Subgroups — C₂³×C₃×C₄×C₈×C₃₇ #72205379

Order 28416.

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×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×C₃×C₈×C₃₇	C₂	1	2	yes	maximal
3	C₂²×C₃×C₄×C₈×C₃₇	C₂	1	28	yes	maximal, direct product factor
4	C₂⁴×C₃×C₄×C₃₇	C₄	1	2	yes	—
5	C₂⁴×C₃×C₄×C₃₇	C₂²	1	1	yes	characteristic
6	C₂²×C₃×C₄²×C₃₇	C₄	1	14	yes	—
7	C₂²×C₃×C₄²×C₃₇	C₂²	1	14	yes	—
8	C₂³×C₃×C₈×C₃₇	C₄	1	32	yes	direct product factor
9	C₂³×C₃×C₈×C₃₇	C₂²	1	28	yes	—
10	C₂×C₃×C₄×C₈×C₃₇	C₂²	1	112	yes	direct product factor
11	C₂³×C₃×C₄×C₃₇	C₈	1	32	yes	direct product factor
12	C₂³×C₃×C₄×C₃₇	C₂×C₄	1	7	yes	—
13	C₂³×C₃×C₄×C₃₇	C₂×C₄	1	16	yes	—
14	C₂³×C₃×C₄×C₃₇	C₂×C₄	1	28	yes	—
15	C₂³×C₃×C₄×C₃₇	C₂³	1	7	yes	—
16	C₂⁵×C₃×C₃₇	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₃×C₈×C₃₇	C₂×C₄	1	224	yes	direct product factor
18	C₂²×C₃×C₈×C₃₇	C₂³	1	56	yes	—
19	C₂×C₃×C₄²×C₃₇	C₂×C₄	1	84	yes	—
20	C₂×C₃×C₄²×C₃₇	C₂³	1	28	yes	—
21	C₃×C₄×C₈×C₃₇	C₂³	1	64	yes	direct product factor
22	C₂³×C₄×C₈×C₃₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₂⁴×C₈×C₃₇	C₂×C₃	1	2	yes	—
24	C₂³×C₄²×C₃₇	C₂×C₃	1	1	yes	characteristic
25	C₂²×C₄×C₈×C₃₇	C₂×C₃	1	28	yes	direct product factor
26	C₂⁴×C₄×C₃₇	C₃×C₄	1	2	yes	—
27	C₂⁴×C₄×C₃₇	C₂²×C₃	1	1	yes	characteristic
28	C₂³×C₈×C₃₇	C₃×C₄	1	32	yes	direct product factor
29	C₂³×C₈×C₃₇	C₂²×C₃	1	28	yes	—
30	C₂²×C₄²×C₃₇	C₃×C₄	1	14	yes	—
31	C₂²×C₄²×C₃₇	C₂²×C₃	1	14	yes	—
32	C₂×C₄×C₈×C₃₇	C₂²×C₃	1	112	yes	direct product factor
33	C₂⁴×C₃×C₃₇	C₄²	1	8	yes	—
34	C₂⁴×C₃×C₃₇	C₂×C₈	1	16	yes	—
35	C₂⁴×C₃×C₃₇	C₂²×C₄	1	7	yes	—
36	C₂²×C₃×C₄×C₃₇	C₄²	1	56	yes	—
37	C₂²×C₃×C₄×C₃₇	C₂×C₈	1	224	yes	direct product factor
38	C₂²×C₃×C₄×C₃₇	C₂²×C₄	1	21	yes	—
39	C₂²×C₃×C₄×C₃₇	C₂²×C₄	1	56	yes	—
40	C₂²×C₃×C₄×C₃₇	C₂²×C₄	1	56	yes	—
41	C₂²×C₃×C₄×C₃₇	C₂⁴	1	7	yes	—
42	C₂×C₃×C₈×C₃₇	C₂²×C₄	1	224	yes	direct product factor
43	C₂×C₃×C₈×C₃₇	C₂⁴	1	16	yes	—
44	C₃×C₄²×C₃₇	C₂²×C₄	1	56	yes	—
45	C₃×C₄²×C₃₇	C₂⁴	1	8	yes	—
46	C₂⁵×C₃₇	C₂×C₃×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₃₇	C₃×C₈	1	32	yes	direct product factor
