Subgroups — C₃₇×#28466 #22649719

Order 9472.

1098 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#495	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₇×#495	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₇×#494	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₇×#464	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×Q₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2545	C₂	1	2	yes	maximal, complemented
7	C₃₇×#2015	C₂	1	2	yes	maximal, complemented
8	C₃₇×#2013	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1970	C₂	1	1	yes	maximal, characteristic
10	C₃₇×#1969	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₄⋊C₄×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₃₇	C₂²	1	2	yes	—
14	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
15	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	—
16	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	—
17	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Q₈×C₃₇	C₂²	1	2	yes	—
19	C₂×#124×C₃₇	C₂²	1	2	yes	—
20	C₂×#124×C₃₇	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₃₇	C₂²	1	2	yes	—
22	C₃₇×#495	—	2	4	no	—
23	C₃₇×#495	—	2	4	no	—
24	C₃₇×#494	—	2	4	no	—
25	C₃₇×#464	—	2	8	no	—
26	C₄×Q₁₆×C₃₇	—	2	4	no	—
27	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
29	C₂×#103×C₃₇	C₂²	1	2	yes	—
30	C₂×#103×C₃₇	C₂²	1	2	yes	—
31	C₂×#102×C₃₇	C₂²	1	2	yes	—
32	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
35	C₃₇×#396	—	2	4	no	—
36	C₃₇×#391	C₂²	1	2	yes	—
37	C₃₇×#390	C₂²	1	2	yes	—
38	C₃₇×#388	—	2	4	no	—
39	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
40	C₃₇×#336	C₂²	1	1	yes	characteristic
41	C₃₇×#336	C₂²	1	1	yes	characteristic
42	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
43	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
44	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
45	C₂×Q₁₆×C₃₇	—	2	4	no	—
46	C₂×Q₁₆×C₃₇	—	2	2	no	—
47	C₂×Q₁₆×C₃₇	—	2	4	no	—
48	C₂×Q₁₆×C₃₇	—	2	2	no	—
49	C₂×Q₁₆×C₃₇	—	2	2	no	—
50	C₂×Q₁₆×C₃₇	—	2	2	no	—
51	C₂×Q₁₆×C₃₇	—	2	2	no	—
52	C₂×Q₁₆×C₃₇	—	4	2	no	—
53	C₂×Q₁₆×C₃₇	D₄	1	4	yes	—
54	C₂×SD₁₆×C₃₇	—	2	4	no	—
55	C₂×SD₁₆×C₃₇	—	2	4	no	—
56	C₂×SD₁₆×C₃₇	—	2	4	no	—
57	C₂×SD₁₆×C₃₇	—	4	2	no	—
58	C₂×SD₁₆×C₃₇	—	4	2	no	—
59	C₂×SD₁₆×C₃₇	—	4	2	no	—
60	C₂×D₈×C₃₇	—	2	2	no	—
61	C₂×D₈×C₃₇	—	2	2	no	—
62	C₂×D₈×C₃₇	—	2	2	no	—
63	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
67	C₄⋊Q₈×C₃₇	—	2	4	no	—
68	C₄⋊Q₈×C₃₇	—	4	2	no	—
69	#124×C₃₇	—	2	4	no	—
70	#124×C₃₇	—	2	4	no	—
71	#124×C₃₇	—	2	4	no	—
72	#124×C₃₇	—	4	2	no	—
73	C₄×Q₈×C₃₇	—	2	4	no	—
74	C₄×Q₈×C₃₇	—	2	4	no	—
75	C₂×C₄⋊C₄×C₃₇	—	2	4	no	—
76	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
77	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
78	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
