Subgroups — C₃₇×#28296 #22649549

Order 9472.

706 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3078	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×#3077	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×SD₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#2064	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2063	C₂	1	2	yes	maximal
7	C₃₇×#1977	C₂	1	2	yes	maximal
8	C₃₇×#1951	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1848	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1801	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1800	C₂	1	1	yes	maximal, characteristic
12	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
13	C₃₇×#533	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
16	C₃₇×#479	—	2	2	no	—
17	C₃₇×#478	—	2	2	no	—
18	C₃₇×#477	—	2	1	no	—
19	C₃₇×#476	—	2	1	no	—
20	C₃₇×#475	—	2	1	no	—
21	C₃₇×#474	—	2	1	no	—
22	C₃₇×#446	—	2	1	no	—
23	C₃₇×#446	—	2	1	no	—
24	C₈×Q₈×C₃₇	—	2	1	no	—
25	C₈×Q₈×C₃₇	—	2	1	no	—
26	C₄×SD₁₆×C₃₇	—	2	1	no	—
27	C₄×SD₁₆×C₃₇	—	2	1	no	—
28	C₄×SD₁₆×C₃₇	—	2	1	no	—
29	C₄×SD₁₆×C₃₇	—	2	1	no	—
30	C₂×#108×C₃₇	C₂²	1	2	yes	—
31	C₂×#108×C₃₇	C₂²	1	2	yes	—
32	C₃₇×#428	C₂²	1	2	yes	—
33	C₃₇×#428	C₂²	1	2	yes	—
34	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
35	C₃₇×#424	C₂²	1	2	yes	—
36	C₃₇×#423	C₂²	1	1	yes	characteristic
37	C₃₇×#423	C₂²	1	1	yes	characteristic
38	C₃₇×#423	C₂²	1	1	yes	characteristic
39	C₃₇×#419	C₂²	1	2	yes	—
40	C₃₇×#418	C₂²	1	2	yes	—
41	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
42	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
43	C₂×#101×C₃₇	C₂²	1	2	yes	—
44	C₂×#100×C₃₇	C₂²	1	2	yes	—
45	C₃₇×#405	C₂²	1	2	yes	—
46	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
47	C₃₇×#343	C₂²	1	2	yes	—
48	C₃₇×#343	C₂²	1	2	yes	—
49	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₃₇	—	2	1	no	—
52	C₂×SD₁₆×C₃₇	—	2	1	no	—
53	C₂×SD₁₆×C₃₇	—	2	1	no	—
54	C₂×SD₁₆×C₃₇	—	2	2	no	—
55	C₂×SD₁₆×C₃₇	Q₈	1	4	yes	complemented
56	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
57	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
58	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
59	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
61	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
62	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
63	#125×C₃₇	D₄	1	2	yes	—
64	C₂²⋊Q₈×C₃₇	—	2	1	no	—
65	C₂²⋊Q₈×C₃₇	—	2	1	no	—
66	C₄×Q₈×C₃₇	—	2	1	no	—
67	C₄×Q₈×C₃₇	—	2	1	no	—
68	C₄×Q₈×C₃₇	—	2	1	no	—
69	C₄×Q₈×C₃₇	—	2	1	no	—
70	C₄×Q₈×C₃₇	—	2	1	no	—
71	C₄×Q₈×C₃₇	—	2	1	no	—
72	C₄×D₄×C₃₇	—	2	1	no	—
73	C₄×D₄×C₃₇	—	2	1	no	—
