Subgroups — C₃₇×#36591 #22657844

Order 9472.

1838 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#2861	C₂	1	2	yes	maximal, complemented
2	C₃₇×#2858	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2595	C₂	1	4	yes	maximal, complemented
4	C₃₇×#2568	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2548	C₂	1	1	yes	maximal, characteristic
6	C₃₇×#2516	C₂	1	4	yes	maximal, complemented
7	C₃₇×#2513	C₂	1	2	yes	maximal, complemented
8	C₃₇×#2448	C₂	1	2	yes	maximal, complemented
9	C₃₇×#2448	C₂	1	2	yes	maximal, complemented
10	C₃₇×#2447	C₂	1	2	yes	maximal, complemented
11	C₃₇×#2367	C₂	1	2	yes	maximal, complemented
12	C₃₇×#2366	C₂	1	1	yes	maximal, characteristic
13	C₃₇×#2365	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₇×#2357	C₂	1	2	yes	maximal, complemented
15	C₄×#125×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#124×C₃₇	C₂	1	2	yes	maximal, complemented
17	C₄²×Q₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
19	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
20	C₂×#125×C₃₇	C₂²	1	1	yes	characteristic
21	C₂×#124×C₃₇	C₂²	1	2	yes	—
22	C₂×#124×C₃₇	C₂²	1	2	yes	—
23	C₂×#124×C₃₇	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₃₇	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₃₇	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₃₇	C₂²	1	2	yes	—
30	C₃₇×#400	C₂²	1	4	yes	—
31	C₃₇×#399	C₂²	1	4	yes	—
32	C₃₇×#397	C₂²	1	4	yes	—
33	C₃₇×#397	C₂²	1	4	yes	—
34	C₃₇×#397	C₂²	1	4	yes	—
35	C₃₇×#394	C₂²	1	4	yes	—
36	C₃₇×#391	C₂²	1	2	yes	—
37	C₃₇×#391	C₂²	1	2	yes	—
38	C₃₇×#391	C₂²	1	2	yes	—
39	C₃₇×#391	C₂²	1	2	yes	—
40	C₃₇×#390	C₂²	1	2	yes	—
41	C₃₇×#390	C₂²	1	2	yes	—
42	C₃₇×#390	C₂²	1	2	yes	—
43	C₃₇×#390	C₂²	1	2	yes	—
44	C₃₇×#390	C₂²	1	2	yes	—
45	C₃₇×#390	C₂²	1	2	yes	—
46	C₃₇×#390	C₂²	1	2	yes	—
47	C₃₇×#390	C₂²	1	2	yes	—
48	C₃₇×#390	C₂²	1	2	yes	—
49	C₃₇×#389	C₂²	1	2	yes	—
50	C₃₇×#389	C₂²	1	1	yes	characteristic
51	C₃₇×#389	C₂²	1	1	yes	characteristic
52	C₃₇×#388	C₂²	1	4	yes	—
53	C₃₇×#388	C₂²	1	4	yes	—
54	C₃₇×#388	C₂²	1	4	yes	—
55	C₃₇×#388	C₂²	1	4	yes	—
56	C₃₇×#388	C₂²	1	4	yes	—
57	C₃₇×#388	C₂²	1	4	yes	—
58	C₃₇×#388	C₂²	1	4	yes	—
59	C₃₇×#388	C₂²	1	4	yes	—
60	C₃₇×#387	C₂²	1	4	yes	—
61	C₃₇×#387	C₂²	1	2	yes	—
62	C₃₇×#387	C₂²	1	2	yes	—
63	C₃₇×#386	C₂²	1	4	yes	—
64	C₃₇×#385	C₂²	1	4	yes	—
65	C₃₇×#382	C₂²	1	2	yes	—
66	C₃₇×#382	C₂²	1	1	yes	characteristic
67	C₃₇×#381	C₂²	1	4	yes	—
68	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
69	C₄×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
70	C₄×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
72	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
73	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
74	C₄×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
75	C₄×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
