Subgroups — C₃₇×#18928 #22640181

Order 9472.

966 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3506	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#3229	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#3226	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₇×#461	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#1654	C₂	1	4	yes	maximal, complemented
6	C₃₇×#1646	C₂	1	4	yes	maximal, complemented
7	C₃₇×#1542	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1480	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1478	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₃₇	—	2	1	no	—
11	C₃₇×#559	—	2	2	no	—
12	C₃₇×#556	—	2	1	no	—
13	C₃₇×#555	C₂²	1	2	yes	—
14	C₃₇×#553	—	2	2	no	—
15	C₃₇×#550	—	2	1	no	—
16	C₃₇×#547	C₂²	1	2	yes	—
17	C₃₇×#538	—	2	2	no	—
18	C₃₇×#535	—	2	1	no	—
19	C₃₇×#533	C₂²	1	1	yes	characteristic
20	C₃₇×#532	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
22	C₃₇×#525	—	2	2	no	—
23	C₃₇×#520	—	2	1	no	—
24	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
25	C₃₇×#500	—	2	1	no	—
26	C₃₇×#498	C₂²	1	2	yes	complemented
27	C₃₇×#487	C₂²	1	2	yes	complemented
28	C₃₇×#486	—	2	1	no	—
29	C₃₇×#483	—	2	2	no	—
30	C₃₇×#480	—	2	2	no	—
31	C₃₇×#475	—	2	2	no	—
32	C₃₇×#474	C₂²	1	4	yes	complemented
33	C₃₇×#461	—	2	2	no	—
34	C₃₇×#461	C₂²	1	4	yes	—
35	C₃₇×#431	C₂²	1	1	yes	characteristic
36	C₃₇×#431	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
38	C₂×#103×C₃₇	—	2	1	no	—
39	C₃₇×#333	C₂²	1	2	yes	complemented
40	C₃₇×#332	C₂²	1	2	yes	complemented
41	C₃₇×D₄⋊C₈	C₂²	1	4	yes	—
42	C₃₇×D₄⋊C₈	C₂²	1	4	yes	complemented
43	C₂×#41×C₃₇	—	2	2	no	—
44	C₂×#41×C₃₇	—	2	1	no	—
45	C₂²×Q₈×C₃₇	—	2	1	no	—
46	C₂²×D₄×C₃₇	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₃₇	—	2	1	no	—
48	C₂×SD₁₆×C₃₇	—	2	4	no	—
49	C₂×SD₁₆×C₃₇	—	4	4	no	—
50	C₂²×C₈×C₃₇	—	2	1	no	—
51	C₄⋊Q₈×C₃₇	—	2	1	no	—
52	C₄⋊Q₈×C₃₇	—	2	1	no	—
53	C₄⋊Q₈×C₃₇	—	2	1	no	—
54	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
55	C₄⋊Q₈×C₃₇	C₂³	1	2	yes	—
56	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
57	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
58	#127×C₃₇	—	2	2	no	—
59	#127×C₃₇	D₄	1	1	yes	characteristic
60	#126×C₃₇	—	2	4	no	—
61	#125×C₃₇	—	2	1	no	—
62	#124×C₃₇	—	2	2	no	—
63	#124×C₃₇	—	2	4	no	—
64	#124×C₃₇	—	2	1	no	—
65	#123×C₃₇	—	2	4	no	—
66	#123×C₃₇	—	2	4	no	—
67	C₂²⋊Q₈×C₃₇	—	2	1	no	—
68	C₂²⋊Q₈×C₃₇	—	2	2	no	—
69	C₂²⋊Q₈×C₃₇	D₄	1	2	yes	—
70	#121×C₃₇	—	2	4	no	—
71	#121×C₃₇	—	2	2	no	—
72	#121×C₃₇	—	2	2	no	—
