Subgroups — C₃₇×#29903 #22651156

Order 9472.

756 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3009	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#2888	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2081	C₂	1	2	yes	maximal, complemented
4	C₃₇×#2080	C₂	1	2	yes	maximal, complemented
5	C₃₇×#2049	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2046	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1915	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1909	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1868	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1858	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1795	C₂	1	1	yes	maximal, characteristic
12	C₂×H(5,𝔽₂)×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×#137×C₃₇	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
15	C₃₇×#568	C₂²	1	1	yes	characteristic
16	C₃₇×#568	C₂²	1	1	yes	characteristic
17	C₃₇×#536	C₂²	1	1	yes	characteristic
18	C₃₇×#452	—	2	2	no	—
19	C₃₇×#450	—	2	2	no	—
20	C₃₇×#430	C₂²	1	2	yes	complemented
21	C₃₇×#424	C₂²	1	2	yes	complemented
22	C₃₇×#421	C₂²	1	2	yes	—
23	C₃₇×#419	C₂²	1	2	yes	complemented
24	C₃₇×#418	C₂²	1	1	yes	characteristic
25	C₃₇×#418	C₂²	1	2	yes	—
26	C₃₇×#416	C₂²	1	1	yes	characteristic
27	C₃₇×#413	—	2	2	no	—
28	C₃₇×#413	C₂²	1	1	yes	characteristic
29	C₃₇×#413	C₂²	1	2	yes	—
30	C₂×#101×C₃₇	C₂²	1	2	yes	complemented
31	C₂×#100×C₃₇	—	2	2	no	—
32	C₂×#100×C₃₇	C₂²	1	2	yes	—
33	C₃₇×#410	C₂²	1	1	yes	characteristic
34	C₃₇×#408	C₂²	1	1	yes	characteristic
35	C₃₇×#344	C₂²	1	2	yes	complemented
36	C₃₇×#344	C₂²	1	2	yes	complemented
37	C₃₇×#341	C₂²	1	2	yes	complemented
38	C₃₇×H(3,ℤ/4)	C₂²	1	2	yes	complemented
39	H(5,𝔽₂)×C₃₇	—	4	2	no	—
40	H(5,𝔽₂)×C₃₇	—	4	2	no	—
41	C₂×#41×C₃₇	—	2	1	no	—
42	C₂×#41×C₃₇	D₄	1	2	yes	—
43	C₂×#41×C₃₇	C₂³	1	1	yes	characteristic
44	C₂×#41×C₃₇	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₃₇	—	2	2	no	—
47	C₂²×D₄×C₃₇	—	2	1	no	—
48	C₂²×D₄×C₃₇	D₄	1	2	yes	—
49	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
50	#137×C₃₇	—	4	2	no	—
51	C₂×Q₁₆×C₃₇	—	2	1	no	—
52	C₂×SD₁₆×C₃₇	—	2	2	no	—
53	C₂×SD₁₆×C₃₇	—	2	1	no	—
54	C₂×SD₁₆×C₃₇	—	4	2	no	—
55	#131×C₃₇	—	4	2	no	—
56	#131×C₃₇	—	4	2	no	—
57	C₂×M₁₆×C₃₇	—	2	2	no	—
58	C₂×M₁₆×C₃₇	—	2	2	no	—
59	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
60	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
61	C₂×M₁₆×C₃₇	C₂³	1	1	yes	characteristic
62	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
63	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
64	C₄⋊Q₈×C₃₇	—	2	1	no	—
65	#124×C₃₇	—	2	1	no	—
66	#123×C₃₇	—	2	2	no	—
67	C₂²⋊Q₈×C₃₇	—	2	2	no	—
68	#117×C₃₇	C₂³	1	1	yes	characteristic
