Subgroups — C₃₇×#28631 #22649884

Order 9472.

778 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3152	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#3141	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₇×#487	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#2931	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#2052	C₂	1	4	yes	maximal, complemented
6	C₃₇×#1997	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#1966	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1908	C₂	1	4	yes	maximal, complemented
9	C₄×#108×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#137×C₃₇	C₂²	1	4	yes	—
11	C₂×#131×C₃₇	C₂²	1	2	yes	—
12	C₃₇×#532	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₃₇×#497	—	2	2	no	—
16	C₃₇×#494	—	2	1	no	—
17	C₃₇×#492	—	2	1	no	—
18	C₃₇×#489	—	2	2	no	—
19	C₃₇×#487	—	2	1	no	—
20	C₃₇×#487	—	2	1	no	—
21	C₃₇×#487	—	2	1	no	—
22	C₃₇×#487	—	2	1	no	—
23	C₃₇×#487	—	2	1	no	—
24	C₃₇×#486	—	2	1	no	—
25	C₃₇×#436	—	2	1	no	—
26	C₃₇×#436	—	2	1	no	—
27	C₈×D₄×C₃₇	—	2	1	no	—
28	C₈×D₄×C₃₇	—	2	1	no	—
29	C₂×#108×C₃₇	C₂²	1	2	yes	—
30	C₃₇×#423	C₂²	1	1	yes	characteristic
31	C₃₇×#417	C₂²	1	4	yes	—
32	C₂×#103×C₃₇	C₂²	1	2	yes	—
33	C₂×#103×C₃₇	C₂²	1	2	yes	—
34	C₂×#101×C₃₇	C₂²	1	4	yes	—
35	C₃₇×#408	C₂²	1	2	yes	—
36	C₄×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
37	C₄×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
39	C₃₇×#343	C₂²	1	4	yes	—
40	C₃₇×#341	C₂²	1	2	yes	—
41	C₂×#41×C₃₇	C₂³	1	2	yes	—
42	C₂²×Q₈×C₃₇	—	2	1	no	—
43	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
44	#137×C₃₇	—	2	8	no	—
45	#137×C₃₇	—	4	4	no	—
46	C₂×Q₁₆×C₃₇	—	2	4	no	—
47	C₂×SD₁₆×C₃₇	—	2	4	no	—
48	#131×C₃₇	—	4	4	no	—
49	C₂×M₁₆×C₃₇	—	2	2	no	—
50	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
51	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
52	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
53	C₂²×C₈×C₃₇	—	2	2	no	—
54	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
56	C₄⋊Q₈×C₃₇	—	2	1	no	—
57	C₄⋊Q₈×C₃₇	—	2	1	no	—
58	C₄⋊Q₈×C₃₇	—	2	1	no	—
59	C₄⋊Q₈×C₃₇	—	2	1	no	—
60	C₄⋊Q₈×C₃₇	—	2	1	no	—
61	C₄⋊Q₈×C₃₇	—	2	1	no	—
62	C₄⋊Q₈×C₃₇	—	2	1	no	—
63	C₄⋊Q₈×C₃₇	—	2	1	no	—
64	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
65	#127×C₃₇	D₄	1	1	yes	characteristic
66	#124×C₃₇	D₄	1	2	yes	—
67	#121×C₃₇	—	2	1	no	—
68	#121×C₃₇	—	2	1	no	—
69	C₄×D₄×C₃₇	—	2	1	no	—
70	C₄×D₄×C₃₇	—	2	1	no	—
71	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
72	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
73	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
74	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
75	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
76	#108×C₃₇	—	2	4	no	—
77	C₄⋊C₈×C₃₇	—	2	1	no	—
78	C₄⋊C₈×C₃₇	—	2	1	no	—
79	#103×C₃₇	—	2	4	no	—
80	#103×C₃₇	—	2	2	no	—
81	#103×C₃₇	—	2	2	no	—
82	#103×C₃₇	—	2	2	no	—
83	#103×C₃₇	—	2	2	no	—
84	#102×C₃₇	—	2	4	no	—
85	#101×C₃₇	—	4	4	no	—
86	C₂²⋊C₈×C₃₇	—	2	2	no	—
87	C₂²⋊C₈×C₃₇	—	2	2	no	—
88	#97×C₃₇	—	2	1	no	—
89	#97×C₃₇	—	2	1	no	—
90	C₄×C₈×C₃₇	—	2	1	no	—
91	C₄×C₈×C₃₇	—	2	1	no	—
92	C₄×C₈×C₃₇	D₄	1	1	yes	characteristic
93	C₄×C₈×C₃₇	D₄	1	1	yes	characteristic
94	C₄×C₈×C₃₇	D₄	1	1	yes	characteristic
95	C₄×C₈×C₃₇	D₄	1	1	yes	characteristic
