Subgroups — C₂×C₃₇×#3069 #22681721

Order 9472.

2618 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#575	C₂	1	1	yes	maximal, characteristic
2	C₂²×#137×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#137×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₇×#568	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#3069	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₃₇×#473	C₂	1	4	yes	maximal, complemented
7	C₂×C₃₇×#471	C₂	1	4	yes	maximal, complemented
8	C₂×C₃₇×#430	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃₇×#413	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#101×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#41×C₃₇	C₂²	1	1	yes	characteristic
12	C₂²×#41×C₃₇	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₃₇	C₂²	1	1	yes	characteristic
14	C₃₇×#575	—	2	4	no	—
15	C₃₇×#575	C₂²	1	8	yes	—
16	C₂×#137×C₃₇	—	2	2	no	—
17	C₂×#137×C₃₇	—	2	4	no	—
18	C₂×#137×C₃₇	—	2	1	no	—
19	C₂×#137×C₃₇	—	2	2	no	—
20	C₂×#137×C₃₇	—	2	2	no	—
21	C₂×#137×C₃₇	—	2	4	no	—
22	C₂×#137×C₃₇	C₂²	1	4	yes	—
23	C₂×#137×C₃₇	C₂²	1	2	yes	—
24	C₂×#137×C₃₇	C₂²	1	8	yes	complemented
25	C₂×#137×C₃₇	C₂²	1	8	yes	complemented
26	C₂×AGL(1,ℤ/8)×C₃₇	—	2	1	no	—
27	C₂×AGL(1,ℤ/8)×C₃₇	C₂²	1	2	yes	—
28	C₂×#135×C₃₇	—	2	2	no	—
29	C₂²×Q₁₆×C₃₇	—	2	1	no	—
30	C₂²×Q₁₆×C₃₇	C₂²	1	2	yes	complemented
31	C₂²×SD₁₆×C₃₇	—	2	1	no	—
32	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	complemented
33	C₃₇×#568	—	2	4	no	—
34	C₃₇×#568	C₂²	1	8	yes	complemented
35	C₂×#131×C₃₇	—	2	2	no	—
36	C₂×#131×C₃₇	C₂²	1	4	yes	—
37	C₂²×M₁₆×C₃₇	—	2	2	no	—
38	C₂²×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
39	C₂²×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
40	C₂²×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
41	C₂²×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
42	C₃₇×#473	C₂²	1	32	yes	complemented
43	C₃₇×#471	C₂²	1	32	yes	complemented
44	C₃₇×#430	C₂²	1	8	yes	complemented
45	C₂×#108×C₃₇	C₂²	1	4	yes	complemented
46	C₃₇×#413	C₂²	1	8	yes	complemented
47	C₂×#101×C₃₇	C₂²	1	4	yes	complemented
48	C₂×#101×C₃₇	C₂²	1	8	yes	complemented
49	C₂×#101×C₃₇	C₂²	1	2	yes	complemented
50	C₂×#100×C₃₇	C₂²	1	2	yes	complemented
51	C₂×#41×C₃₇	—	2	1	no	—
52	C₂×#41×C₃₇	—	2	2	no	—
53	C₂×#41×C₃₇	—	2	1	no	—
54	C₂×#41×C₃₇	—	2	2	no	—
55	C₂×#41×C₃₇	—	2	2	no	—
56	C₂×#41×C₃₇	—	2	1	no	—
57	C₂×#41×C₃₇	—	2	1	no	—
58	C₂×#41×C₃₇	—	2	1	no	—
59	C₂×#41×C₃₇	—	2	1	no	—
60	C₂×#41×C₃₇	—	2	2	no	—
61	C₂×#41×C₃₇	—	2	2	no	—
62	C₂×#41×C₃₇	D₄	1	2	yes	—
63	C₂×#41×C₃₇	D₄	1	4	yes	—
64	C₂×#41×C₃₇	C₂³	1	2	yes	—
65	C₂×#41×C₃₇	C₂³	1	4	yes	—
66	C₂×#41×C₃₇	C₂³	1	4	yes	—
67	C₂²×Q₈×C₃₇	—	2	1	no	—
68	C₂²×Q₈×C₃₇	—	2	2	no	—
69	C₂²×Q₈×C₃₇	—	2	1	no	—
70	C₂²×Q₈×C₃₇	—	2	1	no	—
71	C₂²×Q₈×C₃₇	—	2	1	no	—
72	C₂²×Q₈×C₃₇	—	2	2	no	—
73	C₂²×Q₈×C₃₇	—	2	1	no	—
74	C₂²×Q₈×C₃₇	—	2	2	no	—
75	C₂²×Q₈×C₃₇	D₄	1	1	yes	characteristic
76	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
77	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₃₇	C₂³	1	4	yes	—
79	C₂²×D₄×C₃₇	—	2	1	no	—
80	C₂²×D₄×C₃₇	—	2	1	no	—
81	C₂²×D₄×C₃₇	D₄	1	1	yes	characteristic