74	C₄×D₄×C₃₇	—	2	1	no	—
75	C₄×D₄×C₃₇	—	2	1	no	—
76	#117×C₃₇	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
78	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
80	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
81	C₂×C₄²×C₃₇	—	2	1	no	—
82	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
83	#108×C₃₇	—	2	4	no	—
84	#108×C₃₇	—	4	2	no	—
85	#107×C₃₇	—	2	2	no	—
86	#107×C₃₇	—	2	2	no	—
87	#106×C₃₇	—	2	1	no	—
88	#106×C₃₇	—	2	1	no	—
89	#106×C₃₇	—	2	2	no	—
90	#106×C₃₇	—	2	2	no	—
91	C₄⋊C₈×C₃₇	—	2	2	no	—
92	C₄⋊C₈×C₃₇	—	2	2	no	—
93	C₄⋊C₈×C₃₇	—	2	1	no	—
94	C₄⋊C₈×C₃₇	—	2	1	no	—
95	C₄⋊C₈×C₃₇	—	2	1	no	—
96	C₄⋊C₈×C₃₇	—	2	1	no	—
97	C₄⋊C₈×C₃₇	—	2	1	no	—
98	C₄⋊C₈×C₃₇	—	2	1	no	—
99	#103×C₃₇	—	2	1	no	—
100	#103×C₃₇	—	2	1	no	—
101	#103×C₃₇	—	2	2	no	—
102	#103×C₃₇	—	2	2	no	—
103	#102×C₃₇	—	2	1	no	—
104	#102×C₃₇	—	2	1	no	—
105	#102×C₃₇	—	2	2	no	—
106	#102×C₃₇	—	2	2	no	—
107	#101×C₃₇	—	4	2	no	—
108	#100×C₃₇	—	4	2	no	—
109	#97×C₃₇	—	2	2	no	—
110	C₄×C₈×C₃₇	—	2	2	no	—
111	C₄×C₈×C₃₇	D₄	1	1	yes	characteristic
112	C₄×C₈×C₃₇	D₄	1	1	yes	characteristic
113	C₄×C₈×C₃₇	D₄	1	1	yes	characteristic
114	C₄×C₈×C₃₇	D₄	1	1	yes	characteristic
115	C₂⁴×C₃₇	—	2	1	no	—
116	C₂×Q₈×C₃₇	—	2	1	no	—
117	C₂×Q₈×C₃₇	—	2	1	no	—
118	C₂×Q₈×C₃₇	—	2	1	no	—
119	C₂×Q₈×C₃₇	—	2	1	no	—
120	C₂×Q₈×C₃₇	—	2	1	no	—
121	C₂×Q₈×C₃₇	—	2	1	no	—
122	C₂×Q₈×C₃₇	—	2	1	no	—
123	C₂×Q₈×C₃₇	C₂×Q₈	1	2	yes	—
124	C₂×D₄×C₃₇	—	2	1	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	1	no	—
129	C₂×D₄×C₃₇	C₂×Q₈	1	2	yes	—
130	C₂²×C₄×C₃₇	—	2	1	no	—
131	C₂²×C₄×C₃₇	—	2	1	no	—
132	C₂²×C₄×C₃₇	—	2	1	no	—
133	C₂²×C₄×C₃₇	—	4	1	no	—
134	C₂²×C₄×C₃₇	—	4	1	no	—
135	C₂²×C₄×C₃₇	—	8	2	no	—
136	C₂²×C₄×C₃₇	#41	1	1	yes	characteristic
137	C₂²×C₄×C₃₇	#41	1	1	yes	characteristic
138	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
139	SD₁₆×C₃₇	—	2	4	no	—
140	SD₁₆×C₃₇	—	2	4	no	—
141	M₁₆×C₃₇	—	2	2	no	—
142	M₁₆×C₃₇	—	2	2	no	—
143	M₁₆×C₃₇	—	2	2	no	—
144	M₁₆×C₃₇	—	2	2	no	—
145	M₁₆×C₃₇	—	2	2	no	—
146	M₁₆×C₃₇	—	2	2	no	—
147	C₂×C₈×C₃₇	—	2	1	no	—
148	C₂×C₈×C₃₇	—	2	1	no	—
149	C₂×C₈×C₃₇	—	2	2	no	—
150	C₂×C₈×C₃₇	—	2	2	no	—
151	C₂×C₈×C₃₇	—	2	2	no	—
152	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₃₇	C₂×Q₈	1	2	yes	—
157	C₂×C₈×C₃₇	#41	1	2	yes	—
158	C₄⋊C₄×C₃₇	—	2	2	no	—
159	C₄⋊C₄×C₃₇	—	2	2	no	—
160	C₄⋊C₄×C₃₇	—	2	1	no	—
161	C₄⋊C₄×C₃₇	—	2	1	no	—
162	C₄⋊C₄×C₃₇	—	2	1	no	—
163	C₄⋊C₄×C₃₇	—	2	1	no	—
164	C₄⋊C₄×C₃₇	—	2	1	no	—
165	C₄⋊C₄×C₃₇	—	2	1	no	—
166	C₄⋊C₄×C₃₇	—	4	1	no	—
167	C₄⋊C₄×C₃₇	—	4	1	no	—
168	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
169	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
