Subgroups — C₂×C₃×C₄×C₇²×C₁₆ #72196554

Order 18816.

2160 conjugacy classes of subgroups.

The subgroup lattice has 252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₇²×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₇²×C₁₆	C₂	1	2	yes	maximal
3	C₃×C₄×C₇²×C₁₆	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄×C₇²×C₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₄²×C₇²	C₄	1	1	yes	characteristic
6	C₂²×C₃×C₇²×C₈	C₄	1	1	yes	characteristic
7	C₂²×C₃×C₇²×C₈	C₂²	1	1	yes	characteristic
8	C₃×C₄×C₇²×C₈	C₄	1	2	yes	—
9	C₃×C₄×C₇²×C₈	C₂²	1	2	yes	—
10	C₂×C₃×C₇²×C₁₆	C₄	1	8	yes	direct product factor
11	C₂×C₃×C₇²×C₁₆	C₂²	1	4	yes	—
12	C₂×C₄×C₇²×C₈	C₂×C₃	1	1	yes	characteristic
13	C₂²×C₇²×C₁₆	C₂×C₃	1	2	yes	—
14	C₄×C₇²×C₁₆	C₂×C₃	1	4	yes	direct product factor
15	C₂×C₃×C₄×C₇×C₁₆	C₇	1	8	yes	maximal, direct product factor
16	C₂²×C₃×C₄×C₇²	C₈	1	2	yes	—
17	C₂²×C₃×C₄×C₇²	C₂×C₄	1	1	yes	characteristic
18	C₃×C₄²×C₇²	C₈	1	2	yes	—
19	C₃×C₄²×C₇²	C₂×C₄	1	2	yes	—
20	C₂×C₃×C₇²×C₈	C₈	1	4	yes	—
21	C₂×C₃×C₇²×C₈	C₂×C₄	1	1	yes	characteristic
22	C₂×C₃×C₇²×C₈	C₂×C₄	1	2	yes	—
23	C₂×C₃×C₇²×C₈	C₂×C₄	1	4	yes	—
24	C₂×C₃×C₇²×C₈	C₂³	1	1	yes	characteristic
25	C₃×C₇²×C₁₆	C₂×C₄	1	8	yes	direct product factor
26	C₂²×C₇²×C₈	C₃×C₄	1	1	yes	characteristic
27	C₂²×C₇²×C₈	C₂²×C₃	1	1	yes	characteristic
28	C₂×C₄²×C₇²	C₃×C₄	1	1	yes	characteristic
29	C₂×C₇²×C₁₆	C₃×C₄	1	8	yes	direct product factor
30	C₂×C₇²×C₁₆	C₂²×C₃	1	4	yes	—
31	C₄×C₇²×C₈	C₃×C₄	1	2	yes	—
32	C₄×C₇²×C₈	C₂²×C₃	1	2	yes	—
33	C₂²×C₃×C₇×C₁₆	C₂×C₇	1	16	yes	—
34	C₂×C₃×C₄×C₇×C₈	C₂×C₇	1	8	yes	—
35	C₃×C₄×C₇×C₁₆	C₂×C₇	1	32	yes	direct product factor
36	C₂³×C₃×C₇²	C₂×C₈	1	1	yes	characteristic
37	C₂×C₃×C₄×C₇²	C₁₆	1	8	yes	direct product factor
38	C₂×C₃×C₄×C₇²	C₄²	1	2	yes	—