79	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
81	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
83	C₂×C₄²×C₃₇	—	2	2	no	—
84	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
87	#107×C₃₇	—	2	2	no	—
88	C₄⋊C₈×C₃₇	D₄	1	4	yes	—
89	#103×C₃₇	—	2	4	no	—
90	#103×C₃₇	—	2	4	no	—
91	#102×C₃₇	—	2	4	no	—
92	C₄×C₈×C₃₇	—	2	2	no	—
93	C₄×C₈×C₃₇	—	2	2	no	—
94	C₄×C₈×C₃₇	D₄	1	4	yes	—
95	#95×C₃₇	—	2	4	no	—
96	#95×C₃₇	D₄	1	2	yes	—
97	C₂⁴×C₃₇	—	2	2	no	—
98	C₂×Q₈×C₃₇	—	2	2	no	—
99	C₂×Q₈×C₃₇	—	2	2	no	—
100	C₂×Q₈×C₃₇	—	2	2	no	—
101	C₂×Q₈×C₃₇	—	2	2	no	—
102	C₂×Q₈×C₃₇	—	2	2	no	—
103	C₂×Q₈×C₃₇	—	2	2	no	—
104	C₂×Q₈×C₃₇	—	2	2	no	—
105	C₂×Q₈×C₃₇	—	2	2	no	—
106	C₂×Q₈×C₃₇	—	2	2	no	—
107	C₂×Q₈×C₃₇	—	2	2	no	—
108	C₂×Q₈×C₃₇	—	2	2	no	—
109	C₂×Q₈×C₃₇	C₂×D₄	1	4	yes	—
110	C₂×D₄×C₃₇	—	2	2	no	—
111	C₂×D₄×C₃₇	—	2	2	no	—
112	C₂×D₄×C₃₇	—	2	2	no	—
113	C₂×D₄×C₃₇	—	2	2	no	—
114	C₂×D₄×C₃₇	—	2	2	no	—
115	C₂×D₄×C₃₇	—	2	2	no	—
116	C₂²×C₄×C₃₇	—	2	2	no	—
117	C₂²×C₄×C₃₇	—	2	2	no	—
118	C₂²×C₄×C₃₇	—	2	2	no	—
119	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
124	Q₁₆×C₃₇	—	2	8	no	—
125	Q₁₆×C₃₇	—	4	8	no	—
126	Q₁₆×C₃₇	—	4	4	no	—
127	SD₁₆×C₃₇	—	4	8	no	—
128	SD₁₆×C₃₇	—	4	8	no	—
129	D₈×C₃₇	—	4	4	no	—
130	C₂×C₈×C₃₇	—	2	1	no	—
131	C₂×C₈×C₃₇	—	2	1	no	—
132	C₂×C₈×C₃₇	—	2	1	no	—
133	C₂×C₈×C₃₇	—	2	1	no	—
134	C₂×C₈×C₃₇	—	2	1	no	—
135	C₂×C₈×C₃₇	—	2	1	no	—
136	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
138	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₃₇	#41	1	2	yes	—
142	C₄⋊C₄×C₃₇	—	2	4	no	—
143	C₄⋊C₄×C₃₇	—	2	2	no	—
144	C₄⋊C₄×C₃₇	—	2	2	no	—
145	C₄⋊C₄×C₃₇	—	4	8	no	—
146	C₄⋊C₄×C₃₇	—	4	4	no	—
147	C₂²⋊C₄×C₃₇	—	4	8	no	—
148	C₂²⋊C₄×C₃₇	—	4	4	no	—
149	C₂²⋊C₄×C₃₇	—	4	4	no	—
150	C₂²⋊C₄×C₃₇	—	4	8	no	—
151	C₄²×C₃₇	—	2	1	no	—
152	C₄²×C₃₇	—	2	1	no	—
153	C₄²×C₃₇	—	2	1	no	—
154	C₄²×C₃₇	—	2	1	no	—
155	C₄²×C₃₇	—	4	4	no	—
156	C₄²×C₃₇	C₂×D₄	1	2	yes	—
157	C₄²×C₃₇	C₂×D₄	1	2	yes	—
158	C₂³×C₃₇	—	4	2	no	—
159	C₂³×C₃₇	—	4	2	no	—
160	C₂³×C₃₇	—	4	2	no	—
161	C₂³×C₃₇	—	4	4	no	—
162	C₂³×C₃₇	—	4	4	no	—
163	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
164	Q₈×C₃₇	—	2	4	no	—
165	Q₈×C₃₇	—	2	4	no	—
166	Q₈×C₃₇	—	4	2	no	—
167	Q₈×C₃₇	—	4	2	no	—
168	Q₈×C₃₇	—	4	2	no	—
169	Q₈×C₃₇	—	4	2	no	—
170	Q₈×C₃₇	—	4	2	no	—
171	Q₈×C₃₇	—	4	2	no	—
172	D₄×C₃₇	—	4	2	no	—
173	D₄×C₃₇	—	4	2	no	—
174	D₄×C₃₇	—	4	2	no	—
175	D₄×C₃₇	—	4	2	no	—
176	C₂×C₄×C₃₇	—	2	2	no	—
177	C₂×C₄×C₃₇	—	2	2	no	—
178	C₂×C₄×C₃₇	—	2	2	no	—
179	C₂×C₄×C₃₇	—	2	2	no	—
180	C₂×C₄×C₃₇	—	2	2	no	—
181	C₂×C₄×C₃₇	—	2	4	no	—
182	C₂×C₄×C₃₇	—	2	2	no	—
183	C₂×C₄×C₃₇	—	2	2	no	—
184	C₂×C₄×C₃₇	—	4	2	no	—
185	C₂×C₄×C₃₇	—	4	2	no	—
186	C₂×C₄×C₃₇	—	4	2	no	—
187	C₂×C₄×C₃₇	—	4	2	no	—
188	C₂×C₄×C₃₇	—	4	2	no	—
189	C₂×C₄×C₃₇	—	4	2	no	—
190	C₂×C₄×C₃₇	—	4	4	no	—
191	C₂×C₄×C₃₇	#127	1	2	yes	—
192	C₂×C₄×C₃₇	#127	1	2	yes	—
