Subgroups — C₃×C₄³×C₈×C₁₆ #72201883

Order 24576.

631068 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄³×C₈²	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄⁴×C₁₆	C₂	1	2	yes	maximal
3	C₂×C₃×C₄²×C₈×C₁₆	C₂	1	28	yes	maximal
4	C₄³×C₈×C₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃×C₄⁴×C₈	C₄	1	2	yes	—
6	C₃×C₄⁴×C₈	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₄²×C₈²	C₄	1	14	yes	—
8	C₂×C₃×C₄²×C₈²	C₂²	1	14	yes	—
9	C₂×C₃×C₄³×C₁₆	C₄	1	32	yes	—
10	C₂×C₃×C₄³×C₁₆	C₂²	1	28	yes	—
11	C₂²×C₃×C₄×C₈×C₁₆	C₂²	1	112	yes	—
12	C₃×C₄²×C₈×C₁₆	C₄	1	448	yes	direct product factor
13	C₄³×C₈²	C₂×C₃	1	1	yes	characteristic
14	C₄⁴×C₁₆	C₂×C₃	1	2	yes	—
15	C₂×C₄²×C₈×C₁₆	C₂×C₃	1	28	yes	—
16	C₃×C₄⁵	C₂×C₄	1	1	yes	characteristic
17	C₂×C₃×C₄³×C₈	C₈	1	32	yes	—
18	C₂×C₃×C₄³×C₈	C₂×C₄	1	7	yes	—
19	C₂×C₃×C₄³×C₈	C₂×C₄	1	16	yes	—
20	C₂×C₃×C₄³×C₈	C₂×C₄	1	28	yes	—
21	C₂×C₃×C₄³×C₈	C₂³	1	7	yes	—
22	C₂²×C₃×C₄×C₈²	C₂×C₄	1	84	yes	—
23	C₂²×C₃×C₄×C₈²	C₂³	1	28	yes	—
24	C₃×C₄²×C₈²	C₈	1	224	yes	—
25	C₃×C₄²×C₈²	C₂×C₄	1	224	yes	—
26	C₂²×C₃×C₄²×C₁₆	C₂×C₄	1	224	yes	—
27	C₂²×C₃×C₄²×C₁₆	C₂³	1	56	yes	—
28	C₃×C₄³×C₁₆	C₈	1	512	yes	direct product factor
29	C₃×C₄³×C₁₆	C₂×C₄	1	448	yes	—
30	C₂×C₃×C₄×C₈×C₁₆	C₂×C₄	1	2688	yes	—
31	C₂³×C₃×C₈×C₁₆	C₂³	1	64	yes	—
32	C₄⁴×C₈	C₃×C₄	1	2	yes	—
33	C₄⁴×C₈	C₂²×C₃	1	1	yes	characteristic
34	C₂×C₄²×C₈²	C₃×C₄	1	14	yes	—
35	C₂×C₄²×C₈²	C₂²×C₃	1	14	yes	—
36	C₂×C₄³×C₁₆	C₃×C₄	1	32	yes	—
37	C₂×C₄³×C₁₆	C₂²×C₃	1	28	yes	—
38	C₂²×C₄×C₈×C₁₆	C₂²×C₃	1	112	yes	—
39	C₄²×C₈×C₁₆	C₃×C₄	1	448	yes	direct product factor
40	C₂×C₃×C₄⁴	C₄²	1	8	yes	—
41	C₂×C₃×C₄⁴	C₂×C₈	1	16	yes	—
42	C₂×C₃×C₄⁴	C₂²×C₄	1	7	yes	—
43	C₂²×C₃×C₄²×C₈	C₄²	1	56	yes	—
44	C₂²×C₃×C₄²×C₈	C₂×C₈	1	224	yes	—
45	C₂²×C₃×C₄²×C₈	C₂²×C₄	1	21	yes	—
46	C₂²×C₃×C₄²×C₈	C₂²×C₄	1	56	yes	—
47	C₂²×C₃×C₄²×C₈	C₂²×C₄	1	56	yes	—
48	C₂²×C₃×C₄²×C₈	C₂⁴	1	7	yes	—
49	C₂³×C₃×C₈²	C₂²×C₄	1	56	yes	—
50	C₂³×C₃×C₈²	C₂⁴	1	8	yes	—
51	C₃×C₄³×C₈	C₁₆	1	512	yes	direct product factor
52	C₃×C₄³×C₈	C₄²	1	224	yes	—
53	C₃×C₄³×C₈	C₂×C₈	1	256	yes	—
54	C₃×C₄³×C₈	C₂×C₈	1	112	yes	—
55	C₃×C₄³×C₈	C₂×C₈	1	224	yes	—
56	C₃×C₄³×C₈	C₂²×C₄	1	112	yes	—
57	C₂×C₃×C₄×C₈²	C₄²	1	672	yes	—
58	C₂×C₃×C₄×C₈²	C₂×C₈	1	1344	yes	—
59	C₂×C₃×C₄×C₈²	C₂²×C₄	1	672	yes	—
60	C₂³×C₃×C₄×C₁₆	C₂²×C₄	1	224	yes	—
61	C₂³×C₃×C₄×C₁₆	C₂⁴	1	16	yes	—
62	C₂×C₃×C₄²×C₁₆	C₄²	1	1792	yes	—
63	C₂×C₃×C₄²×C₁₆	C₂×C₈	1	3584	yes	—
64	C₂×C₃×C₄²×C₁₆	C₂²×C₄	1	1344	yes	—
65	C₂²×C₃×C₈×C₁₆	C₂²×C₄	1	1792	yes	—
66	C₃×C₄×C₈×C₁₆	C₄²	1	7168	yes	direct product factor
67	C₄⁵	C₂×C₃×C₄	1	1	yes	characteristic
68	C₂×C₄³×C₈	C₃×C₈	1	32	yes	—
69	C₂×C₄³×C₈	C₂×C₃×C₄	1	7	yes	—
70	C₂×C₄³×C₈	C₂×C₃×C₄	1	16	yes	—
