Subgroups — C₂³×C₃×C₄×C₈×C₃₁ #72201112

Order 23808.

9276 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₄²×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×C₃×C₈×C₃₁	C₂	1	2	yes	maximal
3	C₂²×C₃×C₄×C₈×C₃₁	C₂	1	28	yes	maximal, direct product factor
4	C₂⁴×C₃×C₄×C₃₁	C₄	1	2	yes	—
5	C₂⁴×C₃×C₄×C₃₁	C₂²	1	1	yes	characteristic
6	C₂²×C₃×C₄²×C₃₁	C₄	1	14	yes	—
7	C₂²×C₃×C₄²×C₃₁	C₂²	1	14	yes	—
8	C₂³×C₃×C₈×C₃₁	C₄	1	32	yes	direct product factor
9	C₂³×C₃×C₈×C₃₁	C₂²	1	28	yes	—
10	C₂×C₃×C₄×C₈×C₃₁	C₂²	1	112	yes	direct product factor
11	C₂³×C₃×C₄×C₃₁	C₈	1	32	yes	direct product factor
12	C₂³×C₃×C₄×C₃₁	C₂×C₄	1	7	yes	—
13	C₂³×C₃×C₄×C₃₁	C₂×C₄	1	16	yes	—
14	C₂³×C₃×C₄×C₃₁	C₂×C₄	1	28	yes	—
15	C₂³×C₃×C₄×C₃₁	C₂³	1	7	yes	—
16	C₂⁵×C₃×C₃₁	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₃×C₈×C₃₁	C₂×C₄	1	224	yes	direct product factor
18	C₂²×C₃×C₈×C₃₁	C₂³	1	56	yes	—
19	C₂×C₃×C₄²×C₃₁	C₂×C₄	1	84	yes	—
20	C₂×C₃×C₄²×C₃₁	C₂³	1	28	yes	—
21	C₃×C₄×C₈×C₃₁	C₂³	1	64	yes	direct product factor
22	C₂³×C₄×C₈×C₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₂⁴×C₈×C₃₁	C₂×C₃	1	2	yes	—
24	C₂³×C₄²×C₃₁	C₂×C₃	1	1	yes	characteristic
25	C₂²×C₄×C₈×C₃₁	C₂×C₃	1	28	yes	direct product factor
26	C₂⁴×C₄×C₃₁	C₃×C₄	1	2	yes	—
27	C₂⁴×C₄×C₃₁	C₂²×C₃	1	1	yes	characteristic
28	C₂³×C₈×C₃₁	C₃×C₄	1	32	yes	direct product factor
29	C₂³×C₈×C₃₁	C₂²×C₃	1	28	yes	—
30	C₂²×C₄²×C₃₁	C₃×C₄	1	14	yes	—
31	C₂²×C₄²×C₃₁	C₂²×C₃	1	14	yes	—
32	C₂×C₄×C₈×C₃₁	C₂²×C₃	1	112	yes	direct product factor
33	C₂⁴×C₃×C₃₁	C₄²	1	8	yes	—
34	C₂⁴×C₃×C₃₁	C₂×C₈	1	16	yes	—
35	C₂⁴×C₃×C₃₁	C₂²×C₄	1	7	yes	—
36	C₂²×C₃×C₄×C₃₁	C₄²	1	56	yes	—
37	C₂²×C₃×C₄×C₃₁	C₂×C₈	1	224	yes	direct product factor
38	C₂²×C₃×C₄×C₃₁	C₂²×C₄	1	21	yes	—
39	C₂²×C₃×C₄×C₃₁	C₂²×C₄	1	56	yes	—
40	C₂²×C₃×C₄×C₃₁	C₂²×C₄	1	56	yes	—
41	C₂²×C₃×C₄×C₃₁	C₂⁴	1	7	yes	—
42	C₂×C₃×C₈×C₃₁	C₂²×C₄	1	224	yes	direct product factor
43	C₂×C₃×C₈×C₃₁	C₂⁴	1	16	yes	—
44	C₃×C₄²×C₃₁	C₂²×C₄	1	56	yes	—
45	C₃×C₄²×C₃₁	C₂⁴	1	8	yes	—
46	C₂⁵×C₃₁	C₂×C₃×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₃₁	C₃×C₈	1	32	yes	direct product factor
