Subgroups — C₃₇×#22460 #22643713

Order 9472.

1286 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#578	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#2957	C₂	1	2	yes	maximal, complemented
3	C₃₇×#2889	C₂	1	2	yes	maximal, complemented
4	C₃₇×#1979	C₂	1	2	yes	maximal, complemented
5	C₃₇×#1902	C₂	1	4	yes	maximal, complemented
6	C₃₇×#1813	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#1796	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1757	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×2₋¹⁺⁴×C₃₇	C₂²	1	2	yes	—
10	C₃₇×#578	—	2	4	no	—
11	C₃₇×#578	—	2	4	no	—
12	C₂×#137×C₃₇	C₄	1	4	yes	complemented
13	C₂×#137×C₃₇	C₂²	1	2	yes	—
14	C₂×#135×C₃₇	C₄	1	2	yes	complemented
15	C₂×#135×C₃₇	C₂²	1	1	yes	characteristic
16	C₂²×Q₁₆×C₃₇	C₄	1	2	yes	complemented
17	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
18	C₃₇×#568	C₂²	1	4	yes	—
19	C₂×#131×C₃₇	C₂²	1	1	yes	characteristic
20	C₃₇×#444	—	2	4	no	—
21	C₃₇×#443	—	2	4	no	—
22	C₂×#108×C₃₇	C₂²	1	2	yes	—
23	C₃₇×#421	C₂²	1	4	yes	—
24	C₃₇×#419	C₂²	1	4	yes	—
25	C₃₇×#413	—	2	4	no	—
26	C₃₇×#413	C₂²	1	2	yes	—
27	C₃₇×#413	C₂²	1	1	yes	characteristic
28	C₂×#101×C₃₇	—	2	4	no	—
29	C₂×#101×C₃₇	C₂²	1	4	yes	—
30	C₃₇×#410	C₂²	1	1	yes	characteristic
31	C₃₇×#405	C₂²	1	2	yes	—
32	C₃₇×#344	C₂²	1	2	yes	—
33	C₃₇×#338	C₂²	1	2	yes	—
34	2₋¹⁺⁴×C₃₇	—	2	8	no	—
35	2₋¹⁺⁴×C₃₇	—	4	4	no	—
36	C₂×#41×C₃₇	—	2	2	no	—
37	C₂×#41×C₃₇	—	2	4	no	—
38	C₂×#41×C₃₇	C₂×C₄	1	4	yes	—
39	C₂×#41×C₃₇	C₂³	1	2	yes	—
40	C₂×#41×C₃₇	C₂³	1	1	yes	characteristic
41	C₂²×Q₈×C₃₇	—	2	2	no	—
42	C₂²×Q₈×C₃₇	C₂×C₄	1	4	yes	—
43	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
44	#137×C₃₇	—	2	8	no	—
45	#137×C₃₇	—	2	16	no	—
46	#135×C₃₇	—	2	4	no	—
47	#135×C₃₇	—	2	4	no	—
48	#135×C₃₇	D₄	1	4	yes	—
49	#135×C₃₇	D₄	1	4	yes	—
50	C₂×Q₁₆×C₃₇	—	2	4	no	—
51	C₂×Q₁₆×C₃₇	—	2	4	no	—
52	C₂×Q₁₆×C₃₇	—	2	2	no	—
53	C₂×Q₁₆×C₃₇	—	2	2	no	—
54	C₂×Q₁₆×C₃₇	C₂×C₄	1	2	yes	—
55	C₂×Q₁₆×C₃₇	C₂×C₄	1	4	yes	—
56	C₂×Q₁₆×C₃₇	C₂×C₄	1	2	yes	—
57	C₂×Q₁₆×C₃₇	C₂×C₄	1	1	yes	characteristic
58	C₂×SD₁₆×C₃₇	C₂×C₄	1	4	yes	—
59	C₂×SD₁₆×C₃₇	C₂×C₄	1	2	yes	—
60	C₂×D₈×C₃₇	C₂×C₄	1	1	yes	characteristic
