Subgroups — C₃₇×#60470 #22681723

Order 9472.

2604 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3586	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×#3585	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#577	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#3573	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#3069	C₂	1	6	yes	maximal, complemented
6	C₃₇×#3068	C₂	1	6	yes	maximal, complemented
7	C₃₇×#3067	C₂	1	6	yes	maximal, complemented
8	C₂×C₃₇×#471	C₂	1	6	yes	maximal, complemented
9	C₃₇×#2916	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#2889	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#2888	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₇×#585	C₂²	1	1	yes	characteristic
13	C₂×2₋¹⁺⁴×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×H(5,𝔽₂)×C₃₇	C₂²	1	1	yes	characteristic
15	C₃₇×#578	—	2	4	no	—
16	C₃₇×#577	—	2	4	no	—
17	C₃₇×#577	—	2	4	no	—
18	C₃₇×#577	—	2	4	no	—
19	C₃₇×#577	—	2	4	no	—
20	C₃₇×#576	—	2	4	no	—
21	C₃₇×#575	C₂²	1	6	yes	—
22	C₃₇×#575	C₂²	1	6	yes	complemented
23	C₂×#137×C₃₇	C₂²	1	6	yes	complemented
24	C₂×#137×C₃₇	C₂²	1	3	yes	complemented
25	C₂×AGL(1,ℤ/8)×C₃₇	C₂²	1	6	yes	—
26	C₂×AGL(1,ℤ/8)×C₃₇	C₂²	1	3	yes	complemented
27	C₂×#135×C₃₇	C₂²	1	3	yes	complemented
28	C₂²×SD₁₆×C₃₇	C₂²	1	3	yes	complemented
29	C₃₇×#568	—	2	4	no	—
30	C₃₇×#568	C₂²	1	1	yes	characteristic
31	C₃₇×#568	C₂²	1	1	yes	characteristic
32	C₃₇×#568	C₂²	1	1	yes	characteristic
33	C₃₇×#568	C₂²	1	6	yes	complemented
34	C₂×#131×C₃₇	—	2	4	no	—
35	C₂×#131×C₃₇	C₂²	1	1	yes	characteristic
36	C₂×#131×C₃₇	C₂²	1	6	yes	complemented
37	C₃₇×#473	C₂²	1	12	yes	complemented
38	C₃₇×#472	C₂²	1	12	yes	complemented
39	C₃₇×#471	C₂²	1	12	yes	complemented
40	C₃₇×#471	C₂²	1	24	yes	complemented
41	C₃₇×#471	C₂²	1	4	yes	complemented
42	C₃₇×#430	C₂²	1	6	yes	complemented
43	C₂×#108×C₃₇	C₂²	1	6	yes	complemented
44	C₃₇×#413	C₂²	1	6	yes	complemented
45	C₃₇×#413	C₂²	1	6	yes	complemented
46	C₂×#101×C₃₇	C₂²	1	6	yes	complemented
47	C₂×#100×C₃₇	C₂²	1	6	yes	complemented
48	2₋¹⁺⁴×C₃₇	—	2	1	no	—
49	2₋¹⁺⁴×C₃₇	—	2	4	no	—
50	2₋¹⁺⁴×C₃₇	—	2	4	no	—
51	2₋¹⁺⁴×C₃₇	D₄	1	4	yes	—