193	C₂×C₄×C₃₇	#135	1	4	yes	—
194	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
199	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
200	C₈×C₃₇	—	2	2	no	—
201	C₈×C₃₇	—	2	2	no	—
202	C₈×C₃₇	—	2	2	no	—
203	C₈×C₃₇	#121	1	4	yes	—
204	#28466	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂²×C₃₇	—	8	4	no	—
206	C₂²×C₃₇	—	8	2	no	—
207	C₂²×C₃₇	—	8	2	no	—
208	C₂²×C₃₇	—	8	4	no	—
209	C₂²×C₃₇	—	8	2	no	—
210	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
211	C₂²×C₃₇	D₄²	1	1	yes	characteristic
212	C₂²×C₃₇	#550	1	1	yes	characteristic
213	C₂²×C₃₇	C₂×#135	1	2	yes	—
214	C₂²×C₃₇	#578	1	2	yes	—
215	C₄×C₃₇	—	2	2	no	—
216	C₄×C₃₇	—	2	2	no	—
217	C₄×C₃₇	—	2	4	no	—
218	C₄×C₃₇	—	4	2	no	—
219	C₄×C₃₇	—	4	4	no	—
220	C₄×C₃₇	—	8	2	no	—
221	C₄×C₃₇	—	8	2	no	—
222	C₄×C₃₇	C₂×#121	1	1	yes	characteristic
223	C₄×C₃₇	#535	1	1	yes	characteristic
224	C₄×C₃₇	D₄²	1	1	yes	characteristic
225	C₄×C₃₇	#550	1	1	yes	characteristic
226	C₂×#495	C₂×C₃₇	1	1	yes	characteristic
227	C₂×#495	C₂×C₃₇	1	1	yes	characteristic
228	C₂×#494	C₂×C₃₇	1	1	yes	characteristic, complemented
229	C₂×#464	C₂×C₃₇	1	2	yes	complemented
230	C₂×C₄×Q₁₆	C₂×C₃₇	1	1	yes	characteristic, complemented
231	#2545	C₂×C₃₇	1	2	yes	complemented
232	#2015	C₂×C₃₇	1	2	yes	complemented
233	#2013	C₂×C₃₇	1	2	yes	complemented
234	#1970	C₂×C₃₇	1	1	yes	characteristic
235	#1969	C₂×C₃₇	1	1	yes	characteristic, complemented
236	C₈×C₄⋊C₄	C₂×C₃₇	1	1	yes	characteristic, complemented
237	C₂×C₃₇	—	16	2	no	—
238	C₂×C₃₇	#2541	1	1	yes	characteristic
239	C₂×C₃₇	#3147	1	1	yes	characteristic
240	C₂×C₃₇	#3156	1	1	yes	characteristic
241	C₂×C₃₇	#3285	1	2	yes	—
242	C₂×C₃₇	#3393	1	2	yes	—
243	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
244	C₂²×Q₁₆	C₂²×C₃₇	1	2	yes	—
245	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
246	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
247	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
248	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
249	C₂×C₄⋊Q₈	C₂²×C₃₇	1	2	yes	—
250	C₂×#124	C₂²×C₃₇	1	2	yes	—
251	C₂×#124	C₂²×C₃₇	1	2	yes	—
252	C₂×C₄×Q₈	C₂²×C₃₇	1	2	yes	—
253	#495	—	2	4	no	—
254	#495	—	2	4	no	—
255	#494	—	2	4	no	—
256	#464	—	2	8	no	—
257	C₄×Q₁₆	—	2	4	no	—
258	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
259	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
260	C₂×#103	C₂²×C₃₇	1	2	yes	—
261	C₂×#103	C₂²×C₃₇	1	2	yes	—
262	C₂×#102	C₂²×C₃₇	1	2	yes	—
263	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
264	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
265	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
266	#396	—	2	4	no	—
267	#391	C₂²×C₃₇	1	2	yes	—
268	#390	C₂²×C₃₇	1	2	yes	—
269	#388	—	2	4	no	—
270	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
271	#336	C₂²×C₃₇	1	1	yes	characteristic
