	C₂₅₆	C₃×C₄×C₈	1	4	yes	—
168	C₂₅₆	C₂×C₃×C₁₆	1	8	yes	—
169	C₂₅₆	C₂²×C₃×C₈	1	4	yes	—
170	C₂²×C₃×C₁₆	C₁₂₈	1	2	yes	—
171	C₂²×C₃×C₁₆	C₄×C₃₂	1	1	yes	characteristic
172	C₂²×C₃×C₁₆	C₂×C₆₄	1	1	yes	characteristic
173	C₂×C₃×C₄×C₈	C₁₂₈	1	2	yes	—
174	C₂×C₃×C₄×C₈	C₂×C₆₄	1	1	yes	characteristic
175	C₂×C₃×C₃₂	C₁₂₈	1	8	yes	—
176	C₂×C₃×C₃₂	C₈×C₁₆	1	2	yes	—
177	C₂×C₃×C₃₂	C₄×C₃₂	1	1	yes	characteristic
178	C₂×C₃×C₃₂	C₄×C₃₂	1	1	yes	characteristic
179	C₂×C₃×C₃₂	C₄×C₃₂	1	2	yes	—
180	C₂×C₃×C₃₂	C₂×C₆₄	1	4	yes	—
181	C₂×C₃×C₃₂	C₂×C₆₄	1	4	yes	—
182	C₂×C₃×C₃₂	C₂×C₄×C₁₆	1	1	yes	characteristic
183	C₂×C₃×C₃₂	C₂²×C₃₂	1	1	yes	characteristic
184	C₃×C₄×C₁₆	C₁₂₈	1	2	yes	—
185	C₃×C₄×C₁₆	C₄×C₃₂	1	1	yes	characteristic
186	C₃×C₄×C₁₆	C₂×C₆₄	1	1	yes	characteristic
187	C₃×C₄×C₁₆	C₂×C₆₄	1	1	yes	characteristic
188	C₃×C₄×C₁₆	C₂×C₆₄	1	2	yes	—
189	C₃×C₄×C₁₆	C₂²×C₃₂	1	1	yes	characteristic
190	C₃×C₈²	C₁₂₈	1	2	yes	—
191	C₃×C₈²	C₂×C₆₄	1	2	yes	—
192	C₃×C₆₄	C₈×C₁₆	1	2	yes	—
193	C₃×C₆₄	C₄×C₃₂	1	2	yes	—
194	C₃×C₆₄	C₂×C₆₄	1	8	yes	—
195	C₃×C₆₄	C₂×C₈²	1	1	yes	characteristic
196	C₃×C₆₄	C₂×C₄×C₁₆	1	1	yes	characteristic
197	C₃×C₆₄	C₂²×C₃₂	1	2	yes	—
198	C₂²×C₃₂	C₃×C₆₄	1	2	yes	—
199	C₂²×C₃₂	C₃×C₄×C₁₆	1	1	yes	characteristic
200	C₂²×C₃₂	C₂×C₃×C₃₂	1	1	yes	characteristic
201	C₂×C₄×C₁₆	C₃×C₆₄	1	1	yes	characteristic
202	C₂×C₄×C₁₆	C₂×C₃×C₃₂	1	1	yes	characteristic
203	C₂×C₈²	C₃×C₆₄	1	1	yes	characteristic
204	C₂×C₆₄	C₃×C₆₄	1	8	yes	—
205	C₂×C₆₄	C₃×C₈²	1	2	yes	—
206	C₂×C₆₄	C₃×C₄×C₁₆	1	1	yes	characteristic
207	C₂×C₆₄	C₃×C₄×C₁₆	1	1	yes	characteristic
208	C₂×C₆₄	C₃×C₄×C₁₆	1	2	yes	—
209	C₂×C₆₄	C₂×C₃×C₃₂	1	4	yes	—
210	C₂×C₆₄	C₂×C₃×C₃₂	1	4	yes	—
211	C₂×C₆₄	C₂×C₃×C₄×C₈	1	1	yes	characteristic
212	C₂×C₆₄	C₂²×C₃×C₁₆	1	1	yes	characteristic
213	C₄×C₃₂	C₃×C₆₄	1	2	yes	—
214	C₄×C₃₂	C₃×C₄×C₁₆	1	1	yes	characteristic
215	C₄×C₃₂	C₂×C₃×C₃₂	1	1	yes	characteristic
216	C₄×C₃₂	C₂×C₃×C₃₂	1	1	yes	characteristic