61	#131×C₃₇	—	2	2	no	—
62	#131×C₃₇	—	2	2	no	—
63	#131×C₃₇	—	2	8	no	—
64	#131×C₃₇	—	4	4	no	—
65	C₂×M₁₆×C₃₇	—	2	8	no	—
66	C₂×M₁₆×C₃₇	C₂×C₄	1	2	yes	—
67	C₂×M₁₆×C₃₇	C₂³	1	4	yes	—
68	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
69	C₂×M₁₆×C₃₇	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₃₇	C₂×C₄	1	2	yes	—
71	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
72	#117×C₃₇	C₂³	1	2	yes	—
73	#108×C₃₇	—	2	2	no	—
74	#108×C₃₇	—	2	2	no	—
75	#104×C₃₇	—	2	8	no	—
76	#103×C₃₇	—	4	4	no	—
77	#101×C₃₇	—	2	2	no	—
78	#101×C₃₇	—	2	8	no	—
79	#101×C₃₇	D₄	1	2	yes	—
80	#100×C₃₇	—	2	2	no	—
81	#100×C₃₇	D₄	1	2	yes	—
82	#99×C₃₇	—	2	2	no	—
83	#97×C₃₇	—	2	2	no	—
84	C₄×C₈×C₃₇	—	2	2	no	—
85	#41×C₃₇	—	2	2	no	—
86	#41×C₃₇	—	2	4	no	—
87	#41×C₃₇	—	2	2	no	—
88	#41×C₃₇	—	2	8	no	—
89	#41×C₃₇	—	4	4	no	—
90	#41×C₃₇	—	4	8	no	—
91	#41×C₃₇	—	4	16	no	—
92	#41×C₃₇	C₂×D₄	1	8	yes	—
93	C₂×Q₈×C₃₇	—	2	4	no	—
94	C₂×Q₈×C₃₇	—	2	2	no	—
95	C₂×Q₈×C₃₇	—	2	8	no	—
96	C₂×Q₈×C₃₇	—	2	4	no	—
97	C₂×Q₈×C₃₇	—	2	4	no	—
98	C₂×Q₈×C₃₇	—	4	4	no	—
99	C₂×Q₈×C₃₇	—	4	8	no	—
100	C₂×Q₈×C₃₇	C₂²×C₄	1	4	yes	—
101	C₂×Q₈×C₃₇	C₂²×C₄	1	2	yes	—
102	C₂×Q₈×C₃₇	C₂×D₄	1	1	yes	characteristic
103	C₂×D₄×C₃₇	—	2	2	no	—
104	C₂×D₄×C₃₇	—	2	4	no	—
105	C₂×D₄×C₃₇	C₂²×C₄	1	2	yes	—
106	C₂×D₄×C₃₇	C₂×D₄	1	1	yes	characteristic
107	C₂×D₄×C₃₇	#41	1	2	yes	—
108	C₂²×C₄×C₃₇	—	2	2	no	—
109	C₂²×C₄×C₃₇	—	2	4	no	—
110	C₂²×C₄×C₃₇	—	2	2	no	—
111	C₂²×C₄×C₃₇	—	2	4	no	—
112	C₂²×C₄×C₃₇	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
114	Q₁₆×C₃₇	—	2	8	no	—
115	Q₁₆×C₃₇	—	2	2	no	—
116	Q₁₆×C₃₇	—	2	2	no	—
117	Q₁₆×C₃₇	—	2	4	no	—
118	Q₁₆×C₃₇	C₂²⋊C₄	1	2	yes	—
119	Q₁₆×C₃₇	C₂²⋊C₄	1	2	yes	—
120	SD₁₆×C₃₇	—	2	8	no	—
121	SD₁₆×C₃₇	C₂²⋊C₄	1	8	yes	—
122	D₈×C₃₇	C₂²⋊C₄	1	2	yes	—
123	D₈×C₃₇	C₂²⋊C₄	1	2	yes	—
124	M₁₆×C₃₇	—	2	2	no	—
125	M₁₆×C₃₇	—	2	2	no	—
126	M₁₆×C₃₇	—	2	4	no	—
127	M₁₆×C₃₇	—	2	4	no	—
128	M₁₆×C₃₇	—	2	4	no	—
129	M₁₆×C₃₇	—	4	8	no	—
130	M₁₆×C₃₇	C₂×D₄	1	4	yes	—
131	C₂×C₈×C₃₇	—	2	2	no	—
132	C₂×C₈×C₃₇	—	2	2	no	—
133	C₂×C₈×C₃₇	—	2	2	no	—
134	C₂×C₈×C₃₇	—	2	4	no	—
135	C₂×C₈×C₃₇	—	4	8	no	—
136	C₂×C₈×C₃₇	C₂²×C₄	1	2	yes	—
