Subgroups — C₂²×C₃₇×#478 #22681728

Order 9472.

2574 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#125×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₇×#478	C₂	1	24	yes	maximal, direct product factor
4	C₂²×#107×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#106×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄⋊C₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#102×C₃₇	C₂	1	1	yes	maximal, characteristic
8	C₂²×#102×C₃₇	C₂	1	1	yes	maximal, characteristic
9	C₂³×D₄×C₃₇	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₃₇	—	2	1	no	—
11	C₂³×C₈×C₃₇	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×#125×C₃₇	—	2	6	no	—
14	C₂×#125×C₃₇	C₂²	1	12	yes	complemented
15	C₂×C₄×D₄×C₃₇	—	2	6	no	—
16	C₂×C₄×D₄×C₃₇	C₂²	1	12	yes	—
17	C₂²×C₄⋊C₄×C₃₇	—	2	1	no	—
18	C₂²×C₄⋊C₄×C₃₇	—	2	1	no	—
19	C₂²×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊C₄×C₃₇	—	2	1	no	—
23	C₂²×C₄²×C₃₇	C₂²	1	1	yes	characteristic
24	C₃₇×#478	C₂²	1	64	yes	direct product factor
25	C₂×#107×C₃₇	C₂²	1	12	yes	complemented
26	C₂×#106×C₃₇	C₂²	1	12	yes	complemented
27	C₂×C₄⋊C₈×C₃₇	C₂²	1	12	yes	complemented
28	C₂×#102×C₃₇	C₂²	1	12	yes	—
29	C₂×#102×C₃₇	C₂²	1	12	yes	—
30	C₂⁵×C₃₇	—	2	1	no	—
31	C₂²×D₄×C₃₇	—	2	3	no	—
32	C₂²×D₄×C₃₇	—	2	4	no	—
33	C₂²×D₄×C₃₇	Q₈	1	8	yes	—
34	C₂²×D₄×C₃₇	C₂³	1	6	yes	—
35	C₂³×C₄×C₃₇	—	2	1	no	—
36	C₂³×C₄×C₃₇	—	2	1	no	—
37	C₂³×C₄×C₃₇	—	2	1	no	—
38	C₂³×C₄×C₃₇	—	2	12	no	—
39	C₂³×C₄×C₃₇	—	4	8	no	—
40	C₂³×C₄×C₃₇	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₃₇	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₃₇	—	2	4	no	—
44	C₂²×C₈×C₃₇	—	2	4	no	—
45	C₂²×C₈×C₃₇	C₂³	1	6	yes	—
46	C₂²×C₈×C₃₇	C₂³	1	6	yes	—
47	#125×C₃₇	—	2	24	no	—
48	#125×C₃₇	C₂³	1	16	yes	complemented
49	C₄×D₄×C₃₇	—	2	24	no	—
50	C₄×D₄×C₃₇	C₂³	1	16	yes	—
51	C₂×C₄⋊C₄×C₃₇	—	2	3	no	—
52	C₂×C₄⋊C₄×C₃₇	—	2	3	no	—
53	C₂×C₄⋊C₄×C₃₇	—	2	12	no	—
54	C₂×C₄⋊C₄×C₃₇	—	2	12	no	—
55	C₂×C₄⋊C₄×C₃₇	—	2	3	no	—
56	C₂×C₄⋊C₄×C₃₇	C₂³	1	6	yes	—
57	C₂×C₄⋊C₄×C₃₇	C₂³	1	6	yes	—
58	C₂×C₄⋊C₄×C₃₇	C₂³	1	6	yes	—
59	C₂×C₂²⋊C₄×C₃₇	—	2	12	no	—
60	C₂×C₄²×C₃₇	D₄	1	6	yes	—
61	C₂×C₄²×C₃₇	C₂³	1	6	yes	—
62	#107×C₃₇	C₂³	1	16	yes	complemented
63	#106×C₃₇	C₂³	1	16	yes	complemented
64	C₄⋊C₈×C₃₇	C₂³	1	16	yes	complemented
65	#102×C₃₇	C₂³	1	16	yes	—
66	#102×C₃₇	C₂³	1	16	yes	—
67	C₂⁴×C₃₇	—	2	8	no	—
68	C₂⁴×C₃₇	—	2	6	no	—
69	C₂⁴×C₃₇	—	4	4	no	—