217	C₄×C₃₂	C₂×C₃×C₃₂	1	2	yes	—
218	C₄×C₃₂	C₂²×C₃×C₁₆	1	1	yes	characteristic
219	C₈×C₁₆	C₃×C₆₄	1	2	yes	—
220	C₈×C₁₆	C₂×C₃×C₃₂	1	2	yes	—
221	C₁₂₈	C₃×C₈²	1	2	yes	—
222	C₁₂₈	C₃×C₄×C₁₆	1	2	yes	—
223	C₁₂₈	C₂×C₃×C₃₂	1	8	yes	—
224	C₁₂₈	C₂×C₃×C₄×C₈	1	2	yes	—
225	C₁₂₈	C₂²×C₃×C₁₆	1	2	yes	—
226	C₂²×C₃×C₈	C₂₅₆	1	4	yes	—
227	C₂²×C₃×C₈	C₄×C₆₄	1	1	yes	characteristic
228	C₂²×C₃×C₈	C₂×C₁₂₈	1	1	yes	characteristic
229	C₂×C₃×C₄²	C₂×C₁₂₈	1	1	yes	characteristic
230	C₂×C₃×C₁₆	C₂₅₆	1	8	yes	—
231	C₂×C₃×C₁₆	C₈×C₃₂	1	2	yes	—
232	C₂×C₃×C₁₆	C₄×C₆₄	1	1	yes	characteristic
233	C₂×C₃×C₁₆	C₄×C₆₄	1	1	yes	characteristic
234	C₂×C₃×C₁₆	C₄×C₆₄	1	2	yes	—
235	C₂×C₃×C₁₆	C₂×C₁₂₈	1	4	yes	—
236	C₂×C₃×C₁₆	C₂×C₁₂₈	1	4	yes	—
237	C₂×C₃×C₁₆	C₂×C₄×C₃₂	1	1	yes	characteristic
238	C₂×C₃×C₁₆	C₂²×C₆₄	1	1	yes	characteristic
239	C₃×C₄×C₈	C₂₅₆	1	4	yes	—
240	C₃×C₄×C₈	C₄×C₆₄	1	1	yes	characteristic
241	C₃×C₄×C₈	C₂×C₁₂₈	1	1	yes	characteristic
242	C₃×C₄×C₈	C₂×C₁₂₈	1	1	yes	characteristic
243	C₃×C₄×C₈	C₂×C₁₂₈	1	4	yes	—
244	C₃×C₄×C₈	C₂²×C₆₄	1	1	yes	characteristic
245	C₃×C₃₂	C₈×C₃₂	1	2	yes	—
246	C₃×C₃₂	C₄×C₆₄	1	2	yes	—
247	C₃×C₃₂	C₂×C₁₂₈	1	8	yes	—
248	C₃×C₃₂	C₂×C₈×C₁₆	1	1	yes	characteristic
249	C₃×C₃₂	C₂×C₄×C₃₂	1	1	yes	characteristic
250	C₃×C₃₂	C₂²×C₆₄	1	2	yes	—
251	C₂²×C₁₆	C₃×C₁₂₈	1	2	yes	—
252	C₂²×C₁₆	C₃×C₄×C₃₂	1	1	yes	characteristic
253	C₂²×C₁₆	C₂×C₃×C₆₄	1	1	yes	characteristic
254	C₂×C₄×C₈	C₃×C₁₂₈	1	2	yes	—
255	C₂×C₄×C₈	C₂×C₃×C₆₄	1	1	yes	characteristic
256	C₂×C₃₂	C₃×C₁₂₈	1	8	yes	—
257	C₂×C₃₂	C₃×C₈×C₁₆	1	2	yes	—
258	C₂×C₃₂	C₃×C₄×C₃₂	1	1	yes	characteristic
259	C₂×C₃₂	C₃×C₄×C₃₂	1	1	yes	characteristic
260	C₂×C₃₂	C₃×C₄×C₃₂	1	2	yes	—
261	C₂×C₃₂	C₂×C₃×C₆₄	1	4	yes	—
262	C₂×C₃₂	C₂×C₃×C₆₄	1	4	yes	—
263	C₂×C₃₂	C₂×C₃×C₄×C₁₆	1	1	yes	characteristic
264	C₂×C₃₂	C₂²×C₃×C₃₂	1	1	yes	characteristic
265	C₄×C₁₆	C₃×C₁₂₈	1	2	yes	—
266	C₄×C₁₆	C₃×C₄×C₃₂	1	1	yes	characteristic