48	C₂³×C₄×C₃₁	C₂×C₃×C₄	1	7	yes	—
49	C₂³×C₄×C₃₁	C₂×C₃×C₄	1	16	yes	—
50	C₂³×C₄×C₃₁	C₂×C₃×C₄	1	28	yes	—
51	C₂³×C₄×C₃₁	C₂³×C₃	1	7	yes	—
52	C₂²×C₈×C₃₁	C₂×C₃×C₄	1	224	yes	direct product factor
53	C₂²×C₈×C₃₁	C₂³×C₃	1	56	yes	—
54	C₂×C₄²×C₃₁	C₂×C₃×C₄	1	84	yes	—
55	C₂×C₄²×C₃₁	C₂³×C₃	1	28	yes	—
56	C₄×C₈×C₃₁	C₂³×C₃	1	64	yes	direct product factor
57	C₂³×C₃×C₄×C₈	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
58	C₂³×C₃×C₃₁	C₄×C₈	1	64	yes	direct product factor
59	C₂³×C₃×C₃₁	C₂×C₄²	1	28	yes	—
60	C₂³×C₃×C₃₁	C₂²×C₈	1	56	yes	—
61	C₂³×C₃×C₃₁	C₂³×C₄	1	7	yes	—
62	C₂×C₃×C₄×C₃₁	C₂×C₄²	1	84	yes	—
63	C₂×C₃×C₄×C₃₁	C₂²×C₈	1	224	yes	direct product factor
64	C₂×C₃×C₄×C₃₁	C₂³×C₄	1	7	yes	—
65	C₂×C₃×C₄×C₃₁	C₂³×C₄	1	16	yes	—
66	C₂×C₃×C₄×C₃₁	C₂³×C₄	1	28	yes	—
67	C₂×C₃×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
68	C₃×C₈×C₃₁	C₂³×C₄	1	32	yes	direct product factor
69	C₂⁴×C₃₁	C₃×C₄²	1	8	yes	—
70	C₂⁴×C₃₁	C₂×C₃×C₈	1	16	yes	—
71	C₂⁴×C₃₁	C₂²×C₃×C₄	1	7	yes	—
72	C₂²×C₄×C₃₁	C₃×C₄²	1	56	yes	—
73	C₂²×C₄×C₃₁	C₂×C₃×C₈	1	224	yes	direct product factor
74	C₂²×C₄×C₃₁	C₂²×C₃×C₄	1	21	yes	—
75	C₂²×C₄×C₃₁	C₂²×C₃×C₄	1	56	yes	—
76	C₂²×C₄×C₃₁	C₂²×C₃×C₄	1	56	yes	—
77	C₂²×C₄×C₃₁	C₂⁴×C₃	1	7	yes	—
78	C₂×C₈×C₃₁	C₂²×C₃×C₄	1	224	yes	direct product factor
79	C₂×C₈×C₃₁	C₂⁴×C₃	1	16	yes	—
80	C₄²×C₃₁	C₂²×C₃×C₄	1	56	yes	—
81	C₄²×C₃₁	C₂⁴×C₃	1	8	yes	—
82	C₂⁴×C₃×C₈	C₂×C₃₁	1	2	yes	—
83	C₂³×C₃×C₄²	C₂×C₃₁	1	1	yes	characteristic
84	C₂²×C₃×C₄×C₈	C₂×C₃₁	1	28	yes	direct product factor
85	C₂²×C₃×C₃₁	C₂×C₄×C₈	1	112	yes	direct product factor
86	C₂²×C₃×C₃₁	C₂²×C₄²	1	14	yes	—
87	C₂²×C₃×C₃₁	C₂³×C₈	1	28	yes	—
88	C₂²×C₃×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
89	C₃×C₄×C₃₁	C₂²×C₄²	1	14	yes	—
90	C₃×C₄×C₃₁	C₂³×C₈	1	32	yes	direct product factor
91	C₃×C₄×C₃₁	C₂⁴×C₄	1	2	yes	—
92	C₂³×C₄×C₈	C₃×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
93	C₂³×C₃₁	C₃×C₄×C₈	1	64	yes	direct product factor
94	C₂³×C₃₁	C₂×C₃×C₄²	1	28	yes	—
95	C₂³×C₃₁	C₂²×C₃×C₈	1	56	yes	—
96	C₂³×C₃₁	C₂³×C₃×C₄	1	7	yes	—
97	C₂×C₄×C₃₁	C₂×C₃×C₄²	1	84	yes	—