137	C₂×C₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
141	C₄⋊C₄×C₃₇	—	2	2	no	—
142	C₂²⋊C₄×C₃₇	—	2	2	no	—
143	C₄²×C₃₇	—	2	2	no	—
144	C₂³×C₃₇	—	2	2	no	—
145	C₂³×C₃₇	C₄×D₄	1	2	yes	—
146	C₂³×C₃₇	C₂×#41	1	1	yes	characteristic
147	Q₈×C₃₇	—	2	2	no	—
148	Q₈×C₃₇	—	2	2	no	—
149	Q₈×C₃₇	—	2	4	no	—
150	Q₈×C₃₇	—	2	4	no	—
151	Q₈×C₃₇	—	4	8	no	—
152	Q₈×C₃₇	—	4	4	no	—
153	Q₈×C₃₇	C₂×C₂²⋊C₄	1	4	yes	—
154	D₄×C₃₇	—	2	8	no	—
155	D₄×C₃₇	—	2	4	no	—
156	D₄×C₃₇	—	2	2	no	—
157	D₄×C₃₇	—	2	2	no	—
158	D₄×C₃₇	—	4	8	no	—
159	D₄×C₃₇	C₂×C₂²⋊C₄	1	4	yes	—
160	C₂×C₄×C₃₇	—	2	2	no	—
161	C₂×C₄×C₃₇	—	2	2	no	—
162	C₂×C₄×C₃₇	—	2	2	no	—
163	C₂×C₄×C₃₇	—	2	8	no	—
164	C₂×C₄×C₃₇	—	2	4	no	—
165	C₂×C₄×C₃₇	—	4	8	no	—
166	C₂×C₄×C₃₇	—	4	8	no	—
167	C₂×C₄×C₃₇	—	4	4	no	—
168	C₂×C₄×C₃₇	—	4	2	no	—
169	C₂×C₄×C₃₇	C₄×D₄	1	2	yes	—
170	C₂×C₄×C₃₇	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
172	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
174	C₈×C₃₇	—	2	2	no	—
175	C₈×C₃₇	—	2	4	no	—
176	C₈×C₃₇	—	4	4	no	—
177	C₈×C₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₈×C₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₈×C₃₇	C₂×C₂²⋊C₄	1	2	yes	—
180	#22460	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂²×C₃₇	—	2	2	no	—
182	C₂²×C₃₇	—	2	4	no	—
183	C₂²×C₃₇	—	4	1	no	—
184	C₂²×C₃₇	—	4	2	no	—
185	C₂²×C₃₇	—	8	2	no	—
186	C₂²×C₃₇	C₂×C₄×D₄	1	1	yes	characteristic
187	C₂²×C₃₇	#546	1	2	yes	—
188	C₄×C₃₇	—	2	4	no	—
189	C₄×C₃₇	—	2	2	no	—
190	C₄×C₃₇	—	4	4	no	—
191	C₄×C₃₇	—	8	2	no	—
192	C₄×C₃₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
193	C₄×C₃₇	#518	1	1	yes	characteristic
194	C₄×C₃₇	D₄²	1	2	yes	—
195	C₂×#578	C₂×C₃₇	1	1	yes	characteristic
196	#2957	C₂×C₃₇	1	2	yes	complemented
197	#2889	C₂×C₃₇	1	2	yes	complemented
198	#1979	C₂×C₃₇	1	2	yes	complemented
199	#1902	C₂×C₃₇	1	4	yes	complemented
200	#1813	C₂×C₃₇	1	1	yes	characteristic, complemented
201	#1796	C₂×C₃₇	1	2	yes	complemented
202	#1757	C₂×C₃₇	1	1	yes	characteristic, complemented
203	C₂×C₃₇	—	2	2	no	—
204	C₂×C₃₇	—	2	1	no	—
205	C₂×C₃₇	—	4	2	no	—
206	C₂×C₃₇	—	4	4	no	—
207	C₂×C₃₇	D₄×C₂²⋊C₄	1	1	yes	characteristic
208	C₂×2₋¹⁺⁴	C₂²×C₃₇	1	2	yes	—
