Subgroups — C₃₇×#24631 #22645884

Order 9472.

974 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#459	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×SD₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#2548	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#2354	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2054	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2012	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1983	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1957	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1926	C₂	1	2	yes	maximal, complemented
11	C₃₇×#1803	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
13	C₂²×D₈×C₃₇	C₂²	1	2	yes	—
14	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×#124×C₃₇	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×#117×C₃₇	—	2	1	no	—
19	C₃₇×#459	—	2	4	no	—
20	C₄×SD₁₆×C₃₇	—	2	4	no	—
21	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
24	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
25	C₂×#103×C₃₇	C₂²	1	2	yes	—
26	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
27	C₂×#102×C₃₇	C₂²	1	2	yes	—
28	C₂×#102×C₃₇	C₂²	1	2	yes	—
29	C₂×#102×C₃₇	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
31	C₃₇×#394	—	2	2	no	—
32	C₃₇×#390	—	2	1	no	—
33	C₃₇×#390	—	2	1	no	—
34	C₃₇×#390	C₂²	1	2	yes	—
35	C₃₇×#390	C₂²	1	2	yes	—
36	C₃₇×#388	—	2	2	no	—
37	C₃₇×#384	C₂²	1	1	yes	characteristic
38	C₃₇×#380	—	2	1	no	—
39	C₄×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
40	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
41	C₃₇×#340	C₂²	1	2	yes	—
42	C₃₇×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₃₇	—	2	1	no	—
45	C₂²×D₄×C₃₇	—	2	1	no	—
46	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
47	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₃₇	—	2	1	no	—
49	C₂×SD₁₆×C₃₇	—	2	2	no	—
50	C₂×SD₁₆×C₃₇	—	2	2	no	—
51	C₂×SD₁₆×C₃₇	—	2	2	no	—
52	C₂×D₈×C₃₇	—	2	4	no	—
53	C₂×D₈×C₃₇	—	4	2	no	—
54	C₂×D₈×C₃₇	—	4	2	no	—
55	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
56	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
58	#127×C₃₇	—	2	2	no	—
59	#127×C₃₇	—	2	2	no	—
60	#124×C₃₇	—	2	4	no	—
61	#124×C₃₇	—	4	2	no	—
62	C₄×Q₈×C₃₇	—	2	2	no	—
63	C₄×Q₈×C₃₇	—	2	2	no	—
64	C₄×D₄×C₃₇	—	2	2	no	—
65	C₄×D₄×C₃₇	D₄	1	4	yes	—
66	#117×C₃₇	—	4	4	no	—
67	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
68	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
69	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
70	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
82	C₂×C₄²×C₃₇	—	2	2	no	—
83	C₂×C₄²×C₃₇	—	2	1	no	—
84	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