76	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
77	C₄×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
78	C₄×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
79	C₄×C₂²⋊C₄×C₃₇	C₂²	1	4	yes	—
80	C₄×C₂²⋊C₄×C₃₇	C₂²	1	4	yes	—
81	C₄³×C₃₇	C₂²	1	2	yes	—
82	C₄³×C₃₇	C₂²	1	1	yes	characteristic
83	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
84	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
86	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
87	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
88	C₂³×C₄×C₃₇	C₂³	1	4	yes	—
89	C₄⋊Q₈×C₃₇	—	2	4	no	—
90	#127×C₃₇	—	2	4	no	—
91	#125×C₃₇	—	2	4	no	—
92	#124×C₃₇	—	2	8	no	—
93	#124×C₃₇	—	2	8	no	—
94	#124×C₃₇	—	4	4	no	—
95	C₄×Q₈×C₃₇	—	2	4	no	—
96	C₄×Q₈×C₃₇	—	2	4	no	—
97	C₄×Q₈×C₃₇	—	2	4	no	—
98	C₄×Q₈×C₃₇	—	4	4	no	—
99	C₄×D₄×C₃₇	—	2	8	no	—
100	C₄×D₄×C₃₇	—	4	4	no	—
101	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
118	C₂×C₂²⋊C₄×C₃₇	C₂³	1	4	yes	—
119	C₂×C₂²⋊C₄×C₃₇	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₃₇	C₂³	1	4	yes	—
121	C₂×C₂²⋊C₄×C₃₇	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₃₇	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₃₇	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₃₇	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₃₇	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₃₇	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₃₇	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₃₇	C₂³	1	4	yes	—
129	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
131	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
132	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
135	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
136	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
137	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
138	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
139	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
142	C₂×C₄²×C₃₇	C₂³	1	4	yes	—
143	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
145	#95×C₃₇	C₂³	1	2	yes	—
146	#95×C₃₇	C₂³	1	2	yes	—
147	#95×C₃₇	C₂³	1	4	yes	—
148	#95×C₃₇	C₂³	1	4	yes	—
149	#95×C₃₇	C₂³	1	2	yes	—
150	#95×C₃₇	C₂³	1	2	yes	—
151	#95×C₃₇	C₂³	1	2	yes	—
152	#95×C₃₇	C₂³	1	2	yes	—
153	#95×C₃₇	C₂³	1	4	yes	—
154	#95×C₃₇	C₂³	1	2	yes	—
155	#95×C₃₇	C₂³	1	2	yes	—
156	#95×C₃₇	C₂³	1	2	yes	—
157	#95×C₃₇	C₂³	1	4	yes	—
158	#95×C₃₇	C₂³	1	4	yes	—
159	#95×C₃₇	C₂³	1	4	yes	—
160	C₂⁴×C₃₇	C₂⁴	1	4	yes	—
161	C₂×Q₈×C₃₇	—	2	2	no	—
162	C₂×Q₈×C₃₇	—	2	2	no	—
163	C₂×Q₈×C₃₇	—	2	4	no	—
164	C₂×Q₈×C₃₇	—	2	4	no	—
165	C₂×Q₈×C₃₇	—	2	4	no	—
166	C₂×Q₈×C₃₇	#41	1	4	yes	—
167	C₂×D₄×C₃₇	—	2	4	no	—
168	C₂×D₄×C₃₇	—	2	4	no	—
169	C₂×D₄×C₃₇	—	2	4	no	—
170	C₂×D₄×C₃₇	—	2	4	no	—
171	C₂×D₄×C₃₇	—	2	4	no	—
172	C₂×D₄×C₃₇	—	2	4	no	—
173	C₂×D₄×C₃₇	—	2	4	no	—
174	C₂×D₄×C₃₇	—	4	2	no	—
175	C₂×D₄×C₃₇	—	4	2	no	—