52	H(5,𝔽₂)×C₃₇	—	2	3	no	—
53	H(5,𝔽₂)×C₃₇	—	2	4	no	—
54	H(5,𝔽₂)×C₃₇	—	2	4	no	—
55	H(5,𝔽₂)×C₃₇	D₄	1	4	yes	—
56	C₂×#41×C₃₇	—	2	4	no	—
57	C₂×#41×C₃₇	—	2	1	no	—
58	C₂×#41×C₃₇	—	2	3	no	—
59	C₂×#41×C₃₇	C₂³	1	6	yes	—
60	C₂×#41×C₃₇	C₂³	1	3	yes	—
61	C₂×#41×C₃₇	C₂³	1	3	yes	—
62	C₂×#41×C₃₇	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₃₇	—	2	1	no	—
64	C₂²×Q₈×C₃₇	C₂³	1	3	yes	—
65	C₂²×D₄×C₃₇	—	2	3	no	—
66	C₂²×D₄×C₃₇	C₂³	1	3	yes	—
67	#137×C₃₇	—	2	12	no	—
68	#137×C₃₇	—	2	6	no	—
69	#137×C₃₇	—	2	6	no	—
70	#137×C₃₇	—	2	12	no	—
71	#137×C₃₇	C₂³	1	12	yes	—
72	#137×C₃₇	C₂³	1	4	yes	—
73	AGL(1,ℤ/8)×C₃₇	—	2	12	no	—
74	AGL(1,ℤ/8)×C₃₇	—	2	6	no	—
75	AGL(1,ℤ/8)×C₃₇	—	2	6	no	—
76	AGL(1,ℤ/8)×C₃₇	—	2	12	no	—
77	AGL(1,ℤ/8)×C₃₇	C₂³	1	12	yes	—
78	AGL(1,ℤ/8)×C₃₇	C₂³	1	4	yes	—
79	#135×C₃₇	—	2	12	no	—
80	#135×C₃₇	—	2	12	no	—
81	#135×C₃₇	—	2	6	no	—
82	#135×C₃₇	—	2	6	no	—
83	C₂×Q₁₆×C₃₇	—	2	6	no	—
84	C₂×Q₁₆×C₃₇	C₂³	1	3	yes	—
85	C₂×SD₁₆×C₃₇	—	2	6	no	—
86	C₂×SD₁₆×C₃₇	—	2	6	no	—
87	C₂×SD₁₆×C₃₇	—	2	6	no	—
88	C₂×SD₁₆×C₃₇	—	2	6	no	—
89	C₂×SD₁₆×C₃₇	C₂³	1	3	yes	—
90	C₂×SD₁₆×C₃₇	C₂³	1	6	yes	—
91	C₂×SD₁₆×C₃₇	C₂³	1	1	yes	characteristic
92	C₂×D₈×C₃₇	—	2	6	no	—
93	C₂×D₈×C₃₇	C₂³	1	3	yes	—
94	#131×C₃₇	—	2	4	no	—
95	#131×C₃₇	—	2	4	no	—
96	#131×C₃₇	—	2	4	no	—
97	#131×C₃₇	—	2	12	no	—
98	#131×C₃₇	—	2	6	no	—
99	#131×C₃₇	—	2	6	no	—
100	#131×C₃₇	D₄	1	4	yes	—
101	#131×C₃₇	D₄	1	4	yes	—
102	#131×C₃₇	C₂³	1	4	yes	—
103	#131×C₃₇	C₂³	1	12	yes	—
104	C₂×M₁₆×C₃₇	—	2	12	no	—
105	C₂×M₁₆×C₃₇	—	2	6	no	—
106	C₂×M₁₆×C₃₇	C₂³	1	6	yes	—
107	C₂×M₁₆×C₃₇	C₂³	1	6	yes	—
108	C₂×M₁₆×C₃₇	C₂³	1	6	yes	—
109	C₂×M₁₆×C₃₇	C₂³	1	3	yes	—
110	C₂²×C₈×C₃₇	—	2	6	no	—
111	C₂²×C₈×C₃₇	C₂³	1	3	yes	—
112	#108×C₃₇	C₂³	1	4	yes	—
113	#108×C₃₇	C₂³	1	12	yes	—
114	#101×C₃₇	C₂³	1	12	yes	—
115	#101×C₃₇	C₂³	1	4	yes	—
116	#100×C₃₇	C₂³	1	12	yes	—
117	#100×C₃₇	C₂³	1	4	yes	—
118	C₂⁴×C₃₇	—	2	3	no	—
119	#41×C₃₇	—	2	4	no	—
120	#41×C₃₇	—	2	12	no	—
121	#41×C₃₇	—	2	6	no	—
122	#41×C₃₇	—	2	6	no	—
123	#41×C₃₇	—	2	6	no	—
124	#41×C₃₇	—	2	6	no	—
125	#41×C₃₇	—	2	6	no	—
126	#41×C₃₇	—	2	6	no	—
127	#41×C₃₇	—	4	4	no	—
128	#41×C₃₇	—	4	12	no	—
129	#41×C₃₇	C₂×D₄	1	12	yes	—
130	#41×C₃₇	C₂×D₄	1	4	yes	—