82	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₃₇	—	2	1	no	—
84	C₂³×C₄×C₃₇	—	2	1	no	—
85	C₂³×C₄×C₃₇	—	2	1	no	—
86	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
87	#137×C₃₇	—	2	8	no	—
88	#137×C₃₇	—	2	16	no	—
89	#137×C₃₇	—	2	4	no	—
90	#137×C₃₇	—	2	8	no	—
91	#137×C₃₇	—	2	16	no	—
92	#137×C₃₇	—	2	16	no	—
93	#137×C₃₇	C₂³	1	16	yes	—
94	#137×C₃₇	C₂³	1	8	yes	—
95	AGL(1,ℤ/8)×C₃₇	—	2	4	no	—
96	AGL(1,ℤ/8)×C₃₇	—	2	8	no	—
97	AGL(1,ℤ/8)×C₃₇	C₂³	1	8	yes	—
98	#135×C₃₇	—	2	16	no	—
99	C₂×Q₁₆×C₃₇	—	2	4	no	—
100	C₂×Q₁₆×C₃₇	—	2	8	no	—
101	C₂×Q₁₆×C₃₇	—	2	2	no	—
102	C₂×Q₁₆×C₃₇	—	2	4	no	—
103	C₂×Q₁₆×C₃₇	—	2	4	no	—
104	C₂×Q₁₆×C₃₇	C₂³	1	8	yes	complemented
105	C₂×SD₁₆×C₃₇	—	2	2	no	—
106	C₂×SD₁₆×C₃₇	—	2	4	no	—
107	C₂×SD₁₆×C₃₇	—	2	8	no	—
108	C₂×SD₁₆×C₃₇	—	2	2	no	—
109	C₂×SD₁₆×C₃₇	—	2	4	no	—
110	C₂×SD₁₆×C₃₇	—	2	4	no	—
111	C₂×SD₁₆×C₃₇	C₂³	1	8	yes	complemented
112	C₂×D₈×C₃₇	—	2	2	no	—
113	#131×C₃₇	—	2	16	no	—
114	#131×C₃₇	—	2	8	no	—
115	#131×C₃₇	C₂³	1	16	yes	—
116	C₂×M₁₆×C₃₇	—	2	1	no	—
117	C₂×M₁₆×C₃₇	—	2	2	no	—
118	C₂×M₁₆×C₃₇	—	2	1	no	—
119	C₂×M₁₆×C₃₇	—	2	1	no	—
120	C₂×M₁₆×C₃₇	—	2	2	no	—
121	C₂×M₁₆×C₃₇	—	2	2	no	—
122	C₂×M₁₆×C₃₇	—	2	16	no	—
123	C₂×M₁₆×C₃₇	—	2	4	no	—
124	C₂×M₁₆×C₃₇	D₄	1	2	yes	—
125	C₂×M₁₆×C₃₇	D₄	1	2	yes	—
126	C₂×M₁₆×C₃₇	D₄	1	4	yes	—
127	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
128	C₂×M₁₆×C₃₇	C₂³	1	4	yes	—
129	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
130	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
131	C₂×M₁₆×C₃₇	C₂³	1	4	yes	—
132	C₂×M₁₆×C₃₇	C₂³	1	4	yes	—
133	C₂×M₁₆×C₃₇	C₂³	1	4	yes	—
134	C₂²×C₈×C₃₇	—	2	1	no	—
135	C₂²×C₈×C₃₇	—	2	1	no	—
136	C₂²×C₈×C₃₇	—	2	1	no	—
137	C₂²×C₈×C₃₇	—	2	4	no	—
138	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
139	#108×C₃₇	C₂³	1	16	yes	complemented
140	#101×C₃₇	C₂³	1	16	yes	complemented
141	#101×C₃₇	C₂³	1	8	yes	complemented
142	#100×C₃₇	C₂³	1	8	yes	complemented
143	C₂⁴×C₃₇	—	2	1	no	—
144	C₂⁴×C₃₇	—	2	1	no	—
145	C₂⁴×C₃₇	#41	1	1	yes	characteristic
146	#41×C₃₇	—	2	4	no	—
147	#41×C₃₇	—	2	4	no	—
148	#41×C₃₇	—	2	4	no	—
149	#41×C₃₇	—	2	4	no	—
150	#41×C₃₇	—	2	2	no	—
151	#41×C₃₇	—	2	4	no	—
152	#41×C₃₇	—	2	2	no	—
153	#41×C₃₇	—	2	4	no	—
154	#41×C₃₇	—	2	4	no	—
155	#41×C₃₇	—	2	4	no	—
156	#41×C₃₇	—	2	4	no	—
157	#41×C₃₇	—	4	2	no	—
158	#41×C₃₇	—	4	2	no	—
159	#41×C₃₇	—	4	2	no	—
160	#41×C₃₇	—	4	2	no	—
161	#41×C₃₇	C₂×D₄	1	8	yes	—
162	#41×C₃₇	C₂×D₄	1	4	yes	—
163	#41×C₃₇	C₂⁴	1	4	yes	—
164	C₂×Q₈×C₃₇	—	2	2	no	—
165	C₂×Q₈×C₃₇	—	2	1	no	—
166	C₂×Q₈×C₃₇	—	2	4	no	—
167	C₂×Q₈×C₃₇	—	2	2	no	—
168	C₂×Q₈×C₃₇	—	2	1	no	—
169	C₂×Q₈×C₃₇	—	2	4	no	—
170	C₂×Q₈×C₃₇	—	2	2	no	—
171	C₂×Q₈×C₃₇	—	2	2	no	—
172	C₂×Q₈×C₃₇	—	2	2	no	—
173	C₂×Q₈×C₃₇	—	2	1	no	—
174	C₂×Q₈×C₃₇	—	2	1	no	—
175	C₂×Q₈×C₃₇	—	2	1	no	—
176	C₂×Q₈×C₃₇	—	2	4	no	—
177	C₂×Q₈×C₃₇	—	2	4	no	—
178	C₂×Q₈×C₃₇	—	2	2	no	—
179	C₂×Q₈×C₃₇	—	2	4	no	—
180	C₂×Q₈×C₃₇	—	2	1	no	—
181	C₂×Q₈×C₃₇	—	4	2	no	—
182	C₂×Q₈×C₃₇	—	4	2	no	—
183	C₂×Q₈×C₃₇	—	4	2	no	—
184	C₂×Q₈×C₃₇	—	4	2	no	—
185	C₂×Q₈×C₃₇	—	4	2	no	—
186	C₂×Q₈×C₃₇	—	4	1	no	—
187	C₂×Q₈×C₃₇	—	4	1	no	—
188	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