176	C₂²×C₄×C₃₇	—	2	8	no	—
177	C₂²×C₄×C₃₇	—	4	4	no	—
178	C₂²×C₄×C₃₇	—	4	4	no	—
179	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₃₇	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
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	1	yes	characteristic
189	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
193	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
194	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
195	C₄⋊C₄×C₃₇	—	2	4	no	—
196	C₄⋊C₄×C₃₇	—	2	4	no	—
197	C₄⋊C₄×C₃₇	—	2	4	no	—
198	C₄⋊C₄×C₃₇	—	2	2	no	—
199	C₄⋊C₄×C₃₇	—	2	2	no	—
200	C₄⋊C₄×C₃₇	—	2	4	no	—
201	C₄⋊C₄×C₃₇	—	2	4	no	—
202	C₄⋊C₄×C₃₇	—	2	2	no	—
203	C₄⋊C₄×C₃₇	—	2	2	no	—
204	C₄⋊C₄×C₃₇	—	2	4	no	—
205	C₄⋊C₄×C₃₇	—	2	4	no	—
206	C₄⋊C₄×C₃₇	—	2	2	no	—
207	C₄⋊C₄×C₃₇	—	2	2	no	—
208	C₄⋊C₄×C₃₇	—	4	2	no	—
209	C₄⋊C₄×C₃₇	—	4	2	no	—
210	C₄⋊C₄×C₃₇	—	4	4	no	—
211	C₄⋊C₄×C₃₇	#41	1	4	yes	—
212	C₂²⋊C₄×C₃₇	—	2	8	no	—
213	C₂²⋊C₄×C₃₇	—	2	8	no	—
214	C₂²⋊C₄×C₃₇	—	2	8	no	—
215	C₂²⋊C₄×C₃₇	—	2	8	no	—
216	C₂²⋊C₄×C₃₇	—	2	8	no	—
217	C₂²⋊C₄×C₃₇	—	4	4	no	—
218	C₂²⋊C₄×C₃₇	—	4	4	no	—
219	C₂²⋊C₄×C₃₇	—	4	4	no	—
220	C₂²⋊C₄×C₃₇	—	4	4	no	—
221	C₂²⋊C₄×C₃₇	—	4	4	no	—
222	C₂²⋊C₄×C₃₇	—	4	4	no	—
223	C₄²×C₃₇	—	2	4	no	—
224	C₄²×C₃₇	—	2	4	no	—
225	C₄²×C₃₇	—	2	4	no	—
226	C₄²×C₃₇	—	2	2	no	—
227	C₄²×C₃₇	—	2	2	no	—
228	C₄²×C₃₇	—	2	4	no	—
229	C₄²×C₃₇	—	2	4	no	—
230	C₄²×C₃₇	—	2	4	no	—
231	C₄²×C₃₇	—	2	2	no	—
232	C₄²×C₃₇	—	4	2	no	—
233	C₄²×C₃₇	—	4	1	no	—
234	C₄²×C₃₇	—	4	1	no	—
235	C₄²×C₃₇	—	4	2	no	—
236	C₄²×C₃₇	—	4	4	no	—
237	C₄²×C₃₇	#41	1	4	yes	—
238	C₄²×C₃₇	#41	1	4	yes	—
239	C₂³×C₃₇	—	2	4	no	—
240	C₂³×C₃₇	—	2	4	no	—
241	C₂³×C₃₇	—	2	4	no	—
242	C₂³×C₃₇	—	2	4	no	—
243	C₂³×C₃₇	—	2	4	no	—
244	C₂³×C₃₇	—	2	4	no	—
245	C₂³×C₃₇	—	2	4	no	—
246	C₂³×C₃₇	C₂⁵	1	1	yes	characteristic
247	Q₈×C₃₇	—	2	8	no	—
248	Q₈×C₃₇	—	4	8	no	—
249	D₄×C₃₇	—	4	8	no	—
250	D₄×C₃₇	—	4	8	no	—
251	D₄×C₃₇	—	8	4	no	—
252	C₂×C₄×C₃₇	—	2	1	no	—
253	C₂×C₄×C₃₇	—	2	1	no	—
254	C₂×C₄×C₃₇	—	2	2	no	—
255	C₂×C₄×C₃₇	—	2	2	no	—
256	C₂×C₄×C₃₇	—	2	2	no	—
257	C₂×C₄×C₃₇	—	2	1	no	—
258	C₂×C₄×C₃₇	—	2	1	no	—
259	C₂×C₄×C₃₇	—	2	2	no	—
260	C₂×C₄×C₃₇	—	2	1	no	—
261	C₂×C₄×C₃₇	—	2	1	no	—
262	C₂×C₄×C₃₇	—	2	2	no	—
263	C₂×C₄×C₃₇	—	2	2	no	—
264	C₂×C₄×C₃₇	—	2	2	no	—
265	C₂×C₄×C₃₇	—	2	2	no	—
266	C₂×C₄×C₃₇	—	2	1	no	—
267	C₂×C₄×C₃₇	—	2	1	no	—
268	C₂×C₄×C₃₇	—	2	2	no	—
269	C₂×C₄×C₃₇	—	2	2	no	—
270	C₂×C₄×C₃₇	—	2	4	no	—
271	C₂×C₄×C₃₇	—	2	2	no	—
272	C₂×C₄×C₃₇	—	2	2	no	—
273	C₂×C₄×C₃₇	—	2	4	no	—
274	C₂×C₄×C₃₇	—	2	1	no	—
275	C₂×C₄×C₃₇	—	2	1	no	—
276	C₂×C₄×C₃₇	—	2	2	no	—
277	C₂×C₄×C₃₇	—	2	2	no	—
278	C₂×C₄×C₃₇	—	2	4	no	—
279	C₂×C₄×C₃₇	—	2	2	no	—
280	C₂×C₄×C₃₇	—	2	2	no	—
281	C₂×C₄×C₃₇	—	2	2	no	—
282	C₂×C₄×C₃₇	—	2	2	no	—
283	C₂×C₄×C₃₇	—	2	1	no	—
284	C₂×C₄×C₃₇	—	2	1	no	—
285	C₂×C₄×C₃₇	—	2	2	no	—
286	C₂×C₄×C₃₇	—	2	2	no	—
287	C₂×C₄×C₃₇	—	2	2	no	—
288	C₂×C₄×C₃₇	—	2	2	no	—
