Subgroups — C₃₇×#62850 #22684103

Order 9472.

6846 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3524	C₂	1	8	yes	maximal, complemented
2	C₃₇×#3523	C₂	1	8	yes	maximal, complemented
3	C₃₇×#3518	C₂	1	8	yes	maximal, complemented
4	C₃₇×#3516	C₂	1	8	yes	maximal, complemented
5	C₃₇×#3507	C₂	1	6	yes	maximal, complemented
6	C₃₇×#3502	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#3497	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#3493	C₂	1	6	yes	maximal, complemented
9	C₃₇×#3486	C₂	1	2	yes	maximal, complemented
10	C₃₇×#3461	C₂	1	6	yes	maximal, complemented
11	C₃₇×#3455	C₂	1	6	yes	maximal, complemented
12	C₄×2₋¹⁺⁴×C₃₇	C₂	1	2	yes	maximal, complemented
13	C₂×C₃₇×#519	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×2₋¹⁺⁴×C₃₇	C₂²	1	2	yes	—
15	C₂³×Q₈×C₃₇	C₂²	1	1	yes	characteristic
16	C₃₇×#559	C₂²	1	12	yes	complemented
17	Q₈²×C₃₇	C₂²	1	4	yes	complemented
18	C₃₇×#557	C₂²	1	4	yes	complemented
19	C₃₇×#557	C₂²	1	8	yes	complemented
20	C₃₇×#557	C₂²	1	12	yes	complemented
21	C₃₇×#556	C₂²	1	24	yes	—
22	C₃₇×#556	C₂²	1	24	yes	complemented
23	C₃₇×#556	C₂²	1	12	yes	complemented
24	C₃₇×#555	C₂²	1	24	yes	—
25	C₃₇×#554	C₂²	1	12	yes	complemented
26	C₃₇×#553	C₂²	1	24	yes	—
27	C₃₇×#552	C₂²	1	24	yes	—
28	C₃₇×#552	C₂²	1	24	yes	complemented
29	C₃₇×#550	C₂²	1	4	yes	complemented
30	D₄×Q₈×C₃₇	C₂²	1	8	yes	—
31	D₄×Q₈×C₃₇	C₂²	1	8	yes	—
32	D₄×Q₈×C₃₇	C₂²	1	4	yes	complemented
33	C₃₇×#548	C₂²	1	8	yes	—
34	C₃₇×#548	C₂²	1	8	yes	—
35	C₃₇×#548	C₂²	1	8	yes	complemented
36	C₃₇×#544	C₂²	1	6	yes	—
37	C₃₇×#542	C₂²	1	12	yes	—
38	C₃₇×#542	C₂²	1	12	yes	—
39	C₃₇×#542	C₂²	1	24	yes	complemented
40	C₃₇×#541	C₂²	1	12	yes	—
41	C₃₇×#541	C₂²	1	24	yes	complemented
42	C₃₇×#540	C₂²	1	12	yes	—
43	C₃₇×#539	C₂²	1	12	yes	—
44	C₃₇×#539	C₂²	1	12	yes	—
45	C₃₇×#538	C₂²	1	4	yes	—
46	C₃₇×#538	C₂²	1	12	yes	—
47	C₃₇×#537	C₂²	1	6	yes	—
48	C₃₇×#536	C₂²	1	12	yes	—
49	C₃₇×#533	C₂²	1	6	yes	—
50	C₃₇×#533	C₂²	1	24	yes	complemented
51	C₃₇×#532	C₂²	1	6	yes	—
52	C₃₇×#529	C₂²	1	24	yes	—
53	C₃₇×#529	C₂²	1	24	yes	—
54	C₃₇×#529	C₂²	1	24	yes	—
55	C₃₇×#529	C₂²	1	24	yes	complemented
56	C₃₇×#525	C₂²	1	12	yes	—
57	C₃₇×#520	C₂²	1	12	yes	—
58	C₃₇×#520	C₂²	1	8	yes	complemented
59	C₃₇×#519	C₂²	1	8	yes	—
60	C₃₇×#519	C₂²	1	8	yes	—
61	C₃₇×#519	C₂²	1	2	yes	—
62	C₃₇×#519	C₂²	1	8	yes	complemented
63	C₄×#41×C₃₇	C₂²	1	12	yes	—
64	C₄×#41×C₃₇	C₂²	1	8	yes	complemented
65	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
66	C₂×C₄×Q₈×C₃₇	C₂²	1	3	yes	—
67	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
68	C₂×C₄×Q₈×C₃₇	C₂²	1	3	yes	—
