Subgroups — C₃₇×#60317 #22681570

Order 9472.

1892 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3481	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#2993	C₂	1	4	yes	maximal, complemented
3	C₃₇×#2991	C₂	1	2	yes	maximal, complemented
4	C₃₇×#2979	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2978	C₂	1	4	yes	maximal, complemented
6	C₃₇×#2975	C₂	1	4	yes	maximal, complemented
7	C₃₇×#2969	C₂	1	4	yes	maximal, complemented
8	C₃₇×#2965	C₂	1	2	yes	maximal, complemented
9	D₄×M₁₆×C₃₇	C₂	1	4	yes	maximal, complemented
10	C₃₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#2930	C₂	1	4	yes	maximal, complemented
12	C₂×#131×C₃₇	C₂²	1	2	yes	complemented
13	C₂²×M₁₆×C₃₇	C₂²	1	4	yes	complemented
14	C₃₇×#559	C₄	1	1	yes	characteristic
15	C₃₇×#554	C₄	1	2	yes	—
16	C₃₇×#553	C₄	1	4	yes	—
17	C₃₇×#551	C₄	1	4	yes	—
18	C₃₇×#546	C₄	1	4	yes	—
19	D₄²×C₃₇	C₄	1	1	yes	characteristic
20	C₃₇×#532	C₂²	1	1	yes	characteristic
21	C₃₇×#529	C₂²	1	4	yes	—
22	C₃₇×#525	C₂²	1	4	yes	—
23	C₄×#41×C₃₇	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₃₇	C₂²	1	4	yes	—
25	C₃₇×#446	C₂²	1	2	yes	complemented
26	C₃₇×#446	C₂²	1	2	yes	complemented
27	C₈×Q₈×C₃₇	C₂²	1	4	yes	complemented
28	C₃₇×#436	C₂²	1	2	yes	—
29	C₃₇×#436	C₂²	1	4	yes	—
30	C₃₇×#436	C₂²	1	2	yes	—
31	C₃₇×#436	C₂²	1	8	yes	complemented
32	C₃₇×#436	C₂²	1	8	yes	complemented
33	C₃₇×#436	C₂²	1	4	yes	complemented
34	C₃₇×#436	C₂²	1	8	yes	complemented
35	C₃₇×#436	C₂²	1	4	yes	complemented
36	C₃₇×#435	C₂²	1	4	yes	complemented
37	C₃₇×#435	C₂²	1	8	yes	complemented
38	C₃₇×#435	C₂²	1	8	yes	complemented
39	C₃₇×#435	C₂²	1	4	yes	complemented
40	C₈×D₄×C₃₇	C₂²	1	4	yes	complemented
41	C₈×D₄×C₃₇	C₂²	1	4	yes	complemented
42	C₃₇×#433	C₂²	1	8	yes	complemented
43	C₃₇×#431	C₂²	1	4	yes	complemented
44	C₃₇×#431	C₂²	1	2	yes	complemented
45	C₃₇×#431	C₂²	1	4	yes	complemented
46	C₃₇×#424	C₂²	1	4	yes	complemented
47	C₃₇×#423	C₂²	1	1	yes	characteristic, complemented
48	C₃₇×#423	C₂²	1	4	yes	complemented
49	C₃₇×#408	C₂²	1	4	yes	complemented
50	C₃₇×#408	C₂²	1	2	yes	complemented
51	C₃₇×#407	C₂²	1	4	yes	complemented
52	C₃₇×#407	C₂²	1	8	yes	complemented
53	C₃₇×#405	C₂²	1	4	yes	complemented
54	C₄×M₁₆×C₃₇	C₂²	1	4	yes	complemented
55	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic, complemented
56	C₂×#41×C₃₇	C₂×C₄	1	2	yes	—
57	C₂×#41×C₃₇	C₂³	1	2	yes	—
