Subgroups — C₃₇×#62788 #22684041

Order 9472.

7094 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3523	C₂	1	4	yes	maximal, complemented
2	C₃₇×#3522	C₂	1	4	yes	maximal, complemented
3	C₃₇×#3516	C₂	1	8	yes	maximal, complemented
4	C₃₇×#3507	C₂	1	6	yes	maximal, complemented
5	C₃₇×#3502	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#3497	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#3492	C₂	1	6	yes	maximal, complemented
8	C₃₇×#3486	C₂	1	2	yes	maximal, complemented
9	C₃₇×#3482	C₂	1	8	yes	maximal, complemented
10	C₃₇×#3480	C₂	1	4	yes	maximal, complemented
11	Q₈×#41×C₃₇	C₂	1	4	yes	maximal, complemented
12	C₃₇×#3461	C₂	1	6	yes	maximal, complemented
13	C₃₇×#3444	C₂	1	6	yes	maximal, complemented
14	C₄×2₋¹⁺⁴×C₃₇	C₂	1	2	yes	maximal, complemented
15	C₂²×C₄×Q₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×2₋¹⁺⁴×C₃₇	C₂²	1	2	yes	—
17	C₂³×Q₈×C₃₇	C₂²	1	1	yes	characteristic
18	C₃₇×#559	C₂²	1	12	yes	complemented
19	Q₈²×C₃₇	C₂²	1	4	yes	complemented
20	C₃₇×#557	C₂²	1	12	yes	complemented
21	C₃₇×#557	C₂²	1	4	yes	complemented
22	C₃₇×#557	C₂²	1	8	yes	complemented
23	C₃₇×#556	C₂²	1	12	yes	complemented
24	C₃₇×#556	C₂²	1	24	yes	complemented
25	C₃₇×#554	C₂²	1	24	yes	—
26	C₃₇×#554	C₂²	1	12	yes	complemented
27	C₃₇×#553	C₂²	1	24	yes	—
28	C₃₇×#552	C₂²	1	24	yes	—
29	C₃₇×#552	C₂²	1	24	yes	complemented
30	C₃₇×#550	C₂²	1	4	yes	complemented
31	D₄×Q₈×C₃₇	C₂²	1	8	yes	—
32	D₄×Q₈×C₃₇	C₂²	1	8	yes	—
33	D₄×Q₈×C₃₇	C₂²	1	4	yes	complemented
34	C₃₇×#548	C₂²	1	8	yes	—
35	C₃₇×#548	C₂²	1	8	yes	—
36	C₃₇×#548	C₂²	1	8	yes	complemented
37	C₃₇×#547	C₂²	1	24	yes	—
38	C₃₇×#544	C₂²	1	6	yes	—
39	C₃₇×#542	C₂²	1	24	yes	complemented
40	C₃₇×#541	C₂²	1	24	yes	complemented
41	C₃₇×#539	C₂²	1	24	yes	—
42	C₃₇×#537	C₂²	1	6	yes	—
43	C₃₇×#536	C₂²	1	12	yes	—
44	C₃₇×#533	C₂²	1	6	yes	—
45	C₃₇×#533	C₂²	1	6	yes	—
46	C₃₇×#533	C₂²	1	6	yes	—
47	C₃₇×#533	C₂²	1	24	yes	complemented
48	C₃₇×#532	C₂²	1	6	yes	—
49	C₃₇×#532	C₂²	1	6	yes	—
50	C₃₇×#532	C₂²	1	6	yes	—
51	C₃₇×#529	C₂²	1	12	yes	—
52	C₃₇×#529	C₂²	1	12	yes	—
53	C₃₇×#529	C₂²	1	12	yes	—
54	C₃₇×#529	C₂²	1	12	yes	—
55	C₃₇×#529	C₂²	1	12	yes	—
56	C₃₇×#529	C₂²	1	12	yes	—
57	C₃₇×#529	C₂²	1	24	yes	complemented
58	C₃₇×#525	C₂²	1	4	yes	—
59	C₃₇×#525	C₂²	1	12	yes	—
60	C₃₇×#525	C₂²	1	12	yes	—
61	C₃₇×#520	C₂²	1	12	yes	—
62	C₃₇×#520	C₂²	1	8	yes	complemented
63	C₃₇×#519	C₂²	1	2	yes	—
64	C₃₇×#519	C₂²	1	8	yes	complemented
65	C₄×#41×C₃₇	C₂²	1	12	yes	—
66	C₄×#41×C₃₇	C₂²	1	12	yes	—
67	C₄×#41×C₃₇	C₂²	1	12	yes	—
68	C₄×#41×C₃₇	C₂²	1	8	yes	complemented
69	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
70	C₂×C₄×Q₈×C₃₇	C₂²	1	3	yes	—
71	C₂×C₄×Q₈×C₃₇	C₂²	1	4	yes	—
72	C₂×C₄×Q₈×C₃₇	C₂²	1	4	yes	—
73	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
74	C₂×C₄×Q₈×C₃₇	C₂²	1	3	yes	—
75	C₂×C₄×Q₈×C₃₇	C₂²	1	4	yes	—
76	C₂×C₄×Q₈×C₃₇	C₂²	1	4	yes	—
77	C₂×C₄×Q₈×C₃₇	C₂²	1	8	yes	complemented
78	C₂²×C₄⋊C₄×C₃₇	C₂²	1	3	yes	—
79	C₂²×C₄²×C₃₇	C₂²	1	3	yes	—
80	2₋¹⁺⁴×C₃₇	—	2	16	no	—