69	C₂×C₄×Q₈×C₃₇	C₂²	1	8	yes	complemented
70	C₂×#117×C₃₇	C₂²	1	3	yes	—
71	C₂×#117×C₃₇	C₂²	1	3	yes	—
72	2₋¹⁺⁴×C₃₇	—	2	16	no	—
73	C₂×#41×C₃₇	C₂³	1	12	yes	—
74	C₂×#41×C₃₇	C₂³	1	8	yes	—
75	C₂²×Q₈×C₃₇	—	2	8	no	—
76	C₂²×Q₈×C₃₇	C₂³	1	8	yes	—
77	C₂²×Q₈×C₃₇	C₂³	1	8	yes	—
78	C₂²×Q₈×C₃₇	C₂³	1	3	yes	—
79	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₃₇	C₂³	1	3	yes	—
81	C₄⋊Q₈×C₃₇	C₂³	1	6	yes	—
82	C₄⋊Q₈×C₃₇	C₂³	1	6	yes	—
83	C₄⋊Q₈×C₃₇	C₂³	1	6	yes	—
84	C₄⋊Q₈×C₃₇	C₂³	1	24	yes	—
85	C₄⋊Q₈×C₃₇	C₂³	1	24	yes	—
86	#127×C₃₇	C₂³	1	6	yes	—
87	#126×C₃₇	C₂³	1	8	yes	—
88	#126×C₃₇	C₂³	1	24	yes	—
89	#126×C₃₇	C₂³	1	24	yes	—
90	#126×C₃₇	C₂³	1	24	yes	—
91	#126×C₃₇	C₂³	1	48	yes	—
92	#125×C₃₇	C₂³	1	24	yes	—
93	#125×C₃₇	C₂³	1	24	yes	—
94	#125×C₃₇	C₂³	1	24	yes	—
95	#125×C₃₇	C₂³	1	24	yes	—
96	#125×C₃₇	C₂³	1	12	yes	—
97	#124×C₃₇	C₂³	1	8	yes	—
98	#124×C₃₇	C₂³	1	24	yes	—
99	#124×C₃₇	C₂³	1	24	yes	—
100	#124×C₃₇	C₂³	1	24	yes	—
101	#124×C₃₇	C₂³	1	12	yes	—
102	#123×C₃₇	C₂³	1	24	yes	—
103	#123×C₃₇	C₂³	1	8	yes	—
104	#123×C₃₇	C₂³	1	24	yes	—
105	#123×C₃₇	C₂³	1	24	yes	—
106	#123×C₃₇	C₂³	1	24	yes	—
107	C₂²⋊Q₈×C₃₇	C₂³	1	12	yes	—
108	C₂²⋊Q₈×C₃₇	C₂³	1	12	yes	—
109	C₂²⋊Q₈×C₃₇	C₂³	1	12	yes	—
110	C₂²⋊Q₈×C₃₇	C₂³	1	24	yes	—
111	C₂²⋊Q₈×C₃₇	C₂³	1	24	yes	—
112	C₂²⋊Q₈×C₃₇	C₂³	1	24	yes	—
113	C₂²⋊Q₈×C₃₇	C₂³	1	4	yes	—
114	C₂²⋊Q₈×C₃₇	C₂³	1	24	yes	—
115	C₂²⋊Q₈×C₃₇	C₂³	1	24	yes	—
116	#121×C₃₇	C₂³	1	12	yes	—
117	#121×C₃₇	C₂³	1	12	yes	—
118	#121×C₃₇	C₂³	1	8	yes	—
119	#121×C₃₇	C₂³	1	12	yes	—
120	#121×C₃₇	C₂³	1	24	yes	—
121	#121×C₃₇	C₂³	1	24	yes	—
122	#121×C₃₇	C₂³	1	4	yes	—
123	#120×C₃₇	C₂³	1	8	yes	—
124	C₄×Q₈×C₃₇	C₂³	1	8	yes	—
125	C₄×Q₈×C₃₇	C₂³	1	24	yes	—
126	C₄×Q₈×C₃₇	C₂³	1	4	yes	—
127	C₄×Q₈×C₃₇	C₂³	1	4	yes	—
128	C₄×Q₈×C₃₇	C₂³	1	12	yes	—
129	C₄×Q₈×C₃₇	C₂³	1	12	yes	—
130	C₄×Q₈×C₃₇	C₂³	1	8	yes	—
131	C₄×Q₈×C₃₇	C₂³	1	8	yes	—
132	C₄×Q₈×C₃₇	C₂³	1	12	yes	—
133	C₄×Q₈×C₃₇	C₂³	1	24	yes	—
134	C₄×Q₈×C₃₇	C₂³	1	12	yes	—
135	C₄×Q₈×C₃₇	C₂³	1	12	yes	—
136	C₄×Q₈×C₃₇	C₂³	1	24	yes	—
137	C₄×Q₈×C₃₇	C₂³	1	12	yes	—
138	C₄×D₄×C₃₇	C₂³	1	24	yes	—
139	C₄×D₄×C₃₇	C₂³	1	24	yes	—
140	C₄×D₄×C₃₇	C₂³	1	12	yes	—
141	C₄×D₄×C₃₇	C₂³	1	24	yes	—
142	C₄×D₄×C₃₇	C₂³	1	24	yes	—
143	C₄×D₄×C₃₇	C₂³	1	12	yes	—
144	C₄×D₄×C₃₇	C₂³	1	12	yes	—
145	C₄×D₄×C₃₇	C₂³	1	24	yes	—
146	C₄×D₄×C₃₇	C₂³	1	8	yes	—
147	C₄×D₄×C₃₇	C₂³	1	12	yes	—
148	#117×C₃₇	C₂³	1	12	yes	—
149	#117×C₃₇	C₂³	1	12	yes	—
150	#117×C₃₇	C₂³	1	24	yes	—
151	#117×C₃₇	C₂³	1	12	yes	—
152	#117×C₃₇	C₂³	1	24	yes	—
153	#117×C₃₇	C₂³	1	24	yes	—
154	#117×C₃₇	C₂³	1	48	yes	—
155	C₂×C₄⋊C₄×C₃₇	C₂³	1	3	yes	—
156	C₂×C₄⋊C₄×C₃₇	C₂³	1	24	yes	—