70	C₂⁴×C₃₇	—	4	4	no	—
71	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
72	C₂×D₄×C₃₇	—	2	24	no	—
73	C₂×D₄×C₃₇	—	2	6	no	—
74	C₂×D₄×C₃₇	—	2	12	no	—
75	C₂×D₄×C₃₇	C₂×Q₈	1	24	yes	—
76	C₂×D₄×C₃₇	C₂⁴	1	4	yes	—
77	C₂²×C₄×C₃₇	—	2	4	no	—
78	C₂²×C₄×C₃₇	—	2	4	no	—
79	C₂²×C₄×C₃₇	—	2	6	no	—
80	C₂²×C₄×C₃₇	—	2	6	no	—
81	C₂²×C₄×C₃₇	—	2	6	no	—
82	C₂²×C₄×C₃₇	—	2	16	no	—
83	C₂²×C₄×C₃₇	—	4	48	no	—
84	C₂²×C₄×C₃₇	—	4	4	no	—
85	C₂²×C₄×C₃₇	—	4	4	no	—
86	C₂²×C₄×C₃₇	—	4	4	no	—
87	C₂²×C₄×C₃₇	C₂×D₄	1	6	yes	—
88	C₂²×C₄×C₃₇	C₂×D₄	1	6	yes	—
89	C₂²×C₄×C₃₇	C₂×D₄	1	3	yes	—
90	C₂²×C₄×C₃₇	C₂×Q₈	1	4	yes	—
91	C₂²×C₄×C₃₇	#41	1	4	yes	—
92	C₂²×C₄×C₃₇	C₂⁴	1	3	yes	—
93	C₂×C₈×C₃₇	—	2	12	no	—
94	C₂×C₈×C₃₇	—	2	12	no	—
95	C₂×C₈×C₃₇	C₂⁴	1	4	yes	—
96	C₂×C₈×C₃₇	C₂⁴	1	4	yes	—
97	C₄⋊C₄×C₃₇	—	2	16	no	—
98	C₄⋊C₄×C₃₇	—	2	16	no	—
99	C₄⋊C₄×C₃₇	—	2	6	no	—
100	C₄⋊C₄×C₃₇	—	2	6	no	—
101	C₄⋊C₄×C₃₇	—	2	6	no	—
102	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
103	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
104	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
105	C₂²⋊C₄×C₃₇	—	2	16	no	—
106	C₄²×C₃₇	C₂×D₄	1	12	yes	—
107	C₄²×C₃₇	C₂⁴	1	4	yes	—
108	C₂³×C₃₇	—	2	24	no	—
109	C₂³×C₃₇	—	2	4	no	—
110	C₂³×C₃₇	—	4	12	no	—
111	C₂³×C₃₇	—	4	12	no	—
112	C₂³×C₃₇	—	4	32	no	—
113	C₂³×C₃₇	C₂²⋊Q₈	1	4	yes	—
114	C₂³×C₃₇	#135	1	4	yes	—
115	C₂³×C₃₇	AGL(1,ℤ/8)	1	4	yes	—
116	C₂³×C₃₇	C₂²×D₄	1	3	yes	—
117	D₄×C₃₇	—	2	24	no	—
118	D₄×C₃₇	—	2	4	no	—
119	D₄×C₃₇	C₂²×Q₈	1	8	yes	—
120	C₂×C₄×C₃₇	—	2	12	no	—
121	C₂×C₄×C₃₇	—	2	12	no	—
122	C₂×C₄×C₃₇	—	2	4	no	—
123	C₂×C₄×C₃₇	—	2	4	no	—
124	C₂×C₄×C₃₇	—	2	4	no	—
125	C₂×C₄×C₃₇	—	4	32	no	—
126	C₂×C₄×C₃₇	—	4	12	no	—
127	C₂×C₄×C₃₇	—	4	12	no	—
128	C₂×C₄×C₃₇	—	4	12	no	—
129	C₂×C₄×C₃₇	C₂²⋊Q₈	1	12	yes	—
130	C₂×C₄×C₃₇	C₂²×D₄	1	4	yes	—
131	C₂×C₄×C₃₇	C₂²×D₄	1	4	yes	—
132	C₂×C₄×C₃₇	C₂²×D₄	1	3	yes	—
133	C₂×C₄×C₃₇	C₂²×Q₈	1	6	yes	—
134	C₂×C₄×C₃₇	C₂×#41	1	6	yes	—
135	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
136	C₈×C₃₇	—	2	4	no	—
137	C₈×C₃₇	—	2	4	no	—
138	C₂²×#478	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂²×C₃₇	—	2	8	no	—
140	C₂²×C₃₇	—	4	48	no	—
141	C₂²×C₃₇	—	4	4	no	—
142	C₂²×C₃₇	—	4	4	no	—
143	C₂²×C₃₇	#478	1	16	yes	direct product factor
144	C₂²×C₃₇	C₂×C₂²⋊Q₈	1	6	yes	—
145	C₂²×C₃₇	C₂×#135	1	6	yes	—
146	C₂²×C₃₇	C₂×AGL(1,ℤ/8)	1	6	yes	—
147	C₂²×C₃₇	C₂³×D₄	1	1	yes	characteristic
