Subgroups — C₃₇×#28263 #22649516

Order 9472.

918 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×Q₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×D₈×C₃₇	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2538	C₂	1	2	yes	maximal, complemented
4	C₃₇×#2067	C₂	1	4	yes	maximal, complemented
5	C₃₇×#1970	C₂	1	2	yes	maximal
6	C₃₇×#1942	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1845	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1802	C₂	1	2	yes	maximal, complemented
9	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic
10	C₂×C₂²⋊Q₈×C₃₇	—	2	2	no	—
11	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₃₇	C₂²	1	2	yes	—
13	C₈×Q₈×C₃₇	—	2	4	no	—
14	C₄×D₈×C₃₇	—	2	4	no	—
15	C₂×#107×C₃₇	C₂²	1	2	yes	—
16	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
17	C₂×#107×C₃₇	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
20	C₂×#102×C₃₇	C₂²	1	2	yes	—
21	C₂×#102×C₃₇	C₂²	1	4	yes	—
22	C₂×C₄×C₈×C₃₇	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
24	C₃₇×#396	—	2	4	no	—
25	C₃₇×#390	C₂²	1	4	yes	—
26	C₃₇×#389	C₂²	1	4	yes	—
27	C₃₇×#384	C₂²	1	2	yes	—
28	C₃₇×#380	—	2	2	no	—
29	C₃₇×#340	C₂²	1	4	yes	—
30	C₂²×Q₈×C₃₇	D₄	1	1	yes	characteristic
31	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
32	C₂³×C₄×C₃₇	—	2	2	no	—
33	C₂×D₈×C₃₇	—	2	2	no	—
34	C₂×D₈×C₃₇	—	2	2	no	—
35	C₂×D₈×C₃₇	Q₈	1	4	yes	complemented
36	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
37	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
38	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
39	C₂²⋊Q₈×C₃₇	—	4	8	no	—
40	C₄×Q₈×C₃₇	—	2	2	no	—
41	C₄×Q₈×C₃₇	—	2	2	no	—
42	C₄×D₄×C₃₇	—	2	4	no	—
43	C₄×D₄×C₃₇	—	2	4	no	—
44	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
45	C₂×C₄⋊C₄×C₃₇	—	2	4	no	—
46	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
47	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
50	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
51	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
52	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
53	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
54	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
55	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
56	#107×C₃₇	—	2	2	no	—
57	#107×C₃₇	—	2	4	no	—
58	#107×C₃₇	—	4	2	no	—
59	C₄⋊C₈×C₃₇	—	2	4	no	—
60	C₄⋊C₈×C₃₇	—	2	2	no	—
61	#102×C₃₇	—	2	4	no	—
62	#102×C₃₇	—	4	4	no	—
63	C₄×C₈×C₃₇	—	2	4	no	—
64	C₄×C₈×C₃₇	D₄	1	4	yes	—
65	#95×C₃₇	—	2	4	no	—
66	C₂⁴×C₃₇	—	2	2	no	—
67	C₂×Q₈×C₃₇	—	2	2	no	—
68	C₂×Q₈×C₃₇	—	2	2	no	—
69	C₂×Q₈×C₃₇	D₈	1	4	yes	complemented