39	C₂×C₃×C₄×C₇²	C₂×C₈	1	1	yes	characteristic
40	C₂×C₃×C₄×C₇²	C₂×C₈	1	2	yes	—
41	C₂×C₃×C₄×C₇²	C₂×C₈	1	4	yes	—
42	C₂×C₃×C₄×C₇²	C₂²×C₄	1	1	yes	characteristic
43	C₃×C₇²×C₈	C₄²	1	2	yes	—
44	C₃×C₇²×C₈	C₂×C₈	1	4	yes	—
45	C₃×C₇²×C₈	C₂²×C₄	1	2	yes	—
46	C₂×C₄×C₇×C₁₆	C₃×C₇	1	8	yes	direct product factor
47	C₂²×C₄×C₇²	C₃×C₈	1	2	yes	—
48	C₂²×C₄×C₇²	C₂×C₃×C₄	1	1	yes	characteristic
49	C₂×C₇²×C₈	C₃×C₈	1	4	yes	—
50	C₂×C₇²×C₈	C₂×C₃×C₄	1	1	yes	characteristic
51	C₂×C₇²×C₈	C₂×C₃×C₄	1	2	yes	—
52	C₂×C₇²×C₈	C₂×C₃×C₄	1	4	yes	—
53	C₂×C₇²×C₈	C₂³×C₃	1	1	yes	characteristic
54	C₄²×C₇²	C₃×C₈	1	2	yes	—
55	C₄²×C₇²	C₂×C₃×C₄	1	2	yes	—
56	C₇²×C₁₆	C₂×C₃×C₄	1	8	yes	direct product factor
57	C₂²×C₃×C₇×C₈	C₄×C₇	1	8	yes	—
58	C₂²×C₃×C₇×C₈	C₂²×C₇	1	8	yes	—
59	C₂×C₃×C₄²×C₇	C₄×C₇	1	8	yes	—
60	C₂×C₃×C₇×C₁₆	C₄×C₇	1	64	yes	direct product factor
61	C₂×C₃×C₇×C₁₆	C₂²×C₇	1	32	yes	—
62	C₃×C₄×C₇×C₈	C₄×C₇	1	16	yes	—
63	C₃×C₄×C₇×C₈	C₂²×C₇	1	16	yes	—
64	C₂²×C₃×C₇²	C₄×C₈	1	2	yes	—
65	C₂²×C₃×C₇²	C₂×C₁₆	1	4	yes	—
66	C₂²×C₃×C₇²	C₂²×C₈	1	1	yes	characteristic
67	C₃×C₄×C₇²	C₄×C₈	1	2	yes	—
68	C₃×C₄×C₇²	C₂×C₁₆	1	8	yes	direct product factor
69	C₃×C₄×C₇²	C₂×C₄²	1	1	yes	characteristic
70	C₃×C₄×C₇²	C₂²×C₈	1	1	yes	characteristic
71	C₂²×C₇×C₁₆	C₂×C₃×C₇	1	16	yes	—
72	C₂×C₄×C₇×C₈	C₂×C₃×C₇	1	8	yes	—
73	C₄×C₇×C₁₆	C₂×C₃×C₇	1	32	yes	direct product factor
74	C₂³×C₇²	C₂×C₃×C₈	1	1	yes	characteristic
75	C₂×C₄×C₇²	C₃×C₁₆	1	8	yes	direct product factor
76	C₂×C₄×C₇²	C₃×C₄²	1	2	yes	—
77	C₂×C₄×C₇²	C₂×C₃×C₈	1	1	yes	characteristic
78	C₂×C₄×C₇²	C₂×C₃×C₈	1	2	yes	—
79	C₂×C₄×C₇²	C₂×C₃×C₈	1	4	yes	—
80	C₂×C₄×C₇²	C₂²×C₃×C₄	1	1	yes	characteristic
81	C₇²×C₈	C₃×C₄²	1	2	yes	—
82	C₇²×C₈	C₂×C₃×C₈	1	4	yes	—
83	C₇²×C₈	C₂²×C₃×C₄	1	2	yes	—
84	C₂×C₃×C₄×C₁₆	C₇²	1	1	yes	characteristic, direct product factor, Hall