148	C₄×C₃₇	—	2	4	no	—
149	C₄×C₃₇	—	2	4	no	—
150	C₄×C₃₇	—	4	4	no	—
151	C₄×C₃₇	—	4	4	no	—
152	C₄×C₃₇	—	4	4	no	—
153	C₄×C₃₇	C₂×C₂²⋊Q₈	1	6	yes	—
154	C₄×C₃₇	C₂³×Q₈	1	1	yes	characteristic
155	C₄×C₃₇	C₂²×#41	1	1	yes	characteristic
156	C₂²×#125	C₂×C₃₇	1	1	yes	characteristic, complemented
157	C₂²×C₄×D₄	C₂×C₃₇	1	1	yes	characteristic
158	C₂×#478	C₂×C₃₇	1	24	yes	direct product factor
159	C₂²×#107	C₂×C₃₇	1	1	yes	characteristic, complemented
160	C₂²×#106	C₂×C₃₇	1	1	yes	characteristic, complemented
161	C₂²×C₄⋊C₈	C₂×C₃₇	1	1	yes	characteristic, complemented
162	C₂²×#102	C₂×C₃₇	1	1	yes	characteristic
163	C₂²×#102	C₂×C₃₇	1	1	yes	characteristic
164	C₂×C₃₇	—	4	8	no	—
165	C₂×C₃₇	C₂×#478	1	12	yes	direct product factor
166	C₂×C₃₇	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
167	C₂×C₃₇	C₂²×#135	1	1	yes	characteristic
168	C₂×C₃₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
169	C₂³×D₄	C₂²×C₃₇	1	1	yes	characteristic
170	C₂⁴×C₄	—	2	1	no	—
171	C₂³×C₈	C₂²×C₃₇	1	1	yes	characteristic
172	C₂³×C₈	C₂²×C₃₇	1	1	yes	characteristic
173	C₂×#125	—	2	6	no	—
174	C₂×#125	C₂²×C₃₇	1	12	yes	complemented
175	C₂×C₄×D₄	—	2	6	no	—
176	C₂×C₄×D₄	C₂²×C₃₇	1	12	yes	—
177	C₂²×C₄⋊C₄	—	2	1	no	—
178	C₂²×C₄⋊C₄	—	2	1	no	—
179	C₂²×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
180	C₂²×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
181	C₂²×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
182	C₂²×C₂²⋊C₄	—	2	1	no	—
183	C₂²×C₄²	C₂²×C₃₇	1	1	yes	characteristic
184	#478	C₂²×C₃₇	1	64	yes	direct product factor
185	C₂×#107	C₂²×C₃₇	1	12	yes	complemented
186	C₂×#106	C₂²×C₃₇	1	12	yes	complemented
187	C₂×C₄⋊C₈	C₂²×C₃₇	1	12	yes	complemented
188	C₂×#102	C₂²×C₃₇	1	12	yes	—
189	C₂×#102	C₂²×C₃₇	1	12	yes	—
190	C₃₇	C₂²×#478	1	1	yes	characteristic, direct product factor, Sylow
191	C₂⁵	—	2	1	no	—
192	C₂²×D₄	—	2	3	no	—
193	C₂²×D₄	—	2	4	no	—
194	C₂²×D₄	Q₈×C₃₇	1	8	yes	—
195	C₂²×D₄	C₂³×C₃₇	1	6	yes	—
196	C₂³×C₄	—	2	1	no	—
197	C₂³×C₄	—	2	1	no	—
198	C₂³×C₄	—	2	1	no	—
199	C₂³×C₄	—	2	12	no	—
200	C₂³×C₄	—	4	8	no	—
201	C₂³×C₄	D₄×C₃₇	1	1	yes	characteristic
202	C₂³×C₄	D₄×C₃₇	1	1	yes	characteristic
203	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
204	C₂²×C₈	—	2	4	no	—
205	C₂²×C₈	—	2	4	no	—
206	C₂²×C₈	C₂³×C₃₇	1	6	yes	—
207	C₂²×C₈	C₂³×C₃₇	1	6	yes	—
208	#125	—	2	24	no	—
209	#125	C₂³×C₃₇	1	16	yes	complemented
210	C₄×D₄	—	2	24	no	—
