Subgroups — C₃₇×#28817 #22650070

Order 9472.

758 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#501	C₂	1	2	yes	maximal
2	C₃₇×#2552	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2551	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#2059	C₂	1	2	yes	maximal
5	C₃₇×#2058	C₂	1	2	yes	maximal
6	C₃₇×#1948	C₂	1	1	yes	maximal, characteristic
7	C₃₇×#1947	C₂	1	1	yes	maximal, characteristic
8	C₃₇×#1943	C₂	1	2	yes	maximal
9	C₃₇×#1844	C₂	1	1	yes	maximal, characteristic
10	C₄×#107×C₃₇	C₂	1	1	yes	maximal, characteristic
11	C₃₇×#1770	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊Q₈×C₃₇	—	2	1	no	—
13	C₂×C₄⋊Q₈×C₃₇	C₂²	1	2	yes	—
14	C₂×#125×C₃₇	C₂²	1	2	yes	—
15	C₃₇×#501	—	2	8	no	—
16	C₂×#107×C₃₇	C₂²	1	2	yes	—
17	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
19	C₂×#106×C₃₇	C₂²	1	2	yes	—
20	C₂×#106×C₃₇	C₂²	1	2	yes	—
21	C₂×#106×C₃₇	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
23	C₂×#97×C₃₇	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
25	C₃₇×#398	—	2	2	no	—
26	C₃₇×#395	—	2	2	no	—
27	C₃₇×#389	—	2	1	no	—
28	C₃₇×#389	—	2	1	no	—
29	C₃₇×#389	C₂²	1	2	yes	—
30	C₃₇×#389	C₂²	1	2	yes	—
31	C₃₇×#384	—	2	1	no	—
32	C₃₇×#384	C₂²	1	1	yes	characteristic
33	C₃₇×#384	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
37	C₃₇×#340	C₂²	1	2	yes	—
38	C₃₇×#340	C₂²	1	2	yes	—
39	C₃₇×#340	C₂²	1	1	yes	characteristic
40	C₃₇×#340	C₂²	1	1	yes	characteristic
41	C₃₇×#336	C₂²	1	2	yes	—
42	C₂²×Q₈×C₃₇	—	2	2	no	—
43	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
45	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
46	C₄⋊Q₈×C₃₇	—	2	4	no	—
47	C₄⋊Q₈×C₃₇	—	4	2	no	—
48	C₄⋊Q₈×C₃₇	—	4	4	no	—
49	#125×C₃₇	—	2	4	no	—
50	#125×C₃₇	—	4	2	no	—
51	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
53	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
54	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
57	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
58	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
59	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
60	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₃₇	—	2	1	no	—
69	C₂×C₄²×C₃₇	—	2	1	no	—
70	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
71	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
72	#107×C₃₇	—	2	4	no	—
73	#107×C₃₇	D₄	1	4	yes	—
74	#107×C₃₇	Q₈	1	4	yes	complemented
75	#106×C₃₇	—	2	4	no	—
76	#106×C₃₇	—	2	4	no	—
77	#106×C₃₇	—	4	2	no	—