71	C₂×C₄³×C₈	C₂×C₃×C₄	1	28	yes	—
72	C₂×C₄³×C₈	C₂³×C₃	1	7	yes	—
73	C₂²×C₄×C₈²	C₂×C₃×C₄	1	84	yes	—
74	C₂²×C₄×C₈²	C₂³×C₃	1	28	yes	—
75	C₄²×C₈²	C₃×C₈	1	224	yes	—
76	C₄²×C₈²	C₂×C₃×C₄	1	224	yes	—
77	C₂²×C₄²×C₁₆	C₂×C₃×C₄	1	224	yes	—
78	C₂²×C₄²×C₁₆	C₂³×C₃	1	56	yes	—
79	C₂³×C₈×C₁₆	C₂³×C₃	1	64	yes	—
80	C₄³×C₁₆	C₃×C₈	1	512	yes	direct product factor
81	C₄³×C₁₆	C₂×C₃×C₄	1	448	yes	—
82	C₂×C₄×C₈×C₁₆	C₂×C₃×C₄	1	2688	yes	—
83	C₂⁴×C₃×C₁₆	C₂³×C₄	1	32	yes	—
84	C₂³×C₃×C₄×C₈	C₂×C₄²	1	84	yes	—
85	C₂³×C₃×C₄×C₈	C₂²×C₈	1	224	yes	—
86	C₂³×C₃×C₄×C₈	C₂³×C₄	1	7	yes	—
87	C₂³×C₃×C₄×C₈	C₂³×C₄	1	16	yes	—
88	C₂³×C₃×C₄×C₈	C₂³×C₄	1	28	yes	—
89	C₂³×C₃×C₄×C₈	C₂⁵	1	1	yes	characteristic
90	C₂²×C₃×C₄³	C₄×C₈	1	64	yes	—
91	C₂²×C₃×C₄³	C₂×C₄²	1	28	yes	—
92	C₂²×C₃×C₄³	C₂²×C₈	1	56	yes	—
93	C₂²×C₃×C₄³	C₂³×C₄	1	7	yes	—
94	C₂²×C₃×C₄×C₁₆	C₂×C₄²	1	2688	yes	—
95	C₂²×C₃×C₄×C₁₆	C₂²×C₈	1	3584	yes	—
96	C₂²×C₃×C₄×C₁₆	C₂³×C₄	1	448	yes	—
97	C₂×C₃×C₄²×C₈	C₄×C₈	1	1792	yes	—
98	C₂×C₃×C₄²×C₈	C₄×C₈	1	896	yes	—
99	C₂×C₃×C₄²×C₈	C₄×C₈	1	448	yes	—
100	C₂×C₃×C₄²×C₈	C₂×C₁₆	1	3584	yes	—
101	C₂×C₃×C₄²×C₈	C₂×C₄²	1	672	yes	—
102	C₂×C₃×C₄²×C₈	C₂×C₄²	1	168	yes	—
103	C₂×C₃×C₄²×C₈	C₂×C₄²	1	448	yes	—
104	C₂×C₃×C₄²×C₈	C₂²×C₈	1	336	yes	—
105	C₂×C₃×C₄²×C₈	C₂²×C₈	1	896	yes	—
106	C₂×C₃×C₄²×C₈	C₂²×C₈	1	672	yes	—
107	C₂×C₃×C₄²×C₈	C₂³×C₄	1	168	yes	—
108	C₂²×C₃×C₈²	C₂×C₄²	1	672	yes	—
109	C₂²×C₃×C₈²	C₂²×C₈	1	896	yes	—
110	C₂²×C₃×C₈²	C₂³×C₄	1	224	yes	—
111	C₃×C₄⁴	C₄×C₈	1	128	yes	—
112	C₃×C₄⁴	C₂×C₁₆	1	256	yes	—
113	C₃×C₄⁴	C₂×C₄²	1	56	yes	—
114	C₃×C₄⁴	C₂²×C₈	1	56	yes	—
115	C₃×C₄²×C₁₆	C₄×C₈	1	14336	yes	direct product factor
116	C₃×C₄²×C₁₆	C₂×C₄²	1	3584	yes	—
117	C₂×C₃×C₈×C₁₆	C₂×C₄²	1	7168	yes	—
118	C₃×C₄×C₈²	C₄×C₈	1	5376	yes	—
119	C₃×C₄×C₈²	C₂×C₄²	1	1792	yes	—
120	C₂³×C₄×C₁₆	C₂²×C₃×C₄	1	224	yes	—
121	C₂³×C₄×C₁₆	C₂⁴×C₃	1	16	yes	—
122	C₂²×C₄²×C₈	C₃×C₄²	1	56	yes	—
123	C₂²×C₄²×C₈	C₂×C₃×C₈	1	224	yes	—
124	C₂²×C₄²×C₈	C₂²×C₃×C₄	1	21	yes	—
125	C₂²×C₄²×C₈	C₂²×C₃×C₄	1	56	yes	—
126	C₂²×C₄²×C₈	C₂²×C₃×C₄	1	56	yes	—
127	C₂²×C₄²×C₈	C₂⁴×C₃	1	7	yes	—
128	C₂³×C₈²	C₂²×C₃×C₄	1	56	yes	—
129	C₂³×C₈²	C₂⁴×C₃	1	8	yes	—
130	C₂×C₄⁴	C₃×C₄²	1	8	yes	—
131	C₂×C₄⁴	C₂×C₃×C₈	1	16	yes	—
132	C₂×C₄⁴	C₂²×C₃×C₄	1	7	yes	—
133	C₂×C₄²×C₁₆	C₃×C₄²	1	1792	yes	—
134	C₂×C₄²×C₁₆	C₂×C₃×C₈	1	3584	yes	—
135	C₂×C₄²×C₁₆	C₂²×C₃×C₄	1	1344	yes	—
136	C₂²×C₈×C₁₆	C₂²×C₃×C₄	1	1792	yes	—
137	C₄³×C₈	C₃×C₁₆	1	512	yes	direct product factor
138	C₄³×C₈	C₃×C₄²	1	224	yes	—
139	C₄³×C₈	C₂×C₃×C₈	1	256	yes	—
140	C₄³×C₈	C₂×C₃×C₈	1	112	yes	—
141	C₄³×C₈	C₂×C₃×C₈	1	224	yes	—
142	C₄³×C₈	C₂²×C₃×C₄	1	112	yes	—
143	C₂×C₄×C₈²	C₃×C₄²	1	672	yes	—
144	C₂×C₄×C₈²	C₂×C₃×C₈	1	1344	yes	—
145	C₂×C₄×C₈²	C₂²×C₃×C₄	1	672	yes	—