189	C₂×Q₈×C₃₇	C₂×D₄	1	4	yes	—
190	C₂×Q₈×C₃₇	C₂⁴	1	4	yes	—
191	C₂×Q₈×C₃₇	C₂⁴	1	2	yes	—
192	C₂×D₄×C₃₇	—	2	4	no	—
193	C₂×D₄×C₃₇	—	2	2	no	—
194	C₂×D₄×C₃₇	—	2	4	no	—
195	C₂×D₄×C₃₇	—	2	2	no	—
196	C₂×D₄×C₃₇	—	2	4	no	—
197	C₂×D₄×C₃₇	—	2	2	no	—
198	C₂×D₄×C₃₇	—	2	1	no	—
199	C₂×D₄×C₃₇	—	2	1	no	—
200	C₂×D₄×C₃₇	—	2	1	no	—
201	C₂×D₄×C₃₇	—	2	1	no	—
202	C₂×D₄×C₃₇	—	2	1	no	—
203	C₂×D₄×C₃₇	—	2	1	no	—
204	C₂×D₄×C₃₇	—	4	2	no	—
205	C₂×D₄×C₃₇	—	4	1	no	—
206	C₂×D₄×C₃₇	—	4	1	no	—
207	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
208	C₂×D₄×C₃₇	C₂×D₄	1	4	yes	—
209	C₂×D₄×C₃₇	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₃₇	—	2	1	no	—
211	C₂²×C₄×C₃₇	—	2	4	no	—
212	C₂²×C₄×C₃₇	—	2	2	no	—
213	C₂²×C₄×C₃₇	—	2	2	no	—
214	C₂²×C₄×C₃₇	—	2	4	no	—
215	C₂²×C₄×C₃₇	—	2	1	no	—
216	C₂²×C₄×C₃₇	—	2	4	no	—
217	C₂²×C₄×C₃₇	—	2	2	no	—
218	C₂²×C₄×C₃₇	—	2	4	no	—
219	C₂²×C₄×C₃₇	—	4	2	no	—
220	C₂²×C₄×C₃₇	—	4	1	no	—
221	C₂²×C₄×C₃₇	—	4	1	no	—
222	C₂²×C₄×C₃₇	—	4	2	no	—
223	C₂²×C₄×C₃₇	—	4	1	no	—
224	C₂²×C₄×C₃₇	—	4	1	no	—
225	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
229	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
231	C₂²×C₄×C₃₇	#41	1	1	yes	characteristic
232	C₂²×C₄×C₃₇	#41	1	2	yes	—
233	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
235	Q₁₆×C₃₇	—	2	16	no	—
236	Q₁₆×C₃₇	—	2	8	no	—
237	Q₁₆×C₃₇	—	2	16	no	—
238	SD₁₆×C₃₇	—	2	8	no	—
239	SD₁₆×C₃₇	—	2	16	no	—
240	SD₁₆×C₃₇	—	2	8	no	—
241	SD₁₆×C₃₇	—	2	16	no	—
242	D₈×C₃₇	—	2	8	no	—
243	M₁₆×C₃₇	—	2	4	no	—
244	M₁₆×C₃₇	—	2	2	no	—
245	M₁₆×C₃₇	—	2	4	no	—
246	M₁₆×C₃₇	—	2	2	no	—
247	M₁₆×C₃₇	—	2	4	no	—
248	M₁₆×C₃₇	—	2	2	no	—
249	M₁₆×C₃₇	—	2	16	no	—
250	M₁₆×C₃₇	C₂×D₄	1	8	yes	—
251	M₁₆×C₃₇	C₂×D₄	1	8	yes	—
252	M₁₆×C₃₇	C₂⁴	1	4	yes	—
253	M₁₆×C₃₇	C₂⁴	1	4	yes	—
254	M₁₆×C₃₇	C₂⁴	1	4	yes	—
255	C₂×C₈×C₃₇	—	2	2	no	—
256	C₂×C₈×C₃₇	—	2	4	no	—
257	C₂×C₈×C₃₇	—	2	2	no	—
258	C₂×C₈×C₃₇	—	2	4	no	—
259	C₂×C₈×C₃₇	—	2	2	no	—
260	C₂×C₈×C₃₇	—	2	4	no	—
261	C₂×C₈×C₃₇	—	2	16	no	—
262	C₂×C₈×C₃₇	C₂×D₄	1	4	yes	—
263	C₂×C₈×C₃₇	C₂×D₄	1	4	yes	—
264	C₂×C₈×C₃₇	C₂⁴	1	4	yes	—
265	C₂³×C₃₇	—	2	2	no	—
266	C₂³×C₃₇	—	2	4	no	—
267	C₂³×C₃₇	—	2	2	no	—
268	C₂³×C₃₇	—	4	2	no	—
269	C₂³×C₃₇	—	4	1	no	—
270	C₂³×C₃₇	—	4	1	no	—
271	C₂³×C₃₇	—	8	2	no	—
272	C₂³×C₃₇	—	8	2	no	—
273	C₂³×C₃₇	#121	1	1	yes	characteristic
274	C₂³×C₃₇	#121	1	1	yes	characteristic
275	C₂³×C₃₇	#121	1	2	yes	—
276	C₂³×C₃₇	C₂×#41	1	1	yes	characteristic
277	C₂³×C₃₇	C₂×#41	1	2	yes	—
278	Q₈×C₃₇	—	2	4	no	—
279	Q₈×C₃₇	—	2	2	no	—
280	Q₈×C₃₇	—	2	4	no	—
281	Q₈×C₃₇	—	2	4	no	—
282	Q₈×C₃₇	—	2	2	no	—
283	Q₈×C₃₇	—	2	2	no	—
284	Q₈×C₃₇	—	4	4	no	—
285	Q₈×C₃₇	—	4	2	no	—
286	Q₈×C₃₇	—	4	4	no	—
287	Q₈×C₃₇	—	4	2	no	—
288	Q₈×C₃₇	—	4	1	no	—
289	Q₈×C₃₇	—	4	1	no	—
290	Q₈×C₃₇	C₂²×D₄	1	4	yes	—
291	D₄×C₃₇	—	2	4	no	—
292	D₄×C₃₇	—	2	8	no	—
293	D₄×C₃₇	—	2	4	no	—
294	D₄×C₃₇	—	2	4	no	—
295	D₄×C₃₇	—	2	2	no	—
296	D₄×C₃₇	—	2	2	no	—
297	D₄×C₃₇	—	2	2	no	—
298	D₄×C₃₇	—	4	4	no	—
299	D₄×C₃₇	—	4	4	no	—
300	D₄×C₃₇	—	4	1	no	—
301	D₄×C₃₇	—	4	1	no	—
302	D₄×C₃₇	C₂²×D₄	1	4	yes	—
303	C₂×C₄×C₃₇	—	2	4	no	—
304	C₂×C₄×C₃₇	—	2	2	no	—
305	C₂×C₄×C₃₇	—	2	8	no	—
306	C₂×C₄×C₃₇	—	2	4	no	—
