Subgroups — C₃₇×#28428 #22649681

Order 9472.

976 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#489	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#474	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#464	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₇×#440	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2567	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2544	C₂	1	1	yes	maximal, characteristic
7	C₃₇×#2095	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#2093	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#2015	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#2014	C₂	1	1	yes	maximal, characteristic
11	C₃₇×#1973	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₇×#1969	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₇×#1959	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₇×#1957	C₂	1	1	yes	maximal, characteristic
15	C₃₇×#1771	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
20	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
21	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
22	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
25	C₃₇×#489	—	2	4	no	—
26	C₃₇×#474	—	2	4	no	—
27	C₃₇×#464	—	2	4	no	—
28	C₃₇×#440	—	2	4	no	—
29	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
30	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
31	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
33	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
34	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
35	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
36	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
37	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
38	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
39	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
40	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
41	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
42	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
43	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
44	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
46	C₃₇×#395	—	2	2	no	—
47	C₃₇×#394	—	2	2	no	—
48	C₃₇×#391	C₂²	1	1	yes	characteristic
49	C₃₇×#391	C₂²	1	1	yes	characteristic
50	C₃₇×#391	C₂²	1	1	yes	characteristic
51	C₃₇×#390	C₂²	1	1	yes	characteristic
52	C₃₇×#389	—	2	2	no	—
53	C₃₇×#386	—	2	2	no	—
54	C₃₇×#384	C₂²	1	1	yes	characteristic
55	C₃₇×#384	C₂²	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
57	C₃₇×#336	C₂²	1	1	yes	characteristic
58	C₃₇×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₃₇	—	2	1	no	—
60	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
61	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₃₇	—	2	2	no	—