48	C₂³×C₄×C₃₇	C₂×C₃×C₄	1	7	yes	—
49	C₂³×C₄×C₃₇	C₂×C₃×C₄	1	16	yes	—
50	C₂³×C₄×C₃₇	C₂×C₃×C₄	1	28	yes	—
51	C₂³×C₄×C₃₇	C₂³×C₃	1	7	yes	—
52	C₂²×C₈×C₃₇	C₂×C₃×C₄	1	224	yes	direct product factor
53	C₂²×C₈×C₃₇	C₂³×C₃	1	56	yes	—
54	C₂×C₄²×C₃₇	C₂×C₃×C₄	1	84	yes	—
55	C₂×C₄²×C₃₇	C₂³×C₃	1	28	yes	—
56	C₄×C₈×C₃₇	C₂³×C₃	1	64	yes	direct product factor
57	C₂³×C₃×C₃₇	C₄×C₈	1	64	yes	direct product factor
58	C₂³×C₃×C₃₇	C₂×C₄²	1	28	yes	—
59	C₂³×C₃×C₃₇	C₂²×C₈	1	56	yes	—
60	C₂³×C₃×C₃₇	C₂³×C₄	1	7	yes	—
61	C₂×C₃×C₄×C₃₇	C₂×C₄²	1	84	yes	—
62	C₂×C₃×C₄×C₃₇	C₂²×C₈	1	224	yes	direct product factor
63	C₂×C₃×C₄×C₃₇	C₂³×C₄	1	7	yes	—
64	C₂×C₃×C₄×C₃₇	C₂³×C₄	1	16	yes	—
65	C₂×C₃×C₄×C₃₇	C₂³×C₄	1	28	yes	—
66	C₂×C₃×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
67	C₃×C₈×C₃₇	C₂³×C₄	1	32	yes	direct product factor
68	C₂³×C₃×C₄×C₈	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
69	C₂⁴×C₃₇	C₃×C₄²	1	8	yes	—
70	C₂⁴×C₃₇	C₂×C₃×C₈	1	16	yes	—
71	C₂⁴×C₃₇	C₂²×C₃×C₄	1	7	yes	—
72	C₂²×C₄×C₃₇	C₃×C₄²	1	56	yes	—
73	C₂²×C₄×C₃₇	C₂×C₃×C₈	1	224	yes	direct product factor
74	C₂²×C₄×C₃₇	C₂²×C₃×C₄	1	21	yes	—
75	C₂²×C₄×C₃₇	C₂²×C₃×C₄	1	56	yes	—
76	C₂²×C₄×C₃₇	C₂²×C₃×C₄	1	56	yes	—
77	C₂²×C₄×C₃₇	C₂⁴×C₃	1	7	yes	—
78	C₂×C₈×C₃₇	C₂²×C₃×C₄	1	224	yes	direct product factor
79	C₂×C₈×C₃₇	C₂⁴×C₃	1	16	yes	—
80	C₄²×C₃₇	C₂²×C₃×C₄	1	56	yes	—
81	C₄²×C₃₇	C₂⁴×C₃	1	8	yes	—
82	C₂²×C₃×C₃₇	C₂×C₄×C₈	1	112	yes	direct product factor
83	C₂²×C₃×C₃₇	C₂²×C₄²	1	14	yes	—
84	C₂²×C₃×C₃₇	C₂³×C₈	1	28	yes	—
85	C₂²×C₃×C₃₇	C₂⁴×C₄	1	1	yes	characteristic
86	C₃×C₄×C₃₇	C₂²×C₄²	1	14	yes	—
87	C₃×C₄×C₃₇	C₂³×C₈	1	32	yes	direct product factor
88	C₃×C₄×C₃₇	C₂⁴×C₄	1	2	yes	—
89	C₂⁴×C₃×C₈	C₂×C₃₇	1	2	yes	—
90	C₂³×C₃×C₄²	C₂×C₃₇	1	1	yes	characteristic
91	C₂²×C₃×C₄×C₈	C₂×C₃₇	1	28	yes	direct product factor
92	C₂³×C₃₇	C₃×C₄×C₈	1	64	yes	direct product factor
93	C₂³×C₃₇	C₂×C₃×C₄²	1	28	yes	—
94	C₂³×C₃₇	C₂²×C₃×C₈	1	56	yes	—
95	C₂³×C₃₇	C₂³×C₃×C₄	1	7	yes	—
96	C₂×C₄×C₃₇	C₂×C₃×C₄²	1	84	yes	—
97	C₂×C₄×C₃₇	C₂²×C₃×C₈	1	224	yes	direct product factor
98	C₂×C₄×C₃₇	C₂³×C₃×C₄	1	7	yes	—