272	#336	C₂²×C₃₇	1	1	yes	characteristic
273	C₃₇	#28466	1	1	yes	characteristic, direct product factor, Sylow
274	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
275	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
276	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
277	C₂×Q₁₆	—	2	4	no	—
278	C₂×Q₁₆	—	2	2	no	—
279	C₂×Q₁₆	—	2	4	no	—
280	C₂×Q₁₆	—	2	2	no	—
281	C₂×Q₁₆	—	2	2	no	—
282	C₂×Q₁₆	—	2	2	no	—
283	C₂×Q₁₆	—	2	2	no	—
284	C₂×Q₁₆	—	4	2	no	—
285	C₂×Q₁₆	D₄×C₃₇	1	4	yes	—
286	C₂×SD₁₆	—	2	4	no	—
287	C₂×SD₁₆	—	2	4	no	—
288	C₂×SD₁₆	—	2	4	no	—
289	C₂×SD₁₆	—	4	2	no	—
290	C₂×SD₁₆	—	4	2	no	—
291	C₂×SD₁₆	—	4	2	no	—
292	C₂×D₈	—	2	2	no	—
293	C₂×D₈	—	2	2	no	—
294	C₂×D₈	—	2	2	no	—
295	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
296	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
297	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
298	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
299	C₄⋊Q₈	—	2	4	no	—
300	C₄⋊Q₈	—	4	2	no	—
301	#124	—	2	4	no	—
302	#124	—	2	4	no	—
303	#124	—	2	4	no	—
304	#124	—	4	2	no	—
305	C₄×Q₈	—	2	4	no	—
306	C₄×Q₈	—	2	4	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	4	no	—
309	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
310	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₂²⋊C₄	—	2	4	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	4	no	—
315	C₂×C₄²	—	2	2	no	—
316	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
317	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
318	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
319	#107	—	2	2	no	—
320	C₄⋊C₈	D₄×C₃₇	1	4	yes	—
321	#103	—	2	4	no	—
322	#103	—	2	4	no	—
323	#102	—	2	4	no	—
324	C₄×C₈	—	2	2	no	—
325	C₄×C₈	—	2	2	no	—
326	C₄×C₈	D₄×C₃₇	1	4	yes	—
327	#95	—	2	4	no	—
328	#95	D₄×C₃₇	1	2	yes	—
329	C₂⁴	—	2	2	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	C₂×D₄×C₃₇	1	4	yes	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
352	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
355	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
356	Q₁₆	—	2	8	no	—
357	Q₁₆	—	4	8	no	—
358	Q₁₆	—	4	4	no	—
359	SD₁₆	—	4	8	no	—
360	SD₁₆	—	4	8	no	—
361	D₈	—	4	4	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
369	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
370	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
371	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
372	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
373	C₂×C₈	#41×C₃₇	1	2	yes	—
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	4	8	no	—
378	C₄⋊C₄	—	4	4	no	—
379	C₂²⋊C₄	—	4	8	no	—
380	C₂²⋊C₄	—	4	4	no	—
381	C₂²⋊C₄	—	4	4	no	—
382	C₂²⋊C₄	—	4	8	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	2	1	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	4	4	no	—