267	C₄×C₁₆	C₂×C₃×C₆₄	1	1	yes	characteristic
268	C₄×C₁₆	C₂×C₃×C₆₄	1	1	yes	characteristic
269	C₄×C₁₆	C₂×C₃×C₆₄	1	2	yes	—
270	C₄×C₁₆	C₂²×C₃×C₃₂	1	1	yes	characteristic
271	C₈²	C₃×C₁₂₈	1	2	yes	—
272	C₈²	C₂×C₃×C₆₄	1	2	yes	—
273	C₆₄	C₃×C₈×C₁₆	1	2	yes	—
274	C₆₄	C₃×C₄×C₃₂	1	2	yes	—
275	C₆₄	C₂×C₃×C₆₄	1	8	yes	—
276	C₆₄	C₂×C₃×C₈²	1	1	yes	characteristic
277	C₆₄	C₂×C₃×C₄×C₁₆	1	1	yes	characteristic
278	C₆₄	C₂²×C₃×C₃₂	1	2	yes	—
279	C₂²×C₃×C₄	C₄×C₁₂₈	1	1	yes	characteristic
280	C₂²×C₃×C₄	C₂×C₂₅₆	1	2	yes	—
281	C₂×C₃×C₈	C₅₁₂	1	16	yes	direct product factor
282	C₂×C₃×C₈	C₈×C₆₄	1	2	yes	—
283	C₂×C₃×C₈	C₄×C₁₂₈	1	1	yes	characteristic
284	C₂×C₃×C₈	C₄×C₁₂₈	1	1	yes	characteristic
285	C₂×C₃×C₈	C₄×C₁₂₈	1	2	yes	—
286	C₂×C₃×C₈	C₂×C₂₅₆	1	4	yes	—
287	C₂×C₃×C₈	C₂×C₂₅₆	1	8	yes	—
288	C₂×C₃×C₈	C₂×C₄×C₆₄	1	1	yes	characteristic
289	C₂×C₃×C₈	C₂²×C₁₂₈	1	1	yes	characteristic
290	C₃×C₄²	C₄×C₁₂₈	1	1	yes	characteristic
291	C₃×C₄²	C₂×C₂₅₆	1	2	yes	—
292	C₃×C₄²	C₂²×C₁₂₈	1	1	yes	characteristic
293	C₃×C₁₆	C₈×C₆₄	1	2	yes	—
294	C₃×C₁₆	C₄×C₁₂₈	1	2	yes	—
295	C₃×C₁₆	C₂×C₂₅₆	1	8	yes	—
296	C₃×C₁₆	C₂×C₈×C₃₂	1	1	yes	characteristic
297	C₃×C₁₆	C₂×C₄×C₆₄	1	1	yes	characteristic
298	C₃×C₁₆	C₂²×C₁₂₈	1	2	yes	—
299	C₂²×C₈	C₃×C₂₅₆	1	4	yes	—
300	C₂²×C₈	C₃×C₄×C₆₄	1	1	yes	characteristic
301	C₂²×C₈	C₂×C₃×C₁₂₈	1	1	yes	characteristic
302	C₂×C₄²	C₂×C₃×C₁₂₈	1	1	yes	characteristic
303	C₂×C₁₆	C₃×C₂₅₆	1	8	yes	—
304	C₂×C₁₆	C₃×C₈×C₃₂	1	2	yes	—
305	C₂×C₁₆	C₃×C₄×C₆₄	1	1	yes	characteristic
306	C₂×C₁₆	C₃×C₄×C₆₄	1	1	yes	characteristic
307	C₂×C₁₆	C₃×C₄×C₆₄	1	2	yes	—
308	C₂×C₁₆	C₂×C₃×C₁₂₈	1	4	yes	—
309	C₂×C₁₆	C₂×C₃×C₁₂₈	1	4	yes	—
310	C₂×C₁₆	C₂×C₃×C₄×C₃₂	1	1	yes	characteristic
311	C₂×C₁₆	C₂²×C₃×C₆₄	1	1	yes	characteristic
312	C₄×C₈	C₃×C₂₅₆	1	4	yes	—
313	C₄×C₈	C₃×C₄×C₆₄	1	1	yes	characteristic
314	C₄×C₈	C₂×C₃×C₁₂₈	1	1	yes	characteristic
315	C₄×C₈	C₂×C₃×C₁₂₈	1	1	yes	characteristic
316	C₄×C₈	C₂×C₃×C₁₂₈	1	4	yes	—