78	C₄⋊C₈×C₃₇	Q₈	1	4	yes	complemented
79	#97×C₃₇	—	2	4	no	—
80	C₄×C₈×C₃₇	Q₈	1	4	yes	complemented
81	#95×C₃₇	—	2	1	no	—
82	#95×C₃₇	—	2	1	no	—
83	#95×C₃₇	—	2	2	no	—
84	#95×C₃₇	—	2	2	no	—
85	#95×C₃₇	D₄	1	2	yes	—
86	C₂×Q₈×C₃₇	—	4	4	no	—
87	C₂×Q₈×C₃₇	—	4	4	no	—
88	C₂×Q₈×C₃₇	—	8	2	no	—
89	C₂²×C₄×C₃₇	—	2	1	no	—
90	C₂²×C₄×C₃₇	—	2	1	no	—
91	C₂²×C₄×C₃₇	—	2	1	no	—
92	C₂²×C₄×C₃₇	—	2	1	no	—
93	C₂²×C₄×C₃₇	—	2	2	no	—
94	C₂²×C₄×C₃₇	—	2	2	no	—
95	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
100	C₂×C₈×C₃₇	—	2	2	no	—
101	C₂×C₈×C₃₇	—	2	1	no	—
102	C₂×C₈×C₃₇	—	2	1	no	—
103	C₂×C₈×C₃₇	—	2	2	no	—
104	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
105	C₂×C₈×C₃₇	C₂×Q₈	1	2	yes	—
106	C₂×C₈×C₃₇	C₂×Q₈	1	4	yes	—
107	C₂×C₈×C₃₇	C₂×Q₈	1	2	yes	—
108	C₂×C₈×C₃₇	C₂×Q₈	1	2	yes	—
109	C₄⋊C₄×C₃₇	—	2	2	no	—
110	C₄⋊C₄×C₃₇	—	2	2	no	—
111	C₄⋊C₄×C₃₇	—	2	1	no	—
112	C₄⋊C₄×C₃₇	—	2	1	no	—
113	C₄⋊C₄×C₃₇	—	2	1	no	—
114	C₄⋊C₄×C₃₇	—	2	1	no	—
115	C₄⋊C₄×C₃₇	—	2	2	no	—
116	C₄⋊C₄×C₃₇	—	2	2	no	—
117	C₄⋊C₄×C₃₇	—	2	2	no	—
118	C₄⋊C₄×C₃₇	—	2	2	no	—
119	C₄⋊C₄×C₃₇	—	4	4	no	—
120	C₄⋊C₄×C₃₇	—	4	4	no	—
121	C₄⋊C₄×C₃₇	—	4	4	no	—
122	C₄⋊C₄×C₃₇	—	4	4	no	—
123	C₄⋊C₄×C₃₇	—	4	2	no	—
124	C₄⋊C₄×C₃₇	—	4	2	no	—
125	C₄⋊C₄×C₃₇	—	8	1	no	—
126	C₄⋊C₄×C₃₇	—	8	1	no	—
127	C₄⋊C₄×C₃₇	—	8	2	no	—
128	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
129	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
130	C₄⋊C₄×C₃₇	C₂×Q₈	1	2	yes	—
131	C₄⋊C₄×C₃₇	C₂×Q₈	1	2	yes	—
132	C₄²×C₃₇	—	2	2	no	—
133	C₄²×C₃₇	—	2	2	no	—
134	C₄²×C₃₇	—	4	2	no	—
135	C₄²×C₃₇	—	4	2	no	—
136	C₄²×C₃₇	C₂×Q₈	1	2	yes	—
137	C₄²×C₃₇	C₂×Q₈	1	2	yes	—
138	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
139	Q₈×C₃₇	—	8	8	no	—
140	C₂×C₄×C₃₇	—	2	1	no	—
141	C₂×C₄×C₃₇	—	2	1	no	—
142	C₂×C₄×C₃₇	—	2	2	no	—
143	C₂×C₄×C₃₇	—	2	2	no	—
144	C₂×C₄×C₃₇	—	2	2	no	—
145	C₂×C₄×C₃₇	—	2	2	no	—
146	C₂×C₄×C₃₇	—	2	2	no	—
147	C₂×C₄×C₃₇	—	2	2	no	—
148	C₂×C₄×C₃₇	—	2	2	no	—
149	C₂×C₄×C₃₇	—	2	2	no	—
150	C₂×C₄×C₃₇	—	2	2	no	—
151	C₂×C₄×C₃₇	—	2	2	no	—
152	C₂×C₄×C₃₇	—	4	1	no	—
153	C₂×C₄×C₃₇	—	4	1	no	—
154	C₂×C₄×C₃₇	—	4	1	no	—
155	C₂×C₄×C₃₇	—	4	1	no	—
156	C₂×C₄×C₃₇	—	4	1	no	—
157	C₂×C₄×C₃₇	—	4	1	no	—
158	C₂×C₄×C₃₇	—	4	1	no	—
159	C₂×C₄×C₃₇	—	4	1	no	—
160	C₂×C₄×C₃₇	—	4	2	no	—
161	C₂×C₄×C₃₇	—	4	2	no	—
162	C₂×C₄×C₃₇	—	4	2	no	—
163	C₂×C₄×C₃₇	—	4	2	no	—
164	C₂×C₄×C₃₇	—	4	2	no	—
165	C₂×C₄×C₃₇	—	4	2	no	—
166	C₂×C₄×C₃₇	C₄⋊Q₈	1	2	yes	—
167	C₂×C₄×C₃₇	C₄⋊Q₈	1	2	yes	—
168	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
