Subgroups — C₃₇×#61721 #22682974

Order 9472.

1798 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3501	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#555	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#3357	C₂	1	8	yes	maximal, complemented
4	C₃₇×#3329	C₂	1	8	yes	maximal, complemented
5	C₃₇×#3230	C₂	1	2	yes	maximal, complemented
6	C₃₇×#3193	C₂	1	4	yes	maximal, complemented
7	C₃₇×#3101	C₂	1	2	yes	maximal, complemented
8	C₃₇×#3095	C₂	1	4	yes	maximal, complemented
9	C₃₇×#2975	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#555	—	2	4	no	—
11	C₃₇×#555	C₂²	1	8	yes	—
12	C₃₇×#554	—	2	4	no	—
13	C₃₇×#554	C₂²	1	4	yes	complemented
14	D₄×Q₈×C₃₇	C₂²	1	4	yes	complemented
15	C₃₇×#544	—	2	1	no	—
16	C₃₇×#543	—	2	2	no	—
17	C₃₇×#533	C₂²	1	2	yes	—
18	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
19	C₂×#124×C₃₇	—	2	2	no	—
20	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	4	yes	—
21	C₂×#121×C₃₇	—	2	1	no	—
22	C₂×#121×C₃₇	C₂²	1	2	yes	—
23	C₃₇×#518	—	2	1	no	—
24	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
26	C₂×#117×C₃₇	—	2	1	no	—
27	C₂×#117×C₃₇	C₂²	1	2	yes	—
28	C₃₇×#500	C₂²	1	4	yes	complemented
29	C₃₇×#487	C₂²	1	4	yes	complemented
30	C₃₇×#485	C₂²	1	16	yes	complemented
31	C₃₇×#484	C₂²	1	8	yes	—
32	C₃₇×#483	C₂²	1	4	yes	—
33	C₃₇×#480	C₂²	1	8	yes	complemented
34	C₃₇×#477	C₂²	1	8	yes	complemented
35	C₃₇×#476	C₂²	1	4	yes	complemented
36	C₃₇×#468	C₂²	1	16	yes	complemented
37	C₃₇×#461	C₂²	1	4	yes	complemented
38	C₃₇×#450	C₂²	1	4	yes	—
39	C₃₇×#448	C₂²	1	8	yes	complemented
40	C₄×SD₁₆×C₃₇	C₂²	1	8	yes	complemented
41	C₃₇×#436	C₂²	1	8	yes	complemented
42	C₃₇×#431	C₂²	1	2	yes	—
43	C₃₇×#428	C₂²	1	8	yes	complemented
44	C₃₇×#419	C₂²	1	8	yes	complemented
45	C₃₇×#407	C₂²	1	4	yes	—
46	C₂²×Q₈×C₃₇	—	2	1	no	—
47	C₂²×Q₈×C₃₇	C₂³	1	4	yes	—
48	C₂²×D₄×C₃₇	—	2	2	no	—
49	C₂²×D₄×C₃₇	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₃₇	—	2	1	no	—
52	C₂³×C₄×C₃₇	C₂³	1	2	yes	—
53	C₂×SD₁₆×C₃₇	C₂³	1	8	yes	—
54	C₂×M₁₆×C₃₇	C₂³	1	8	yes	—
55	C₄⋊Q₈×C₃₇	—	2	4	no	—
56	C₄⋊Q₈×C₃₇	—	2	2	no	—
57	C₄⋊Q₈×C₃₇	C₂³	1	2	yes	—
58	C₄⋊Q₈×C₃₇	C₂³	1	4	yes	—
59	C₄⋊Q₈×C₃₇	C₂³	1	2	yes	—
60	#125×C₃₇	—	2	4	no	—
61	#125×C₃₇	—	2	2	no	—
62	#124×C₃₇	—	2	16	no	—
63	C₂²⋊Q₈×C₃₇	—	2	4	no	—
64	C₂²⋊Q₈×C₃₇	—	2	4	no	—
65	C₂²⋊Q₈×C₃₇	—	2	2	no	—
66	C₂²⋊Q₈×C₃₇	—	2	8	no	—
67	C₂²⋊Q₈×C₃₇	—	2	8	no	—
68	C₂²⋊Q₈×C₃₇	C₂³	1	4	yes	—
69	C₂²⋊Q₈×C₃₇	C₂³	1	8	yes	—