307	C₂×C₄×C₃₇	—	2	4	no	—
308	C₂×C₄×C₃₇	—	2	2	no	—
309	C₂×C₄×C₃₇	—	2	4	no	—
310	C₂×C₄×C₃₇	—	4	1	no	—
311	C₂×C₄×C₃₇	—	4	4	no	—
312	C₂×C₄×C₃₇	—	4	2	no	—
313	C₂×C₄×C₃₇	—	4	4	no	—
314	C₂×C₄×C₃₇	—	4	1	no	—
315	C₂×C₄×C₃₇	—	4	2	no	—
316	C₂×C₄×C₃₇	—	4	4	no	—
317	C₂×C₄×C₃₇	—	4	4	no	—
318	C₂×C₄×C₃₇	#121	1	2	yes	—
319	C₂×C₄×C₃₇	#121	1	2	yes	—
320	C₂×C₄×C₃₇	#121	1	2	yes	—
321	C₂×C₄×C₃₇	#121	1	2	yes	—
322	C₂×C₄×C₃₇	#121	1	2	yes	—
323	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
324	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
325	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
326	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
327	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
328	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
331	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
334	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
335	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
336	C₈×C₃₇	—	2	4	no	—
337	C₈×C₃₇	—	2	4	no	—
338	C₈×C₃₇	—	2	4	no	—
339	C₈×C₃₇	C₂²×D₄	1	8	yes	—
340	C₂×#3069	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
341	C₂²×C₃₇	—	2	2	no	—
342	C₂²×C₃₇	—	2	2	no	—
343	C₂²×C₃₇	—	2	2	no	—
344	C₂²×C₃₇	—	2	4	no	—
345	C₂²×C₃₇	—	4	2	no	—
346	C₂²×C₃₇	—	4	2	no	—
347	C₂²×C₃₇	—	4	4	no	—
348	C₂²×C₃₇	—	4	2	no	—
349	C₂²×C₃₇	—	8	4	no	—
350	C₂²×C₃₇	—	8	2	no	—
351	C₂²×C₃₇	—	8	2	no	—
352	C₂²×C₃₇	—	8	2	no	—
353	C₂²×C₃₇	C₂×#121	1	2	yes	—
354	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
355	C₂²×C₃₇	C₂×#121	1	2	yes	—
356	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
357	C₂²×C₃₇	C₂²×#41	1	1	yes	characteristic
358	C₄×C₃₇	—	2	4	no	—
359	C₄×C₃₇	—	4	2	no	—
360	C₄×C₃₇	—	4	4	no	—
361	C₄×C₃₇	C₂×#121	1	2	yes	—
362	C₄×C₃₇	C₂×#121	1	1	yes	characteristic
363	C₄×C₃₇	C₂×#121	1	2	yes	—
364	C₄×C₃₇	C₂×#121	1	1	yes	characteristic
365	C₄×C₃₇	C₂³×D₄	1	1	yes	characteristic
366	C₄×C₃₇	C₂³×D₄	1	1	yes	characteristic
367	C₂×#575	C₂×C₃₇	1	1	yes	characteristic
368	C₂²×#137	C₂×C₃₇	1	1	yes	characteristic, complemented
369	C₂²×#137	C₂×C₃₇	1	1	yes	characteristic, complemented
370	C₂×#568	C₂×C₃₇	1	1	yes	characteristic, complemented
371	#3069	C₂×C₃₇	1	16	yes	direct product factor
372	C₂×#473	C₂×C₃₇	1	4	yes	complemented
373	C₂×#471	C₂×C₃₇	1	4	yes	complemented
374	C₂×#430	C₂×C₃₇	1	1	yes	characteristic, complemented
375	C₂×#413	C₂×C₃₇	1	1	yes	characteristic, complemented
376	C₂²×#101	C₂×C₃₇	1	1	yes	characteristic, complemented
377	C₂×C₃₇	—	2	2	no	—
378	C₂×C₃₇	—	2	1	no	—
379	C₂×C₃₇	—	2	1	no	—
380	C₂×C₃₇	—	2	2	no	—
381	C₂×C₃₇	—	4	4	no	—
382	C₂×C₃₇	—	8	2	no	—
383	C₂×C₃₇	#3069	1	2	yes	direct product factor
384	C₂×C₃₇	C₂²×#121	1	1	yes	characteristic
385	C₂²×#41	C₂²×C₃₇	1	1	yes	characteristic
386	C₂²×#41	C₂²×C₃₇	1	1	yes	characteristic
387	C₂³×Q₈	C₂²×C₃₇	1	1	yes	characteristic
388	#575	—	2	4	no	—
389	#575	C₂²×C₃₇	1	8	yes	—
390	C₂×#137	—	2	2	no	—
391	C₂×#137	—	2	4	no	—
392	C₂×#137	—	2	1	no	—
393	C₂×#137	—	2	2	no	—
394	C₂×#137	—	2	2	no	—
395	C₂×#137	—	2	4	no	—
396	C₂×#137	C₂²×C₃₇	1	4	yes	—
397	C₂×#137	C₂²×C₃₇	1	2	yes	—
398	C₂×#137	C₂²×C₃₇	1	8	yes	complemented