131	#41×C₃₇	C₂×D₄	1	4	yes	—
132	#41×C₃₇	C₂⁴	1	4	yes	—
133	C₂×Q₈×C₃₇	—	2	4	no	—
134	C₂×Q₈×C₃₇	—	2	3	no	—
135	C₂×Q₈×C₃₇	—	2	6	no	—
136	C₂×Q₈×C₃₇	—	2	6	no	—
137	C₂×Q₈×C₃₇	—	4	4	no	—
138	C₂×Q₈×C₃₇	C₂×D₄	1	6	yes	—
139	C₂×Q₈×C₃₇	#41	1	1	yes	characteristic
140	C₂×Q₈×C₃₇	C₂⁴	1	3	yes	—
141	C₂×Q₈×C₃₇	C₂⁴	1	1	yes	characteristic
142	C₂×D₄×C₃₇	—	2	6	no	—
143	C₂×D₄×C₃₇	—	2	12	no	—
144	C₂×D₄×C₃₇	—	2	3	no	—
145	C₂×D₄×C₃₇	—	2	3	no	—
146	C₂×D₄×C₃₇	—	2	6	no	—
147	C₂×D₄×C₃₇	—	2	6	no	—
148	C₂×D₄×C₃₇	—	2	3	no	—
149	C₂×D₄×C₃₇	—	4	12	no	—
150	C₂×D₄×C₃₇	C₂×D₄	1	6	yes	—
151	C₂×D₄×C₃₇	#41	1	3	yes	—
152	C₂×D₄×C₃₇	C₂⁴	1	1	yes	characteristic
153	C₂×D₄×C₃₇	C₂⁴	1	3	yes	—
154	C₂²×C₄×C₃₇	—	2	6	no	—
155	C₂²×C₄×C₃₇	—	2	3	no	—
156	C₂²×C₄×C₃₇	—	2	3	no	—
157	C₂²×C₄×C₃₇	—	2	3	no	—
158	C₂²×C₄×C₃₇	C₂⁴	1	3	yes	—
159	Q₁₆×C₃₇	—	2	12	no	—
160	Q₁₆×C₃₇	—	2	4	no	—
161	Q₁₆×C₃₇	—	2	6	no	—
162	SD₁₆×C₃₇	—	2	12	no	—
163	SD₁₆×C₃₇	—	2	4	no	—
164	SD₁₆×C₃₇	—	2	12	no	—
165	SD₁₆×C₃₇	—	2	4	no	—
166	SD₁₆×C₃₇	—	2	3	no	—
167	SD₁₆×C₃₇	—	2	3	no	—
168	SD₁₆×C₃₇	—	2	12	no	—
169	SD₁₆×C₃₇	—	2	1	no	—
170	SD₁₆×C₃₇	—	2	1	no	—
171	D₈×C₃₇	—	2	12	no	—
172	D₈×C₃₇	—	2	4	no	—
173	D₈×C₃₇	—	2	6	no	—
174	M₁₆×C₃₇	—	2	6	no	—
175	M₁₆×C₃₇	—	2	6	no	—
176	M₁₆×C₃₇	—	2	6	no	—
177	M₁₆×C₃₇	—	2	12	no	—
178	M₁₆×C₃₇	—	2	4	no	—
179	M₁₆×C₃₇	C₂×D₄	1	12	yes	—
180	M₁₆×C₃₇	C₂⁴	1	4	yes	—
181	M₁₆×C₃₇	C₂⁴	1	4	yes	—
182	M₁₆×C₃₇	C₂⁴	1	4	yes	—
183	C₂×C₈×C₃₇	—	2	6	no	—
184	C₂×C₈×C₃₇	—	2	6	no	—
185	C₂×C₈×C₃₇	—	2	6	no	—
186	C₂×C₈×C₃₇	—	2	4	no	—
187	C₂×C₈×C₃₇	—	2	12	no	—
188	C₂×C₈×C₃₇	C₂×D₄	1	6	yes	—
189	C₂×C₈×C₃₇	C₂×D₄	1	6	yes	—
190	C₂×C₈×C₃₇	C₂⁴	1	1	yes	characteristic
191	C₂×C₈×C₃₇	C₂⁴	1	3	yes	—
192	C₂³×C₃₇	—	2	6	no	—
193	C₂³×C₃₇	—	2	1	no	—
194	C₂³×C₃₇	—	2	3	no	—
195	C₂³×C₃₇	—	4	6	no	—
196	C₂³×C₃₇	—	16	3	no	—
197	C₂³×C₃₇	C₂×#41	1	3	yes	—
198	Q₈×C₃₇	—	2	6	no	—
199	Q₈×C₃₇	—	2	3	no	—
200	Q₈×C₃₇	—	2	3	no	—
201	Q₈×C₃₇	—	2	1	no	—
202	Q₈×C₃₇	—	2	1	no	—
203	Q₈×C₃₇	—	4	6	no	—
204	Q₈×C₃₇	#121	1	4	yes	—
205	Q₈×C₃₇	C₂²×D₄	1	4	yes	—
206	D₄×C₃₇	—	2	12	no	—
207	D₄×C₃₇	—	2	4	no	—
208	D₄×C₃₇	—	2	6	no	—
209	D₄×C₃₇	—	2	1	no	—
210	D₄×C₃₇	—	2	3	no	—
211	D₄×C₃₇	—	2	1	no	—
212	D₄×C₃₇	—	2	3	no	—