85	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
86	#106×C₃₇	—	2	2	no	—
87	C₄⋊C₈×C₃₇	—	2	2	no	—
88	C₄⋊C₈×C₃₇	—	4	2	no	—
89	#103×C₃₇	—	2	2	no	—
90	#103×C₃₇	—	4	2	no	—
91	#102×C₃₇	—	2	2	no	—
92	#102×C₃₇	—	2	4	no	—
93	#102×C₃₇	—	2	4	no	—
94	#102×C₃₇	—	4	2	no	—
95	C₄×C₈×C₃₇	—	2	2	no	—
96	#95×C₃₇	—	2	2	no	—
97	#95×C₃₇	D₄	1	2	yes	—
98	C₂⁴×C₃₇	—	2	1	no	—
99	C₂⁴×C₃₇	—	2	2	no	—
100	C₂×Q₈×C₃₇	—	2	1	no	—
101	C₂×Q₈×C₃₇	—	2	1	no	—
102	C₂×Q₈×C₃₇	—	2	1	no	—
103	C₂×Q₈×C₃₇	—	2	1	no	—
104	C₂×Q₈×C₃₇	—	2	1	no	—
105	C₂×Q₈×C₃₇	#41	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	—	2	1	no	—
110	C₂×D₄×C₃₇	—	2	2	no	—
111	C₂×D₄×C₃₇	—	2	2	no	—
112	C₂×D₄×C₃₇	—	2	2	no	—
113	C₂×D₄×C₃₇	—	2	1	no	—
114	C₂×D₄×C₃₇	—	2	1	no	—
115	C₂×D₄×C₃₇	—	2	2	no	—
116	C₂×D₄×C₃₇	—	2	2	no	—
117	C₂×D₄×C₃₇	—	4	2	no	—
118	C₂×D₄×C₃₇	—	4	2	no	—
119	C₂×D₄×C₃₇	—	4	2	no	—
120	C₂×D₄×C₃₇	—	4	2	no	—
121	C₂×D₄×C₃₇	—	8	1	no	—
122	C₂×D₄×C₃₇	—	8	1	no	—
123	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₃₇	—	2	1	no	—
125	C₂²×C₄×C₃₇	—	2	1	no	—
126	C₂²×C₄×C₃₇	—	2	4	no	—
127	C₂²×C₄×C₃₇	—	2	2	no	—
128	C₂²×C₄×C₃₇	—	2	1	no	—
129	C₂²×C₄×C₃₇	—	4	2	no	—
130	C₂²×C₄×C₃₇	—	4	2	no	—
131	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
136	SD₁₆×C₃₇	—	2	8	no	—
137	D₈×C₃₇	—	4	8	no	—
138	C₂×C₈×C₃₇	—	2	1	no	—
139	C₂×C₈×C₃₇	—	2	1	no	—
140	C₂×C₈×C₃₇	—	2	1	no	—
141	C₂×C₈×C₃₇	—	2	2	no	—
142	C₂×C₈×C₃₇	—	2	1	no	—
143	C₂×C₈×C₃₇	—	2	2	no	—
144	C₂×C₈×C₃₇	—	2	1	no	—
145	C₂×C₈×C₃₇	—	2	2	no	—
146	C₂×C₈×C₃₇	#41	1	2	yes	—
147	C₄⋊C₄×C₃₇	—	2	2	no	—
148	C₄⋊C₄×C₃₇	—	2	2	no	—
149	C₄⋊C₄×C₃₇	—	2	1	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	2	no	—
154	C₄⋊C₄×C₃₇	—	4	2	no	—
155	C₄⋊C₄×C₃₇	—	4	2	no	—
156	C₄⋊C₄×C₃₇	—	8	1	no	—
157	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
158	C₂²⋊C₄×C₃₇	—	2	4	no	—
159	C₂²⋊C₄×C₃₇	—	4	4	no	—
160	C₂²⋊C₄×C₃₇	—	4	4	no	—
161	C₂²⋊C₄×C₃₇	—	4	4	no	—
162	C₂²⋊C₄×C₃₇	—	8	2	no	—
163	C₂²⋊C₄×C₃₇	—	8	2	no	—
164	C₂²⋊C₄×C₃₇	—	8	2	no	—
165	C₄²×C₃₇	—	2	2	no	—
166	C₄²×C₃₇	—	2	2	no	—
167	C₄²×C₃₇	—	4	4	no	—
168	C₄²×C₃₇	—	4	2	no	—
169	C₄²×C₃₇	C₂×D₄	1	2	yes	—
170	C₄²×C₃₇	#41	1	2	yes	—
171	C₂³×C₃₇	—	2	2	no	—
172	C₂³×C₃₇	—	4	1	no	—
173	C₂³×C₃₇	—	4	1	no	—
174	C₂³×C₃₇	—	4	1	no	—
175	C₂³×C₃₇	—	4	1	no	—
176	C₂³×C₃₇	—	4	1	no	—
177	C₂³×C₃₇	—	4	1	no	—
178	C₂³×C₃₇	—	4	2	no	—
179	C₂³×C₃₇	—	4	2	no	—
180	C₂³×C₃₇	—	4	2	no	—
181	C₂³×C₃₇	—	4	2	no	—
182	C₂³×C₃₇	—	4	2	no	—
183	C₂³×C₃₇	—	4	2	no	—
184	C₂³×C₃₇	—	4	2	no	—
185	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
186	Q₈×C₃₇	—	2	2	no	—
187	Q₈×C₃₇	—	2	2	no	—
188	Q₈×C₃₇	—	4	1	no	—
189	Q₈×C₃₇	—	4	1	no	—
190	D₄×C₃₇	—	2	2	no	—
191	D₄×C₃₇	—	2	2	no	—
192	D₄×C₃₇	—	4	2	no	—
193	D₄×C₃₇	—	4	2	no	—
194	D₄×C₃₇	—	4	1	no	—
195	D₄×C₃₇	—	4	2	no	—
