Subgroups — C₃₇×#18885 #22640138

Order 9472.

888 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3503	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#3249	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#3230	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#3076	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#1649	C₂	1	2	yes	maximal, complemented
6	C₃₇×#1648	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1637	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1636	C₂	1	2	yes	maximal, complemented
9	C₂×C₃₇×#332	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1481	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1477	C₂	1	1	yes	maximal, characteristic
12	Q₈²×C₃₇	—	2	1	no	—
13	C₃₇×#557	C₂²	1	2	yes	—
14	C₃₇×#554	—	2	1	no	—
15	C₃₇×#554	—	2	2	no	—
16	D₄×Q₈×C₃₇	—	2	2	no	—
17	D₄×Q₈×C₃₇	C₂²	1	2	yes	—
18	C₃₇×#544	—	2	2	no	—
19	C₃₇×#544	—	2	1	no	—
20	C₃₇×#533	—	2	1	no	—
21	C₃₇×#533	C₂²	1	1	yes	characteristic
22	C₃₇×#533	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₃₇	—	2	1	no	—
24	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
25	C₃₇×#520	—	2	1	no	—
26	C₄×#41×C₃₇	C₂²	1	1	yes	characteristic
27	C₃₇×#500	C₂²	1	2	yes	—
28	C₃₇×#487	C₂²	1	2	yes	—
29	C₃₇×#484	—	2	2	no	—
30	C₃₇×#479	—	2	1	no	—
31	C₃₇×#478	—	2	1	no	—
32	C₃₇×#477	—	2	2	no	—
33	C₃₇×#477	—	2	1	no	—
34	C₃₇×#477	C₂²	1	1	yes	characteristic
35	C₃₇×#477	C₂²	1	2	yes	—
36	C₃₇×#476	C₂²	1	1	yes	characteristic
37	C₃₇×#475	C₂²	1	1	yes	characteristic
38	C₃₇×#474	C₂²	1	1	yes	characteristic
39	C₃₇×#467	—	2	2	no	—
40	C₃₇×#462	—	2	1	no	—
41	C₃₇×#462	C₂²	1	2	yes	—
42	C₃₇×#431	C₂²	1	1	yes	characteristic
43	C₃₇×#427	—	2	1	no	—
44	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
46	C₃₇×#416	—	2	1	no	—
47	C₃₇×#332	C₂²	1	2	yes	—
48	C₃₇×#332	C₂²	1	2	yes	—
49	C₃₇×Q₈⋊C₈	C₂²	1	2	yes	—
50	C₃₇×Q₈⋊C₈	C₂²	1	2	yes	—
51	C₃₇×Q₈⋊C₈	C₂²	1	2	yes	—
52	C₃₇×D₄⋊C₈	C₂²	1	2	yes	—
53	C₂×#41×C₃₇	D₄	1	1	yes	characteristic
54	C₂²×Q₈×C₃₇	—	2	2	no	—
55	C₂²×Q₈×C₃₇	—	2	1	no	—
56	C₂×Q₁₆×C₃₇	—	2	2	no	—
57	C₂²×C₈×C₃₇	—	2	1	no	—
58	C₂²×C₈×C₃₇	—	2	1	no	—
59	C₄⋊Q₈×C₃₇	—	2	2	no	—
60	C₄⋊Q₈×C₃₇	—	2	2	no	—
61	C₄⋊Q₈×C₃₇	—	2	4	no	—
62	C₄⋊Q₈×C₃₇	—	2	2	no	—
63	C₄⋊Q₈×C₃₇	—	2	2	no	—
64	C₄⋊Q₈×C₃₇	—	2	1	no	—
65	C₄⋊Q₈×C₃₇	—	2	1	no	—
66	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
67	C₄⋊Q₈×C₃₇	D₄	1	2	yes	—
68	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