213	D₄×C₃₇	—	4	6	no	—
214	D₄×C₃₇	—	4	6	no	—
215	D₄×C₃₇	—	4	6	no	—
216	D₄×C₃₇	#121	1	12	yes	—
217	D₄×C₃₇	C₂²×D₄	1	4	yes	—
218	C₂×C₄×C₃₇	—	2	6	no	—
219	C₂×C₄×C₃₇	—	2	12	no	—
220	C₂×C₄×C₃₇	—	2	4	no	—
221	C₂×C₄×C₃₇	—	2	1	no	—
222	C₂×C₄×C₃₇	—	2	3	no	—
223	C₂×C₄×C₃₇	—	4	6	no	—
224	C₂×C₄×C₃₇	—	4	6	no	—
225	C₂×C₄×C₃₇	—	4	6	no	—
226	C₂×C₄×C₃₇	C₂²×D₄	1	6	yes	—
227	C₂×C₄×C₃₇	C₂²×D₄	1	6	yes	—
228	C₂×C₄×C₃₇	C₂×#41	1	3	yes	—
229	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
230	C₈×C₃₇	—	2	4	no	—
231	C₈×C₃₇	—	2	4	no	—
232	C₈×C₃₇	—	2	4	no	—
233	C₈×C₃₇	C₂²×D₄	1	1	yes	characteristic
234	C₈×C₃₇	C₂²×D₄	1	6	yes	—
235	C₈×C₃₇	C₂²×D₄	1	1	yes	characteristic
236	#60470	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₂²×C₃₇	—	2	4	no	—
238	C₂²×C₃₇	—	4	3	no	—
239	C₂²×C₃₇	—	4	1	no	—
240	C₂²×C₃₇	—	4	3	no	—
241	C₂²×C₃₇	—	8	6	no	—
242	C₂²×C₃₇	—	8	1	no	—
243	C₂²×C₃₇	—	8	3	no	—
244	C₂²×C₃₇	—	16	6	no	—
245	C₂²×C₃₇	C₂×#121	1	6	yes	—
246	C₂²×C₃₇	C₂²×#41	1	1	yes	characteristic
247	C₄×C₃₇	—	2	4	no	—
248	C₄×C₃₇	—	4	1	no	—
249	C₄×C₃₇	—	4	3	no	—
250	C₄×C₃₇	C₂×#121	1	6	yes	—
251	C₄×C₃₇	C₂³×D₄	1	1	yes	characteristic
252	C₄×C₃₇	C₂³×D₄	1	1	yes	characteristic
253	#3586	C₂×C₃₇	1	1	yes	characteristic, complemented
254	#3585	C₂×C₃₇	1	1	yes	characteristic, complemented
255	C₂×#577	C₂×C₃₇	1	1	yes	characteristic, complemented
256	#3573	C₂×C₃₇	1	1	yes	characteristic, complemented
257	#3069	C₂×C₃₇	1	6	yes	complemented
258	#3068	C₂×C₃₇	1	6	yes	complemented
259	#3067	C₂×C₃₇	1	6	yes	complemented
260	C₂×#471	C₂×C₃₇	1	6	yes	complemented
261	#2916	C₂×C₃₇	1	1	yes	characteristic, complemented
262	#2889	C₂×C₃₇	1	1	yes	characteristic, complemented
263	#2888	C₂×C₃₇	1	1	yes	characteristic, complemented
264	C₂×C₃₇	—	2	1	no	—
265	C₂×C₃₇	—	2	6	no	—
266	C₂×C₃₇	—	4	4	no	—
267	C₂×C₃₇	—	8	1	no	—
268	C₂×C₃₇	—	8	3	no	—
269	C₂×C₃₇	C₂²×#121	1	1	yes	characteristic
270	#585	C₂²×C₃₇	1	1	yes	characteristic
271	C₂×2₋¹⁺⁴	C₂²×C₃₇	1	1	yes	characteristic
272	C₂×H(5,𝔽₂)	C₂²×C₃₇	1	1	yes	characteristic
273	#578	—	2	4	no	—
274	#577	—	2	4	no	—
275	#577	—	2	4	no	—
276	#577	—	2	4	no	—
277	#577	—	2	4	no	—
278	#576	—	2	4	no	—