58	C₂²×D₄×C₃₇	C₂×C₄	1	4	yes	—
59	C₂³×C₄×C₃₇	C₂³	1	4	yes	—
60	#131×C₃₇	—	4	4	no	—
61	C₂×M₁₆×C₃₇	—	4	8	no	—
62	C₂×M₁₆×C₃₇	C₂³	1	4	yes	—
63	C₂×M₁₆×C₃₇	C₂³	1	8	yes	—
64	C₂×M₁₆×C₃₇	C₂³	1	4	yes	—
65	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
66	C₂×M₁₆×C₃₇	C₂³	1	4	yes	—
67	C₂×M₁₆×C₃₇	C₂³	1	4	yes	—
68	C₂²×C₈×C₃₇	C₂³	1	4	yes	—
69	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₃₇	C₂³	1	4	yes	—
71	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
72	C₄⋊Q₈×C₃₇	C₂×C₄	1	1	yes	characteristic
73	#127×C₃₇	C₂×C₄	1	1	yes	characteristic
74	#126×C₃₇	C₂×C₄	1	8	yes	—
75	#125×C₃₇	C₂×C₄	1	4	yes	—
76	#124×C₃₇	C₂×C₄	1	4	yes	—
77	#124×C₃₇	C₂×C₄	1	2	yes	—
78	#123×C₃₇	C₂×C₄	1	4	yes	—
79	#123×C₃₇	C₂×C₄	1	4	yes	—
80	#123×C₃₇	C₂×C₄	1	8	yes	—
81	C₂²⋊Q₈×C₃₇	C₂×C₄	1	8	yes	—
82	C₂²⋊Q₈×C₃₇	C₂×C₄	1	4	yes	—
83	#121×C₃₇	C₂×C₄	1	8	yes	—
84	#121×C₃₇	C₂×C₄	1	4	yes	—
85	#121×C₃₇	C₂×C₄	1	4	yes	—
86	#120×C₃₇	C₂×C₄	1	4	yes	—
87	#120×C₃₇	C₂×C₄	1	4	yes	—
88	C₄×Q₈×C₃₇	C₂×C₄	1	2	yes	—
89	C₄×Q₈×C₃₇	C₂³	1	2	yes	—
90	C₄×D₄×C₃₇	C₂×C₄	1	2	yes	—
91	C₄×D₄×C₃₇	C₂×C₄	1	4	yes	—
92	C₄×D₄×C₃₇	C₂×C₄	1	4	yes	—
93	C₄×D₄×C₃₇	C₂×C₄	1	8	yes	—
94	C₄×D₄×C₃₇	C₂×C₄	1	4	yes	—
95	C₄×D₄×C₃₇	C₂³	1	4	yes	—
96	C₄×D₄×C₃₇	C₂³	1	8	yes	—
97	C₄×D₄×C₃₇	C₂³	1	4	yes	—
98	C₄×D₄×C₃₇	C₂³	1	2	yes	—
99	#117×C₃₇	C₂×C₄	1	4	yes	—
100	#117×C₃₇	C₂×C₄	1	2	yes	—
101	#117×C₃₇	C₂³	1	4	yes	—
102	C₂×C₄⋊C₄×C₃₇	C₂×C₄	1	4	yes	—
103	C₂×C₂²⋊C₄×C₃₇	C₂×C₄	1	8	yes	—
104	C₂×C₄²×C₃₇	C₂³	1	4	yes	—
105	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
106	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
107	C₄⋊C₈×C₃₇	C₂³	1	4	yes	—
108	C₄⋊C₈×C₃₇	C₂³	1	8	yes	—
109	C₄⋊C₈×C₃₇	C₂³	1	4	yes	—
110	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
111	C₄⋊C₈×C₃₇	C₂³	1	4	yes	—
112	C₂²⋊C₈×C₃₇	C₂³	1	4	yes	—
113	C₂²⋊C₈×C₃₇	C₂³	1	4	yes	—
114	C₂²⋊C₈×C₃₇	C₂³	1	8	yes	—
115	C₂²⋊C₈×C₃₇	C₂³	1	8	yes	—
116	C₂²⋊C₈×C₃₇	C₂³	1	8	yes	—
117	C₂²⋊C₈×C₃₇	C₂³	1	4	yes	—
118	#97×C₃₇	C₂³	1	4	yes	—
119	#97×C₃₇	C₂³	1	4	yes	—
120	C₄×C₈×C₃₇	C₂³	1	2	yes	—
121	C₄×C₈×C₃₇	C₂³	1	2	yes	—
122	C₄×C₈×C₃₇	C₂³	1	4	yes	—
123	C₄×C₈×C₃₇	C₂³	1	8	yes	—
124	C₂⁴×C₃₇	C₂²×C₄	1	4	yes	—
125	#41×C₃₇	—	4	2	no	—
126	#41×C₃₇	—	4	2	no	—
127	#41×C₃₇	—	4	4	no	—
128	C₂×Q₈×C₃₇	C₂²×C₄	1	2	yes	—
129	C₂×Q₈×C₃₇	C₂²×C₄	1	2	yes	—
130	C₂×D₄×C₃₇	—	4	8	no	—
131	C₂×D₄×C₃₇	C₂²×C₄	1	2	yes	—