196	D₄×C₃₇	—	4	1	no	—
197	D₄×C₃₇	—	4	2	no	—
198	D₄×C₃₇	—	8	4	no	—
199	D₄×C₃₇	—	8	4	no	—
200	C₂×C₄×C₃₇	—	2	1	no	—
201	C₂×C₄×C₃₇	—	2	1	no	—
202	C₂×C₄×C₃₇	—	2	2	no	—
203	C₂×C₄×C₃₇	—	2	2	no	—
204	C₂×C₄×C₃₇	—	2	2	no	—
205	C₂×C₄×C₃₇	—	2	2	no	—
206	C₂×C₄×C₃₇	—	2	2	no	—
207	C₂×C₄×C₃₇	—	2	2	no	—
208	C₂×C₄×C₃₇	—	2	2	no	—
209	C₂×C₄×C₃₇	—	2	2	no	—
210	C₂×C₄×C₃₇	—	4	1	no	—
211	C₂×C₄×C₃₇	—	4	1	no	—
212	C₂×C₄×C₃₇	—	4	1	no	—
213	C₂×C₄×C₃₇	—	4	1	no	—
214	C₂×C₄×C₃₇	—	4	8	no	—
215	C₂×C₄×C₃₇	—	4	1	no	—
216	C₂×C₄×C₃₇	—	4	2	no	—
217	C₂×C₄×C₃₇	—	4	2	no	—
218	C₂×C₄×C₃₇	—	4	1	no	—
219	C₂×C₄×C₃₇	—	4	2	no	—
220	C₂×C₄×C₃₇	—	4	1	no	—
221	C₂×C₄×C₃₇	#121	1	2	yes	—
222	C₂×C₄×C₃₇	#121	1	2	yes	—
223	C₂×C₄×C₃₇	#135	1	2	yes	—
224	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
225	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
227	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
228	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
229	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
230	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
231	C₈×C₃₇	—	2	2	no	—
232	C₈×C₃₇	—	4	1	no	—
233	C₈×C₃₇	—	4	2	no	—
234	#24631	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂²×C₃₇	—	4	2	no	—
236	C₂²×C₃₇	—	4	2	no	—
237	C₂²×C₃₇	—	4	2	no	—
238	C₂²×C₃₇	—	8	1	no	—
239	C₂²×C₃₇	—	8	1	no	—
240	C₂²×C₃₇	—	8	1	no	—
241	C₂²×C₃₇	—	8	1	no	—
242	C₂²×C₃₇	—	8	2	no	—
243	C₂²×C₃₇	—	8	2	no	—
244	C₂²×C₃₇	—	8	2	no	—
245	C₂²×C₃₇	—	8	2	no	—
246	C₂²×C₃₇	—	8	2	no	—
247	C₂²×C₃₇	—	8	2	no	—
248	C₂²×C₃₇	—	8	2	no	—
249	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
250	C₂²×C₃₇	#546	1	1	yes	characteristic
251	C₂²×C₃₇	#550	1	1	yes	characteristic
252	C₂²×C₃₇	C₂×#135	1	1	yes	characteristic
253	C₂²×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
254	C₂²×C₃₇	#576	1	1	yes	characteristic
255	C₂²×C₃₇	#577	1	1	yes	characteristic
256	C₄×C₃₇	—	2	2	no	—
257	C₄×C₃₇	—	4	2	no	—
258	C₄×C₃₇	—	4	2	no	—
259	C₄×C₃₇	—	4	2	no	—
260	C₄×C₃₇	—	4	2	no	—
261	C₄×C₃₇	—	8	2	no	—
262	C₄×C₃₇	—	8	1	no	—
263	C₄×C₃₇	#463	1	4	yes	—
264	C₄×C₃₇	#525	1	1	yes	characteristic
265	C₄×C₃₇	#535	1	1	yes	characteristic
266	C₄×C₃₇	#553	1	1	yes	characteristic
267	C₄×C₃₇	#555	1	1	yes	characteristic
268	C₂×#459	C₂×C₃₇	1	1	yes	characteristic
269	C₂×C₄×SD₁₆	C₂×C₃₇	1	1	yes	characteristic, complemented
270	#2548	C₂×C₃₇	1	1	yes	characteristic, complemented
271	#2354	C₂×C₃₇	1	1	yes	characteristic, complemented
272	#2054	C₂×C₃₇	1	2	yes	complemented
273	#2012	C₂×C₃₇	1	2	yes	complemented
274	#1983	C₂×C₃₇	1	2	yes	complemented
275	#1957	C₂×C₃₇	1	1	yes	characteristic, complemented
276	#1939	C₂×C₃₇	1	1	yes	characteristic, complemented
277	#1926	C₂×C₃₇	1	2	yes	complemented
