Subgroups — C₃₇×#35079 #22656332

Order 9472.

2098 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#2857	C₂	1	2	yes	maximal, complemented
2	C₃₇×#2851	C₂	1	2	yes	maximal, complemented
3	C₃₇×#2667	C₂	1	2	yes	maximal, complemented
4	C₃₇×#2665	C₂	1	2	yes	maximal, complemented
5	C₃₇×#2569	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2549	C₂	1	2	yes	maximal, complemented
7	C₃₇×#2442	C₂	1	2	yes	maximal, complemented
8	C₃₇×#2441	C₂	1	2	yes	maximal, complemented
9	C₃₇×#2440	C₂	1	2	yes	maximal, complemented
10	C₃₇×#2439	C₂	1	2	yes	maximal, complemented
11	C₃₇×#2437	C₂	1	4	yes	maximal
12	C₃₇×#2329	C₂	1	4	yes	maximal, complemented
13	C₃₇×#2280	C₂	1	1	yes	maximal, characteristic
14	C₂×C₃₇×#380	C₂	1	1	yes	maximal, characteristic
15	C₂×C₄×C₂²⋊C₄×C₃₇	C₂	1	1	yes	maximal, characteristic
16	C₂⁴×C₄×C₃₇	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₃₇	C₂²	1	2	yes	complemented
18	C₂×#125×C₃₇	C₂²	1	2	yes	complemented
19	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	4	yes	—
20	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	4	yes	—
21	C₂×#117×C₃₇	C₂²	1	2	yes	—
22	C₂²×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₃₇	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₃₇	C₂²	1	2	yes	—
25	C₂²×C₄²×C₃₇	C₂²	1	2	yes	—
26	C₃₇×#400	C₂²	1	4	yes	complemented
27	C₃₇×#399	C₂²	1	4	yes	—
28	C₃₇×#398	C₂²	1	4	yes	complemented
29	C₃₇×#398	C₂²	1	4	yes	complemented
30	C₃₇×#396	C₂²	1	4	yes	—
31	C₃₇×#396	C₂²	1	4	yes	—
32	C₃₇×#395	C₂²	1	4	yes	complemented
33	C₃₇×#393	C₂²	1	4	yes	—
34	C₃₇×#391	C₂²	1	4	yes	complemented
35	C₃₇×#391	C₂²	1	4	yes	complemented
36	C₃₇×#389	C₂²	1	4	yes	complemented
37	C₃₇×#389	C₂²	1	2	yes	complemented
38	C₃₇×#389	C₂²	1	2	yes	complemented
39	C₃₇×#389	C₂²	1	2	yes	complemented
40	C₃₇×#389	C₂²	1	2	yes	complemented
41	C₃₇×#389	C₂²	1	4	yes	complemented
42	C₃₇×#387	C₂²	1	4	yes	complemented
43	C₃₇×#387	C₂²	1	4	yes	complemented
44	C₃₇×#387	C₂²	1	4	yes	complemented
45	C₃₇×#387	C₂²	1	4	yes	complemented
46	C₃₇×#385	C₂²	1	4	yes	—
47	C₃₇×#385	C₂²	1	4	yes	—
48	C₃₇×#385	C₂²	1	4	yes	—
49	C₃₇×#385	C₂²	1	4	yes	—
50	C₃₇×#384	C₂²	1	2	yes	complemented
51	C₃₇×#382	C₂²	1	2	yes	complemented
52	C₃₇×#381	C₂²	1	2	yes	—
53	C₃₇×#380	C₂²	1	2	yes	—
54	C₃₇×#380	C₂²	1	4	yes	—
55	C₃₇×#380	C₂²	1	4	yes	—
56	C₃₇×#380	C₂²	1	1	yes	characteristic
57	C₃₇×#380	C₂²	1	2	yes	—
58	C₃₇×#380	C₂²	1	1	yes	characteristic
59	C₃₇×#380	C₂²	1	2	yes	—
60	C₃₇×#380	C₂²	1	2	yes	—
61	C₃₇×#380	C₂²	1	1	yes	characteristic
62	C₃₇×#380	C₂²	1	1	yes	characteristic
63	C₃₇×#379	C₂²	1	2	yes	—
64	C₄×C₂²⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
65	C₄×C₂²⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
66	C₄×C₂²⋊C₄×C₃₇	C₂²	1	2	yes	—
67	C₄×C₂²⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
68	C₄×C₂²⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
69	C₄×C₂²⋊C₄×C₃₇	C₂²	1	2	yes	—