98	C₂×C₄×C₃₁	C₂²×C₃×C₈	1	224	yes	direct product factor
99	C₂×C₄×C₃₁	C₂³×C₃×C₄	1	7	yes	—
100	C₂×C₄×C₃₁	C₂³×C₃×C₄	1	16	yes	—
101	C₂×C₄×C₃₁	C₂³×C₃×C₄	1	28	yes	—
102	C₂×C₄×C₃₁	C₂⁵×C₃	1	1	yes	characteristic
103	C₈×C₃₁	C₂³×C₃×C₄	1	32	yes	direct product factor
104	C₂⁴×C₃×C₄	C₄×C₃₁	1	2	yes	—
105	C₂⁴×C₃×C₄	C₂²×C₃₁	1	1	yes	characteristic
106	C₂³×C₃×C₈	C₄×C₃₁	1	32	yes	direct product factor
107	C₂³×C₃×C₈	C₂²×C₃₁	1	28	yes	—
108	C₂²×C₃×C₄²	C₄×C₃₁	1	14	yes	—
109	C₂²×C₃×C₄²	C₂²×C₃₁	1	14	yes	—
110	C₂×C₃×C₄×C₈	C₂²×C₃₁	1	112	yes	direct product factor
111	C₂×C₃×C₃₁	C₂²×C₄×C₈	1	28	yes	direct product factor
112	C₂×C₃×C₃₁	C₂³×C₄²	1	1	yes	characteristic
113	C₂×C₃×C₃₁	C₂⁴×C₈	1	2	yes	—
114	C₂⁴×C₈	C₂×C₃×C₃₁	1	2	yes	—
115	C₂³×C₄²	C₂×C₃×C₃₁	1	1	yes	characteristic
116	C₂²×C₄×C₈	C₂×C₃×C₃₁	1	28	yes	direct product factor
117	C₂²×C₃₁	C₂×C₃×C₄×C₈	1	112	yes	direct product factor
118	C₂²×C₃₁	C₂²×C₃×C₄²	1	14	yes	—
119	C₂²×C₃₁	C₂³×C₃×C₈	1	28	yes	—
120	C₂²×C₃₁	C₂⁴×C₃×C₄	1	1	yes	characteristic
121	C₄×C₃₁	C₂²×C₃×C₄²	1	14	yes	—
122	C₄×C₃₁	C₂³×C₃×C₈	1	32	yes	direct product factor
123	C₄×C₃₁	C₂⁴×C₃×C₄	1	2	yes	—
124	C₂⁵×C₃	C₂×C₄×C₃₁	1	1	yes	characteristic
125	C₂³×C₃×C₄	C₈×C₃₁	1	32	yes	direct product factor
126	C₂³×C₃×C₄	C₂×C₄×C₃₁	1	7	yes	—
127	C₂³×C₃×C₄	C₂×C₄×C₃₁	1	16	yes	—
128	C₂³×C₃×C₄	C₂×C₄×C₃₁	1	28	yes	—
129	C₂³×C₃×C₄	C₂³×C₃₁	1	7	yes	—
130	C₂²×C₃×C₈	C₂×C₄×C₃₁	1	224	yes	direct product factor
131	C₂²×C₃×C₈	C₂³×C₃₁	1	56	yes	—
132	C₂×C₃×C₄²	C₂×C₄×C₃₁	1	84	yes	—
133	C₂×C₃×C₄²	C₂³×C₃₁	1	28	yes	—
134	C₃×C₄×C₈	C₂³×C₃₁	1	64	yes	direct product factor
135	C₃×C₃₁	C₂³×C₄×C₈	1	1	yes	characteristic, direct product factor, Hall
136	C₂⁴×C₄	C₃×C₄×C₃₁	1	2	yes	—
137	C₂⁴×C₄	C₂²×C₃×C₃₁	1	1	yes	characteristic
138	C₂³×C₈	C₃×C₄×C₃₁	1	32	yes	direct product factor
139	C₂³×C₈	C₂²×C₃×C₃₁	1	28	yes	—
140	C₂²×C₄²	C₃×C₄×C₃₁	1	14	yes	—
141	C₂²×C₄²	C₂²×C₃×C₃₁	1	14	yes	—
142	C₂×C₄×C₈	C₂²×C₃×C₃₁	1	112	yes	direct product factor
143	C₂×C₃₁	C₂²×C₃×C₄×C₈	1	28	yes	direct product factor
144	C₂×C₃₁	C₂³×C₃×C₄²	1	1	yes	characteristic
145	C₂×C₃₁	C₂⁴×C₃×C₈	1	2	yes	—