170	C₂²⋊C₄×C₃₇	—	2	2	no	—
171	C₂²⋊C₄×C₃₇	—	4	1	no	—
172	C₂²⋊C₄×C₃₇	—	4	1	no	—
173	C₄²×C₃₇	—	2	2	no	—
174	C₄²×C₃₇	—	4	1	no	—
175	C₄²×C₃₇	—	4	1	no	—
176	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
180	C₂³×C₃₇	—	2	2	no	—
181	C₂³×C₃₇	—	4	1	no	—
182	C₂³×C₃₇	—	4	1	no	—
183	C₂³×C₃₇	—	8	1	no	—
184	C₂³×C₃₇	—	8	1	no	—
185	C₂³×C₃₇	C₂×#41	1	1	yes	characteristic
186	Q₈×C₃₇	—	2	2	no	—
187	Q₈×C₃₇	—	2	2	no	—
188	Q₈×C₃₇	—	4	2	no	—
189	Q₈×C₃₇	—	4	1	no	—
190	Q₈×C₃₇	—	4	1	no	—
191	Q₈×C₃₇	—	4	2	no	—
192	D₄×C₃₇	—	2	2	no	—
193	D₄×C₃₇	—	2	2	no	—
194	D₄×C₃₇	—	4	1	no	—
195	D₄×C₃₇	—	4	1	no	—
196	C₂×C₄×C₃₇	—	2	2	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	—	4	1	no	—
201	C₂×C₄×C₃₇	—	4	1	no	—
202	C₂×C₄×C₃₇	—	4	1	no	—
203	C₂×C₄×C₃₇	—	4	1	no	—
204	C₂×C₄×C₃₇	—	4	1	no	—
205	C₂×C₄×C₃₇	—	8	2	no	—
206	C₂×C₄×C₃₇	—	8	2	no	—
207	C₂×C₄×C₃₇	—	8	1	no	—
208	C₂×C₄×C₃₇	—	8	1	no	—
209	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
210	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
211	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
212	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
213	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₃₇	C₂²×Q₈	1	1	yes	characteristic
216	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
218	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
219	C₈×C₃₇	—	2	1	no	—
220	C₈×C₃₇	—	2	1	no	—
221	C₈×C₃₇	—	4	2	no	—
222	C₈×C₃₇	—	4	2	no	—
223	C₈×C₃₇	—	4	2	no	—
224	C₈×C₃₇	C₂²⋊Q₈	1	2	yes	—
225	C₈×C₃₇	C₂²⋊Q₈	1	2	yes	—
226	#28296	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₂²×C₃₇	—	2	1	no	—
228	C₂²×C₃₇	—	2	1	no	—
229	C₂²×C₃₇	—	4	2	no	—
230	C₂²×C₃₇	—	8	2	no	—
231	C₂²×C₃₇	—	8	2	no	—
232	C₂²×C₃₇	—	8	1	no	—
233	C₂²×C₃₇	—	8	1	no	—
234	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
235	C₂²×C₃₇	#554	1	1	yes	characteristic
236	C₂²×C₃₇	#556	1	1	yes	characteristic
237	C₄×C₃₇	—	2	1	no	—
238	C₄×C₃₇	—	2	1	no	—
239	C₄×C₃₇	—	2	1	no	—
240	C₄×C₃₇	—	4	2	no	—
241	C₄×C₃₇	—	4	2	no	—
242	C₄×C₃₇	—	4	2	no	—
243	C₄×C₃₇	—	8	1	no	—
244	C₄×C₃₇	—	8	1	no	—
245	C₄×C₃₇	#471	1	2	yes	—
246	C₄×C₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
247	C₄×C₃₇	#537	1	1	yes	characteristic
248	C₄×C₃₇	D₄×Q₈	1	1	yes	characteristic
249	C₄×C₃₇	#550	1	1	yes	characteristic
250	#3078	C₂×C₃₇	1	1	yes	characteristic, complemented
251	#3077	C₂×C₃₇	1	1	yes	characteristic
252	#2960	C₂×C₃₇	1	1	yes	characteristic, complemented
253	C₂×C₄×SD₁₆	C₂×C₃₇	1	1	yes	characteristic
254	#2064	C₂×C₃₇	1	2	yes	complemented
255	#2063	C₂×C₃₇	1	2	yes	—
256	#1977	C₂×C₃₇	1	2	yes	—
257	#1951	C₂×C₃₇	1	2	yes	complemented