132	C₂×D₄×C₃₇	C₂²×C₄	1	4	yes	—
133	C₂×D₄×C₃₇	C₂²×C₄	1	4	yes	—
134	C₂×D₄×C₃₇	C₂²×C₄	1	8	yes	—
135	C₂×D₄×C₃₇	C₂²×C₄	1	2	yes	—
136	C₂×D₄×C₃₇	C₂²×C₄	1	4	yes	—
137	C₂²×C₄×C₃₇	—	4	4	no	—
138	C₂²×C₄×C₃₇	—	4	4	no	—
139	C₂²×C₄×C₃₇	C₂²×C₄	1	4	yes	—
140	C₂²×C₄×C₃₇	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₃₇	C₂²×C₄	1	4	yes	—
142	C₂²×C₄×C₃₇	C₂²×C₄	1	8	yes	—
143	C₂²×C₄×C₃₇	C₂²×C₄	1	4	yes	—
144	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
145	C₂²×C₄×C₃₇	C₂⁴	1	4	yes	—
146	C₂²×C₄×C₃₇	C₂⁴	1	4	yes	—
147	M₁₆×C₃₇	—	2	8	no	—
148	M₁₆×C₃₇	—	4	8	no	—
149	M₁₆×C₃₇	—	4	4	no	—
150	M₁₆×C₃₇	—	4	4	no	—
151	M₁₆×C₃₇	—	4	4	no	—
152	M₁₆×C₃₇	—	4	2	no	—
153	C₂×C₈×C₃₇	—	2	8	no	—
154	C₂×C₈×C₃₇	—	2	2	no	—
155	C₂×C₈×C₃₇	—	4	1	no	—
156	C₂×C₈×C₃₇	—	4	4	no	—
157	C₂×C₈×C₃₇	C₂⁴	1	4	yes	—
158	C₂×C₈×C₃₇	C₂⁴	1	2	yes	—
159	C₂×C₈×C₃₇	C₂⁴	1	1	yes	characteristic
160	C₂×C₈×C₃₇	C₂⁴	1	4	yes	—
161	C₂×C₈×C₃₇	C₂⁴	1	4	yes	—
162	C₂×C₈×C₃₇	C₂⁴	1	1	yes	characteristic
163	C₄⋊C₄×C₃₇	C₂²×C₄	1	2	yes	—
164	C₄⋊C₄×C₃₇	C₂²×C₄	1	4	yes	—
165	C₄⋊C₄×C₃₇	C₂²×C₄	1	8	yes	—
166	C₄⋊C₄×C₃₇	C₂²×C₄	1	2	yes	—
167	C₄⋊C₄×C₃₇	C₂²×C₄	1	4	yes	—
168	C₄⋊C₄×C₃₇	C₂²×C₄	1	4	yes	—
169	C₄⋊C₄×C₃₇	C₂²×C₄	1	8	yes	—
170	C₂²⋊C₄×C₃₇	C₂²×C₄	1	4	yes	—
171	C₂²⋊C₄×C₃₇	C₂²×C₄	1	8	yes	—
172	C₂²⋊C₄×C₃₇	C₂²×C₄	1	8	yes	—
173	C₂²⋊C₄×C₃₇	C₂²×C₄	1	8	yes	—
174	C₂²⋊C₄×C₃₇	C₂²×C₄	1	4	yes	—
175	C₂²⋊C₄×C₃₇	C₂²×C₄	1	4	yes	—
176	C₂²⋊C₄×C₃₇	C₂²×C₄	1	4	yes	—
177	C₂²⋊C₄×C₃₇	C₂²×C₄	1	4	yes	—
178	C₄²×C₃₇	C₂²×C₄	1	1	yes	characteristic
179	C₄²×C₃₇	C₂²×C₄	1	4	yes	—
180	C₄²×C₃₇	C₂²×C₄	1	4	yes	—
181	C₄²×C₃₇	C₂²×C₄	1	1	yes	characteristic
182	C₄²×C₃₇	C₂⁴	1	2	yes	—
183	C₄²×C₃₇	C₂⁴	1	4	yes	—
184	C₂³×C₃₇	—	4	4	no	—
185	C₂³×C₃₇	—	4	8	no	—
186	C₂³×C₃₇	C₂³×C₄	1	4	yes	—
187	C₂³×C₃₇	C₂³×C₄	1	4	yes	—
188	C₂³×C₃₇	C₂³×C₄	1	1	yes	characteristic
189	Q₈×C₃₇	—	2	4	no	—
190	Q₈×C₃₇	—	4	2	no	—
191	D₄×C₃₇	—	2	4	no	—
192	D₄×C₃₇	—	2	8	no	—
193	D₄×C₃₇	—	4	8	no	—
194	D₄×C₃₇	—	4	4	no	—
195	D₄×C₃₇	—	4	2	no	—
196	D₄×C₃₇	—	4	4	no	—
197	C₂×C₄×C₃₇	—	2	8	no	—
198	C₂×C₄×C₃₇	—	2	4	no	—
199	C₂×C₄×C₃₇	—	2	4	no	—
200	C₂×C₄×C₃₇	—	2	1	no	—
201	C₂×C₄×C₃₇	—	2	4	no	—
202	C₂×C₄×C₃₇	—	2	1	no	—
203	C₂×C₄×C₃₇	—	2	4	no	—
204	C₂×C₄×C₃₇	—	2	4	no	—
205	C₂×C₄×C₃₇	—	4	4	no	—
206	C₂×C₄×C₃₇	—	4	8	no	—
207	C₂×C₄×C₃₇	—	4	4	no	—
208	C₂×C₄×C₃₇	C₂³×C₄	1	2	yes	—
209	C₂×C₄×C₃₇	C₂³×C₄	1	4	yes	—
210	C₂×C₄×C₃₇	C₂³×C₄	1	1	yes	characteristic