99	C₂×C₄×C₃₇	C₂³×C₃×C₄	1	16	yes	—
100	C₂×C₄×C₃₇	C₂³×C₃×C₄	1	28	yes	—
101	C₂×C₄×C₃₇	C₂⁵×C₃	1	1	yes	characteristic
102	C₈×C₃₇	C₂³×C₃×C₄	1	32	yes	direct product factor
103	C₂³×C₄×C₈	C₃×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
104	C₂×C₃×C₃₇	C₂²×C₄×C₈	1	28	yes	direct product factor
105	C₂×C₃×C₃₇	C₂³×C₄²	1	1	yes	characteristic
106	C₂×C₃×C₃₇	C₂⁴×C₈	1	2	yes	—
107	C₂⁴×C₃×C₄	C₄×C₃₇	1	2	yes	—
108	C₂⁴×C₃×C₄	C₂²×C₃₇	1	1	yes	characteristic
109	C₂³×C₃×C₈	C₄×C₃₇	1	32	yes	direct product factor
110	C₂³×C₃×C₈	C₂²×C₃₇	1	28	yes	—
111	C₂²×C₃×C₄²	C₄×C₃₇	1	14	yes	—
112	C₂²×C₃×C₄²	C₂²×C₃₇	1	14	yes	—
113	C₂×C₃×C₄×C₈	C₂²×C₃₇	1	112	yes	direct product factor
114	C₂²×C₃₇	C₂×C₃×C₄×C₈	1	112	yes	direct product factor
115	C₂²×C₃₇	C₂²×C₃×C₄²	1	14	yes	—
116	C₂²×C₃₇	C₂³×C₃×C₈	1	28	yes	—
117	C₂²×C₃₇	C₂⁴×C₃×C₄	1	1	yes	characteristic
118	C₄×C₃₇	C₂²×C₃×C₄²	1	14	yes	—
119	C₄×C₃₇	C₂³×C₃×C₈	1	32	yes	direct product factor
120	C₄×C₃₇	C₂⁴×C₃×C₄	1	2	yes	—
121	C₂⁴×C₈	C₂×C₃×C₃₇	1	2	yes	—
122	C₂³×C₄²	C₂×C₃×C₃₇	1	1	yes	characteristic
123	C₂²×C₄×C₈	C₂×C₃×C₃₇	1	28	yes	direct product factor
124	C₃×C₃₇	C₂³×C₄×C₈	1	1	yes	characteristic, direct product factor, Hall
125	C₂⁵×C₃	C₂×C₄×C₃₇	1	1	yes	characteristic
126	C₂³×C₃×C₄	C₈×C₃₇	1	32	yes	direct product factor
127	C₂³×C₃×C₄	C₂×C₄×C₃₇	1	7	yes	—
128	C₂³×C₃×C₄	C₂×C₄×C₃₇	1	16	yes	—
129	C₂³×C₃×C₄	C₂×C₄×C₃₇	1	28	yes	—
130	C₂³×C₃×C₄	C₂³×C₃₇	1	7	yes	—
131	C₂²×C₃×C₈	C₂×C₄×C₃₇	1	224	yes	direct product factor
132	C₂²×C₃×C₈	C₂³×C₃₇	1	56	yes	—
133	C₂×C₃×C₄²	C₂×C₄×C₃₇	1	84	yes	—
134	C₂×C₃×C₄²	C₂³×C₃₇	1	28	yes	—
135	C₃×C₄×C₈	C₂³×C₃₇	1	64	yes	direct product factor
136	C₂×C₃₇	C₂²×C₃×C₄×C₈	1	28	yes	direct product factor
137	C₂×C₃₇	C₂³×C₃×C₄²	1	1	yes	characteristic
138	C₂×C₃₇	C₂⁴×C₃×C₈	1	2	yes	—
139	C₂⁴×C₄	C₃×C₄×C₃₇	1	2	yes	—
140	C₂⁴×C₄	C₂²×C₃×C₃₇	1	1	yes	characteristic
141	C₂³×C₈	C₃×C₄×C₃₇	1	32	yes	direct product factor
142	C₂³×C₈	C₂²×C₃×C₃₇	1	28	yes	—
143	C₂²×C₄²	C₃×C₄×C₃₇	1	14	yes	—
144	C₂²×C₄²	C₂²×C₃×C₃₇	1	14	yes	—
145	C₂×C₄×C₈	C₂²×C₃×C₃₇	1	112	yes	direct product factor