69	#117×C₃₇	C₂³	1	2	yes	—
70	#108×C₃₇	—	4	2	no	—
71	C₄⋊C₈×C₃₇	—	4	2	no	—
72	#104×C₃₇	—	4	2	no	—
73	#103×C₃₇	—	2	1	no	—
74	#103×C₃₇	—	4	2	no	—
75	#102×C₃₇	—	2	1	no	—
76	#102×C₃₇	—	2	2	no	—
77	#102×C₃₇	—	4	2	no	—
78	#101×C₃₇	—	2	2	no	—
79	#101×C₃₇	—	2	1	no	—
80	#101×C₃₇	—	4	2	no	—
81	#100×C₃₇	—	2	2	no	—
82	#100×C₃₇	—	2	4	no	—
83	#100×C₃₇	—	2	1	no	—
84	#99×C₃₇	—	2	2	no	—
85	C₂²⋊C₈×C₃₇	—	2	2	no	—
86	C₂⁴×C₃₇	—	2	2	no	—
87	C₂⁴×C₃₇	—	2	1	no	—
88	#41×C₃₇	—	2	2	no	—
89	#41×C₃₇	—	2	2	no	—
90	#41×C₃₇	—	2	2	no	—
91	#41×C₃₇	—	2	2	no	—
92	#41×C₃₇	—	4	2	no	—
93	#41×C₃₇	—	4	2	no	—
94	#41×C₃₇	—	4	4	no	—
95	C₂×Q₈×C₃₇	—	2	1	no	—
96	C₂×Q₈×C₃₇	—	2	1	no	—
97	C₂×Q₈×C₃₇	—	2	2	no	—
98	C₂×Q₈×C₃₇	—	2	2	no	—
99	C₂×Q₈×C₃₇	C₂×D₄	1	1	yes	characteristic
100	C₂×Q₈×C₃₇	#41	1	1	yes	characteristic
101	C₂×D₄×C₃₇	—	2	2	no	—
102	C₂×D₄×C₃₇	—	2	1	no	—
103	C₂×D₄×C₃₇	—	2	2	no	—
104	C₂×D₄×C₃₇	—	2	1	no	—
105	C₂×D₄×C₃₇	—	2	2	no	—
106	C₂×D₄×C₃₇	—	2	2	no	—
107	C₂×D₄×C₃₇	—	4	2	no	—
108	C₂×D₄×C₃₇	—	4	2	no	—
109	C₂×D₄×C₃₇	—	4	8	no	—
110	C₂×D₄×C₃₇	—	4	4	no	—
111	C₂×D₄×C₃₇	C₂×D₄	1	1	yes	characteristic
112	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
113	C₂×D₄×C₃₇	#41	1	2	yes	—
114	C₂×D₄×C₃₇	#41	1	1	yes	characteristic
115	C₂²×C₄×C₃₇	—	2	2	no	—
116	C₂²×C₄×C₃₇	—	2	1	no	—
117	C₂²×C₄×C₃₇	—	2	1	no	—
118	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
120	Q₁₆×C₃₇	—	4	2	no	—
121	SD₁₆×C₃₇	—	4	4	no	—
122	SD₁₆×C₃₇	—	4	2	no	—
123	M₁₆×C₃₇	—	2	2	no	—
124	M₁₆×C₃₇	—	2	2	no	—
125	M₁₆×C₃₇	—	2	2	no	—
126	M₁₆×C₃₇	—	2	2	no	—
127	M₁₆×C₃₇	—	2	2	no	—
128	M₁₆×C₃₇	—	2	2	no	—
129	M₁₆×C₃₇	—	2	2	no	—
130	M₁₆×C₃₇	—	4	2	no	—
131	M₁₆×C₃₇	—	4	2	no	—
132	C₂×C₈×C₃₇	—	2	1	no	—
133	C₂×C₈×C₃₇	—	2	1	no	—
134	C₂×C₈×C₃₇	—	2	2	no	—
135	C₂×C₈×C₃₇	—	2	2	no	—
136	C₂×C₈×C₃₇	—	2	2	no	—
137	C₂×C₈×C₃₇	—	2	2	no	—
138	C₂×C₈×C₃₇	—	4	2	no	—
139	C₂×C₈×C₃₇	—	4	2	no	—
140	C₄⋊C₄×C₃₇	—	2	1	no	—
141	C₄⋊C₄×C₃₇	—	2	2	no	—
142	C₄⋊C₄×C₃₇	—	4	2	no	—
143	C₂²⋊C₄×C₃₇	—	2	2	no	—
144	C₂²⋊C₄×C₃₇	—	2	1	no	—
145	C₂²⋊C₄×C₃₇	—	4	2	no	—
146	C₄²×C₃₇	—	2	1	no	—
147	C₄²×C₃₇	—	2	2	no	—
148	C₂³×C₃₇	—	2	2	no	—
149	C₂³×C₃₇	—	2	1	no	—
150	C₂³×C₃₇	—	4	4	no	—
151	C₂³×C₃₇	—	4	2	no	—
152	C₂³×C₃₇	—	16	1	no	—
153	C₂³×C₃₇	—	16	2	no	—
154	C₂³×C₃₇	#123	1	2	yes	—
155	C₂³×C₃₇	C₂×#41	1	1	yes	characteristic
156	Q₈×C₃₇	—	2	2	no	—
157	Q₈×C₃₇	—	2	1	no	—
158	Q₈×C₃₇	—	2	1	no	—
159	Q₈×C₃₇	—	4	1	no	—
160	Q₈×C₃₇	—	4	1	no	—
161	Q₈×C₃₇	—	4	2	no	—
162	D₄×C₃₇	—	2	4	no	—
163	D₄×C₃₇	—	2	2	no	—
164	D₄×C₃₇	—	2	1	no	—
165	D₄×C₃₇	—	2	2	no	—
166	D₄×C₃₇	—	2	1	no	—
167	D₄×C₃₇	—	2	2	no	—
168	D₄×C₃₇	—	4	4	no	—
169	D₄×C₃₇	—	4	4	no	—
170	D₄×C₃₇	—	4	2	no	—
171	D₄×C₃₇	—	4	2	no	—
172	C₂×C₄×C₃₇	—	2	2	no	—
173	C₂×C₄×C₃₇	—	2	2	no	—