81	C₂×#41×C₃₇	C₂³	1	12	yes	—
82	C₂×#41×C₃₇	C₂³	1	8	yes	—
83	C₂×#41×C₃₇	C₂³	1	4	yes	—
84	C₂×#41×C₃₇	C₂³	1	12	yes	—
85	C₂²×Q₈×C₃₇	—	2	8	no	—
86	C₂²×Q₈×C₃₇	C₂³	1	8	yes	—
87	C₂²×Q₈×C₃₇	C₂³	1	3	yes	—
88	C₂²×Q₈×C₃₇	C₂³	1	4	yes	—
89	C₂²×Q₈×C₃₇	C₂³	1	4	yes	—
90	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₃₇	C₂³	1	3	yes	—
92	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₃₇	C₂³	1	3	yes	—
94	C₄⋊Q₈×C₃₇	C₂³	1	6	yes	—
95	C₄⋊Q₈×C₃₇	C₂³	1	6	yes	—
96	C₄⋊Q₈×C₃₇	C₂³	1	6	yes	—
97	C₄⋊Q₈×C₃₇	C₂³	1	24	yes	—
98	C₄⋊Q₈×C₃₇	C₂³	1	24	yes	—
99	#127×C₃₇	C₂³	1	6	yes	—
100	#126×C₃₇	C₂³	1	24	yes	—
101	#126×C₃₇	C₂³	1	24	yes	—
102	#126×C₃₇	C₂³	1	48	yes	—
103	#125×C₃₇	C₂³	1	12	yes	—
104	#125×C₃₇	C₂³	1	12	yes	—
105	#125×C₃₇	C₂³	1	12	yes	—
106	#125×C₃₇	C₂³	1	24	yes	—
107	#125×C₃₇	C₂³	1	48	yes	—
108	#124×C₃₇	C₂³	1	12	yes	—
109	#124×C₃₇	C₂³	1	12	yes	—
110	#124×C₃₇	C₂³	1	12	yes	—
111	#124×C₃₇	C₂³	1	24	yes	—
112	#123×C₃₇	C₂³	1	8	yes	—
113	#123×C₃₇	C₂³	1	24	yes	—
114	#123×C₃₇	C₂³	1	24	yes	—
115	#123×C₃₇	C₂³	1	48	yes	—
116	C₂²⋊Q₈×C₃₇	C₂³	1	4	yes	—
117	C₂²⋊Q₈×C₃₇	C₂³	1	4	yes	—
118	C₂²⋊Q₈×C₃₇	C₂³	1	12	yes	—
119	C₂²⋊Q₈×C₃₇	C₂³	1	12	yes	—
120	C₂²⋊Q₈×C₃₇	C₂³	1	12	yes	—
121	C₂²⋊Q₈×C₃₇	C₂³	1	12	yes	—
122	C₂²⋊Q₈×C₃₇	C₂³	1	24	yes	—
123	C₂²⋊Q₈×C₃₇	C₂³	1	24	yes	—
124	C₂²⋊Q₈×C₃₇	C₂³	1	24	yes	—
125	C₂²⋊Q₈×C₃₇	C₂³	1	48	yes	—
126	#121×C₃₇	C₂³	1	4	yes	—
127	#121×C₃₇	C₂³	1	4	yes	—
128	#121×C₃₇	C₂³	1	12	yes	—
129	#121×C₃₇	C₂³	1	12	yes	—
130	#121×C₃₇	C₂³	1	12	yes	—
131	#121×C₃₇	C₂³	1	12	yes	—
132	#121×C₃₇	C₂³	1	24	yes	—
133	#120×C₃₇	C₂³	1	8	yes	—
134	C₄×Q₈×C₃₇	C₂³	1	8	yes	—
135	C₄×Q₈×C₃₇	C₂³	1	8	yes	—
136	C₄×Q₈×C₃₇	C₂³	1	4	yes	—
137	C₄×Q₈×C₃₇	C₂³	1	12	yes	—
138	C₄×Q₈×C₃₇	C₂³	1	24	yes	—
139	C₄×Q₈×C₃₇	C₂³	1	12	yes	—
140	C₄×Q₈×C₃₇	C₂³	1	12	yes	—
141	C₄×Q₈×C₃₇	C₂³	1	12	yes	—
142	C₄×Q₈×C₃₇	C₂³	1	12	yes	—
143	C₄×Q₈×C₃₇	C₂³	1	12	yes	—
144	C₄×Q₈×C₃₇	C₂³	1	12	yes	—
145	C₄×Q₈×C₃₇	C₂³	1	12	yes	—
146	C₄×Q₈×C₃₇	C₂³	1	4	yes	—
147	C₄×Q₈×C₃₇	C₂³	1	4	yes	—
148	C₄×Q₈×C₃₇	C₂³	1	12	yes	—
149	C₄×Q₈×C₃₇	C₂³	1	12	yes	—
150	C₄×Q₈×C₃₇	C₂³	1	4	yes	—
151	C₄×D₄×C₃₇	C₂³	1	24	yes	—
152	C₄×D₄×C₃₇	C₂³	1	24	yes	—
153	C₄×D₄×C₃₇	C₂³	1	12	yes	—
154	C₄×D₄×C₃₇	C₂³	1	8	yes	—
155	C₄×D₄×C₃₇	C₂³	1	8	yes	—
156	C₄×D₄×C₃₇	C₂³	1	24	yes	—
157	C₄×D₄×C₃₇	C₂³	1	24	yes	—
158	C₄×D₄×C₃₇	C₂³	1	24	yes	—
159	C₄×D₄×C₃₇	C₂³	1	12	yes	—
160	C₄×D₄×C₃₇	C₂³	1	12	yes	—
161	C₄×D₄×C₃₇	C₂³	1	12	yes	—
162	C₄×D₄×C₃₇	C₂³	1	12	yes	—
163	C₄×D₄×C₃₇	C₂³	1	12	yes	—
164	#117×C₃₇	C₂³	1	12	yes	—
165	#117×C₃₇	C₂³	1	24	yes	—
166	#117×C₃₇	C₂³	1	24	yes	—
167	#117×C₃₇	C₂³	1	4	yes	—
168	#117×C₃₇	C₂³	1	12	yes	—
169	#117×C₃₇	C₂³	1	24	yes	—
170	#117×C₃₇	C₂³	1	24	yes	—
171	C₂×C₄⋊C₄×C₃₇	C₂³	1	3	yes	—
172	C₂×C₄⋊C₄×C₃₇	C₂³	1	24	yes	—
173	C₂×C₄⋊C₄×C₃₇	C₂³	1	3	yes	—
174	C₂×C₄⋊C₄×C₃₇	C₂³	1	6	yes	—
175	C₂×C₄⋊C₄×C₃₇	C₂³	1	12	yes	—
176	C₂×C₄⋊C₄×C₃₇	C₂³	1	12	yes	—
177	C₂×C₄²×C₃₇	C₂³	1	6	yes	—
178	C₂×C₄²×C₃₇	C₂³	1	3	yes	—
179	C₂×C₄²×C₃₇	C₂³	1	3	yes	—
180	C₂×C₄²×C₃₇	C₂³	1	6	yes	—