209	#578	—	2	4	no	—
210	#578	—	2	4	no	—
211	C₂×#137	C₄×C₃₇	1	4	yes	complemented
212	C₂×#137	C₂²×C₃₇	1	2	yes	—
213	C₂×#135	C₄×C₃₇	1	2	yes	complemented
214	C₂×#135	C₂²×C₃₇	1	1	yes	characteristic
215	C₂²×Q₁₆	C₄×C₃₇	1	2	yes	complemented
216	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
217	#568	C₂²×C₃₇	1	4	yes	—
218	C₂×#131	C₂²×C₃₇	1	1	yes	characteristic
219	#444	—	2	4	no	—
220	#443	—	2	4	no	—
221	C₂×#108	C₂²×C₃₇	1	2	yes	—
222	#421	C₂²×C₃₇	1	4	yes	—
223	#419	C₂²×C₃₇	1	4	yes	—
224	#413	—	2	4	no	—
225	#413	C₂²×C₃₇	1	2	yes	—
226	#413	C₂²×C₃₇	1	1	yes	characteristic
227	C₂×#101	—	2	4	no	—
228	C₂×#101	C₂²×C₃₇	1	4	yes	—
229	#410	C₂²×C₃₇	1	1	yes	characteristic
230	#405	C₂²×C₃₇	1	2	yes	—
231	#344	C₂²×C₃₇	1	2	yes	—
232	#338	C₂²×C₃₇	1	2	yes	—
233	C₃₇	#22460	1	1	yes	characteristic, direct product factor, Sylow
234	2₋¹⁺⁴	—	2	8	no	—
235	2₋¹⁺⁴	—	4	4	no	—
236	C₂×#41	—	2	2	no	—
237	C₂×#41	—	2	4	no	—
238	C₂×#41	C₂×C₄×C₃₇	1	4	yes	—
239	C₂×#41	C₂³×C₃₇	1	2	yes	—
240	C₂×#41	C₂³×C₃₇	1	1	yes	characteristic
241	C₂²×Q₈	—	2	2	no	—
242	C₂²×Q₈	C₂×C₄×C₃₇	1	4	yes	—
243	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
244	#137	—	2	8	no	—
245	#137	—	2	16	no	—
246	#135	—	2	4	no	—
247	#135	—	2	4	no	—
248	#135	D₄×C₃₇	1	4	yes	—
249	#135	D₄×C₃₇	1	4	yes	—
250	C₂×Q₁₆	—	2	4	no	—
251	C₂×Q₁₆	—	2	4	no	—
252	C₂×Q₁₆	—	2	2	no	—
253	C₂×Q₁₆	—	2	2	no	—
254	C₂×Q₁₆	C₂×C₄×C₃₇	1	2	yes	—
255	C₂×Q₁₆	C₂×C₄×C₃₇	1	4	yes	—
256	C₂×Q₁₆	C₂×C₄×C₃₇	1	2	yes	—
257	C₂×Q₁₆	C₂×C₄×C₃₇	1	1	yes	characteristic
258	C₂×SD₁₆	C₂×C₄×C₃₇	1	4	yes	—
259	C₂×SD₁₆	C₂×C₄×C₃₇	1	2	yes	—
260	C₂×D₈	C₂×C₄×C₃₇	1	1	yes	characteristic
261	#131	—	2	2	no	—
262	#131	—	2	2	no	—
263	#131	—	2	8	no	—
264	#131	—	4	4	no	—
265	C₂×M₁₆	—	2	8	no	—
266	C₂×M₁₆	C₂×C₄×C₃₇	1	2	yes	—
267	C₂×M₁₆	C₂³×C₃₇	1	4	yes	—
268	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
269	C₂×M₁₆	C₂³×C₃₇	1	1	yes	characteristic
270	C₂²×C₈	C₂×C₄×C₃₇	1	2	yes	—
271	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
272	#117	C₂³×C₃₇	1	2	yes	—
273	#108	—	2	2	no	—
274	#108	—	2	2	no	—
275	#104	—	2	8	no	—
276	#103	—	4	4	no	—
277	#101	—	2	2	no	—
278	#101	—	2	8	no	—