70	C₄×C₂²⋊C₄×C₃₇	C₂²	1	2	yes	—
71	C₄×C₂²⋊C₄×C₃₇	C₂²	1	2	yes	—
72	C₂×#95×C₃₇	C₂²	1	1	yes	characteristic
73	C₂×#95×C₃₇	C₂²	1	1	yes	characteristic
74	C₂×#95×C₃₇	C₂²	1	2	yes	—
75	C₂⁵×C₃₇	C₂³	1	1	yes	characteristic
76	C₂²×Q₈×C₃₇	C₂³	1	4	yes	—
77	C₂³×C₄×C₃₇	—	4	4	no	—
78	C₂³×C₄×C₃₇	Q₈	1	8	yes	complemented
79	C₂³×C₄×C₃₇	C₂³	1	2	yes	—
80	C₂³×C₄×C₃₇	C₂³	1	2	yes	—
81	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₃₇	C₂³	1	4	yes	—
85	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
88	C₄⋊Q₈×C₃₇	—	4	4	no	—
89	#125×C₃₇	—	4	4	no	—
90	C₂²⋊Q₈×C₃₇	—	2	16	no	—
91	C₂²⋊Q₈×C₃₇	—	4	8	no	—
92	#117×C₃₇	—	4	4	no	—
93	C₂×C₄⋊C₄×C₃₇	—	4	4	no	—
94	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
95	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
97	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
99	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
101	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
102	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
103	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
104	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
105	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
106	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
107	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
108	C₂×C₂²⋊C₄×C₃₇	—	2	8	no	—
109	C₂×C₂²⋊C₄×C₃₇	—	4	4	no	—
110	C₂×C₂²⋊C₄×C₃₇	C₂³	1	2	yes	—
111	C₂×C₂²⋊C₄×C₃₇	C₂³	1	4	yes	—
112	C₂×C₂²⋊C₄×C₃₇	C₂³	1	4	yes	—
113	C₂×C₂²⋊C₄×C₃₇	C₂³	1	2	yes	—
114	C₂×C₂²⋊C₄×C₃₇	C₂³	1	2	yes	—
115	C₂×C₂²⋊C₄×C₃₇	C₂³	1	2	yes	—
116	C₂×C₂²⋊C₄×C₃₇	C₂³	1	2	yes	—
117	C₂×C₂²⋊C₄×C₃₇	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₃₇	C₂³	1	2	yes	—
119	C₂×C₂²⋊C₄×C₃₇	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₃₇	C₂³	1	2	yes	—
121	C₂×C₄²×C₃₇	—	4	4	no	—
122	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
123	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
124	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
125	C₂×C₄²×C₃₇	C₂³	1	4	yes	—
126	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
127	#95×C₃₇	C₂³	1	2	yes	—
128	#95×C₃₇	C₂³	1	2	yes	—
129	#95×C₃₇	C₂³	1	1	yes	characteristic
130	#95×C₃₇	C₂³	1	1	yes	characteristic
131	#95×C₃₇	C₂³	1	1	yes	characteristic
132	#95×C₃₇	C₂³	1	1	yes	characteristic
133	#95×C₃₇	C₂³	1	2	yes	—
134	#95×C₃₇	C₂³	1	4	yes	—
135	#95×C₃₇	C₂³	1	2	yes	—
136	#95×C₃₇	C₂³	1	2	yes	—
137	#95×C₃₇	C₂³	1	2	yes	—
138	#95×C₃₇	C₂³	1	4	yes	—
139	#95×C₃₇	C₂³	1	4	yes	—
140	#95×C₃₇	C₂³	1	4	yes	—
141	#95×C₃₇	C₂³	1	4	yes	—
142	#95×C₃₇	C₂³	1	4	yes	—
143	#95×C₃₇	C₂³	1	4	yes	—
144	#95×C₃₇	C₂³	1	4	yes	—
145	C₂⁴×C₃₇	—	2	4	no	—
146	C₂⁴×C₃₇	—	2	2	no	—
147	C₂⁴×C₃₇	—	2	2	no	—
148	C₂⁴×C₃₇	—	4	2	no	—
149	C₂⁴×C₃₇	C₂×Q₈	1	4	yes	—
150	C₂⁴×C₃₇	C₂⁴	1	1	yes	characteristic
151	C₂⁴×C₃₇	C₂⁴	1	1	yes	characteristic
152	C₂⁴×C₃₇	C₂⁴	1	1	yes	characteristic