181	C₂×C₄²×C₃₇	C₂³	1	6	yes	—
182	C₂×C₄²×C₃₇	C₂³	1	24	yes	—
183	C₂×C₄²×C₃₇	C₂³	1	3	yes	—
184	C₂×C₄²×C₃₇	C₂³	1	6	yes	—
185	C₂×C₄²×C₃₇	C₂³	1	3	yes	—
186	C₂⁴×C₃₇	C₂⁴	1	1	yes	characteristic
187	#41×C₃₇	—	2	32	no	—
188	#41×C₃₇	—	2	48	no	—
189	#41×C₃₇	—	2	16	no	—
190	#41×C₃₇	—	4	24	no	—
191	C₂×Q₈×C₃₇	—	2	16	no	—
192	C₂×Q₈×C₃₇	—	2	16	no	—
193	C₂×Q₈×C₃₇	—	2	32	no	—
194	C₂×Q₈×C₃₇	—	2	12	no	—
195	C₂×Q₈×C₃₇	#41	1	8	yes	complemented
196	C₂×Q₈×C₃₇	C₂⁴	1	4	yes	—
197	C₂×Q₈×C₃₇	C₂⁴	1	12	yes	—
198	C₂×Q₈×C₃₇	C₂⁴	1	12	yes	—
199	C₂×Q₈×C₃₇	C₂⁴	1	12	yes	—
200	C₂×Q₈×C₃₇	C₂⁴	1	4	yes	—
201	C₂×D₄×C₃₇	C₂⁴	1	8	yes	—
202	C₂×D₄×C₃₇	C₂⁴	1	4	yes	—
203	C₂×D₄×C₃₇	C₂⁴	1	8	yes	—
204	C₂×D₄×C₃₇	C₂⁴	1	8	yes	—
205	C₂×D₄×C₃₇	C₂⁴	1	12	yes	—
206	C₂×D₄×C₃₇	C₂⁴	1	12	yes	—
207	C₂²×C₄×C₃₇	—	2	12	no	—
208	C₂²×C₄×C₃₇	—	2	4	no	—
209	C₂²×C₄×C₃₇	—	4	6	no	—
210	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₃₇	C₂⁴	1	6	yes	—
214	C₂²×C₄×C₃₇	C₂⁴	1	6	yes	—
215	C₂²×C₄×C₃₇	C₂⁴	1	6	yes	—
216	C₂²×C₄×C₃₇	C₂⁴	1	3	yes	—
217	C₂²×C₄×C₃₇	C₂⁴	1	24	yes	—
218	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₃₇	C₂⁴	1	8	yes	—
221	C₂²×C₄×C₃₇	C₂⁴	1	3	yes	—
222	C₂²×C₄×C₃₇	C₂⁴	1	6	yes	—
223	C₂²×C₄×C₃₇	C₂⁴	1	3	yes	—
224	C₂²×C₄×C₃₇	C₂⁴	1	24	yes	—
225	C₂²×C₄×C₃₇	C₂⁴	1	3	yes	—
226	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
227	C₄⋊C₄×C₃₇	C₂⁴	1	12	yes	—
228	C₄⋊C₄×C₃₇	C₂⁴	1	12	yes	—
229	C₄⋊C₄×C₃₇	C₂⁴	1	24	yes	—
230	C₄⋊C₄×C₃₇	C₂⁴	1	12	yes	—
231	C₄⋊C₄×C₃₇	C₂⁴	1	24	yes	—
232	C₄⋊C₄×C₃₇	C₂⁴	1	12	yes	—
233	C₄⋊C₄×C₃₇	C₂⁴	1	8	yes	—
234	C₄⋊C₄×C₃₇	C₂⁴	1	8	yes	—
235	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
236	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
237	C₄⋊C₄×C₃₇	C₂⁴	1	12	yes	—
238	C₄⋊C₄×C₃₇	C₂⁴	1	12	yes	—
239	C₄⋊C₄×C₃₇	C₂⁴	1	24	yes	—
240	C₄⋊C₄×C₃₇	C₂⁴	1	24	yes	—
241	C₄⋊C₄×C₃₇	C₂⁴	1	24	yes	—
242	C₂²⋊C₄×C₃₇	C₂⁴	1	8	yes	—
243	C₂²⋊C₄×C₃₇	C₂⁴	1	8	yes	—
244	C₂²⋊C₄×C₃₇	C₂⁴	1	24	yes	—
245	C₂²⋊C₄×C₃₇	C₂⁴	1	8	yes	—
246	C₂²⋊C₄×C₃₇	C₂⁴	1	8	yes	—
247	C₂²⋊C₄×C₃₇	C₂⁴	1	8	yes	—
248	C₂²⋊C₄×C₃₇	C₂⁴	1	24	yes	—
249	C₂²⋊C₄×C₃₇	C₂⁴	1	24	yes	—
250	C₂²⋊C₄×C₃₇	C₂⁴	1	24	yes	—
251	C₄²×C₃₇	C₂⁴	1	6	yes	—
252	C₄²×C₃₇	C₂⁴	1	6	yes	—
253	C₄²×C₃₇	C₂⁴	1	6	yes	—
254	C₄²×C₃₇	C₂⁴	1	6	yes	—
255	C₄²×C₃₇	C₂⁴	1	6	yes	—
256	C₄²×C₃₇	C₂⁴	1	6	yes	—
257	C₄²×C₃₇	C₂⁴	1	24	yes	—
258	C₄²×C₃₇	C₂⁴	1	24	yes	—
259	C₄²×C₃₇	C₂⁴	1	6	yes	—
260	C₄²×C₃₇	C₂⁴	1	6	yes	—
261	C₄²×C₃₇	C₂⁴	1	8	yes	—
262	C₂³×C₃₇	—	2	2	no	—
263	C₂³×C₃₇	—	2	2	no	—
264	C₂³×C₃₇	—	2	2	no	—
265	C₂³×C₃₇	C₂⁵	1	8	yes	—
266	C₂³×C₃₇	C₂⁵	1	1	yes	characteristic
267	C₂³×C₃₇	C₂⁵	1	1	yes	characteristic
268	C₂³×C₃₇	C₂⁵	1	1	yes	characteristic
269	Q₈×C₃₇	—	2	24	no	—
270	Q₈×C₃₇	—	2	24	no	—
271	Q₈×C₃₇	—	2	8	no	—
272	Q₈×C₃₇	—	4	12	no	—
273	Q₈×C₃₇	C₂×#41	1	16	yes	—
274	D₄×C₃₇	—	2	16	no	—
275	D₄×C₃₇	—	2	16	no	—
276	D₄×C₃₇	—	2	16	no	—
277	D₄×C₃₇	—	2	24	no	—
278	D₄×C₃₇	—	2	8	no	—
279	D₄×C₃₇	—	4	12	no	—
280	C₂×C₄×C₃₇	—	2	6	no	—
281	C₂×C₄×C₃₇	—	2	2	no	—
282	C₂×C₄×C₃₇	—	2	12	no	—
