Subgroups — C₃₇×#29731 #22650984

Order 9472.

1122 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#467	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊C₈×C₃₇	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2848	C₂	1	2	yes	maximal
4	C₃₇×#2076	C₂	1	2	yes	maximal, complemented
5	C₃₇×#2036	C₂	1	4	yes	maximal, complemented
6	C₃₇×#2001	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1892	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1808	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁴×C₄×C₃₇	C₂²	1	1	yes	characteristic
10	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic, complemented
11	C₂³×C₈×C₃₇	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	2	yes	—
14	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	4	yes	—
15	C₃₇×#467	—	2	4	no	—
16	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic, complemented
17	C₂×#107×C₃₇	C₂²	1	2	yes	complemented
18	C₂×#103×C₃₇	C₂²	1	2	yes	complemented
19	C₂×#103×C₃₇	C₂²	1	4	yes	complemented
20	C₂×C₂²⋊C₈×C₃₇	—	2	4	no	—
21	C₂×C₂²⋊C₈×C₃₇	C₂²	1	2	yes	—
22	C₂×C₂²⋊C₈×C₃₇	C₂²	1	2	yes	—
23	C₃₇×#385	—	2	2	no	—
24	C₃₇×#385	—	2	4	no	—
25	C₃₇×#380	C₂²	1	2	yes	—
26	C₃₇×#380	C₂²	1	4	yes	—
27	C₃₇×#379	—	2	2	no	—
28	C₃₇×#340	C₂²	1	4	yes	complemented
29	C₃₇×#340	C₂²	1	2	yes	complemented
30	C₂⁵×C₃₇	D₄	1	1	yes	characteristic
31	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
32	C₂³×C₄×C₃₇	—	2	2	no	—
33	C₂³×C₄×C₃₇	—	2	2	no	—
34	C₂³×C₄×C₃₇	—	4	2	no	—
35	C₂³×C₄×C₃₇	—	4	2	no	—
36	C₂³×C₄×C₃₇	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₃₇	D₄	1	2	yes	—
38	C₂³×C₄×C₃₇	C₂³	1	2	yes	—
39	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
40	C₂×Q₁₆×C₃₇	—	2	2	no	—
41	C₂×Q₁₆×C₃₇	—	4	2	no	—
42	C₂²×C₈×C₃₇	—	2	2	no	—
43	C₂²×C₈×C₃₇	—	4	2	no	—
44	C₂²×C₈×C₃₇	—	4	2	no	—
45	C₂²×C₈×C₃₇	D₄	1	4	yes	—
46	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
47	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
49	C₂²⋊Q₈×C₃₇	—	2	4	no	—
50	C₂²⋊Q₈×C₃₇	—	2	4	no	—
51	C₂²⋊Q₈×C₃₇	—	4	4	no	—
52	C₂²⋊Q₈×C₃₇	—	4	4	no	—
53	C₂×C₄⋊C₄×C₃₇	—	2	4	no	—
54	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
57	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
58	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
60	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
61	#107×C₃₇	—	2	2	no	—
62	#107×C₃₇	—	4	2	no	—
63	#103×C₃₇	—	2	4	no	—
64	#103×C₃₇	—	4	4	no	—
65	C₂²⋊C₈×C₃₇	—	2	4	no	—
66	C₂²⋊C₈×C₃₇	—	2	4	no	—
67	#95×C₃₇	—	2	4	no	—
68	#95×C₃₇	—	2	2	no	—
69	C₂⁴×C₃₇	—	2	2	no	—
70	C₂⁴×C₃₇	—	2	2	no	—