96	#41×C₃₇	—	2	4	no	—
97	#41×C₃₇	—	2	4	no	—
98	C₂×Q₈×C₃₇	—	2	2	no	—
99	C₂×Q₈×C₃₇	—	2	2	no	—
100	C₂×Q₈×C₃₇	—	2	4	no	—
101	C₂×Q₈×C₃₇	—	2	4	no	—
102	C₂×Q₈×C₃₇	—	4	1	no	—
103	C₂×Q₈×C₃₇	—	4	1	no	—
104	C₂×Q₈×C₃₇	—	8	2	no	—
105	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
106	C₂×D₄×C₃₇	—	2	2	no	—
107	C₂×D₄×C₃₇	—	2	1	no	—
108	C₂×D₄×C₃₇	—	2	1	no	—
109	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₃₇	—	2	2	no	—
111	C₂²×C₄×C₃₇	—	2	2	no	—
112	C₂²×C₄×C₃₇	—	2	2	no	—
113	C₂²×C₄×C₃₇	#41	1	1	yes	characteristic
114	C₂²×C₄×C₃₇	#41	1	1	yes	characteristic
115	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
116	Q₁₆×C₃₇	—	4	8	no	—
117	SD₁₆×C₃₇	—	4	8	no	—
118	M₁₆×C₃₇	—	2	2	no	—
119	M₁₆×C₃₇	—	2	2	no	—
120	M₁₆×C₃₇	—	2	2	no	—
121	M₁₆×C₃₇	—	2	4	no	—
122	M₁₆×C₃₇	—	4	4	no	—
123	M₁₆×C₃₇	#41	1	4	yes	—
124	C₂×C₈×C₃₇	—	2	2	no	—
125	C₂×C₈×C₃₇	—	2	2	no	—
126	C₂×C₈×C₃₇	—	2	2	no	—
127	C₂×C₈×C₃₇	—	2	2	no	—
128	C₂×C₈×C₃₇	—	2	2	no	—
129	C₂×C₈×C₃₇	—	4	4	no	—
130	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
134	C₄⋊C₄×C₃₇	—	2	1	no	—
135	C₄⋊C₄×C₃₇	—	2	1	no	—
136	C₄⋊C₄×C₃₇	—	2	2	no	—
137	C₄⋊C₄×C₃₇	—	2	2	no	—
138	C₄⋊C₄×C₃₇	—	4	1	no	—
139	C₄⋊C₄×C₃₇	—	4	1	no	—
140	C₄⋊C₄×C₃₇	—	4	1	no	—
141	C₄⋊C₄×C₃₇	—	4	1	no	—
142	C₄⋊C₄×C₃₇	—	4	1	no	—
143	C₄⋊C₄×C₃₇	—	4	1	no	—
144	C₂²⋊C₄×C₃₇	—	2	2	no	—
145	C₂²⋊C₄×C₃₇	—	2	2	no	—
146	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
150	C₂³×C₃₇	—	2	2	no	—
151	C₂³×C₃₇	C₂×#41	1	1	yes	characteristic
152	Q₈×C₃₇	—	2	4	no	—
153	Q₈×C₃₇	—	4	2	no	—
154	Q₈×C₃₇	—	4	2	no	—
155	Q₈×C₃₇	—	4	4	no	—
156	Q₈×C₃₇	—	8	2	no	—
157	Q₈×C₃₇	—	8	2	no	—
158	D₄×C₃₇	—	2	4	no	—
159	D₄×C₃₇	—	4	4	no	—
160	D₄×C₃₇	—	4	2	no	—
161	D₄×C₃₇	—	4	2	no	—
162	C₂×C₄×C₃₇	—	2	2	no	—
163	C₂×C₄×C₃₇	—	2	2	no	—
164	C₂×C₄×C₃₇	—	2	2	no	—
165	C₂×C₄×C₃₇	—	4	2	no	—
166	C₂×C₄×C₃₇	—	4	2	no	—
167	C₂×C₄×C₃₇	—	4	2	no	—
168	C₂×C₄×C₃₇	—	4	2	no	—
169	C₂×C₄×C₃₇	—	4	4	no	—
170	C₂×C₄×C₃₇	—	8	2	no	—
171	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
172	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
173	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
174	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
175	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
178	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
179	C₈×C₃₇	—	2	1	no	—
180	C₈×C₃₇	—	2	1	no	—
181	C₈×C₃₇	—	2	1	no	—
182	C₈×C₃₇	—	2	1	no	—
183	C₈×C₃₇	—	2	4	no	—
184	C₈×C₃₇	—	4	2	no	—
185	C₈×C₃₇	—	4	2	no	—
186	#28631	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂²×C₃₇	—	2	1	no	—
188	C₂²×C₃₇	—	2	1	no	—
189	C₂²×C₃₇	—	4	2	no	—
190	C₂²×C₃₇	—	4	2	no	—
191	C₂²×C₃₇	—	4	2	no	—
192	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
193	C₂²×C₃₇	#559	1	2	yes	—
194	C₄×C₃₇	—	2	1	no	—
195	C₄×C₃₇	—	2	1	no	—
196	C₄×C₃₇	—	4	2	no	—
197	C₄×C₃₇	—	8	2	no	—
198	C₄×C₃₇	—	8	2	no	—
199	C₄×C₃₇	#471	1	2	yes	—
200	C₄×C₃₇	#473	1	2	yes	—
201	C₄×C₃₇	#532	1	1	yes	characteristic
202	C₄×C₃₇	#535	1	1	yes	characteristic
203	C₄×C₃₇	#546	1	2	yes	—
204	#3152	C₂×C₃₇	1	1	yes	characteristic
205	#3141	C₂×C₃₇	1	1	yes	characteristic
206	C₂×#487	C₂×C₃₇	1	1	yes	characteristic, complemented
207	#2931	C₂×C₃₇	1	1	yes	characteristic
208	#2052	C₂×C₃₇	1	4	yes	complemented