69	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
70	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
71	C₄⋊Q₈×C₃₇	C₂³	1	2	yes	—
72	#125×C₃₇	—	2	2	no	—
73	#125×C₃₇	—	2	4	no	—
74	#125×C₃₇	—	2	2	no	—
75	#125×C₃₇	—	2	1	no	—
76	#125×C₃₇	—	2	1	no	—
77	C₂²⋊Q₈×C₃₇	—	2	2	no	—
78	C₂²⋊Q₈×C₃₇	—	2	4	no	—
79	C₂²⋊Q₈×C₃₇	—	2	4	no	—
80	C₂²⋊Q₈×C₃₇	—	2	1	no	—
81	C₂²⋊Q₈×C₃₇	—	2	2	no	—
82	C₂²⋊Q₈×C₃₇	—	2	4	no	—
83	C₂²⋊Q₈×C₃₇	—	2	1	no	—
84	C₂²⋊Q₈×C₃₇	—	2	1	no	—
85	C₂²⋊Q₈×C₃₇	D₄	1	2	yes	—
86	C₄×Q₈×C₃₇	—	2	2	no	—
87	C₄×Q₈×C₃₇	—	2	2	no	—
88	C₄×Q₈×C₃₇	—	2	2	no	—
89	C₄×Q₈×C₃₇	—	2	1	no	—
90	C₄×Q₈×C₃₇	—	2	1	no	—
91	C₄×Q₈×C₃₇	—	2	1	no	—
92	C₄×Q₈×C₃₇	D₄	1	1	yes	characteristic
93	C₄×Q₈×C₃₇	C₂³	1	2	yes	—
94	C₄×Q₈×C₃₇	C₂³	1	1	yes	characteristic
95	C₄×D₄×C₃₇	—	2	4	no	—
96	C₄×D₄×C₃₇	—	2	2	no	—
97	C₄×D₄×C₃₇	—	2	1	no	—
98	C₄×D₄×C₃₇	—	2	1	no	—
99	C₄×D₄×C₃₇	D₄	1	1	yes	characteristic
100	C₄×D₄×C₃₇	C₂³	1	1	yes	characteristic
101	#117×C₃₇	—	2	2	no	—
102	#117×C₃₇	—	2	1	no	—
103	#117×C₃₇	—	2	1	no	—
104	#117×C₃₇	—	2	1	no	—
105	#117×C₃₇	D₄	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
107	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
108	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
109	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
110	C₂×C₄²×C₃₇	—	2	1	no	—
111	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
112	#107×C₃₇	—	2	1	no	—
113	#107×C₃₇	—	2	1	no	—
114	#107×C₃₇	—	2	2	no	—
115	#107×C₃₇	—	2	4	no	—
116	#106×C₃₇	—	2	1	no	—
117	#106×C₃₇	—	2	1	no	—
118	C₄⋊C₈×C₃₇	—	2	1	no	—
119	C₄⋊C₈×C₃₇	—	2	1	no	—
120	C₄⋊C₈×C₃₇	—	2	1	no	—
121	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
122	C₄⋊C₈×C₃₇	C₂³	1	1	yes	characteristic
123	C₄⋊C₈×C₃₇	C₂³	1	1	yes	characteristic
124	#103×C₃₇	—	2	1	no	—
125	#103×C₃₇	—	2	1	no	—
126	#103×C₃₇	—	2	2	no	—
127	#103×C₃₇	—	2	2	no	—
128	#103×C₃₇	—	2	4	no	—
129	#102×C₃₇	—	2	1	no	—
130	#102×C₃₇	—	2	1	no	—
131	C₂²⋊C₈×C₃₇	—	2	1	no	—
132	C₄×C₈×C₃₇	C₂³	1	2	yes	—
133	#41×C₃₇	—	2	2	no	—
134	#41×C₃₇	Q₁₆	1	4	yes	complemented
135	C₂×Q₈×C₃₇	—	2	4	no	—
136	C₂×Q₈×C₃₇	—	2	1	no	—
137	C₂×Q₈×C₃₇	—	2	2	no	—
138	C₂×Q₈×C₃₇	—	2	2	no	—
139	C₂×Q₈×C₃₇	—	2	1	no	—
140	C₂×Q₈×C₃₇	—	2	1	no	—
141	C₂×Q₈×C₃₇	—	8	1	no	—
142	C₂×Q₈×C₃₇	—	8	1	no	—
143	C₂×Q₈×C₃₇	—	8	2	no	—
144	C₂×Q₈×C₃₇	—	8	2	no	—
145	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
146	C₂×Q₈×C₃₇	C₂×D₄	1	1	yes	characteristic