73	#121×C₃₇	—	2	2	no	—
74	#121×C₃₇	—	2	1	no	—
75	#121×C₃₇	D₄	1	2	yes	—
76	#120×C₃₇	—	2	4	no	—
77	C₄×Q₈×C₃₇	—	2	2	no	—
78	C₄×Q₈×C₃₇	—	2	1	no	—
79	C₄×Q₈×C₃₇	D₄	1	2	yes	—
80	C₄×D₄×C₃₇	—	2	4	no	—
81	C₄×D₄×C₃₇	—	2	2	no	—
82	C₄×D₄×C₃₇	—	2	4	no	—
83	C₄×D₄×C₃₇	—	2	1	no	—
84	C₄×D₄×C₃₇	—	2	1	no	—
85	C₄×D₄×C₃₇	—	2	1	no	—
86	C₄×D₄×C₃₇	D₄	1	2	yes	—
87	C₄×D₄×C₃₇	C₂³	1	2	yes	—
88	C₄×D₄×C₃₇	C₂³	1	2	yes	—
89	#117×C₃₇	—	2	1	no	—
90	#117×C₃₇	—	2	2	no	—
91	#117×C₃₇	—	2	2	no	—
92	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
93	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
94	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
95	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
97	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
98	#107×C₃₇	—	2	4	no	—
99	#106×C₃₇	—	2	4	no	—
100	C₄⋊C₈×C₃₇	—	2	1	no	—
101	C₄⋊C₈×C₃₇	—	2	1	no	—
102	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
103	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
104	#103×C₃₇	—	2	4	no	—
105	#103×C₃₇	—	2	4	no	—
106	#102×C₃₇	—	2	4	no	—
107	C₂²⋊C₈×C₃₇	—	2	1	no	—
108	C₂²⋊C₈×C₃₇	—	2	1	no	—
109	C₄×C₈×C₃₇	—	2	1	no	—
110	C₄×C₈×C₃₇	C₂³	1	2	yes	—
111	C₂⁴×C₃₇	—	2	1	no	—
112	#41×C₃₇	—	4	2	no	—
113	#41×C₃₇	—	4	2	no	—
114	#41×C₃₇	—	8	4	no	—
115	C₂×Q₈×C₃₇	—	2	1	no	—
116	C₂×Q₈×C₃₇	—	2	1	no	—
117	C₂×Q₈×C₃₇	—	2	2	no	—
118	C₂×Q₈×C₃₇	—	4	1	no	—
119	C₂×Q₈×C₃₇	—	4	2	no	—
120	C₂×Q₈×C₃₇	—	4	2	no	—
121	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
122	C₂×D₄×C₃₇	—	2	2	no	—
123	C₂×D₄×C₃₇	—	2	4	no	—
124	C₂×D₄×C₃₇	—	2	4	no	—
125	C₂×D₄×C₃₇	—	2	1	no	—
126	C₂×D₄×C₃₇	—	2	1	no	—
127	C₂×D₄×C₃₇	—	2	1	no	—
128	C₂×D₄×C₃₇	—	2	2	no	—
129	C₂×D₄×C₃₇	—	2	2	no	—
130	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
131	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₃₇	—	2	4	no	—
133	C₂²×C₄×C₃₇	—	2	1	no	—
134	C₂²×C₄×C₃₇	—	2	2	no	—
135	C₂²×C₄×C₃₇	—	2	2	no	—
136	C₂²×C₄×C₃₇	—	2	2	no	—
137	C₂²×C₄×C₃₇	—	4	1	no	—
138	C₂²×C₄×C₃₇	—	8	2	no	—
139	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
142	SD₁₆×C₃₇	—	4	8	no	—
143	C₂×C₈×C₃₇	—	2	2	no	—
144	C₂×C₈×C₃₇	—	2	2	no	—
145	C₂×C₈×C₃₇	—	2	2	no	—
146	C₂×C₈×C₃₇	—	4	2	no	—
147	C₄⋊C₄×C₃₇	—	2	4	no	—
148	C₄⋊C₄×C₃₇	—	2	1	no	—
149	C₄⋊C₄×C₃₇	—	2	2	no	—
150	C₄⋊C₄×C₃₇	—	2	1	no	—
151	C₄⋊C₄×C₃₇	—	2	2	no	—
152	C₄⋊C₄×C₃₇	—	2	1	no	—
153	C₄⋊C₄×C₃₇	—	2	1	no	—
154	C₄⋊C₄×C₃₇	—	2	1	no	—
155	C₄⋊C₄×C₃₇	—	2	2	no	—
156	C₄⋊C₄×C₃₇	—	2	2	no	—
157	C₄⋊C₄×C₃₇	—	4	1	no	—
158	C₄⋊C₄×C₃₇	—	4	1	no	—