211	C₄×D₄	C₂³×C₃₇	1	16	yes	—
212	C₂×C₄⋊C₄	—	2	12	no	—
213	C₂×C₄⋊C₄	—	2	12	no	—
214	C₂×C₄⋊C₄	—	2	3	no	—
215	C₂×C₄⋊C₄	—	2	3	no	—
216	C₂×C₄⋊C₄	—	2	3	no	—
217	C₂×C₄⋊C₄	C₂³×C₃₇	1	6	yes	—
218	C₂×C₄⋊C₄	C₂³×C₃₇	1	6	yes	—
219	C₂×C₄⋊C₄	C₂³×C₃₇	1	6	yes	—
220	C₂×C₂²⋊C₄	—	2	12	no	—
221	C₂×C₄²	D₄×C₃₇	1	6	yes	—
222	C₂×C₄²	C₂³×C₃₇	1	6	yes	—
223	#107	C₂³×C₃₇	1	16	yes	complemented
224	#106	C₂³×C₃₇	1	16	yes	complemented
225	C₄⋊C₈	C₂³×C₃₇	1	16	yes	complemented
226	#102	C₂³×C₃₇	1	16	yes	—
227	#102	C₂³×C₃₇	1	16	yes	—
228	C₂⁴	—	2	8	no	—
229	C₂⁴	—	2	6	no	—
230	C₂⁴	—	4	4	no	—
231	C₂⁴	—	4	4	no	—
232	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
233	C₂×D₄	—	2	24	no	—
234	C₂×D₄	—	2	6	no	—
235	C₂×D₄	—	2	12	no	—
236	C₂×D₄	C₂×Q₈×C₃₇	1	24	yes	—
237	C₂×D₄	C₂⁴×C₃₇	1	4	yes	—
238	C₂²×C₄	—	2	4	no	—
239	C₂²×C₄	—	2	4	no	—
240	C₂²×C₄	—	2	6	no	—
241	C₂²×C₄	—	2	6	no	—
242	C₂²×C₄	—	2	6	no	—
243	C₂²×C₄	—	2	16	no	—
244	C₂²×C₄	—	4	48	no	—
245	C₂²×C₄	—	4	4	no	—
246	C₂²×C₄	—	4	4	no	—
247	C₂²×C₄	—	4	4	no	—
248	C₂²×C₄	C₂×D₄×C₃₇	1	6	yes	—
249	C₂²×C₄	C₂×D₄×C₃₇	1	6	yes	—
250	C₂²×C₄	C₂×D₄×C₃₇	1	3	yes	—
251	C₂²×C₄	C₂×Q₈×C₃₇	1	4	yes	—
252	C₂²×C₄	#41×C₃₇	1	4	yes	—
253	C₂²×C₄	C₂⁴×C₃₇	1	3	yes	—
254	C₂×C₈	—	2	12	no	—
255	C₂×C₈	—	2	12	no	—
256	C₂×C₈	C₂⁴×C₃₇	1	4	yes	—
257	C₂×C₈	C₂⁴×C₃₇	1	4	yes	—
258	C₄⋊C₄	—	2	16	no	—
259	C₄⋊C₄	—	2	16	no	—
260	C₄⋊C₄	—	2	6	no	—
261	C₄⋊C₄	—	2	6	no	—
262	C₄⋊C₄	—	2	6	no	—
263	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
264	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
265	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
266	C₂²⋊C₄	—	2	16	no	—
267	C₄²	C₂×D₄×C₃₇	1	12	yes	—
268	C₄²	C₂⁴×C₃₇	1	4	yes	—
269	C₂³	—	2	24	no	—
270	C₂³	—	2	4	no	—
271	C₂³	—	4	12	no	—
272	C₂³	—	4	12	no	—
273	C₂³	—	4	32	no	—
274	C₂³	C₂²⋊Q₈×C₃₇	1	4	yes	—
275	C₂³	#135×C₃₇	1	4	yes	—
276	C₂³	AGL(1,ℤ/8)×C₃₇	1	4	yes	—
277	C₂³	C₂²×D₄×C₃₇	1	3	yes	—
278	D₄	—	2	24	no	—
279	D₄	—	2	4	no	—
280	D₄	C₂²×Q₈×C₃₇	1	8	yes	—
281	C₂×C₄	—	2	12	no	—
282	C₂×C₄	—	2	12	no	—
283	C₂×C₄	—	2	4	no	—
284	C₂×C₄	—	2	4	no	—
285	C₂×C₄	—	2	4	no	—
286	C₂×C₄	—	4	32	no	—
287	C₂×C₄	—	4	12	no	—
288	C₂×C₄	—	4	12	no	—
289	C₂×C₄	—	4	12	no	—
290	C₂×C₄	C₂²⋊Q₈×C₃₇	1	12	yes	—
291	C₂×C₄	C₂²×D₄×C₃₇	1	4	yes	—
292	C₂×C₄	C₂²×D₄×C₃₇	1	4	yes	—
293	C₂×C₄	C₂²×D₄×C₃₇	1	3	yes	—
294	C₂×C₄	C₂²×Q₈×C₃₇	1	6	yes	—
295	C₂×C₄	C₂×#41×C₃₇	1	6	yes	—