63	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₃₇	—	2	1	no	—
66	C₂×Q₁₆×C₃₇	—	2	2	no	—
67	C₂×Q₁₆×C₃₇	—	2	2	no	—
68	C₂×Q₁₆×C₃₇	—	4	1	no	—
69	C₂×SD₁₆×C₃₇	—	2	2	no	—
70	C₂×SD₁₆×C₃₇	—	2	2	no	—
71	C₂×SD₁₆×C₃₇	—	2	2	no	—
72	C₂×SD₁₆×C₃₇	—	2	2	no	—
73	C₂×SD₁₆×C₃₇	—	2	2	no	—
74	C₂×SD₁₆×C₃₇	—	4	1	no	—
75	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
79	C₄⋊Q₈×C₃₇	—	2	2	no	—
80	C₄⋊Q₈×C₃₇	—	2	2	no	—
81	#127×C₃₇	—	2	2	no	—
82	#127×C₃₇	—	4	1	no	—
83	#124×C₃₇	—	2	2	no	—
84	#124×C₃₇	—	2	2	no	—
85	#124×C₃₇	—	2	2	no	—
86	#124×C₃₇	—	4	1	no	—
87	C₄×Q₈×C₃₇	—	2	2	no	—
88	C₄×Q₈×C₃₇	—	2	2	no	—
89	C₄×D₄×C₃₇	—	2	2	no	—
90	C₄×D₄×C₃₇	—	2	2	no	—
91	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
92	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
93	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
94	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
95	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
96	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
102	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
105	C₂×C₄²×C₃₇	—	2	1	no	—
106	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
109	#107×C₃₇	—	2	2	no	—
110	#107×C₃₇	—	2	2	no	—
111	#107×C₃₇	—	2	2	no	—
112	C₄⋊C₈×C₃₇	D₄	1	4	yes	complemented
113	#103×C₃₇	—	2	2	no	—
114	#103×C₃₇	—	2	2	no	—
115	#103×C₃₇	—	2	2	no	—
116	#103×C₃₇	—	2	2	no	—
117	#102×C₃₇	—	2	2	no	—
118	#102×C₃₇	—	2	2	no	—
119	#102×C₃₇	—	2	2	no	—
120	#102×C₃₇	—	2	2	no	—
121	#102×C₃₇	—	2	2	no	—
122	#102×C₃₇	—	2	2	no	—
123	#97×C₃₇	—	4	1	no	—
124	#97×C₃₇	D₄	1	4	yes	complemented
125	C₄×C₈×C₃₇	—	4	1	no	—
126	#95×C₃₇	—	2	2	no	—
127	#95×C₃₇	—	2	2	no	—
128	#95×C₃₇	—	2	2	no	—
129	#95×C₃₇	D₄	1	2	yes	—
130	C₂⁴×C₃₇	—	2	1	no	—
131	C₂⁴×C₃₇	—	2	1	no	—
132	C₂×Q₈×C₃₇	—	2	1	no	—
133	C₂×Q₈×C₃₇	—	2	1	no	—
134	C₂×Q₈×C₃₇	—	2	1	no	—
135	C₂×Q₈×C₃₇	—	2	1	no	—
136	C₂×Q₈×C₃₇	—	2	1	no	—
137	C₂×Q₈×C₃₇	—	2	1	no	—
138	C₂×Q₈×C₃₇	—	2	1	no	—
139	C₂×Q₈×C₃₇	—	2	1	no	—
140	C₂×Q₈×C₃₇	—	2	1	no	—
141	C₂×Q₈×C₃₇	—	2	1	no	—
142	C₂×Q₈×C₃₇	—	2	1	no	—
143	C₂×Q₈×C₃₇	—	4	2	no	—
144	C₂×Q₈×C₃₇	—	8	2	no	—
145	C₂×Q₈×C₃₇	#41	1	2	yes	—
146	C₂×D₄×C₃₇	—	2	1	no	—
147	C₂×D₄×C₃₇	—	2	1	no	—
148	C₂×D₄×C₃₇	—	2	1	no	—
149	C₂×D₄×C₃₇	—	2	1	no	—
150	C₂×D₄×C₃₇	—	2	1	no	—
151	C₂×D₄×C₃₇	—	2	1	no	—
152	C₂×D₄×C₃₇	—	2	1	no	—
153	C₂×D₄×C₃₇	—	2	1	no	—
154	C₂×D₄×C₃₇	—	2	1	no	—
155	C₂×D₄×C₃₇	—	2	1	no	—
156	C₂×D₄×C₃₇	—	2	1	no	—
157	C₂×D₄×C₃₇	—	4	4	no	—
158	C₂×D₄×C₃₇	—	4	4	no	—
159	C₂×D₄×C₃₇	—	8	2	no	—
160	C₂×D₄×C₃₇	#41	1	2	yes	—
161	C₂²×C₄×C₃₇	—	2	1	no	—
162	C₂²×C₄×C₃₇	—	2	1	no	—
163	C₂²×C₄×C₃₇	—	2	1	no	—
164	C₂²×C₄×C₃₇	—	2	1	no	—
165	C₂²×C₄×C₃₇	—	2	1	no	—
166	C₂²×C₄×C₃₇	—	2	1	no	—
167	C₂²×C₄×C₃₇	—	4	2	no	—
168	C₂²×C₄×C₃₇	—	8	2	no	—
169	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