279	#575	C₂²×C₃₇	1	6	yes	—
280	#575	C₂²×C₃₇	1	6	yes	complemented
281	C₂×#137	C₂²×C₃₇	1	6	yes	complemented
282	C₂×#137	C₂²×C₃₇	1	3	yes	complemented
283	C₂×AGL(1,ℤ/8)	C₂²×C₃₇	1	6	yes	—
284	C₂×AGL(1,ℤ/8)	C₂²×C₃₇	1	3	yes	complemented
285	C₂×#135	C₂²×C₃₇	1	3	yes	complemented
286	C₂²×SD₁₆	C₂²×C₃₇	1	3	yes	complemented
287	#568	—	2	4	no	—
288	#568	C₂²×C₃₇	1	1	yes	characteristic
289	#568	C₂²×C₃₇	1	1	yes	characteristic
290	#568	C₂²×C₃₇	1	1	yes	characteristic
291	#568	C₂²×C₃₇	1	6	yes	complemented
292	C₂×#131	—	2	4	no	—
293	C₂×#131	C₂²×C₃₇	1	1	yes	characteristic
294	C₂×#131	C₂²×C₃₇	1	6	yes	complemented
295	#473	C₂²×C₃₇	1	12	yes	complemented
296	#472	C₂²×C₃₇	1	12	yes	complemented
297	#471	C₂²×C₃₇	1	12	yes	complemented
298	#471	C₂²×C₃₇	1	24	yes	complemented
299	#471	C₂²×C₃₇	1	4	yes	complemented
300	#430	C₂²×C₃₇	1	6	yes	complemented
301	C₂×#108	C₂²×C₃₇	1	6	yes	complemented
302	#413	C₂²×C₃₇	1	6	yes	complemented
303	#413	C₂²×C₃₇	1	6	yes	complemented
304	C₂×#101	C₂²×C₃₇	1	6	yes	complemented
305	C₂×#100	C₂²×C₃₇	1	6	yes	complemented
306	C₃₇	#60470	1	1	yes	characteristic, direct product factor, Sylow
307	2₋¹⁺⁴	—	2	1	no	—
308	2₋¹⁺⁴	—	2	4	no	—
309	2₋¹⁺⁴	—	2	4	no	—
310	2₋¹⁺⁴	D₄×C₃₇	1	4	yes	—
311	H(5,𝔽₂)	—	2	3	no	—
312	H(5,𝔽₂)	—	2	4	no	—
313	H(5,𝔽₂)	—	2	4	no	—
314	H(5,𝔽₂)	D₄×C₃₇	1	4	yes	—
315	C₂×#41	—	2	4	no	—
316	C₂×#41	—	2	1	no	—
317	C₂×#41	—	2	3	no	—
318	C₂×#41	C₂³×C₃₇	1	6	yes	—
319	C₂×#41	C₂³×C₃₇	1	3	yes	—
320	C₂×#41	C₂³×C₃₇	1	3	yes	—
321	C₂×#41	C₂³×C₃₇	1	1	yes	characteristic
322	C₂²×Q₈	—	2	1	no	—
323	C₂²×Q₈	C₂³×C₃₇	1	3	yes	—
324	C₂²×D₄	—	2	3	no	—
325	C₂²×D₄	C₂³×C₃₇	1	3	yes	—
326	#137	—	2	12	no	—
327	#137	—	2	6	no	—
328	#137	—	2	6	no	—
329	#137	—	2	12	no	—
330	#137	C₂³×C₃₇	1	12	yes	—
331	#137	C₂³×C₃₇	1	4	yes	—
332	AGL(1,ℤ/8)	—	2	12	no	—
333	AGL(1,ℤ/8)	—	2	6	no	—
334	AGL(1,ℤ/8)	—	2	6	no	—
335	AGL(1,ℤ/8)	—	2	12	no	—
336	AGL(1,ℤ/8)	C₂³×C₃₇	1	12	yes	—
337	AGL(1,ℤ/8)	C₂³×C₃₇	1	4	yes	—
338	#135	—	2	12	no	—
339	#135	—	2	12	no	—
340	#135	—	2	6	no	—
341	#135	—	2	6	no	—
342	C₂×Q₁₆	—	2	6	no	—
343	C₂×Q₁₆	C₂³×C₃₇	1	3	yes	—
344	C₂×SD₁₆	—	2	6	no	—
345	C₂×SD₁₆	—	2	6	no	—
346	C₂×SD₁₆	—	2	6	no	—