71	C₂⁴×C₃₇	—	4	2	no	—
72	C₂⁴×C₃₇	—	4	2	no	—
73	C₂⁴×C₃₇	Q₁₆	1	4	yes	complemented
74	C₂⁴×C₃₇	C₂×D₄	1	2	yes	—
75	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
76	C₂×Q₈×C₃₇	—	2	2	no	—
77	C₂×Q₈×C₃₇	—	2	2	no	—
78	C₂×Q₈×C₃₇	—	2	4	no	—
79	C₂×Q₈×C₃₇	—	2	4	no	—
80	C₂²×C₄×C₃₇	—	2	2	no	—
81	C₂²×C₄×C₃₇	—	2	2	no	—
82	C₂²×C₄×C₃₇	—	2	2	no	—
83	C₂²×C₄×C₃₇	—	2	4	no	—
84	C₂²×C₄×C₃₇	—	2	2	no	—
85	C₂²×C₄×C₃₇	—	2	2	no	—
86	C₂²×C₄×C₃₇	—	2	4	no	—
87	C₂²×C₄×C₃₇	—	2	4	no	—
88	C₂²×C₄×C₃₇	—	2	2	no	—
89	C₂²×C₄×C₃₇	—	2	4	no	—
90	C₂²×C₄×C₃₇	—	2	2	no	—
91	C₂²×C₄×C₃₇	—	4	4	no	—
92	C₂²×C₄×C₃₇	—	4	2	no	—
93	C₂²×C₄×C₃₇	—	4	4	no	—
94	C₂²×C₄×C₃₇	—	4	4	no	—
95	C₂²×C₄×C₃₇	—	4	8	no	—
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	2	yes	—
99	C₂²×C₄×C₃₇	#41	1	2	yes	—
100	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
101	Q₁₆×C₃₇	—	4	4	no	—
102	C₂×C₈×C₃₇	—	2	2	no	—
103	C₂×C₈×C₃₇	—	2	2	no	—
104	C₂×C₈×C₃₇	—	2	2	no	—
105	C₂×C₈×C₃₇	—	2	4	no	—
106	C₂×C₈×C₃₇	—	4	4	no	—
107	C₂×C₈×C₃₇	—	4	4	no	—
108	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
109	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
110	C₄⋊C₄×C₃₇	—	2	2	no	—
111	C₄⋊C₄×C₃₇	—	2	2	no	—
112	C₄⋊C₄×C₃₇	—	2	4	no	—
113	C₄⋊C₄×C₃₇	—	2	4	no	—
114	C₄⋊C₄×C₃₇	—	4	8	no	—
115	C₄⋊C₄×C₃₇	—	4	4	no	—
116	C₂²⋊C₄×C₃₇	—	4	8	no	—
117	C₂²⋊C₄×C₃₇	—	4	8	no	—
118	C₂²⋊C₄×C₃₇	—	4	4	no	—
119	C₂²⋊C₄×C₃₇	—	4	4	no	—
120	C₂³×C₃₇	—	2	2	no	—
121	C₂³×C₃₇	—	2	2	no	—
122	C₂³×C₃₇	—	2	2	no	—
123	C₂³×C₃₇	—	2	4	no	—
124	C₂³×C₃₇	—	2	2	no	—
125	C₂³×C₃₇	—	2	4	no	—
126	C₂³×C₃₇	—	2	8	no	—
127	C₂³×C₃₇	—	4	8	no	—
128	C₂³×C₃₇	—	4	4	no	—
129	C₂³×C₃₇	—	4	8	no	—
130	C₂³×C₃₇	—	4	4	no	—
131	C₂³×C₃₇	#121	1	2	yes	—
132	C₂³×C₃₇	C₂×Q₁₆	1	4	yes	—
133	C₂³×C₃₇	C₂×Q₁₆	1	2	yes	—
134	C₂³×C₃₇	#135	1	2	yes	—
135	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
136	Q₈×C₃₇	—	4	2	no	—
137	Q₈×C₃₇	—	4	2	no	—
138	Q₈×C₃₇	—	4	4	no	—
139	C₂×C₄×C₃₇	—	2	2	no	—
140	C₂×C₄×C₃₇	—	2	2	no	—
141	C₂×C₄×C₃₇	—	2	2	no	—
142	C₂×C₄×C₃₇	—	2	4	no	—
143	C₂×C₄×C₃₇	—	2	2	no	—
144	C₂×C₄×C₃₇	—	2	4	no	—
145	C₂×C₄×C₃₇	—	4	8	no	—
146	C₂×C₄×C₃₇	—	4	4	no	—
147	C₂×C₄×C₃₇	—	4	2	no	—
148	C₂×C₄×C₃₇	—	4	2	no	—
149	C₂×C₄×C₃₇	—	4	4	no	—
150	C₂×C₄×C₃₇	—	4	2	no	—
151	C₂×C₄×C₃₇	—	4	2	no	—
152	C₂×C₄×C₃₇	—	4	4	no	—
153	C₂×C₄×C₃₇	—	4	4	no	—
154	C₂×C₄×C₃₇	—	4	4	no	—
155	C₂×C₄×C₃₇	—	4	4	no	—
156	C₂×C₄×C₃₇	—	4	4	no	—
157	C₂×C₄×C₃₇	#121	1	2	yes	—
158	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
161	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
162	C₈×C₃₇	—	2	2	no	—