169	C₂×C₄×C₃₇	#137	1	2	yes	—
170	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₃₇	C₂²×Q₈	1	1	yes	characteristic
172	C₂×C₄×C₃₇	C₂²×Q₈	1	1	yes	characteristic
173	C₂×C₄×C₃₇	C₂²×Q₈	1	1	yes	characteristic
174	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
175	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
176	C₈×C₃₇	—	2	2	no	—
177	C₈×C₃₇	—	2	4	no	—
178	C₈×C₃₇	C₄⋊Q₈	1	4	yes	complemented
179	#28817	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂²×C₃₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
181	C₂²×C₃₇	D₄²	1	1	yes	characteristic
182	C₂²×C₃₇	D₄×Q₈	1	1	yes	characteristic
183	C₂²×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
184	C₂²×C₃₇	C₂×#137	1	1	yes	characteristic
185	C₂²×C₃₇	#577	1	1	yes	characteristic
186	C₂²×C₃₇	#577	1	1	yes	characteristic
187	C₄×C₃₇	—	2	2	no	—
188	C₄×C₃₇	—	4	2	no	—
189	C₄×C₃₇	—	4	2	no	—
190	C₄×C₃₇	—	4	2	no	—
191	C₄×C₃₇	—	4	2	no	—
192	C₄×C₃₇	—	4	2	no	—
193	C₄×C₃₇	—	4	2	no	—
194	C₄×C₃₇	—	8	2	no	—
195	C₄×C₃₇	—	8	2	no	—
196	C₄×C₃₇	#501	1	4	yes	complemented
197	C₄×C₃₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
198	C₄×C₃₇	#544	1	1	yes	characteristic
199	C₄×C₃₇	D₄×Q₈	1	1	yes	characteristic
200	C₄×C₃₇	Q₈²	1	1	yes	characteristic
201	C₂×#501	C₂×C₃₇	1	2	yes	—
202	#2552	C₂×C₃₇	1	1	yes	characteristic
203	#2551	C₂×C₃₇	1	1	yes	characteristic
204	#2059	C₂×C₃₇	1	2	yes	—
205	#2058	C₂×C₃₇	1	2	yes	—
206	#1948	C₂×C₃₇	1	1	yes	characteristic
207	#1947	C₂×C₃₇	1	1	yes	characteristic
208	#1943	C₂×C₃₇	1	2	yes	—
209	#1844	C₂×C₃₇	1	1	yes	characteristic
210	C₄×#107	C₂×C₃₇	1	1	yes	characteristic
211	#1770	C₂×C₃₇	1	1	yes	characteristic
212	C₂×C₃₇	#2551	1	1	yes	characteristic
213	C₂×C₃₇	C₂×#501	1	1	yes	characteristic
214	C₂×C₃₇	#3163	1	1	yes	characteristic
215	C₂×C₃₇	#3272	1	1	yes	characteristic
216	C₂×C₃₇	#3278	1	1	yes	characteristic
217	C₂×C₃₇	#3384	1	1	yes	characteristic
218	C₂×C₃₇	#3387	1	1	yes	characteristic
219	C₂×C₄⋊Q₈	—	2	1	no	—
220	C₂×C₄⋊Q₈	C₂²×C₃₇	1	2	yes	—
221	C₂×#125	C₂²×C₃₇	1	2	yes	—
222	#501	—	2	8	no	—
223	C₂×#107	C₂²×C₃₇	1	2	yes	—
224	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
225	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
226	C₂×#106	C₂²×C₃₇	1	2	yes	—
227	C₂×#106	C₂²×C₃₇	1	2	yes	—
228	C₂×#106	C₂²×C₃₇	1	2	yes	—
229	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
230	C₂×#97	C₂²×C₃₇	1	2	yes	—
231	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