70	C₂×D₄×C₃₇	—	2	2	no	—
71	C₂×D₄×C₃₇	—	2	2	no	—
72	C₂×D₄×C₃₇	—	2	2	no	—
73	C₂×D₄×C₃₇	—	2	2	no	—
74	C₂×D₄×C₃₇	—	2	2	no	—
75	C₂×D₄×C₃₇	C₂×Q₈	1	4	yes	—
76	C₂²×C₄×C₃₇	—	2	2	no	—
77	C₂²×C₄×C₃₇	—	2	4	no	—
78	C₂²×C₄×C₃₇	—	4	4	no	—
79	C₂²×C₄×C₃₇	—	4	4	no	—
80	C₂²×C₄×C₃₇	—	4	4	no	—
81	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
82	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
84	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
86	D₈×C₃₇	—	2	8	no	—
87	C₂×C₈×C₃₇	—	2	1	no	—
88	C₂×C₈×C₃₇	—	2	1	no	—
89	C₂×C₈×C₃₇	—	2	2	no	—
90	C₂×C₈×C₃₇	—	2	2	no	—
91	C₂×C₈×C₃₇	—	2	2	no	—
92	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
93	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
94	C₂×C₈×C₃₇	C₂×Q₈	1	2	yes	—
95	C₂×C₈×C₃₇	#41	1	2	yes	—
96	C₄⋊C₄×C₃₇	—	2	4	no	—
97	C₄⋊C₄×C₃₇	—	2	2	no	—
98	C₄⋊C₄×C₃₇	—	2	2	no	—
99	C₄⋊C₄×C₃₇	—	2	4	no	—
100	C₄⋊C₄×C₃₇	—	2	2	no	—
101	C₄⋊C₄×C₃₇	—	2	4	no	—
102	C₄⋊C₄×C₃₇	—	4	4	no	—
103	C₄⋊C₄×C₃₇	—	4	8	no	—
104	C₄⋊C₄×C₃₇	—	8	2	no	—
105	C₂²⋊C₄×C₃₇	—	4	4	no	—
106	C₂²⋊C₄×C₃₇	—	4	8	no	—
107	C₂²⋊C₄×C₃₇	—	8	4	no	—
108	C₄²×C₃₇	—	2	2	no	—
109	C₄²×C₃₇	—	2	2	no	—
110	C₄²×C₃₇	C₂×D₄	1	2	yes	—
111	C₄²×C₃₇	#41	1	2	yes	—
112	C₂³×C₃₇	—	2	4	no	—
113	C₂³×C₃₇	—	4	2	no	—
114	C₂³×C₃₇	—	4	2	no	—
115	C₂³×C₃₇	—	4	2	no	—
116	C₂³×C₃₇	—	4	2	no	—
117	C₂³×C₃₇	—	4	2	no	—
118	C₂³×C₃₇	—	4	2	no	—
119	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
120	Q₈×C₃₇	—	2	8	no	—
121	D₄×C₃₇	—	2	4	no	—
122	D₄×C₃₇	—	2	4	no	—
123	D₄×C₃₇	—	4	2	no	—
124	D₄×C₃₇	—	4	2	no	—
125	C₂×C₄×C₃₇	—	2	2	no	—
126	C₂×C₄×C₃₇	—	2	2	no	—
127	C₂×C₄×C₃₇	—	2	1	no	—
128	C₂×C₄×C₃₇	—	2	1	no	—
129	C₂×C₄×C₃₇	—	2	2	no	—
130	C₂×C₄×C₃₇	—	2	2	no	—
131	C₂×C₄×C₃₇	—	2	2	no	—
132	C₂×C₄×C₃₇	—	4	2	no	—
133	C₂×C₄×C₃₇	—	4	4	no	—
134	C₂×C₄×C₃₇	—	4	4	no	—
135	C₂×C₄×C₃₇	—	4	2	no	—
136	C₂×C₄×C₃₇	—	4	2	no	—
137	C₂×C₄×C₃₇	—	4	4	no	—
138	C₂×C₄×C₃₇	—	8	8	no	—
139	C₂×C₄×C₃₇	#121	1	2	yes	—
140	C₂×C₄×C₃₇	#121	1	2	yes	—
141	C₂×C₄×C₃₇	C₂×D₈	1	4	yes	—
142	C₂×C₄×C₃₇	C₂×D₈	1	2	yes	—
143	C₂×C₄×C₃₇	#135	1	2	yes	—
144	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
145	C₂×C₄×C₃₇	C₂²×Q₈	1	1	yes	characteristic
146	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
147	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
148	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
149	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
150	C₈×C₃₇	—	2	2	no	—
151	C₈×C₃₇	—	4	2	no	—
152	C₈×C₃₇	C₂²⋊Q₈	1	4	yes	complemented
153	#28263	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂²×C₃₇	—	4	4	no	—