283	C₂×C₄×C₃₇	—	2	12	no	—
284	C₂×C₄×C₃₇	—	2	12	no	—
285	C₂×C₄×C₃₇	—	2	48	no	—
286	C₂×C₄×C₃₇	—	2	2	no	—
287	C₂×C₄×C₃₇	—	2	2	no	—
288	C₂×C₄×C₃₇	—	2	2	no	—
289	C₂×C₄×C₃₇	—	2	2	no	—
290	C₂×C₄×C₃₇	—	2	16	no	—
291	C₂×C₄×C₃₇	—	4	3	no	—
292	C₂×C₄×C₃₇	—	4	6	no	—
293	C₂×C₄×C₃₇	—	4	3	no	—
294	C₂×C₄×C₃₇	—	4	24	no	—
295	C₂×C₄×C₃₇	C₂×#41	1	12	yes	—
296	C₂×C₄×C₃₇	2₋¹⁺⁴	1	4	yes	complemented
297	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
298	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
299	C₂×C₄×C₃₇	C₂⁵	1	6	yes	—
300	C₂×C₄×C₃₇	C₂⁵	1	8	yes	—
301	C₂×C₄×C₃₇	C₂⁵	1	6	yes	—
302	C₂×C₄×C₃₇	C₂⁵	1	8	yes	—
303	C₂×C₄×C₃₇	C₂⁵	1	8	yes	—
304	C₂×C₄×C₃₇	C₂⁵	1	6	yes	—
305	C₂×C₄×C₃₇	C₂⁵	1	6	yes	—
306	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
307	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
308	#62788	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
309	C₂²×C₃₇	—	2	8	no	—
310	C₂²×C₃₇	—	2	1	no	—
311	C₂²×C₃₇	—	2	1	no	—
312	C₂²×C₃₇	—	2	1	no	—
313	C₂²×C₃₇	—	2	1	no	—
314	C₂²×C₃₇	—	2	1	no	—
315	C₂²×C₃₇	—	2	1	no	—
316	C₂²×C₃₇	—	2	8	no	—
317	C₂²×C₃₇	—	2	8	no	—
318	C₂²×C₃₇	—	2	8	no	—
319	C₂²×C₃₇	C₂²×#41	1	2	yes	—
320	C₂²×C₃₇	C₂×2₋¹⁺⁴	1	2	yes	—
321	C₂²×C₃₇	#585	1	2	yes	—
322	C₂²×C₃₇	C₂⁶	1	1	yes	characteristic
323	C₄×C₃₇	—	2	8	no	—
324	C₄×C₃₇	—	2	6	no	—
325	C₄×C₃₇	—	2	1	no	—
326	C₄×C₃₇	—	2	1	no	—
327	C₄×C₃₇	—	2	8	no	—
328	C₄×C₃₇	—	2	6	no	—
329	C₄×C₃₇	—	2	6	no	—
330	C₄×C₃₇	—	2	8	no	—
331	C₄×C₃₇	C₂²×#41	1	12	yes	—
332	C₄×C₃₇	C₂×2₋¹⁺⁴	1	2	yes	—
333	C₄×C₃₇	C₂×2₋¹⁺⁴	1	2	yes	—
334	#3523	C₂×C₃₇	1	4	yes	complemented
335	#3522	C₂×C₃₇	1	4	yes	complemented
336	#3516	C₂×C₃₇	1	8	yes	complemented
337	#3507	C₂×C₃₇	1	6	yes	complemented
338	#3502	C₂×C₃₇	1	1	yes	characteristic, complemented
339	#3497	C₂×C₃₇	1	1	yes	characteristic, complemented
340	#3492	C₂×C₃₇	1	6	yes	complemented
341	#3486	C₂×C₃₇	1	2	yes	complemented
342	#3482	C₂×C₃₇	1	8	yes	complemented
343	#3480	C₂×C₃₇	1	4	yes	complemented
344	Q₈×#41	C₂×C₃₇	1	4	yes	complemented
345	#3461	C₂×C₃₇	1	6	yes	complemented
346	#3444	C₂×C₃₇	1	6	yes	complemented
347	C₄×2₋¹⁺⁴	C₂×C₃₇	1	2	yes	complemented
348	C₂²×C₄×Q₈	C₂×C₃₇	1	1	yes	characteristic, complemented
349	C₂×C₃₇	—	2	2	no	—
350	C₂×C₃₇	—	2	2	no	—
351	C₂×C₃₇	—	2	2	no	—
352	C₂×C₃₇	—	4	8	no	—
353	C₂×C₃₇	C₂³×#41	1	1	yes	characteristic
354	C₂×C₃₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
355	C₂×C₃₇	C₂×#585	1	1	yes	characteristic
356	C₂×2₋¹⁺⁴	C₂²×C₃₇	1	2	yes	—
357	C₂³×Q₈	C₂²×C₃₇	1	1	yes	characteristic
358	#559	C₂²×C₃₇	1	12	yes	complemented
359	Q₈²	C₂²×C₃₇	1	4	yes	complemented
360	#557	C₂²×C₃₇	1	12	yes	complemented
361	#557	C₂²×C₃₇	1	4	yes	complemented
362	#557	C₂²×C₃₇	1	8	yes	complemented
363	#556	C₂²×C₃₇	1	12	yes	complemented
364	#556	C₂²×C₃₇	1	24	yes	complemented
365	#554	C₂²×C₃₇	1	24	yes	—
366	#554	C₂²×C₃₇	1	12	yes	complemented
367	#553	C₂²×C₃₇	1	24	yes	—
368	#552	C₂²×C₃₇	1	24	yes	—
369	#552	C₂²×C₃₇	1	24	yes	complemented
370	#550	C₂²×C₃₇	1	4	yes	complemented