147	C₂×D₄×C₃₇	—	2	1	no	—
148	C₂×D₄×C₃₇	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₃₇	—	2	1	no	—
150	C₂²×C₄×C₃₇	—	2	4	no	—
151	C₂²×C₄×C₃₇	—	2	2	no	—
152	C₂²×C₄×C₃₇	—	2	1	no	—
153	C₂²×C₄×C₃₇	—	2	1	no	—
154	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
157	Q₁₆×C₃₇	—	8	2	no	—
158	C₂×C₈×C₃₇	—	2	2	no	—
159	C₂×C₈×C₃₇	—	2	1	no	—
160	C₂×C₈×C₃₇	—	2	1	no	—
161	C₂×C₈×C₃₇	—	2	2	no	—
162	C₂×C₈×C₃₇	—	4	2	no	—
163	C₂×C₈×C₃₇	—	8	1	no	—
164	C₄⋊C₄×C₃₇	—	2	4	no	—
165	C₄⋊C₄×C₃₇	—	2	4	no	—
166	C₄⋊C₄×C₃₇	—	2	4	no	—
167	C₄⋊C₄×C₃₇	—	2	4	no	—
168	C₄⋊C₄×C₃₇	—	2	1	no	—
169	C₄⋊C₄×C₃₇	—	2	2	no	—
170	C₄⋊C₄×C₃₇	—	2	1	no	—
171	C₄⋊C₄×C₃₇	—	2	2	no	—
172	C₄⋊C₄×C₃₇	—	2	1	no	—
173	C₄⋊C₄×C₃₇	—	2	1	no	—
174	C₄⋊C₄×C₃₇	—	2	2	no	—
175	C₄⋊C₄×C₃₇	—	2	2	no	—
176	C₄⋊C₄×C₃₇	—	2	1	no	—
177	C₄⋊C₄×C₃₇	—	2	2	no	—
178	C₄⋊C₄×C₃₇	—	2	1	no	—
179	C₄⋊C₄×C₃₇	—	2	1	no	—
180	C₄⋊C₄×C₃₇	—	2	1	no	—
181	C₄⋊C₄×C₃₇	—	2	1	no	—
182	C₄⋊C₄×C₃₇	—	4	1	no	—
183	C₄⋊C₄×C₃₇	—	4	1	no	—
184	C₄⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
185	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
186	C₄⋊C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
187	C₄⋊C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
188	C₂²⋊C₄×C₃₇	—	2	4	no	—
189	C₂²⋊C₄×C₃₇	—	2	2	no	—
190	C₂²⋊C₄×C₃₇	—	2	1	no	—
191	C₂²⋊C₄×C₃₇	—	2	1	no	—
192	C₂²⋊C₄×C₃₇	—	2	1	no	—
193	C₂²⋊C₄×C₃₇	—	4	1	no	—
194	C₄²×C₃₇	—	2	4	no	—
195	C₄²×C₃₇	—	2	1	no	—
196	C₄²×C₃₇	—	2	1	no	—
197	C₄²×C₃₇	—	2	1	no	—
198	C₄²×C₃₇	—	2	2	no	—
199	C₄²×C₃₇	—	4	1	no	—
200	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
201	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
202	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
204	C₂³×C₃₇	—	2	1	no	—
205	C₂³×C₃₇	#120	1	1	yes	characteristic
206	Q₈×C₃₇	—	2	1	no	—
207	Q₈×C₃₇	—	2	2	no	—
208	Q₈×C₃₇	—	2	2	no	—
209	Q₈×C₃₇	—	4	2	no	—
210	Q₈×C₃₇	—	4	2	no	—
211	Q₈×C₃₇	—	4	2	no	—
212	Q₈×C₃₇	—	4	2	no	—
213	Q₈×C₃₇	—	4	1	no	—
214	Q₈×C₃₇	—	4	1	no	—
215	Q₈×C₃₇	—	8	2	no	—
216	Q₈×C₃₇	—	8	4	no	—
217	Q₈×C₃₇	C₂×Q₁₆	1	2	yes	—
218	D₄×C₃₇	—	2	4	no	—
219	D₄×C₃₇	—	2	1	no	—
220	D₄×C₃₇	C₂×Q₁₆	1	2	yes	—
221	C₂×C₄×C₃₇	—	2	1	no	—
222	C₂×C₄×C₃₇	—	2	1	no	—
223	C₂×C₄×C₃₇	—	2	1	no	—
224	C₂×C₄×C₃₇	—	2	4	no	—
225	C₂×C₄×C₃₇	—	2	2	no	—
226	C₂×C₄×C₃₇	—	2	1	no	—
227	C₂×C₄×C₃₇	—	2	1	no	—
228	C₂×C₄×C₃₇	—	2	2	no	—
229	C₂×C₄×C₃₇	—	2	4	no	—
230	C₂×C₄×C₃₇	—	4	1	no	—
231	C₂×C₄×C₃₇	—	4	2	no	—