209	#1997	C₂×C₃₇	1	1	yes	characteristic, complemented
210	#1966	C₂×C₃₇	1	1	yes	characteristic, complemented
211	#1908	C₂×C₃₇	1	4	yes	complemented
212	C₄×#108	C₂×C₃₇	1	1	yes	characteristic, complemented
213	C₂×C₃₇	—	2	2	no	—
214	C₂×C₃₇	—	8	2	no	—
215	C₂×C₃₇	#2544	1	1	yes	characteristic
216	C₂×C₃₇	C₂×#471	1	1	yes	characteristic
217	C₂×C₃₇	C₂×#473	1	1	yes	characteristic
218	C₂×#137	C₂²×C₃₇	1	4	yes	—
219	C₂×#131	C₂²×C₃₇	1	2	yes	—
220	#532	C₂²×C₃₇	1	1	yes	characteristic
221	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
222	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
223	#497	—	2	2	no	—
224	#494	—	2	1	no	—
225	#492	—	2	1	no	—
226	#489	—	2	2	no	—
227	#487	—	2	1	no	—
228	#487	—	2	1	no	—
229	#487	—	2	1	no	—
230	#487	—	2	1	no	—
231	#487	—	2	1	no	—
232	#486	—	2	1	no	—
233	#436	—	2	1	no	—
234	#436	—	2	1	no	—
235	C₈×D₄	—	2	1	no	—
236	C₈×D₄	—	2	1	no	—
237	C₂×#108	C₂²×C₃₇	1	2	yes	—
238	#423	C₂²×C₃₇	1	1	yes	characteristic
239	#417	C₂²×C₃₇	1	4	yes	—
240	C₂×#103	C₂²×C₃₇	1	2	yes	—
241	C₂×#103	C₂²×C₃₇	1	2	yes	—
242	C₂×#101	C₂²×C₃₇	1	4	yes	—
243	#408	C₂²×C₃₇	1	2	yes	—
244	C₄×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
245	C₄×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
246	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
247	#343	C₂²×C₃₇	1	4	yes	—
248	#341	C₂²×C₃₇	1	2	yes	—
249	C₃₇	#28631	1	1	yes	characteristic, direct product factor, Sylow
250	C₂×#41	C₂³×C₃₇	1	2	yes	—
251	C₂²×Q₈	—	2	1	no	—
252	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
253	#137	—	2	8	no	—
254	#137	—	4	4	no	—
255	C₂×Q₁₆	—	2	4	no	—
256	C₂×SD₁₆	—	2	4	no	—
257	#131	—	4	4	no	—
258	C₂×M₁₆	—	2	2	no	—
259	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
260	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
261	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
262	C₂²×C₈	—	2	2	no	—
263	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
265	C₄⋊Q₈	—	2	1	no	—
266	C₄⋊Q₈	—	2	1	no	—
267	C₄⋊Q₈	—	2	1	no	—
268	C₄⋊Q₈	—	2	1	no	—
269	C₄⋊Q₈	—	2	1	no	—
270	C₄⋊Q₈	—	2	1	no	—
271	C₄⋊Q₈	—	2	1	no	—
272	C₄⋊Q₈	—	2	1	no	—
273	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
274	#127	D₄×C₃₇	1	1	yes	characteristic
275	#124	D₄×C₃₇	1	2	yes	—
276	#121	—	2	1	no	—
277	#121	—	2	1	no	—
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
284	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
285	#108	—	2	4	no	—
286	C₄⋊C₈	—	2	1	no	—
287	C₄⋊C₈	—	2	1	no	—
288	#103	—	2	4	no	—
289	#103	—	2	2	no	—
290	#103	—	2	2	no	—
291	#103	—	2	2	no	—
292	#103	—	2	2	no	—
293	#102	—	2	4	no	—
294	#101	—	4	4	no	—
295	C₂²⋊C₈	—	2	2	no	—
296	C₂²⋊C₈	—	2	2	no	—
297	#97	—	2	1	no	—
298	#97	—	2	1	no	—
299	C₄×C₈	—	2	1	no	—
300	C₄×C₈	—	2	1	no	—
301	C₄×C₈	D₄×C₃₇	1	1	yes	characteristic
302	C₄×C₈	D₄×C₃₇	1	1	yes	characteristic
303	C₄×C₈	D₄×C₃₇	1	1	yes	characteristic
304	C₄×C₈	D₄×C₃₇	1	1	yes	characteristic
305	#41	—	2	4	no	—
306	#41	—	2	4	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	4	no	—
310	C₂×Q₈	—	2	4	no	—
311	C₂×Q₈	—	4	1	no	—
312	C₂×Q₈	—	4	1	no	—
313	C₂×Q₈	—	8	2	no	—
314	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	#41×C₃₇	1	1	yes	characteristic
323	C₂²×C₄	#41×C₃₇	1	1	yes	characteristic