371	D₄×Q₈	C₂²×C₃₇	1	8	yes	—
372	D₄×Q₈	C₂²×C₃₇	1	8	yes	—
373	D₄×Q₈	C₂²×C₃₇	1	4	yes	complemented
374	#548	C₂²×C₃₇	1	8	yes	—
375	#548	C₂²×C₃₇	1	8	yes	—
376	#548	C₂²×C₃₇	1	8	yes	complemented
377	#547	C₂²×C₃₇	1	24	yes	—
378	#544	C₂²×C₃₇	1	6	yes	—
379	#542	C₂²×C₃₇	1	24	yes	complemented
380	#541	C₂²×C₃₇	1	24	yes	complemented
381	#539	C₂²×C₃₇	1	24	yes	—
382	#537	C₂²×C₃₇	1	6	yes	—
383	#536	C₂²×C₃₇	1	12	yes	—
384	#533	C₂²×C₃₇	1	6	yes	—
385	#533	C₂²×C₃₇	1	6	yes	—
386	#533	C₂²×C₃₇	1	6	yes	—
387	#533	C₂²×C₃₇	1	24	yes	complemented
388	#532	C₂²×C₃₇	1	6	yes	—
389	#532	C₂²×C₃₇	1	6	yes	—
390	#532	C₂²×C₃₇	1	6	yes	—
391	#529	C₂²×C₃₇	1	12	yes	—
392	#529	C₂²×C₃₇	1	12	yes	—
393	#529	C₂²×C₃₇	1	12	yes	—
394	#529	C₂²×C₃₇	1	12	yes	—
395	#529	C₂²×C₃₇	1	12	yes	—
396	#529	C₂²×C₃₇	1	12	yes	—
397	#529	C₂²×C₃₇	1	24	yes	complemented
398	#525	C₂²×C₃₇	1	4	yes	—
399	#525	C₂²×C₃₇	1	12	yes	—
400	#525	C₂²×C₃₇	1	12	yes	—
401	#520	C₂²×C₃₇	1	12	yes	—
402	#520	C₂²×C₃₇	1	8	yes	complemented
403	#519	C₂²×C₃₇	1	2	yes	—
404	#519	C₂²×C₃₇	1	8	yes	complemented
405	C₄×#41	C₂²×C₃₇	1	12	yes	—
406	C₄×#41	C₂²×C₃₇	1	12	yes	—
407	C₄×#41	C₂²×C₃₇	1	12	yes	—
408	C₄×#41	C₂²×C₃₇	1	8	yes	complemented
409	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
410	C₂×C₄×Q₈	C₂²×C₃₇	1	3	yes	—
411	C₂×C₄×Q₈	C₂²×C₃₇	1	4	yes	—
412	C₂×C₄×Q₈	C₂²×C₃₇	1	4	yes	—
413	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
414	C₂×C₄×Q₈	C₂²×C₃₇	1	3	yes	—
415	C₂×C₄×Q₈	C₂²×C₃₇	1	4	yes	—
416	C₂×C₄×Q₈	C₂²×C₃₇	1	4	yes	—
417	C₂×C₄×Q₈	C₂²×C₃₇	1	8	yes	complemented
418	C₂²×C₄⋊C₄	C₂²×C₃₇	1	3	yes	—
419	C₂²×C₄²	C₂²×C₃₇	1	3	yes	—
420	C₃₇	#62788	1	1	yes	characteristic, direct product factor, Sylow
421	2₋¹⁺⁴	—	2	16	no	—
422	C₂×#41	C₂³×C₃₇	1	4	yes	—
423	C₂×#41	C₂³×C₃₇	1	12	yes	—
424	C₂×#41	C₂³×C₃₇	1	8	yes	—
425	C₂×#41	C₂³×C₃₇	1	12	yes	—
426	C₂²×Q₈	—	2	8	no	—
427	C₂²×Q₈	C₂³×C₃₇	1	3	yes	—
428	C₂²×Q₈	C₂³×C₃₇	1	4	yes	—
429	C₂²×Q₈	C₂³×C₃₇	1	4	yes	—
430	C₂²×Q₈	C₂³×C₃₇	1	8	yes	—
431	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
432	C₂³×C₄	C₂³×C₃₇	1	3	yes	—
433	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
434	C₂³×C₄	C₂³×C₃₇	1	3	yes	—
435	C₄⋊Q₈	C₂³×C₃₇	1	6	yes	—
436	C₄⋊Q₈	C₂³×C₃₇	1	6	yes	—
437	C₄⋊Q₈	C₂³×C₃₇	1	6	yes	—
438	C₄⋊Q₈	C₂³×C₃₇	1	24	yes	—
439	C₄⋊Q₈	C₂³×C₃₇	1	24	yes	—
440	#127	C₂³×C₃₇	1	6	yes	—
441	#126	C₂³×C₃₇	1	24	yes	—
442	#126	C₂³×C₃₇	1	24	yes	—
443	#126	C₂³×C₃₇	1	48	yes	—
444	#125	C₂³×C₃₇	1	12	yes	—
445	#125	C₂³×C₃₇	1	12	yes	—
446	#125	C₂³×C₃₇	1	12	yes	—
447	#125	C₂³×C₃₇	1	24	yes	—
448	#125	C₂³×C₃₇	1	48	yes	—
449	#124	C₂³×C₃₇	1	12	yes	—
450	#124	C₂³×C₃₇	1	12	yes	—
451	#124	C₂³×C₃₇	1	12	yes	—
452	#124	C₂³×C₃₇	1	24	yes	—
453	#123	C₂³×C₃₇	1	8	yes	—
454	#123	C₂³×C₃₇	1	24	yes	—
455	#123	C₂³×C₃₇	1	24	yes	—
456	#123	C₂³×C₃₇	1	48	yes	—
457	C₂²⋊Q₈	C₂³×C₃₇	1	4	yes	—
458	C₂²⋊Q₈	C₂³×C₃₇	1	4	yes	—
459	C₂²⋊Q₈	C₂³×C₃₇	1	12	yes	—
460	C₂²⋊Q₈	C₂³×C₃₇	1	12	yes	—
461	C₂²⋊Q₈	C₂³×C₃₇	1	12	yes	—
462	C₂²⋊Q₈	C₂³×C₃₇	1	12	yes	—
463	C₂²⋊Q₈	C₂³×C₃₇	1	24	yes	—