174	Q₁₆×C₃₇	—	4	4	no	—
175	SD₁₆×C₃₇	—	2	8	no	—
176	SD₁₆×C₃₇	—	4	4	no	—
177	C₂×C₈×C₃₇	—	2	1	no	—
178	C₂×C₈×C₃₇	—	2	1	no	—
179	C₂×C₈×C₃₇	—	2	1	no	—
180	C₂×C₈×C₃₇	—	2	1	no	—
181	C₂×C₈×C₃₇	—	2	1	no	—
182	C₂×C₈×C₃₇	—	2	1	no	—
183	C₂×C₈×C₃₇	—	2	1	no	—
184	C₂×C₈×C₃₇	—	2	1	no	—
185	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
186	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
187	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
188	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
189	C₄⋊C₄×C₃₇	—	2	4	no	—
190	C₄⋊C₄×C₃₇	—	2	1	no	—
191	C₄⋊C₄×C₃₇	—	2	1	no	—
192	C₄⋊C₄×C₃₇	—	2	1	no	—
193	C₄⋊C₄×C₃₇	—	2	1	no	—
194	C₄⋊C₄×C₃₇	—	2	1	no	—
195	C₄⋊C₄×C₃₇	—	2	1	no	—
196	C₄⋊C₄×C₃₇	—	2	1	no	—
197	C₄⋊C₄×C₃₇	—	2	1	no	—
198	C₄⋊C₄×C₃₇	—	4	2	no	—
199	C₄⋊C₄×C₃₇	—	4	2	no	—
200	C₄⋊C₄×C₃₇	—	8	2	no	—
201	C₄⋊C₄×C₃₇	—	8	2	no	—
202	C₂²⋊C₄×C₃₇	—	4	4	no	—
203	C₂²⋊C₄×C₃₇	—	4	2	no	—
204	C₂²⋊C₄×C₃₇	—	4	2	no	—
205	C₂²⋊C₄×C₃₇	—	4	2	no	—
206	C₂²⋊C₄×C₃₇	—	8	2	no	—
207	C₄²×C₃₇	—	2	1	no	—
208	C₄²×C₃₇	—	2	1	no	—
209	C₄²×C₃₇	—	2	1	no	—
210	C₄²×C₃₇	—	2	1	no	—
211	C₄²×C₃₇	—	4	2	no	—
212	C₄²×C₃₇	C₂×D₄	1	2	yes	—
213	C₄²×C₃₇	C₂×D₄	1	2	yes	—
214	C₂³×C₃₇	—	2	2	no	—
215	C₂³×C₃₇	—	4	1	no	—
216	C₂³×C₃₇	—	4	1	no	—
217	C₂³×C₃₇	—	4	2	no	—
218	C₂³×C₃₇	—	4	2	no	—
219	C₂³×C₃₇	—	4	1	no	—
220	C₂³×C₃₇	—	4	1	no	—
221	C₂³×C₃₇	—	4	1	no	—
222	C₂³×C₃₇	—	4	2	no	—
223	C₂³×C₃₇	—	4	2	no	—
224	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
225	Q₈×C₃₇	—	2	2	no	—
226	Q₈×C₃₇	—	2	2	no	—
227	Q₈×C₃₇	—	4	1	no	—
228	Q₈×C₃₇	—	4	1	no	—
229	Q₈×C₃₇	—	4	1	no	—
230	Q₈×C₃₇	—	4	1	no	—
231	Q₈×C₃₇	—	4	1	no	—
232	Q₈×C₃₇	—	4	1	no	—
233	Q₈×C₃₇	—	8	4	no	—
234	D₄×C₃₇	—	2	2	no	—
235	D₄×C₃₇	—	2	2	no	—
236	D₄×C₃₇	—	4	1	no	—
237	D₄×C₃₇	—	4	1	no	—
238	D₄×C₃₇	—	4	1	no	—
239	D₄×C₃₇	—	4	1	no	—
240	D₄×C₃₇	—	4	1	no	—
241	D₄×C₃₇	—	4	1	no	—
242	D₄×C₃₇	—	8	8	no	—
243	C₂×C₄×C₃₇	—	2	2	no	—
244	C₂×C₄×C₃₇	—	2	2	no	—
245	C₂×C₄×C₃₇	—	2	2	no	—
246	C₂×C₄×C₃₇	—	2	2	no	—
247	C₂×C₄×C₃₇	—	2	2	no	—
248	C₂×C₄×C₃₇	—	2	2	no	—
249	C₂×C₄×C₃₇	—	2	2	no	—
250	C₂×C₄×C₃₇	—	2	2	no	—
251	C₂×C₄×C₃₇	—	4	1	no	—
252	C₂×C₄×C₃₇	—	4	1	no	—
253	C₂×C₄×C₃₇	—	4	1	no	—
254	C₂×C₄×C₃₇	—	4	1	no	—
255	C₂×C₄×C₃₇	—	4	1	no	—
256	C₂×C₄×C₃₇	—	4	1	no	—
257	C₂×C₄×C₃₇	—	4	1	no	—
258	C₂×C₄×C₃₇	—	4	1	no	—
259	C₂×C₄×C₃₇	—	4	1	no	—
260	C₂×C₄×C₃₇	—	4	2	no	—
261	C₂×C₄×C₃₇	—	4	2	no	—
262	C₂×C₄×C₃₇	—	4	2	no	—
263	C₂×C₄×C₃₇	—	4	2	no	—
264	C₂×C₄×C₃₇	—	8	4	no	—
265	C₂×C₄×C₃₇	#127	1	2	yes	—
266	C₂×C₄×C₃₇	#127	1	2	yes	—
267	C₂×C₄×C₃₇	#137	1	4	yes	—
268	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
271	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
272	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
273	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