317	C₄×C₈	C₂²×C₃×C₆₄	1	1	yes	characteristic
318	C₃₂	C₃×C₈×C₃₂	1	2	yes	—
319	C₃₂	C₃×C₄×C₆₄	1	2	yes	—
320	C₃₂	C₂×C₃×C₁₂₈	1	8	yes	—
321	C₃₂	C₂×C₃×C₈×C₁₆	1	1	yes	characteristic
322	C₃₂	C₂×C₃×C₄×C₃₂	1	1	yes	characteristic
323	C₃₂	C₂²×C₃×C₆₄	1	2	yes	—
324	C₂³×C₃	C₄×C₂₅₆	1	1	yes	characteristic
325	C₂×C₃×C₄	C₂×C₅₁₂	1	8	yes	—
326	C₂×C₃×C₄	C₄×C₂₅₆	1	1	yes	characteristic
327	C₂×C₃×C₄	C₄×C₂₅₆	1	2	yes	—
328	C₂×C₃×C₄	C₄×C₂₅₆	1	2	yes	—
329	C₂×C₃×C₄	C₂²×C₂₅₆	1	2	yes	—
330	C₂×C₃×C₄	C₈×C₁₂₈	1	2	yes	—
331	C₂×C₃×C₄	C₂×C₄×C₁₂₈	1	1	yes	characteristic
332	C₃×C₈	C₂×C₅₁₂	1	16	yes	direct product factor
333	C₃×C₈	C₄×C₂₅₆	1	2	yes	—
334	C₃×C₈	C₂²×C₂₅₆	1	2	yes	—
335	C₃×C₈	C₈×C₁₂₈	1	2	yes	—
336	C₃×C₈	C₂×C₄×C₁₂₈	1	1	yes	characteristic
337	C₃×C₈	C₂×C₈×C₆₄	1	1	yes	characteristic
338	C₂²×C₄	C₂×C₃×C₂₅₆	1	2	yes	—
339	C₂²×C₄	C₃×C₄×C₁₂₈	1	1	yes	characteristic
340	C₂×C₈	C₃×C₅₁₂	1	16	yes	direct product factor
341	C₂×C₈	C₂×C₃×C₂₅₆	1	4	yes	—
342	C₂×C₈	C₂×C₃×C₂₅₆	1	8	yes	—
343	C₂×C₈	C₃×C₄×C₁₂₈	1	1	yes	characteristic
344	C₂×C₈	C₃×C₄×C₁₂₈	1	1	yes	characteristic
345	C₂×C₈	C₃×C₄×C₁₂₈	1	2	yes	—
346	C₂×C₈	C₃×C₈×C₆₄	1	2	yes	—
347	C₂×C₈	C₂²×C₃×C₁₂₈	1	1	yes	characteristic
348	C₂×C₈	C₂×C₃×C₄×C₆₄	1	1	yes	characteristic
349	C₄²	C₂×C₃×C₂₅₆	1	2	yes	—
350	C₄²	C₃×C₄×C₁₂₈	1	1	yes	characteristic
351	C₄²	C₂²×C₃×C₁₂₈	1	1	yes	characteristic
352	C₁₆	C₂×C₃×C₂₅₆	1	8	yes	—
353	C₁₆	C₃×C₄×C₁₂₈	1	2	yes	—
354	C₁₆	C₃×C₈×C₆₄	1	2	yes	—
355	C₁₆	C₂²×C₃×C₁₂₈	1	2	yes	—
356	C₁₆	C₂×C₃×C₄×C₆₄	1	1	yes	characteristic
357	C₁₆	C₂×C₃×C₈×C₃₂	1	1	yes	characteristic
358	C₂²×C₃	C₄×C₅₁₂	1	4	yes	—
359	C₂²×C₃	C₈×C₂₅₆	1	2	yes	—
360	C₂²×C₃	C₂×C₄×C₂₅₆	1	1	yes	characteristic
361	C₃×C₄	C₄×C₅₁₂	1	4	yes	—
362	C₃×C₄	C₂²×C₅₁₂	1	4	yes	—
363	C₃×C₄	C₈×C₂₅₆	1	2	yes	—
364	C₃×C₄	C₂×C₄×C₂₅₆	1	1	yes	characteristic
365	C₃×C₄	C₂×C₈×C₁₂₈	1	1	yes	characteristic
366	C₂³	C₃×C₄×C₂₅₆	1	1	yes	characteristic