211	C₂×C₄×C₃₇	C₂³×C₄	1	4	yes	—
212	C₂×C₄×C₃₇	C₂³×C₄	1	4	yes	—
213	C₂×C₄×C₃₇	C₂³×C₄	1	4	yes	—
214	C₂×C₄×C₃₇	C₂³×C₄	1	2	yes	—
215	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
216	C₈×C₃₇	—	2	4	no	—
217	C₈×C₃₇	—	2	1	no	—
218	C₈×C₃₇	—	2	4	no	—
219	C₈×C₃₇	—	2	2	no	—
220	C₈×C₃₇	—	2	4	no	—
221	C₈×C₃₇	H(5,𝔽₂)	1	2	yes	—
222	#60317	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
223	C₂²×C₃₇	—	2	4	no	—
224	C₂²×C₃₇	—	2	4	no	—
225	C₂²×C₃₇	—	2	1	no	—
226	C₂²×C₃₇	—	2	2	no	—
227	C₂²×C₃₇	—	2	4	no	—
228	C₂²×C₃₇	—	2	4	no	—
229	C₂²×C₃₇	—	2	8	no	—
230	C₂²×C₃₇	—	8	8	no	—
231	C₂²×C₃₇	C₂⁴×C₄	1	1	yes	characteristic
232	C₄×C₃₇	—	2	4	no	—
233	C₄×C₃₇	—	2	4	no	—
234	C₄×C₃₇	—	2	1	no	—
235	C₄×C₃₇	—	2	2	no	—
236	C₄×C₃₇	—	2	4	no	—
237	C₄×C₃₇	—	2	4	no	—
238	C₄×C₃₇	#568	1	4	yes	—
239	C₄×C₃₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
240	C₄×C₃₇	#585	1	1	yes	characteristic
241	#3481	C₂×C₃₇	1	1	yes	characteristic
242	#2993	C₂×C₃₇	1	4	yes	complemented
243	#2991	C₂×C₃₇	1	2	yes	complemented
244	#2979	C₂×C₃₇	1	1	yes	characteristic, complemented
245	#2978	C₂×C₃₇	1	4	yes	complemented
246	#2975	C₂×C₃₇	1	4	yes	complemented
247	#2969	C₂×C₃₇	1	4	yes	complemented
248	#2965	C₂×C₃₇	1	2	yes	complemented
249	D₄×M₁₆	C₂×C₃₇	1	4	yes	complemented
250	#2931	C₂×C₃₇	1	1	yes	characteristic, complemented
251	#2930	C₂×C₃₇	1	4	yes	complemented
252	C₂×C₃₇	—	4	1	no	—
253	C₂×C₃₇	—	4	4	no	—
254	C₂×C₃₇	—	4	4	no	—
255	C₂×C₃₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
256	C₂×C₃₇	C₂×#568	1	2	yes	—
257	C₂×#131	C₂²×C₃₇	1	2	yes	complemented
258	C₂²×M₁₆	C₂²×C₃₇	1	4	yes	complemented
259	#559	C₄×C₃₇	1	1	yes	characteristic
260	#554	C₄×C₃₇	1	2	yes	—
261	#553	C₄×C₃₇	1	4	yes	—
262	#551	C₄×C₃₇	1	4	yes	—
263	#546	C₄×C₃₇	1	4	yes	—
264	D₄²	C₄×C₃₇	1	1	yes	characteristic
265	#532	C₂²×C₃₇	1	1	yes	characteristic
266	#529	C₂²×C₃₇	1	4	yes	—
267	#525	C₂²×C₃₇	1	4	yes	—
268	C₄×#41	C₂²×C₃₇	1	2	yes	—
269	C₂×C₄×D₄	C₂²×C₃₇	1	4	yes	—
270	#446	C₂²×C₃₇	1	2	yes	complemented
271	#446	C₂²×C₃₇	1	2	yes	complemented
272	C₈×Q₈	C₂²×C₃₇	1	4	yes	complemented
273	#436	C₂²×C₃₇	1	2	yes	—
274	#436	C₂²×C₃₇	1	4	yes	—
275	#436	C₂²×C₃₇	1	2	yes	—
276	#436	C₂²×C₃₇	1	8	yes	complemented
277	#436	C₂²×C₃₇	1	8	yes	complemented
278	#436	C₂²×C₃₇	1	4	yes	complemented
279	#436	C₂²×C₃₇	1	8	yes	complemented
280	#436	C₂²×C₃₇	1	4	yes	complemented
