Subgroups — C₃₇×#29962 #22651215

Order 9472.

950 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#2629	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×#2309	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2094	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#2093	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2067	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2065	C₂	1	2	yes	maximal, complemented
7	C₃₇×#2025	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#2025	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1854	C₂	1	2	yes	maximal, complemented
10	C₃₇×#1798	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1786	C₂	1	2	yes	maximal
12	C₂³×D₄×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×#125×C₃₇	C₂²	1	1	yes	characteristic, complemented
14	C₂×#117×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×#117×C₃₇	C₂²	1	1	yes	characteristic
16	C₂×#107×C₃₇	C₂²	1	2	yes	complemented
17	C₂×#106×C₃₇	C₂²	1	2	yes	complemented
18	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	complemented
19	C₂×#102×C₃₇	C₂²	1	2	yes	—
20	C₂×#102×C₃₇	C₂²	1	2	yes	—
21	C₂×#102×C₃₇	C₂²	1	2	yes	—
22	C₂×#102×C₃₇	C₂²	1	2	yes	—
23	C₂×C₂²⋊C₈×C₃₇	C₂²	1	2	yes	—
24	C₃₇×#398	—	2	2	no	—
25	C₃₇×#396	—	2	2	no	—
26	C₃₇×#390	—	2	2	no	—
27	C₃₇×#390	C₂²	1	1	yes	characteristic
28	C₃₇×#390	C₂²	1	1	yes	characteristic
29	C₃₇×#390	C₂²	1	1	yes	characteristic
30	C₃₇×#390	C₂²	1	1	yes	characteristic
31	C₃₇×#389	C₂²	1	2	yes	complemented
32	C₃₇×#384	C₂²	1	1	yes	characteristic, complemented
33	C₃₇×#380	C₂²	1	2	yes	—
34	C₃₇×#379	—	2	2	no	—
35	C₃₇×#340	C₂²	1	2	yes	complemented
36	C₃₇×#340	C₂²	1	2	yes	complemented
37	C₃₇×#336	C₂²	1	1	yes	characteristic, complemented
38	C₃₇×#336	C₂²	1	1	yes	characteristic, complemented
39	C₂⁵×C₃₇	—	2	1	no	—
40	C₂²×D₄×C₃₇	—	2	1	no	—
41	C₂²×D₄×C₃₇	—	2	2	no	—
42	C₂²×D₄×C₃₇	—	4	2	no	—
43	C₂²×D₄×C₃₇	—	4	2	no	—
44	C₂²×D₄×C₃₇	Q₈	1	4	yes	—
45	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
49	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
50	#125×C₃₇	—	4	2	no	—
51	#117×C₃₇	—	4	2	no	—
52	#117×C₃₇	—	4	2	no	—
53	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
57	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
61	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₃₇	D₄	1	2	yes	—
68	C₂×C₄²×C₃₇	—	2	1	no	—
69	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
71	#107×C₃₇	—	4	2	no	—
72	#106×C₃₇	—	4	2	no	—
73	C₄⋊C₈×C₃₇	—	4	2	no	—
74	#102×C₃₇	—	4	2	no	—
75	#102×C₃₇	—	4	2	no	—
76	#102×C₃₇	—	4	2	no	—
77	#102×C₃₇	—	4	2	no	—
78	C₂²⋊C₈×C₃₇	—	2	4	no	—
79	#95×C₃₇	—	2	2	no	—
80	#95×C₃₇	—	2	2	no	—
81	C₂⁴×C₃₇	—	2	1	no	—
82	C₂⁴×C₃₇	—	2	1	no	—
83	C₂⁴×C₃₇	—	2	4	no	—
84	C₂⁴×C₃₇	—	4	2	no	—