85	C₂²×C₃×C₄×C₇	C₇×C₈	1	16	yes	—
86	C₂²×C₃×C₄×C₇	C₂×C₄×C₇	1	8	yes	—
87	C₂×C₃×C₇×C₈	C₇×C₈	1	32	yes	—
88	C₂×C₃×C₇×C₈	C₂×C₄×C₇	1	8	yes	—
89	C₂×C₃×C₇×C₈	C₂×C₄×C₇	1	16	yes	—
90	C₂×C₃×C₇×C₈	C₂×C₄×C₇	1	32	yes	—
91	C₂×C₃×C₇×C₈	C₂³×C₇	1	8	yes	—
92	C₃×C₄²×C₇	C₇×C₈	1	16	yes	—
93	C₃×C₄²×C₇	C₂×C₄×C₇	1	16	yes	—
94	C₃×C₇×C₁₆	C₂×C₄×C₇	1	64	yes	direct product factor
95	C₂×C₃×C₇²	C₄×C₁₆	1	4	yes	direct product factor
96	C₂×C₃×C₇²	C₂×C₄×C₈	1	1	yes	characteristic
97	C₂×C₃×C₇²	C₂²×C₁₆	1	2	yes	—
98	C₂²×C₇×C₈	C₃×C₄×C₇	1	8	yes	—
99	C₂²×C₇×C₈	C₂²×C₃×C₇	1	8	yes	—
100	C₂×C₄²×C₇	C₃×C₄×C₇	1	8	yes	—
101	C₂×C₇×C₁₆	C₃×C₄×C₇	1	64	yes	direct product factor
102	C₂×C₇×C₁₆	C₂²×C₃×C₇	1	32	yes	—
103	C₄×C₇×C₈	C₃×C₄×C₇	1	16	yes	—
104	C₄×C₇×C₈	C₂²×C₃×C₇	1	16	yes	—
105	C₂²×C₇²	C₃×C₄×C₈	1	2	yes	—
106	C₂²×C₇²	C₂×C₃×C₁₆	1	4	yes	—
107	C₂²×C₇²	C₂²×C₃×C₈	1	1	yes	characteristic
108	C₄×C₇²	C₃×C₄×C₈	1	2	yes	—
109	C₄×C₇²	C₂×C₃×C₁₆	1	8	yes	direct product factor
110	C₄×C₇²	C₂×C₃×C₄²	1	1	yes	characteristic
111	C₄×C₇²	C₂²×C₃×C₈	1	1	yes	characteristic
112	C₂²×C₃×C₁₆	C₂×C₇²	1	2	yes	—
113	C₂×C₃×C₄×C₈	C₂×C₇²	1	1	yes	characteristic
114	C₃×C₄×C₁₆	C₂×C₇²	1	4	yes	direct product factor
115	C₂³×C₃×C₇	C₂×C₇×C₈	1	8	yes	—
116	C₂×C₃×C₄×C₇	C₇×C₁₆	1	64	yes	direct product factor
117	C₂×C₃×C₄×C₇	C₄²×C₇	1	16	yes	—
118	C₂×C₃×C₄×C₇	C₂×C₇×C₈	1	8	yes	—
119	C₂×C₃×C₄×C₇	C₂×C₇×C₈	1	16	yes	—
120	C₂×C₃×C₄×C₇	C₂×C₇×C₈	1	32	yes	—
121	C₂×C₃×C₄×C₇	C₂²×C₄×C₇	1	8	yes	—
122	C₃×C₇×C₈	C₄²×C₇	1	16	yes	—
123	C₃×C₇×C₈	C₂×C₇×C₈	1	32	yes	—
124	C₃×C₇×C₈	C₂²×C₄×C₇	1	16	yes	—
125	C₃×C₇²	C₂×C₄×C₁₆	1	1	yes	characteristic, direct product factor, Hall
126	C₂×C₄×C₁₆	C₃×C₇²	1	1	yes	characteristic, direct product factor, Sylow
127	C₂²×C₄×C₇	C₃×C₇×C₈	1	16	yes	—
128	C₂²×C₄×C₇	C₂×C₃×C₄×C₇	1	8	yes	—