289	C₂×C₄×C₃₇	—	8	8	no	—
290	C₂×C₄×C₃₇	C₂×#41	1	4	yes	—
291	C₂×C₄×C₃₇	C₂×#41	1	4	yes	—
292	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
293	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
294	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
295	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
296	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
297	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
298	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
299	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
300	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
301	#36591	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
302	C₂²×C₃₇	—	4	4	no	—
303	C₂²×C₃₇	—	4	4	no	—
304	C₂²×C₃₇	—	4	4	no	—
305	C₂²×C₃₇	—	4	4	no	—
306	C₂²×C₃₇	—	4	4	no	—
307	C₂²×C₃₇	—	4	4	no	—
308	C₂²×C₃₇	—	4	4	no	—
309	C₂²×C₃₇	C₂²×#41	1	1	yes	characteristic
310	C₂²×C₃₇	C₂²×#41	1	1	yes	characteristic
311	C₂²×C₃₇	C₂²×#41	1	1	yes	characteristic
312	C₂²×C₃₇	C₂²×#41	1	1	yes	characteristic
313	C₂²×C₃₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
314	C₂²×C₃₇	#585	1	1	yes	characteristic
315	C₂²×C₃₇	#585	1	1	yes	characteristic
316	C₄×C₃₇	—	2	4	no	—
317	C₄×C₃₇	—	2	2	no	—
318	C₄×C₃₇	—	2	2	no	—
319	C₄×C₃₇	—	2	2	no	—
320	C₄×C₃₇	—	2	4	no	—
321	C₄×C₃₇	—	4	4	no	—
322	C₄×C₃₇	—	4	2	no	—
323	C₄×C₃₇	—	4	2	no	—
324	C₄×C₃₇	—	4	2	no	—
325	C₄×C₃₇	—	4	1	no	—
326	C₄×C₃₇	—	4	2	no	—
327	C₄×C₃₇	—	4	2	no	—
328	C₄×C₃₇	—	4	1	no	—
329	C₄×C₃₇	—	4	2	no	—
330	C₄×C₃₇	#529	1	4	yes	—
331	C₄×C₃₇	#559	1	4	yes	—
332	#2861	C₂×C₃₇	1	2	yes	complemented
333	#2858	C₂×C₃₇	1	1	yes	characteristic
334	#2595	C₂×C₃₇	1	4	yes	complemented
335	#2568	C₂×C₃₇	1	1	yes	characteristic, complemented
336	#2548	C₂×C₃₇	1	1	yes	characteristic
337	#2516	C₂×C₃₇	1	4	yes	complemented
338	#2513	C₂×C₃₇	1	2	yes	complemented
339	#2448	C₂×C₃₇	1	2	yes	complemented
340	#2448	C₂×C₃₇	1	2	yes	complemented
341	#2447	C₂×C₃₇	1	2	yes	complemented
342	#2367	C₂×C₃₇	1	2	yes	complemented
343	#2366	C₂×C₃₇	1	1	yes	characteristic
344	#2365	C₂×C₃₇	1	1	yes	characteristic, complemented
345	#2357	C₂×C₃₇	1	2	yes	complemented
346	C₄×#125	C₂×C₃₇	1	1	yes	characteristic, complemented
347	C₄×#124	C₂×C₃₇	1	2	yes	complemented
348	C₄²×Q₈	C₂×C₃₇	1	1	yes	characteristic, complemented
349	C₂×C₃₇	—	8	4	no	—
350	C₂×C₃₇	C₂×#529	1	1	yes	characteristic
351	C₂×C₃₇	C₂×#559	1	1	yes	characteristic
352	C₂×C₃₇	#3480	1	1	yes	characteristic
353	C₂×C₃₇	#3480	1	1	yes	characteristic
354	C₂×C₃₇	#3510	1	1	yes	characteristic
355	C₂×C₃₇	#3514	1	1	yes	characteristic
356	C₂×C₃₇	#3517	1	1	yes	characteristic
357	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
358	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
359	C₂×#125	C₂²×C₃₇	1	1	yes	characteristic
360	C₂×#124	C₂²×C₃₇	1	2	yes	—
361	C₂×#124	C₂²×C₃₇	1	2	yes	—