232	C₂×C₄×C₃₇	—	4	1	no	—
233	C₂×C₄×C₃₇	—	4	1	no	—
234	C₂×C₄×C₃₇	—	4	1	no	—
235	C₂×C₄×C₃₇	—	4	1	no	—
236	C₂×C₄×C₃₇	—	8	2	no	—
237	C₂×C₄×C₃₇	—	8	4	no	—
238	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
239	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
240	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
241	C₂×C₄×C₃₇	C₂×Q₁₆	1	2	yes	—
242	C₂×C₄×C₃₇	#137	1	2	yes	—
243	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
246	C₈×C₃₇	—	4	2	no	—
247	C₈×C₃₇	—	4	1	no	—
248	C₈×C₃₇	—	4	1	no	—
249	C₈×C₃₇	—	4	2	no	—
250	#18885	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
251	C₂²×C₃₇	—	2	1	no	—
252	C₂²×C₃₇	—	2	1	no	—
253	C₂²×C₃₇	—	2	2	no	—
254	C₂²×C₃₇	—	4	1	no	—
255	C₂²×C₃₇	—	4	1	no	—
256	C₂²×C₃₇	#451	1	2	yes	—
257	C₂²×C₃₇	C₂×#120	1	1	yes	characteristic
258	C₄×C₃₇	—	2	2	no	—
259	C₄×C₃₇	—	2	1	no	—
260	C₄×C₃₇	—	2	1	no	—
261	C₄×C₃₇	—	2	1	no	—
262	C₄×C₃₇	—	4	1	no	—
263	C₄×C₃₇	—	4	2	no	—
264	C₄×C₃₇	—	4	4	no	—
265	C₄×C₃₇	—	4	1	no	—
266	C₄×C₃₇	—	4	2	no	—
267	C₄×C₃₇	—	8	1	no	—
268	C₄×C₃₇	—	8	1	no	—
269	C₄×C₃₇	#451	1	2	yes	—
270	C₄×C₃₇	C₂²×Q₁₆	1	1	yes	characteristic
271	C₄×C₃₇	C₂×#137	1	1	yes	characteristic
272	C₄×C₃₇	#576	1	1	yes	characteristic
273	C₄×C₃₇	#577	1	1	yes	characteristic
274	#3503	C₂×C₃₇	1	1	yes	characteristic
275	#3249	C₂×C₃₇	1	1	yes	characteristic, complemented
276	#3230	C₂×C₃₇	1	1	yes	characteristic, complemented
277	#3076	C₂×C₃₇	1	1	yes	characteristic
278	#1649	C₂×C₃₇	1	2	yes	complemented
279	#1648	C₂×C₃₇	1	2	yes	complemented
280	#1637	C₂×C₃₇	1	2	yes	complemented
281	#1636	C₂×C₃₇	1	2	yes	complemented
282	C₂×#332	C₂×C₃₇	1	1	yes	characteristic, complemented
283	#1481	C₂×C₃₇	1	1	yes	characteristic, complemented
284	#1477	C₂×C₃₇	1	1	yes	characteristic
285	C₂×C₃₇	—	2	2	no	—
286	C₂×C₃₇	—	4	2	no	—
287	C₂×C₃₇	C₂×#451	1	1	yes	characteristic
288	C₂×C₃₇	#3012	1	1	yes	characteristic
289	C₂×C₃₇	#3020	1	1	yes	characteristic
290	Q₈²	—	2	1	no	—
291	#557	C₂²×C₃₇	1	2	yes	—
292	#554	—	2	1	no	—
293	#554	—	2	2	no	—
294	D₄×Q₈	—	2	2	no	—
295	D₄×Q₈	C₂²×C₃₇	1	2	yes	—
296	#544	—	2	2	no	—
297	#544	—	2	1	no	—
298	#533	—	2	1	no	—
299	#533	C₂²×C₃₇	1	1	yes	characteristic
300	#533	C₂²×C₃₇	1	1	yes	characteristic
301	C₂×C₄⋊Q₈	—	2	1	no	—
302	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
303	#520	—	2	1	no	—
304	C₄×#41	C₂²×C₃₇	1	1	yes	characteristic
305	#500	C₂²×C₃₇	1	2	yes	—
306	#487	C₂²×C₃₇	1	2	yes	—