157	C₂×C₄⋊C₄×C₃₇	C₂³	1	3	yes	—
158	C₂×C₄⋊C₄×C₃₇	C₂³	1	3	yes	—
159	C₂×C₄⋊C₄×C₃₇	C₂³	1	3	yes	—
160	C₂×C₂²⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
161	C₂×C₂²⋊C₄×C₃₇	C₂³	1	3	yes	—
162	C₂×C₄²×C₃₇	C₂³	1	6	yes	—
163	C₂×C₄²×C₃₇	C₂³	1	24	yes	—
164	C₂×C₄²×C₃₇	C₂³	1	3	yes	—
165	C₂×C₄²×C₃₇	C₂³	1	3	yes	—
166	C₂⁴×C₃₇	C₂⁴	1	1	yes	characteristic
167	#41×C₃₇	—	2	32	no	—
168	#41×C₃₇	—	2	48	no	—
169	C₂×Q₈×C₃₇	—	2	32	no	—
170	C₂×Q₈×C₃₇	—	2	32	no	—
171	C₂×Q₈×C₃₇	—	2	12	no	—
172	C₂×Q₈×C₃₇	#41	1	8	yes	—
173	C₂×Q₈×C₃₇	C₂⁴	1	12	yes	—
174	C₂×Q₈×C₃₇	C₂⁴	1	12	yes	—
175	C₂×Q₈×C₃₇	C₂⁴	1	4	yes	—
176	C₂×Q₈×C₃₇	C₂⁴	1	12	yes	—
177	C₂×Q₈×C₃₇	C₂⁴	1	4	yes	—
178	C₂×D₄×C₃₇	C₂⁴	1	8	yes	—
179	C₂×D₄×C₃₇	C₂⁴	1	12	yes	—
180	C₂×D₄×C₃₇	C₂⁴	1	8	yes	—
181	C₂×D₄×C₃₇	C₂⁴	1	8	yes	—
182	C₂×D₄×C₃₇	C₂⁴	1	12	yes	—
183	C₂×D₄×C₃₇	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₃₇	—	2	12	no	—
185	C₂²×C₄×C₃₇	C₂⁴	1	3	yes	—
186	C₂²×C₄×C₃₇	C₂⁴	1	24	yes	—
187	C₂²×C₄×C₃₇	C₂⁴	1	12	yes	—
188	C₂²×C₄×C₃₇	C₂⁴	1	3	yes	—
189	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₃₇	C₂⁴	1	3	yes	—
192	C₂²×C₄×C₃₇	C₂⁴	1	8	yes	—
193	C₂²×C₄×C₃₇	C₂⁴	1	24	yes	—
194	C₂²×C₄×C₃₇	C₂⁴	1	3	yes	—
195	C₄⋊C₄×C₃₇	C₂⁴	1	12	yes	—
196	C₄⋊C₄×C₃₇	C₂⁴	1	12	yes	—
197	C₄⋊C₄×C₃₇	C₂⁴	1	24	yes	—
198	C₄⋊C₄×C₃₇	C₂⁴	1	12	yes	—
199	C₄⋊C₄×C₃₇	C₂⁴	1	6	yes	—
200	C₄⋊C₄×C₃₇	C₂⁴	1	12	yes	—
201	C₄⋊C₄×C₃₇	C₂⁴	1	6	yes	—
202	C₄⋊C₄×C₃₇	C₂⁴	1	12	yes	—
203	C₄⋊C₄×C₃₇	C₂⁴	1	8	yes	—
204	C₄⋊C₄×C₃₇	C₂⁴	1	24	yes	—
205	C₄⋊C₄×C₃₇	C₂⁴	1	24	yes	—
206	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
207	C₄⋊C₄×C₃₇	C₂⁴	1	12	yes	—
208	C₄⋊C₄×C₃₇	C₂⁴	1	12	yes	—
209	C₄⋊C₄×C₃₇	C₂⁴	1	24	yes	—
210	C₄⋊C₄×C₃₇	C₂⁴	1	8	yes	—
211	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
212	C₂²⋊C₄×C₃₇	C₂⁴	1	2	yes	—
213	C₂²⋊C₄×C₃₇	C₂⁴	1	12	yes	—
214	C₂²⋊C₄×C₃₇	C₂⁴	1	2	yes	—
215	C₂²⋊C₄×C₃₇	C₂⁴	1	8	yes	—
216	C₂²⋊C₄×C₃₇	C₂⁴	1	8	yes	—
217	C₂²⋊C₄×C₃₇	C₂⁴	1	24	yes	—
218	C₂²⋊C₄×C₃₇	C₂⁴	1	24	yes	—
219	C₂²⋊C₄×C₃₇	C₂⁴	1	24	yes	—
220	C₂²⋊C₄×C₃₇	C₂⁴	1	8	yes	—
221	C₂²⋊C₄×C₃₇	C₂⁴	1	8	yes	—
222	C₂²⋊C₄×C₃₇	C₂⁴	1	24	yes	—
223	C₂²⋊C₄×C₃₇	C₂⁴	1	8	yes	—
224	C₄²×C₃₇	C₂⁴	1	12	yes	—
225	C₄²×C₃₇	C₂⁴	1	8	yes	—
226	C₄²×C₃₇	C₂⁴	1	24	yes	—
227	C₄²×C₃₇	C₂⁴	1	24	yes	—
228	C₄²×C₃₇	C₂⁴	1	24	yes	—
229	C₄²×C₃₇	C₂⁴	1	6	yes	—
230	C₄²×C₃₇	C₂⁴	1	6	yes	—
231	C₂³×C₃₇	—	2	2	no	—
232	C₂³×C₃₇	—	4	1	no	—
233	C₂³×C₃₇	—	4	1	no	—
234	C₂³×C₃₇	C₂⁵	1	2	yes	—
235	C₂³×C₃₇	C₂⁵	1	8	yes	—
236	C₂³×C₃₇	C₂⁵	1	1	yes	characteristic
237	Q₈×C₃₇	—	2	24	no	—
238	Q₈×C₃₇	—	2	24	no	—
239	Q₈×C₃₇	—	4	4	no	—
240	Q₈×C₃₇	—	4	12	no	—
241	Q₈×C₃₇	C₂×#41	1	16	yes	—