362	C₂×#124	C₂²×C₃₇	1	2	yes	—
363	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
364	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
365	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
366	C₂×C₄×Q₈	C₂²×C₃₇	1	2	yes	—
367	C₂×C₄×D₄	C₂²×C₃₇	1	2	yes	—
368	C₂×C₄×D₄	C₂²×C₃₇	1	2	yes	—
369	#400	C₂²×C₃₇	1	4	yes	—
370	#399	C₂²×C₃₇	1	4	yes	—
371	#397	C₂²×C₃₇	1	4	yes	—
372	#397	C₂²×C₃₇	1	4	yes	—
373	#397	C₂²×C₃₇	1	4	yes	—
374	#394	C₂²×C₃₇	1	4	yes	—
375	#391	C₂²×C₃₇	1	2	yes	—
376	#391	C₂²×C₃₇	1	2	yes	—
377	#391	C₂²×C₃₇	1	2	yes	—
378	#391	C₂²×C₃₇	1	2	yes	—
379	#390	C₂²×C₃₇	1	2	yes	—
380	#390	C₂²×C₃₇	1	2	yes	—
381	#390	C₂²×C₃₇	1	2	yes	—
382	#390	C₂²×C₃₇	1	2	yes	—
383	#390	C₂²×C₃₇	1	2	yes	—
384	#390	C₂²×C₃₇	1	2	yes	—
385	#390	C₂²×C₃₇	1	2	yes	—
386	#390	C₂²×C₃₇	1	2	yes	—
387	#390	C₂²×C₃₇	1	2	yes	—
388	#389	C₂²×C₃₇	1	1	yes	characteristic
389	#389	C₂²×C₃₇	1	1	yes	characteristic
390	#389	C₂²×C₃₇	1	2	yes	—
391	#388	C₂²×C₃₇	1	4	yes	—
392	#388	C₂²×C₃₇	1	4	yes	—
393	#388	C₂²×C₃₇	1	4	yes	—
394	#388	C₂²×C₃₇	1	4	yes	—
395	#388	C₂²×C₃₇	1	4	yes	—
396	#388	C₂²×C₃₇	1	4	yes	—
397	#388	C₂²×C₃₇	1	4	yes	—
398	#388	C₂²×C₃₇	1	4	yes	—
399	#387	C₂²×C₃₇	1	2	yes	—
400	#387	C₂²×C₃₇	1	2	yes	—
401	#387	C₂²×C₃₇	1	4	yes	—
402	#386	C₂²×C₃₇	1	4	yes	—
403	#385	C₂²×C₃₇	1	4	yes	—
404	#382	C₂²×C₃₇	1	1	yes	characteristic
405	#382	C₂²×C₃₇	1	2	yes	—
406	#381	C₂²×C₃₇	1	4	yes	—
407	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
408	C₄×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
409	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
410	C₄×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
411	C₄×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
412	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
413	C₄×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
414	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
415	C₄×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
416	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
417	C₄×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
418	C₄×C₂²⋊C₄	C₂²×C₃₇	1	4	yes	—
419	C₄×C₂²⋊C₄	C₂²×C₃₇	1	4	yes	—
420	C₄³	C₂²×C₃₇	1	1	yes	characteristic
421	C₄³	C₂²×C₃₇	1	2	yes	—
422	C₃₇	#36591	1	1	yes	characteristic, direct product factor, Sylow
423	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
424	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
425	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
426	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
427	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
428	C₂³×C₄	C₂³×C₃₇	1	4	yes	—
429	C₄⋊Q₈	—	2	4	no	—
430	#127	—	2	4	no	—
431	#125	—	2	4	no	—
432	#124	—	2	8	no	—
433	#124	—	2	8	no	—
434	#124	—	4	4	no	—
435	C₄×Q₈	—	2	4	no	—
436	C₄×Q₈	—	2	4	no	—
437	C₄×Q₈	—	2	4	no	—
438	C₄×Q₈	—	4	4	no	—
439	C₄×D₄	—	2	8	no	—