146	C₄×C₈×C₁₆	C₃×C₄²	1	7168	yes	direct product factor
147	C₂⁴×C₃×C₈	C₂²×C₄²	1	14	yes	—
148	C₂⁴×C₃×C₈	C₂³×C₈	1	32	yes	—
149	C₂⁴×C₃×C₈	C₂⁴×C₄	1	2	yes	—
150	C₂³×C₃×C₄²	C₂×C₄×C₈	1	112	yes	—
151	C₂³×C₃×C₄²	C₂²×C₄²	1	14	yes	—
152	C₂³×C₃×C₄²	C₂³×C₈	1	28	yes	—
153	C₂³×C₃×C₄²	C₂⁴×C₄	1	1	yes	characteristic
154	C₂³×C₃×C₁₆	C₂²×C₄²	1	448	yes	—
155	C₂³×C₃×C₁₆	C₂³×C₈	1	512	yes	—
156	C₂²×C₃×C₄×C₈	C₄³	1	336	yes	—
157	C₂²×C₃×C₄×C₈	C₂×C₄×C₈	1	1344	yes	—
158	C₂²×C₃×C₄×C₈	C₂×C₄×C₈	1	2688	yes	—
159	C₂²×C₃×C₄×C₈	C₂×C₄×C₈	1	672	yes	—
160	C₂²×C₃×C₄×C₈	C₂²×C₁₆	1	3584	yes	—
161	C₂²×C₃×C₄×C₈	C₂²×C₄²	1	336	yes	—
162	C₂²×C₃×C₄×C₈	C₂²×C₄²	1	84	yes	—
163	C₂²×C₃×C₄×C₈	C₂²×C₄²	1	224	yes	—
164	C₂²×C₃×C₄×C₈	C₂³×C₈	1	112	yes	—
165	C₂²×C₃×C₄×C₈	C₂³×C₈	1	448	yes	—
166	C₂²×C₃×C₄×C₈	C₂³×C₈	1	224	yes	—
167	C₂²×C₃×C₄×C₈	C₂⁴×C₄	1	28	yes	—
168	C₂×C₃×C₄³	C₈²	1	512	yes	—
169	C₂×C₃×C₄³	C₄×C₁₆	1	1024	yes	—
170	C₂×C₃×C₄³	C₄³	1	112	yes	—
171	C₂×C₃×C₄³	C₂×C₄×C₈	1	112	yes	—
172	C₂×C₃×C₄³	C₂×C₄×C₈	1	448	yes	—
173	C₂×C₃×C₄³	C₂×C₄×C₈	1	448	yes	—
174	C₂×C₃×C₄³	C₂²×C₁₆	1	896	yes	—
175	C₂×C₃×C₄³	C₂²×C₄²	1	84	yes	—
176	C₂×C₃×C₄³	C₂³×C₈	1	84	yes	—
177	C₂×C₃×C₄×C₁₆	C₄³	1	3584	yes	—
178	C₂×C₃×C₄×C₁₆	C₂×C₄×C₈	1	21504	yes	—
179	C₂×C₃×C₄×C₁₆	C₂²×C₄²	1	1792	yes	—
180	C₃×C₄²×C₈	C₈²	1	3584	yes	—
181	C₃×C₄²×C₈	C₄×C₁₆	1	14336	yes	direct product factor
182	C₃×C₄²×C₈	C₄³	1	896	yes	—
183	C₃×C₄²×C₈	C₂×C₄×C₈	1	3584	yes	—
184	C₃×C₄²×C₈	C₂×C₄×C₈	1	1344	yes	—
185	C₃×C₄²×C₈	C₂×C₄×C₈	1	2688	yes	—
186	C₃×C₄²×C₈	C₂²×C₄²	1	448	yes	—
187	C₂×C₃×C₈²	C₄³	1	896	yes	—
188	C₂×C₃×C₈²	C₂×C₄×C₈	1	5376	yes	—
189	C₂×C₃×C₈²	C₂²×C₄²	1	896	yes	—
190	C₃×C₈×C₁₆	C₄³	1	4096	yes	direct product factor
191	C₂⁴×C₁₆	C₂³×C₃×C₄	1	32	yes	—
192	C₂³×C₄×C₈	C₂×C₃×C₄²	1	84	yes	—
193	C₂³×C₄×C₈	C₂²×C₃×C₈	1	224	yes	—
194	C₂³×C₄×C₈	C₂³×C₃×C₄	1	7	yes	—
195	C₂³×C₄×C₈	C₂³×C₃×C₄	1	16	yes	—
196	C₂³×C₄×C₈	C₂³×C₃×C₄	1	28	yes	—
197	C₂³×C₄×C₈	C₂⁵×C₃	1	1	yes	characteristic
198	C₂²×C₄³	C₃×C₄×C₈	1	64	yes	—
199	C₂²×C₄³	C₂×C₃×C₄²	1	28	yes	—
200	C₂²×C₄³	C₂²×C₃×C₈	1	56	yes	—
201	C₂²×C₄³	C₂³×C₃×C₄	1	7	yes	—
202	C₂²×C₄×C₁₆	C₂×C₃×C₄²	1	2688	yes	—
203	C₂²×C₄×C₁₆	C₂²×C₃×C₈	1	3584	yes	—
204	C₂²×C₄×C₁₆	C₂³×C₃×C₄	1	448	yes	—
205	C₂×C₄²×C₈	C₃×C₄×C₈	1	1792	yes	—
206	C₂×C₄²×C₈	C₃×C₄×C₈	1	896	yes	—
207	C₂×C₄²×C₈	C₃×C₄×C₈	1	448	yes	—
208	C₂×C₄²×C₈	C₂×C₃×C₁₆	1	3584	yes	—
209	C₂×C₄²×C₈	C₂×C₃×C₄²	1	672	yes	—
210	C₂×C₄²×C₈	C₂×C₃×C₄²	1	168	yes	—
211	C₂×C₄²×C₈	C₂×C₃×C₄²	1	448	yes	—
212	C₂×C₄²×C₈	C₂²×C₃×C₈	1	336	yes	—
213	C₂×C₄²×C₈	C₂²×C₃×C₈	1	896	yes	—
214	C₂×C₄²×C₈	C₂²×C₃×C₈	1	672	yes	—
215	C₂×C₄²×C₈	C₂³×C₃×C₄	1	168	yes	—
216	C₂²×C₈²	C₂×C₃×C₄²	1	672	yes	—
217	C₂²×C₈²	C₂²×C₃×C₈	1	896	yes	—