159	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
160	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
161	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
162	C₂²⋊C₄×C₃₇	—	2	4	no	—
163	C₂²⋊C₄×C₃₇	—	2	4	no	—
164	C₂²⋊C₄×C₃₇	—	2	4	no	—
165	C₂²⋊C₄×C₃₇	—	2	2	no	—
166	C₂²⋊C₄×C₃₇	—	2	2	no	—
167	C₂²⋊C₄×C₃₇	—	2	2	no	—
168	C₂²⋊C₄×C₃₇	—	2	2	no	—
169	C₂²⋊C₄×C₃₇	—	2	2	no	—
170	C₄²×C₃₇	—	2	4	no	—
171	C₄²×C₃₇	—	2	2	no	—
172	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
176	C₂³×C₃₇	—	2	2	no	—
177	C₂³×C₃₇	—	2	2	no	—
178	C₂³×C₃₇	—	4	2	no	—
179	C₂³×C₃₇	—	8	1	no	—
180	C₂³×C₃₇	—	8	1	no	—
181	C₂³×C₃₇	#120	1	1	yes	characteristic
182	Q₈×C₃₇	—	4	2	no	—
183	Q₈×C₃₇	—	4	2	no	—
184	Q₈×C₃₇	—	4	2	no	—
185	Q₈×C₃₇	—	4	2	no	—
186	Q₈×C₃₇	—	4	2	no	—
187	Q₈×C₃₇	—	8	2	no	—
188	D₄×C₃₇	—	2	2	no	—
189	D₄×C₃₇	—	2	2	no	—
190	D₄×C₃₇	—	2	4	no	—
191	D₄×C₃₇	—	4	4	no	—
192	D₄×C₃₇	—	4	2	no	—
193	D₄×C₃₇	—	4	2	no	—
194	D₄×C₃₇	—	8	1	no	—
195	D₄×C₃₇	—	8	4	no	—
196	D₄×C₃₇	—	8	4	no	—
197	C₂×C₄×C₃₇	—	2	2	no	—
198	C₂×C₄×C₃₇	—	2	2	no	—
199	C₂×C₄×C₃₇	—	2	2	no	—
200	C₂×C₄×C₃₇	—	2	2	no	—
201	C₂×C₄×C₃₇	—	2	2	no	—
202	C₂×C₄×C₃₇	—	4	1	no	—
203	C₂×C₄×C₃₇	—	4	2	no	—
204	C₂×C₄×C₃₇	—	4	2	no	—
205	C₂×C₄×C₃₇	—	4	4	no	—
206	C₂×C₄×C₃₇	—	4	2	no	—
207	C₂×C₄×C₃₇	—	8	2	no	—
208	C₂×C₄×C₃₇	—	8	1	no	—
209	C₂×C₄×C₃₇	—	8	4	no	—
210	C₂×C₄×C₃₇	—	8	2	no	—
211	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
212	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
213	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
214	C₂×C₄×C₃₇	#135	1	2	yes	—
215	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
216	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
219	C₈×C₃₇	—	4	2	no	—
220	C₈×C₃₇	—	4	2	no	—
221	C₈×C₃₇	—	4	2	no	—
222	#18928	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
223	C₂²×C₃₇	—	2	1	no	—
224	C₂²×C₃₇	—	2	1	no	—
225	C₂²×C₃₇	—	4	2	no	—
226	C₂²×C₃₇	—	4	2	no	—
227	C₂²×C₃₇	—	4	2	no	—
228	C₂²×C₃₇	—	4	2	no	—
229	C₂²×C₃₇	—	4	2	no	—
230	C₂²×C₃₇	—	4	2	no	—
231	C₂²×C₃₇	—	8	4	no	—
232	C₂²×C₃₇	#449	1	2	yes	—
233	C₂²×C₃₇	C₂×#120	1	1	yes	characteristic
234	C₄×C₃₇	—	2	1	no	—
235	C₄×C₃₇	—	2	1	no	—
236	C₄×C₃₇	—	2	1	no	—
237	C₄×C₃₇	—	4	2	no	—
238	C₄×C₃₇	—	4	2	no	—
239	C₄×C₃₇	—	4	2	no	—
240	C₄×C₃₇	—	4	2	no	—
241	C₄×C₃₇	—	8	2	no	—
242	C₄×C₃₇	#449	1	2	yes	—
243	C₄×C₃₇	C₂×#135	1	1	yes	characteristic
244	C₄×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
245	C₄×C₃₇	#577	1	2	yes	—
246	#3506	C₂×C₃₇	1	1	yes	characteristic
247	#3229	C₂×C₃₇	1	1	yes	characteristic, complemented