70	#121×C₃₇	—	2	8	no	—
71	#121×C₃₇	—	2	4	no	—
72	#121×C₃₇	C₂³	1	8	yes	—
73	C₄×Q₈×C₃₇	—	2	2	no	—
74	C₄×Q₈×C₃₇	C₂³	1	4	yes	—
75	C₄×D₄×C₃₇	—	2	4	no	—
76	C₄×D₄×C₃₇	—	2	4	no	—
77	C₄×D₄×C₃₇	—	2	2	no	—
78	C₄×D₄×C₃₇	D₄	1	4	yes	—
79	C₄×D₄×C₃₇	C₂³	1	4	yes	—
80	C₄×D₄×C₃₇	C₂³	1	4	yes	—
81	#117×C₃₇	—	2	2	no	—
82	#117×C₃₇	—	2	4	no	—
83	#117×C₃₇	—	2	8	no	—
84	#117×C₃₇	C₂³	1	8	yes	—
85	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
86	C₂×C₄⋊C₄×C₃₇	—	2	4	no	—
87	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
93	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₃₇	D₄	1	2	yes	—
96	C₂×C₄²×C₃₇	—	2	2	no	—
97	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
98	#107×C₃₇	C₂³	1	16	yes	—
99	#106×C₃₇	C₂³	1	8	yes	—
100	C₄⋊C₈×C₃₇	C₂³	1	4	yes	—
101	#103×C₃₇	C₂³	1	8	yes	—
102	#103×C₃₇	C₂³	1	16	yes	—
103	#102×C₃₇	C₂³	1	8	yes	—
104	C₂²⋊C₈×C₃₇	C₂³	1	4	yes	—
105	C₂²⋊C₈×C₃₇	C₂³	1	8	yes	—
106	C₄×C₈×C₃₇	C₂³	1	4	yes	—
107	C₂⁴×C₃₇	—	2	1	no	—
108	C₂⁴×C₃₇	C₂×D₄	1	2	yes	—
109	C₂×Q₈×C₃₇	—	2	2	no	—
110	C₂×Q₈×C₃₇	—	2	4	no	—
111	C₂×Q₈×C₃₇	—	2	4	no	—
112	C₂×Q₈×C₃₇	—	4	8	no	—
113	C₂×Q₈×C₃₇	—	8	2	no	—
114	C₂×Q₈×C₃₇	C₂⁴	1	4	yes	—
115	C₂×D₄×C₃₇	—	2	8	no	—
116	C₂×D₄×C₃₇	—	2	4	no	—
117	C₂×D₄×C₃₇	—	2	1	no	—
118	C₂×D₄×C₃₇	—	4	2	no	—
119	C₂×D₄×C₃₇	—	8	4	no	—
120	C₂×D₄×C₃₇	C₂×D₄	1	4	yes	—
121	C₂×D₄×C₃₇	C₂⁴	1	2	yes	—
122	C₂²×C₄×C₃₇	—	2	1	no	—
123	C₂²×C₄×C₃₇	—	2	2	no	—
124	C₂²×C₄×C₃₇	—	2	4	no	—
125	C₂²×C₄×C₃₇	—	2	4	no	—
126	C₂²×C₄×C₃₇	—	2	4	no	—
127	C₂²×C₄×C₃₇	—	4	4	no	—
128	C₂²×C₄×C₃₇	—	4	4	no	—
129	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₃₇	C₂×D₄	1	4	yes	—
132	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
134	C₂²×C₄×C₃₇	C₂⁴	1	4	yes	—
135	SD₁₆×C₃₇	—	4	8	no	—
136	M₁₆×C₃₇	—	4	8	no	—
137	C₂×C₈×C₃₇	C₂⁴	1	8	yes	—
138	C₄⋊C₄×C₃₇	—	2	4	no	—
139	C₄⋊C₄×C₃₇	—	2	4	no	—
140	C₄⋊C₄×C₃₇	—	2	8	no	—
141	C₄⋊C₄×C₃₇	—	2	1	no	—
142	C₄⋊C₄×C₃₇	—	2	2	no	—
143	C₄⋊C₄×C₃₇	—	2	4	no	—
144	C₄⋊C₄×C₃₇	—	2	2	no	—
145	C₄⋊C₄×C₃₇	—	2	2	no	—
146	C₄⋊C₄×C₃₇	—	2	2	no	—
147	C₄⋊C₄×C₃₇	—	2	4	no	—
148	C₄⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
149	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
150	C₄⋊C₄×C₃₇	C₂⁴	1	2	yes	—
151	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
152	C₂²⋊C₄×C₃₇	—	2	4	no	—
153	C₂²⋊C₄×C₃₇	—	2	8	no	—
154	C₂²⋊C₄×C₃₇	—	2	8	no	—
155	C₂²⋊C₄×C₃₇	—	2	8	no	—
156	C₂²⋊C₄×C₃₇	—	2	4	no	—
157	C₂²⋊C₄×C₃₇	C₂×D₄	1	8	yes	—
158	C₄²×C₃₇	—	2	8	no	—