218	C₂²×C₈²	C₂³×C₃×C₄	1	224	yes	—
219	C₄⁴	C₃×C₄×C₈	1	128	yes	—
220	C₄⁴	C₂×C₃×C₁₆	1	256	yes	—
221	C₄⁴	C₂×C₃×C₄²	1	56	yes	—
222	C₄⁴	C₂²×C₃×C₈	1	56	yes	—
223	C₄²×C₁₆	C₃×C₄×C₈	1	14336	yes	direct product factor
224	C₄²×C₁₆	C₂×C₃×C₄²	1	3584	yes	—
225	C₂×C₈×C₁₆	C₂×C₃×C₄²	1	7168	yes	—
226	C₄×C₈²	C₃×C₄×C₈	1	5376	yes	—
227	C₄×C₈²	C₂×C₃×C₄²	1	1792	yes	—
228	C₂⁴×C₃×C₄	C₂²×C₄×C₈	1	28	yes	—
229	C₂⁴×C₃×C₄	C₂³×C₄²	1	1	yes	characteristic
230	C₂⁴×C₃×C₄	C₂⁴×C₈	1	2	yes	—
231	C₂³×C₃×C₈	C₂×C₄³	1	84	yes	—
232	C₂³×C₃×C₈	C₂²×C₄×C₈	1	112	yes	—
233	C₂³×C₃×C₈	C₂²×C₄×C₈	1	448	yes	—
234	C₂³×C₃×C₈	C₂²×C₄×C₈	1	224	yes	—
235	C₂³×C₃×C₈	C₂³×C₁₆	1	512	yes	—
236	C₂³×C₃×C₈	C₂³×C₄²	1	28	yes	—
237	C₂³×C₃×C₈	C₂⁴×C₈	1	32	yes	—
238	C₂²×C₃×C₄²	C₂×C₈²	1	896	yes	—
239	C₂²×C₃×C₄²	C₄²×C₈	1	448	yes	—
240	C₂²×C₃×C₄²	C₂×C₄×C₁₆	1	1792	yes	—
241	C₂²×C₃×C₄²	C₂×C₄³	1	84	yes	—
242	C₂²×C₃×C₄²	C₂²×C₄×C₈	1	336	yes	—
243	C₂²×C₃×C₄²	C₂²×C₄×C₈	1	84	yes	—
244	C₂²×C₃×C₄²	C₂²×C₄×C₈	1	224	yes	—
245	C₂²×C₃×C₄²	C₂³×C₁₆	1	448	yes	—
246	C₂²×C₃×C₄²	C₂³×C₄²	1	14	yes	—
247	C₂²×C₃×C₄²	C₂⁴×C₈	1	14	yes	—
248	C₂²×C₃×C₁₆	C₂×C₄³	1	896	yes	—
249	C₂²×C₃×C₁₆	C₂²×C₄×C₈	1	3584	yes	—
250	C₂×C₃×C₄×C₈	C₂×C₈²	1	5376	yes	—
251	C₂×C₃×C₄×C₈	C₄²×C₈	1	3584	yes	—
252	C₂×C₃×C₄×C₈	C₄²×C₈	1	1344	yes	—
253	C₂×C₃×C₄×C₈	C₄²×C₈	1	2688	yes	—
254	C₂×C₃×C₄×C₈	C₂×C₄×C₁₆	1	21504	yes	—
255	C₂×C₃×C₄×C₈	C₂×C₄³	1	112	yes	—
256	C₂×C₃×C₄×C₈	C₂×C₄³	1	448	yes	—
257	C₂×C₃×C₄×C₈	C₂×C₄³	1	448	yes	—
258	C₂×C₃×C₄×C₈	C₂²×C₄×C₈	1	1344	yes	—
259	C₂×C₃×C₄×C₈	C₂²×C₄×C₈	1	2688	yes	—
260	C₂×C₃×C₄×C₈	C₂²×C₄×C₈	1	672	yes	—
261	C₂×C₃×C₄×C₈	C₂³×C₄²	1	112	yes	—
262	C₃×C₄³	C₈×C₁₆	1	4096	yes	direct product factor
263	C₃×C₄³	C₂×C₈²	1	896	yes	—
264	C₃×C₄³	C₄²×C₈	1	896	yes	—
265	C₃×C₄³	C₂×C₄×C₁₆	1	3584	yes	—
266	C₃×C₄³	C₂×C₄³	1	112	yes	—
267	C₃×C₄³	C₂²×C₄×C₈	1	336	yes	—
268	C₃×C₄×C₁₆	C₄²×C₈	1	14336	yes	direct product factor
269	C₃×C₄×C₁₆	C₂×C₄³	1	1024	yes	—
270	C₃×C₈²	C₄²×C₈	1	3584	yes	—
271	C₃×C₈²	C₂×C₄³	1	512	yes	—
272	C₂⁴×C₈	C₂²×C₃×C₄²	1	14	yes	—
273	C₂⁴×C₈	C₂³×C₃×C₈	1	32	yes	—
274	C₂⁴×C₈	C₂⁴×C₃×C₄	1	2	yes	—
275	C₂³×C₄²	C₂×C₃×C₄×C₈	1	112	yes	—
276	C₂³×C₄²	C₂²×C₃×C₄²	1	14	yes	—
277	C₂³×C₄²	C₂³×C₃×C₈	1	28	yes	—
278	C₂³×C₄²	C₂⁴×C₃×C₄	1	1	yes	characteristic
279	C₂³×C₁₆	C₂²×C₃×C₄²	1	448	yes	—
280	C₂³×C₁₆	C₂³×C₃×C₈	1	512	yes	—
281	C₂²×C₄×C₈	C₃×C₄³	1	336	yes	—
282	C₂²×C₄×C₈	C₂×C₃×C₄×C₈	1	1344	yes	—
283	C₂²×C₄×C₈	C₂×C₃×C₄×C₈	1	2688	yes	—
284	C₂²×C₄×C₈	C₂×C₃×C₄×C₈	1	672	yes	—
285	C₂²×C₄×C₈	C₂²×C₃×C₁₆	1	3584	yes	—
286	C₂²×C₄×C₈	C₂²×C₃×C₄²	1	336	yes	—
287	C₂²×C₄×C₈	C₂²×C₃×C₄²	1	84	yes	—
288	C₂²×C₄×C₈	C₂²×C₃×C₄²	1	224	yes	—
289	C₂²×C₄×C₈	C₂³×C₃×C₈	1	112	yes	—
290	C₂²×C₄×C₈	C₂³×C₃×C₈	1	448	yes	—