278	#1803	C₂×C₃₇	1	1	yes	characteristic, complemented
279	C₂×C₃₇	—	8	2	no	—
280	C₂×C₃₇	—	16	2	no	—
281	C₂×C₃₇	#2414	1	1	yes	characteristic
282	C₂×C₃₇	C₂×#463	1	1	yes	characteristic
283	C₂×C₃₇	#3045	1	1	yes	characteristic
284	C₂×C₃₇	#3305	1	1	yes	characteristic
285	C₂×C₃₇	#3332	1	1	yes	characteristic
286	C₂×C₃₇	#3394	1	1	yes	characteristic
287	C₂×C₃₇	#3399	1	1	yes	characteristic
288	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
289	C₂²×D₈	C₂²×C₃₇	1	2	yes	—
290	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
291	C₂×#124	C₂²×C₃₇	1	2	yes	—
292	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
293	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
294	C₂×#117	—	2	1	no	—
295	#459	—	2	4	no	—
296	C₄×SD₁₆	—	2	4	no	—
297	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
298	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
299	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
300	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
301	C₂×#103	C₂²×C₃₇	1	2	yes	—
302	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
303	C₂×#102	C₂²×C₃₇	1	2	yes	—
304	C₂×#102	C₂²×C₃₇	1	2	yes	—
305	C₂×#102	C₂²×C₃₇	1	2	yes	—
306	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
307	#394	—	2	2	no	—
308	#390	—	2	1	no	—
309	#390	—	2	1	no	—
310	#390	C₂²×C₃₇	1	2	yes	—
311	#390	C₂²×C₃₇	1	2	yes	—
312	#388	—	2	2	no	—
313	#384	C₂²×C₃₇	1	1	yes	characteristic
314	#380	—	2	1	no	—
315	C₄×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
316	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
317	#340	C₂²×C₃₇	1	2	yes	—
318	#336	C₂²×C₃₇	1	2	yes	—
319	C₃₇	#24631	1	1	yes	characteristic, direct product factor, Sylow
320	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
321	C₂²×D₄	—	2	1	no	—
322	C₂²×D₄	—	2	1	no	—
323	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
324	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
325	C₂³×C₄	—	2	1	no	—
326	C₂×SD₁₆	—	2	2	no	—
327	C₂×SD₁₆	—	2	2	no	—
328	C₂×SD₁₆	—	2	2	no	—
329	C₂×D₈	—	2	4	no	—
330	C₂×D₈	—	4	2	no	—
331	C₂×D₈	—	4	2	no	—
332	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
333	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
334	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
335	#127	—	2	2	no	—
336	#127	—	2	2	no	—
337	#124	—	2	4	no	—
338	#124	—	4	2	no	—
339	C₄×Q₈	—	2	2	no	—
340	C₄×Q₈	—	2	2	no	—
341	C₄×D₄	—	2	2	no	—
342	C₄×D₄	D₄×C₃₇	1	4	yes	—
343	#117	—	4	4	no	—
344	C₂×C₄⋊C₄	—	2	1	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×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
351	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
352	C₂×C₂²⋊C₄	—	2	1	no	—
353	C₂×C₂²⋊C₄	—	2	2	no	—