159	C₄²×C₃₇	—	2	4	no	—
160	C₄²×C₃₇	C₂×D₄	1	2	yes	—
161	C₄²×C₃₇	C₂⁴	1	2	yes	—
162	C₂³×C₃₇	—	2	4	no	—
163	C₂³×C₃₇	—	2	2	no	—
164	C₂³×C₃₇	—	4	2	no	—
165	C₂³×C₃₇	—	4	2	no	—
166	C₂³×C₃₇	—	4	2	no	—
167	C₂³×C₃₇	—	4	2	no	—
168	C₂³×C₃₇	—	4	2	no	—
169	C₂³×C₃₇	C₂²×D₄	1	4	yes	—
170	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
171	Q₈×C₃₇	—	2	8	no	—
172	Q₈×C₃₇	—	8	2	no	—
173	Q₈×C₃₇	—	8	4	no	—
174	Q₈×C₃₇	—	8	4	no	—
175	D₄×C₃₇	—	2	8	no	—
176	D₄×C₃₇	—	2	4	no	—
177	D₄×C₃₇	—	4	2	no	—
178	D₄×C₃₇	—	8	8	no	—
179	C₂×C₄×C₃₇	—	2	8	no	—
180	C₂×C₄×C₃₇	—	2	2	no	—
181	C₂×C₄×C₃₇	—	2	2	no	—
182	C₂×C₄×C₃₇	—	2	4	no	—
183	C₂×C₄×C₃₇	—	2	4	no	—
184	C₂×C₄×C₃₇	—	2	4	no	—
185	C₂×C₄×C₃₇	—	4	4	no	—
186	C₂×C₄×C₃₇	—	4	2	no	—
187	C₂×C₄×C₃₇	—	4	1	no	—
188	C₂×C₄×C₃₇	—	4	4	no	—
189	C₂×C₄×C₃₇	—	4	2	no	—
190	C₂×C₄×C₃₇	—	4	8	no	—
191	C₂×C₄×C₃₇	—	8	4	no	—
192	C₂×C₄×C₃₇	—	8	4	no	—
193	C₂×C₄×C₃₇	#137	1	4	yes	—
194	C₂×C₄×C₃₇	C₂²×D₄	1	4	yes	—
195	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
199	C₈×C₃₇	—	2	8	no	—
200	#61721	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₂²×C₃₇	—	2	1	no	—
202	C₂²×C₃₇	—	2	1	no	—
203	C₂²×C₃₇	—	2	4	no	—
204	C₂²×C₃₇	—	2	4	no	—
205	C₂²×C₃₇	—	2	4	no	—
206	C₂²×C₃₇	—	4	2	no	—
207	C₂²×C₃₇	—	4	2	no	—
208	C₂²×C₃₇	—	4	2	no	—
209	C₂²×C₃₇	—	8	4	no	—
210	C₂²×C₃₇	—	8	4	no	—
211	C₂²×C₃₇	C₂×#137	1	2	yes	—
212	C₂²×C₃₇	C₂³×D₄	1	1	yes	characteristic
213	C₄×C₃₇	—	2	2	no	—
214	C₄×C₃₇	—	2	1	no	—
215	C₄×C₃₇	—	2	4	no	—
216	C₄×C₃₇	—	4	4	no	—
217	C₄×C₃₇	—	4	4	no	—
218	C₄×C₃₇	—	4	4	no	—
219	C₄×C₃₇	—	4	2	no	—
220	C₄×C₃₇	C₂×#137	1	4	yes	—
221	C₄×C₃₇	#585	1	2	yes	—
222	#3501	C₂×C₃₇	1	1	yes	characteristic, complemented
223	C₂×#555	C₂×C₃₇	1	1	yes	characteristic
224	#3357	C₂×C₃₇	1	8	yes	complemented
225	#3329	C₂×C₃₇	1	8	yes	complemented
226	#3230	C₂×C₃₇	1	2	yes	complemented
227	#3193	C₂×C₃₇	1	4	yes	complemented
228	#3101	C₂×C₃₇	1	2	yes	complemented
229	#3095	C₂×C₃₇	1	4	yes	complemented
230	#2975	C₂×C₃₇	1	1	yes	characteristic, complemented
231	C₂×C₃₇	—	2	2	no	—
232	C₂×C₃₇	—	4	4	no	—
233	C₂×C₃₇	—	8	2	no	—
234	C₂×C₃₇	#3485	1	1	yes	characteristic
235	C₂×C₃₇	C₂²×#137	1	1	yes	characteristic
236	C₂×C₃₇	#3585	1	1	yes	characteristic
237	#555	—	2	4	no	—
238	#555	C₂²×C₃₇	1	8	yes	—
239	#554	—	2	4	no	—
240	#554	C₂²×C₃₇	1	4	yes	complemented
241	D₄×Q₈	C₂²×C₃₇	1	4	yes	complemented
242	#544	—	2	1	no	—
243	#543	—	2	2	no	—
244	#533	C₂²×C₃₇	1	2	yes	—