174	C₂×C₄×C₃₇	—	2	1	no	—
175	C₂×C₄×C₃₇	—	4	4	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	#123	1	2	yes	—
182	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
185	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
186	C₈×C₃₇	—	4	1	no	—
187	C₈×C₃₇	—	4	2	no	—
188	C₈×C₃₇	—	4	2	no	—
189	C₈×C₃₇	—	4	1	no	—
190	C₈×C₃₇	—	4	2	no	—
191	#29903	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂²×C₃₇	—	2	2	no	—
193	C₂²×C₃₇	—	4	1	no	—
194	C₂²×C₃₇	—	4	2	no	—
195	C₂²×C₃₇	—	4	2	no	—
196	C₂²×C₃₇	—	4	1	no	—
197	C₂²×C₃₇	—	8	2	no	—
198	C₂²×C₃₇	—	8	1	no	—
199	C₂²×C₃₇	—	16	2	no	—
200	C₂²×C₃₇	—	16	4	no	—
201	C₂²×C₃₇	C₂×#123	1	1	yes	characteristic
202	C₂²×C₃₇	#538	1	2	yes	—
203	C₄×C₃₇	—	2	2	no	—
204	C₄×C₃₇	—	4	1	no	—
205	C₄×C₃₇	—	8	1	no	—
206	C₄×C₃₇	—	8	2	no	—
207	C₄×C₃₇	—	8	1	no	—
208	C₄×C₃₇	#534	1	1	yes	characteristic
209	C₄×C₃₇	#534	1	1	yes	characteristic
210	C₄×C₃₇	#538	1	2	yes	—
211	#3009	C₂×C₃₇	1	1	yes	characteristic
212	#2888	C₂×C₃₇	1	1	yes	characteristic
213	#2081	C₂×C₃₇	1	2	yes	complemented
214	#2080	C₂×C₃₇	1	2	yes	complemented
215	#2049	C₂×C₃₇	1	2	yes	complemented
216	#2046	C₂×C₃₇	1	2	yes	complemented
217	#1915	C₂×C₃₇	1	1	yes	characteristic, complemented
218	#1909	C₂×C₃₇	1	1	yes	characteristic, complemented
219	#1868	C₂×C₃₇	1	1	yes	characteristic, complemented
220	#1858	C₂×C₃₇	1	1	yes	characteristic, complemented
221	#1795	C₂×C₃₇	1	1	yes	characteristic
222	C₂×C₃₇	—	2	1	no	—
223	C₂×C₃₇	—	2	2	no	—
224	C₂×C₃₇	—	4	2	no	—
225	C₂×C₃₇	—	8	2	no	—
226	C₂×C₃₇	—	8	1	no	—
227	C₂×C₃₇	#2622	1	1	yes	characteristic
228	C₂×H(5,𝔽₂)	C₂²×C₃₇	1	1	yes	characteristic
229	C₂×#137	C₂²×C₃₇	1	1	yes	characteristic
230	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
231	#568	C₂²×C₃₇	1	1	yes	characteristic
232	#568	C₂²×C₃₇	1	1	yes	characteristic
233	#536	C₂²×C₃₇	1	1	yes	characteristic
234	#452	—	2	2	no	—
235	#450	—	2	2	no	—
236	#430	C₂²×C₃₇	1	2	yes	complemented
237	#424	C₂²×C₃₇	1	2	yes	complemented
238	#421	C₂²×C₃₇	1	2	yes	—
239	#419	C₂²×C₃₇	1	2	yes	complemented
240	#418	C₂²×C₃₇	1	1	yes	characteristic
241	#418	C₂²×C₃₇	1	2	yes	—
242	#416	C₂²×C₃₇	1	1	yes	characteristic
243	#413	—	2	2	no	—
244	#413	C₂²×C₃₇	1	2	yes	—
245	#413	C₂²×C₃₇	1	1	yes	characteristic
246	C₂×#101	C₂²×C₃₇	1	2	yes	complemented
247	C₂×#100	—	2	2	no	—
248	C₂×#100	C₂²×C₃₇	1	2	yes	—
249	#410	C₂²×C₃₇	1	1	yes	characteristic
250	#408	C₂²×C₃₇	1	1	yes	characteristic
251	#344	C₂²×C₃₇	1	2	yes	complemented
252	#344	C₂²×C₃₇	1	2	yes	complemented
253	#341	C₂²×C₃₇	1	2	yes	complemented
254	H(3,ℤ/4)	C₂²×C₃₇	1	2	yes	complemented
255	C₃₇	#29903	1	1	yes	characteristic, direct product factor, Sylow
256	H(5,𝔽₂)	—	4	2	no	—
257	H(5,𝔽₂)	—	4	2	no	—