307	#484	—	2	2	no	—
308	#479	—	2	1	no	—
309	#478	—	2	1	no	—
310	#477	—	2	2	no	—
311	#477	—	2	1	no	—
312	#477	C₂²×C₃₇	1	1	yes	characteristic
313	#477	C₂²×C₃₇	1	2	yes	—
314	#476	C₂²×C₃₇	1	1	yes	characteristic
315	#475	C₂²×C₃₇	1	1	yes	characteristic
316	#474	C₂²×C₃₇	1	1	yes	characteristic
317	#467	—	2	2	no	—
318	#462	—	2	1	no	—
319	#462	C₂²×C₃₇	1	2	yes	—
320	#431	C₂²×C₃₇	1	1	yes	characteristic
321	#427	—	2	1	no	—
322	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
323	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
324	#416	—	2	1	no	—
325	#332	C₂²×C₃₇	1	2	yes	—
326	#332	C₂²×C₃₇	1	2	yes	—
327	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	—
328	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	—
329	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	—
330	D₄⋊C₈	C₂²×C₃₇	1	2	yes	—
331	C₃₇	#18885	1	1	yes	characteristic, direct product factor, Sylow
332	C₂×#41	D₄×C₃₇	1	1	yes	characteristic
333	C₂²×Q₈	—	2	2	no	—
334	C₂²×Q₈	—	2	1	no	—
335	C₂×Q₁₆	—	2	2	no	—
336	C₂²×C₈	—	2	1	no	—
337	C₂²×C₈	—	2	1	no	—
338	C₄⋊Q₈	—	2	2	no	—
339	C₄⋊Q₈	—	2	2	no	—
340	C₄⋊Q₈	—	2	4	no	—
341	C₄⋊Q₈	—	2	2	no	—
342	C₄⋊Q₈	—	2	2	no	—
343	C₄⋊Q₈	—	2	1	no	—
344	C₄⋊Q₈	—	2	1	no	—
345	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
346	C₄⋊Q₈	D₄×C₃₇	1	2	yes	—
347	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
348	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
349	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
350	C₄⋊Q₈	C₂³×C₃₇	1	2	yes	—
351	#125	—	2	2	no	—
352	#125	—	2	4	no	—
353	#125	—	2	2	no	—
354	#125	—	2	1	no	—
355	#125	—	2	1	no	—
356	C₂²⋊Q₈	—	2	2	no	—
357	C₂²⋊Q₈	—	2	4	no	—
358	C₂²⋊Q₈	—	2	4	no	—
359	C₂²⋊Q₈	—	2	1	no	—
360	C₂²⋊Q₈	—	2	2	no	—
361	C₂²⋊Q₈	—	2	4	no	—
362	C₂²⋊Q₈	—	2	1	no	—
363	C₂²⋊Q₈	—	2	1	no	—
364	C₂²⋊Q₈	D₄×C₃₇	1	2	yes	—
365	C₄×Q₈	—	2	2	no	—
366	C₄×Q₈	—	2	2	no	—
367	C₄×Q₈	—	2	2	no	—
368	C₄×Q₈	—	2	1	no	—
369	C₄×Q₈	—	2	1	no	—
370	C₄×Q₈	—	2	1	no	—
371	C₄×Q₈	D₄×C₃₇	1	1	yes	characteristic
372	C₄×Q₈	C₂³×C₃₇	1	1	yes	characteristic
373	C₄×Q₈	C₂³×C₃₇	1	2	yes	—
374	C₄×D₄	—	2	4	no	—
375	C₄×D₄	—	2	2	no	—
376	C₄×D₄	—	2	1	no	—
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	D₄×C₃₇	1	1	yes	characteristic
379	C₄×D₄	C₂³×C₃₇	1	1	yes	characteristic
380	#117	—	2	2	no	—
381	#117	—	2	1	no	—
382	#117	—	2	1	no	—
383	#117	—	2	1	no	—
384	#117	D₄×C₃₇	1	1	yes	characteristic
385	C₂×C₄⋊C₄	—	2	2	no	—