258	#1848	C₂×C₃₇	1	1	yes	characteristic, complemented
259	#1801	C₂×C₃₇	1	1	yes	characteristic, complemented
260	#1800	C₂×C₃₇	1	1	yes	characteristic
261	C₂×C₃₇	—	2	1	no	—
262	C₂×C₃₇	—	2	1	no	—
263	C₂×C₃₇	—	8	2	no	—
264	C₂×C₃₇	#2538	1	1	yes	characteristic
265	C₂×C₃₇	C₂×#471	1	1	yes	characteristic
266	C₂×C₃₇	#3067	1	1	yes	characteristic
267	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
268	#533	C₂²×C₃₇	1	1	yes	characteristic
269	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
270	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
271	#479	—	2	2	no	—
272	#478	—	2	2	no	—
273	#477	—	2	1	no	—
274	#476	—	2	1	no	—
275	#475	—	2	1	no	—
276	#474	—	2	1	no	—
277	#446	—	2	1	no	—
278	#446	—	2	1	no	—
279	C₈×Q₈	—	2	1	no	—
280	C₈×Q₈	—	2	1	no	—
281	C₄×SD₁₆	—	2	1	no	—
282	C₄×SD₁₆	—	2	1	no	—
283	C₄×SD₁₆	—	2	1	no	—
284	C₄×SD₁₆	—	2	1	no	—
285	C₂×#108	C₂²×C₃₇	1	2	yes	—
286	C₂×#108	C₂²×C₃₇	1	2	yes	—
287	#428	C₂²×C₃₇	1	2	yes	—
288	#428	C₂²×C₃₇	1	2	yes	—
289	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
290	#424	C₂²×C₃₇	1	2	yes	—
291	#423	C₂²×C₃₇	1	1	yes	characteristic
292	#423	C₂²×C₃₇	1	1	yes	characteristic
293	#423	C₂²×C₃₇	1	1	yes	characteristic
294	#419	C₂²×C₃₇	1	2	yes	—
295	#418	C₂²×C₃₇	1	2	yes	—
296	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
297	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
298	C₂×#101	C₂²×C₃₇	1	2	yes	—
299	C₂×#100	C₂²×C₃₇	1	2	yes	—
300	#405	C₂²×C₃₇	1	2	yes	—
301	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
302	#343	C₂²×C₃₇	1	2	yes	—
303	#343	C₂²×C₃₇	1	2	yes	—
304	C₃₇	#28296	1	1	yes	characteristic, direct product factor, Sylow
305	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
306	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
307	C₂³×C₄	—	2	1	no	—
308	C₂×SD₁₆	—	2	1	no	—
309	C₂×SD₁₆	—	2	1	no	—
310	C₂×SD₁₆	—	2	2	no	—
311	C₂×SD₁₆	Q₈×C₃₇	1	4	yes	complemented
312	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
313	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
314	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
315	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
316	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
317	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
318	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
319	#125	D₄×C₃₇	1	2	yes	—
320	C₂²⋊Q₈	—	2	1	no	—
321	C₂²⋊Q₈	—	2	1	no	—
322	C₄×Q₈	—	2	1	no	—
323	C₄×Q₈	—	2	1	no	—
324	C₄×Q₈	—	2	1	no	—
325	C₄×Q₈	—	2	1	no	—
326	C₄×Q₈	—	2	1	no	—
327	C₄×Q₈	—	2	1	no	—
328	C₄×D₄	—	2	1	no	—
329	C₄×D₄	—	2	1	no	—
330	C₄×D₄	—	2	1	no	—
331	C₄×D₄	—	2	1	no	—