281	#435	C₂²×C₃₇	1	4	yes	complemented
282	#435	C₂²×C₃₇	1	8	yes	complemented
283	#435	C₂²×C₃₇	1	8	yes	complemented
284	#435	C₂²×C₃₇	1	4	yes	complemented
285	C₈×D₄	C₂²×C₃₇	1	4	yes	complemented
286	C₈×D₄	C₂²×C₃₇	1	4	yes	complemented
287	#433	C₂²×C₃₇	1	8	yes	complemented
288	#431	C₂²×C₃₇	1	4	yes	complemented
289	#431	C₂²×C₃₇	1	2	yes	complemented
290	#431	C₂²×C₃₇	1	4	yes	complemented
291	#424	C₂²×C₃₇	1	4	yes	complemented
292	#423	C₂²×C₃₇	1	1	yes	characteristic, complemented
293	#423	C₂²×C₃₇	1	4	yes	complemented
294	#408	C₂²×C₃₇	1	4	yes	complemented
295	#408	C₂²×C₃₇	1	2	yes	complemented
296	#407	C₂²×C₃₇	1	4	yes	complemented
297	#407	C₂²×C₃₇	1	8	yes	complemented
298	#405	C₂²×C₃₇	1	4	yes	complemented
299	C₄×M₁₆	C₂²×C₃₇	1	4	yes	complemented
300	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic, complemented
301	C₃₇	#60317	1	1	yes	characteristic, direct product factor, Sylow
302	C₂×#41	C₂×C₄×C₃₇	1	2	yes	—
303	C₂×#41	C₂³×C₃₇	1	2	yes	—
304	C₂²×D₄	C₂×C₄×C₃₇	1	4	yes	—
305	C₂³×C₄	C₂³×C₃₇	1	4	yes	—
306	#131	—	4	4	no	—
307	C₂×M₁₆	—	4	8	no	—
308	C₂×M₁₆	C₂³×C₃₇	1	4	yes	—
309	C₂×M₁₆	C₂³×C₃₇	1	8	yes	—
310	C₂×M₁₆	C₂³×C₃₇	1	4	yes	—
311	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
312	C₂×M₁₆	C₂³×C₃₇	1	4	yes	—
313	C₂×M₁₆	C₂³×C₃₇	1	4	yes	—
314	C₂²×C₈	C₂³×C₃₇	1	4	yes	—
315	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
316	C₂²×C₈	C₂³×C₃₇	1	4	yes	—
317	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
318	C₄⋊Q₈	C₂×C₄×C₃₇	1	1	yes	characteristic
319	#127	C₂×C₄×C₃₇	1	1	yes	characteristic
320	#126	C₂×C₄×C₃₇	1	8	yes	—
321	#125	C₂×C₄×C₃₇	1	4	yes	—
322	#124	C₂×C₄×C₃₇	1	4	yes	—
323	#124	C₂×C₄×C₃₇	1	2	yes	—
324	#123	C₂×C₄×C₃₇	1	4	yes	—
325	#123	C₂×C₄×C₃₇	1	4	yes	—
326	#123	C₂×C₄×C₃₇	1	8	yes	—
327	C₂²⋊Q₈	C₂×C₄×C₃₇	1	8	yes	—
328	C₂²⋊Q₈	C₂×C₄×C₃₇	1	4	yes	—
329	#121	C₂×C₄×C₃₇	1	8	yes	—
330	#121	C₂×C₄×C₃₇	1	4	yes	—
331	#121	C₂×C₄×C₃₇	1	4	yes	—
332	#120	C₂×C₄×C₃₇	1	4	yes	—
333	#120	C₂×C₄×C₃₇	1	4	yes	—
334	C₄×Q₈	C₂×C₄×C₃₇	1	2	yes	—
335	C₄×Q₈	C₂³×C₃₇	1	2	yes	—
336	C₄×D₄	C₂×C₄×C₃₇	1	4	yes	—
337	C₄×D₄	C₂×C₄×C₃₇	1	8	yes	—
338	C₄×D₄	C₂×C₄×C₃₇	1	4	yes	—
339	C₄×D₄	C₂×C₄×C₃₇	1	2	yes	—
340	C₄×D₄	C₂×C₄×C₃₇	1	4	yes	—
341	C₄×D₄	C₂³×C₃₇	1	2	yes	—
342	C₄×D₄	C₂³×C₃₇	1	8	yes	—
343	C₄×D₄	C₂³×C₃₇	1	4	yes	—
344	C₄×D₄	C₂³×C₃₇	1	4	yes	—
345	#117	C₂×C₄×C₃₇	1	4	yes	—