85	C₂⁴×C₃₇	—	4	2	no	—
86	C₂⁴×C₃₇	—	8	2	no	—
87	C₂⁴×C₃₇	—	8	2	no	—
88	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
89	C₂×D₄×C₃₇	—	2	4	no	—
90	C₂×D₄×C₃₇	—	2	1	no	—
91	C₂×D₄×C₃₇	—	2	1	no	—
92	C₂×D₄×C₃₇	—	2	2	no	—
93	C₂×D₄×C₃₇	—	2	2	no	—
94	C₂×D₄×C₃₇	—	2	2	no	—
95	C₂×D₄×C₃₇	—	2	2	no	—
96	C₂×D₄×C₃₇	—	4	8	no	—
97	C₂×D₄×C₃₇	—	4	2	no	—
98	C₂×D₄×C₃₇	—	4	2	no	—
99	C₂×D₄×C₃₇	—	4	8	no	—
100	C₂×D₄×C₃₇	C₂×Q₈	1	2	yes	—
101	C₂×D₄×C₃₇	C₂×Q₈	1	2	yes	—
102	C₂²×C₄×C₃₇	—	2	2	no	—
103	C₂²×C₄×C₃₇	—	2	2	no	—
104	C₂²×C₄×C₃₇	—	2	2	no	—
105	C₂²×C₄×C₃₇	—	2	2	no	—
106	C₂²×C₄×C₃₇	—	2	1	no	—
107	C₂²×C₄×C₃₇	—	2	1	no	—
108	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₃₇	C₂×Q₈	1	2	yes	—
112	C₂²×C₄×C₃₇	#41	1	2	yes	—
113	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
114	C₂×C₈×C₃₇	—	2	2	no	—
115	C₂×C₈×C₃₇	—	2	2	no	—
116	C₂×C₈×C₃₇	—	2	2	no	—
117	C₂×C₈×C₃₇	—	2	2	no	—
118	C₂×C₈×C₃₇	—	2	2	no	—
119	C₂×C₈×C₃₇	—	2	2	no	—
120	C₄⋊C₄×C₃₇	—	2	2	no	—
121	C₄⋊C₄×C₃₇	—	2	2	no	—
122	C₄⋊C₄×C₃₇	—	2	2	no	—
123	C₄⋊C₄×C₃₇	—	2	2	no	—
124	C₄⋊C₄×C₃₇	—	2	2	no	—
125	C₄⋊C₄×C₃₇	—	2	2	no	—
126	C₄⋊C₄×C₃₇	—	4	2	no	—
127	C₄⋊C₄×C₃₇	—	4	4	no	—
128	C₄⋊C₄×C₃₇	—	8	2	no	—
129	C₄⋊C₄×C₃₇	—	8	2	no	—
130	C₂²⋊C₄×C₃₇	—	4	2	no	—
131	C₂²⋊C₄×C₃₇	—	4	2	no	—
132	C₂²⋊C₄×C₃₇	—	8	2	no	—
133	C₂²⋊C₄×C₃₇	—	8	2	no	—
134	C₂²⋊C₄×C₃₇	—	8	2	no	—
135	C₂²⋊C₄×C₃₇	—	8	2	no	—
136	C₂²⋊C₄×C₃₇	—	8	2	no	—
137	C₄²×C₃₇	—	2	2	no	—
138	C₄²×C₃₇	—	2	2	no	—
139	C₄²×C₃₇	—	4	2	no	—
140	C₂³×C₃₇	—	2	1	no	—
141	C₂³×C₃₇	—	2	1	no	—
142	C₂³×C₃₇	—	2	2	no	—
143	C₂³×C₃₇	—	2	2	no	—
144	C₂³×C₃₇	—	2	2	no	—
145	C₂³×C₃₇	—	2	2	no	—
146	C₂³×C₃₇	—	4	8	no	—
147	C₂³×C₃₇	—	4	1	no	—
148	C₂³×C₃₇	—	4	1	no	—
149	C₂³×C₃₇	—	4	1	no	—
150	C₂³×C₃₇	—	4	1	no	—
151	C₂³×C₃₇	—	4	2	no	—
152	C₂³×C₃₇	—	4	2	no	—
153	C₂³×C₃₇	—	4	2	no	—
154	C₂³×C₃₇	—	4	2	no	—
155	C₂³×C₃₇	—	8	8	no	—
156	C₂³×C₃₇	—	8	8	no	—
157	C₂³×C₃₇	—	8	4	no	—
158	C₂³×C₃₇	—	8	4	no	—
159	C₂³×C₃₇	C₂²⋊Q₈	1	2	yes	—
160	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
161	D₄×C₃₇	—	2	4	no	—
162	D₄×C₃₇	—	2	4	no	—
163	D₄×C₃₇	—	4	8	no	—
164	D₄×C₃₇	—	4	2	no	—
165	D₄×C₃₇	—	4	2	no	—
166	C₂×C₄×C₃₇	—	2	1	no	—
167	C₂×C₄×C₃₇	—	2	1	no	—
168	C₂×C₄×C₃₇	—	2	4	no	—
169	C₂×C₄×C₃₇	—	2	4	no	—
170	C₂×C₄×C₃₇	—	2	2	no	—
171	C₂×C₄×C₃₇	—	2	2	no	—
172	C₂×C₄×C₃₇	—	2	2	no	—
173	C₂×C₄×C₃₇	—	2	2	no	—
174	C₂×C₄×C₃₇	—	2	2	no	—
175	C₂×C₄×C₃₇	—	2	2	no	—
176	C₂×C₄×C₃₇	—	4	2	no	—
177	C₂×C₄×C₃₇	—	4	1	no	—
178	C₂×C₄×C₃₇	—	4	1	no	—
179	C₂×C₄×C₃₇	—	4	2	no	—
180	C₂×C₄×C₃₇	—	4	2	no	—
181	C₂×C₄×C₃₇	—	4	2	no	—
182	C₂×C₄×C₃₇	—	4	2	no	—
183	C₂×C₄×C₃₇	—	4	2	no	—
184	C₂×C₄×C₃₇	—	4	2	no	—
185	C₂×C₄×C₃₇	—	4	2	no	—
186	C₂×C₄×C₃₇	C₂²⋊Q₈	1	2	yes	—
187	C₂×C₄×C₃₇	C₂²×Q₈	1	1	yes	characteristic