258	C₂×#41	—	2	1	no	—
259	C₂×#41	D₄×C₃₇	1	2	yes	—
260	C₂×#41	C₂³×C₃₇	1	1	yes	characteristic
261	C₂×#41	C₂³×C₃₇	1	1	yes	characteristic
262	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
263	C₂²×D₄	—	2	2	no	—
264	C₂²×D₄	—	2	1	no	—
265	C₂²×D₄	D₄×C₃₇	1	2	yes	—
266	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
267	#137	—	4	2	no	—
268	C₂×Q₁₆	—	2	1	no	—
269	C₂×SD₁₆	—	2	2	no	—
270	C₂×SD₁₆	—	2	1	no	—
271	C₂×SD₁₆	—	4	2	no	—
272	#131	—	4	2	no	—
273	#131	—	4	2	no	—
274	C₂×M₁₆	—	2	2	no	—
275	C₂×M₁₆	—	2	2	no	—
276	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
277	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
278	C₂×M₁₆	C₂³×C₃₇	1	1	yes	characteristic
279	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
280	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
281	C₄⋊Q₈	—	2	1	no	—
282	#124	—	2	1	no	—
283	#123	—	2	2	no	—
284	C₂²⋊Q₈	—	2	2	no	—
285	#117	C₂³×C₃₇	1	1	yes	characteristic
286	#117	C₂³×C₃₇	1	2	yes	—
287	#108	—	4	2	no	—
288	C₄⋊C₈	—	4	2	no	—
289	#104	—	4	2	no	—
290	#103	—	2	1	no	—
291	#103	—	4	2	no	—
292	#102	—	2	1	no	—
293	#102	—	2	2	no	—
294	#102	—	4	2	no	—
295	#101	—	2	2	no	—
296	#101	—	2	1	no	—
297	#101	—	4	2	no	—
298	#100	—	2	2	no	—
299	#100	—	2	4	no	—
300	#100	—	2	1	no	—
301	#99	—	2	2	no	—
302	C₂²⋊C₈	—	2	2	no	—
303	C₂⁴	—	2	2	no	—
304	C₂⁴	—	2	1	no	—
305	#41	—	2	2	no	—
306	#41	—	2	2	no	—
307	#41	—	2	2	no	—
308	#41	—	2	2	no	—
309	#41	—	4	2	no	—
310	#41	—	4	2	no	—
311	#41	—	4	4	no	—
312	C₂×Q₈	—	2	1	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	C₂×D₄×C₃₇	1	1	yes	characteristic
317	C₂×Q₈	#41×C₃₇	1	1	yes	characteristic
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	4	2	no	—
325	C₂×D₄	—	4	2	no	—
326	C₂×D₄	—	4	8	no	—
327	C₂×D₄	—	4	4	no	—
328	C₂×D₄	C₂×D₄×C₃₇	1	1	yes	characteristic
329	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
330	C₂×D₄	#41×C₃₇	1	2	yes	—
331	C₂×D₄	#41×C₃₇	1	1	yes	characteristic
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
336	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
337	Q₁₆	—	4	2	no	—
338	SD₁₆	—	4	4	no	—
339	SD₁₆	—	4	2	no	—
340	M₁₆	—	2	2	no	—
341	M₁₆	—	2	2	no	—
342	M₁₆	—	2	2	no	—
343	M₁₆	—	2	2	no	—
344	M₁₆	—	2	2	no	—
345	M₁₆	—	2	2	no	—
346	M₁₆	—	2	2	no	—
347	M₁₆	—	4	2	no	—
348	M₁₆	—	4	2	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	4	2	no	—
356	C₂×C₈	—	4	2	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	4	2	no	—
360	C₂²⋊C₄	—	2	2	no	—
361	C₂²⋊C₄	—	2	1	no	—
362	C₂²⋊C₄	—	4	2	no	—
363	C₄²	—	2	1	no	—
364	C₄²	—	2	2	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	4	4	no	—
368	C₂³	—	4	2	no	—
369	C₂³	—	16	1	no	—
370	C₂³	—	16	2	no	—
371	C₂³	#123×C₃₇	1	2	yes	—