346	#117	C₂×C₄×C₃₇	1	2	yes	—
347	#117	C₂³×C₃₇	1	4	yes	—
348	C₂×C₄⋊C₄	C₂×C₄×C₃₇	1	4	yes	—
349	C₂×C₂²⋊C₄	C₂×C₄×C₃₇	1	8	yes	—
350	C₂×C₄²	C₂³×C₃₇	1	4	yes	—
351	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
352	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
353	C₄⋊C₈	C₂³×C₃₇	1	4	yes	—
354	C₄⋊C₈	C₂³×C₃₇	1	8	yes	—
355	C₄⋊C₈	C₂³×C₃₇	1	4	yes	—
356	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
357	C₄⋊C₈	C₂³×C₃₇	1	4	yes	—
358	C₂²⋊C₈	C₂³×C₃₇	1	4	yes	—
359	C₂²⋊C₈	C₂³×C₃₇	1	4	yes	—
360	C₂²⋊C₈	C₂³×C₃₇	1	8	yes	—
361	C₂²⋊C₈	C₂³×C₃₇	1	8	yes	—
362	C₂²⋊C₈	C₂³×C₃₇	1	8	yes	—
363	C₂²⋊C₈	C₂³×C₃₇	1	4	yes	—
364	#97	C₂³×C₃₇	1	4	yes	—
365	#97	C₂³×C₃₇	1	4	yes	—
366	C₄×C₈	C₂³×C₃₇	1	2	yes	—
367	C₄×C₈	C₂³×C₃₇	1	2	yes	—
368	C₄×C₈	C₂³×C₃₇	1	4	yes	—
369	C₄×C₈	C₂³×C₃₇	1	8	yes	—
370	C₂⁴	C₂²×C₄×C₃₇	1	4	yes	—
371	#41	—	4	2	no	—
372	#41	—	4	2	no	—
373	#41	—	4	4	no	—
374	C₂×Q₈	C₂²×C₄×C₃₇	1	2	yes	—
375	C₂×Q₈	C₂²×C₄×C₃₇	1	2	yes	—
376	C₂×D₄	—	4	8	no	—
377	C₂×D₄	C₂²×C₄×C₃₇	1	2	yes	—
378	C₂×D₄	C₂²×C₄×C₃₇	1	4	yes	—
379	C₂×D₄	C₂²×C₄×C₃₇	1	4	yes	—
380	C₂×D₄	C₂²×C₄×C₃₇	1	8	yes	—
381	C₂×D₄	C₂²×C₄×C₃₇	1	2	yes	—
382	C₂×D₄	C₂²×C₄×C₃₇	1	4	yes	—
383	C₂²×C₄	—	4	4	no	—
384	C₂²×C₄	—	4	4	no	—
385	C₂²×C₄	C₂²×C₄×C₃₇	1	4	yes	—
386	C₂²×C₄	C₂²×C₄×C₃₇	1	2	yes	—
387	C₂²×C₄	C₂²×C₄×C₃₇	1	4	yes	—
388	C₂²×C₄	C₂²×C₄×C₃₇	1	8	yes	—
389	C₂²×C₄	C₂²×C₄×C₃₇	1	4	yes	—
390	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
391	C₂²×C₄	C₂⁴×C₃₇	1	4	yes	—
392	C₂²×C₄	C₂⁴×C₃₇	1	4	yes	—
393	M₁₆	—	2	8	no	—
394	M₁₆	—	4	8	no	—
395	M₁₆	—	4	4	no	—
396	M₁₆	—	4	4	no	—
397	M₁₆	—	4	4	no	—
398	M₁₆	—	4	2	no	—
399	C₂×C₈	—	2	8	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	4	1	no	—
402	C₂×C₈	—	4	4	no	—
403	C₂×C₈	C₂⁴×C₃₇	1	4	yes	—
404	C₂×C₈	C₂⁴×C₃₇	1	2	yes	—
405	C₂×C₈	C₂⁴×C₃₇	1	1	yes	characteristic
406	C₂×C₈	C₂⁴×C₃₇	1	4	yes	—
407	C₂×C₈	C₂⁴×C₃₇	1	4	yes	—
408	C₂×C₈	C₂⁴×C₃₇	1	1	yes	characteristic
409	C₄⋊C₄	C₂²×C₄×C₃₇	1	2	yes	—
410	C₄⋊C₄	C₂²×C₄×C₃₇	1	4	yes	—
411	C₄⋊C₄	C₂²×C₄×C₃₇	1	8	yes	—
412	C₄⋊C₄	C₂²×C₄×C₃₇	1	2	yes	—
413	C₄⋊C₄	C₂²×C₄×C₃₇	1	4	yes	—
414	C₄⋊C₄	C₂²×C₄×C₃₇	1	4	yes	—
415	C₄⋊C₄	C₂²×C₄×C₃₇	1	8	yes	—
416	C₂²⋊C₄	C₂²×C₄×C₃₇	1	4	yes	—
417	C₂²⋊C₄	C₂²×C₄×C₃₇	1	8	yes	—
418	C₂²⋊C₄	C₂²×C₄×C₃₇	1	8	yes	—
419	C₂²⋊C₄	C₂²×C₄×C₃₇	1	8	yes	—
420	C₂²⋊C₄	C₂²×C₄×C₃₇	1	4	yes	—
421	C₂²⋊C₄	C₂²×C₄×C₃₇	1	4	yes	—
422	C₂²⋊C₄	C₂²×C₄×C₃₇	1	4	yes	—