146	C₂⁴×C₃	C₄²×C₃₇	1	8	yes	—
147	C₂⁴×C₃	C₂×C₈×C₃₇	1	16	yes	—
148	C₂⁴×C₃	C₂²×C₄×C₃₇	1	7	yes	—
149	C₂²×C₃×C₄	C₄²×C₃₇	1	56	yes	—
150	C₂²×C₃×C₄	C₂×C₈×C₃₇	1	224	yes	direct product factor
151	C₂²×C₃×C₄	C₂²×C₄×C₃₇	1	21	yes	—
152	C₂²×C₃×C₄	C₂²×C₄×C₃₇	1	56	yes	—
153	C₂²×C₃×C₄	C₂²×C₄×C₃₇	1	56	yes	—
154	C₂²×C₃×C₄	C₂⁴×C₃₇	1	7	yes	—
155	C₂×C₃×C₈	C₂²×C₄×C₃₇	1	224	yes	direct product factor
156	C₂×C₃×C₈	C₂⁴×C₃₇	1	16	yes	—
157	C₃×C₄²	C₂²×C₄×C₃₇	1	56	yes	—
158	C₃×C₄²	C₂⁴×C₃₇	1	8	yes	—
159	C₃₇	C₂³×C₃×C₄×C₈	1	1	yes	characteristic, direct product factor, Sylow
160	C₂⁵	C₂×C₃×C₄×C₃₇	1	1	yes	characteristic
161	C₂³×C₄	C₃×C₈×C₃₇	1	32	yes	direct product factor
162	C₂³×C₄	C₂×C₃×C₄×C₃₇	1	7	yes	—
163	C₂³×C₄	C₂×C₃×C₄×C₃₇	1	16	yes	—
164	C₂³×C₄	C₂×C₃×C₄×C₃₇	1	28	yes	—
165	C₂³×C₄	C₂³×C₃×C₃₇	1	7	yes	—
166	C₂²×C₈	C₂×C₃×C₄×C₃₇	1	224	yes	direct product factor
167	C₂²×C₈	C₂³×C₃×C₃₇	1	56	yes	—
168	C₂×C₄²	C₂×C₃×C₄×C₃₇	1	84	yes	—
169	C₂×C₄²	C₂³×C₃×C₃₇	1	28	yes	—
170	C₄×C₈	C₂³×C₃×C₃₇	1	64	yes	direct product factor
171	C₂³×C₃	C₄×C₈×C₃₇	1	64	yes	direct product factor
172	C₂³×C₃	C₂×C₄²×C₃₇	1	28	yes	—
173	C₂³×C₃	C₂²×C₈×C₃₇	1	56	yes	—
174	C₂³×C₃	C₂³×C₄×C₃₇	1	7	yes	—
175	C₂×C₃×C₄	C₂×C₄²×C₃₇	1	84	yes	—
176	C₂×C₃×C₄	C₂²×C₈×C₃₇	1	224	yes	direct product factor
177	C₂×C₃×C₄	C₂³×C₄×C₃₇	1	7	yes	—
178	C₂×C₃×C₄	C₂³×C₄×C₃₇	1	16	yes	—
179	C₂×C₃×C₄	C₂³×C₄×C₃₇	1	28	yes	—
180	C₂×C₃×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
181	C₃×C₈	C₂³×C₄×C₃₇	1	32	yes	direct product factor
182	C₂⁴	C₃×C₄²×C₃₇	1	8	yes	—
183	C₂⁴	C₂×C₃×C₈×C₃₇	1	16	yes	—
184	C₂⁴	C₂²×C₃×C₄×C₃₇	1	7	yes	—
185	C₂²×C₄	C₃×C₄²×C₃₇	1	56	yes	—
186	C₂²×C₄	C₂×C₃×C₈×C₃₇	1	224	yes	direct product factor
187	C₂²×C₄	C₂²×C₃×C₄×C₃₇	1	21	yes	—
188	C₂²×C₄	C₂²×C₃×C₄×C₃₇	1	56	yes	—
189	C₂²×C₄	C₂²×C₃×C₄×C₃₇	1	56	yes	—
190	C₂²×C₄	C₂⁴×C₃×C₃₇	1	7	yes	—
191	C₂×C₈	C₂²×C₃×C₄×C₃₇	1	224	yes	direct product factor
192	C₂×C₈	C₂⁴×C₃×C₃₇	1	16	yes	—
193	C₄²	C₂²×C₃×C₄×C₃₇	1	56	yes	—
194	C₄²	C₂⁴×C₃×C₃₇	1	8	yes	—
195	C₂²×C₃	C₂×C₄×C₈×C₃₇	1	112	yes	direct product factor