232	#398	—	2	2	no	—
233	#395	—	2	2	no	—
234	#389	—	2	1	no	—
235	#389	—	2	1	no	—
236	#389	C₂²×C₃₇	1	2	yes	—
237	#389	C₂²×C₃₇	1	2	yes	—
238	#384	—	2	1	no	—
239	#384	C₂²×C₃₇	1	1	yes	characteristic
240	#384	C₂²×C₃₇	1	1	yes	characteristic
241	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
242	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
243	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
244	#340	C₂²×C₃₇	1	1	yes	characteristic
245	#340	C₂²×C₃₇	1	2	yes	—
246	#340	C₂²×C₃₇	1	1	yes	characteristic
247	#340	C₂²×C₃₇	1	2	yes	—
248	#336	C₂²×C₃₇	1	2	yes	—
249	C₃₇	#28817	1	1	yes	characteristic, direct product factor, Sylow
250	C₂²×Q₈	—	2	2	no	—
251	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
253	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
254	C₄⋊Q₈	—	2	4	no	—
255	C₄⋊Q₈	—	4	2	no	—
256	C₄⋊Q₈	—	4	4	no	—
257	#125	—	2	4	no	—
258	#125	—	4	2	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
269	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
275	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
276	C₂×C₄²	—	2	1	no	—
277	C₂×C₄²	—	2	1	no	—
278	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
279	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
280	#107	—	2	4	no	—
281	#107	D₄×C₃₇	1	4	yes	—
282	#107	Q₈×C₃₇	1	4	yes	complemented
283	#106	—	2	4	no	—
284	#106	—	2	4	no	—
285	#106	—	4	2	no	—
286	C₄⋊C₈	Q₈×C₃₇	1	4	yes	complemented
287	#97	—	2	4	no	—
288	C₄×C₈	Q₈×C₃₇	1	4	yes	complemented
289	#95	—	2	1	no	—
290	#95	—	2	1	no	—
291	#95	—	2	2	no	—
292	#95	—	2	2	no	—
293	#95	D₄×C₃₇	1	2	yes	—
294	C₂×Q₈	—	4	4	no	—
295	C₂×Q₈	—	4	4	no	—
296	C₂×Q₈	—	8	2	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
305	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
307	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
313	C₂×C₈	C₂×Q₈×C₃₇	1	2	yes	—
314	C₂×C₈	C₂×Q₈×C₃₇	1	4	yes	—
315	C₂×C₈	C₂×Q₈×C₃₇	1	2	yes	—
316	C₂×C₈	C₂×Q₈×C₃₇	1	2	yes	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	4	4	no	—
328	C₄⋊C₄	—	4	4	no	—
329	C₄⋊C₄	—	4	4	no	—
330	C₄⋊C₄	—	4	4	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₄⋊C₄	—	8	1	no	—
334	C₄⋊C₄	—	8	1	no	—
335	C₄⋊C₄	—	8	2	no	—
336	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
337	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
338	C₄⋊C₄	C₂×Q₈×C₃₇	1	2	yes	—
339	C₄⋊C₄	C₂×Q₈×C₃₇	1	2	yes	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	4	2	no	—
343	C₄²	—	4	2	no	—