291	C₂²×C₄×C₈	C₂³×C₃×C₈	1	224	yes	—
292	C₂²×C₄×C₈	C₂⁴×C₃×C₄	1	28	yes	—
293	C₂×C₄³	C₃×C₈²	1	512	yes	—
294	C₂×C₄³	C₃×C₄×C₁₆	1	1024	yes	—
295	C₂×C₄³	C₃×C₄³	1	112	yes	—
296	C₂×C₄³	C₂×C₃×C₄×C₈	1	112	yes	—
297	C₂×C₄³	C₂×C₃×C₄×C₈	1	448	yes	—
298	C₂×C₄³	C₂×C₃×C₄×C₈	1	448	yes	—
299	C₂×C₄³	C₂²×C₃×C₁₆	1	896	yes	—
300	C₂×C₄³	C₂²×C₃×C₄²	1	84	yes	—
301	C₂×C₄³	C₂³×C₃×C₈	1	84	yes	—
302	C₂×C₄×C₁₆	C₃×C₄³	1	3584	yes	—
303	C₂×C₄×C₁₆	C₂×C₃×C₄×C₈	1	21504	yes	—
304	C₂×C₄×C₁₆	C₂²×C₃×C₄²	1	1792	yes	—
305	C₄²×C₈	C₃×C₈²	1	3584	yes	—
306	C₄²×C₈	C₃×C₄×C₁₆	1	14336	yes	direct product factor
307	C₄²×C₈	C₃×C₄³	1	896	yes	—
308	C₄²×C₈	C₂×C₃×C₄×C₈	1	3584	yes	—
309	C₄²×C₈	C₂×C₃×C₄×C₈	1	1344	yes	—
310	C₄²×C₈	C₂×C₃×C₄×C₈	1	2688	yes	—
311	C₄²×C₈	C₂²×C₃×C₄²	1	448	yes	—
312	C₂×C₈²	C₃×C₄³	1	896	yes	—
313	C₂×C₈²	C₂×C₃×C₄×C₈	1	5376	yes	—
314	C₂×C₈²	C₂²×C₃×C₄²	1	896	yes	—
315	C₈×C₁₆	C₃×C₄³	1	4096	yes	direct product factor
316	C₂⁵×C₃	C₂³×C₄×C₈	1	1	yes	characteristic
317	C₂³×C₃×C₄	C₂²×C₈²	1	224	yes	—
318	C₂³×C₃×C₄	C₂×C₄²×C₈	1	168	yes	—
319	C₂³×C₃×C₄	C₂²×C₄×C₁₆	1	448	yes	—
320	C₂³×C₃×C₄	C₂²×C₄³	1	7	yes	—
321	C₂³×C₃×C₄	C₂³×C₄×C₈	1	7	yes	—
322	C₂³×C₃×C₄	C₂³×C₄×C₈	1	16	yes	—
323	C₂³×C₃×C₄	C₂³×C₄×C₈	1	28	yes	—
324	C₂³×C₃×C₄	C₂⁴×C₁₆	1	32	yes	—
325	C₂²×C₃×C₈	C₄⁴	1	56	yes	—
326	C₂²×C₃×C₈	C₂²×C₈²	1	896	yes	—
327	C₂²×C₃×C₈	C₂×C₄²×C₈	1	336	yes	—
328	C₂²×C₃×C₈	C₂×C₄²×C₈	1	896	yes	—
329	C₂²×C₃×C₈	C₂×C₄²×C₈	1	672	yes	—
330	C₂²×C₃×C₈	C₂²×C₄×C₁₆	1	3584	yes	—
331	C₂²×C₃×C₈	C₂²×C₄³	1	56	yes	—
332	C₂²×C₃×C₈	C₂³×C₄×C₈	1	224	yes	—
333	C₂×C₃×C₄²	C₄×C₈²	1	1792	yes	—
334	C₂×C₃×C₄²	C₂×C₈×C₁₆	1	7168	yes	—
335	C₂×C₃×C₄²	C₄²×C₁₆	1	3584	yes	—
336	C₂×C₃×C₄²	C₄⁴	1	56	yes	—
337	C₂×C₃×C₄²	C₂²×C₈²	1	672	yes	—
338	C₂×C₃×C₄²	C₂×C₄²×C₈	1	672	yes	—
339	C₂×C₃×C₄²	C₂×C₄²×C₈	1	168	yes	—
340	C₂×C₃×C₄²	C₂×C₄²×C₈	1	448	yes	—
341	C₂×C₃×C₄²	C₂²×C₄×C₁₆	1	2688	yes	—
342	C₂×C₃×C₄²	C₂²×C₄³	1	28	yes	—
343	C₂×C₃×C₄²	C₂³×C₄×C₈	1	84	yes	—
344	C₂×C₃×C₁₆	C₄⁴	1	256	yes	—
345	C₂×C₃×C₁₆	C₂×C₄²×C₈	1	3584	yes	—
346	C₃×C₄×C₈	C₄×C₈²	1	5376	yes	—
347	C₃×C₄×C₈	C₄²×C₁₆	1	14336	yes	direct product factor
348	C₃×C₄×C₈	C₄⁴	1	128	yes	—
349	C₃×C₄×C₈	C₂×C₄²×C₈	1	1792	yes	—
350	C₃×C₄×C₈	C₂×C₄²×C₈	1	896	yes	—
351	C₃×C₄×C₈	C₂×C₄²×C₈	1	448	yes	—
352	C₃×C₄×C₈	C₂²×C₄³	1	64	yes	—
353	C₂⁴×C₄	C₂²×C₃×C₄×C₈	1	28	yes	—
354	C₂⁴×C₄	C₂³×C₃×C₄²	1	1	yes	characteristic
355	C₂⁴×C₄	C₂⁴×C₃×C₈	1	2	yes	—
356	C₂³×C₈	C₂×C₃×C₄³	1	84	yes	—
357	C₂³×C₈	C₂²×C₃×C₄×C₈	1	112	yes	—
358	C₂³×C₈	C₂²×C₃×C₄×C₈	1	448	yes	—
359	C₂³×C₈	C₂²×C₃×C₄×C₈	1	224	yes	—
360	C₂³×C₈	C₂³×C₃×C₁₆	1	512	yes	—
361	C₂³×C₈	C₂³×C₃×C₄²	1	28	yes	—
362	C₂³×C₈	C₂⁴×C₃×C₈	1	32	yes	—
363	C₂²×C₄²	C₂×C₃×C₈²	1	896	yes	—