347	C₂×SD₁₆	—	2	6	no	—
348	C₂×SD₁₆	C₂³×C₃₇	1	3	yes	—
349	C₂×SD₁₆	C₂³×C₃₇	1	6	yes	—
350	C₂×SD₁₆	C₂³×C₃₇	1	1	yes	characteristic
351	C₂×D₈	—	2	6	no	—
352	C₂×D₈	C₂³×C₃₇	1	3	yes	—
353	#131	—	2	4	no	—
354	#131	—	2	4	no	—
355	#131	—	2	4	no	—
356	#131	—	2	12	no	—
357	#131	—	2	6	no	—
358	#131	—	2	6	no	—
359	#131	D₄×C₃₇	1	4	yes	—
360	#131	D₄×C₃₇	1	4	yes	—
361	#131	C₂³×C₃₇	1	4	yes	—
362	#131	C₂³×C₃₇	1	12	yes	—
363	C₂×M₁₆	—	2	12	no	—
364	C₂×M₁₆	—	2	6	no	—
365	C₂×M₁₆	C₂³×C₃₇	1	6	yes	—
366	C₂×M₁₆	C₂³×C₃₇	1	6	yes	—
367	C₂×M₁₆	C₂³×C₃₇	1	6	yes	—
368	C₂×M₁₆	C₂³×C₃₇	1	3	yes	—
369	C₂²×C₈	—	2	6	no	—
370	C₂²×C₈	C₂³×C₃₇	1	3	yes	—
371	#108	C₂³×C₃₇	1	4	yes	—
372	#108	C₂³×C₃₇	1	12	yes	—
373	#101	C₂³×C₃₇	1	12	yes	—
374	#101	C₂³×C₃₇	1	4	yes	—
375	#100	C₂³×C₃₇	1	12	yes	—
376	#100	C₂³×C₃₇	1	4	yes	—
377	C₂⁴	—	2	3	no	—
378	#41	—	2	4	no	—
379	#41	—	2	12	no	—
380	#41	—	2	6	no	—
381	#41	—	2	6	no	—
382	#41	—	2	6	no	—
383	#41	—	2	6	no	—
384	#41	—	2	6	no	—
385	#41	—	2	6	no	—
386	#41	—	4	4	no	—
387	#41	—	4	12	no	—
388	#41	C₂×D₄×C₃₇	1	12	yes	—
389	#41	C₂×D₄×C₃₇	1	4	yes	—
390	#41	C₂×D₄×C₃₇	1	4	yes	—
391	#41	C₂⁴×C₃₇	1	4	yes	—
392	C₂×Q₈	—	2	4	no	—
393	C₂×Q₈	—	2	3	no	—
394	C₂×Q₈	—	2	6	no	—
395	C₂×Q₈	—	2	6	no	—
396	C₂×Q₈	—	4	4	no	—
397	C₂×Q₈	C₂×D₄×C₃₇	1	6	yes	—
398	C₂×Q₈	#41×C₃₇	1	1	yes	characteristic
399	C₂×Q₈	C₂⁴×C₃₇	1	3	yes	—
400	C₂×Q₈	C₂⁴×C₃₇	1	1	yes	characteristic
401	C₂×D₄	—	2	6	no	—
402	C₂×D₄	—	2	12	no	—
403	C₂×D₄	—	2	3	no	—
404	C₂×D₄	—	2	3	no	—
405	C₂×D₄	—	2	6	no	—
406	C₂×D₄	—	2	6	no	—
407	C₂×D₄	—	2	3	no	—
408	C₂×D₄	—	4	12	no	—
409	C₂×D₄	C₂×D₄×C₃₇	1	6	yes	—
410	C₂×D₄	#41×C₃₇	1	3	yes	—
411	C₂×D₄	C₂⁴×C₃₇	1	1	yes	characteristic
412	C₂×D₄	C₂⁴×C₃₇	1	3	yes	—
413	C₂²×C₄	—	2	6	no	—
414	C₂²×C₄	—	2	3	no	—
415	C₂²×C₄	—	2	3	no	—
416	C₂²×C₄	—	2	3	no	—
417	C₂²×C₄	C₂⁴×C₃₇	1	3	yes	—
418	Q₁₆	—	2	12	no	—
419	Q₁₆	—	2	4	no	—
420	Q₁₆	—	2	6	no	—
421	SD₁₆	—	2	12	no	—
422	SD₁₆	—	2	4	no	—
423	SD₁₆	—	2	12	no	—
424	SD₁₆	—	2	4	no	—
425	SD₁₆	—	2	3	no	—
426	SD₁₆	—	2	3	no	—
427	SD₁₆	—	2	12	no	—
428	SD₁₆	—	2	1	no	—
429	SD₁₆	—	2	1	no	—
430	D₈	—	2	12	no	—
431	D₈	—	2	4	no	—
432	D₈	—	2	6	no	—
433	M₁₆	—	2	6	no	—
434	M₁₆	—	2	6	no	—