196	C₂²×C₃	C₂²×C₄²×C₃₇	1	14	yes	—
197	C₂²×C₃	C₂³×C₈×C₃₇	1	28	yes	—
198	C₂²×C₃	C₂⁴×C₄×C₃₇	1	1	yes	characteristic
199	C₃×C₄	C₂²×C₄²×C₃₇	1	14	yes	—
200	C₃×C₄	C₂³×C₈×C₃₇	1	32	yes	direct product factor
201	C₃×C₄	C₂⁴×C₄×C₃₇	1	2	yes	—
202	C₂³	C₃×C₄×C₈×C₃₇	1	64	yes	direct product factor
203	C₂³	C₂×C₃×C₄²×C₃₇	1	28	yes	—
204	C₂³	C₂²×C₃×C₈×C₃₇	1	56	yes	—
205	C₂³	C₂³×C₃×C₄×C₃₇	1	7	yes	—
206	C₂×C₄	C₂×C₃×C₄²×C₃₇	1	84	yes	—
207	C₂×C₄	C₂²×C₃×C₈×C₃₇	1	224	yes	direct product factor
208	C₂×C₄	C₂⁵×C₃×C₃₇	1	1	yes	characteristic
209	C₂×C₄	C₂³×C₃×C₄×C₃₇	1	7	yes	—
210	C₂×C₄	C₂³×C₃×C₄×C₃₇	1	16	yes	—
211	C₂×C₄	C₂³×C₃×C₄×C₃₇	1	28	yes	—
212	C₈	C₂³×C₃×C₄×C₃₇	1	32	yes	direct product factor
213	C₂×C₃	C₂²×C₄×C₈×C₃₇	1	28	yes	direct product factor
214	C₂×C₃	C₂³×C₄²×C₃₇	1	1	yes	characteristic
215	C₂×C₃	C₂⁴×C₈×C₃₇	1	2	yes	—
216	C₂²	C₂×C₃×C₄×C₈×C₃₇	1	112	yes	direct product factor
217	C₂²	C₂³×C₃×C₈×C₃₇	1	28	yes	—
218	C₂²	C₂²×C₃×C₄²×C₃₇	1	14	yes	—
219	C₂²	C₂⁴×C₃×C₄×C₃₇	1	1	yes	characteristic
220	C₄	C₂³×C₃×C₈×C₃₇	1	32	yes	direct product factor
221	C₄	C₂²×C₃×C₄²×C₃₇	1	14	yes	—
222	C₄	C₂⁴×C₃×C₄×C₃₇	1	2	yes	—
223	C₃	C₂³×C₄×C₈×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
224	C₂	C₂²×C₃×C₄×C₈×C₃₇	1	28	yes	direct product factor
225	C₂	C₂⁴×C₃×C₈×C₃₇	1	2	yes	—
226	C₂	C₂³×C₃×C₄²×C₃₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂⁵×C₃×C₃₇
socle, prime radical	C₂⁵×C₃×C₃₇	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×C₃₇	C₂	direct (N × H)
8. C₂³×C₃×C₈×C₃₇	C₄	direct (N × H)
10. C₂×C₃×C₄×C₈×C₃₇	C₂²	direct (N × H)
11. C₂³×C₃×C₄×C₃₇	C₈	direct (N × H)
17. C₂²×C₃×C₈×C₃₇	C₂×C₄	direct (N × H)
21. C₃×C₄×C₈×C₃₇	C₂³	direct (N × H)
22. C₂³×C₄×C₈×C₃₇	C₃	direct (N × H)
25. C₂²×C₄×C₈×C₃₇	C₂×C₃	direct (N × H)
28. C₂³×C₈×C₃₇	C₃×C₄	direct (N × H)
32. C₂×C₄×C₈×C₃₇	C₂²×C₃	direct (N × H)
37. C₂²×C₃×C₄×C₃₇	C₂×C₈	direct (N × H)
42. C₂×C₃×C₈×C₃₇	C₂²×C₄	direct (N × H)
47. C₂³×C₄×C₃₇	C₃×C₈	direct (N × H)
52. C₂²×C₈×C₃₇	C₂×C₃×C₄	direct (N × H)
56. C₄×C₈×C₃₇	C₂³×C₃	direct (N × H)
57. C₂³×C₃×C₃₇	C₄×C₈	direct (N × H)