155	C₂²×C₃₇	—	4	4	no	—
156	C₂²×C₃₇	—	4	4	no	—
157	C₂²×C₃₇	—	8	2	no	—
158	C₂²×C₃₇	—	8	2	no	—
159	C₂²×C₃₇	—	8	2	no	—
160	C₂²×C₃₇	—	8	2	no	—
161	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
162	C₂²×C₃₇	D₄×Q₈	1	1	yes	characteristic
163	C₂²×C₃₇	#550	1	1	yes	characteristic
164	C₂²×C₃₇	C₂²×D₈	1	1	yes	characteristic
165	C₂²×C₃₇	C₂×#135	1	1	yes	characteristic
166	C₂²×C₃₇	#576	1	1	yes	characteristic
167	C₂²×C₃₇	#578	1	1	yes	characteristic
168	C₄×C₃₇	—	2	4	no	—
169	C₄×C₃₇	—	2	2	no	—
170	C₄×C₃₇	—	4	2	no	—
171	C₄×C₃₇	—	8	4	no	—
172	C₄×C₃₇	—	8	2	no	—
173	C₄×C₃₇	#466	1	4	yes	—
174	C₄×C₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
175	C₄×C₃₇	#537	1	1	yes	characteristic
176	C₄×C₃₇	#554	1	1	yes	characteristic
177	C₄×C₃₇	#556	1	1	yes	characteristic
178	C₂×C₈×Q₈	C₂×C₃₇	1	1	yes	characteristic, complemented
179	C₂×C₄×D₈	C₂×C₃₇	1	1	yes	characteristic
180	#2538	C₂×C₃₇	1	2	yes	complemented
181	#2067	C₂×C₃₇	1	4	yes	complemented
182	#1970	C₂×C₃₇	1	2	yes	—
183	#1942	C₂×C₃₇	1	2	yes	complemented
184	#1845	C₂×C₃₇	1	1	yes	characteristic, complemented
185	#1802	C₂×C₃₇	1	2	yes	complemented
186	C₂×C₃₇	—	8	4	no	—
187	C₂×C₃₇	#2538	1	1	yes	characteristic
188	C₂×C₃₇	C₂×#466	1	1	yes	characteristic
189	C₂×C₃₇	#3061	1	1	yes	characteristic
190	C₂×C₃₇	Q₈×D₈	1	1	yes	characteristic
191	C₂×C₃₇	#3380	1	1	yes	characteristic
192	C₂×C₃₇	#3391	1	1	yes	characteristic
193	C₂×C₃₇	#3393	1	1	yes	characteristic
194	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
195	C₂×C₂²⋊Q₈	—	2	2	no	—
196	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
197	C₂×C₄×D₄	C₂²×C₃₇	1	2	yes	—
198	C₈×Q₈	—	2	4	no	—
199	C₄×D₈	—	2	4	no	—
200	C₂×#107	C₂²×C₃₇	1	2	yes	—
201	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
202	C₂×#107	C₂²×C₃₇	1	2	yes	—
203	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
204	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
205	C₂×#102	C₂²×C₃₇	1	2	yes	—
206	C₂×#102	C₂²×C₃₇	1	4	yes	—
207	C₂×C₄×C₈	C₂²×C₃₇	1	2	yes	—
208	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
209	#396	—	2	4	no	—
210	#390	C₂²×C₃₇	1	4	yes	—
211	#389	C₂²×C₃₇	1	4	yes	—
212	#384	C₂²×C₃₇	1	2	yes	—
213	#380	—	2	2	no	—
214	#340	C₂²×C₃₇	1	4	yes	—
215	C₃₇	#28263	1	1	yes	characteristic, direct product factor, Sylow
216	C₂²×Q₈	D₄×C₃₇	1	1	yes	characteristic
217	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
218	C₂³×C₄	—	2	2	no	—
219	C₂×D₈	—	2	2	no	—
220	C₂×D₈	—	2	2	no	—
221	C₂×D₈	Q₈×C₃₇	1	4	yes	complemented
222	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
223	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