163	C₈×C₃₇	—	2	2	no	—
164	C₈×C₃₇	—	4	2	no	—
165	#29731	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂²×C₃₇	—	2	2	no	—
167	C₂²×C₃₇	—	2	4	no	—
168	C₂²×C₃₇	—	2	4	no	—
169	C₂²×C₃₇	—	2	2	no	—
170	C₂²×C₃₇	—	2	8	no	—
171	C₂²×C₃₇	—	2	4	no	—
172	C₂²×C₃₇	—	4	16	no	—
173	C₂²×C₃₇	—	4	2	no	—
174	C₂²×C₃₇	—	4	4	no	—
175	C₂²×C₃₇	—	4	2	no	—
176	C₂²×C₃₇	#467	1	4	yes	—
177	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
178	C₂²×C₃₇	#534	1	2	yes	—
179	C₂²×C₃₇	C₂²×Q₁₆	1	1	yes	characteristic
180	C₂²×C₃₇	C₂×#135	1	1	yes	characteristic
181	C₂²×C₃₇	#575	1	2	yes	—
182	C₄×C₃₇	—	2	2	no	—
183	C₄×C₃₇	—	4	2	no	—
184	C₄×C₃₇	—	8	2	no	—
185	C₄×C₃₇	—	8	4	no	—
186	C₄×C₃₇	—	8	2	no	—
187	C₄×C₃₇	#534	1	1	yes	characteristic
188	C₄×C₃₇	#535	1	1	yes	characteristic
189	C₄×C₃₇	#538	1	2	yes	—
190	C₂×#467	C₂×C₃₇	1	1	yes	characteristic, complemented
191	C₂²×C₂²⋊C₈	C₂×C₃₇	1	1	yes	characteristic
192	#2848	C₂×C₃₇	1	2	yes	—
193	#2076	C₂×C₃₇	1	2	yes	complemented
194	#2036	C₂×C₃₇	1	4	yes	complemented
195	#2001	C₂×C₃₇	1	2	yes	complemented
196	#1892	C₂×C₃₇	1	2	yes	complemented
197	#1808	C₂×C₃₇	1	1	yes	characteristic, complemented
198	C₂×C₃₇	—	2	4	no	—
199	C₂×C₃₇	—	4	4	no	—
200	C₂×C₃₇	#2617	1	1	yes	characteristic
201	C₂×C₃₇	C₂×#467	1	1	yes	characteristic
202	C₂×C₃₇	#3054	1	1	yes	characteristic
203	C₂×C₃₇	#3189	1	2	yes	—
204	C₂×C₃₇	#3191	1	2	yes	—
205	C₂⁴×C₄	C₂²×C₃₇	1	1	yes	characteristic
206	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic, complemented
207	C₂³×C₈	C₂²×C₃₇	1	1	yes	characteristic
208	C₂³×C₈	C₂²×C₃₇	1	1	yes	characteristic
209	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	2	yes	—
210	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	4	yes	—
211	#467	—	2	4	no	—
212	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic, complemented
213	C₂×#107	C₂²×C₃₇	1	2	yes	complemented
214	C₂×#103	C₂²×C₃₇	1	2	yes	complemented
215	C₂×#103	C₂²×C₃₇	1	4	yes	complemented
216	C₂×C₂²⋊C₈	—	2	4	no	—
217	C₂×C₂²⋊C₈	C₂²×C₃₇	1	2	yes	—
218	C₂×C₂²⋊C₈	C₂²×C₃₇	1	2	yes	—
219	#385	—	2	2	no	—
220	#385	—	2	4	no	—
221	#380	C₂²×C₃₇	1	2	yes	—
222	#380	C₂²×C₃₇	1	4	yes	—
223	#379	—	2	2	no	—
224	#340	C₂²×C₃₇	1	2	yes	complemented
225	#340	C₂²×C₃₇	1	4	yes	complemented
226	C₃₇	#29731	1	1	yes	characteristic, direct product factor, Sylow
227	C₂⁵	D₄×C₃₇	1	1	yes	characteristic
228	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
229	C₂³×C₄	—	2	2	no	—
230	C₂³×C₄	—	2	2	no	—
231	C₂³×C₄	—	4	2	no	—
232	C₂³×C₄	—	4	2	no	—
233	C₂³×C₄	D₄×C₃₇	1	1	yes	characteristic
234	C₂³×C₄	D₄×C₃₇	1	2	yes	—