242	D₄×C₃₇	—	2	16	no	—
243	D₄×C₃₇	—	2	24	no	—
244	D₄×C₃₇	—	4	8	no	—
245	D₄×C₃₇	—	4	4	no	—
246	D₄×C₃₇	—	4	12	no	—
247	D₄×C₃₇	—	4	8	no	—
248	C₂×C₄×C₃₇	—	2	6	no	—
249	C₂×C₄×C₃₇	—	2	24	no	—
250	C₂×C₄×C₃₇	—	2	48	no	—
251	C₂×C₄×C₃₇	—	4	3	no	—
252	C₂×C₄×C₃₇	—	4	1	no	—
253	C₂×C₄×C₃₇	—	4	24	no	—
254	C₂×C₄×C₃₇	—	4	8	no	—
255	C₂×C₄×C₃₇	—	4	1	no	—
256	C₂×C₄×C₃₇	—	4	3	no	—
257	C₂×C₄×C₃₇	C₂×#41	1	12	yes	—
258	C₂×C₄×C₃₇	C₂⁵	1	2	yes	—
259	C₂×C₄×C₃₇	C₂⁵	1	6	yes	—
260	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
261	C₂×C₄×C₃₇	C₂⁵	1	8	yes	—
262	C₂×C₄×C₃₇	C₂⁵	1	6	yes	—
263	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
264	C₂×C₄×C₃₇	C₂⁵	1	6	yes	—
265	C₂×C₄×C₃₇	C₂⁵	1	8	yes	—
266	C₂×C₄×C₃₇	C₂⁵	1	8	yes	—
267	C₂×C₄×C₃₇	C₂⁵	1	6	yes	—
268	#62850	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
269	C₂²×C₃₇	—	2	1	no	—
270	C₂²×C₃₇	—	2	1	no	—
271	C₂²×C₃₇	—	2	2	no	—
272	C₂²×C₃₇	—	2	8	no	—
273	C₂²×C₃₇	—	2	8	no	—
274	C₂²×C₃₇	—	2	8	no	—
275	C₂²×C₃₇	—	2	2	no	—
276	C₂²×C₃₇	—	2	2	no	—
277	C₂²×C₃₇	—	4	4	no	—
278	C₂²×C₃₇	C₂²×#41	1	2	yes	—
279	C₂²×C₃₇	C₂⁶	1	1	yes	characteristic
280	C₄×C₃₇	—	2	8	no	—
281	C₄×C₃₇	—	2	6	no	—
282	C₄×C₃₇	—	2	6	no	—
283	C₄×C₃₇	—	2	2	no	—
284	C₄×C₃₇	—	2	8	no	—
285	C₄×C₃₇	—	2	1	no	—
286	C₄×C₃₇	—	2	6	no	—
287	C₄×C₃₇	—	2	8	no	—
288	C₄×C₃₇	—	2	1	no	—
289	C₄×C₃₇	C₂²×#41	1	12	yes	—
290	#3524	C₂×C₃₇	1	8	yes	complemented
291	#3523	C₂×C₃₇	1	8	yes	complemented
292	#3518	C₂×C₃₇	1	8	yes	complemented
293	#3516	C₂×C₃₇	1	8	yes	complemented
294	#3507	C₂×C₃₇	1	6	yes	complemented
295	#3502	C₂×C₃₇	1	1	yes	characteristic, complemented
296	#3497	C₂×C₃₇	1	1	yes	characteristic, complemented
297	#3493	C₂×C₃₇	1	6	yes	complemented
298	#3486	C₂×C₃₇	1	2	yes	complemented
299	#3461	C₂×C₃₇	1	6	yes	complemented
300	#3455	C₂×C₃₇	1	6	yes	complemented
301	C₄×2₋¹⁺⁴	C₂×C₃₇	1	2	yes	complemented
302	C₂×#519	C₂×C₃₇	1	1	yes	characteristic, complemented
303	C₂×C₃₇	—	2	2	no	—
304	C₂×C₃₇	—	4	8	no	—
305	C₂×C₃₇	—	4	2	no	—
306	C₂×C₃₇	C₂³×#41	1	1	yes	characteristic
307	C₂×C₃₇	2₋¹⁺⁶	1	1	yes	characteristic
308	C₂×C₃₇	2₋¹⁺⁶	1	1	yes	characteristic
309	C₂×2₋¹⁺⁴	C₂²×C₃₇	1	2	yes	—
310	C₂³×Q₈	C₂²×C₃₇	1	1	yes	characteristic
311	#559	C₂²×C₃₇	1	12	yes	complemented
312	Q₈²	C₂²×C₃₇	1	4	yes	complemented
313	#557	C₂²×C₃₇	1	4	yes	complemented
314	#557	C₂²×C₃₇	1	8	yes	complemented
315	#557	C₂²×C₃₇	1	12	yes	complemented
316	#556	C₂²×C₃₇	1	24	yes	—
317	#556	C₂²×C₃₇	1	24	yes	complemented
318	#556	C₂²×C₃₇	1	12	yes	complemented
319	#555	C₂²×C₃₇	1	24	yes	—
320	#554	C₂²×C₃₇	1	12	yes	complemented
321	#553	C₂²×C₃₇	1	24	yes	—
322	#552	C₂²×C₃₇	1	24	yes	—