153	C₂×Q₈×C₃₇	—	2	8	no	—
154	C₂×Q₈×C₃₇	—	4	4	no	—
155	C₂×Q₈×C₃₇	—	4	4	no	—
156	C₂²×C₄×C₃₇	—	2	4	no	—
157	C₂²×C₄×C₃₇	—	2	4	no	—
158	C₂²×C₄×C₃₇	—	2	4	no	—
159	C₂²×C₄×C₃₇	—	2	4	no	—
160	C₂²×C₄×C₃₇	—	2	4	no	—
161	C₂²×C₄×C₃₇	—	2	8	no	—
162	C₂²×C₄×C₃₇	—	2	4	no	—
163	C₂²×C₄×C₃₇	—	2	4	no	—
164	C₂²×C₄×C₃₇	—	4	16	no	—
165	C₂²×C₄×C₃₇	—	4	2	no	—
166	C₂²×C₄×C₃₇	—	4	2	no	—
167	C₂²×C₄×C₃₇	—	4	2	no	—
168	C₂²×C₄×C₃₇	—	4	2	no	—
169	C₂²×C₄×C₃₇	—	4	2	no	—
170	C₂²×C₄×C₃₇	—	4	4	no	—
171	C₂²×C₄×C₃₇	—	4	4	no	—
172	C₂²×C₄×C₃₇	C₂×Q₈	1	4	yes	—
173	C₂²×C₄×C₃₇	C₂×Q₈	1	4	yes	—
174	C₂²×C₄×C₃₇	C₂×Q₈	1	4	yes	—
175	C₂²×C₄×C₃₇	C₂×Q₈	1	4	yes	—
176	C₂²×C₄×C₃₇	C₂×Q₈	1	4	yes	—
177	C₂²×C₄×C₃₇	C₂×Q₈	1	4	yes	—
178	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₃₇	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₃₇	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₃₇	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₃₇	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
185	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
186	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
187	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
190	C₄⋊C₄×C₃₇	—	2	8	no	—
191	C₄⋊C₄×C₃₇	—	2	8	no	—
192	C₄⋊C₄×C₃₇	—	2	8	no	—
193	C₄⋊C₄×C₃₇	—	2	4	no	—
194	C₄⋊C₄×C₃₇	—	2	4	no	—
195	C₄⋊C₄×C₃₇	—	2	4	no	—
196	C₄⋊C₄×C₃₇	—	2	4	no	—
197	C₄⋊C₄×C₃₇	—	4	4	no	—
198	C₄⋊C₄×C₃₇	—	4	4	no	—
199	C₄⋊C₄×C₃₇	—	4	4	no	—
200	C₄⋊C₄×C₃₇	—	4	4	no	—
201	C₄⋊C₄×C₃₇	—	4	4	no	—
202	C₄⋊C₄×C₃₇	—	4	4	no	—
203	C₄⋊C₄×C₃₇	—	4	4	no	—
204	C₂²⋊C₄×C₃₇	—	2	4	no	—
205	C₂²⋊C₄×C₃₇	—	2	8	no	—
206	C₂²⋊C₄×C₃₇	—	2	8	no	—
207	C₂²⋊C₄×C₃₇	—	2	4	no	—
208	C₂²⋊C₄×C₃₇	—	2	4	no	—
209	C₂²⋊C₄×C₃₇	—	2	4	no	—
210	C₂²⋊C₄×C₃₇	—	2	4	no	—
211	C₂²⋊C₄×C₃₇	—	4	2	no	—
212	C₂²⋊C₄×C₃₇	—	4	2	no	—
213	C₂²⋊C₄×C₃₇	—	4	4	no	—
214	C₂²⋊C₄×C₃₇	#41	1	8	yes	—
215	C₄²×C₃₇	—	2	4	no	—
216	C₄²×C₃₇	—	2	4	no	—
217	C₄²×C₃₇	—	4	2	no	—
218	C₄²×C₃₇	—	4	2	no	—
219	C₄²×C₃₇	—	4	4	no	—
220	C₂³×C₃₇	—	2	2	no	—
221	C₂³×C₃₇	—	2	2	no	—
222	C₂³×C₃₇	—	2	2	no	—
223	C₂³×C₃₇	—	2	1	no	—
224	C₂³×C₃₇	—	2	1	no	—
225	C₂³×C₃₇	—	2	8	no	—
226	C₂³×C₃₇	—	2	8	no	—
227	C₂³×C₃₇	—	2	2	no	—
228	C₂³×C₃₇	—	2	1	no	—
229	C₂³×C₃₇	—	2	2	no	—
230	C₂³×C₃₇	—	2	1	no	—
231	C₂³×C₃₇	—	4	4	no	—
232	C₂³×C₃₇	—	4	8	no	—
233	C₂³×C₃₇	—	4	8	no	—
234	C₂³×C₃₇	C₂²×Q₈	1	2	yes	—
235	C₂³×C₃₇	C₂²×Q₈	1	2	yes	—
236	C₂³×C₃₇	C₂²×Q₈	1	2	yes	—
237	C₂³×C₃₇	C₂×#41	1	4	yes	—
238	C₂³×C₃₇	H(5,𝔽₂)	1	2	yes	—
239	C₂³×C₃₇	2₋¹⁺⁴	1	2	yes	—
240	C₂³×C₃₇	C₂⁵	1	1	yes	characteristic
241	Q₈×C₃₇	—	8	8	no	—
242	C₂×C₄×C₃₇	—	2	2	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	8	no	—
250	C₂×C₄×C₃₇	—	2	8	no	—
251	C₂×C₄×C₃₇	—	2	8	no	—
252	C₂×C₄×C₃₇	—	2	2	no	—
253	C₂×C₄×C₃₇	—	2	2	no	—
254	C₂×C₄×C₃₇	—	2	4	no	—
255	C₂×C₄×C₃₇	—	2	4	no	—
256	C₂×C₄×C₃₇	—	2	4	no	—
257	C₂×C₄×C₃₇	—	2	4	no	—
258	C₂×C₄×C₃₇	—	2	2	no	—
259	C₂×C₄×C₃₇	—	2	2	no	—
260	C₂×C₄×C₃₇	—	2	4	no	—