296	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
297	C₈	—	2	4	no	—
298	C₈	—	2	4	no	—
299	C₂²	—	2	8	no	—
300	C₂²	—	4	4	no	—
301	C₂²	—	4	4	no	—
302	C₂²	—	4	48	no	—
303	C₂²	C₃₇×#478	1	16	yes	direct product factor
304	C₂²	C₂×C₂²⋊Q₈×C₃₇	1	6	yes	—
305	C₂²	C₂×#135×C₃₇	1	6	yes	—
306	C₂²	C₂×AGL(1,ℤ/8)×C₃₇	1	6	yes	—
307	C₂²	C₂³×D₄×C₃₇	1	1	yes	characteristic
308	C₄	—	2	4	no	—
309	C₄	—	2	4	no	—
310	C₄	—	4	4	no	—
311	C₄	—	4	4	no	—
312	C₄	—	4	4	no	—
313	C₄	C₂×C₂²⋊Q₈×C₃₇	1	6	yes	—
314	C₄	C₂³×Q₈×C₃₇	1	1	yes	characteristic
315	C₄	C₂²×#41×C₃₇	1	1	yes	characteristic
316	C₂	—	4	8	no	—
317	C₂	C₂×C₃₇×#478	1	12	yes	direct product factor
318	C₂	C₂²×C₂²⋊Q₈×C₃₇	1	1	yes	characteristic
319	C₂	C₂²×#135×C₃₇	1	1	yes	characteristic
320	C₂	C₂²×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₃₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₇
prime radical	C₂³×D₄×C₃₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃₇ ◁ C₂²×C₄²×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#125×C₃₇	C₂	semidirect
3. C₂×C₃₇×#478	C₂	direct (N × H)
4. C₂²×#107×C₃₇	C₂	semidirect
5. C₂²×#106×C₃₇	C₂	semidirect
6. C₂²×C₄⋊C₈×C₃₇	C₂	semidirect
14. C₂×#125×C₃₇	C₂²	semidirect
24. C₃₇×#478	C₂²	direct (N × H)
25. C₂×#107×C₃₇	C₂²	semidirect
26. C₂×#106×C₃₇	C₂²	semidirect
27. C₂×C₄⋊C₈×C₃₇	C₂²	semidirect
48. #125×C₃₇	C₂³	semidirect
62. #107×C₃₇	C₂³	semidirect
63. #106×C₃₇	C₂³	semidirect
64. C₄⋊C₈×C₃₇	C₂³	semidirect
138. C₂²×#478	C₃₇	direct (N × H)
143. C₂²×C₃₇	#478	direct (N × H)
156. C₂²×#125	C₂×C₃₇	semidirect
158. C₂×#478	C₂×C₃₇	direct (N × H)
159. C₂²×#107	C₂×C₃₇	semidirect
160. C₂²×#106	C₂×C₃₇	semidirect
161. C₂²×C₄⋊C₈	C₂×C₃₇	semidirect
165. C₂×C₃₇	C₂×#478	direct (N × H)
174. C₂×#125	C₂²×C₃₇	semidirect
184. #478	C₂²×C₃₇	direct (N × H)
185. C₂×#107	C₂²×C₃₇	semidirect
186. C₂×#106	C₂²×C₃₇	semidirect
187. C₂×C₄⋊C₈	C₂²×C₃₇	semidirect
190. C₃₇	C₂²×#478	direct (N × H)
209. #125	C₂³×C₃₇	semidirect
223. #107	C₂³×C₃₇	semidirect
224. #106	C₂³×C₃₇	semidirect
225. C₄⋊C₈	C₂³×C₃₇	semidirect
303. C₂²	C₃₇×#478	direct (N × H)
317. C₂	C₂×C₃₇×#478	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#125×C₃₇	2
C₂²×C₄×D₄×C₃₇	2
C₂×C₃₇×#478	2
C₂²×#107×C₃₇	2
C₂²×#106×C₃₇	2
C₂²×C₄⋊C₈×C₃₇	2
C₂²×#102×C₃₇	2
C₂²×#478	37

Subgroups — C22×C37×#478 #22681728

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃₇×#478 #22681728