323	#552	C₂²×C₃₇	1	24	yes	complemented
324	#550	C₂²×C₃₇	1	4	yes	complemented
325	D₄×Q₈	C₂²×C₃₇	1	8	yes	—
326	D₄×Q₈	C₂²×C₃₇	1	8	yes	—
327	D₄×Q₈	C₂²×C₃₇	1	4	yes	complemented
328	#548	C₂²×C₃₇	1	8	yes	—
329	#548	C₂²×C₃₇	1	8	yes	—
330	#548	C₂²×C₃₇	1	8	yes	complemented
331	#544	C₂²×C₃₇	1	6	yes	—
332	#542	C₂²×C₃₇	1	12	yes	—
333	#542	C₂²×C₃₇	1	12	yes	—
334	#542	C₂²×C₃₇	1	24	yes	complemented
335	#541	C₂²×C₃₇	1	12	yes	—
336	#541	C₂²×C₃₇	1	24	yes	complemented
337	#540	C₂²×C₃₇	1	12	yes	—
338	#539	C₂²×C₃₇	1	12	yes	—
339	#539	C₂²×C₃₇	1	12	yes	—
340	#538	C₂²×C₃₇	1	4	yes	—
341	#538	C₂²×C₃₇	1	12	yes	—
342	#537	C₂²×C₃₇	1	6	yes	—
343	#536	C₂²×C₃₇	1	12	yes	—
344	#533	C₂²×C₃₇	1	6	yes	—
345	#533	C₂²×C₃₇	1	24	yes	complemented
346	#532	C₂²×C₃₇	1	6	yes	—
347	#529	C₂²×C₃₇	1	24	yes	—
348	#529	C₂²×C₃₇	1	24	yes	—
349	#529	C₂²×C₃₇	1	24	yes	—
350	#529	C₂²×C₃₇	1	24	yes	complemented
351	#525	C₂²×C₃₇	1	12	yes	—
352	#520	C₂²×C₃₇	1	12	yes	—
353	#520	C₂²×C₃₇	1	8	yes	complemented
354	#519	C₂²×C₃₇	1	8	yes	—
355	#519	C₂²×C₃₇	1	8	yes	—
356	#519	C₂²×C₃₇	1	2	yes	—
357	#519	C₂²×C₃₇	1	8	yes	complemented
358	C₄×#41	C₂²×C₃₇	1	12	yes	—
359	C₄×#41	C₂²×C₃₇	1	8	yes	complemented
360	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
361	C₂×C₄×Q₈	C₂²×C₃₇	1	3	yes	—
362	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
363	C₂×C₄×Q₈	C₂²×C₃₇	1	3	yes	—
364	C₂×C₄×Q₈	C₂²×C₃₇	1	8	yes	complemented
365	C₂×#117	C₂²×C₃₇	1	3	yes	—
366	C₂×#117	C₂²×C₃₇	1	3	yes	—
367	C₃₇	#62850	1	1	yes	characteristic, direct product factor, Sylow
368	2₋¹⁺⁴	—	2	16	no	—
369	C₂×#41	C₂³×C₃₇	1	12	yes	—
370	C₂×#41	C₂³×C₃₇	1	8	yes	—
371	C₂²×Q₈	—	2	8	no	—
372	C₂²×Q₈	C₂³×C₃₇	1	3	yes	—
373	C₂²×Q₈	C₂³×C₃₇	1	8	yes	—
374	C₂²×Q₈	C₂³×C₃₇	1	8	yes	—
375	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
376	C₂³×C₄	C₂³×C₃₇	1	3	yes	—
377	C₄⋊Q₈	C₂³×C₃₇	1	6	yes	—
378	C₄⋊Q₈	C₂³×C₃₇	1	6	yes	—
379	C₄⋊Q₈	C₂³×C₃₇	1	6	yes	—
380	C₄⋊Q₈	C₂³×C₃₇	1	24	yes	—
381	C₄⋊Q₈	C₂³×C₃₇	1	24	yes	—
382	#127	C₂³×C₃₇	1	6	yes	—
383	#126	C₂³×C₃₇	1	8	yes	—
384	#126	C₂³×C₃₇	1	24	yes	—
385	#126	C₂³×C₃₇	1	24	yes	—
386	#126	C₂³×C₃₇	1	24	yes	—
387	#126	C₂³×C₃₇	1	48	yes	—
388	#125	C₂³×C₃₇	1	24	yes	—
389	#125	C₂³×C₃₇	1	24	yes	—
390	#125	C₂³×C₃₇	1	24	yes	—
391	#125	C₂³×C₃₇	1	24	yes	—
392	#125	C₂³×C₃₇	1	12	yes	—
393	#124	C₂³×C₃₇	1	8	yes	—
394	#124	C₂³×C₃₇	1	24	yes	—
395	#124	C₂³×C₃₇	1	24	yes	—
396	#124	C₂³×C₃₇	1	24	yes	—
397	#124	C₂³×C₃₇	1	12	yes	—
398	#123	C₂³×C₃₇	1	24	yes	—
399	#123	C₂³×C₃₇	1	8	yes	—
400	#123	C₂³×C₃₇	1	24	yes	—
401	#123	C₂³×C₃₇	1	24	yes	—
402	#123	C₂³×C₃₇	1	24	yes	—