261	C₂×C₄×C₃₇	—	2	4	no	—
262	C₂×C₄×C₃₇	—	2	4	no	—
263	C₂×C₄×C₃₇	—	2	4	no	—
264	C₂×C₄×C₃₇	—	2	4	no	—
265	C₂×C₄×C₃₇	—	2	4	no	—
266	C₂×C₄×C₃₇	—	2	4	no	—
267	C₂×C₄×C₃₇	—	2	2	no	—
268	C₂×C₄×C₃₇	—	2	4	no	—
269	C₂×C₄×C₃₇	—	2	2	no	—
270	C₂×C₄×C₃₇	—	4	4	no	—
271	C₂×C₄×C₃₇	—	4	4	no	—
272	C₂×C₄×C₃₇	—	4	4	no	—
273	C₂×C₄×C₃₇	—	4	8	no	—
274	C₂×C₄×C₃₇	—	4	8	no	—
275	C₂×C₄×C₃₇	—	8	8	no	—
276	C₂×C₄×C₃₇	C₂²×Q₈	1	2	yes	—
277	C₂×C₄×C₃₇	C₂²×Q₈	1	2	yes	—
278	C₂×C₄×C₃₇	C₂²×Q₈	1	2	yes	—
279	C₂×C₄×C₃₇	C₂²×Q₈	1	2	yes	—
280	C₂×C₄×C₃₇	C₂×#41	1	4	yes	—
281	C₂×C₄×C₃₇	C₂×#41	1	4	yes	—
282	C₂×C₄×C₃₇	H(5,𝔽₂)	1	4	yes	—
283	#35079	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
284	C₂²×C₃₇	—	2	2	no	—
285	C₂²×C₃₇	—	2	2	no	—
286	C₂²×C₃₇	—	2	2	no	—
287	C₂²×C₃₇	—	2	2	no	—
288	C₂²×C₃₇	—	2	4	no	—
289	C₂²×C₃₇	—	2	4	no	—
290	C₂²×C₃₇	—	2	4	no	—
291	C₂²×C₃₇	—	2	4	no	—
292	C₂²×C₃₇	—	2	2	no	—
293	C₂²×C₃₇	—	2	2	no	—
294	C₂²×C₃₇	—	2	2	no	—
295	C₂²×C₃₇	—	4	16	no	—
296	C₂²×C₃₇	—	4	2	no	—
297	C₂²×C₃₇	—	4	2	no	—
298	C₂²×C₃₇	#533	1	4	yes	—
299	C₂²×C₃₇	#544	1	4	yes	—
300	C₂²×C₃₇	C₂³×Q₈	1	1	yes	characteristic
301	C₂²×C₃₇	C₂²×#41	1	2	yes	—
302	C₂²×C₃₇	C₂×H(5,𝔽₂)	1	2	yes	—
303	C₂²×C₃₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
304	C₂²×C₃₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
305	C₄×C₃₇	—	2	2	no	—
306	C₄×C₃₇	—	2	2	no	—
307	C₄×C₃₇	—	2	2	no	—
308	C₄×C₃₇	—	2	4	no	—
309	C₄×C₃₇	—	2	4	no	—
310	C₄×C₃₇	—	4	2	no	—
311	C₄×C₃₇	—	4	4	no	—
312	C₄×C₃₇	—	4	4	no	—
313	C₄×C₃₇	—	4	4	no	—
314	C₄×C₃₇	—	4	4	no	—
315	C₄×C₃₇	—	4	2	no	—
316	C₄×C₃₇	#543	1	4	yes	—
317	#2857	C₂×C₃₇	1	2	yes	complemented
318	#2851	C₂×C₃₇	1	2	yes	complemented
319	#2667	C₂×C₃₇	1	2	yes	complemented
320	#2665	C₂×C₃₇	1	2	yes	complemented
321	#2569	C₂×C₃₇	1	2	yes	complemented
322	#2549	C₂×C₃₇	1	2	yes	complemented
323	#2442	C₂×C₃₇	1	2	yes	complemented
324	#2441	C₂×C₃₇	1	2	yes	complemented
325	#2440	C₂×C₃₇	1	2	yes	complemented
326	#2439	C₂×C₃₇	1	2	yes	complemented
327	#2437	C₂×C₃₇	1	4	yes	—
328	#2329	C₂×C₃₇	1	4	yes	complemented
329	#2280	C₂×C₃₇	1	1	yes	characteristic
330	C₂×#380	C₂×C₃₇	1	1	yes	characteristic
331	C₂×C₄×C₂²⋊C₄	C₂×C₃₇	1	1	yes	characteristic
332	C₂×C₃₇	—	2	4	no	—
333	C₂×C₃₇	—	2	4	no	—
334	C₂×C₃₇	—	4	2	no	—
335	C₂×C₃₇	C₂×#533	1	1	yes	characteristic
336	C₂×C₃₇	C₂×#543	1	1	yes	characteristic
337	C₂×C₃₇	C₂×#544	1	1	yes	characteristic
338	C₂×C₃₇	#3519	1	2	yes	—
339	C₂×C₃₇	#3520	1	2	yes	—
340	C₂⁴×C₄	C₂²×C₃₇	1	1	yes	characteristic
341	C₂×C₄⋊Q₈	C₂²×C₃₇	1	2	yes	complemented
342	C₂×#125	C₂²×C₃₇	1	2	yes	complemented
343	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	4	yes	—
344	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	4	yes	—
345	C₂×#117	C₂²×C₃₇	1	2	yes	—
346	C₂²×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
347	C₂²×C₂²⋊C₄	C₂²×C₃₇	1	2	yes	—
348	C₂²×C₂²⋊C₄	C₂²×C₃₇	1	2	yes	—
349	C₂²×C₄²	C₂²×C₃₇	1	2	yes	—