388	C₄²	C₂×D₄×C₃₇	1	2	yes	—
389	C₄²	C₂×D₄×C₃₇	1	2	yes	—
390	C₂³	—	4	2	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	4	no	—
394	C₂³	—	4	4	no	—
395	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
396	Q₈	—	2	4	no	—
397	Q₈	—	2	4	no	—
398	Q₈	—	4	2	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	4	2	no	—
401	Q₈	—	4	2	no	—
402	Q₈	—	4	2	no	—
403	Q₈	—	4	2	no	—
404	D₄	—	4	2	no	—
405	D₄	—	4	2	no	—
406	D₄	—	4	2	no	—
407	D₄	—	4	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	#127×C₃₇	1	2	yes	—
424	C₂×C₄	#127×C₃₇	1	2	yes	—
425	C₂×C₄	#135×C₃₇	1	4	yes	—
426	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
427	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
428	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
429	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
430	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
431	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
432	C₈	—	2	2	no	—
433	C₈	—	2	2	no	—
434	C₈	—	2	2	no	—
435	C₈	#121×C₃₇	1	4	yes	—
436	C₂²	—	8	4	no	—
437	C₂²	—	8	2	no	—
438	C₂²	—	8	2	no	—
439	C₂²	—	8	4	no	—
440	C₂²	—	8	2	no	—
441	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
442	C₂²	D₄²×C₃₇	1	1	yes	characteristic
443	C₂²	C₃₇×#550	1	1	yes	characteristic
444	C₂²	C₂×#135×C₃₇	1	2	yes	—
445	C₂²	C₃₇×#578	1	2	yes	—
446	C₄	—	2	2	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	4	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	4	no	—
451	C₄	—	8	2	no	—
452	C₄	—	8	2	no	—
453	C₄	C₂×#121×C₃₇	1	1	yes	characteristic
454	C₄	C₃₇×#535	1	1	yes	characteristic
455	C₄	D₄²×C₃₇	1	1	yes	characteristic
456	C₄	C₃₇×#550	1	1	yes	characteristic
457	C₂	—	16	2	no	—
458	C₂	C₃₇×#2541	1	1	yes	characteristic
459	C₂	C₃₇×#3147	1	1	yes	characteristic
460	C₂	C₃₇×#3156	1	1	yes	characteristic
461	C₂	C₃₇×#3285	1	2	yes	—
462	C₂	C₃₇×#3393	1	2	yes	—

	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 ◁ C₄×C₄⋊C₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₃₇×#494	C₂	semidirect
4. C₂×C₃₇×#464	C₂	semidirect
5. C₂×C₄×Q₁₆×C₃₇	C₂	semidirect
6. C₃₇×#2545	C₂	semidirect
7. C₃₇×#2015	C₂	semidirect
8. C₃₇×#2013	C₂	semidirect
10. C₃₇×#1969	C₂	semidirect
11. C₈×C₄⋊C₄×C₃₇	C₂	semidirect
204. #28466	C₃₇	direct (N × H)
228. C₂×#494	C₂×C₃₇	semidirect
229. C₂×#464	C₂×C₃₇	semidirect
230. C₂×C₄×Q₁₆	C₂×C₃₇	semidirect
231. #2545	C₂×C₃₇	semidirect
232. #2015	C₂×C₃₇	semidirect
233. #2013	C₂×C₃₇	semidirect
235. #1969	C₂×C₃₇	semidirect
236. C₈×C₄⋊C₄	C₂×C₃₇	semidirect
273. C₃₇	#28466	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×#495	2
C₂×C₃₇×#494	2
C₂×C₃₇×#464	2
C₂×C₄×Q₁₆×C₃₇	2
C₃₇×#2545	2
C₃₇×#2015	2
C₃₇×#2013	2
C₃₇×#1970	2
C₃₇×#1969	2
C₈×C₄⋊C₄×C₃₇	2
#28466	37

Subgroups — C37×#28466 #22649719

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28466 #22649719