248	#3226	C₂×C₃₇	1	1	yes	characteristic, complemented
249	C₂×#461	C₂×C₃₇	1	1	yes	characteristic, complemented
250	#1654	C₂×C₃₇	1	4	yes	complemented
251	#1646	C₂×C₃₇	1	4	yes	complemented
252	#1542	C₂×C₃₇	1	1	yes	characteristic, complemented
253	#1480	C₂×C₃₇	1	1	yes	characteristic, complemented
254	#1478	C₂×C₃₇	1	1	yes	characteristic, complemented
255	C₂×C₃₇	—	2	2	no	—
256	C₂×C₃₇	—	8	2	no	—
257	C₂×C₃₇	—	8	2	no	—
258	C₂×C₃₇	C₂×#449	1	1	yes	characteristic
259	C₂×C₃₇	#3009	1	1	yes	characteristic
260	C₂×C₃₇	#3022	1	1	yes	characteristic
261	C₂²×SD₁₆	—	2	1	no	—
262	#559	—	2	2	no	—
263	#556	—	2	1	no	—
264	#555	C₂²×C₃₇	1	2	yes	—
265	#553	—	2	2	no	—
266	#550	—	2	1	no	—
267	#547	C₂²×C₃₇	1	2	yes	—
268	#538	—	2	2	no	—
269	#535	—	2	1	no	—
270	#533	C₂²×C₃₇	1	1	yes	characteristic
271	#532	C₂²×C₃₇	1	1	yes	characteristic
272	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
273	#525	—	2	2	no	—
274	#520	—	2	1	no	—
275	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
276	#500	—	2	1	no	—
277	#498	C₂²×C₃₇	1	2	yes	complemented
278	#487	C₂²×C₃₇	1	2	yes	complemented
279	#486	—	2	1	no	—
280	#483	—	2	2	no	—
281	#480	—	2	2	no	—
282	#475	—	2	2	no	—
283	#474	C₂²×C₃₇	1	4	yes	complemented
284	#461	—	2	2	no	—
285	#461	C₂²×C₃₇	1	4	yes	—
286	#431	C₂²×C₃₇	1	1	yes	characteristic
287	#431	C₂²×C₃₇	1	1	yes	characteristic
288	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
289	C₂×#103	—	2	1	no	—
290	#333	C₂²×C₃₇	1	2	yes	complemented
291	#332	C₂²×C₃₇	1	2	yes	complemented
292	D₄⋊C₈	C₂²×C₃₇	1	4	yes	—
293	D₄⋊C₈	C₂²×C₃₇	1	4	yes	complemented
294	C₃₇	#18928	1	1	yes	characteristic, direct product factor, Sylow
295	C₂×#41	—	2	2	no	—
296	C₂×#41	—	2	1	no	—
297	C₂²×Q₈	—	2	1	no	—
298	C₂²×D₄	D₄×C₃₇	1	1	yes	characteristic
299	C₂³×C₄	—	2	1	no	—
300	C₂×SD₁₆	—	2	4	no	—
301	C₂×SD₁₆	—	4	4	no	—
302	C₂²×C₈	—	2	1	no	—
303	C₄⋊Q₈	—	2	1	no	—
304	C₄⋊Q₈	—	2	1	no	—
305	C₄⋊Q₈	—	2	1	no	—
306	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
307	C₄⋊Q₈	C₂³×C₃₇	1	2	yes	—
308	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
309	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
310	#127	—	2	2	no	—
311	#127	D₄×C₃₇	1	1	yes	characteristic
312	#126	—	2	4	no	—
313	#125	—	2	1	no	—
314	#124	—	2	2	no	—
315	#124	—	2	4	no	—
316	#124	—	2	1	no	—
317	#123	—	2	4	no	—
318	#123	—	2	4	no	—
319	C₂²⋊Q₈	—	2	1	no	—
320	C₂²⋊Q₈	—	2	2	no	—
321	C₂²⋊Q₈	D₄×C₃₇	1	2	yes	—
322	#121	—	2	4	no	—
323	#121	—	2	2	no	—
324	#121	—	2	2	no	—
325	#121	—	2	2	no	—