350	#400	C₂²×C₃₇	1	4	yes	complemented
351	#399	C₂²×C₃₇	1	4	yes	—
352	#398	C₂²×C₃₇	1	4	yes	complemented
353	#398	C₂²×C₃₇	1	4	yes	complemented
354	#396	C₂²×C₃₇	1	4	yes	—
355	#396	C₂²×C₃₇	1	4	yes	—
356	#395	C₂²×C₃₇	1	4	yes	complemented
357	#393	C₂²×C₃₇	1	4	yes	—
358	#391	C₂²×C₃₇	1	4	yes	complemented
359	#391	C₂²×C₃₇	1	4	yes	complemented
360	#389	C₂²×C₃₇	1	4	yes	complemented
361	#389	C₂²×C₃₇	1	4	yes	complemented
362	#389	C₂²×C₃₇	1	2	yes	complemented
363	#389	C₂²×C₃₇	1	2	yes	complemented
364	#389	C₂²×C₃₇	1	2	yes	complemented
365	#389	C₂²×C₃₇	1	2	yes	complemented
366	#387	C₂²×C₃₇	1	4	yes	complemented
367	#387	C₂²×C₃₇	1	4	yes	complemented
368	#387	C₂²×C₃₇	1	4	yes	complemented
369	#387	C₂²×C₃₇	1	4	yes	complemented
370	#385	C₂²×C₃₇	1	4	yes	—
371	#385	C₂²×C₃₇	1	4	yes	—
372	#385	C₂²×C₃₇	1	4	yes	—
373	#385	C₂²×C₃₇	1	4	yes	—
374	#384	C₂²×C₃₇	1	2	yes	complemented
375	#382	C₂²×C₃₇	1	2	yes	complemented
376	#381	C₂²×C₃₇	1	2	yes	—
377	#380	C₂²×C₃₇	1	4	yes	—
378	#380	C₂²×C₃₇	1	2	yes	—
379	#380	C₂²×C₃₇	1	4	yes	—
380	#380	C₂²×C₃₇	1	1	yes	characteristic
381	#380	C₂²×C₃₇	1	2	yes	—
382	#380	C₂²×C₃₇	1	1	yes	characteristic
383	#380	C₂²×C₃₇	1	2	yes	—
384	#380	C₂²×C₃₇	1	1	yes	characteristic
385	#380	C₂²×C₃₇	1	2	yes	—
386	#380	C₂²×C₃₇	1	1	yes	characteristic
387	#379	C₂²×C₃₇	1	2	yes	—
388	C₄×C₂²⋊C₄	C₂²×C₃₇	1	2	yes	—
389	C₄×C₂²⋊C₄	C₂²×C₃₇	1	2	yes	—
390	C₄×C₂²⋊C₄	C₂²×C₃₇	1	2	yes	—
391	C₄×C₂²⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
392	C₄×C₂²⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
393	C₄×C₂²⋊C₄	C₂²×C₃₇	1	2	yes	—
394	C₄×C₂²⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
395	C₄×C₂²⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
396	C₂×#95	C₂²×C₃₇	1	1	yes	characteristic
397	C₂×#95	C₂²×C₃₇	1	2	yes	—
398	C₂×#95	C₂²×C₃₇	1	1	yes	characteristic
399	C₃₇	#35079	1	1	yes	characteristic, direct product factor, Sylow
400	C₂⁵	C₂³×C₃₇	1	1	yes	characteristic
401	C₂²×Q₈	C₂³×C₃₇	1	4	yes	—
402	C₂³×C₄	—	4	4	no	—
403	C₂³×C₄	Q₈×C₃₇	1	8	yes	complemented
404	C₂³×C₄	C₂³×C₃₇	1	2	yes	—
405	C₂³×C₄	C₂³×C₃₇	1	2	yes	—
406	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
407	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
408	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
409	C₂³×C₄	C₂³×C₃₇	1	4	yes	—
410	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
411	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
412	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
413	C₄⋊Q₈	—	4	4	no	—
414	#125	—	4	4	no	—
415	C₂²⋊Q₈	—	2	16	no	—
416	C₂²⋊Q₈	—	4	8	no	—
417	#117	—	4	4	no	—
418	C₂×C₄⋊C₄	—	4	4	no	—
419	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
420	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
421	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
423	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