235	C₂³×C₄	C₂³×C₃₇	1	2	yes	—
236	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
237	C₂×Q₁₆	—	2	2	no	—
238	C₂×Q₁₆	—	4	2	no	—
239	C₂²×C₈	—	2	2	no	—
240	C₂²×C₈	—	4	2	no	—
241	C₂²×C₈	—	4	2	no	—
242	C₂²×C₈	D₄×C₃₇	1	4	yes	—
243	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
244	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
245	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
246	C₂²⋊Q₈	—	2	4	no	—
247	C₂²⋊Q₈	—	2	4	no	—
248	C₂²⋊Q₈	—	4	4	no	—
249	C₂²⋊Q₈	—	4	4	no	—
250	C₂×C₄⋊C₄	—	2	4	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
253	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
254	C₂×C₂²⋊C₄	—	2	4	no	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	—	2	4	no	—
257	C₂×C₂²⋊C₄	—	2	2	no	—
258	#107	—	2	2	no	—
259	#107	—	4	2	no	—
260	#103	—	2	4	no	—
261	#103	—	4	4	no	—
262	C₂²⋊C₈	—	2	4	no	—
263	C₂²⋊C₈	—	2	4	no	—
264	#95	—	2	4	no	—
265	#95	—	2	2	no	—
266	C₂⁴	—	2	2	no	—
267	C₂⁴	—	2	2	no	—
268	C₂⁴	—	4	2	no	—
269	C₂⁴	—	4	2	no	—
270	C₂⁴	Q₁₆×C₃₇	1	4	yes	complemented
271	C₂⁴	C₂×D₄×C₃₇	1	2	yes	—
272	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
273	C₂×Q₈	—	2	2	no	—
274	C₂×Q₈	—	2	2	no	—
275	C₂×Q₈	—	2	4	no	—
276	C₂×Q₈	—	2	4	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	4	4	no	—
289	C₂²×C₄	—	4	2	no	—
290	C₂²×C₄	—	4	4	no	—
291	C₂²×C₄	—	4	4	no	—
292	C₂²×C₄	—	4	8	no	—
293	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
294	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
296	C₂²×C₄	#41×C₃₇	1	2	yes	—
297	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
298	Q₁₆	—	4	4	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	4	no	—
303	C₂×C₈	—	4	4	no	—
304	C₂×C₈	—	4	4	no	—
305	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
306	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	4	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	4	8	no	—
312	C₄⋊C₄	—	4	4	no	—
313	C₂²⋊C₄	—	4	8	no	—
314	C₂²⋊C₄	—	4	8	no	—
315	C₂²⋊C₄	—	4	4	no	—
316	C₂²⋊C₄	—	4	4	no	—
317	C₂³	—	2	2	no	—
318	C₂³	—	2	2	no	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	4	no	—
321	C₂³	—	2	2	no	—
322	C₂³	—	2	4	no	—
323	C₂³	—	2	8	no	—
324	C₂³	—	4	8	no	—
325	C₂³	—	4	4	no	—
326	C₂³	—	4	8	no	—
327	C₂³	—	4	4	no	—
328	C₂³	#121×C₃₇	1	2	yes	—
329	C₂³	C₂×Q₁₆×C₃₇	1	4	yes	—
330	C₂³	C₂×Q₁₆×C₃₇	1	2	yes	—
331	C₂³	#135×C₃₇	1	2	yes	—
332	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
333	Q₈	—	4	2	no	—
334	Q₈	—	4	2	no	—
335	Q₈	—	4	4	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	4	8	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	#121×C₃₇	1	2	yes	—