62. C₂×C₃×C₄×C₃₇	C₂²×C₈	direct (N × H)
67. C₃×C₈×C₃₇	C₂³×C₄	direct (N × H)
68. C₂³×C₃×C₄×C₈	C₃₇	direct (N × H)
73. C₂²×C₄×C₃₇	C₂×C₃×C₈	direct (N × H)
78. C₂×C₈×C₃₇	C₂²×C₃×C₄	direct (N × H)
82. C₂²×C₃×C₃₇	C₂×C₄×C₈	direct (N × H)
87. C₃×C₄×C₃₇	C₂³×C₈	direct (N × H)
91. C₂²×C₃×C₄×C₈	C₂×C₃₇	direct (N × H)
92. C₂³×C₃₇	C₃×C₄×C₈	direct (N × H)
97. C₂×C₄×C₃₇	C₂²×C₃×C₈	direct (N × H)
102. C₈×C₃₇	C₂³×C₃×C₄	direct (N × H)
103. C₂³×C₄×C₈	C₃×C₃₇	direct (N × H)
104. C₂×C₃×C₃₇	C₂²×C₄×C₈	direct (N × H)
109. C₂³×C₃×C₈	C₄×C₃₇	direct (N × H)
113. C₂×C₃×C₄×C₈	C₂²×C₃₇	direct (N × H)
114. C₂²×C₃₇	C₂×C₃×C₄×C₈	direct (N × H)
119. C₄×C₃₇	C₂³×C₃×C₈	direct (N × H)
123. C₂²×C₄×C₈	C₂×C₃×C₃₇	direct (N × H)
124. C₃×C₃₇	C₂³×C₄×C₈	direct (N × H)
126. C₂³×C₃×C₄	C₈×C₃₇	direct (N × H)
131. C₂²×C₃×C₈	C₂×C₄×C₃₇	direct (N × H)
135. C₃×C₄×C₈	C₂³×C₃₇	direct (N × H)
136. C₂×C₃₇	C₂²×C₃×C₄×C₈	direct (N × H)
141. C₂³×C₈	C₃×C₄×C₃₇	direct (N × H)
145. C₂×C₄×C₈	C₂²×C₃×C₃₇	direct (N × H)
150. C₂²×C₃×C₄	C₂×C₈×C₃₇	direct (N × H)
155. C₂×C₃×C₈	C₂²×C₄×C₃₇	direct (N × H)
159. C₃₇	C₂³×C₃×C₄×C₈	direct (N × H)
161. C₂³×C₄	C₃×C₈×C₃₇	direct (N × H)
166. C₂²×C₈	C₂×C₃×C₄×C₃₇	direct (N × H)
170. C₄×C₈	C₂³×C₃×C₃₇	direct (N × H)
171. C₂³×C₃	C₄×C₈×C₃₇	direct (N × H)
176. C₂×C₃×C₄	C₂²×C₈×C₃₇	direct (N × H)
181. C₃×C₈	C₂³×C₄×C₃₇	direct (N × H)
186. C₂²×C₄	C₂×C₃×C₈×C₃₇	direct (N × H)
191. C₂×C₈	C₂²×C₃×C₄×C₃₇	direct (N × H)
195. C₂²×C₃	C₂×C₄×C₈×C₃₇	direct (N × H)
200. C₃×C₄	C₂³×C₈×C₃₇	direct (N × H)
202. C₂³	C₃×C₄×C₈×C₃₇	direct (N × H)
207. C₂×C₄	C₂²×C₃×C₈×C₃₇	direct (N × H)
212. C₈	C₂³×C₃×C₄×C₃₇	direct (N × H)
213. C₂×C₃	C₂²×C₄×C₈×C₃₇	direct (N × H)
216. C₂²	C₂×C₃×C₄×C₈×C₃₇	direct (N × H)
220. C₄	C₂³×C₃×C₈×C₃₇	direct (N × H)
223. C₃	C₂³×C₄×C₈×C₃₇	direct (N × H)
224. C₂	C₂²×C₃×C₄×C₈×C₃₇	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×C₃₇	2
C₂⁴×C₃×C₈×C₃₇	2
C₂²×C₃×C₄×C₈×C₃₇	2
C₂³×C₄×C₈×C₃₇	3
C₂³×C₃×C₄×C₈	37

Subgroups — C23×C3×C4×C8×C37 #72205379

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₃×C₄×C₈×C₃₇ #72205379