326	#121	—	2	1	no	—
327	#121	D₄×C₃₇	1	2	yes	—
328	#120	—	2	4	no	—
329	C₄×Q₈	—	2	2	no	—
330	C₄×Q₈	—	2	1	no	—
331	C₄×Q₈	D₄×C₃₇	1	2	yes	—
332	C₄×D₄	—	2	4	no	—
333	C₄×D₄	—	2	2	no	—
334	C₄×D₄	—	2	4	no	—
335	C₄×D₄	—	2	1	no	—
336	C₄×D₄	—	2	1	no	—
337	C₄×D₄	—	2	1	no	—
338	C₄×D₄	D₄×C₃₇	1	2	yes	—
339	C₄×D₄	C₂³×C₃₇	1	2	yes	—
340	C₄×D₄	C₂³×C₃₇	1	2	yes	—
341	#117	—	2	1	no	—
342	#117	—	2	2	no	—
343	#117	—	2	2	no	—
344	C₂×C₄⋊C₄	—	2	2	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
348	C₂×C₂²⋊C₄	—	2	1	no	—
349	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
350	#107	—	2	4	no	—
351	#106	—	2	4	no	—
352	C₄⋊C₈	—	2	1	no	—
353	C₄⋊C₈	—	2	1	no	—
354	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
355	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
356	#103	—	2	4	no	—
357	#103	—	2	4	no	—
358	#102	—	2	4	no	—
359	C₂²⋊C₈	—	2	1	no	—
360	C₂²⋊C₈	—	2	1	no	—
361	C₄×C₈	—	2	1	no	—
362	C₄×C₈	C₂³×C₃₇	1	2	yes	—
363	C₂⁴	—	2	1	no	—
364	#41	—	4	2	no	—
365	#41	—	4	2	no	—
366	#41	—	8	4	no	—
367	C₂×Q₈	—	2	1	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	4	1	no	—
371	C₂×Q₈	—	4	2	no	—
372	C₂×Q₈	—	4	2	no	—
373	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	4	no	—
376	C₂×D₄	—	2	4	no	—
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
383	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	4	1	no	—
390	C₂²×C₄	—	8	2	no	—
391	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
394	SD₁₆	—	4	8	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	4	2	no	—
399	C₄⋊C₄	—	2	4	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	4	1	no	—
410	C₄⋊C₄	—	4	1	no	—
411	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
412	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
413	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₄²	—	2	4	no	—
423	C₄²	—	2	2	no	—
424	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
425	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
426	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
427	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
428	C₂³	—	2	2	no	—
429	C₂³	—	2	2	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	8	1	no	—
432	C₂³	—	8	1	no	—
433	C₂³	#120×C₃₇	1	1	yes	characteristic
434	Q₈	—	4	2	no	—
435	Q₈	—	4	2	no	—
436	Q₈	—	4	2	no	—
437	Q₈	—	4	2	no	—
438	Q₈	—	4	2	no	—
439	Q₈	—	8	2	no	—
440	D₄	—	2	2	no	—
441	D₄	—	2	2	no	—
442	D₄	—	2	4	no	—
443	D₄	—	4	4	no	—
444	D₄	—	4	2	no	—
445	D₄	—	4	2	no	—
446	D₄	—	8	1	no	—
447	D₄	—	8	4	no	—