364	C₂²×C₄²	C₃×C₄²×C₈	1	448	yes	—
365	C₂²×C₄²	C₂×C₃×C₄×C₁₆	1	1792	yes	—
366	C₂²×C₄²	C₂×C₃×C₄³	1	84	yes	—
367	C₂²×C₄²	C₂²×C₃×C₄×C₈	1	336	yes	—
368	C₂²×C₄²	C₂²×C₃×C₄×C₈	1	84	yes	—
369	C₂²×C₄²	C₂²×C₃×C₄×C₈	1	224	yes	—
370	C₂²×C₄²	C₂³×C₃×C₁₆	1	448	yes	—
371	C₂²×C₄²	C₂³×C₃×C₄²	1	14	yes	—
372	C₂²×C₄²	C₂⁴×C₃×C₈	1	14	yes	—
373	C₂²×C₁₆	C₂×C₃×C₄³	1	896	yes	—
374	C₂²×C₁₆	C₂²×C₃×C₄×C₈	1	3584	yes	—
375	C₂×C₄×C₈	C₂×C₃×C₈²	1	5376	yes	—
376	C₂×C₄×C₈	C₃×C₄²×C₈	1	3584	yes	—
377	C₂×C₄×C₈	C₃×C₄²×C₈	1	1344	yes	—
378	C₂×C₄×C₈	C₃×C₄²×C₈	1	2688	yes	—
379	C₂×C₄×C₈	C₂×C₃×C₄×C₁₆	1	21504	yes	—
380	C₂×C₄×C₈	C₂×C₃×C₄³	1	112	yes	—
381	C₂×C₄×C₈	C₂×C₃×C₄³	1	448	yes	—
382	C₂×C₄×C₈	C₂×C₃×C₄³	1	448	yes	—
383	C₂×C₄×C₈	C₂²×C₃×C₄×C₈	1	1344	yes	—
384	C₂×C₄×C₈	C₂²×C₃×C₄×C₈	1	2688	yes	—
385	C₂×C₄×C₈	C₂²×C₃×C₄×C₈	1	672	yes	—
386	C₂×C₄×C₈	C₂³×C₃×C₄²	1	112	yes	—
387	C₄³	C₃×C₈×C₁₆	1	4096	yes	direct product factor
388	C₄³	C₂×C₃×C₈²	1	896	yes	—
389	C₄³	C₃×C₄²×C₈	1	896	yes	—
390	C₄³	C₂×C₃×C₄×C₁₆	1	3584	yes	—
391	C₄³	C₂×C₃×C₄³	1	112	yes	—
392	C₄³	C₂²×C₃×C₄×C₈	1	336	yes	—
393	C₄×C₁₆	C₃×C₄²×C₈	1	14336	yes	direct product factor
394	C₄×C₁₆	C₂×C₃×C₄³	1	1024	yes	—
395	C₈²	C₃×C₄²×C₈	1	3584	yes	—
396	C₈²	C₂×C₃×C₄³	1	512	yes	—
397	C₂⁴×C₃	C₂³×C₈²	1	8	yes	—
398	C₂⁴×C₃	C₂²×C₄²×C₈	1	7	yes	—
399	C₂⁴×C₃	C₂³×C₄×C₁₆	1	16	yes	—
400	C₂²×C₃×C₄	C₂×C₄×C₈²	1	672	yes	—
401	C₂²×C₃×C₄	C₄³×C₈	1	112	yes	—
402	C₂²×C₃×C₄	C₂²×C₈×C₁₆	1	1792	yes	—
403	C₂²×C₃×C₄	C₂×C₄²×C₁₆	1	1344	yes	—
404	C₂²×C₃×C₄	C₂×C₄⁴	1	7	yes	—
405	C₂²×C₃×C₄	C₂³×C₈²	1	56	yes	—
406	C₂²×C₃×C₄	C₂²×C₄²×C₈	1	21	yes	—
407	C₂²×C₃×C₄	C₂²×C₄²×C₈	1	56	yes	—
408	C₂²×C₃×C₄	C₂²×C₄²×C₈	1	56	yes	—
409	C₂²×C₃×C₄	C₂³×C₄×C₁₆	1	224	yes	—
410	C₂×C₃×C₈	C₂×C₄×C₈²	1	1344	yes	—
411	C₂×C₃×C₈	C₄³×C₈	1	256	yes	—
412	C₂×C₃×C₈	C₄³×C₈	1	112	yes	—
413	C₂×C₃×C₈	C₄³×C₈	1	224	yes	—
414	C₂×C₃×C₈	C₂×C₄²×C₁₆	1	3584	yes	—
415	C₂×C₃×C₈	C₂×C₄⁴	1	16	yes	—
416	C₂×C₃×C₈	C₂²×C₄²×C₈	1	224	yes	—
417	C₃×C₄²	C₄×C₈×C₁₆	1	7168	yes	direct product factor
418	C₃×C₄²	C₂×C₄×C₈²	1	672	yes	—
419	C₃×C₄²	C₄³×C₈	1	224	yes	—
420	C₃×C₄²	C₂×C₄²×C₁₆	1	1792	yes	—
421	C₃×C₄²	C₂×C₄⁴	1	8	yes	—
422	C₃×C₄²	C₂²×C₄²×C₈	1	56	yes	—
423	C₃×C₁₆	C₄³×C₈	1	512	yes	direct product factor
424	C₂⁵	C₂³×C₃×C₄×C₈	1	1	yes	characteristic
425	C₂³×C₄	C₂²×C₃×C₈²	1	224	yes	—
426	C₂³×C₄	C₂×C₃×C₄²×C₈	1	168	yes	—
427	C₂³×C₄	C₂²×C₃×C₄×C₁₆	1	448	yes	—
428	C₂³×C₄	C₂²×C₃×C₄³	1	7	yes	—
429	C₂³×C₄	C₂³×C₃×C₄×C₈	1	7	yes	—
430	C₂³×C₄	C₂³×C₃×C₄×C₈	1	16	yes	—
431	C₂³×C₄	C₂³×C₃×C₄×C₈	1	28	yes	—
432	C₂³×C₄	C₂⁴×C₃×C₁₆	1	32	yes	—
433	C₂²×C₈	C₃×C₄⁴	1	56	yes	—
434	C₂²×C₈	C₂²×C₃×C₈²	1	896	yes	—
435	C₂²×C₈	C₂×C₃×C₄²×C₈	1	336	yes	—
436	C₂²×C₈	C₂×C₃×C₄²×C₈	1	896	yes	—