440	C₄×D₄	—	4	4	no	—
441	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
444	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
445	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
446	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
447	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
448	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
449	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
450	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
451	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
453	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
454	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
455	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
456	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
457	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
458	C₂×C₂²⋊C₄	C₂³×C₃₇	1	4	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₃₇	1	4	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₃₇	1	4	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₃₇	1	4	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₃₇	1	4	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₃₇	1	4	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₃₇	1	4	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₃₇	1	4	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₃₇	1	4	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₃₇	1	4	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₃₇	1	4	yes	—
469	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
470	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
471	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
472	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
473	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
474	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
475	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
476	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
477	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
478	C₂×C₄²	C₂³×C₃₇	1	4	yes	—
479	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
480	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
481	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
482	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
483	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
484	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
485	#95	C₂³×C₃₇	1	2	yes	—
486	#95	C₂³×C₃₇	1	2	yes	—
487	#95	C₂³×C₃₇	1	4	yes	—
488	#95	C₂³×C₃₇	1	4	yes	—
489	#95	C₂³×C₃₇	1	2	yes	—
490	#95	C₂³×C₃₇	1	2	yes	—
491	#95	C₂³×C₃₇	1	2	yes	—
492	#95	C₂³×C₃₇	1	2	yes	—
493	#95	C₂³×C₃₇	1	4	yes	—
494	#95	C₂³×C₃₇	1	2	yes	—
495	#95	C₂³×C₃₇	1	2	yes	—
496	#95	C₂³×C₃₇	1	2	yes	—
497	#95	C₂³×C₃₇	1	4	yes	—
498	#95	C₂³×C₃₇	1	4	yes	—
499	#95	C₂³×C₃₇	1	4	yes	—