399	C₂×#137	C₂²×C₃₇	1	8	yes	complemented
400	C₂×AGL(1,ℤ/8)	—	2	1	no	—
401	C₂×AGL(1,ℤ/8)	C₂²×C₃₇	1	2	yes	—
402	C₂×#135	—	2	2	no	—
403	C₂²×Q₁₆	—	2	1	no	—
404	C₂²×Q₁₆	C₂²×C₃₇	1	2	yes	complemented
405	C₂²×SD₁₆	—	2	1	no	—
406	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	complemented
407	#568	—	2	4	no	—
408	#568	C₂²×C₃₇	1	8	yes	complemented
409	C₂×#131	—	2	2	no	—
410	C₂×#131	C₂²×C₃₇	1	4	yes	—
411	C₂²×M₁₆	—	2	2	no	—
412	C₂²×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
413	C₂²×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
414	C₂²×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
415	C₂²×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
416	#473	C₂²×C₃₇	1	32	yes	complemented
417	#471	C₂²×C₃₇	1	32	yes	complemented
418	#430	C₂²×C₃₇	1	8	yes	complemented
419	C₂×#108	C₂²×C₃₇	1	4	yes	complemented
420	#413	C₂²×C₃₇	1	8	yes	complemented
421	C₂×#101	C₂²×C₃₇	1	4	yes	complemented
422	C₂×#101	C₂²×C₃₇	1	8	yes	complemented
423	C₂×#101	C₂²×C₃₇	1	2	yes	complemented
424	C₂×#100	C₂²×C₃₇	1	2	yes	complemented
425	C₃₇	C₂×#3069	1	1	yes	characteristic, direct product factor, Sylow
426	C₂×#41	—	2	1	no	—
427	C₂×#41	—	2	2	no	—
428	C₂×#41	—	2	1	no	—
429	C₂×#41	—	2	2	no	—
430	C₂×#41	—	2	2	no	—
431	C₂×#41	—	2	1	no	—
432	C₂×#41	—	2	1	no	—
433	C₂×#41	—	2	1	no	—
434	C₂×#41	—	2	1	no	—
435	C₂×#41	—	2	2	no	—
436	C₂×#41	—	2	2	no	—
437	C₂×#41	D₄×C₃₇	1	2	yes	—
438	C₂×#41	D₄×C₃₇	1	4	yes	—
439	C₂×#41	C₂³×C₃₇	1	2	yes	—
440	C₂×#41	C₂³×C₃₇	1	4	yes	—
441	C₂×#41	C₂³×C₃₇	1	4	yes	—
442	C₂²×Q₈	—	2	1	no	—
443	C₂²×Q₈	—	2	2	no	—
444	C₂²×Q₈	—	2	1	no	—
445	C₂²×Q₈	—	2	1	no	—
446	C₂²×Q₈	—	2	1	no	—
447	C₂²×Q₈	—	2	2	no	—
448	C₂²×Q₈	—	2	1	no	—
449	C₂²×Q₈	—	2	2	no	—
450	C₂²×Q₈	D₄×C₃₇	1	1	yes	characteristic
451	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
452	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
453	C₂²×Q₈	C₂³×C₃₇	1	4	yes	—
454	C₂²×D₄	—	2	1	no	—
455	C₂²×D₄	—	2	1	no	—
456	C₂²×D₄	D₄×C₃₇	1	1	yes	characteristic
457	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
458	C₂³×C₄	—	2	1	no	—
459	C₂³×C₄	—	2	1	no	—
460	C₂³×C₄	—	2	1	no	—
461	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
462	#137	—	2	8	no	—
463	#137	—	2	16	no	—
464	#137	—	2	4	no	—
465	#137	—	2	8	no	—
466	#137	—	2	16	no	—
467	#137	—	2	16	no	—
468	#137	C₂³×C₃₇	1	16	yes	—
469	#137	C₂³×C₃₇	1	8	yes	—
470	AGL(1,ℤ/8)	—	2	4	no	—
471	AGL(1,ℤ/8)	—	2	8	no	—
472	AGL(1,ℤ/8)	C₂³×C₃₇	1	8	yes	—
473	#135	—	2	16	no	—
474	C₂×Q₁₆	—	2	4	no	—
475	C₂×Q₁₆	—	2	8	no	—
476	C₂×Q₁₆	—	2	2	no	—
477	C₂×Q₁₆	—	2	4	no	—
478	C₂×Q₁₆	—	2	4	no	—
479	C₂×Q₁₆	C₂³×C₃₇	1	8	yes	complemented
480	C₂×SD₁₆	—	2	2	no	—
481	C₂×SD₁₆	—	2	4	no	—
482	C₂×SD₁₆	—	2	8	no	—
483	C₂×SD₁₆	—	2	2	no	—
484	C₂×SD₁₆	—	2	4	no	—
485	C₂×SD₁₆	—	2	4	no	—
486	C₂×SD₁₆	C₂³×C₃₇	1	8	yes	complemented
487	C₂×D₈	—	2	2	no	—
488	#131	—	2	16	no	—
489	#131	—	2	8	no	—
490	#131	C₂³×C₃₇	1	16	yes	—
491	C₂×M₁₆	—	2	1	no	—
492	C₂×M₁₆	—	2	2	no	—
493	C₂×M₁₆	—	2	1	no	—
494	C₂×M₁₆	—	2	1	no	—
495	C₂×M₁₆	—	2	2	no	—
496	C₂×M₁₆	—	2	2	no	—
497	C₂×M₁₆	—	2	16	no	—
498	C₂×M₁₆	—	2	4	no	—