403	C₂²⋊Q₈	C₂³×C₃₇	1	12	yes	—
404	C₂²⋊Q₈	C₂³×C₃₇	1	12	yes	—
405	C₂²⋊Q₈	C₂³×C₃₇	1	12	yes	—
406	C₂²⋊Q₈	C₂³×C₃₇	1	24	yes	—
407	C₂²⋊Q₈	C₂³×C₃₇	1	24	yes	—
408	C₂²⋊Q₈	C₂³×C₃₇	1	24	yes	—
409	C₂²⋊Q₈	C₂³×C₃₇	1	4	yes	—
410	C₂²⋊Q₈	C₂³×C₃₇	1	24	yes	—
411	C₂²⋊Q₈	C₂³×C₃₇	1	24	yes	—
412	#121	C₂³×C₃₇	1	12	yes	—
413	#121	C₂³×C₃₇	1	12	yes	—
414	#121	C₂³×C₃₇	1	8	yes	—
415	#121	C₂³×C₃₇	1	12	yes	—
416	#121	C₂³×C₃₇	1	24	yes	—
417	#121	C₂³×C₃₇	1	24	yes	—
418	#121	C₂³×C₃₇	1	4	yes	—
419	#120	C₂³×C₃₇	1	8	yes	—
420	C₄×Q₈	C₂³×C₃₇	1	8	yes	—
421	C₄×Q₈	C₂³×C₃₇	1	24	yes	—
422	C₄×Q₈	C₂³×C₃₇	1	4	yes	—
423	C₄×Q₈	C₂³×C₃₇	1	4	yes	—
424	C₄×Q₈	C₂³×C₃₇	1	12	yes	—
425	C₄×Q₈	C₂³×C₃₇	1	12	yes	—
426	C₄×Q₈	C₂³×C₃₇	1	12	yes	—
427	C₄×Q₈	C₂³×C₃₇	1	8	yes	—
428	C₄×Q₈	C₂³×C₃₇	1	24	yes	—
429	C₄×Q₈	C₂³×C₃₇	1	12	yes	—
430	C₄×Q₈	C₂³×C₃₇	1	8	yes	—
431	C₄×Q₈	C₂³×C₃₇	1	12	yes	—
432	C₄×Q₈	C₂³×C₃₇	1	12	yes	—
433	C₄×Q₈	C₂³×C₃₇	1	24	yes	—
434	C₄×D₄	C₂³×C₃₇	1	8	yes	—
435	C₄×D₄	C₂³×C₃₇	1	12	yes	—
436	C₄×D₄	C₂³×C₃₇	1	24	yes	—
437	C₄×D₄	C₂³×C₃₇	1	12	yes	—
438	C₄×D₄	C₂³×C₃₇	1	24	yes	—
439	C₄×D₄	C₂³×C₃₇	1	24	yes	—
440	C₄×D₄	C₂³×C₃₇	1	24	yes	—
441	C₄×D₄	C₂³×C₃₇	1	12	yes	—
442	C₄×D₄	C₂³×C₃₇	1	12	yes	—
443	C₄×D₄	C₂³×C₃₇	1	24	yes	—
444	#117	C₂³×C₃₇	1	12	yes	—
445	#117	C₂³×C₃₇	1	12	yes	—
446	#117	C₂³×C₃₇	1	24	yes	—
447	#117	C₂³×C₃₇	1	12	yes	—
448	#117	C₂³×C₃₇	1	24	yes	—
449	#117	C₂³×C₃₇	1	24	yes	—
450	#117	C₂³×C₃₇	1	48	yes	—
451	C₂×C₄⋊C₄	C₂³×C₃₇	1	3	yes	—
452	C₂×C₄⋊C₄	C₂³×C₃₇	1	3	yes	—
453	C₂×C₄⋊C₄	C₂³×C₃₇	1	3	yes	—
454	C₂×C₄⋊C₄	C₂³×C₃₇	1	3	yes	—
455	C₂×C₄⋊C₄	C₂³×C₃₇	1	24	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
457	C₂×C₂²⋊C₄	C₂³×C₃₇	1	3	yes	—
458	C₂×C₄²	C₂³×C₃₇	1	3	yes	—
459	C₂×C₄²	C₂³×C₃₇	1	6	yes	—
460	C₂×C₄²	C₂³×C₃₇	1	3	yes	—
461	C₂×C₄²	C₂³×C₃₇	1	24	yes	—
462	C₂⁴	C₂⁴×C₃₇	1	1	yes	characteristic
463	#41	—	2	32	no	—
464	#41	—	2	48	no	—
465	C₂×Q₈	—	2	32	no	—
466	C₂×Q₈	—	2	32	no	—
467	C₂×Q₈	—	2	12	no	—
468	C₂×Q₈	#41×C₃₇	1	8	yes	—
469	C₂×Q₈	C₂⁴×C₃₇	1	12	yes	—
470	C₂×Q₈	C₂⁴×C₃₇	1	12	yes	—
471	C₂×Q₈	C₂⁴×C₃₇	1	4	yes	—
472	C₂×Q₈	C₂⁴×C₃₇	1	12	yes	—
473	C₂×Q₈	C₂⁴×C₃₇	1	4	yes	—
474	C₂×D₄	C₂⁴×C₃₇	1	8	yes	—
475	C₂×D₄	C₂⁴×C₃₇	1	12	yes	—
476	C₂×D₄	C₂⁴×C₃₇	1	8	yes	—
477	C₂×D₄	C₂⁴×C₃₇	1	8	yes	—
478	C₂×D₄	C₂⁴×C₃₇	1	12	yes	—
479	C₂×D₄	C₂⁴×C₃₇	1	4	yes	—
480	C₂²×C₄	—	2	12	no	—
481	C₂²×C₄	C₂⁴×C₃₇	1	3	yes	—
482	C₂²×C₄	C₂⁴×C₃₇	1	24	yes	—
483	C₂²×C₄	C₂⁴×C₃₇	1	12	yes	—
484	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
485	C₂²×C₄	C₂⁴×C₃₇	1	3	yes	—
486	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
487	C₂²×C₄	C₂⁴×C₃₇	1	3	yes	—