464	C₂²⋊Q₈	C₂³×C₃₇	1	24	yes	—
465	C₂²⋊Q₈	C₂³×C₃₇	1	24	yes	—
466	C₂²⋊Q₈	C₂³×C₃₇	1	48	yes	—
467	#121	C₂³×C₃₇	1	4	yes	—
468	#121	C₂³×C₃₇	1	4	yes	—
469	#121	C₂³×C₃₇	1	12	yes	—
470	#121	C₂³×C₃₇	1	12	yes	—
471	#121	C₂³×C₃₇	1	12	yes	—
472	#121	C₂³×C₃₇	1	12	yes	—
473	#121	C₂³×C₃₇	1	24	yes	—
474	#120	C₂³×C₃₇	1	8	yes	—
475	C₄×Q₈	C₂³×C₃₇	1	4	yes	—
476	C₄×Q₈	C₂³×C₃₇	1	4	yes	—
477	C₄×Q₈	C₂³×C₃₇	1	12	yes	—
478	C₄×Q₈	C₂³×C₃₇	1	12	yes	—
479	C₄×Q₈	C₂³×C₃₇	1	4	yes	—
480	C₄×Q₈	C₂³×C₃₇	1	4	yes	—
481	C₄×Q₈	C₂³×C₃₇	1	12	yes	—
482	C₄×Q₈	C₂³×C₃₇	1	12	yes	—
483	C₄×Q₈	C₂³×C₃₇	1	12	yes	—
484	C₄×Q₈	C₂³×C₃₇	1	8	yes	—
485	C₄×Q₈	C₂³×C₃₇	1	24	yes	—
486	C₄×Q₈	C₂³×C₃₇	1	12	yes	—
487	C₄×Q₈	C₂³×C₃₇	1	12	yes	—
488	C₄×Q₈	C₂³×C₃₇	1	12	yes	—
489	C₄×Q₈	C₂³×C₃₇	1	12	yes	—
490	C₄×Q₈	C₂³×C₃₇	1	12	yes	—
491	C₄×Q₈	C₂³×C₃₇	1	8	yes	—
492	C₄×D₄	C₂³×C₃₇	1	8	yes	—
493	C₄×D₄	C₂³×C₃₇	1	8	yes	—
494	C₄×D₄	C₂³×C₃₇	1	12	yes	—
495	C₄×D₄	C₂³×C₃₇	1	24	yes	—
496	C₄×D₄	C₂³×C₃₇	1	12	yes	—
497	C₄×D₄	C₂³×C₃₇	1	24	yes	—
498	C₄×D₄	C₂³×C₃₇	1	24	yes	—
499	C₄×D₄	C₂³×C₃₇	1	24	yes	—
500	C₄×D₄	C₂³×C₃₇	1	12	yes	—
501	C₄×D₄	C₂³×C₃₇	1	12	yes	—
502	C₄×D₄	C₂³×C₃₇	1	12	yes	—
503	C₄×D₄	C₂³×C₃₇	1	12	yes	—
504	C₄×D₄	C₂³×C₃₇	1	24	yes	—
505	#117	C₂³×C₃₇	1	4	yes	—
506	#117	C₂³×C₃₇	1	12	yes	—
507	#117	C₂³×C₃₇	1	24	yes	—
508	#117	C₂³×C₃₇	1	12	yes	—
509	#117	C₂³×C₃₇	1	24	yes	—
510	#117	C₂³×C₃₇	1	24	yes	—
511	#117	C₂³×C₃₇	1	24	yes	—
512	C₂×C₄⋊C₄	C₂³×C₃₇	1	3	yes	—
513	C₂×C₄⋊C₄	C₂³×C₃₇	1	3	yes	—
514	C₂×C₄⋊C₄	C₂³×C₃₇	1	6	yes	—
515	C₂×C₄⋊C₄	C₂³×C₃₇	1	12	yes	—
516	C₂×C₄⋊C₄	C₂³×C₃₇	1	12	yes	—
517	C₂×C₄⋊C₄	C₂³×C₃₇	1	24	yes	—
518	C₂×C₄²	C₂³×C₃₇	1	3	yes	—
519	C₂×C₄²	C₂³×C₃₇	1	6	yes	—
520	C₂×C₄²	C₂³×C₃₇	1	6	yes	—
521	C₂×C₄²	C₂³×C₃₇	1	3	yes	—
522	C₂×C₄²	C₂³×C₃₇	1	6	yes	—
523	C₂×C₄²	C₂³×C₃₇	1	3	yes	—
524	C₂×C₄²	C₂³×C₃₇	1	6	yes	—
525	C₂×C₄²	C₂³×C₃₇	1	3	yes	—
526	C₂×C₄²	C₂³×C₃₇	1	24	yes	—
527	C₂⁴	C₂⁴×C₃₇	1	1	yes	characteristic
528	#41	—	2	32	no	—
529	#41	—	2	48	no	—
530	#41	—	2	16	no	—
531	#41	—	4	24	no	—
532	C₂×Q₈	—	2	16	no	—
533	C₂×Q₈	—	2	16	no	—
534	C₂×Q₈	—	2	32	no	—
535	C₂×Q₈	—	2	12	no	—
536	C₂×Q₈	#41×C₃₇	1	8	yes	complemented
537	C₂×Q₈	C₂⁴×C₃₇	1	4	yes	—
538	C₂×Q₈	C₂⁴×C₃₇	1	12	yes	—
539	C₂×Q₈	C₂⁴×C₃₇	1	12	yes	—
540	C₂×Q₈	C₂⁴×C₃₇	1	12	yes	—
541	C₂×Q₈	C₂⁴×C₃₇	1	4	yes	—
542	C₂×D₄	C₂⁴×C₃₇	1	8	yes	—
543	C₂×D₄	C₂⁴×C₃₇	1	4	yes	—
544	C₂×D₄	C₂⁴×C₃₇	1	8	yes	—
545	C₂×D₄	C₂⁴×C₃₇	1	8	yes	—
546	C₂×D₄	C₂⁴×C₃₇	1	12	yes	—
547	C₂×D₄	C₂⁴×C₃₇	1	12	yes	—
548	C₂²×C₄	—	2	12	no	—
549	C₂²×C₄	—	2	4	no	—
550	C₂²×C₄	—	4	6	no	—
551	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
554	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
555	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
556	C₂²×C₄	C₂⁴×C₃₇	1	8	yes	—
557	C₂²×C₄	C₂⁴×C₃₇	1	6	yes	—
558	C₂²×C₄	C₂⁴×C₃₇	1	6	yes	—
559	C₂²×C₄	C₂⁴×C₃₇	1	6	yes	—
560	C₂²×C₄	C₂⁴×C₃₇	1	3	yes	—
561	C₂²×C₄	C₂⁴×C₃₇	1	24	yes	—
562	C₂²×C₄	C₂⁴×C₃₇	1	3	yes	—
563	C₂²×C₄	C₂⁴×C₃₇	1	6	yes	—
564	C₂²×C₄	C₂⁴×C₃₇	1	3	yes	—