499	C₂×M₁₆	D₄×C₃₇	1	2	yes	—
500	C₂×M₁₆	D₄×C₃₇	1	2	yes	—
501	C₂×M₁₆	D₄×C₃₇	1	4	yes	—
502	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
503	C₂×M₁₆	C₂³×C₃₇	1	4	yes	—
504	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
505	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
506	C₂×M₁₆	C₂³×C₃₇	1	4	yes	—
507	C₂×M₁₆	C₂³×C₃₇	1	4	yes	—
508	C₂×M₁₆	C₂³×C₃₇	1	4	yes	—
509	C₂²×C₈	—	2	1	no	—
510	C₂²×C₈	—	2	1	no	—
511	C₂²×C₈	—	2	1	no	—
512	C₂²×C₈	—	2	4	no	—
513	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
514	#108	C₂³×C₃₇	1	16	yes	complemented
515	#101	C₂³×C₃₇	1	16	yes	complemented
516	#101	C₂³×C₃₇	1	8	yes	complemented
517	#100	C₂³×C₃₇	1	8	yes	complemented
518	C₂⁴	—	2	1	no	—
519	C₂⁴	—	2	1	no	—
520	C₂⁴	#41×C₃₇	1	1	yes	characteristic
521	#41	—	2	4	no	—
522	#41	—	2	4	no	—
523	#41	—	2	4	no	—
524	#41	—	2	4	no	—
525	#41	—	2	2	no	—
526	#41	—	2	4	no	—
527	#41	—	2	2	no	—
528	#41	—	2	4	no	—
529	#41	—	2	4	no	—
530	#41	—	2	4	no	—
531	#41	—	2	4	no	—
532	#41	—	4	2	no	—
533	#41	—	4	2	no	—
534	#41	—	4	2	no	—
535	#41	—	4	2	no	—
536	#41	C₂×D₄×C₃₇	1	8	yes	—
537	#41	C₂×D₄×C₃₇	1	4	yes	—
538	#41	C₂⁴×C₃₇	1	4	yes	—
539	C₂×Q₈	—	2	1	no	—
540	C₂×Q₈	—	2	2	no	—
541	C₂×Q₈	—	2	4	no	—
542	C₂×Q₈	—	2	2	no	—
543	C₂×Q₈	—	2	1	no	—
544	C₂×Q₈	—	2	2	no	—
545	C₂×Q₈	—	2	2	no	—
546	C₂×Q₈	—	2	4	no	—
547	C₂×Q₈	—	2	2	no	—
548	C₂×Q₈	—	2	1	no	—
549	C₂×Q₈	—	2	1	no	—
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	2	4	no	—
552	C₂×Q₈	—	2	4	no	—
553	C₂×Q₈	—	2	2	no	—
554	C₂×Q₈	—	2	4	no	—
555	C₂×Q₈	—	2	1	no	—
556	C₂×Q₈	—	4	1	no	—
557	C₂×Q₈	—	4	2	no	—
558	C₂×Q₈	—	4	1	no	—
559	C₂×Q₈	—	4	2	no	—
560	C₂×Q₈	—	4	2	no	—
561	C₂×Q₈	—	4	2	no	—
562	C₂×Q₈	—	4	2	no	—
563	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
564	C₂×Q₈	C₂×D₄×C₃₇	1	4	yes	—
565	C₂×Q₈	C₂⁴×C₃₇	1	4	yes	—
566	C₂×Q₈	C₂⁴×C₃₇	1	2	yes	—
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	—	2	4	no	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	2	4	no	—
571	C₂×D₄	—	2	4	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	2	1	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	2	1	no	—
579	C₂×D₄	—	4	1	no	—
580	C₂×D₄	—	4	1	no	—
581	C₂×D₄	—	4	2	no	—
582	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
583	C₂×D₄	C₂×D₄×C₃₇	1	4	yes	—
584	C₂×D₄	C₂⁴×C₃₇	1	2	yes	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	4	no	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	4	no	—
593	C₂²×C₄	—	2	4	no	—
594	C₂²×C₄	—	4	1	no	—
595	C₂²×C₄	—	4	1	no	—
596	C₂²×C₄	—	4	2	no	—
597	C₂²×C₄	—	4	1	no	—
598	C₂²×C₄	—	4	1	no	—
599	C₂²×C₄	—	4	2	no	—
600	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
601	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
602	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
603	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
604	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
605	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
606	C₂²×C₄	#41×C₃₇	1	1	yes	characteristic
607	C₂²×C₄	#41×C₃₇	1	2	yes	—
608	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
610	Q₁₆	—	2	16	no	—
611	Q₁₆	—	2	8	no	—