245	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
246	C₂×#124	—	2	2	no	—
247	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	4	yes	—
248	C₂×#121	—	2	1	no	—
249	C₂×#121	C₂²×C₃₇	1	2	yes	—
250	#518	—	2	1	no	—
251	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
252	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
253	C₂×#117	—	2	1	no	—
254	C₂×#117	C₂²×C₃₇	1	2	yes	—
255	#500	C₂²×C₃₇	1	4	yes	complemented
256	#487	C₂²×C₃₇	1	4	yes	complemented
257	#485	C₂²×C₃₇	1	16	yes	complemented
258	#484	C₂²×C₃₇	1	8	yes	—
259	#483	C₂²×C₃₇	1	4	yes	—
260	#480	C₂²×C₃₇	1	8	yes	complemented
261	#477	C₂²×C₃₇	1	8	yes	complemented
262	#476	C₂²×C₃₇	1	4	yes	complemented
263	#468	C₂²×C₃₇	1	16	yes	complemented
264	#461	C₂²×C₃₇	1	4	yes	complemented
265	#450	C₂²×C₃₇	1	4	yes	—
266	#448	C₂²×C₃₇	1	8	yes	complemented
267	C₄×SD₁₆	C₂²×C₃₇	1	8	yes	complemented
268	#436	C₂²×C₃₇	1	8	yes	complemented
269	#431	C₂²×C₃₇	1	2	yes	—
270	#428	C₂²×C₃₇	1	8	yes	complemented
271	#419	C₂²×C₃₇	1	8	yes	complemented
272	#407	C₂²×C₃₇	1	4	yes	—
273	C₃₇	#61721	1	1	yes	characteristic, direct product factor, Sylow
274	C₂²×Q₈	—	2	1	no	—
275	C₂²×Q₈	C₂³×C₃₇	1	4	yes	—
276	C₂²×D₄	—	2	2	no	—
277	C₂²×D₄	D₄×C₃₇	1	1	yes	characteristic
278	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
279	C₂³×C₄	—	2	1	no	—
280	C₂³×C₄	C₂³×C₃₇	1	2	yes	—
281	C₂×SD₁₆	C₂³×C₃₇	1	8	yes	—
282	C₂×M₁₆	C₂³×C₃₇	1	8	yes	—
283	C₄⋊Q₈	—	2	4	no	—
284	C₄⋊Q₈	—	2	2	no	—
285	C₄⋊Q₈	C₂³×C₃₇	1	2	yes	—
286	C₄⋊Q₈	C₂³×C₃₇	1	4	yes	—
287	C₄⋊Q₈	C₂³×C₃₇	1	2	yes	—
288	#125	—	2	4	no	—
289	#125	—	2	2	no	—
290	#124	—	2	16	no	—
291	C₂²⋊Q₈	—	2	4	no	—
292	C₂²⋊Q₈	—	2	4	no	—
293	C₂²⋊Q₈	—	2	2	no	—
294	C₂²⋊Q₈	—	2	8	no	—
295	C₂²⋊Q₈	—	2	8	no	—
296	C₂²⋊Q₈	C₂³×C₃₇	1	4	yes	—
297	C₂²⋊Q₈	C₂³×C₃₇	1	8	yes	—
298	#121	—	2	8	no	—
299	#121	—	2	4	no	—
300	#121	C₂³×C₃₇	1	8	yes	—
301	C₄×Q₈	—	2	2	no	—
302	C₄×Q₈	C₂³×C₃₇	1	4	yes	—
303	C₄×D₄	—	2	4	no	—
304	C₄×D₄	—	2	4	no	—
305	C₄×D₄	—	2	2	no	—
306	C₄×D₄	D₄×C₃₇	1	4	yes	—
307	C₄×D₄	C₂³×C₃₇	1	4	yes	—
308	C₄×D₄	C₂³×C₃₇	1	4	yes	—
309	#117	—	2	4	no	—
310	#117	—	2	2	no	—
311	#117	—	2	8	no	—
312	#117	C₂³×C₃₇	1	8	yes	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	4	no	—
315	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
316	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
318	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
319	C₂×C₂²⋊C₄	—	2	2	no	—