423	C₂²⋊C₄	C₂²×C₄×C₃₇	1	4	yes	—
424	C₄²	C₂²×C₄×C₃₇	1	1	yes	characteristic
425	C₄²	C₂²×C₄×C₃₇	1	4	yes	—
426	C₄²	C₂²×C₄×C₃₇	1	4	yes	—
427	C₄²	C₂²×C₄×C₃₇	1	1	yes	characteristic
428	C₄²	C₂⁴×C₃₇	1	2	yes	—
429	C₄²	C₂⁴×C₃₇	1	4	yes	—
430	C₂³	—	4	4	no	—
431	C₂³	—	4	8	no	—
432	C₂³	C₂³×C₄×C₃₇	1	4	yes	—
433	C₂³	C₂³×C₄×C₃₇	1	4	yes	—
434	C₂³	C₂³×C₄×C₃₇	1	1	yes	characteristic
435	Q₈	—	2	4	no	—
436	Q₈	—	4	2	no	—
437	D₄	—	2	4	no	—
438	D₄	—	2	8	no	—
439	D₄	—	4	8	no	—
440	D₄	—	4	4	no	—
441	D₄	—	4	2	no	—
442	D₄	—	4	4	no	—
443	C₂×C₄	—	2	8	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	4	4	no	—
452	C₂×C₄	—	4	8	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	C₂³×C₄×C₃₇	1	2	yes	—
455	C₂×C₄	C₂³×C₄×C₃₇	1	4	yes	—
456	C₂×C₄	C₂³×C₄×C₃₇	1	1	yes	characteristic
457	C₂×C₄	C₂³×C₄×C₃₇	1	4	yes	—
458	C₂×C₄	C₂³×C₄×C₃₇	1	4	yes	—
459	C₂×C₄	C₂³×C₄×C₃₇	1	4	yes	—
460	C₂×C₄	C₂³×C₄×C₃₇	1	2	yes	—
461	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
462	C₈	—	2	4	no	—
463	C₈	—	2	1	no	—
464	C₈	—	2	4	no	—
465	C₈	—	2	2	no	—
466	C₈	—	2	4	no	—
467	C₈	H(5,𝔽₂)×C₃₇	1	2	yes	—
468	C₂²	—	2	4	no	—
469	C₂²	—	2	4	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	4	no	—
473	C₂²	—	2	4	no	—
474	C₂²	—	2	8	no	—
475	C₂²	—	8	8	no	—
476	C₂²	C₂⁴×C₄×C₃₇	1	1	yes	characteristic
477	C₄	—	2	4	no	—
478	C₄	—	2	4	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	2	no	—
481	C₄	—	2	4	no	—
482	C₄	—	2	4	no	—
483	C₄	C₃₇×#568	1	4	yes	—
484	C₄	C₂×H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
485	C₄	C₃₇×#585	1	1	yes	characteristic
486	C₂	—	4	4	no	—
487	C₂	—	4	4	no	—
488	C₂	—	4	1	no	—
489	C₂	C₄×H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
490	C₂	C₂×C₃₇×#568	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₃₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₃₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₃₇
socle	C₂²×C₃₇	C₂⁴×C₄
prime radical	C₃₇×#3481	C₂
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
2. C₃₇×#2993	C₂	semidirect
3. C₃₇×#2991	C₂	semidirect
4. C₃₇×#2979	C₂	semidirect
5. C₃₇×#2978	C₂	semidirect
6. C₃₇×#2975	C₂	semidirect
7. C₃₇×#2969	C₂	semidirect
8. C₃₇×#2965	C₂	semidirect
9. D₄×M₁₆×C₃₇	C₂	semidirect
10. C₃₇×#2931	C₂	semidirect
11. C₃₇×#2930	C₂	semidirect
12. C₂×#131×C₃₇	C₂²	semidirect
13. C₂²×M₁₆×C₃₇	C₂²	semidirect
25. C₃₇×#446	C₂²	semidirect