354	C₂×C₂²⋊C₄	—	2	2	no	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	—	2	2	no	—
359	C₂×C₄²	—	2	2	no	—
360	C₂×C₄²	—	2	1	no	—
361	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
362	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
363	#106	—	2	2	no	—
364	C₄⋊C₈	—	2	2	no	—
365	C₄⋊C₈	—	4	2	no	—
366	#103	—	2	2	no	—
367	#103	—	4	2	no	—
368	#102	—	2	2	no	—
369	#102	—	2	4	no	—
370	#102	—	2	4	no	—
371	#102	—	4	2	no	—
372	C₄×C₈	—	2	2	no	—
373	#95	—	2	2	no	—
374	#95	D₄×C₃₇	1	2	yes	—
375	C₂⁴	—	2	1	no	—
376	C₂⁴	—	2	2	no	—
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	2	1	no	—
382	C₂×Q₈	#41×C₃₇	1	2	yes	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	1	no	—
385	C₂×D₄	—	2	1	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	4	2	no	—
395	C₂×D₄	—	4	2	no	—
396	C₂×D₄	—	4	2	no	—
397	C₂×D₄	—	4	2	no	—
398	C₂×D₄	—	8	1	no	—
399	C₂×D₄	—	8	1	no	—
400	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	4	2	no	—
407	C₂²×C₄	—	4	2	no	—
408	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
409	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
410	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
412	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
413	SD₁₆	—	2	8	no	—
414	D₈	—	4	8	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	#41×C₃₇	1	2	yes	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	4	2	no	—
432	C₄⋊C₄	—	4	2	no	—
433	C₄⋊C₄	—	8	1	no	—
434	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
435	C₂²⋊C₄	—	2	4	no	—
436	C₂²⋊C₄	—	4	4	no	—
437	C₂²⋊C₄	—	4	4	no	—
438	C₂²⋊C₄	—	4	4	no	—
439	C₂²⋊C₄	—	8	2	no	—
440	C₂²⋊C₄	—	8	2	no	—
441	C₂²⋊C₄	—	8	2	no	—
442	C₄²	—	2	2	no	—
443	C₄²	—	2	2	no	—
444	C₄²	—	4	4	no	—
445	C₄²	—	4	2	no	—
446	C₄²	C₂×D₄×C₃₇	1	2	yes	—
447	C₄²	#41×C₃₇	1	2	yes	—
448	C₂³	—	2	2	no	—
449	C₂³	—	4	1	no	—
450	C₂³	—	4	1	no	—
451	C₂³	—	4	1	no	—
452	C₂³	—	4	1	no	—
453	C₂³	—	4	1	no	—
454	C₂³	—	4	1	no	—
455	C₂³	—	4	2	no	—
456	C₂³	—	4	2	no	—
457	C₂³	—	4	2	no	—
458	C₂³	—	4	2	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	4	2	no	—
461	C₂³	—	4	2	no	—
462	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
463	Q₈	—	2	2	no	—
464	Q₈	—	2	2	no	—
465	Q₈	—	4	1	no	—
466	Q₈	—	4	1	no	—
467	D₄	—	2	2	no	—
468	D₄	—	2	2	no	—
469	D₄	—	4	2	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	1	no	—
472	D₄	—	4	2	no	—
473	D₄	—	4	1	no	—
474	D₄	—	4	2	no	—
475	D₄	—	8	4	no	—
476	D₄	—	8	4	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	8	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	#121×C₃₇	1	2	yes	—
499	C₂×C₄	#121×C₃₇	1	2	yes	—
500	C₂×C₄	#135×C₃₇	1	2	yes	—
501	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
502	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