274	C₈×C₃₇	—	2	2	no	—
275	C₈×C₃₇	—	2	2	no	—
276	C₈×C₃₇	—	2	2	no	—
277	C₈×C₃₇	—	2	2	no	—
278	#28428	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
279	C₂²×C₃₇	—	4	2	no	—
280	C₂²×C₃₇	—	4	4	no	—
281	C₂²×C₃₇	—	8	2	no	—
282	C₂²×C₃₇	—	8	1	no	—
283	C₂²×C₃₇	—	8	1	no	—
284	C₂²×C₃₇	—	8	2	no	—
285	C₂²×C₃₇	—	8	1	no	—
286	C₂²×C₃₇	—	8	1	no	—
287	C₂²×C₃₇	—	8	1	no	—
288	C₂²×C₃₇	—	8	2	no	—
289	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
290	C₂²×C₃₇	#546	1	1	yes	characteristic
291	C₂²×C₃₇	#548	1	1	yes	characteristic
292	C₂²×C₃₇	C₂×#137	1	2	yes	—
293	C₂²×C₃₇	#576	1	2	yes	—
294	C₄×C₃₇	—	2	2	no	—
295	C₄×C₃₇	—	2	2	no	—
296	C₄×C₃₇	—	2	4	no	—
297	C₄×C₃₇	—	4	2	no	—
298	C₄×C₃₇	—	4	2	no	—
299	C₄×C₃₇	—	8	1	no	—
300	C₄×C₃₇	—	8	1	no	—
301	C₄×C₃₇	—	8	1	no	—
302	C₄×C₃₇	—	8	1	no	—
303	C₄×C₃₇	—	8	1	no	—
304	C₄×C₃₇	#525	1	1	yes	characteristic
305	C₄×C₃₇	#537	1	1	yes	characteristic
306	C₄×C₃₇	#546	1	1	yes	characteristic
307	C₄×C₃₇	#548	1	1	yes	characteristic
308	C₂×#489	C₂×C₃₇	1	1	yes	characteristic, complemented
309	C₂×#474	C₂×C₃₇	1	1	yes	characteristic, complemented
310	C₂×#464	C₂×C₃₇	1	1	yes	characteristic, complemented
311	C₂×#440	C₂×C₃₇	1	1	yes	characteristic, complemented
312	#2567	C₂×C₃₇	1	1	yes	characteristic, complemented
313	#2544	C₂×C₃₇	1	1	yes	characteristic
314	#2095	C₂×C₃₇	1	1	yes	characteristic, complemented
315	#2093	C₂×C₃₇	1	1	yes	characteristic, complemented
316	#2015	C₂×C₃₇	1	1	yes	characteristic, complemented
317	#2014	C₂×C₃₇	1	1	yes	characteristic
318	#1973	C₂×C₃₇	1	1	yes	characteristic, complemented
319	#1969	C₂×C₃₇	1	1	yes	characteristic, complemented
320	#1959	C₂×C₃₇	1	1	yes	characteristic, complemented
321	#1957	C₂×C₃₇	1	1	yes	characteristic
322	#1771	C₂×C₃₇	1	1	yes	characteristic, complemented
323	C₂×C₃₇	—	8	2	no	—
324	C₂×C₃₇	—	16	1	no	—
325	C₂×C₃₇	#2540	1	1	yes	characteristic
326	C₂×C₃₇	#3152	1	1	yes	characteristic
327	C₂×C₃₇	#3155	1	1	yes	characteristic
328	C₂×C₃₇	#3314	1	2	yes	—
329	C₂×C₃₇	#3375	1	2	yes	—
330	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
331	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
332	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
333	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
334	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
335	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
336	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
337	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
338	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
339	#489	—	2	4	no	—
340	#474	—	2	4	no	—
341	#464	—	2	4	no	—
342	#440	—	2	4	no	—
343	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
344	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