386	C₂×C₄⋊C₄	—	2	2	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
389	C₂×C₄²	—	2	1	no	—
390	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
391	#107	—	2	1	no	—
392	#107	—	2	1	no	—
393	#107	—	2	2	no	—
394	#107	—	2	4	no	—
395	#106	—	2	1	no	—
396	#106	—	2	1	no	—
397	C₄⋊C₈	—	2	1	no	—
398	C₄⋊C₈	—	2	1	no	—
399	C₄⋊C₈	—	2	1	no	—
400	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
401	C₄⋊C₈	C₂³×C₃₇	1	1	yes	characteristic
402	C₄⋊C₈	C₂³×C₃₇	1	1	yes	characteristic
403	#103	—	2	1	no	—
404	#103	—	2	1	no	—
405	#103	—	2	2	no	—
406	#103	—	2	2	no	—
407	#103	—	2	4	no	—
408	#102	—	2	1	no	—
409	#102	—	2	1	no	—
410	C₂²⋊C₈	—	2	1	no	—
411	C₄×C₈	C₂³×C₃₇	1	2	yes	—
412	#41	—	2	2	no	—
413	#41	Q₁₆×C₃₇	1	4	yes	complemented
414	C₂×Q₈	—	2	4	no	—
415	C₂×Q₈	—	2	1	no	—
416	C₂×Q₈	—	2	2	no	—
417	C₂×Q₈	—	2	2	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	—	8	1	no	—
421	C₂×Q₈	—	8	1	no	—
422	C₂×Q₈	—	8	2	no	—
423	C₂×Q₈	—	8	2	no	—
424	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
425	C₂×Q₈	C₂×D₄×C₃₇	1	1	yes	characteristic
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	C₂×D₄×C₃₇	1	1	yes	characteristic
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
436	Q₁₆	—	8	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	4	2	no	—
442	C₂×C₈	—	8	1	no	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	—	2	4	no	—
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	4	1	no	—
462	C₄⋊C₄	—	4	1	no	—
463	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
464	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
465	C₄⋊C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
466	C₄⋊C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
467	C₂²⋊C₄	—	2	4	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	2	1	no	—
470	C₂²⋊C₄	—	2	1	no	—
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	4	1	no	—
473	C₄²	—	2	4	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	2	no	—
478	C₄²	—	4	1	no	—
479	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
480	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
481	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
482	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
483	C₂³	—	2	1	no	—
484	C₂³	#120×C₃₇	1	1	yes	characteristic
485	Q₈	—	2	1	no	—
486	Q₈	—	2	2	no	—
487	Q₈	—	2	2	no	—
488	Q₈	—	4	2	no	—
489	Q₈	—	4	2	no	—
490	Q₈	—	4	2	no	—
491	Q₈	—	4	2	no	—
492	Q₈	—	4	1	no	—