355	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
356	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
357	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
358	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
359	C₈	—	2	2	no	—
360	C₈	—	2	2	no	—
361	C₈	—	4	2	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	4	no	—
364	C₂²	—	2	4	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	8	no	—
367	C₂²	—	2	4	no	—
368	C₂²	—	4	16	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	4	4	no	—
371	C₂²	—	4	2	no	—
372	C₂²	C₃₇×#467	1	4	yes	—
373	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
374	C₂²	C₃₇×#534	1	2	yes	—
375	C₂²	C₂²×Q₁₆×C₃₇	1	1	yes	characteristic
376	C₂²	C₂×#135×C₃₇	1	1	yes	characteristic
377	C₂²	C₃₇×#575	1	2	yes	—
378	C₄	—	2	2	no	—
379	C₄	—	4	2	no	—
380	C₄	—	8	2	no	—
381	C₄	—	8	4	no	—
382	C₄	—	8	2	no	—
383	C₄	C₃₇×#534	1	1	yes	characteristic
384	C₄	C₃₇×#535	1	1	yes	characteristic
385	C₄	C₃₇×#538	1	2	yes	—
386	C₂	—	2	4	no	—
387	C₂	—	4	4	no	—
388	C₂	C₃₇×#2617	1	1	yes	characteristic
389	C₂	C₂×C₃₇×#467	1	1	yes	characteristic
390	C₂	C₃₇×#3054	1	1	yes	characteristic
391	C₂	C₃₇×#3189	1	2	yes	—
392	C₂	C₃₇×#3191	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂⁵×C₃₇	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₂⁴×C₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#467	C₂	semidirect
4. C₃₇×#2076	C₂	semidirect
5. C₃₇×#2036	C₂	semidirect
6. C₃₇×#2001	C₂	semidirect
7. C₃₇×#1892	C₂	semidirect
8. C₃₇×#1808	C₂	semidirect
10. C₂²×Q₁₆×C₃₇	C₂²	semidirect
16. C₂×#107×C₃₇	C₂²	semidirect
17. C₂×#107×C₃₇	C₂²	semidirect
18. C₂×#103×C₃₇	C₂²	semidirect
19. C₂×#103×C₃₇	C₂²	semidirect
28. C₃₇×#340	C₂²	semidirect
29. C₃₇×#340	C₂²	semidirect
73. C₂⁴×C₃₇	Q₁₆	semidirect
165. #29731	C₃₇	direct (N × H)
190. C₂×#467	C₂×C₃₇	semidirect
193. #2076	C₂×C₃₇	semidirect
194. #2036	C₂×C₃₇	semidirect
195. #2001	C₂×C₃₇	semidirect
196. #1892	C₂×C₃₇	semidirect
197. #1808	C₂×C₃₇	semidirect
206. C₂²×Q₁₆	C₂²×C₃₇	semidirect
212. C₂×#107	C₂²×C₃₇	semidirect
213. C₂×#107	C₂²×C₃₇	semidirect
214. C₂×#103	C₂²×C₃₇	semidirect
215. C₂×#103	C₂²×C₃₇	semidirect
224. #340	C₂²×C₃₇	semidirect
225. #340	C₂²×C₃₇	semidirect
226. C₃₇	#29731	direct (N × H)
270. C₂⁴	Q₁₆×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₇×#467	2
C₂²×C₂²⋊C₈×C₃₇	2
C₃₇×#2848	2
C₃₇×#2076	2
C₃₇×#2036	2
C₃₇×#2001	2
C₃₇×#1892	2
C₃₇×#1808	2
#29731	37

Subgroups — C37×#29731 #22650984

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#29731 #22650984