424	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
425	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
426	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
427	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
428	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
429	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
430	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
431	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
432	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
433	C₂×C₂²⋊C₄	—	2	8	no	—
434	C₂×C₂²⋊C₄	—	4	4	no	—
435	C₂×C₂²⋊C₄	C₂³×C₃₇	1	4	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₃₇	1	2	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₃₇	1	2	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₃₇	1	2	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₃₇	1	2	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₃₇	1	4	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₃₇	1	2	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₃₇	1	2	yes	—
443	C₂×C₂²⋊C₄	C₂³×C₃₇	1	2	yes	—
444	C₂×C₂²⋊C₄	C₂³×C₃₇	1	4	yes	—
445	C₂×C₂²⋊C₄	C₂³×C₃₇	1	2	yes	—
446	C₂×C₄²	—	4	4	no	—
447	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
448	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
449	C₂×C₄²	C₂³×C₃₇	1	4	yes	—
450	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
451	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
452	#95	C₂³×C₃₇	1	2	yes	—
453	#95	C₂³×C₃₇	1	2	yes	—
454	#95	C₂³×C₃₇	1	1	yes	characteristic
455	#95	C₂³×C₃₇	1	1	yes	characteristic
456	#95	C₂³×C₃₇	1	1	yes	characteristic
457	#95	C₂³×C₃₇	1	1	yes	characteristic
458	#95	C₂³×C₃₇	1	2	yes	—
459	#95	C₂³×C₃₇	1	4	yes	—
460	#95	C₂³×C₃₇	1	2	yes	—
461	#95	C₂³×C₃₇	1	2	yes	—
462	#95	C₂³×C₃₇	1	2	yes	—
463	#95	C₂³×C₃₇	1	4	yes	—
464	#95	C₂³×C₃₇	1	4	yes	—
465	#95	C₂³×C₃₇	1	4	yes	—
466	#95	C₂³×C₃₇	1	4	yes	—
467	#95	C₂³×C₃₇	1	4	yes	—
468	#95	C₂³×C₃₇	1	4	yes	—
469	#95	C₂³×C₃₇	1	4	yes	—
470	C₂⁴	—	2	4	no	—
471	C₂⁴	—	2	2	no	—
472	C₂⁴	—	2	2	no	—
473	C₂⁴	—	4	2	no	—
474	C₂⁴	C₂×Q₈×C₃₇	1	4	yes	—
475	C₂⁴	C₂⁴×C₃₇	1	1	yes	characteristic
476	C₂⁴	C₂⁴×C₃₇	1	1	yes	characteristic
477	C₂⁴	C₂⁴×C₃₇	1	1	yes	characteristic
478	C₂×Q₈	—	2	8	no	—
479	C₂×Q₈	—	4	4	no	—
480	C₂×Q₈	—	4	4	no	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	2	4	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	—	2	4	no	—
486	C₂²×C₄	—	2	8	no	—
487	C₂²×C₄	—	2	4	no	—
488	C₂²×C₄	—	2	4	no	—
489	C₂²×C₄	—	4	16	no	—
490	C₂²×C₄	—	4	2	no	—
491	C₂²×C₄	—	4	2	no	—
492	C₂²×C₄	—	4	2	no	—
493	C₂²×C₄	—	4	2	no	—
494	C₂²×C₄	—	4	2	no	—
495	C₂²×C₄	—	4	4	no	—
496	C₂²×C₄	—	4	4	no	—
497	C₂²×C₄	C₂×Q₈×C₃₇	1	4	yes	—
498	C₂²×C₄	C₂×Q₈×C₃₇	1	4	yes	—
499	C₂²×C₄	C₂×Q₈×C₃₇	1	4	yes	—
500	C₂²×C₄	C₂×Q₈×C₃₇	1	4	yes	—
501	C₂²×C₄	C₂×Q₈×C₃₇	1	4	yes	—
502	C₂²×C₄	C₂×Q₈×C₃₇	1	4	yes	—
503	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