493	Q₈	—	4	1	no	—
494	Q₈	—	8	2	no	—
495	Q₈	—	8	4	no	—
496	Q₈	C₂×Q₁₆×C₃₇	1	2	yes	—
497	D₄	—	2	4	no	—
498	D₄	—	2	1	no	—
499	D₄	C₂×Q₁₆×C₃₇	1	2	yes	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	8	2	no	—
516	C₂×C₄	—	8	4	no	—
517	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
518	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
519	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
520	C₂×C₄	C₂×Q₁₆×C₃₇	1	2	yes	—
521	C₂×C₄	#137×C₃₇	1	2	yes	—
522	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
523	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
524	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
525	C₈	—	4	2	no	—
526	C₈	—	4	1	no	—
527	C₈	—	4	1	no	—
528	C₈	—	4	2	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	4	1	no	—
534	C₂²	C₃₇×#451	1	2	yes	—
535	C₂²	C₂×#120×C₃₇	1	1	yes	characteristic
536	C₄	—	2	2	no	—
537	C₄	—	2	1	no	—
538	C₄	—	2	1	no	—
539	C₄	—	2	1	no	—
540	C₄	—	4	1	no	—
541	C₄	—	4	2	no	—
542	C₄	—	4	4	no	—
543	C₄	—	4	1	no	—
544	C₄	—	4	2	no	—
545	C₄	—	8	1	no	—
546	C₄	—	8	1	no	—
547	C₄	C₃₇×#451	1	2	yes	—
548	C₄	C₂²×Q₁₆×C₃₇	1	1	yes	characteristic
549	C₄	C₂×#137×C₃₇	1	1	yes	characteristic
550	C₄	C₃₇×#576	1	1	yes	characteristic
551	C₄	C₃₇×#577	1	1	yes	characteristic
552	C₂	—	2	2	no	—
553	C₂	—	4	2	no	—
554	C₂	C₂×C₃₇×#451	1	1	yes	characteristic
555	C₂	C₃₇×#3012	1	1	yes	characteristic
556	C₂	C₃₇×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₇
prime radical	C₂×#41×C₃₇	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₇×#3249	C₂	semidirect
3. C₃₇×#3230	C₂	semidirect
5. C₃₇×#1649	C₂	semidirect
6. C₃₇×#1648	C₂	semidirect
7. C₃₇×#1637	C₂	semidirect
8. C₃₇×#1636	C₂	semidirect
9. C₂×C₃₇×#332	C₂	semidirect
10. C₃₇×#1481	C₂	semidirect
134. #41×C₃₇	Q₁₆	semidirect
250. #18885	C₃₇	direct (N × H)
275. #3249	C₂×C₃₇	semidirect
276. #3230	C₂×C₃₇	semidirect
278. #1649	C₂×C₃₇	semidirect
279. #1648	C₂×C₃₇	semidirect
280. #1637	C₂×C₃₇	semidirect
281. #1636	C₂×C₃₇	semidirect
282. C₂×#332	C₂×C₃₇	semidirect
283. #1481	C₂×C₃₇	semidirect
331. C₃₇	#18885	direct (N × H)
413. #41	Q₁₆×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₃₇×#3503	2
C₃₇×#3249	2
C₃₇×#3230	2
C₃₇×#3076	2
C₃₇×#1649	2
C₃₇×#1648	2
C₃₇×#1637	2
C₃₇×#1636	2
C₂×C₃₇×#332	2
C₃₇×#1481	2
C₃₇×#1477	2
#18885	37

Subgroups — C37×#18885 #22640138

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#18885 #22640138