320	C₂×C₂²⋊C₄	—	2	4	no	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₂²⋊C₄	D₄×C₃₇	1	2	yes	—
324	C₂×C₄²	—	2	2	no	—
325	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
326	#107	C₂³×C₃₇	1	16	yes	—
327	#106	C₂³×C₃₇	1	8	yes	—
328	C₄⋊C₈	C₂³×C₃₇	1	4	yes	—
329	#103	C₂³×C₃₇	1	8	yes	—
330	#103	C₂³×C₃₇	1	16	yes	—
331	#102	C₂³×C₃₇	1	8	yes	—
332	C₂²⋊C₈	C₂³×C₃₇	1	4	yes	—
333	C₂²⋊C₈	C₂³×C₃₇	1	8	yes	—
334	C₄×C₈	C₂³×C₃₇	1	4	yes	—
335	C₂⁴	—	2	1	no	—
336	C₂⁴	C₂×D₄×C₃₇	1	2	yes	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	4	no	—
339	C₂×Q₈	—	2	4	no	—
340	C₂×Q₈	—	4	8	no	—
341	C₂×Q₈	—	8	2	no	—
342	C₂×Q₈	C₂⁴×C₃₇	1	4	yes	—
343	C₂×D₄	—	2	8	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	4	2	no	—
347	C₂×D₄	—	8	4	no	—
348	C₂×D₄	C₂×D₄×C₃₇	1	4	yes	—
349	C₂×D₄	C₂⁴×C₃₇	1	2	yes	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	4	4	no	—
356	C₂²×C₄	—	4	4	no	—
357	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
358	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₃₇	1	4	yes	—
360	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
361	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
362	C₂²×C₄	C₂⁴×C₃₇	1	4	yes	—
363	SD₁₆	—	4	8	no	—
364	M₁₆	—	4	8	no	—
365	C₂×C₈	C₂⁴×C₃₇	1	8	yes	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	8	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
377	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
378	C₄⋊C₄	C₂⁴×C₃₇	1	2	yes	—
379	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
380	C₂²⋊C₄	—	2	4	no	—
381	C₂²⋊C₄	—	2	8	no	—
382	C₂²⋊C₄	—	2	8	no	—
383	C₂²⋊C₄	—	2	8	no	—
384	C₂²⋊C₄	—	2	4	no	—
385	C₂²⋊C₄	C₂×D₄×C₃₇	1	8	yes	—
386	C₄²	—	2	8	no	—
387	C₄²	—	2	4	no	—
388	C₄²	C₂×D₄×C₃₇	1	2	yes	—
389	C₄²	C₂⁴×C₃₇	1	2	yes	—
390	C₂³	—	2	4	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	C₂²×D₄×C₃₇	1	4	yes	—
398	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
399	Q₈	—	2	8	no	—
400	Q₈	—	8	4	no	—
401	Q₈	—	8	4	no	—
402	Q₈	—	8	2	no	—
403	D₄	—	2	8	no	—
404	D₄	—	2	4	no	—
405	D₄	—	4	2	no	—
406	D₄	—	8	8	no	—
407	C₂×C₄	—	2	8	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	8	no	—
419	C₂×C₄	—	8	4	no	—
420	C₂×C₄	—	8	4	no	—
421	C₂×C₄	#137×C₃₇	1	4	yes	—
422	C₂×C₄	C₂²×D₄×C₃₇	1	4	yes	—
423	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
424	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
425	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