146	C₂⁴×C₃	C₄²×C₃₁	1	8	yes	—
147	C₂⁴×C₃	C₂×C₈×C₃₁	1	16	yes	—
148	C₂⁴×C₃	C₂²×C₄×C₃₁	1	7	yes	—
149	C₂²×C₃×C₄	C₄²×C₃₁	1	56	yes	—
150	C₂²×C₃×C₄	C₂×C₈×C₃₁	1	224	yes	direct product factor
151	C₂²×C₃×C₄	C₂²×C₄×C₃₁	1	21	yes	—
152	C₂²×C₃×C₄	C₂²×C₄×C₃₁	1	56	yes	—
153	C₂²×C₃×C₄	C₂²×C₄×C₃₁	1	56	yes	—
154	C₂²×C₃×C₄	C₂⁴×C₃₁	1	7	yes	—
155	C₂×C₃×C₈	C₂²×C₄×C₃₁	1	224	yes	direct product factor
156	C₂×C₃×C₈	C₂⁴×C₃₁	1	16	yes	—
157	C₃×C₄²	C₂²×C₄×C₃₁	1	56	yes	—
158	C₃×C₄²	C₂⁴×C₃₁	1	8	yes	—
159	C₂⁵	C₂×C₃×C₄×C₃₁	1	1	yes	characteristic
160	C₂³×C₄	C₃×C₈×C₃₁	1	32	yes	direct product factor
161	C₂³×C₄	C₂×C₃×C₄×C₃₁	1	7	yes	—
162	C₂³×C₄	C₂×C₃×C₄×C₃₁	1	16	yes	—
163	C₂³×C₄	C₂×C₃×C₄×C₃₁	1	28	yes	—
164	C₂³×C₄	C₂³×C₃×C₃₁	1	7	yes	—
165	C₂²×C₈	C₂×C₃×C₄×C₃₁	1	224	yes	direct product factor
166	C₂²×C₈	C₂³×C₃×C₃₁	1	56	yes	—
167	C₂×C₄²	C₂×C₃×C₄×C₃₁	1	84	yes	—
168	C₂×C₄²	C₂³×C₃×C₃₁	1	28	yes	—
169	C₄×C₈	C₂³×C₃×C₃₁	1	64	yes	direct product factor
170	C₃₁	C₂³×C₃×C₄×C₈	1	1	yes	characteristic, direct product factor, Sylow
171	C₂³×C₃	C₄×C₈×C₃₁	1	64	yes	direct product factor
172	C₂³×C₃	C₂×C₄²×C₃₁	1	28	yes	—
173	C₂³×C₃	C₂²×C₈×C₃₁	1	56	yes	—
174	C₂³×C₃	C₂³×C₄×C₃₁	1	7	yes	—
175	C₂×C₃×C₄	C₂×C₄²×C₃₁	1	84	yes	—
176	C₂×C₃×C₄	C₂²×C₈×C₃₁	1	224	yes	direct product factor
177	C₂×C₃×C₄	C₂³×C₄×C₃₁	1	7	yes	—
178	C₂×C₃×C₄	C₂³×C₄×C₃₁	1	16	yes	—
179	C₂×C₃×C₄	C₂³×C₄×C₃₁	1	28	yes	—
180	C₂×C₃×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
181	C₃×C₈	C₂³×C₄×C₃₁	1	32	yes	direct product factor
182	C₂⁴	C₃×C₄²×C₃₁	1	8	yes	—
183	C₂⁴	C₂×C₃×C₈×C₃₁	1	16	yes	—
184	C₂⁴	C₂²×C₃×C₄×C₃₁	1	7	yes	—
185	C₂²×C₄	C₃×C₄²×C₃₁	1	56	yes	—
186	C₂²×C₄	C₂×C₃×C₈×C₃₁	1	224	yes	direct product factor
187	C₂²×C₄	C₂²×C₃×C₄×C₃₁	1	21	yes	—
188	C₂²×C₄	C₂²×C₃×C₄×C₃₁	1	56	yes	—
189	C₂²×C₄	C₂²×C₃×C₄×C₃₁	1	56	yes	—
190	C₂²×C₄	C₂⁴×C₃×C₃₁	1	7	yes	—
191	C₂×C₈	C₂²×C₃×C₄×C₃₁	1	224	yes	direct product factor
192	C₂×C₈	C₂⁴×C₃×C₃₁	1	16	yes	—
193	C₄²	C₂²×C₃×C₄×C₃₁	1	56	yes	—
194	C₄²	C₂⁴×C₃×C₃₁	1	8	yes	—
195	C₂²×C₃	C₂×C₄×C₈×C₃₁	1	112	yes	direct product factor