345	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
346	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
347	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
348	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
349	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
350	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
351	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
352	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
353	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
354	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
355	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
356	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
357	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
358	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
359	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
360	#395	—	2	2	no	—
361	#394	—	2	2	no	—
362	#391	C₂²×C₃₇	1	1	yes	characteristic
363	#391	C₂²×C₃₇	1	1	yes	characteristic
364	#391	C₂²×C₃₇	1	1	yes	characteristic
365	#390	C₂²×C₃₇	1	1	yes	characteristic
366	#389	—	2	2	no	—
367	#386	—	2	2	no	—
368	#384	C₂²×C₃₇	1	1	yes	characteristic
369	#384	C₂²×C₃₇	1	1	yes	characteristic
370	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
371	#336	C₂²×C₃₇	1	1	yes	characteristic
372	#336	C₂²×C₃₇	1	1	yes	characteristic
373	C₃₇	#28428	1	1	yes	characteristic, direct product factor, Sylow
374	C₂²×Q₈	—	2	1	no	—
375	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
376	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
377	C₂²×D₄	—	2	2	no	—
378	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
379	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
380	C₂³×C₄	—	2	1	no	—
381	C₂×Q₁₆	—	2	2	no	—
382	C₂×Q₁₆	—	2	2	no	—
383	C₂×Q₁₆	—	4	1	no	—
384	C₂×SD₁₆	—	2	2	no	—
385	C₂×SD₁₆	—	2	2	no	—
386	C₂×SD₁₆	—	2	2	no	—
387	C₂×SD₁₆	—	2	2	no	—
388	C₂×SD₁₆	—	2	2	no	—
389	C₂×SD₁₆	—	4	1	no	—
390	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
391	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
392	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
393	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
394	C₄⋊Q₈	—	2	2	no	—
395	C₄⋊Q₈	—	2	2	no	—
396	#127	—	2	2	no	—
397	#127	—	4	1	no	—
398	#124	—	2	2	no	—
399	#124	—	2	2	no	—
400	#124	—	2	2	no	—
401	#124	—	4	1	no	—
402	C₄×Q₈	—	2	2	no	—
403	C₄×Q₈	—	2	2	no	—
404	C₄×D₄	—	2	2	no	—
405	C₄×D₄	—	2	2	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	2	no	—
409	C₂×C₄⋊C₄	—	2	2	no	—
410	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
411	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₂²⋊C₄	—	2	2	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	2	2	no	—
420	C₂×C₄²	—	2	1	no	—
421	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