332	#117	C₂³×C₃₇	1	2	yes	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
335	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
336	C₂×C₂²⋊C₄	—	2	1	no	—
337	C₂×C₄²	—	2	1	no	—
338	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
339	#108	—	2	4	no	—
340	#108	—	4	2	no	—
341	#107	—	2	2	no	—
342	#107	—	2	2	no	—
343	#106	—	2	1	no	—
344	#106	—	2	1	no	—
345	#106	—	2	2	no	—
346	#106	—	2	2	no	—
347	C₄⋊C₈	—	2	2	no	—
348	C₄⋊C₈	—	2	2	no	—
349	C₄⋊C₈	—	2	1	no	—
350	C₄⋊C₈	—	2	1	no	—
351	C₄⋊C₈	—	2	1	no	—
352	C₄⋊C₈	—	2	1	no	—
353	C₄⋊C₈	—	2	1	no	—
354	C₄⋊C₈	—	2	1	no	—
355	#103	—	2	1	no	—
356	#103	—	2	1	no	—
357	#103	—	2	2	no	—
358	#103	—	2	2	no	—
359	#102	—	2	1	no	—
360	#102	—	2	1	no	—
361	#102	—	2	2	no	—
362	#102	—	2	2	no	—
363	#101	—	4	2	no	—
364	#100	—	4	2	no	—
365	#97	—	2	2	no	—
366	C₄×C₈	—	2	2	no	—
367	C₄×C₈	D₄×C₃₇	1	1	yes	characteristic
368	C₄×C₈	D₄×C₃₇	1	1	yes	characteristic
369	C₄×C₈	D₄×C₃₇	1	1	yes	characteristic
370	C₄×C₈	D₄×C₃₇	1	1	yes	characteristic
371	C₂⁴	—	2	1	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	2	1	no	—
375	C₂×Q₈	—	2	1	no	—
376	C₂×Q₈	—	2	1	no	—
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×Q₈	C₂×Q₈×C₃₇	1	2	yes	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	2	1	no	—
384	C₂×D₄	—	2	1	no	—
385	C₂×D₄	C₂×Q₈×C₃₇	1	2	yes	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	4	1	no	—
390	C₂²×C₄	—	4	1	no	—
391	C₂²×C₄	—	8	2	no	—
392	C₂²×C₄	#41×C₃₇	1	1	yes	characteristic
393	C₂²×C₄	#41×C₃₇	1	1	yes	characteristic
394	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
395	SD₁₆	—	2	4	no	—
396	SD₁₆	—	2	4	no	—
397	M₁₆	—	2	2	no	—
398	M₁₆	—	2	2	no	—
399	M₁₆	—	2	2	no	—
400	M₁₆	—	2	2	no	—
401	M₁₆	—	2	2	no	—
402	M₁₆	—	2	2	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
409	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
410	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
411	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
412	C₂×C₈	C₂×Q₈×C₃₇	1	2	yes	—
413	C₂×C₈	#41×C₃₇	1	2	yes	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	4	1	no	—
423	C₄⋊C₄	—	4	1	no	—
424	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
425	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	4	1	no	—
428	C₂²⋊C₄	—	4	1	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	4	1	no	—
431	C₄²	—	4	1	no	—
432	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
433	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
434	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
435	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
436	C₂³	—	2	2	no	—
437	C₂³	—	4	1	no	—
438	C₂³	—	4	1	no	—
439	C₂³	—	8	1	no	—