488	C₂²×C₄	C₂⁴×C₃₇	1	8	yes	—
489	C₂²×C₄	C₂⁴×C₃₇	1	24	yes	—
490	C₂²×C₄	C₂⁴×C₃₇	1	3	yes	—
491	C₄⋊C₄	C₂⁴×C₃₇	1	12	yes	—
492	C₄⋊C₄	C₂⁴×C₃₇	1	12	yes	—
493	C₄⋊C₄	C₂⁴×C₃₇	1	24	yes	—
494	C₄⋊C₄	C₂⁴×C₃₇	1	12	yes	—
495	C₄⋊C₄	C₂⁴×C₃₇	1	6	yes	—
496	C₄⋊C₄	C₂⁴×C₃₇	1	12	yes	—
497	C₄⋊C₄	C₂⁴×C₃₇	1	6	yes	—
498	C₄⋊C₄	C₂⁴×C₃₇	1	12	yes	—
499	C₄⋊C₄	C₂⁴×C₃₇	1	8	yes	—
500	C₄⋊C₄	C₂⁴×C₃₇	1	24	yes	—
501	C₄⋊C₄	C₂⁴×C₃₇	1	24	yes	—
502	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
503	C₄⋊C₄	C₂⁴×C₃₇	1	12	yes	—
504	C₄⋊C₄	C₂⁴×C₃₇	1	12	yes	—
505	C₄⋊C₄	C₂⁴×C₃₇	1	24	yes	—
506	C₄⋊C₄	C₂⁴×C₃₇	1	8	yes	—
507	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
508	C₂²⋊C₄	C₂⁴×C₃₇	1	2	yes	—
509	C₂²⋊C₄	C₂⁴×C₃₇	1	12	yes	—
510	C₂²⋊C₄	C₂⁴×C₃₇	1	2	yes	—
511	C₂²⋊C₄	C₂⁴×C₃₇	1	8	yes	—
512	C₂²⋊C₄	C₂⁴×C₃₇	1	8	yes	—
513	C₂²⋊C₄	C₂⁴×C₃₇	1	24	yes	—
514	C₂²⋊C₄	C₂⁴×C₃₇	1	24	yes	—
515	C₂²⋊C₄	C₂⁴×C₃₇	1	24	yes	—
516	C₂²⋊C₄	C₂⁴×C₃₇	1	8	yes	—
517	C₂²⋊C₄	C₂⁴×C₃₇	1	8	yes	—
518	C₂²⋊C₄	C₂⁴×C₃₇	1	24	yes	—
519	C₂²⋊C₄	C₂⁴×C₃₇	1	8	yes	—
520	C₄²	C₂⁴×C₃₇	1	12	yes	—
521	C₄²	C₂⁴×C₃₇	1	8	yes	—
522	C₄²	C₂⁴×C₃₇	1	24	yes	—
523	C₄²	C₂⁴×C₃₇	1	24	yes	—
524	C₄²	C₂⁴×C₃₇	1	24	yes	—
525	C₄²	C₂⁴×C₃₇	1	6	yes	—
526	C₄²	C₂⁴×C₃₇	1	6	yes	—
527	C₂³	—	2	2	no	—
528	C₂³	—	4	1	no	—
529	C₂³	—	4	1	no	—
530	C₂³	C₂⁵×C₃₇	1	2	yes	—
531	C₂³	C₂⁵×C₃₇	1	8	yes	—
532	C₂³	C₂⁵×C₃₇	1	1	yes	characteristic
533	Q₈	—	2	24	no	—
534	Q₈	—	2	24	no	—
535	Q₈	—	4	4	no	—
536	Q₈	—	4	12	no	—
537	Q₈	C₂×#41×C₃₇	1	16	yes	—
538	D₄	—	2	16	no	—
539	D₄	—	2	24	no	—
540	D₄	—	4	8	no	—
541	D₄	—	4	4	no	—
542	D₄	—	4	12	no	—
543	D₄	—	4	8	no	—
544	C₂×C₄	—	2	6	no	—
545	C₂×C₄	—	2	24	no	—
546	C₂×C₄	—	2	48	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	3	no	—
549	C₂×C₄	—	4	24	no	—
550	C₂×C₄	—	4	8	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	3	no	—
553	C₂×C₄	C₂×#41×C₃₇	1	12	yes	—
554	C₂×C₄	C₂⁵×C₃₇	1	2	yes	—
555	C₂×C₄	C₂⁵×C₃₇	1	6	yes	—
556	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
557	C₂×C₄	C₂⁵×C₃₇	1	8	yes	—
558	C₂×C₄	C₂⁵×C₃₇	1	6	yes	—
559	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
560	C₂×C₄	C₂⁵×C₃₇	1	6	yes	—
561	C₂×C₄	C₂⁵×C₃₇	1	8	yes	—
562	C₂×C₄	C₂⁵×C₃₇	1	8	yes	—
563	C₂×C₄	C₂⁵×C₃₇	1	6	yes	—
564	C₂²	—	2	1	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	2	8	no	—
568	C₂²	—	2	8	no	—
569	C₂²	—	2	8	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	4	4	no	—
573	C₂²	C₂²×#41×C₃₇	1	2	yes	—
574	C₂²	C₂⁶×C₃₇	1	1	yes	characteristic
575	C₄	—	2	8	no	—
576	C₄	—	2	6	no	—
577	C₄	—	2	6	no	—
578	C₄	—	2	2	no	—
579	C₄	—	2	8	no	—
580	C₄	—	2	1	no	—
581	C₄	—	2	6	no	—
582	C₄	—	2	8	no	—