612	Q₁₆	—	2	16	no	—
613	SD₁₆	—	2	8	no	—
614	SD₁₆	—	2	16	no	—
615	SD₁₆	—	2	8	no	—
616	SD₁₆	—	2	16	no	—
617	D₈	—	2	8	no	—
618	M₁₆	—	2	4	no	—
619	M₁₆	—	2	2	no	—
620	M₁₆	—	2	4	no	—
621	M₁₆	—	2	2	no	—
622	M₁₆	—	2	4	no	—
623	M₁₆	—	2	2	no	—
624	M₁₆	—	2	16	no	—
625	M₁₆	C₂×D₄×C₃₇	1	8	yes	—
626	M₁₆	C₂×D₄×C₃₇	1	8	yes	—
627	M₁₆	C₂⁴×C₃₇	1	4	yes	—
628	M₁₆	C₂⁴×C₃₇	1	4	yes	—
629	M₁₆	C₂⁴×C₃₇	1	4	yes	—
630	C₂×C₈	—	2	2	no	—
631	C₂×C₈	—	2	4	no	—
632	C₂×C₈	—	2	2	no	—
633	C₂×C₈	—	2	2	no	—
634	C₂×C₈	—	2	4	no	—
635	C₂×C₈	—	2	4	no	—
636	C₂×C₈	—	2	16	no	—
637	C₂×C₈	C₂×D₄×C₃₇	1	4	yes	—
638	C₂×C₈	C₂×D₄×C₃₇	1	4	yes	—
639	C₂×C₈	C₂⁴×C₃₇	1	4	yes	—
640	C₂³	—	2	2	no	—
641	C₂³	—	2	4	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	4	2	no	—
644	C₂³	—	4	1	no	—
645	C₂³	—	4	1	no	—
646	C₂³	—	8	2	no	—
647	C₂³	—	8	2	no	—
648	C₂³	#121×C₃₇	1	1	yes	characteristic
649	C₂³	#121×C₃₇	1	1	yes	characteristic
650	C₂³	#121×C₃₇	1	2	yes	—
651	C₂³	C₂×#41×C₃₇	1	1	yes	characteristic
652	C₂³	C₂×#41×C₃₇	1	2	yes	—
653	Q₈	—	2	4	no	—
654	Q₈	—	2	2	no	—
655	Q₈	—	2	4	no	—
656	Q₈	—	2	4	no	—
657	Q₈	—	2	2	no	—
658	Q₈	—	2	2	no	—
659	Q₈	—	4	4	no	—
660	Q₈	—	4	2	no	—
661	Q₈	—	4	4	no	—
662	Q₈	—	4	2	no	—
663	Q₈	—	4	1	no	—
664	Q₈	—	4	1	no	—
665	Q₈	C₂²×D₄×C₃₇	1	4	yes	—
666	D₄	—	2	4	no	—
667	D₄	—	2	8	no	—
668	D₄	—	2	4	no	—
669	D₄	—	2	4	no	—
670	D₄	—	2	2	no	—
671	D₄	—	2	2	no	—
672	D₄	—	2	2	no	—
673	D₄	—	4	4	no	—
674	D₄	—	4	4	no	—
675	D₄	—	4	1	no	—
676	D₄	—	4	1	no	—
677	D₄	C₂²×D₄×C₃₇	1	4	yes	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	8	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	2	4	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	4	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	4	no	—
688	C₂×C₄	—	4	2	no	—
689	C₂×C₄	—	4	4	no	—
690	C₂×C₄	—	4	2	no	—
691	C₂×C₄	—	4	4	no	—
692	C₂×C₄	—	4	4	no	—
693	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
694	C₂×C₄	#121×C₃₇	1	2	yes	—
695	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
696	C₂×C₄	#121×C₃₇	1	2	yes	—
697	C₂×C₄	#121×C₃₇	1	2	yes	—
698	C₂×C₄	#121×C₃₇	1	2	yes	—
699	C₂×C₄	#121×C₃₇	1	2	yes	—
700	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
701	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
702	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
703	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
704	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
705	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
706	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
708	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
709	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
710	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
711	C₈	—	2	4	no	—
712	C₈	—	2	4	no	—
713	C₈	—	2	4	no	—
714	C₈	C₂²×D₄×C₃₇	1	8	yes	—
715	C₂²	—	2	2	no	—
716	C₂²	—	2	2	no	—
717	C₂²	—	2	2	no	—
718	C₂²	—	2	4	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	4	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	8	4	no	—
724	C₂²	—	8	2	no	—
725	C₂²	—	8	2	no	—
726	C₂²	—	8	2	no	—
727	C₂²	C₂×#121×C₃₇	1	2	yes	—
728	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