503	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
504	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
505	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
506	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
507	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
508	C₈	—	2	2	no	—
509	C₈	—	4	2	no	—
510	C₈	—	4	1	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	8	1	no	—
515	C₂²	—	8	1	no	—
516	C₂²	—	8	1	no	—
517	C₂²	—	8	1	no	—
518	C₂²	—	8	2	no	—
519	C₂²	—	8	2	no	—
520	C₂²	—	8	2	no	—
521	C₂²	—	8	2	no	—
522	C₂²	—	8	2	no	—
523	C₂²	—	8	2	no	—
524	C₂²	—	8	2	no	—
525	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
526	C₂²	C₃₇×#546	1	1	yes	characteristic
527	C₂²	C₃₇×#550	1	1	yes	characteristic
528	C₂²	C₂×#135×C₃₇	1	1	yes	characteristic
529	C₂²	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
530	C₂²	C₃₇×#576	1	1	yes	characteristic
531	C₂²	C₃₇×#577	1	1	yes	characteristic
532	C₄	—	2	2	no	—
533	C₄	—	4	2	no	—
534	C₄	—	4	2	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	2	no	—
537	C₄	—	8	2	no	—
538	C₄	—	8	1	no	—
539	C₄	C₃₇×#463	1	4	yes	—
540	C₄	C₃₇×#525	1	1	yes	characteristic
541	C₄	C₃₇×#535	1	1	yes	characteristic
542	C₄	C₃₇×#553	1	1	yes	characteristic
543	C₄	C₃₇×#555	1	1	yes	characteristic
544	C₂	—	8	2	no	—
545	C₂	—	16	2	no	—
546	C₂	C₃₇×#2414	1	1	yes	characteristic
547	C₂	C₂×C₃₇×#463	1	1	yes	characteristic
548	C₂	C₃₇×#3045	1	1	yes	characteristic
549	C₂	C₃₇×#3305	1	1	yes	characteristic
550	C₂	C₃₇×#3332	1	1	yes	characteristic
551	C₂	C₃₇×#3394	1	1	yes	characteristic
552	C₂	C₃₇×#3399	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂×C₃₇×#459	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₄×C₄⋊C₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×SD₁₆×C₃₇	C₂	semidirect
3. C₃₇×#2548	C₂	semidirect
4. C₃₇×#2354	C₂	semidirect
5. C₃₇×#2054	C₂	semidirect
6. C₃₇×#2012	C₂	semidirect
7. C₃₇×#1983	C₂	semidirect
8. C₃₇×#1957	C₂	semidirect
9. C₃₇×#1939	C₂	semidirect
10. C₃₇×#1926	C₂	semidirect
11. C₃₇×#1803	C₂	semidirect
234. #24631	C₃₇	direct (N × H)
269. C₂×C₄×SD₁₆	C₂×C₃₇	semidirect
270. #2548	C₂×C₃₇	semidirect
271. #2354	C₂×C₃₇	semidirect
272. #2054	C₂×C₃₇	semidirect
273. #2012	C₂×C₃₇	semidirect
274. #1983	C₂×C₃₇	semidirect
275. #1957	C₂×C₃₇	semidirect
276. #1939	C₂×C₃₇	semidirect
277. #1926	C₂×C₃₇	semidirect
278. #1803	C₂×C₃₇	semidirect
319. C₃₇	#24631	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₇×#459	2
C₂×C₄×SD₁₆×C₃₇	2
C₃₇×#2548	2
C₃₇×#2354	2
C₃₇×#2054	2
C₃₇×#2012	2
C₃₇×#1983	2
C₃₇×#1957	2
C₃₇×#1939	2
C₃₇×#1926	2
C₃₇×#1803	2
#24631	37

Subgroups — C37×#24631 #22645884

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#24631 #22645884