437	C₂²×C₈	C₂×C₃×C₄²×C₈	1	672	yes	—
438	C₂²×C₈	C₂²×C₃×C₄×C₁₆	1	3584	yes	—
439	C₂²×C₈	C₂²×C₃×C₄³	1	56	yes	—
440	C₂²×C₈	C₂³×C₃×C₄×C₈	1	224	yes	—
441	C₂×C₄²	C₃×C₄×C₈²	1	1792	yes	—
442	C₂×C₄²	C₂×C₃×C₈×C₁₆	1	7168	yes	—
443	C₂×C₄²	C₃×C₄²×C₁₆	1	3584	yes	—
444	C₂×C₄²	C₃×C₄⁴	1	56	yes	—
445	C₂×C₄²	C₂²×C₃×C₈²	1	672	yes	—
446	C₂×C₄²	C₂×C₃×C₄²×C₈	1	672	yes	—
447	C₂×C₄²	C₂×C₃×C₄²×C₈	1	168	yes	—
448	C₂×C₄²	C₂×C₃×C₄²×C₈	1	448	yes	—
449	C₂×C₄²	C₂²×C₃×C₄×C₁₆	1	2688	yes	—
450	C₂×C₄²	C₂²×C₃×C₄³	1	28	yes	—
451	C₂×C₄²	C₂³×C₃×C₄×C₈	1	84	yes	—
452	C₂×C₁₆	C₃×C₄⁴	1	256	yes	—
453	C₂×C₁₆	C₂×C₃×C₄²×C₈	1	3584	yes	—
454	C₄×C₈	C₃×C₄×C₈²	1	5376	yes	—
455	C₄×C₈	C₃×C₄²×C₁₆	1	14336	yes	direct product factor
456	C₄×C₈	C₃×C₄⁴	1	128	yes	—
457	C₄×C₈	C₂×C₃×C₄²×C₈	1	1792	yes	—
458	C₄×C₈	C₂×C₃×C₄²×C₈	1	896	yes	—
459	C₄×C₈	C₂×C₃×C₄²×C₈	1	448	yes	—
460	C₄×C₈	C₂²×C₃×C₄³	1	64	yes	—
461	C₂³×C₃	C₂³×C₈×C₁₆	1	64	yes	—
462	C₂³×C₃	C₂²×C₄²×C₁₆	1	56	yes	—
463	C₂³×C₃	C₂²×C₄×C₈²	1	28	yes	—
464	C₂³×C₃	C₂×C₄³×C₈	1	7	yes	—
465	C₂×C₃×C₄	C₂×C₄×C₈×C₁₆	1	2688	yes	—
466	C₂×C₃×C₄	C₄³×C₁₆	1	448	yes	—
467	C₂×C₃×C₄	C₂²×C₄²×C₁₆	1	224	yes	—
468	C₂×C₃×C₄	C₄²×C₈²	1	224	yes	—
469	C₂×C₃×C₄	C₂²×C₄×C₈²	1	84	yes	—
470	C₂×C₃×C₄	C₂×C₄³×C₈	1	7	yes	—
471	C₂×C₃×C₄	C₂×C₄³×C₈	1	16	yes	—
472	C₂×C₃×C₄	C₂×C₄³×C₈	1	28	yes	—
473	C₂×C₃×C₄	C₄⁵	1	1	yes	characteristic
474	C₃×C₈	C₄³×C₁₆	1	512	yes	direct product factor
475	C₃×C₈	C₄²×C₈²	1	224	yes	—
476	C₃×C₈	C₂×C₄³×C₈	1	32	yes	—
477	C₂⁴	C₂³×C₃×C₄×C₁₆	1	16	yes	—
478	C₂⁴	C₂³×C₃×C₈²	1	8	yes	—
479	C₂⁴	C₂²×C₃×C₄²×C₈	1	7	yes	—
480	C₂²×C₄	C₂²×C₃×C₈×C₁₆	1	1792	yes	—
481	C₂²×C₄	C₂×C₃×C₄²×C₁₆	1	1344	yes	—
482	C₂²×C₄	C₂³×C₃×C₄×C₁₆	1	224	yes	—
483	C₂²×C₄	C₂×C₃×C₄×C₈²	1	672	yes	—
484	C₂²×C₄	C₃×C₄³×C₈	1	112	yes	—
485	C₂²×C₄	C₂³×C₃×C₈²	1	56	yes	—
486	C₂²×C₄	C₂²×C₃×C₄²×C₈	1	21	yes	—
487	C₂²×C₄	C₂²×C₃×C₄²×C₈	1	56	yes	—
488	C₂²×C₄	C₂²×C₃×C₄²×C₈	1	56	yes	—
489	C₂²×C₄	C₂×C₃×C₄⁴	1	7	yes	—
490	C₂×C₈	C₂×C₃×C₄²×C₁₆	1	3584	yes	—
491	C₂×C₈	C₂×C₃×C₄×C₈²	1	1344	yes	—
492	C₂×C₈	C₃×C₄³×C₈	1	256	yes	—
493	C₂×C₈	C₃×C₄³×C₈	1	112	yes	—
494	C₂×C₈	C₃×C₄³×C₈	1	224	yes	—
495	C₂×C₈	C₂²×C₃×C₄²×C₈	1	224	yes	—
496	C₂×C₈	C₂×C₃×C₄⁴	1	16	yes	—
497	C₄²	C₃×C₄×C₈×C₁₆	1	7168	yes	direct product factor
498	C₄²	C₂×C₃×C₄²×C₁₆	1	1792	yes	—
499	C₄²	C₂×C₃×C₄×C₈²	1	672	yes	—
500	C₄²	C₃×C₄³×C₈	1	224	yes	—
501	C₄²	C₂²×C₃×C₄²×C₈	1	56	yes	—
502	C₄²	C₂×C₃×C₄⁴	1	8	yes	—
503	C₁₆	C₃×C₄³×C₈	1	512	yes	direct product factor
504	C₂²×C₃	C₂²×C₄×C₈×C₁₆	1	112	yes	—
505	C₂²×C₃	C₂×C₄³×C₁₆	1	28	yes	—
506	C₂²×C₃	C₂×C₄²×C₈²	1	14	yes	—
507	C₂²×C₃	C₄⁴×C₈	1	1	yes	characteristic
508	C₃×C₄	C₄²×C₈×C₁₆	1	448	yes	direct product factor
509	C₃×C₄	C₂×C₄³×C₁₆	1	32	yes	—