500	C₂⁴	C₂⁴×C₃₇	1	4	yes	—
501	C₂×Q₈	—	2	2	no	—
502	C₂×Q₈	—	2	2	no	—
503	C₂×Q₈	—	2	4	no	—
504	C₂×Q₈	—	2	4	no	—
505	C₂×Q₈	—	2	4	no	—
506	C₂×Q₈	#41×C₃₇	1	4	yes	—
507	C₂×D₄	—	2	4	no	—
508	C₂×D₄	—	2	4	no	—
509	C₂×D₄	—	2	4	no	—
510	C₂×D₄	—	2	4	no	—
511	C₂×D₄	—	2	4	no	—
512	C₂×D₄	—	2	4	no	—
513	C₂×D₄	—	2	4	no	—
514	C₂×D₄	—	4	2	no	—
515	C₂×D₄	—	4	2	no	—
516	C₂²×C₄	—	2	8	no	—
517	C₂²×C₄	—	4	4	no	—
518	C₂²×C₄	—	4	4	no	—
519	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
520	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
521	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
522	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
523	C₂²×C₄	C₂⁴×C₃₇	1	4	yes	—
524	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
525	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
526	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
527	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
528	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
529	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
530	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
531	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
532	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
533	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
534	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
535	C₄⋊C₄	—	2	4	no	—
536	C₄⋊C₄	—	2	4	no	—
537	C₄⋊C₄	—	2	4	no	—
538	C₄⋊C₄	—	2	2	no	—
539	C₄⋊C₄	—	2	2	no	—
540	C₄⋊C₄	—	2	4	no	—
541	C₄⋊C₄	—	2	4	no	—
542	C₄⋊C₄	—	2	2	no	—
543	C₄⋊C₄	—	2	2	no	—
544	C₄⋊C₄	—	2	4	no	—
545	C₄⋊C₄	—	2	4	no	—
546	C₄⋊C₄	—	2	2	no	—
547	C₄⋊C₄	—	2	2	no	—
548	C₄⋊C₄	—	4	2	no	—
549	C₄⋊C₄	—	4	2	no	—
550	C₄⋊C₄	—	4	4	no	—
551	C₄⋊C₄	#41×C₃₇	1	4	yes	—
552	C₂²⋊C₄	—	2	8	no	—
553	C₂²⋊C₄	—	2	8	no	—
554	C₂²⋊C₄	—	2	8	no	—
555	C₂²⋊C₄	—	2	8	no	—
556	C₂²⋊C₄	—	2	8	no	—
557	C₂²⋊C₄	—	4	4	no	—
558	C₂²⋊C₄	—	4	4	no	—
559	C₂²⋊C₄	—	4	4	no	—
560	C₂²⋊C₄	—	4	4	no	—
561	C₂²⋊C₄	—	4	4	no	—
562	C₂²⋊C₄	—	4	4	no	—
563	C₄²	—	2	4	no	—
564	C₄²	—	2	4	no	—
565	C₄²	—	2	4	no	—
566	C₄²	—	2	2	no	—
567	C₄²	—	2	2	no	—
568	C₄²	—	2	4	no	—
569	C₄²	—	2	4	no	—
570	C₄²	—	2	4	no	—
571	C₄²	—	2	2	no	—
572	C₄²	—	4	2	no	—
573	C₄²	—	4	1	no	—
574	C₄²	—	4	1	no	—
575	C₄²	—	4	2	no	—
576	C₄²	—	4	4	no	—
577	C₄²	#41×C₃₇	1	4	yes	—
578	C₄²	#41×C₃₇	1	4	yes	—
579	C₂³	—	2	4	no	—
580	C₂³	—	2	4	no	—
581	C₂³	—	2	4	no	—
582	C₂³	—	2	4	no	—
583	C₂³	—	2	4	no	—
584	C₂³	—	2	4	no	—
585	C₂³	—	2	4	no	—
586	C₂³	C₂⁵×C₃₇	1	1	yes	characteristic
587	Q₈	—	2	8	no	—
588	Q₈	—	4	8	no	—
589	D₄	—	4	8	no	—
590	D₄	—	4	8	no	—
591	D₄	—	8	4	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	8	8	no	—
630	C₂×C₄	C₂×#41×C₃₇	1	4	yes	—
631	C₂×C₄	C₂×#41×C₃₇	1	4	yes	—
632	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
633	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