426	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
427	C₈	—	2	8	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	8	4	no	—
437	C₂²	—	8	4	no	—
438	C₂²	C₂×#137×C₃₇	1	2	yes	—
439	C₂²	C₂³×D₄×C₃₇	1	1	yes	characteristic
440	C₄	—	2	1	no	—
441	C₄	—	2	4	no	—
442	C₄	—	2	2	no	—
443	C₄	—	4	4	no	—
444	C₄	—	4	2	no	—
445	C₄	—	4	4	no	—
446	C₄	—	4	4	no	—
447	C₄	C₂×#137×C₃₇	1	4	yes	—
448	C₄	C₃₇×#585	1	2	yes	—
449	C₂	—	2	2	no	—
450	C₂	—	4	4	no	—
451	C₂	—	8	2	no	—
452	C₂	C₃₇×#3485	1	1	yes	characteristic
453	C₂	C₂²×#137×C₃₇	1	1	yes	characteristic
454	C₂	C₃₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₇
prime radical	C₂×C₃₇×#555	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂×C₄×D₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×#3501	C₂	semidirect
3. C₃₇×#3357	C₂	semidirect
4. C₃₇×#3329	C₂	semidirect
5. C₃₇×#3230	C₂	semidirect
6. C₃₇×#3193	C₂	semidirect
7. C₃₇×#3101	C₂	semidirect
8. C₃₇×#3095	C₂	semidirect
9. C₃₇×#2975	C₂	semidirect
13. C₃₇×#554	C₂²	semidirect
14. D₄×Q₈×C₃₇	C₂²	semidirect
28. C₃₇×#500	C₂²	semidirect
29. C₃₇×#487	C₂²	semidirect
30. C₃₇×#485	C₂²	semidirect
33. C₃₇×#480	C₂²	semidirect
34. C₃₇×#477	C₂²	semidirect
35. C₃₇×#476	C₂²	semidirect
36. C₃₇×#468	C₂²	semidirect
37. C₃₇×#461	C₂²	semidirect
39. C₃₇×#448	C₂²	semidirect
40. C₄×SD₁₆×C₃₇	C₂²	semidirect
41. C₃₇×#436	C₂²	semidirect
43. C₃₇×#428	C₂²	semidirect
44. C₃₇×#419	C₂²	semidirect
200. #61721	C₃₇	direct (N × H)
222. #3501	C₂×C₃₇	semidirect
224. #3357	C₂×C₃₇	semidirect
225. #3329	C₂×C₃₇	semidirect
226. #3230	C₂×C₃₇	semidirect
227. #3193	C₂×C₃₇	semidirect
228. #3101	C₂×C₃₇	semidirect
229. #3095	C₂×C₃₇	semidirect
230. #2975	C₂×C₃₇	semidirect
240. #554	C₂²×C₃₇	semidirect
241. D₄×Q₈	C₂²×C₃₇	semidirect
255. #500	C₂²×C₃₇	semidirect
256. #487	C₂²×C₃₇	semidirect
257. #485	C₂²×C₃₇	semidirect
260. #480	C₂²×C₃₇	semidirect
261. #477	C₂²×C₃₇	semidirect
262. #476	C₂²×C₃₇	semidirect
263. #468	C₂²×C₃₇	semidirect
264. #461	C₂²×C₃₇	semidirect
266. #448	C₂²×C₃₇	semidirect
267. C₄×SD₁₆	C₂²×C₃₇	semidirect
268. #436	C₂²×C₃₇	semidirect
270. #428	C₂²×C₃₇	semidirect
271. #419	C₂²×C₃₇	semidirect
273. C₃₇	#61721	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×#3501	2
C₂×C₃₇×#555	2
C₃₇×#3357	2
C₃₇×#3329	2
C₃₇×#3230	2
C₃₇×#3193	2
C₃₇×#3101	2
C₃₇×#3095	2
C₃₇×#2975	2
#61721	37

Subgroups — C37×#61721 #22682974

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#61721 #22682974