224	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
225	C₂²⋊Q₈	—	4	8	no	—
226	C₄×Q₈	—	2	2	no	—
227	C₄×Q₈	—	2	2	no	—
228	C₄×D₄	—	2	4	no	—
229	C₄×D₄	—	2	4	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	—	2	4	no	—
232	C₂×C₄⋊C₄	—	2	2	no	—
233	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
234	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
235	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
236	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
237	C₂×C₂²⋊C₄	—	2	2	no	—
238	C₂×C₂²⋊C₄	—	2	4	no	—
239	C₂×C₂²⋊C₄	—	2	4	no	—
240	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
241	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
242	#107	—	2	2	no	—
243	#107	—	2	4	no	—
244	#107	—	4	2	no	—
245	C₄⋊C₈	—	2	4	no	—
246	C₄⋊C₈	—	2	2	no	—
247	#102	—	2	4	no	—
248	#102	—	4	4	no	—
249	C₄×C₈	—	2	4	no	—
250	C₄×C₈	D₄×C₃₇	1	4	yes	—
251	#95	—	2	4	no	—
252	C₂⁴	—	2	2	no	—
253	C₂×Q₈	—	2	2	no	—
254	C₂×Q₈	—	2	2	no	—
255	C₂×Q₈	D₈×C₃₇	1	4	yes	complemented
256	C₂×D₄	—	2	2	no	—
257	C₂×D₄	—	2	2	no	—
258	C₂×D₄	—	2	2	no	—
259	C₂×D₄	—	2	2	no	—
260	C₂×D₄	—	2	2	no	—
261	C₂×D₄	C₂×Q₈×C₃₇	1	4	yes	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	4	4	no	—
265	C₂²×C₄	—	4	4	no	—
266	C₂²×C₄	—	4	4	no	—
267	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
268	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
269	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
270	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
271	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
272	D₈	—	2	8	no	—
273	C₂×C₈	—	2	1	no	—
274	C₂×C₈	—	2	1	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
279	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
280	C₂×C₈	C₂×Q₈×C₃₇	1	2	yes	—
281	C₂×C₈	#41×C₃₇	1	2	yes	—
282	C₄⋊C₄	—	2	4	no	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	—	2	2	no	—
285	C₄⋊C₄	—	2	4	no	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	—	4	4	no	—
289	C₄⋊C₄	—	4	8	no	—
290	C₄⋊C₄	—	8	2	no	—
291	C₂²⋊C₄	—	4	4	no	—
292	C₂²⋊C₄	—	4	8	no	—
293	C₂²⋊C₄	—	8	4	no	—
294	C₄²	—	2	2	no	—
295	C₄²	—	2	2	no	—
296	C₄²	C₂×D₄×C₃₇	1	2	yes	—
297	C₄²	#41×C₃₇	1	2	yes	—
298	C₂³	—	2	4	no	—
299	C₂³	—	4	2	no	—
300	C₂³	—	4	2	no	—
301	C₂³	—	4	2	no	—
302	C₂³	—	4	2	no	—
303	C₂³	—	4	2	no	—
304	C₂³	—	4	2	no	—
305	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
306	Q₈	—	2	8	no	—
307	D₄	—	2	4	no	—
308	D₄	—	2	4	no	—
309	D₄	—	4	2	no	—
310	D₄	—	4	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	8	8	no	—
325	C₂×C₄	#121×C₃₇	1	2	yes	—