129	C₂×C₇×C₈	C₃×C₇×C₈	1	32	yes	—
130	C₂×C₇×C₈	C₂×C₃×C₄×C₇	1	8	yes	—
131	C₂×C₇×C₈	C₂×C₃×C₄×C₇	1	16	yes	—
132	C₂×C₇×C₈	C₂×C₃×C₄×C₇	1	32	yes	—
133	C₂×C₇×C₈	C₂³×C₃×C₇	1	8	yes	—
134	C₄²×C₇	C₃×C₇×C₈	1	16	yes	—
135	C₄²×C₇	C₂×C₃×C₄×C₇	1	16	yes	—
136	C₇×C₁₆	C₂×C₃×C₄×C₇	1	64	yes	direct product factor
137	C₂×C₇²	C₃×C₄×C₁₆	1	4	yes	direct product factor
138	C₂×C₇²	C₂×C₃×C₄×C₈	1	1	yes	characteristic
139	C₂×C₇²	C₂²×C₃×C₁₆	1	2	yes	—
140	C₂²×C₃×C₈	C₄×C₇²	1	1	yes	characteristic
141	C₂²×C₃×C₈	C₂²×C₇²	1	1	yes	characteristic
142	C₂×C₃×C₄²	C₄×C₇²	1	1	yes	characteristic
143	C₂×C₃×C₁₆	C₄×C₇²	1	8	yes	direct product factor
144	C₂×C₃×C₁₆	C₂²×C₇²	1	4	yes	—
145	C₃×C₄×C₈	C₄×C₇²	1	2	yes	—
146	C₃×C₄×C₈	C₂²×C₇²	1	2	yes	—
147	C₂²×C₃×C₇	C₄×C₇×C₈	1	16	yes	—
148	C₂²×C₃×C₇	C₂×C₇×C₁₆	1	32	yes	—
149	C₂²×C₃×C₇	C₂²×C₇×C₈	1	8	yes	—
150	C₃×C₄×C₇	C₄×C₇×C₈	1	16	yes	—
151	C₃×C₄×C₇	C₂×C₇×C₁₆	1	64	yes	direct product factor
152	C₃×C₄×C₇	C₂×C₄²×C₇	1	8	yes	—
153	C₃×C₄×C₇	C₂²×C₇×C₈	1	8	yes	—
154	C₂²×C₁₆	C₂×C₃×C₇²	1	2	yes	—
155	C₂×C₄×C₈	C₂×C₃×C₇²	1	1	yes	characteristic
156	C₄×C₁₆	C₂×C₃×C₇²	1	4	yes	direct product factor
157	C₂³×C₇	C₂×C₃×C₇×C₈	1	8	yes	—
158	C₂×C₄×C₇	C₃×C₇×C₁₆	1	64	yes	direct product factor
159	C₂×C₄×C₇	C₃×C₄²×C₇	1	16	yes	—
160	C₂×C₄×C₇	C₂×C₃×C₇×C₈	1	8	yes	—
161	C₂×C₄×C₇	C₂×C₃×C₇×C₈	1	16	yes	—
162	C₂×C₄×C₇	C₂×C₃×C₇×C₈	1	32	yes	—
163	C₂×C₄×C₇	C₂²×C₃×C₄×C₇	1	8	yes	—
164	C₇×C₈	C₃×C₄²×C₇	1	16	yes	—
165	C₇×C₈	C₂×C₃×C₇×C₈	1	32	yes	—
166	C₇×C₈	C₂²×C₃×C₄×C₇	1	16	yes	—
167	C₇²	C₂×C₃×C₄×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
168	C₂²×C₃×C₄	C₇²×C₈	1	2	yes	—
169	C₂²×C₃×C₄	C₂×C₄×C₇²	1	1	yes	characteristic
170	C₂×C₃×C₈	C₇²×C₈	1	4	yes	—
171	C₂×C₃×C₈	C₂×C₄×C₇²	1	1	yes	characteristic
172	C₂×C₃×C₈	C₂×C₄×C₇²	1	2	yes	—