583	C₄	—	2	1	no	—
584	C₄	C₂²×#41×C₃₇	1	12	yes	—
585	C₂	—	2	2	no	—
586	C₂	—	4	2	no	—
587	C₂	—	4	8	no	—
588	C₂	C₂³×#41×C₃₇	1	1	yes	characteristic
589	C₂	C₃₇×2₋¹⁺⁶	1	1	yes	characteristic
590	C₂	C₃₇×2₋¹⁺⁶	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×#3524	C₂	semidirect
2. C₃₇×#3523	C₂	semidirect
3. C₃₇×#3518	C₂	semidirect
4. C₃₇×#3516	C₂	semidirect
5. C₃₇×#3507	C₂	semidirect
6. C₃₇×#3502	C₂	semidirect
7. C₃₇×#3497	C₂	semidirect
8. C₃₇×#3493	C₂	semidirect
9. C₃₇×#3486	C₂	semidirect
10. C₃₇×#3461	C₂	semidirect
11. C₃₇×#3455	C₂	semidirect
12. C₄×2₋¹⁺⁴×C₃₇	C₂	semidirect
13. C₂×C₃₇×#519	C₂	semidirect
16. C₃₇×#559	C₂²	semidirect
17. Q₈²×C₃₇	C₂²	semidirect
18. C₃₇×#557	C₂²	semidirect
19. C₃₇×#557	C₂²	semidirect
20. C₃₇×#557	C₂²	semidirect
22. C₃₇×#556	C₂²	semidirect
23. C₃₇×#556	C₂²	semidirect
25. C₃₇×#554	C₂²	semidirect
28. C₃₇×#552	C₂²	semidirect
29. C₃₇×#550	C₂²	semidirect
32. D₄×Q₈×C₃₇	C₂²	semidirect
35. C₃₇×#548	C₂²	semidirect
39. C₃₇×#542	C₂²	semidirect
41. C₃₇×#541	C₂²	semidirect
50. C₃₇×#533	C₂²	semidirect
55. C₃₇×#529	C₂²	semidirect
58. C₃₇×#520	C₂²	semidirect
62. C₃₇×#519	C₂²	semidirect
64. C₄×#41×C₃₇	C₂²	semidirect
69. C₂×C₄×Q₈×C₃₇	C₂²	semidirect
268. #62850	C₃₇	direct (N × H)
290. #3524	C₂×C₃₇	semidirect
291. #3523	C₂×C₃₇	semidirect
292. #3518	C₂×C₃₇	semidirect
293. #3516	C₂×C₃₇	semidirect
294. #3507	C₂×C₃₇	semidirect
295. #3502	C₂×C₃₇	semidirect
296. #3497	C₂×C₃₇	semidirect
297. #3493	C₂×C₃₇	semidirect
298. #3486	C₂×C₃₇	semidirect
299. #3461	C₂×C₃₇	semidirect
300. #3455	C₂×C₃₇	semidirect
301. C₄×2₋¹⁺⁴	C₂×C₃₇	semidirect
302. C₂×#519	C₂×C₃₇	semidirect
311. #559	C₂²×C₃₇	semidirect
312. Q₈²	C₂²×C₃₇	semidirect
313. #557	C₂²×C₃₇	semidirect
314. #557	C₂²×C₃₇	semidirect
315. #557	C₂²×C₃₇	semidirect
317. #556	C₂²×C₃₇	semidirect
318. #556	C₂²×C₃₇	semidirect
320. #554	C₂²×C₃₇	semidirect
323. #552	C₂²×C₃₇	semidirect
324. #550	C₂²×C₃₇	semidirect
327. D₄×Q₈	C₂²×C₃₇	semidirect
330. #548	C₂²×C₃₇	semidirect
334. #542	C₂²×C₃₇	semidirect
336. #541	C₂²×C₃₇	semidirect
345. #533	C₂²×C₃₇	semidirect
350. #529	C₂²×C₃₇	semidirect
353. #520	C₂²×C₃₇	semidirect
357. #519	C₂²×C₃₇	semidirect
359. C₄×#41	C₂²×C₃₇	semidirect
364. C₂×C₄×Q₈	C₂²×C₃₇	semidirect
367. C₃₇	#62850	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×#3524	2
C₃₇×#3523	2
C₃₇×#3518	2
C₃₇×#3516	2
C₃₇×#3507	2
C₃₇×#3502	2
C₃₇×#3497	2
C₃₇×#3493	2
C₃₇×#3486	2
C₃₇×#3461	2
C₃₇×#3455	2
C₄×2₋¹⁺⁴×C₃₇	2
C₂×C₃₇×#519	2
#62850	37

Subgroups — C37×#62850 #22684103

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#62850 #22684103