504	C₂²×C₄	C₂⁴×C₃₇	1	4	yes	—
505	C₂²×C₄	C₂⁴×C₃₇	1	4	yes	—
506	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
507	C₂²×C₄	C₂⁴×C₃₇	1	4	yes	—
508	C₂²×C₄	C₂⁴×C₃₇	1	4	yes	—
509	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
510	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
511	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
512	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
513	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
514	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
515	C₄⋊C₄	—	2	8	no	—
516	C₄⋊C₄	—	2	8	no	—
517	C₄⋊C₄	—	2	8	no	—
518	C₄⋊C₄	—	2	4	no	—
519	C₄⋊C₄	—	2	4	no	—
520	C₄⋊C₄	—	2	4	no	—
521	C₄⋊C₄	—	2	4	no	—
522	C₄⋊C₄	—	4	4	no	—
523	C₄⋊C₄	—	4	4	no	—
524	C₄⋊C₄	—	4	4	no	—
525	C₄⋊C₄	—	4	4	no	—
526	C₄⋊C₄	—	4	4	no	—
527	C₄⋊C₄	—	4	4	no	—
528	C₄⋊C₄	—	4	4	no	—
529	C₂²⋊C₄	—	2	4	no	—
530	C₂²⋊C₄	—	2	8	no	—
531	C₂²⋊C₄	—	2	8	no	—
532	C₂²⋊C₄	—	2	4	no	—
533	C₂²⋊C₄	—	2	4	no	—
534	C₂²⋊C₄	—	2	4	no	—
535	C₂²⋊C₄	—	2	4	no	—
536	C₂²⋊C₄	—	4	2	no	—
537	C₂²⋊C₄	—	4	2	no	—
538	C₂²⋊C₄	—	4	4	no	—
539	C₂²⋊C₄	#41×C₃₇	1	8	yes	—
540	C₄²	—	2	4	no	—
541	C₄²	—	2	4	no	—
542	C₄²	—	4	2	no	—
543	C₄²	—	4	2	no	—
544	C₄²	—	4	4	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	2	2	no	—
547	C₂³	—	2	2	no	—
548	C₂³	—	2	1	no	—
549	C₂³	—	2	1	no	—
550	C₂³	—	2	8	no	—
551	C₂³	—	2	8	no	—
552	C₂³	—	2	2	no	—
553	C₂³	—	2	1	no	—
554	C₂³	—	2	2	no	—
555	C₂³	—	2	1	no	—
556	C₂³	—	4	4	no	—
557	C₂³	—	4	8	no	—
558	C₂³	—	4	8	no	—
559	C₂³	C₂²×Q₈×C₃₇	1	2	yes	—
560	C₂³	C₂²×Q₈×C₃₇	1	2	yes	—
561	C₂³	C₂²×Q₈×C₃₇	1	2	yes	—
562	C₂³	C₂×#41×C₃₇	1	4	yes	—
563	C₂³	H(5,𝔽₂)×C₃₇	1	2	yes	—
564	C₂³	2₋¹⁺⁴×C₃₇	1	2	yes	—
565	C₂³	C₂⁵×C₃₇	1	1	yes	characteristic
566	Q₈	—	8	8	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	8	no	—
575	C₂×C₄	—	2	8	no	—
576	C₂×C₄	—	2	8	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	4	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	4	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	4	4	no	—
596	C₂×C₄	—	4	4	no	—
597	C₂×C₄	—	4	4	no	—
598	C₂×C₄	—	4	8	no	—
599	C₂×C₄	—	4	8	no	—
600	C₂×C₄	—	8	8	no	—
601	C₂×C₄	C₂²×Q₈×C₃₇	1	2	yes	—
602	C₂×C₄	C₂²×Q₈×C₃₇	1	2	yes	—
603	C₂×C₄	C₂²×Q₈×C₃₇	1	2	yes	—
604	C₂×C₄	C₂²×Q₈×C₃₇	1	2	yes	—
605	C₂×C₄	C₂×#41×C₃₇	1	4	yes	—
606	C₂×C₄	C₂×#41×C₃₇	1	4	yes	—
607	C₂×C₄	H(5,𝔽₂)×C₃₇	1	4	yes	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	4	no	—
613	C₂²	—	2	4	no	—
614	C₂²	—	2	4	no	—
615	C₂²	—	2	4	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	4	16	no	—
620	C₂²	—	4	2	no	—
621	C₂²	—	4	2	no	—
622	C₂²	C₃₇×#533	1	4	yes	—
623	C₂²	C₃₇×#544	1	4	yes	—
624	C₂²	C₂³×Q₈×C₃₇	1	1	yes	characteristic
625	C₂²	C₂²×#41×C₃₇	1	2	yes	—
626	C₂²	C₂×H(5,𝔽₂)×C₃₇	1	2	yes	—
627	C₂²	C₂×H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
628	C₂²	C₂×2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
629	C₄	—	2	2	no	—