173	C₂×C₃×C₈	C₂×C₄×C₇²	1	4	yes	—
174	C₂×C₃×C₈	C₂³×C₇²	1	1	yes	characteristic
175	C₃×C₄²	C₇²×C₈	1	2	yes	—
176	C₃×C₄²	C₂×C₄×C₇²	1	2	yes	—
177	C₃×C₁₆	C₂×C₄×C₇²	1	8	yes	direct product factor
178	C₂×C₃×C₇	C₄×C₇×C₁₆	1	32	yes	direct product factor
179	C₂×C₃×C₇	C₂×C₄×C₇×C₈	1	8	yes	—
180	C₂×C₃×C₇	C₂²×C₇×C₁₆	1	16	yes	—
181	C₂²×C₈	C₃×C₄×C₇²	1	1	yes	characteristic
182	C₂²×C₈	C₂²×C₃×C₇²	1	1	yes	characteristic
183	C₂×C₄²	C₃×C₄×C₇²	1	1	yes	characteristic
184	C₂×C₁₆	C₃×C₄×C₇²	1	8	yes	direct product factor
185	C₂×C₁₆	C₂²×C₃×C₇²	1	4	yes	—
186	C₄×C₈	C₃×C₄×C₇²	1	2	yes	—
187	C₄×C₈	C₂²×C₃×C₇²	1	2	yes	—
188	C₂²×C₇	C₃×C₄×C₇×C₈	1	16	yes	—
189	C₂²×C₇	C₂×C₃×C₇×C₁₆	1	32	yes	—
190	C₂²×C₇	C₂²×C₃×C₇×C₈	1	8	yes	—
191	C₄×C₇	C₃×C₄×C₇×C₈	1	16	yes	—
192	C₄×C₇	C₂×C₃×C₇×C₁₆	1	64	yes	direct product factor
193	C₄×C₇	C₂×C₃×C₄²×C₇	1	8	yes	—
194	C₄×C₇	C₂²×C₃×C₇×C₈	1	8	yes	—
195	C₂³×C₃	C₂×C₇²×C₈	1	1	yes	characteristic
196	C₂×C₃×C₄	C₇²×C₁₆	1	8	yes	direct product factor
197	C₂×C₃×C₄	C₄²×C₇²	1	2	yes	—
198	C₂×C₃×C₄	C₂×C₇²×C₈	1	1	yes	characteristic
199	C₂×C₃×C₄	C₂×C₇²×C₈	1	2	yes	—
200	C₂×C₃×C₄	C₂×C₇²×C₈	1	4	yes	—
201	C₂×C₃×C₄	C₂²×C₄×C₇²	1	1	yes	characteristic
202	C₃×C₈	C₄²×C₇²	1	2	yes	—
203	C₃×C₈	C₂×C₇²×C₈	1	4	yes	—
204	C₃×C₈	C₂²×C₄×C₇²	1	2	yes	—
205	C₃×C₇	C₂×C₄×C₇×C₁₆	1	8	yes	direct product factor
206	C₂²×C₄	C₃×C₇²×C₈	1	2	yes	—
207	C₂²×C₄	C₂×C₃×C₄×C₇²	1	1	yes	characteristic
208	C₂×C₈	C₃×C₇²×C₈	1	4	yes	—
209	C₂×C₈	C₂×C₃×C₄×C₇²	1	1	yes	characteristic
210	C₂×C₈	C₂×C₃×C₄×C₇²	1	2	yes	—
211	C₂×C₈	C₂×C₃×C₄×C₇²	1	4	yes	—
212	C₂×C₈	C₂³×C₃×C₇²	1	1	yes	characteristic
213	C₄²	C₃×C₇²×C₈	1	2	yes	—
214	C₄²	C₂×C₃×C₄×C₇²	1	2	yes	—
215	C₁₆	C₂×C₃×C₄×C₇²	1	8	yes	direct product factor
216	C₂×C₇	C₃×C₄×C₇×C₁₆	1	32	yes	direct product factor
217	C₂×C₇	C₂×C₃×C₄×C₇×C₈	1	8	yes	—