729	C₂²	C₂×#121×C₃₇	1	2	yes	—
730	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
731	C₂²	C₂²×#41×C₃₇	1	1	yes	characteristic
732	C₄	—	2	4	no	—
733	C₄	—	4	2	no	—
734	C₄	—	4	4	no	—
735	C₄	C₂×#121×C₃₇	1	2	yes	—
736	C₄	C₂×#121×C₃₇	1	1	yes	characteristic
737	C₄	C₂×#121×C₃₇	1	2	yes	—
738	C₄	C₂×#121×C₃₇	1	1	yes	characteristic
739	C₄	C₂³×D₄×C₃₇	1	1	yes	characteristic
740	C₄	C₂³×D₄×C₃₇	1	1	yes	characteristic
741	C₂	—	2	2	no	—
742	C₂	—	2	1	no	—
743	C₂	—	2	1	no	—
744	C₂	—	2	2	no	—
745	C₂	—	4	4	no	—
746	C₂	—	8	2	no	—
747	C₂	C₃₇×#3069	1	2	yes	direct product factor
748	C₂	C₂²×#121×C₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#121
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₇
prime radical	C₂×C₃₇×#575	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂³×C₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#137×C₃₇	C₂	semidirect
3. C₂²×#137×C₃₇	C₂	semidirect
4. C₂×C₃₇×#568	C₂	semidirect
5. C₃₇×#3069	C₂	direct (N × H)
6. C₂×C₃₇×#473	C₂	semidirect
7. C₂×C₃₇×#471	C₂	semidirect
8. C₂×C₃₇×#430	C₂	semidirect
9. C₂×C₃₇×#413	C₂	semidirect
10. C₂²×#101×C₃₇	C₂	semidirect
24. C₂×#137×C₃₇	C₂²	semidirect
25. C₂×#137×C₃₇	C₂²	semidirect
30. C₂²×Q₁₆×C₃₇	C₂²	semidirect
32. C₂²×SD₁₆×C₃₇	C₂²	semidirect
34. C₃₇×#568	C₂²	semidirect
42. C₃₇×#473	C₂²	semidirect
43. C₃₇×#471	C₂²	semidirect
44. C₃₇×#430	C₂²	semidirect
45. C₂×#108×C₃₇	C₂²	semidirect
46. C₃₇×#413	C₂²	semidirect
47. C₂×#101×C₃₇	C₂²	semidirect
48. C₂×#101×C₃₇	C₂²	semidirect
49. C₂×#101×C₃₇	C₂²	semidirect
50. C₂×#100×C₃₇	C₂²	semidirect
104. C₂×Q₁₆×C₃₇	C₂³	semidirect
111. C₂×SD₁₆×C₃₇	C₂³	semidirect
139. #108×C₃₇	C₂³	semidirect
140. #101×C₃₇	C₂³	semidirect
141. #101×C₃₇	C₂³	semidirect
142. #100×C₃₇	C₂³	semidirect
340. C₂×#3069	C₃₇	direct (N × H)
368. C₂²×#137	C₂×C₃₇	semidirect
369. C₂²×#137	C₂×C₃₇	semidirect
370. C₂×#568	C₂×C₃₇	semidirect
371. #3069	C₂×C₃₇	direct (N × H)
372. C₂×#473	C₂×C₃₇	semidirect
373. C₂×#471	C₂×C₃₇	semidirect
374. C₂×#430	C₂×C₃₇	semidirect
375. C₂×#413	C₂×C₃₇	semidirect
376. C₂²×#101	C₂×C₃₇	semidirect
383. C₂×C₃₇	#3069	direct (N × H)
398. C₂×#137	C₂²×C₃₇	semidirect
399. C₂×#137	C₂²×C₃₇	semidirect
404. C₂²×Q₁₆	C₂²×C₃₇	semidirect
406. C₂²×SD₁₆	C₂²×C₃₇	semidirect
408. #568	C₂²×C₃₇	semidirect
416. #473	C₂²×C₃₇	semidirect
417. #471	C₂²×C₃₇	semidirect
418. #430	C₂²×C₃₇	semidirect
419. C₂×#108	C₂²×C₃₇	semidirect
420. #413	C₂²×C₃₇	semidirect
421. C₂×#101	C₂²×C₃₇	semidirect
422. C₂×#101	C₂²×C₃₇	semidirect
423. C₂×#101	C₂²×C₃₇	semidirect
424. C₂×#100	C₂²×C₃₇	semidirect
425. C₃₇	C₂×#3069	direct (N × H)
479. C₂×Q₁₆	C₂³×C₃₇	semidirect
486. C₂×SD₁₆	C₂³×C₃₇	semidirect
514. #108	C₂³×C₃₇	semidirect
515. #101	C₂³×C₃₇	semidirect
516. #101	C₂³×C₃₇	semidirect
517. #100	C₂³×C₃₇	semidirect
747. C₂	C₃₇×#3069	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×C₃₇×#575	2
C₂²×#137×C₃₇	2
C₂×C₃₇×#568	2
C₃₇×#3069	2
C₂×C₃₇×#473	2
C₂×C₃₇×#471	2
C₂×C₃₇×#430	2
C₂×C₃₇×#413	2
C₂²×#101×C₃₇	2
C₂×#3069	37

Subgroups — C2×C37×#3069 #22681721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₇×#3069 #22681721