448	D₄	—	8	4	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	4	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	8	2	no	—
460	C₂×C₄	—	8	1	no	—
461	C₂×C₄	—	8	4	no	—
462	C₂×C₄	—	8	2	no	—
463	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
464	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
465	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
466	C₂×C₄	#135×C₃₇	1	2	yes	—
467	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
468	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
469	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
470	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
471	C₈	—	4	2	no	—
472	C₈	—	4	2	no	—
473	C₈	—	4	2	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	8	4	no	—
483	C₂²	C₃₇×#449	1	2	yes	—
484	C₂²	C₂×#120×C₃₇	1	1	yes	characteristic
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	2	no	—
492	C₄	—	8	2	no	—
493	C₄	C₃₇×#449	1	2	yes	—
494	C₄	C₂×#135×C₃₇	1	1	yes	characteristic
495	C₄	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
496	C₄	C₃₇×#577	1	2	yes	—
497	C₂	—	2	2	no	—
498	C₂	—	8	2	no	—
499	C₂	—	8	2	no	—
500	C₂	C₂×C₃₇×#449	1	1	yes	characteristic
501	C₂	C₃₇×#3009	1	1	yes	characteristic
502	C₂	C₃₇×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₇
prime radical	C₃₇×#3506	C₂
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×#3229	C₂	semidirect
3. C₃₇×#3226	C₂	semidirect
4. C₂×C₃₇×#461	C₂	semidirect
5. C₃₇×#1654	C₂	semidirect
6. C₃₇×#1646	C₂	semidirect
7. C₃₇×#1542	C₂	semidirect
8. C₃₇×#1480	C₂	semidirect
9. C₃₇×#1478	C₂	semidirect
26. C₃₇×#498	C₂²	semidirect
27. C₃₇×#487	C₂²	semidirect
32. C₃₇×#474	C₂²	semidirect
39. C₃₇×#333	C₂²	semidirect
40. C₃₇×#332	C₂²	semidirect
42. C₃₇×D₄⋊C₈	C₂²	semidirect
222. #18928	C₃₇	direct (N × H)
247. #3229	C₂×C₃₇	semidirect
248. #3226	C₂×C₃₇	semidirect
249. C₂×#461	C₂×C₃₇	semidirect
250. #1654	C₂×C₃₇	semidirect
251. #1646	C₂×C₃₇	semidirect
252. #1542	C₂×C₃₇	semidirect
253. #1480	C₂×C₃₇	semidirect
254. #1478	C₂×C₃₇	semidirect
277. #498	C₂²×C₃₇	semidirect
278. #487	C₂²×C₃₇	semidirect
283. #474	C₂²×C₃₇	semidirect
290. #333	C₂²×C₃₇	semidirect
291. #332	C₂²×C₃₇	semidirect
293. D₄⋊C₈	C₂²×C₃₇	semidirect
294. C₃₇	#18928	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×#3506	2
C₃₇×#3229	2
C₃₇×#3226	2
C₂×C₃₇×#461	2
C₃₇×#1654	2
C₃₇×#1646	2
C₃₇×#1542	2
C₃₇×#1480	2
C₃₇×#1478	2
#18928	37

Subgroups — C37×#18928 #22640181

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#18928 #22640181