218	C₂×C₇	C₂²×C₃×C₇×C₁₆	1	16	yes	—
219	C₂²×C₃	C₄×C₇²×C₈	1	2	yes	—
220	C₂²×C₃	C₂×C₇²×C₁₆	1	4	yes	—
221	C₂²×C₃	C₂²×C₇²×C₈	1	1	yes	characteristic
222	C₃×C₄	C₄×C₇²×C₈	1	2	yes	—
223	C₃×C₄	C₂×C₇²×C₁₆	1	8	yes	direct product factor
224	C₃×C₄	C₂×C₄²×C₇²	1	1	yes	characteristic
225	C₃×C₄	C₂²×C₇²×C₈	1	1	yes	characteristic
226	C₂³	C₂×C₃×C₇²×C₈	1	1	yes	characteristic
227	C₂×C₄	C₃×C₇²×C₁₆	1	8	yes	direct product factor
228	C₂×C₄	C₂×C₃×C₇²×C₈	1	1	yes	characteristic
229	C₂×C₄	C₂×C₃×C₇²×C₈	1	2	yes	—
230	C₂×C₄	C₂×C₃×C₇²×C₈	1	4	yes	—
231	C₂×C₄	C₃×C₄²×C₇²	1	2	yes	—
232	C₂×C₄	C₂²×C₃×C₄×C₇²	1	1	yes	characteristic
233	C₈	C₂×C₃×C₇²×C₈	1	4	yes	—
234	C₈	C₃×C₄²×C₇²	1	2	yes	—
235	C₈	C₂²×C₃×C₄×C₇²	1	2	yes	—
236	C₇	C₂×C₃×C₄×C₇×C₁₆	1	8	yes	direct product factor
237	C₂×C₃	C₄×C₇²×C₁₆	1	4	yes	direct product factor
238	C₂×C₃	C₂²×C₇²×C₁₆	1	2	yes	—
239	C₂×C₃	C₂×C₄×C₇²×C₈	1	1	yes	characteristic
240	C₂²	C₂×C₃×C₇²×C₁₆	1	4	yes	—
241	C₂²	C₃×C₄×C₇²×C₈	1	2	yes	—
242	C₂²	C₂²×C₃×C₇²×C₈	1	1	yes	characteristic
243	C₄	C₂×C₃×C₇²×C₁₆	1	8	yes	direct product factor
244	C₄	C₃×C₄×C₇²×C₈	1	2	yes	—
245	C₄	C₂²×C₃×C₇²×C₈	1	1	yes	characteristic
246	C₄	C₂×C₃×C₄²×C₇²	1	1	yes	characteristic
247	C₃	C₂×C₄×C₇²×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
248	C₂	C₃×C₄×C₇²×C₁₆	1	4	yes	direct product factor
249	C₂	C₂²×C₃×C₇²×C₁₆	1	2	yes	—
250	C₂	C₂×C₃×C₄×C₇²×C₈	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₈	C₂³×C₃×C₇²
socle, prime radical	C₂³×C₃×C₇²	C₂×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×C₄×C₇²×C₁₆	C₂	direct (N × H)
4. C₂×C₄×C₇²×C₁₆	C₃	direct (N × H)
10. C₂×C₃×C₇²×C₁₆	C₄	direct (N × H)
14. C₄×C₇²×C₁₆	C₂×C₃	direct (N × H)
15. C₂×C₃×C₄×C₇×C₁₆	C₇	direct (N × H)
25. C₃×C₇²×C₁₆	C₂×C₄	direct (N × H)