422	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
423	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
424	#107	—	2	2	no	—
425	#107	—	2	2	no	—
426	#107	—	2	2	no	—
427	C₄⋊C₈	D₄×C₃₇	1	4	yes	complemented
428	#103	—	2	2	no	—
429	#103	—	2	2	no	—
430	#103	—	2	2	no	—
431	#103	—	2	2	no	—
432	#102	—	2	2	no	—
433	#102	—	2	2	no	—
434	#102	—	2	2	no	—
435	#102	—	2	2	no	—
436	#102	—	2	2	no	—
437	#102	—	2	2	no	—
438	#97	—	4	1	no	—
439	#97	D₄×C₃₇	1	4	yes	complemented
440	C₄×C₈	—	4	1	no	—
441	#95	—	2	2	no	—
442	#95	—	2	2	no	—
443	#95	—	2	2	no	—
444	#95	D₄×C₃₇	1	2	yes	—
445	C₂⁴	—	2	1	no	—
446	C₂⁴	—	2	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	4	2	no	—
459	C₂×Q₈	—	8	2	no	—
460	C₂×Q₈	#41×C₃₇	1	2	yes	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	4	4	no	—
473	C₂×D₄	—	4	4	no	—
474	C₂×D₄	—	8	2	no	—
475	C₂×D₄	#41×C₃₇	1	2	yes	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	4	2	no	—
483	C₂²×C₄	—	8	2	no	—
484	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
485	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
486	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
487	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
488	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
489	Q₁₆	—	4	4	no	—
490	SD₁₆	—	2	8	no	—
491	SD₁₆	—	4	4	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
501	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
502	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
503	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
504	C₄⋊C₄	—	2	4	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	4	2	no	—
514	C₄⋊C₄	—	4	2	no	—
515	C₄⋊C₄	—	8	2	no	—
516	C₄⋊C₄	—	8	2	no	—
517	C₂²⋊C₄	—	4	4	no	—
518	C₂²⋊C₄	—	4	2	no	—
519	C₂²⋊C₄	—	4	2	no	—
520	C₂²⋊C₄	—	4	2	no	—
521	C₂²⋊C₄	—	8	2	no	—
522	C₄²	—	2	1	no	—
523	C₄²	—	2	1	no	—
524	C₄²	—	2	1	no	—
525	C₄²	—	2	1	no	—
526	C₄²	—	4	2	no	—
527	C₄²	C₂×D₄×C₃₇	1	2	yes	—
528	C₄²	C₂×D₄×C₃₇	1	2	yes	—
529	C₂³	—	2	2	no	—
530	C₂³	—	4	1	no	—
531	C₂³	—	4	1	no	—
532	C₂³	—	4	2	no	—
533	C₂³	—	4	2	no	—
534	C₂³	—	4	1	no	—
535	C₂³	—	4	1	no	—
536	C₂³	—	4	1	no	—
537	C₂³	—	4	2	no	—
538	C₂³	—	4	2	no	—
539	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
540	Q₈	—	2	2	no	—
541	Q₈	—	2	2	no	—
542	Q₈	—	4	1	no	—
543	Q₈	—	4	1	no	—
544	Q₈	—	4	1	no	—
545	Q₈	—	4	1	no	—
546	Q₈	—	4	1	no	—
547	Q₈	—	4	1	no	—
548	Q₈	—	8	4	no	—
549	D₄	—	2	2	no	—
550	D₄	—	2	2	no	—
551	D₄	—	4	1	no	—
552	D₄	—	4	1	no	—
553	D₄	—	4	1	no	—
554	D₄	—	4	1	no	—
555	D₄	—	4	1	no	—
556	D₄	—	4	1	no	—
557	D₄	—	8	8	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	2	no	—
577	C₂×C₄	—	4	2	no	—
578	C₂×C₄	—	4	2	no	—
579	C₂×C₄	—	8	4	no	—
580	C₂×C₄	#127×C₃₇	1	2	yes	—
581	C₂×C₄	#127×C₃₇	1	2	yes	—