188	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
190	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
191	C₈×C₃₇	—	4	2	no	—
192	C₈×C₃₇	—	4	2	no	—
193	#29962	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂²×C₃₇	—	2	4	no	—
195	C₂²×C₃₇	—	2	2	no	—
196	C₂²×C₃₇	—	4	2	no	—
197	C₂²×C₃₇	—	4	1	no	—
198	C₂²×C₃₇	—	4	1	no	—
199	C₂²×C₃₇	—	4	4	no	—
200	C₂²×C₃₇	—	4	4	no	—
201	C₂²×C₃₇	—	4	2	no	—
202	C₂²×C₃₇	—	4	2	no	—
203	C₂²×C₃₇	—	8	16	no	—
204	C₂²×C₃₇	—	8	2	no	—
205	C₂²×C₃₇	—	8	2	no	—
206	C₂²×C₃₇	—	8	1	no	—
207	C₂²×C₃₇	—	8	1	no	—
208	C₂²×C₃₇	—	8	1	no	—
209	C₂²×C₃₇	—	8	1	no	—
210	C₂²×C₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
211	C₂²×C₃₇	#534	1	1	yes	characteristic
212	C₂²×C₃₇	#535	1	1	yes	characteristic
213	C₂²×C₃₇	#576	1	2	yes	—
214	C₂²×C₃₇	#577	1	2	yes	—
215	C₄×C₃₇	—	2	2	no	—
216	C₄×C₃₇	—	4	2	no	—
217	C₄×C₃₇	—	4	2	no	—
218	C₄×C₃₇	—	8	2	no	—
219	C₄×C₃₇	—	8	1	no	—
220	C₄×C₃₇	—	8	2	no	—
221	C₄×C₃₇	—	8	1	no	—
222	C₄×C₃₇	#538	1	2	yes	—
223	C₄×C₃₇	#543	1	2	yes	—
224	#2629	C₂×C₃₇	1	1	yes	characteristic, complemented
225	#2309	C₂×C₃₇	1	1	yes	characteristic
226	#2094	C₂×C₃₇	1	1	yes	characteristic, complemented
227	#2093	C₂×C₃₇	1	1	yes	characteristic, complemented
228	#2067	C₂×C₃₇	1	2	yes	complemented
229	#2065	C₂×C₃₇	1	2	yes	complemented
230	#2025	C₂×C₃₇	1	1	yes	characteristic, complemented
231	#2025	C₂×C₃₇	1	1	yes	characteristic, complemented
232	#1854	C₂×C₃₇	1	2	yes	complemented
233	#1798	C₂×C₃₇	1	1	yes	characteristic, complemented
234	#1786	C₂×C₃₇	1	2	yes	—
235	C₂×C₃₇	—	4	2	no	—
236	C₂×C₃₇	—	8	2	no	—
237	C₂×C₃₇	—	8	2	no	—
238	C₂×C₃₇	#2626	1	1	yes	characteristic
239	C₂×C₃₇	#3081	1	2	yes	—
240	C₂×C₃₇	#3198	1	2	yes	—
241	C₂×C₃₇	#3220	1	1	yes	characteristic
242	C₂×C₃₇	#3222	1	1	yes	characteristic
243	C₂³×D₄	C₂²×C₃₇	1	1	yes	characteristic
244	C₂×#125	C₂²×C₃₇	1	1	yes	characteristic, complemented
245	C₂×#117	C₂²×C₃₇	1	1	yes	characteristic
246	C₂×#117	C₂²×C₃₇	1	1	yes	characteristic
247	C₂×#107	C₂²×C₃₇	1	2	yes	complemented
248	C₂×#106	C₂²×C₃₇	1	2	yes	complemented
249	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	complemented
250	C₂×#102	C₂²×C₃₇	1	2	yes	—
251	C₂×#102	C₂²×C₃₇	1	2	yes	—
252	C₂×#102	C₂²×C₃₇	1	2	yes	—
253	C₂×#102	C₂²×C₃₇	1	2	yes	—
254	C₂×C₂²⋊C₈	C₂²×C₃₇	1	2	yes	—
255	#398	—	2	2	no	—
256	#396	—	2	2	no	—
257	#390	—	2	2	no	—
258	#390	C₂²×C₃₇	1	1	yes	characteristic
259	#390	C₂²×C₃₇	1	1	yes	characteristic
260	#390	C₂²×C₃₇	1	1	yes	characteristic
261	#390	C₂²×C₃₇	1	1	yes	characteristic
262	#389	C₂²×C₃₇	1	2	yes	complemented
263	#384	C₂²×C₃₇	1	1	yes	characteristic, complemented
264	#380	C₂²×C₃₇	1	2	yes	—
265	#379	—	2	2	no	—
266	#340	C₂²×C₃₇	1	2	yes	complemented
267	#340	C₂²×C₃₇	1	2	yes	complemented