435	M₁₆	—	2	6	no	—
436	M₁₆	—	2	12	no	—
437	M₁₆	—	2	4	no	—
438	M₁₆	C₂×D₄×C₃₇	1	12	yes	—
439	M₁₆	C₂⁴×C₃₇	1	4	yes	—
440	M₁₆	C₂⁴×C₃₇	1	4	yes	—
441	M₁₆	C₂⁴×C₃₇	1	4	yes	—
442	C₂×C₈	—	2	6	no	—
443	C₂×C₈	—	2	6	no	—
444	C₂×C₈	—	2	6	no	—
445	C₂×C₈	—	2	4	no	—
446	C₂×C₈	—	2	12	no	—
447	C₂×C₈	C₂×D₄×C₃₇	1	6	yes	—
448	C₂×C₈	C₂×D₄×C₃₇	1	6	yes	—
449	C₂×C₈	C₂⁴×C₃₇	1	1	yes	characteristic
450	C₂×C₈	C₂⁴×C₃₇	1	3	yes	—
451	C₂³	—	2	6	no	—
452	C₂³	—	2	1	no	—
453	C₂³	—	2	3	no	—
454	C₂³	—	4	6	no	—
455	C₂³	—	16	3	no	—
456	C₂³	C₂×#41×C₃₇	1	3	yes	—
457	Q₈	—	2	6	no	—
458	Q₈	—	2	3	no	—
459	Q₈	—	2	3	no	—
460	Q₈	—	2	1	no	—
461	Q₈	—	2	1	no	—
462	Q₈	—	4	6	no	—
463	Q₈	#121×C₃₇	1	4	yes	—
464	Q₈	C₂²×D₄×C₃₇	1	4	yes	—
465	D₄	—	2	12	no	—
466	D₄	—	2	4	no	—
467	D₄	—	2	6	no	—
468	D₄	—	2	1	no	—
469	D₄	—	2	3	no	—
470	D₄	—	2	1	no	—
471	D₄	—	2	3	no	—
472	D₄	—	4	6	no	—
473	D₄	—	4	6	no	—
474	D₄	—	4	6	no	—
475	D₄	#121×C₃₇	1	12	yes	—
476	D₄	C₂²×D₄×C₃₇	1	4	yes	—
477	C₂×C₄	—	2	6	no	—
478	C₂×C₄	—	2	12	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	3	no	—
482	C₂×C₄	—	4	6	no	—
483	C₂×C₄	—	4	6	no	—
484	C₂×C₄	—	4	6	no	—
485	C₂×C₄	C₂²×D₄×C₃₇	1	6	yes	—
486	C₂×C₄	C₂²×D₄×C₃₇	1	6	yes	—
487	C₂×C₄	C₂×#41×C₃₇	1	3	yes	—
488	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
489	C₈	—	2	4	no	—
490	C₈	—	2	4	no	—
491	C₈	—	2	4	no	—
492	C₈	C₂²×D₄×C₃₇	1	1	yes	characteristic
493	C₈	C₂²×D₄×C₃₇	1	6	yes	—
494	C₈	C₂²×D₄×C₃₇	1	1	yes	characteristic
495	C₂²	—	2	4	no	—
496	C₂²	—	4	3	no	—
497	C₂²	—	4	1	no	—
498	C₂²	—	4	3	no	—
499	C₂²	—	8	6	no	—
500	C₂²	—	8	3	no	—
501	C₂²	—	8	1	no	—
502	C₂²	—	16	6	no	—
503	C₂²	C₂×#121×C₃₇	1	6	yes	—
504	C₂²	C₂²×#41×C₃₇	1	1	yes	characteristic
505	C₄	—	2	4	no	—
506	C₄	—	4	1	no	—
507	C₄	—	4	3	no	—
508	C₄	C₂×#121×C₃₇	1	6	yes	—
509	C₄	C₂³×D₄×C₃₇	1	1	yes	characteristic
510	C₄	C₂³×D₄×C₃₇	1	1	yes	characteristic
511	C₂	—	2	1	no	—
512	C₂	—	2	6	no	—
513	C₂	—	4	4	no	—
514	C₂	—	8	3	no	—
515	C₂	—	8	1	no	—
516	C₂	C₂²×#121×C₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃₇	C₂²×#121
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₇ ◁ C₂×#41×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×#3586	C₂	semidirect