565	C₂²×C₄	C₂⁴×C₃₇	1	24	yes	—
566	C₂²×C₄	C₂⁴×C₃₇	1	3	yes	—
567	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
568	C₄⋊C₄	C₂⁴×C₃₇	1	12	yes	—
569	C₄⋊C₄	C₂⁴×C₃₇	1	12	yes	—
570	C₄⋊C₄	C₂⁴×C₃₇	1	24	yes	—
571	C₄⋊C₄	C₂⁴×C₃₇	1	12	yes	—
572	C₄⋊C₄	C₂⁴×C₃₇	1	24	yes	—
573	C₄⋊C₄	C₂⁴×C₃₇	1	12	yes	—
574	C₄⋊C₄	C₂⁴×C₃₇	1	8	yes	—
575	C₄⋊C₄	C₂⁴×C₃₇	1	8	yes	—
576	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
577	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
578	C₄⋊C₄	C₂⁴×C₃₇	1	12	yes	—
579	C₄⋊C₄	C₂⁴×C₃₇	1	12	yes	—
580	C₄⋊C₄	C₂⁴×C₃₇	1	24	yes	—
581	C₄⋊C₄	C₂⁴×C₃₇	1	24	yes	—
582	C₄⋊C₄	C₂⁴×C₃₇	1	24	yes	—
583	C₂²⋊C₄	C₂⁴×C₃₇	1	8	yes	—
584	C₂²⋊C₄	C₂⁴×C₃₇	1	8	yes	—
585	C₂²⋊C₄	C₂⁴×C₃₇	1	24	yes	—
586	C₂²⋊C₄	C₂⁴×C₃₇	1	8	yes	—
587	C₂²⋊C₄	C₂⁴×C₃₇	1	8	yes	—
588	C₂²⋊C₄	C₂⁴×C₃₇	1	8	yes	—
589	C₂²⋊C₄	C₂⁴×C₃₇	1	24	yes	—
590	C₂²⋊C₄	C₂⁴×C₃₇	1	24	yes	—
591	C₂²⋊C₄	C₂⁴×C₃₇	1	24	yes	—
592	C₄²	C₂⁴×C₃₇	1	6	yes	—
593	C₄²	C₂⁴×C₃₇	1	6	yes	—
594	C₄²	C₂⁴×C₃₇	1	6	yes	—
595	C₄²	C₂⁴×C₃₇	1	8	yes	—
596	C₄²	C₂⁴×C₃₇	1	6	yes	—
597	C₄²	C₂⁴×C₃₇	1	6	yes	—
598	C₄²	C₂⁴×C₃₇	1	6	yes	—
599	C₄²	C₂⁴×C₃₇	1	6	yes	—
600	C₄²	C₂⁴×C₃₇	1	6	yes	—
601	C₄²	C₂⁴×C₃₇	1	24	yes	—
602	C₄²	C₂⁴×C₃₇	1	24	yes	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	2	2	no	—
606	C₂³	C₂⁵×C₃₇	1	8	yes	—
607	C₂³	C₂⁵×C₃₇	1	1	yes	characteristic
608	C₂³	C₂⁵×C₃₇	1	1	yes	characteristic
609	C₂³	C₂⁵×C₃₇	1	1	yes	characteristic
610	Q₈	—	2	24	no	—
611	Q₈	—	2	24	no	—
612	Q₈	—	2	8	no	—
613	Q₈	—	4	12	no	—
614	Q₈	C₂×#41×C₃₇	1	16	yes	—
615	D₄	—	2	16	no	—
616	D₄	—	2	16	no	—
617	D₄	—	2	16	no	—
618	D₄	—	2	24	no	—
619	D₄	—	2	8	no	—
620	D₄	—	4	12	no	—
621	C₂×C₄	—	2	6	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	12	no	—
624	C₂×C₄	—	2	12	no	—
625	C₂×C₄	—	2	12	no	—
626	C₂×C₄	—	2	48	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	16	no	—
632	C₂×C₄	—	4	3	no	—
633	C₂×C₄	—	4	6	no	—
634	C₂×C₄	—	4	3	no	—
635	C₂×C₄	—	4	24	no	—
636	C₂×C₄	C₂×#41×C₃₇	1	12	yes	—
637	C₂×C₄	2₋¹⁺⁴×C₃₇	1	4	yes	complemented
638	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
639	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
640	C₂×C₄	C₂⁵×C₃₇	1	6	yes	—
641	C₂×C₄	C₂⁵×C₃₇	1	8	yes	—
642	C₂×C₄	C₂⁵×C₃₇	1	6	yes	—
643	C₂×C₄	C₂⁵×C₃₇	1	8	yes	—
644	C₂×C₄	C₂⁵×C₃₇	1	8	yes	—
645	C₂×C₄	C₂⁵×C₃₇	1	6	yes	—
646	C₂×C₄	C₂⁵×C₃₇	1	6	yes	—
647	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
648	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
649	C₂²	—	2	8	no	—
650	C₂²	—	2	1	no	—
651	C₂²	—	2	1	no	—
652	C₂²	—	2	1	no	—
653	C₂²	—	2	1	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	8	no	—
657	C₂²	—	2	8	no	—
658	C₂²	—	2	8	no	—
659	C₂²	C₂²×#41×C₃₇	1	2	yes	—
660	C₂²	C₂×2₋¹⁺⁴×C₃₇	1	2	yes	—
661	C₂²	C₃₇×#585	1	2	yes	—
662	C₂²	C₂⁶×C₃₇	1	1	yes	characteristic
663	C₄	—	2	8	no	—
664	C₄	—	2	6	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	8	no	—
668	C₄	—	2	6	no	—
669	C₄	—	2	6	no	—
670	C₄	—	2	8	no	—
671	C₄	C₂²×#41×C₃₇	1	12	yes	—
672	C₄	C₂×2₋¹⁺⁴×C₃₇	1	2	yes	—