372	C₂³	C₂×#41×C₃₇	1	1	yes	characteristic
373	Q₈	—	2	2	no	—
374	Q₈	—	2	1	no	—
375	Q₈	—	2	1	no	—
376	Q₈	—	4	1	no	—
377	Q₈	—	4	1	no	—
378	Q₈	—	4	2	no	—
379	D₄	—	2	4	no	—
380	D₄	—	2	2	no	—
381	D₄	—	2	1	no	—
382	D₄	—	2	2	no	—
383	D₄	—	2	1	no	—
384	D₄	—	2	2	no	—
385	D₄	—	4	4	no	—
386	D₄	—	4	4	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	#123×C₃₇	1	2	yes	—
399	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
400	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
401	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
402	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
403	C₈	—	4	1	no	—
404	C₈	—	4	2	no	—
405	C₈	—	4	2	no	—
406	C₈	—	4	1	no	—
407	C₈	—	4	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	8	2	no	—
414	C₂²	—	8	1	no	—
415	C₂²	—	16	2	no	—
416	C₂²	—	16	4	no	—
417	C₂²	C₂×#123×C₃₇	1	1	yes	characteristic
418	C₂²	C₃₇×#538	1	2	yes	—
419	C₄	—	2	2	no	—
420	C₄	—	4	1	no	—
421	C₄	—	8	1	no	—
422	C₄	—	8	2	no	—
423	C₄	—	8	1	no	—
424	C₄	C₃₇×#534	1	1	yes	characteristic
425	C₄	C₃₇×#534	1	1	yes	characteristic
426	C₄	C₃₇×#538	1	2	yes	—
427	C₂	—	2	1	no	—
428	C₂	—	2	2	no	—
429	C₂	—	4	2	no	—
430	C₂	—	8	2	no	—
431	C₂	—	8	1	no	—
432	C₂	C₃₇×#2622	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃₇	#2622
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂×H(5,𝔽₂)×C₃₇	C₂²
LCS	G ▷ C₂²×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
3. C₃₇×#2081	C₂	semidirect
4. C₃₇×#2080	C₂	semidirect
5. C₃₇×#2049	C₂	semidirect
6. C₃₇×#2046	C₂	semidirect
7. C₃₇×#1915	C₂	semidirect
8. C₃₇×#1909	C₂	semidirect
9. C₃₇×#1868	C₂	semidirect
10. C₃₇×#1858	C₂	semidirect
20. C₃₇×#430	C₂²	semidirect
21. C₃₇×#424	C₂²	semidirect
23. C₃₇×#419	C₂²	semidirect
30. C₂×#101×C₃₇	C₂²	semidirect
35. C₃₇×#344	C₂²	semidirect
36. C₃₇×#344	C₂²	semidirect
37. C₃₇×#341	C₂²	semidirect
38. C₃₇×H(3,ℤ/4)	C₂²	semidirect
191. #29903	C₃₇	direct (N × H)
213. #2081	C₂×C₃₇	semidirect
214. #2080	C₂×C₃₇	semidirect
215. #2049	C₂×C₃₇	semidirect
216. #2046	C₂×C₃₇	semidirect
217. #1915	C₂×C₃₇	semidirect
218. #1909	C₂×C₃₇	semidirect
219. #1868	C₂×C₃₇	semidirect
220. #1858	C₂×C₃₇	semidirect
236. #430	C₂²×C₃₇	semidirect
237. #424	C₂²×C₃₇	semidirect
239. #419	C₂²×C₃₇	semidirect
246. C₂×#101	C₂²×C₃₇	semidirect
251. #344	C₂²×C₃₇	semidirect
252. #344	C₂²×C₃₇	semidirect
253. #341	C₂²×C₃₇	semidirect
254. H(3,ℤ/4)	C₂²×C₃₇	semidirect
255. C₃₇	#29903	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×#3009	2
C₃₇×#2888	2
C₃₇×#2081	2
C₃₇×#2080	2
C₃₇×#2049	2
C₃₇×#2046	2
C₃₇×#1915	2
C₃₇×#1909	2
C₃₇×#1868	2
C₃₇×#1858	2
C₃₇×#1795	2
#29903	37

Subgroups — C37×#29903 #22651156

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#29903 #22651156