510	C₃×C₄	C₂×C₄²×C₈²	1	14	yes	—
511	C₃×C₄	C₄⁴×C₈	1	2	yes	—
512	C₂³	C₂³×C₃×C₈×C₁₆	1	64	yes	—
513	C₂³	C₂²×C₃×C₄²×C₁₆	1	56	yes	—
514	C₂³	C₂²×C₃×C₄×C₈²	1	28	yes	—
515	C₂³	C₂×C₃×C₄³×C₈	1	7	yes	—
516	C₂×C₄	C₂×C₃×C₄×C₈×C₁₆	1	2688	yes	—
517	C₂×C₄	C₃×C₄³×C₁₆	1	448	yes	—
518	C₂×C₄	C₂²×C₃×C₄²×C₁₆	1	224	yes	—
519	C₂×C₄	C₃×C₄²×C₈²	1	224	yes	—
520	C₂×C₄	C₂²×C₃×C₄×C₈²	1	84	yes	—
521	C₂×C₄	C₂×C₃×C₄³×C₈	1	7	yes	—
522	C₂×C₄	C₂×C₃×C₄³×C₈	1	16	yes	—
523	C₂×C₄	C₂×C₃×C₄³×C₈	1	28	yes	—
524	C₂×C₄	C₃×C₄⁵	1	1	yes	characteristic
525	C₈	C₃×C₄³×C₁₆	1	512	yes	direct product factor
526	C₈	C₃×C₄²×C₈²	1	224	yes	—
527	C₈	C₂×C₃×C₄³×C₈	1	32	yes	—
528	C₂×C₃	C₂×C₄²×C₈×C₁₆	1	28	yes	—
529	C₂×C₃	C₄⁴×C₁₆	1	2	yes	—
530	C₂×C₃	C₄³×C₈²	1	1	yes	characteristic
531	C₂²	C₂²×C₃×C₄×C₈×C₁₆	1	112	yes	—
532	C₂²	C₂×C₃×C₄³×C₁₆	1	28	yes	—
533	C₂²	C₂×C₃×C₄²×C₈²	1	14	yes	—
534	C₂²	C₃×C₄⁴×C₈	1	1	yes	characteristic
535	C₄	C₃×C₄²×C₈×C₁₆	1	448	yes	direct product factor
536	C₄	C₂×C₃×C₄³×C₁₆	1	32	yes	—
537	C₄	C₂×C₃×C₄²×C₈²	1	14	yes	—
538	C₄	C₃×C₄⁴×C₈	1	2	yes	—
539	C₃	C₄³×C₈×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
540	C₂	C₂×C₃×C₄²×C₈×C₁₆	1	28	yes	—
541	C₂	C₃×C₄⁴×C₁₆	1	2	yes	—
542	C₂	C₃×C₄³×C₈²	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂³×C₄×C₈	C₂⁵×C₃
socle, prime radical	C₂⁵×C₃	C₂³×C₄×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄³×C₈×C₁₆	C₃	direct (N × H)
12. C₃×C₄²×C₈×C₁₆	C₄	direct (N × H)
28. C₃×C₄³×C₁₆	C₈	direct (N × H)
39. C₄²×C₈×C₁₆	C₃×C₄	direct (N × H)
51. C₃×C₄³×C₈	C₁₆	direct (N × H)
66. C₃×C₄×C₈×C₁₆	C₄²	direct (N × H)
80. C₄³×C₁₆	C₃×C₈	direct (N × H)
115. C₃×C₄²×C₁₆	C₄×C₈	direct (N × H)
137. C₄³×C₈	C₃×C₁₆	direct (N × H)
146. C₄×C₈×C₁₆	C₃×C₄²	direct (N × H)
181. C₃×C₄²×C₈	C₄×C₁₆	direct (N × H)
190. C₃×C₈×C₁₆	C₄³	direct (N × H)
223. C₄²×C₁₆	C₃×C₄×C₈	direct (N × H)
262. C₃×C₄³	C₈×C₁₆	direct (N × H)
268. C₃×C₄×C₁₆	C₄²×C₈	direct (N × H)
306. C₄²×C₈	C₃×C₄×C₁₆	direct (N × H)
315. C₈×C₁₆	C₃×C₄³	direct (N × H)
347. C₃×C₄×C₈	C₄²×C₁₆	direct (N × H)
387. C₄³	C₃×C₈×C₁₆	direct (N × H)
393. C₄×C₁₆	C₃×C₄²×C₈	direct (N × H)
417. C₃×C₄²	C₄×C₈×C₁₆	direct (N × H)
423. C₃×C₁₆	C₄³×C₈	direct (N × H)
455. C₄×C₈	C₃×C₄²×C₁₆	direct (N × H)
474. C₃×C₈	C₄³×C₁₆	direct (N × H)
497. C₄²	C₃×C₄×C₈×C₁₆	direct (N × H)
503. C₁₆	C₃×C₄³×C₈	direct (N × H)
508. C₃×C₄	C₄²×C₈×C₁₆	direct (N × H)
525. C₈	C₃×C₄³×C₁₆	direct (N × H)
535. C₄	C₃×C₄²×C₈×C₁₆	direct (N × H)
539. C₃	C₄³×C₈×C₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄³×C₈²	2
C₃×C₄⁴×C₁₆	2
C₂×C₃×C₄²×C₈×C₁₆	2
C₄³×C₈×C₁₆	3

Subgroups — C3×C43×C8×C16 #72201883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄³×C₈×C₁₆ #72201883