196	C₂²×C₃	C₂²×C₄²×C₃₁	1	14	yes	—
197	C₂²×C₃	C₂³×C₈×C₃₁	1	28	yes	—
198	C₂²×C₃	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
199	C₃×C₄	C₂²×C₄²×C₃₁	1	14	yes	—
200	C₃×C₄	C₂³×C₈×C₃₁	1	32	yes	direct product factor
201	C₃×C₄	C₂⁴×C₄×C₃₁	1	2	yes	—
202	C₂³	C₃×C₄×C₈×C₃₁	1	64	yes	direct product factor
203	C₂³	C₂×C₃×C₄²×C₃₁	1	28	yes	—
204	C₂³	C₂²×C₃×C₈×C₃₁	1	56	yes	—
205	C₂³	C₂³×C₃×C₄×C₃₁	1	7	yes	—
206	C₂×C₄	C₂×C₃×C₄²×C₃₁	1	84	yes	—
207	C₂×C₄	C₂²×C₃×C₈×C₃₁	1	224	yes	direct product factor
208	C₂×C₄	C₂⁵×C₃×C₃₁	1	1	yes	characteristic
209	C₂×C₄	C₂³×C₃×C₄×C₃₁	1	7	yes	—
210	C₂×C₄	C₂³×C₃×C₄×C₃₁	1	16	yes	—
211	C₂×C₄	C₂³×C₃×C₄×C₃₁	1	28	yes	—
212	C₈	C₂³×C₃×C₄×C₃₁	1	32	yes	direct product factor
213	C₂×C₃	C₂²×C₄×C₈×C₃₁	1	28	yes	direct product factor
214	C₂×C₃	C₂³×C₄²×C₃₁	1	1	yes	characteristic
215	C₂×C₃	C₂⁴×C₈×C₃₁	1	2	yes	—
216	C₂²	C₂×C₃×C₄×C₈×C₃₁	1	112	yes	direct product factor
217	C₂²	C₂³×C₃×C₈×C₃₁	1	28	yes	—
218	C₂²	C₂²×C₃×C₄²×C₃₁	1	14	yes	—
219	C₂²	C₂⁴×C₃×C₄×C₃₁	1	1	yes	characteristic
220	C₄	C₂³×C₃×C₈×C₃₁	1	32	yes	direct product factor
221	C₄	C₂²×C₃×C₄²×C₃₁	1	14	yes	—
222	C₄	C₂⁴×C₃×C₄×C₃₁	1	2	yes	—
223	C₃	C₂³×C₄×C₈×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
224	C₂	C₂²×C₃×C₄×C₈×C₃₁	1	28	yes	direct product factor
225	C₂	C₂⁴×C₃×C₈×C₃₁	1	2	yes	—
226	C₂	C₂³×C₃×C₄²×C₃₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂⁵×C₃×C₃₁
socle, prime radical	C₂⁵×C₃×C₃₁	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂²×C₃×C₄×C₈×C₃₁	C₂	direct (N × H)
8. C₂³×C₃×C₈×C₃₁	C₄	direct (N × H)
10. C₂×C₃×C₄×C₈×C₃₁	C₂²	direct (N × H)
11. C₂³×C₃×C₄×C₃₁	C₈	direct (N × H)
17. C₂²×C₃×C₈×C₃₁	C₂×C₄	direct (N × H)
21. C₃×C₄×C₈×C₃₁	C₂³	direct (N × H)
22. C₂³×C₄×C₈×C₃₁	C₃	direct (N × H)
25. C₂²×C₄×C₈×C₃₁	C₂×C₃	direct (N × H)
28. C₂³×C₈×C₃₁	C₃×C₄	direct (N × H)
32. C₂×C₄×C₈×C₃₁	C₂²×C₃	direct (N × H)
37. C₂²×C₃×C₄×C₃₁	C₂×C₈	direct (N × H)
42. C₂×C₃×C₈×C₃₁	C₂²×C₄	direct (N × H)
47. C₂³×C₄×C₃₁	C₃×C₈	direct (N × H)
52. C₂²×C₈×C₃₁	C₂×C₃×C₄	direct (N × H)
56. C₄×C₈×C₃₁	C₂³×C₃	direct (N × H)
57. C₂³×C₃×C₄×C₈	C₃₁	direct (N × H)