634	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
635	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
636	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
637	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
638	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
639	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
640	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
641	C₂²	—	4	4	no	—
642	C₂²	—	4	4	no	—
643	C₂²	—	4	4	no	—
644	C₂²	—	4	4	no	—
645	C₂²	—	4	4	no	—
646	C₂²	—	4	4	no	—
647	C₂²	—	4	4	no	—
648	C₂²	C₂²×#41×C₃₇	1	1	yes	characteristic
649	C₂²	C₂²×#41×C₃₇	1	1	yes	characteristic
650	C₂²	C₂²×#41×C₃₇	1	1	yes	characteristic
651	C₂²	C₂²×#41×C₃₇	1	1	yes	characteristic
652	C₂²	C₂×H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
653	C₂²	C₃₇×#585	1	1	yes	characteristic
654	C₂²	C₃₇×#585	1	1	yes	characteristic
655	C₄	—	2	4	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	4	no	—
660	C₄	—	4	4	no	—
661	C₄	—	4	2	no	—
662	C₄	—	4	2	no	—
663	C₄	—	4	2	no	—
664	C₄	—	4	2	no	—
665	C₄	—	4	1	no	—
666	C₄	—	4	2	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	2	no	—
669	C₄	C₃₇×#529	1	4	yes	—
670	C₄	C₃₇×#559	1	4	yes	—
671	C₂	—	8	4	no	—
672	C₂	C₂×C₃₇×#529	1	1	yes	characteristic
673	C₂	C₂×C₃₇×#559	1	1	yes	characteristic
674	C₂	C₃₇×#3480	1	1	yes	characteristic
675	C₂	C₃₇×#3480	1	1	yes	characteristic
676	C₂	C₃₇×#3510	1	1	yes	characteristic
677	C₂	C₃₇×#3514	1	1	yes	characteristic
678	C₂	C₃₇×#3517	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₇
prime radical	C₂×#127×C₃₇	C₂²
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×#2861	C₂	semidirect
3. C₃₇×#2595	C₂	semidirect
4. C₃₇×#2568	C₂	semidirect
6. C₃₇×#2516	C₂	semidirect
7. C₃₇×#2513	C₂	semidirect
8. C₃₇×#2448	C₂	semidirect
9. C₃₇×#2448	C₂	semidirect
10. C₃₇×#2447	C₂	semidirect
11. C₃₇×#2367	C₂	semidirect
13. C₃₇×#2365	C₂	semidirect
14. C₃₇×#2357	C₂	semidirect
15. C₄×#125×C₃₇	C₂	semidirect
16. C₄×#124×C₃₇	C₂	semidirect
17. C₄²×Q₈×C₃₇	C₂	semidirect
301. #36591	C₃₇	direct (N × H)
332. #2861	C₂×C₃₇	semidirect
334. #2595	C₂×C₃₇	semidirect
335. #2568	C₂×C₃₇	semidirect
337. #2516	C₂×C₃₇	semidirect
338. #2513	C₂×C₃₇	semidirect
339. #2448	C₂×C₃₇	semidirect
340. #2448	C₂×C₃₇	semidirect
341. #2447	C₂×C₃₇	semidirect
342. #2367	C₂×C₃₇	semidirect
344. #2365	C₂×C₃₇	semidirect
345. #2357	C₂×C₃₇	semidirect
346. C₄×#125	C₂×C₃₇	semidirect
347. C₄×#124	C₂×C₃₇	semidirect
348. C₄²×Q₈	C₂×C₃₇	semidirect
422. C₃₇	#36591	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×#2861	2
C₃₇×#2858	2
C₃₇×#2595	2
C₃₇×#2568	2
C₃₇×#2548	2
C₃₇×#2516	2
C₃₇×#2513	2
C₃₇×#2448	2
C₃₇×#2447	2
C₃₇×#2367	2
C₃₇×#2366	2
C₃₇×#2365	2
C₃₇×#2357	2
C₄×#125×C₃₇	2
C₄×#124×C₃₇	2
C₄²×Q₈×C₃₇	2
#36591	37

Subgroups — C37×#36591 #22657844

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#36591 #22657844