673	C₄	C₂×2₋¹⁺⁴×C₃₇	1	2	yes	—
674	C₂	—	2	2	no	—
675	C₂	—	2	2	no	—
676	C₂	—	2	2	no	—
677	C₂	—	4	8	no	—
678	C₂	C₂³×#41×C₃₇	1	1	yes	characteristic
679	C₂	C₂²×2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
680	C₂	C₂×C₃₇×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃₇
socle	C₂²×C₃₇	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×#3523	C₂	semidirect
2. C₃₇×#3522	C₂	semidirect
3. C₃₇×#3516	C₂	semidirect
4. C₃₇×#3507	C₂	semidirect
5. C₃₇×#3502	C₂	semidirect
6. C₃₇×#3497	C₂	semidirect
7. C₃₇×#3492	C₂	semidirect
8. C₃₇×#3486	C₂	semidirect
9. C₃₇×#3482	C₂	semidirect
10. C₃₇×#3480	C₂	semidirect
11. Q₈×#41×C₃₇	C₂	semidirect
12. C₃₇×#3461	C₂	semidirect
13. C₃₇×#3444	C₂	semidirect
14. C₄×2₋¹⁺⁴×C₃₇	C₂	semidirect
15. C₂²×C₄×Q₈×C₃₇	C₂	semidirect
18. C₃₇×#559	C₂²	semidirect
19. Q₈²×C₃₇	C₂²	semidirect
20. C₃₇×#557	C₂²	semidirect
21. C₃₇×#557	C₂²	semidirect
22. C₃₇×#557	C₂²	semidirect
23. C₃₇×#556	C₂²	semidirect
24. C₃₇×#556	C₂²	semidirect
26. C₃₇×#554	C₂²	semidirect
29. C₃₇×#552	C₂²	semidirect
30. C₃₇×#550	C₂²	semidirect
33. D₄×Q₈×C₃₇	C₂²	semidirect
36. C₃₇×#548	C₂²	semidirect
39. C₃₇×#542	C₂²	semidirect
40. C₃₇×#541	C₂²	semidirect
47. C₃₇×#533	C₂²	semidirect
57. C₃₇×#529	C₂²	semidirect
62. C₃₇×#520	C₂²	semidirect
64. C₃₇×#519	C₂²	semidirect
68. C₄×#41×C₃₇	C₂²	semidirect
77. C₂×C₄×Q₈×C₃₇	C₂²	semidirect
195. C₂×Q₈×C₃₇	#41	semidirect
296. C₂×C₄×C₃₇	2₋¹⁺⁴	semidirect
308. #62788	C₃₇	direct (N × H)
334. #3523	C₂×C₃₇	semidirect
335. #3522	C₂×C₃₇	semidirect
336. #3516	C₂×C₃₇	semidirect
337. #3507	C₂×C₃₇	semidirect
338. #3502	C₂×C₃₇	semidirect
339. #3497	C₂×C₃₇	semidirect
340. #3492	C₂×C₃₇	semidirect
341. #3486	C₂×C₃₇	semidirect
342. #3482	C₂×C₃₇	semidirect
343. #3480	C₂×C₃₇	semidirect
344. Q₈×#41	C₂×C₃₇	semidirect
345. #3461	C₂×C₃₇	semidirect
346. #3444	C₂×C₃₇	semidirect
347. C₄×2₋¹⁺⁴	C₂×C₃₇	semidirect
348. C₂²×C₄×Q₈	C₂×C₃₇	semidirect
358. #559	C₂²×C₃₇	semidirect
359. Q₈²	C₂²×C₃₇	semidirect
360. #557	C₂²×C₃₇	semidirect
361. #557	C₂²×C₃₇	semidirect
362. #557	C₂²×C₃₇	semidirect
363. #556	C₂²×C₃₇	semidirect
364. #556	C₂²×C₃₇	semidirect
366. #554	C₂²×C₃₇	semidirect
369. #552	C₂²×C₃₇	semidirect
370. #550	C₂²×C₃₇	semidirect
373. D₄×Q₈	C₂²×C₃₇	semidirect
376. #548	C₂²×C₃₇	semidirect
379. #542	C₂²×C₃₇	semidirect
380. #541	C₂²×C₃₇	semidirect
387. #533	C₂²×C₃₇	semidirect
397. #529	C₂²×C₃₇	semidirect
402. #520	C₂²×C₃₇	semidirect
404. #519	C₂²×C₃₇	semidirect
408. C₄×#41	C₂²×C₃₇	semidirect
417. C₂×C₄×Q₈	C₂²×C₃₇	semidirect
420. C₃₇	#62788	direct (N × H)
536. C₂×Q₈	#41×C₃₇	semidirect
637. C₂×C₄	2₋¹⁺⁴×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₃₇×#3523	2
C₃₇×#3522	2
C₃₇×#3516	2
C₃₇×#3507	2
C₃₇×#3502	2
C₃₇×#3497	2
C₃₇×#3492	2
C₃₇×#3486	2
C₃₇×#3482	2
C₃₇×#3480	2
Q₈×#41×C₃₇	2
C₃₇×#3461	2
C₃₇×#3444	2
C₄×2₋¹⁺⁴×C₃₇	2
C₂²×C₄×Q₈×C₃₇	2
#62788	37

Subgroups — C37×#62788 #22684041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#62788 #22684041