630	C₄	—	2	2	no	—
631	C₄	—	2	2	no	—
632	C₄	—	2	4	no	—
633	C₄	—	2	4	no	—
634	C₄	—	4	2	no	—
635	C₄	—	4	4	no	—
636	C₄	—	4	4	no	—
637	C₄	—	4	4	no	—
638	C₄	—	4	2	no	—
639	C₄	—	4	4	no	—
640	C₄	C₃₇×#543	1	4	yes	—
641	C₂	—	2	4	no	—
642	C₂	—	2	4	no	—
643	C₂	—	4	2	no	—
644	C₂	C₂×C₃₇×#533	1	1	yes	characteristic
645	C₂	C₂×C₃₇×#543	1	1	yes	characteristic
646	C₂	C₂×C₃₇×#544	1	1	yes	characteristic
647	C₂	C₃₇×#3519	1	2	yes	—
648	C₂	C₃₇×#3520	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₇
prime radical	C₂⁵×C₃₇	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×#2857	C₂	semidirect
2. C₃₇×#2851	C₂	semidirect
3. C₃₇×#2667	C₂	semidirect
4. C₃₇×#2665	C₂	semidirect
5. C₃₇×#2569	C₂	semidirect
6. C₃₇×#2549	C₂	semidirect
7. C₃₇×#2442	C₂	semidirect
8. C₃₇×#2441	C₂	semidirect
9. C₃₇×#2440	C₂	semidirect
10. C₃₇×#2439	C₂	semidirect
12. C₃₇×#2329	C₂	semidirect
17. C₂×C₄⋊Q₈×C₃₇	C₂²	semidirect
18. C₂×#125×C₃₇	C₂²	semidirect
26. C₃₇×#400	C₂²	semidirect
28. C₃₇×#398	C₂²	semidirect
29. C₃₇×#398	C₂²	semidirect
32. C₃₇×#395	C₂²	semidirect
34. C₃₇×#391	C₂²	semidirect
35. C₃₇×#391	C₂²	semidirect
36. C₃₇×#389	C₂²	semidirect
37. C₃₇×#389	C₂²	semidirect
38. C₃₇×#389	C₂²	semidirect
39. C₃₇×#389	C₂²	semidirect
40. C₃₇×#389	C₂²	semidirect
41. C₃₇×#389	C₂²	semidirect
42. C₃₇×#387	C₂²	semidirect
43. C₃₇×#387	C₂²	semidirect
44. C₃₇×#387	C₂²	semidirect
45. C₃₇×#387	C₂²	semidirect
50. C₃₇×#384	C₂²	semidirect
51. C₃₇×#382	C₂²	semidirect
78. C₂³×C₄×C₃₇	Q₈	semidirect
283. #35079	C₃₇	direct (N × H)
317. #2857	C₂×C₃₇	semidirect
318. #2851	C₂×C₃₇	semidirect
319. #2667	C₂×C₃₇	semidirect
320. #2665	C₂×C₃₇	semidirect
321. #2569	C₂×C₃₇	semidirect
322. #2549	C₂×C₃₇	semidirect
323. #2442	C₂×C₃₇	semidirect
324. #2441	C₂×C₃₇	semidirect
325. #2440	C₂×C₃₇	semidirect
326. #2439	C₂×C₃₇	semidirect
328. #2329	C₂×C₃₇	semidirect
341. C₂×C₄⋊Q₈	C₂²×C₃₇	semidirect
342. C₂×#125	C₂²×C₃₇	semidirect
350. #400	C₂²×C₃₇	semidirect
352. #398	C₂²×C₃₇	semidirect
353. #398	C₂²×C₃₇	semidirect
356. #395	C₂²×C₃₇	semidirect
358. #391	C₂²×C₃₇	semidirect
359. #391	C₂²×C₃₇	semidirect
360. #389	C₂²×C₃₇	semidirect
361. #389	C₂²×C₃₇	semidirect
362. #389	C₂²×C₃₇	semidirect
363. #389	C₂²×C₃₇	semidirect
364. #389	C₂²×C₃₇	semidirect
365. #389	C₂²×C₃₇	semidirect
366. #387	C₂²×C₃₇	semidirect
367. #387	C₂²×C₃₇	semidirect
368. #387	C₂²×C₃₇	semidirect
369. #387	C₂²×C₃₇	semidirect
374. #384	C₂²×C₃₇	semidirect
375. #382	C₂²×C₃₇	semidirect
399. C₃₇	#35079	direct (N × H)
403. C₂³×C₄	Q₈×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₃₇×#2857	2
C₃₇×#2851	2
C₃₇×#2667	2
C₃₇×#2665	2
C₃₇×#2569	2
C₃₇×#2549	2
C₃₇×#2442	2
C₃₇×#2441	2
C₃₇×#2440	2
C₃₇×#2439	2
C₃₇×#2437	2
C₃₇×#2329	2
C₃₇×#2280	2
C₂×C₃₇×#380	2
C₂×C₄×C₂²⋊C₄×C₃₇	2
#35079	37

Subgroups — C37×#35079 #22656332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#35079 #22656332