26. C₃₇×#446	C₂²	semidirect
27. C₈×Q₈×C₃₇	C₂²	semidirect
31. C₃₇×#436	C₂²	semidirect
32. C₃₇×#436	C₂²	semidirect
33. C₃₇×#436	C₂²	semidirect
34. C₃₇×#436	C₂²	semidirect
35. C₃₇×#436	C₂²	semidirect
36. C₃₇×#435	C₂²	semidirect
37. C₃₇×#435	C₂²	semidirect
38. C₃₇×#435	C₂²	semidirect
39. C₃₇×#435	C₂²	semidirect
40. C₈×D₄×C₃₇	C₂²	semidirect
41. C₈×D₄×C₃₇	C₂²	semidirect
42. C₃₇×#433	C₂²	semidirect
43. C₃₇×#431	C₂²	semidirect
44. C₃₇×#431	C₂²	semidirect
45. C₃₇×#431	C₂²	semidirect
46. C₃₇×#424	C₂²	semidirect
47. C₃₇×#423	C₂²	semidirect
48. C₃₇×#423	C₂²	semidirect
49. C₃₇×#408	C₂²	semidirect
50. C₃₇×#408	C₂²	semidirect
51. C₃₇×#407	C₂²	semidirect
52. C₃₇×#407	C₂²	semidirect
53. C₃₇×#405	C₂²	semidirect
54. C₄×M₁₆×C₃₇	C₂²	semidirect
55. C₂×C₄×C₈×C₃₇	C₂²	semidirect
222. #60317	C₃₇	direct (N × H)
242. #2993	C₂×C₃₇	semidirect
243. #2991	C₂×C₃₇	semidirect
244. #2979	C₂×C₃₇	semidirect
245. #2978	C₂×C₃₇	semidirect
246. #2975	C₂×C₃₇	semidirect
247. #2969	C₂×C₃₇	semidirect
248. #2965	C₂×C₃₇	semidirect
249. D₄×M₁₆	C₂×C₃₇	semidirect
250. #2931	C₂×C₃₇	semidirect
251. #2930	C₂×C₃₇	semidirect
257. C₂×#131	C₂²×C₃₇	semidirect
258. C₂²×M₁₆	C₂²×C₃₇	semidirect
270. #446	C₂²×C₃₇	semidirect
271. #446	C₂²×C₃₇	semidirect
272. C₈×Q₈	C₂²×C₃₇	semidirect
276. #436	C₂²×C₃₇	semidirect
277. #436	C₂²×C₃₇	semidirect
278. #436	C₂²×C₃₇	semidirect
279. #436	C₂²×C₃₇	semidirect
280. #436	C₂²×C₃₇	semidirect
281. #435	C₂²×C₃₇	semidirect
282. #435	C₂²×C₃₇	semidirect
283. #435	C₂²×C₃₇	semidirect
284. #435	C₂²×C₃₇	semidirect
285. C₈×D₄	C₂²×C₃₇	semidirect
286. C₈×D₄	C₂²×C₃₇	semidirect
287. #433	C₂²×C₃₇	semidirect
288. #431	C₂²×C₃₇	semidirect
289. #431	C₂²×C₃₇	semidirect
290. #431	C₂²×C₃₇	semidirect
291. #424	C₂²×C₃₇	semidirect
292. #423	C₂²×C₃₇	semidirect
293. #423	C₂²×C₃₇	semidirect
294. #408	C₂²×C₃₇	semidirect
295. #408	C₂²×C₃₇	semidirect
296. #407	C₂²×C₃₇	semidirect
297. #407	C₂²×C₃₇	semidirect
298. #405	C₂²×C₃₇	semidirect
299. C₄×M₁₆	C₂²×C₃₇	semidirect
300. C₂×C₄×C₈	C₂²×C₃₇	semidirect
301. C₃₇	#60317	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₇×#3481	2
C₃₇×#2993	2
C₃₇×#2991	2
C₃₇×#2979	2
C₃₇×#2978	2
C₃₇×#2975	2
C₃₇×#2969	2
C₃₇×#2965	2
D₄×M₁₆×C₃₇	2
C₃₇×#2931	2
C₃₇×#2930	2
#60317	37

Subgroups — C37×#60317 #22681570

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#60317 #22681570