367	C₂×C₄	C₂×C₃×C₅₁₂	1	8	yes	—
368	C₂×C₄	C₃×C₄×C₂₅₆	1	1	yes	characteristic
369	C₂×C₄	C₃×C₄×C₂₅₆	1	2	yes	—
370	C₂×C₄	C₃×C₄×C₂₅₆	1	2	yes	—
371	C₂×C₄	C₂²×C₃×C₂₅₆	1	2	yes	—
372	C₂×C₄	C₃×C₈×C₁₂₈	1	2	yes	—
373	C₂×C₄	C₂×C₃×C₄×C₁₂₈	1	1	yes	characteristic
374	C₈	C₂×C₃×C₅₁₂	1	16	yes	direct product factor
375	C₈	C₃×C₄×C₂₅₆	1	2	yes	—
376	C₈	C₂²×C₃×C₂₅₆	1	2	yes	—
377	C₈	C₃×C₈×C₁₂₈	1	2	yes	—
378	C₈	C₂×C₃×C₄×C₁₂₈	1	1	yes	characteristic
379	C₈	C₂×C₃×C₈×C₆₄	1	1	yes	characteristic
380	C₂×C₃	C₈×C₅₁₂	1	4	yes	direct product factor
381	C₂×C₃	C₂×C₄×C₅₁₂	1	2	yes	—
382	C₂×C₃	C₂×C₈×C₂₅₆	1	1	yes	characteristic
383	C₂²	C₃×C₄×C₅₁₂	1	4	yes	—
384	C₂²	C₃×C₈×C₂₅₆	1	2	yes	—
385	C₂²	C₂×C₃×C₄×C₂₅₆	1	1	yes	characteristic
386	C₄	C₃×C₄×C₅₁₂	1	4	yes	—
387	C₄	C₂²×C₃×C₅₁₂	1	4	yes	—
388	C₄	C₃×C₈×C₂₅₆	1	2	yes	—
389	C₄	C₂×C₃×C₄×C₂₅₆	1	1	yes	characteristic
390	C₄	C₂×C₃×C₈×C₁₂₈	1	1	yes	characteristic
391	C₃	C₂×C₈×C₅₁₂	1	1	yes	characteristic, direct product factor, Sylow
392	C₂	C₃×C₈×C₅₁₂	1	4	yes	direct product factor
393	C₂	C₂×C₃×C₄×C₅₁₂	1	2	yes	—
394	C₂	C₂×C₃×C₈×C₂₅₆	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₂₅₆	C₂³×C₃
socle, prime radical	C₂³×C₃	C₄×C₂₅₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×C₈×C₅₁₂	C₂	direct (N × H)
4. C₂×C₈×C₅₁₂	C₃	direct (N × H)
15. C₈×C₅₁₂	C₂×C₃	direct (N × H)
28. C₂×C₃×C₅₁₂	C₈	direct (N × H)
57. C₃×C₅₁₂	C₂×C₈	direct (N × H)
70. C₂×C₅₁₂	C₃×C₈	direct (N × H)
116. C₅₁₂	C₂×C₃×C₈	direct (N × H)
281. C₂×C₃×C₈	C₅₁₂	direct (N × H)
332. C₃×C₈	C₂×C₅₁₂	direct (N × H)
340. C₂×C₈	C₃×C₅₁₂	direct (N × H)
374. C₈	C₂×C₃×C₅₁₂	direct (N × H)
380. C₂×C₃	C₈×C₅₁₂	direct (N × H)
391. C₃	C₂×C₈×C₅₁₂	direct (N × H)
392. C₂	C₃×C₈×C₅₁₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₈×C₂₅₆	2
C₂×C₃×C₄×C₅₁₂	2
C₃×C₈×C₅₁₂	2
C₂×C₈×C₅₁₂	3

Subgroups — C2×C3×C8×C512 #72201821

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₈×C₅₁₂ #72201821