29. C₂×C₇²×C₁₆	C₃×C₄	direct (N × H)
35. C₃×C₄×C₇×C₁₆	C₂×C₇	direct (N × H)
37. C₂×C₃×C₄×C₇²	C₁₆	direct (N × H)
46. C₂×C₄×C₇×C₁₆	C₃×C₇	direct (N × H)
56. C₇²×C₁₆	C₂×C₃×C₄	direct (N × H)
60. C₂×C₃×C₇×C₁₆	C₄×C₇	direct (N × H)
68. C₃×C₄×C₇²	C₂×C₁₆	direct (N × H)
73. C₄×C₇×C₁₆	C₂×C₃×C₇	direct (N × H)
75. C₂×C₄×C₇²	C₃×C₁₆	direct (N × H)
84. C₂×C₃×C₄×C₁₆	C₇²	direct (N × H)
94. C₃×C₇×C₁₆	C₂×C₄×C₇	direct (N × H)
95. C₂×C₃×C₇²	C₄×C₁₆	direct (N × H)
101. C₂×C₇×C₁₆	C₃×C₄×C₇	direct (N × H)
109. C₄×C₇²	C₂×C₃×C₁₆	direct (N × H)
114. C₃×C₄×C₁₆	C₂×C₇²	direct (N × H)
116. C₂×C₃×C₄×C₇	C₇×C₁₆	direct (N × H)
125. C₃×C₇²	C₂×C₄×C₁₆	direct (N × H)
126. C₂×C₄×C₁₆	C₃×C₇²	direct (N × H)
136. C₇×C₁₆	C₂×C₃×C₄×C₇	direct (N × H)
137. C₂×C₇²	C₃×C₄×C₁₆	direct (N × H)
143. C₂×C₃×C₁₆	C₄×C₇²	direct (N × H)
151. C₃×C₄×C₇	C₂×C₇×C₁₆	direct (N × H)
156. C₄×C₁₆	C₂×C₃×C₇²	direct (N × H)
158. C₂×C₄×C₇	C₃×C₇×C₁₆	direct (N × H)
167. C₇²	C₂×C₃×C₄×C₁₆	direct (N × H)
177. C₃×C₁₆	C₂×C₄×C₇²	direct (N × H)
178. C₂×C₃×C₇	C₄×C₇×C₁₆	direct (N × H)
184. C₂×C₁₆	C₃×C₄×C₇²	direct (N × H)
192. C₄×C₇	C₂×C₃×C₇×C₁₆	direct (N × H)
196. C₂×C₃×C₄	C₇²×C₁₆	direct (N × H)
205. C₃×C₇	C₂×C₄×C₇×C₁₆	direct (N × H)
215. C₁₆	C₂×C₃×C₄×C₇²	direct (N × H)
216. C₂×C₇	C₃×C₄×C₇×C₁₆	direct (N × H)
223. C₃×C₄	C₂×C₇²×C₁₆	direct (N × H)
227. C₂×C₄	C₃×C₇²×C₁₆	direct (N × H)
236. C₇	C₂×C₃×C₄×C₇×C₁₆	direct (N × H)
237. C₂×C₃	C₄×C₇²×C₁₆	direct (N × H)
243. C₄	C₂×C₃×C₇²×C₁₆	direct (N × H)
247. C₃	C₂×C₄×C₇²×C₁₆	direct (N × H)
248. C₂	C₃×C₄×C₇²×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
C₂×C₃×C₄×C₇²×C₈	2
C₂²×C₃×C₇²×C₁₆	2
C₃×C₄×C₇²×C₁₆	2
C₂×C₄×C₇²×C₁₆	3
C₂×C₃×C₄×C₇×C₁₆	7

Subgroups — C2×C3×C4×C72×C16 #72196554

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄×C₇²×C₁₆ #72196554