58. C₂³×C₃×C₃₁	C₄×C₈	direct (N × H)
63. C₂×C₃×C₄×C₃₁	C₂²×C₈	direct (N × H)
68. C₃×C₈×C₃₁	C₂³×C₄	direct (N × H)
73. C₂²×C₄×C₃₁	C₂×C₃×C₈	direct (N × H)
78. C₂×C₈×C₃₁	C₂²×C₃×C₄	direct (N × H)
84. C₂²×C₃×C₄×C₈	C₂×C₃₁	direct (N × H)
85. C₂²×C₃×C₃₁	C₂×C₄×C₈	direct (N × H)
90. C₃×C₄×C₃₁	C₂³×C₈	direct (N × H)
92. C₂³×C₄×C₈	C₃×C₃₁	direct (N × H)
93. C₂³×C₃₁	C₃×C₄×C₈	direct (N × H)
98. C₂×C₄×C₃₁	C₂²×C₃×C₈	direct (N × H)
103. C₈×C₃₁	C₂³×C₃×C₄	direct (N × H)
106. C₂³×C₃×C₈	C₄×C₃₁	direct (N × H)
110. C₂×C₃×C₄×C₈	C₂²×C₃₁	direct (N × H)
111. C₂×C₃×C₃₁	C₂²×C₄×C₈	direct (N × H)
116. C₂²×C₄×C₈	C₂×C₃×C₃₁	direct (N × H)
117. C₂²×C₃₁	C₂×C₃×C₄×C₈	direct (N × H)
122. C₄×C₃₁	C₂³×C₃×C₈	direct (N × H)
125. C₂³×C₃×C₄	C₈×C₃₁	direct (N × H)
130. C₂²×C₃×C₈	C₂×C₄×C₃₁	direct (N × H)
134. C₃×C₄×C₈	C₂³×C₃₁	direct (N × H)
135. C₃×C₃₁	C₂³×C₄×C₈	direct (N × H)
138. C₂³×C₈	C₃×C₄×C₃₁	direct (N × H)
142. C₂×C₄×C₈	C₂²×C₃×C₃₁	direct (N × H)
143. C₂×C₃₁	C₂²×C₃×C₄×C₈	direct (N × H)
150. C₂²×C₃×C₄	C₂×C₈×C₃₁	direct (N × H)
155. C₂×C₃×C₈	C₂²×C₄×C₃₁	direct (N × H)
160. C₂³×C₄	C₃×C₈×C₃₁	direct (N × H)
165. C₂²×C₈	C₂×C₃×C₄×C₃₁	direct (N × H)
169. C₄×C₈	C₂³×C₃×C₃₁	direct (N × H)
170. C₃₁	C₂³×C₃×C₄×C₈	direct (N × H)
171. C₂³×C₃	C₄×C₈×C₃₁	direct (N × H)
176. C₂×C₃×C₄	C₂²×C₈×C₃₁	direct (N × H)
181. C₃×C₈	C₂³×C₄×C₃₁	direct (N × H)
186. C₂²×C₄	C₂×C₃×C₈×C₃₁	direct (N × H)
191. C₂×C₈	C₂²×C₃×C₄×C₃₁	direct (N × H)
195. C₂²×C₃	C₂×C₄×C₈×C₃₁	direct (N × H)
200. C₃×C₄	C₂³×C₈×C₃₁	direct (N × H)
202. C₂³	C₃×C₄×C₈×C₃₁	direct (N × H)
207. C₂×C₄	C₂²×C₃×C₈×C₃₁	direct (N × H)
212. C₈	C₂³×C₃×C₄×C₃₁	direct (N × H)
213. C₂×C₃	C₂²×C₄×C₈×C₃₁	direct (N × H)
216. C₂²	C₂×C₃×C₄×C₈×C₃₁	direct (N × H)
220. C₄	C₂³×C₃×C₈×C₃₁	direct (N × H)
223. C₃	C₂³×C₄×C₈×C₃₁	direct (N × H)
224. C₂	C₂²×C₃×C₄×C₈×C₃₁	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×C₃×C₄²×C₃₁	2
C₂⁴×C₃×C₈×C₃₁	2
C₂²×C₃×C₄×C₈×C₃₁	2
C₂³×C₄×C₈×C₃₁	3
C₂³×C₃×C₄×C₈	31

Subgroups — C23×C3×C4×C8×C31 #72201112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₃×C₄×C₈×C₃₁ #72201112