279	#101	D₄×C₃₇	1	2	yes	—
280	#100	—	2	2	no	—
281	#100	D₄×C₃₇	1	2	yes	—
282	#99	—	2	2	no	—
283	#97	—	2	2	no	—
284	C₄×C₈	—	2	2	no	—
285	#41	—	2	2	no	—
286	#41	—	2	4	no	—
287	#41	—	2	2	no	—
288	#41	—	2	8	no	—
289	#41	—	4	4	no	—
290	#41	—	4	8	no	—
291	#41	—	4	16	no	—
292	#41	C₂×D₄×C₃₇	1	8	yes	—
293	C₂×Q₈	—	2	4	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	8	no	—
296	C₂×Q₈	—	2	4	no	—
297	C₂×Q₈	—	2	4	no	—
298	C₂×Q₈	—	4	4	no	—
299	C₂×Q₈	—	4	8	no	—
300	C₂×Q₈	C₂²×C₄×C₃₇	1	4	yes	—
301	C₂×Q₈	C₂²×C₄×C₃₇	1	2	yes	—
302	C₂×Q₈	C₂×D₄×C₃₇	1	1	yes	characteristic
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	C₂²×C₄×C₃₇	1	2	yes	—
306	C₂×D₄	C₂×D₄×C₃₇	1	1	yes	characteristic
307	C₂×D₄	#41×C₃₇	1	2	yes	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	C₂²×C₄×C₃₇	1	2	yes	—
313	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
314	Q₁₆	—	2	8	no	—
315	Q₁₆	—	2	2	no	—
316	Q₁₆	—	2	2	no	—
317	Q₁₆	—	2	4	no	—
318	Q₁₆	C₂²⋊C₄×C₃₇	1	2	yes	—
319	Q₁₆	C₂²⋊C₄×C₃₇	1	2	yes	—
320	SD₁₆	—	2	8	no	—
321	SD₁₆	C₂²⋊C₄×C₃₇	1	8	yes	—
322	D₈	C₂²⋊C₄×C₃₇	1	2	yes	—
323	D₈	C₂²⋊C₄×C₃₇	1	2	yes	—
324	M₁₆	—	2	2	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	2	4	no	—
327	M₁₆	—	2	4	no	—
328	M₁₆	—	2	4	no	—
329	M₁₆	—	4	8	no	—
330	M₁₆	C₂×D₄×C₃₇	1	4	yes	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	4	no	—
335	C₂×C₈	—	4	8	no	—
336	C₂×C₈	C₂²×C₄×C₃₇	1	2	yes	—
337	C₂×C₈	C₂²×C₄×C₃₇	1	1	yes	characteristic
338	C₂×C₈	C₂²×C₄×C₃₇	1	1	yes	characteristic
339	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
340	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
341	C₄⋊C₄	—	2	2	no	—
342	C₂²⋊C₄	—	2	2	no	—
343	C₄²	—	2	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	C₄×D₄×C₃₇	1	2	yes	—
346	C₂³	C₂×#41×C₃₇	1	1	yes	characteristic
347	Q₈	—	2	2	no	—
348	Q₈	—	2	2	no	—
349	Q₈	—	2	4	no	—
350	Q₈	—	2	4	no	—
351	Q₈	—	4	8	no	—
352	Q₈	—	4	4	no	—
353	Q₈	C₂×C₂²⋊C₄×C₃₇	1	4	yes	—
354	D₄	—	2	8	no	—
355	D₄	—	2	4	no	—
356	D₄	—	2	2	no	—
357	D₄	—	2	2	no	—
358	D₄	—	4	8	no	—
359	D₄	C₂×C₂²⋊C₄×C₃₇	1	4	yes	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	8	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	4	8	no	—