2. C₃₇×#3585	C₂	semidirect
3. C₂×C₃₇×#577	C₂	semidirect
4. C₃₇×#3573	C₂	semidirect
5. C₃₇×#3069	C₂	semidirect
6. C₃₇×#3068	C₂	semidirect
7. C₃₇×#3067	C₂	semidirect
8. C₂×C₃₇×#471	C₂	semidirect
9. C₃₇×#2916	C₂	semidirect
10. C₃₇×#2889	C₂	semidirect
11. C₃₇×#2888	C₂	semidirect
22. C₃₇×#575	C₂²	semidirect
23. C₂×#137×C₃₇	C₂²	semidirect
24. C₂×#137×C₃₇	C₂²	semidirect
26. C₂×AGL(1,ℤ/8)×C₃₇	C₂²	semidirect
27. C₂×#135×C₃₇	C₂²	semidirect
28. C₂²×SD₁₆×C₃₇	C₂²	semidirect
33. C₃₇×#568	C₂²	semidirect
36. C₂×#131×C₃₇	C₂²	semidirect
37. C₃₇×#473	C₂²	semidirect
38. C₃₇×#472	C₂²	semidirect
39. C₃₇×#471	C₂²	semidirect
40. C₃₇×#471	C₂²	semidirect
41. C₃₇×#471	C₂²	semidirect
42. C₃₇×#430	C₂²	semidirect
43. C₂×#108×C₃₇	C₂²	semidirect
44. C₃₇×#413	C₂²	semidirect
45. C₃₇×#413	C₂²	semidirect
46. C₂×#101×C₃₇	C₂²	semidirect
47. C₂×#100×C₃₇	C₂²	semidirect
236. #60470	C₃₇	direct (N × H)
253. #3586	C₂×C₃₇	semidirect
254. #3585	C₂×C₃₇	semidirect
255. C₂×#577	C₂×C₃₇	semidirect
256. #3573	C₂×C₃₇	semidirect
257. #3069	C₂×C₃₇	semidirect
258. #3068	C₂×C₃₇	semidirect
259. #3067	C₂×C₃₇	semidirect
260. C₂×#471	C₂×C₃₇	semidirect
261. #2916	C₂×C₃₇	semidirect
262. #2889	C₂×C₃₇	semidirect
263. #2888	C₂×C₃₇	semidirect
280. #575	C₂²×C₃₇	semidirect
281. C₂×#137	C₂²×C₃₇	semidirect
282. C₂×#137	C₂²×C₃₇	semidirect
284. C₂×AGL(1,ℤ/8)	C₂²×C₃₇	semidirect
285. C₂×#135	C₂²×C₃₇	semidirect
286. C₂²×SD₁₆	C₂²×C₃₇	semidirect
291. #568	C₂²×C₃₇	semidirect
294. C₂×#131	C₂²×C₃₇	semidirect
295. #473	C₂²×C₃₇	semidirect
296. #472	C₂²×C₃₇	semidirect
297. #471	C₂²×C₃₇	semidirect
298. #471	C₂²×C₃₇	semidirect
299. #471	C₂²×C₃₇	semidirect
300. #430	C₂²×C₃₇	semidirect
301. C₂×#108	C₂²×C₃₇	semidirect
302. #413	C₂²×C₃₇	semidirect
303. #413	C₂²×C₃₇	semidirect
304. C₂×#101	C₂²×C₃₇	semidirect
305. C₂×#100	C₂²×C₃₇	semidirect
306. C₃₇	#60470	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×#3586	2
C₃₇×#3585	2
C₂×C₃₇×#577	2
C₃₇×#3573	2
C₃₇×#3069	2
C₃₇×#3068	2
C₃₇×#3067	2
C₂×C₃₇×#471	2
C₃₇×#2916	2
C₃₇×#2889	2
C₃₇×#2888	2
#60470	37

Subgroups — C37×#60470 #22681723

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#60470 #22681723