326	C₂×C₄	#121×C₃₇	1	2	yes	—
327	C₂×C₄	C₂×D₈×C₃₇	1	4	yes	—
328	C₂×C₄	C₂×D₈×C₃₇	1	2	yes	—
329	C₂×C₄	#135×C₃₇	1	2	yes	—
330	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
331	C₂×C₄	C₂²×Q₈×C₃₇	1	1	yes	characteristic
332	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
333	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
334	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
335	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
336	C₈	—	2	2	no	—
337	C₈	—	4	2	no	—
338	C₈	C₂²⋊Q₈×C₃₇	1	4	yes	complemented
339	C₂²	—	4	4	no	—
340	C₂²	—	4	4	no	—
341	C₂²	—	4	4	no	—
342	C₂²	—	8	2	no	—
343	C₂²	—	8	2	no	—
344	C₂²	—	8	2	no	—
345	C₂²	—	8	2	no	—
346	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
347	C₂²	D₄×Q₈×C₃₇	1	1	yes	characteristic
348	C₂²	C₃₇×#550	1	1	yes	characteristic
349	C₂²	C₂²×D₈×C₃₇	1	1	yes	characteristic
350	C₂²	C₂×#135×C₃₇	1	1	yes	characteristic
351	C₂²	C₃₇×#576	1	1	yes	characteristic
352	C₂²	C₃₇×#578	1	1	yes	characteristic
353	C₄	—	2	4	no	—
354	C₄	—	2	2	no	—
355	C₄	—	4	2	no	—
356	C₄	—	8	4	no	—
357	C₄	—	8	2	no	—
358	C₄	C₃₇×#466	1	4	yes	—
359	C₄	C₂×C₂²⋊Q₈×C₃₇	1	1	yes	characteristic
360	C₄	C₃₇×#537	1	1	yes	characteristic
361	C₄	C₃₇×#554	1	1	yes	characteristic
362	C₄	C₃₇×#556	1	1	yes	characteristic
363	C₂	—	8	4	no	—
364	C₂	C₃₇×#2538	1	1	yes	characteristic
365	C₂	C₂×C₃₇×#466	1	1	yes	characteristic
366	C₂	C₃₇×#3061	1	1	yes	characteristic
367	C₂	Q₈×D₈×C₃₇	1	1	yes	characteristic
368	C₂	C₃₇×#3380	1	1	yes	characteristic
369	C₂	C₃₇×#3391	1	1	yes	characteristic
370	C₂	C₃₇×#3393	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂²×D₈×C₃₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₂×C₄×Q₈×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₈×Q₈×C₃₇	C₂	semidirect
3. C₃₇×#2538	C₂	semidirect
4. C₃₇×#2067	C₂	semidirect
6. C₃₇×#1942	C₂	semidirect
7. C₃₇×#1845	C₂	semidirect
8. C₃₇×#1802	C₂	semidirect
35. C₂×D₈×C₃₇	Q₈	semidirect
69. C₂×Q₈×C₃₇	D₈	semidirect
152. C₈×C₃₇	C₂²⋊Q₈	semidirect
153. #28263	C₃₇	direct (N × H)
178. C₂×C₈×Q₈	C₂×C₃₇	semidirect
180. #2538	C₂×C₃₇	semidirect
181. #2067	C₂×C₃₇	semidirect
183. #1942	C₂×C₃₇	semidirect
184. #1845	C₂×C₃₇	semidirect
185. #1802	C₂×C₃₇	semidirect
215. C₃₇	#28263	direct (N × H)
221. C₂×D₈	Q₈×C₃₇	semidirect
255. C₂×Q₈	D₈×C₃₇	semidirect
338. C₈	C₂²⋊Q₈×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×Q₈×C₃₇	2
C₂×C₄×D₈×C₃₇	2
C₃₇×#2538	2
C₃₇×#2067	2
C₃₇×#1970	2
C₃₇×#1942	2
C₃₇×#1845	2
C₃₇×#1802	2
#28263	37

Subgroups — C37×#28263 #22649516

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28263 #22649516