268	#336	C₂²×C₃₇	1	1	yes	characteristic, complemented
269	#336	C₂²×C₃₇	1	1	yes	characteristic, complemented
270	C₃₇	#29962	1	1	yes	characteristic, direct product factor, Sylow
271	C₂⁵	—	2	1	no	—
272	C₂²×D₄	—	2	1	no	—
273	C₂²×D₄	—	2	2	no	—
274	C₂²×D₄	—	4	2	no	—
275	C₂²×D₄	—	4	2	no	—
276	C₂²×D₄	Q₈×C₃₇	1	4	yes	—
277	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
278	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
279	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
280	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
281	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
282	#125	—	4	2	no	—
283	#117	—	4	2	no	—
284	#117	—	4	2	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₂²⋊C₄	D₄×C₃₇	1	2	yes	—
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
302	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
303	#107	—	4	2	no	—
304	#106	—	4	2	no	—
305	C₄⋊C₈	—	4	2	no	—
306	#102	—	4	2	no	—
307	#102	—	4	2	no	—
308	#102	—	4	2	no	—
309	#102	—	4	2	no	—
310	C₂²⋊C₈	—	2	4	no	—
311	#95	—	2	2	no	—
312	#95	—	2	2	no	—
313	C₂⁴	—	2	1	no	—
314	C₂⁴	—	2	1	no	—
315	C₂⁴	—	2	4	no	—
316	C₂⁴	—	4	2	no	—
317	C₂⁴	—	4	2	no	—
318	C₂⁴	—	8	2	no	—
319	C₂⁴	—	8	2	no	—
320	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
321	C₂×D₄	—	2	4	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	4	8	no	—
329	C₂×D₄	—	4	2	no	—
330	C₂×D₄	—	4	2	no	—
331	C₂×D₄	—	4	8	no	—
332	C₂×D₄	C₂×Q₈×C₃₇	1	2	yes	—
333	C₂×D₄	C₂×Q₈×C₃₇	1	2	yes	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
341	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
342	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
343	C₂²×C₄	C₂×Q₈×C₃₇	1	2	yes	—
344	C₂²×C₄	#41×C₃₇	1	2	yes	—
345	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₄⋊C₄	—	4	4	no	—
360	C₄⋊C₄	—	8	2	no	—
361	C₄⋊C₄	—	8	2	no	—
362	C₂²⋊C₄	—	4	2	no	—
363	C₂²⋊C₄	—	4	2	no	—
364	C₂²⋊C₄	—	8	2	no	—
365	C₂²⋊C₄	—	8	2	no	—
366	C₂²⋊C₄	—	8	2	no	—
367	C₂²⋊C₄	—	8	2	no	—
368	C₂²⋊C₄	—	8	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	4	2	no	—
372	C₂³	—	2	1	no	—
373	C₂³	—	2	1	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	2	no	—
378	C₂³	—	4	8	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	1	no	—
383	C₂³	—	4	2	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	4	2	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	8	8	no	—
388	C₂³	—	8	8	no	—
389	C₂³	—	8	4	no	—
390	C₂³	—	8	4	no	—
391	C₂³	C₂²⋊Q₈×C₃₇	1	2	yes	—
392	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
393	D₄	—	2	4	no	—
394	D₄	—	2	4	no	—
395	D₄	—	4	8	no	—
396	D₄	—	4	2	no	—
397	D₄	—	4	2	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	C₂²⋊Q₈×C₃₇	1	2	yes	—
419	C₂×C₄	C₂²×Q₈×C₃₇	1	1	yes	characteristic