366	C₂×C₄	—	4	8	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	C₄×D₄×C₃₇	1	2	yes	—
370	C₂×C₄	C₂³×C₄×C₃₇	1	1	yes	characteristic
371	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
372	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
373	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
374	C₈	—	2	4	no	—
375	C₈	—	2	2	no	—
376	C₈	—	4	4	no	—
377	C₈	C₂×C₂²⋊C₄×C₃₇	1	1	yes	characteristic
378	C₈	C₂×C₂²⋊C₄×C₃₇	1	1	yes	characteristic
379	C₈	C₂×C₂²⋊C₄×C₃₇	1	2	yes	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	4	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	C₂×C₄×D₄×C₃₇	1	1	yes	characteristic
386	C₂²	C₃₇×#546	1	2	yes	—
387	C₄	—	2	4	no	—
388	C₄	—	2	2	no	—
389	C₄	—	4	4	no	—
390	C₄	—	8	2	no	—
391	C₄	C₂²×C₂²⋊C₄×C₃₇	1	1	yes	characteristic
392	C₄	C₃₇×#518	1	1	yes	characteristic
393	C₄	D₄²×C₃₇	1	2	yes	—
394	C₂	—	2	2	no	—
395	C₂	—	2	1	no	—
396	C₂	—	4	2	no	—
397	C₂	—	4	4	no	—
398	C₂	D₄×C₂²⋊C₄×C₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃₇	D₄×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂×C₃₇×#578	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₇ ◁ C₂²×C₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₇×#2957	C₂	semidirect
3. C₃₇×#2889	C₂	semidirect
4. C₃₇×#1979	C₂	semidirect
5. C₃₇×#1902	C₂	semidirect
6. C₃₇×#1813	C₂	semidirect
7. C₃₇×#1796	C₂	semidirect
8. C₃₇×#1757	C₂	semidirect
12. C₂×#137×C₃₇	C₄	semidirect
14. C₂×#135×C₃₇	C₄	semidirect
16. C₂²×Q₁₆×C₃₇	C₄	semidirect
180. #22460	C₃₇	direct (N × H)
196. #2957	C₂×C₃₇	semidirect
197. #2889	C₂×C₃₇	semidirect
198. #1979	C₂×C₃₇	semidirect
199. #1902	C₂×C₃₇	semidirect
200. #1813	C₂×C₃₇	semidirect
201. #1796	C₂×C₃₇	semidirect
202. #1757	C₂×C₃₇	semidirect
211. C₂×#137	C₄×C₃₇	semidirect
213. C₂×#135	C₄×C₃₇	semidirect
215. C₂²×Q₁₆	C₄×C₃₇	semidirect
233. C₃₇	#22460	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×#578	2
C₃₇×#2957	2
C₃₇×#2889	2
C₃₇×#1979	2
C₃₇×#1902	2
C₃₇×#1813	2
C₃₇×#1796	2
C₃₇×#1757	2
#22460	37

Subgroups — C37×#22460 #22643713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#22460 #22643713