582	C₂×C₄	#137×C₃₇	1	4	yes	—
583	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
584	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
585	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
586	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
587	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
588	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
589	C₈	—	2	2	no	—
590	C₈	—	2	2	no	—
591	C₈	—	2	2	no	—
592	C₈	—	2	2	no	—
593	C₂²	—	4	2	no	—
594	C₂²	—	4	4	no	—
595	C₂²	—	8	2	no	—
596	C₂²	—	8	1	no	—
597	C₂²	—	8	1	no	—
598	C₂²	—	8	2	no	—
599	C₂²	—	8	1	no	—
600	C₂²	—	8	1	no	—
601	C₂²	—	8	1	no	—
602	C₂²	—	8	2	no	—
603	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
604	C₂²	C₃₇×#546	1	1	yes	characteristic
605	C₂²	C₃₇×#548	1	1	yes	characteristic
606	C₂²	C₂×#137×C₃₇	1	2	yes	—
607	C₂²	C₃₇×#576	1	2	yes	—
608	C₄	—	2	2	no	—
609	C₄	—	2	2	no	—
610	C₄	—	2	4	no	—
611	C₄	—	4	2	no	—
612	C₄	—	4	2	no	—
613	C₄	—	8	1	no	—
614	C₄	—	8	1	no	—
615	C₄	—	8	1	no	—
616	C₄	—	8	1	no	—
617	C₄	—	8	1	no	—
618	C₄	C₃₇×#525	1	1	yes	characteristic
619	C₄	C₃₇×#537	1	1	yes	characteristic
620	C₄	C₃₇×#546	1	1	yes	characteristic
621	C₄	C₃₇×#548	1	1	yes	characteristic
622	C₂	—	8	2	no	—
623	C₂	—	16	1	no	—
624	C₂	C₃₇×#2540	1	1	yes	characteristic
625	C₂	C₃₇×#3152	1	1	yes	characteristic
626	C₂	C₃₇×#3155	1	1	yes	characteristic
627	C₂	C₃₇×#3314	1	2	yes	—
628	C₂	C₃₇×#3375	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂×#127×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
1. C₂×C₃₇×#489	C₂	semidirect
2. C₂×C₃₇×#474	C₂	semidirect
3. C₂×C₃₇×#464	C₂	semidirect
4. C₂×C₃₇×#440	C₂	semidirect
5. C₃₇×#2567	C₂	semidirect
7. C₃₇×#2095	C₂	semidirect
8. C₃₇×#2093	C₂	semidirect
9. C₃₇×#2015	C₂	semidirect
11. C₃₇×#1973	C₂	semidirect
12. C₃₇×#1969	C₂	semidirect
13. C₃₇×#1959	C₂	semidirect
15. C₃₇×#1771	C₂	semidirect
112. C₄⋊C₈×C₃₇	D₄	semidirect
124. #97×C₃₇	D₄	semidirect
278. #28428	C₃₇	direct (N × H)
308. C₂×#489	C₂×C₃₇	semidirect
309. C₂×#474	C₂×C₃₇	semidirect
310. C₂×#464	C₂×C₃₇	semidirect
311. C₂×#440	C₂×C₃₇	semidirect
312. #2567	C₂×C₃₇	semidirect
314. #2095	C₂×C₃₇	semidirect
315. #2093	C₂×C₃₇	semidirect
316. #2015	C₂×C₃₇	semidirect
318. #1973	C₂×C₃₇	semidirect
319. #1969	C₂×C₃₇	semidirect
320. #1959	C₂×C₃₇	semidirect
322. #1771	C₂×C₃₇	semidirect
373. C₃₇	#28428	direct (N × H)
427. C₄⋊C₈	D₄×C₃₇	semidirect
439. #97	D₄×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₇×#489	2
C₂×C₃₇×#474	2
C₂×C₃₇×#464	2
C₂×C₃₇×#440	2
C₃₇×#2567	2
C₃₇×#2544	2
C₃₇×#2095	2
C₃₇×#2093	2
C₃₇×#2015	2
C₃₇×#2014	2
C₃₇×#1973	2
C₃₇×#1969	2
C₃₇×#1959	2
C₃₇×#1957	2
C₃₇×#1771	2
#28428	37

Subgroups — C37×#28428 #22649681

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28428 #22649681