440	C₂³	—	8	1	no	—
441	C₂³	C₂×#41×C₃₇	1	1	yes	characteristic
442	Q₈	—	2	2	no	—
443	Q₈	—	2	2	no	—
444	Q₈	—	4	2	no	—
445	Q₈	—	4	1	no	—
446	Q₈	—	4	1	no	—
447	Q₈	—	4	2	no	—
448	D₄	—	2	2	no	—
449	D₄	—	2	2	no	—
450	D₄	—	4	1	no	—
451	D₄	—	4	1	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	8	2	no	—
462	C₂×C₄	—	8	2	no	—
463	C₂×C₄	—	8	1	no	—
464	C₂×C₄	—	8	1	no	—
465	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
466	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
467	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
468	C₂×C₄	#121×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	C₂×C₄	C₂²×Q₈×C₃₇	1	1	yes	characteristic
472	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
473	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
474	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
475	C₈	—	2	1	no	—
476	C₈	—	2	1	no	—
477	C₈	—	4	2	no	—
478	C₈	—	4	2	no	—
479	C₈	—	4	2	no	—
480	C₈	C₂²⋊Q₈×C₃₇	1	2	yes	—
481	C₈	C₂²⋊Q₈×C₃₇	1	2	yes	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	8	2	no	—
486	C₂²	—	8	2	no	—
487	C₂²	—	8	1	no	—
488	C₂²	—	8	1	no	—
489	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
490	C₂²	C₃₇×#554	1	1	yes	characteristic
491	C₂²	C₃₇×#556	1	1	yes	characteristic
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	4	2	no	—
496	C₄	—	4	2	no	—
497	C₄	—	4	2	no	—
498	C₄	—	8	1	no	—
499	C₄	—	8	1	no	—
500	C₄	C₃₇×#471	1	2	yes	—
501	C₄	C₂×C₂²⋊Q₈×C₃₇	1	1	yes	characteristic
502	C₄	C₃₇×#537	1	1	yes	characteristic
503	C₄	D₄×Q₈×C₃₇	1	1	yes	characteristic
504	C₄	C₃₇×#550	1	1	yes	characteristic
505	C₂	—	2	1	no	—
506	C₂	—	2	1	no	—
507	C₂	—	8	2	no	—
508	C₂	C₃₇×#2538	1	1	yes	characteristic
509	C₂	C₂×C₃₇×#471	1	1	yes	characteristic
510	C₂	C₃₇×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂²×D₄×C₃₇	C₂³
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
1. C₃₇×#3078	C₂	semidirect
3. C₃₇×#2960	C₂	semidirect
5. C₃₇×#2064	C₂	semidirect
8. C₃₇×#1951	C₂	semidirect
9. C₃₇×#1848	C₂	semidirect
10. C₃₇×#1801	C₂	semidirect
55. C₂×SD₁₆×C₃₇	Q₈	semidirect
226. #28296	C₃₇	direct (N × H)
250. #3078	C₂×C₃₇	semidirect
252. #2960	C₂×C₃₇	semidirect
254. #2064	C₂×C₃₇	semidirect
257. #1951	C₂×C₃₇	semidirect
258. #1848	C₂×C₃₇	semidirect
259. #1801	C₂×C₃₇	semidirect
304. C₃₇	#28296	direct (N × H)
311. C₂×SD₁₆	Q₈×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₃₇×#3078	2
C₃₇×#3077	2
C₃₇×#2960	2
C₂×C₄×SD₁₆×C₃₇	2
C₃₇×#2064	2
C₃₇×#2063	2
C₃₇×#1977	2
C₃₇×#1951	2
C₃₇×#1848	2
C₃₇×#1801	2
C₃₇×#1800	2
#28296	37

Subgroups — C37×#28296 #22649549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28296 #22649549