420	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
421	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
422	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
423	C₈	—	4	2	no	—
424	C₈	—	4	2	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	4	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	1	no	—
429	C₂²	—	4	1	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	8	16	no	—
435	C₂²	—	8	2	no	—
436	C₂²	—	8	2	no	—
437	C₂²	—	8	1	no	—
438	C₂²	—	8	1	no	—
439	C₂²	—	8	1	no	—
440	C₂²	—	8	1	no	—
441	C₂²	C₂×C₂²⋊Q₈×C₃₇	1	1	yes	characteristic
442	C₂²	C₃₇×#534	1	1	yes	characteristic
443	C₂²	C₃₇×#535	1	1	yes	characteristic
444	C₂²	C₃₇×#576	1	2	yes	—
445	C₂²	C₃₇×#577	1	2	yes	—
446	C₄	—	2	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	8	2	no	—
450	C₄	—	8	1	no	—
451	C₄	—	8	2	no	—
452	C₄	—	8	1	no	—
453	C₄	C₃₇×#538	1	2	yes	—
454	C₄	C₃₇×#543	1	2	yes	—
455	C₂	—	4	2	no	—
456	C₂	—	8	2	no	—
457	C₂	—	8	2	no	—
458	C₂	C₃₇×#2626	1	1	yes	characteristic
459	C₂	C₃₇×#3081	1	2	yes	—
460	C₂	C₃₇×#3198	1	2	yes	—
461	C₂	C₃₇×#3220	1	1	yes	characteristic
462	C₂	C₃₇×#3222	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂³×D₄×C₃₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₂×#117×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×#2629	C₂	semidirect
3. C₃₇×#2094	C₂	semidirect
4. C₃₇×#2093	C₂	semidirect
5. C₃₇×#2067	C₂	semidirect
6. C₃₇×#2065	C₂	semidirect
7. C₃₇×#2025	C₂	semidirect
8. C₃₇×#2025	C₂	semidirect
9. C₃₇×#1854	C₂	semidirect
10. C₃₇×#1798	C₂	semidirect
13. C₂×#125×C₃₇	C₂²	semidirect
16. C₂×#107×C₃₇	C₂²	semidirect
17. C₂×#106×C₃₇	C₂²	semidirect
18. C₂×C₄⋊C₈×C₃₇	C₂²	semidirect
31. C₃₇×#389	C₂²	semidirect
32. C₃₇×#384	C₂²	semidirect
35. C₃₇×#340	C₂²	semidirect
36. C₃₇×#340	C₂²	semidirect
37. C₃₇×#336	C₂²	semidirect
38. C₃₇×#336	C₂²	semidirect
193. #29962	C₃₇	direct (N × H)
224. #2629	C₂×C₃₇	semidirect
226. #2094	C₂×C₃₇	semidirect
227. #2093	C₂×C₃₇	semidirect
228. #2067	C₂×C₃₇	semidirect
229. #2065	C₂×C₃₇	semidirect
230. #2025	C₂×C₃₇	semidirect
231. #2025	C₂×C₃₇	semidirect
232. #1854	C₂×C₃₇	semidirect
233. #1798	C₂×C₃₇	semidirect
244. C₂×#125	C₂²×C₃₇	semidirect
247. C₂×#107	C₂²×C₃₇	semidirect
248. C₂×#106	C₂²×C₃₇	semidirect
249. C₂×C₄⋊C₈	C₂²×C₃₇	semidirect
262. #389	C₂²×C₃₇	semidirect
263. #384	C₂²×C₃₇	semidirect
266. #340	C₂²×C₃₇	semidirect
267. #340	C₂²×C₃₇	semidirect
268. #336	C₂²×C₃₇	semidirect
269. #336	C₂²×C₃₇	semidirect
270. C₃₇	#29962	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×#2629	2
C₃₇×#2309	2
C₃₇×#2094	2
C₃₇×#2093	2
C₃₇×#2067	2
C₃₇×#2065	2
C₃₇×#2025	2
C₃₇×#1854	2
C₃₇×#1798	2
C₃₇×#1786	2
#29962	37

Subgroups — C37×#29962 #22651215

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#29962 #22651215