344	C₄²	C₂×Q₈×C₃₇	1	2	yes	—
345	C₄²	C₂×Q₈×C₃₇	1	2	yes	—
346	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
347	Q₈	—	8	8	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	C₄⋊Q₈×C₃₇	1	2	yes	—
375	C₂×C₄	C₄⋊Q₈×C₃₇	1	2	yes	—
376	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
377	C₂×C₄	#137×C₃₇	1	2	yes	—
378	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
379	C₂×C₄	C₂²×Q₈×C₃₇	1	1	yes	characteristic
380	C₂×C₄	C₂²×Q₈×C₃₇	1	1	yes	characteristic
381	C₂×C₄	C₂²×Q₈×C₃₇	1	1	yes	characteristic
382	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
383	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
384	C₈	—	2	2	no	—
385	C₈	—	2	4	no	—
386	C₈	C₄⋊Q₈×C₃₇	1	4	yes	complemented
387	C₂²	C₂×C₄⋊Q₈×C₃₇	1	1	yes	characteristic
388	C₂²	D₄²×C₃₇	1	1	yes	characteristic
389	C₂²	D₄×Q₈×C₃₇	1	1	yes	characteristic
390	C₂²	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
391	C₂²	C₂×#137×C₃₇	1	1	yes	characteristic
392	C₂²	C₃₇×#577	1	1	yes	characteristic
393	C₂²	C₃₇×#577	1	1	yes	characteristic
394	C₄	—	2	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	2	no	—
397	C₄	—	4	2	no	—
398	C₄	—	4	2	no	—
399	C₄	—	4	2	no	—
400	C₄	—	4	2	no	—
401	C₄	—	8	2	no	—
402	C₄	—	8	2	no	—
403	C₄	C₃₇×#501	1	4	yes	complemented
404	C₄	C₂×C₄⋊Q₈×C₃₇	1	1	yes	characteristic
405	C₄	C₃₇×#544	1	1	yes	characteristic
406	C₄	D₄×Q₈×C₃₇	1	1	yes	characteristic
407	C₄	Q₈²×C₃₇	1	1	yes	characteristic
408	C₂	C₃₇×#2551	1	1	yes	characteristic
409	C₂	C₂×C₃₇×#501	1	1	yes	characteristic
410	C₂	C₃₇×#3163	1	1	yes	characteristic
411	C₂	C₃₇×#3272	1	1	yes	characteristic
412	C₂	C₃₇×#3278	1	1	yes	characteristic
413	C₂	C₃₇×#3384	1	1	yes	characteristic
414	C₂	C₃₇×#3387	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
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
74. #107×C₃₇	Q₈	semidirect
78. C₄⋊C₈×C₃₇	Q₈	semidirect
80. C₄×C₈×C₃₇	Q₈	semidirect
178. C₈×C₃₇	C₄⋊Q₈	semidirect
179. #28817	C₃₇	direct (N × H)
196. C₄×C₃₇	#501	semidirect
249. C₃₇	#28817	direct (N × H)
282. #107	Q₈×C₃₇	semidirect
286. C₄⋊C₈	Q₈×C₃₇	semidirect
288. C₄×C₈	Q₈×C₃₇	semidirect
386. C₈	C₄⋊Q₈×C₃₇	semidirect
403. C₄	C₃₇×#501	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₇×#501	2
C₃₇×#2552	2
C₃₇×#2551	2
C₃₇×#2059	2
C₃₇×#2058	2
C₃₇×#1948	2
C₃₇×#1947	2
C₃₇×#1943	2
C₃₇×#1844	2
C₄×#107×C₃₇	2
C₃₇×#1770	2
#28817	37

Subgroups — C37×#28817 #22650070

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28817 #22650070