324	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
325	Q₁₆	—	4	8	no	—
326	SD₁₆	—	4	8	no	—
327	M₁₆	—	2	2	no	—
328	M₁₆	—	2	2	no	—
329	M₁₆	—	2	2	no	—
330	M₁₆	—	2	4	no	—
331	M₁₆	—	4	4	no	—
332	M₁₆	#41×C₃₇	1	4	yes	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	4	4	no	—
339	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
340	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
341	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
342	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	4	1	no	—
348	C₄⋊C₄	—	4	1	no	—
349	C₄⋊C₄	—	4	1	no	—
350	C₄⋊C₄	—	4	1	no	—
351	C₄⋊C₄	—	4	1	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₂²⋊C₄	—	2	2	no	—
354	C₂²⋊C₄	—	2	2	no	—
355	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
356	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
357	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
358	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
359	C₂³	—	2	2	no	—
360	C₂³	C₂×#41×C₃₇	1	1	yes	characteristic
361	Q₈	—	2	4	no	—
362	Q₈	—	4	2	no	—
363	Q₈	—	4	2	no	—
364	Q₈	—	4	4	no	—
365	Q₈	—	8	2	no	—
366	Q₈	—	8	2	no	—
367	D₄	—	2	4	no	—
368	D₄	—	4	4	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	8	2	no	—
380	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
381	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
382	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
383	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
384	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
385	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
386	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
387	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
388	C₈	—	2	1	no	—
389	C₈	—	2	1	no	—
390	C₈	—	2	1	no	—
391	C₈	—	2	1	no	—
392	C₈	—	2	4	no	—
393	C₈	—	4	2	no	—
394	C₈	—	4	2	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	2	no	—
400	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
401	C₂²	C₃₇×#559	1	2	yes	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	4	2	no	—
405	C₄	—	8	2	no	—
406	C₄	—	8	2	no	—
407	C₄	C₃₇×#471	1	2	yes	—
408	C₄	C₃₇×#473	1	2	yes	—
409	C₄	C₃₇×#532	1	1	yes	characteristic
410	C₄	C₃₇×#535	1	1	yes	characteristic
411	C₄	C₃₇×#546	1	2	yes	—
412	C₂	—	2	2	no	—
413	C₂	—	8	2	no	—
414	C₂	C₃₇×#2544	1	1	yes	characteristic
415	C₂	C₂×C₃₇×#471	1	1	yes	characteristic
416	C₂	C₂×C₃₇×#473	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₃₇×#532	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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
3. C₂×C₃₇×#487	C₂	semidirect
5. C₃₇×#2052	C₂	semidirect
6. C₃₇×#1997	C₂	semidirect
7. C₃₇×#1966	C₂	semidirect
8. C₃₇×#1908	C₂	semidirect
9. C₄×#108×C₃₇	C₂	semidirect
186. #28631	C₃₇	direct (N × H)
206. C₂×#487	C₂×C₃₇	semidirect
208. #2052	C₂×C₃₇	semidirect
209. #1997	C₂×C₃₇	semidirect
210. #1966	C₂×C₃₇	semidirect
211. #1908	C₂×C₃₇	semidirect
212. C₄×#108	C₂×C₃₇	semidirect
249. C₃₇	#28631	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×#3152	2
C₃₇×#3141	2
C₂×C₃₇×#487	2
C₃₇×#2931	2
C₃₇×#2052	2
C₃₇×#1997	2
C₃₇×#1966	2
C₃₇×#1908	2
C₄×#108×C₃₇	2
#28631	37

Subgroups — C37×#28631 #22649884

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28631 #22649884