Subgroups — C₃₇×#29751 #22651004

Order 9472.

942 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#469	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×#3006	C₂	1	2	yes	maximal, complemented
3	C₃₇×#2879	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#2079	C₂	1	2	yes	maximal, complemented
5	C₃₇×#2051	C₂	1	4	yes	maximal, complemented
6	C₃₇×#2018	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1900	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1811	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₃₇	C₂²	1	1	yes	characteristic
10	C₂×AGL(1,ℤ/8)×C₃₇	C₂²	1	4	yes	—
11	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic, complemented
12	C₂²×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×#121×C₃₇	C₂²	1	2	yes	—
15	C₃₇×#469	—	2	2	no	—
16	C₃₇×#469	—	2	2	no	—
17	C₃₇×#449	—	2	4	no	—
18	C₃₇×#448	—	2	2	no	—
19	C₃₇×#447	—	2	2	no	—
20	C₂×#108×C₃₇	C₂²	1	2	yes	complemented
21	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic, complemented
22	C₃₇×#417	C₂²	1	4	yes	—
23	C₂×#102×C₃₇	C₂²	1	2	yes	complemented
24	C₂×#100×C₃₇	C₂²	1	4	yes	complemented
25	C₃₇×#408	—	2	2	no	—
26	C₃₇×#408	C₂²	1	2	yes	—
27	C₃₇×#408	C₂²	1	2	yes	—
28	C₃₇×#407	—	2	2	no	—
29	C₃₇×#407	C₂²	1	2	yes	—
30	C₃₇×#343	C₂²	1	4	yes	complemented
31	C₃₇×#341	C₂²	1	2	yes	complemented
32	C₂×#41×C₃₇	—	2	1	no	—
33	C₂×#41×C₃₇	—	2	1	no	—
34	C₂×#41×C₃₇	—	4	2	no	—
35	C₂×#41×C₃₇	—	4	2	no	—
36	C₂×#41×C₃₇	D₄	1	2	yes	—
37	C₂×#41×C₃₇	C₂³	1	2	yes	—
38	C₂²×Q₈×C₃₇	D₄	1	1	yes	characteristic
39	C₂²×D₄×C₃₇	—	2	1	no	—
40	C₂²×D₄×C₃₇	—	2	2	no	—
41	C₂²×D₄×C₃₇	D₄	1	1	yes	characteristic
42	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
43	C₂³×C₄×C₃₇	—	2	1	no	—
44	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
45	AGL(1,ℤ/8)×C₃₇	—	4	4	no	—
46	AGL(1,ℤ/8)×C₃₇	—	4	4	no	—
47	C₂×SD₁₆×C₃₇	—	2	4	no	—
48	C₂×D₈×C₃₇	—	2	4	no	—
49	C₂×D₈×C₃₇	—	2	2	no	—
50	C₂×D₈×C₃₇	—	4	2	no	—
51	C₂×M₁₆×C₃₇	—	2	1	no	—
52	C₂×M₁₆×C₃₇	—	4	2	no	—
53	C₂×M₁₆×C₃₇	—	4	2	no	—
54	C₂×M₁₆×C₃₇	D₄	1	2	yes	—
55	C₂×M₁₆×C₃₇	D₄	1	2	yes	—
56	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
57	C₂×M₁₆×C₃₇	C₂³	1	4	yes	—
58	C₂²×C₈×C₃₇	—	2	1	no	—
59	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
61	#121×C₃₇	—	2	2	no	—
62	#121×C₃₇	—	2	2	no	—
63	#121×C₃₇	—	2	2	no	—
64	#121×C₃₇	—	2	2	no	—
65	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
67	#108×C₃₇	—	4	2	no	—
68	#106×C₃₇	—	2	2	no	—
69	#103×C₃₇	—	2	4	no	—
70	#102×C₃₇	—	2	4	no	—
71	#102×C₃₇	—	2	4	no	—
72	#100×C₃₇	—	4	4	no	—
73	C₂²⋊C₈×C₃₇	—	2	2	no	—
74	C₂²⋊C₈×C₃₇	—	2	2	no	—
75	C₂²⋊C₈×C₃₇	—	2	4	no	—
76	C₂²⋊C₈×C₃₇	—	2	4	no	—
77	C₂⁴×C₃₇	—	2	1	no	—
78	C₂⁴×C₃₇	—	2	2	no	—
79	C₂⁴×C₃₇	#41	1	1	yes	characteristic
80	#41×C₃₇	—	2	4	no	—
81	#41×C₃₇	—	2	4	no	—
82	#41×C₃₇	—	4	4	no	—
83	#41×C₃₇	—	4	4	no	—
84	#41×C₃₇	—	4	2	no	—
85	#41×C₃₇	—	4	2	no	—
86	C₂×Q₈×C₃₇	—	2	1	no	—
87	C₂×Q₈×C₃₇	—	4	2	no	—
88	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
89	C₂×D₄×C₃₇	—	2	2	no	—
90	C₂×D₄×C₃₇	—	2	2	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	4	no	—
95	C₂×D₄×C₃₇	—	2	4	no	—
96	C₂×D₄×C₃₇	—	4	2	no	—
97	C₂×D₄×C₃₇	—	4	4	no	—
98	C₂×D₄×C₃₇	—	4	2	no	—
99	C₂×D₄×C₃₇	—	4	2	no	—
100	C₂×D₄×C₃₇	—	8	4	no	—
101	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₃₇	—	2	2	no	—
103	C₂²×C₄×C₃₇	—	2	2	no	—
104	C₂²×C₄×C₃₇	—	2	1	no	—
105	C₂²×C₄×C₃₇	—	2	2	no	—
106	C₂²×C₄×C₃₇	—	2	2	no	—
107	C₂²×C₄×C₃₇	—	2	2	no	—
108	C₂²×C₄×C₃₇	—	4	2	no	—
109	C₂²×C₄×C₃₇	—	4	2	no	—
110	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₃₇	#41	1	1	yes	characteristic
115	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
116	SD₁₆×C₃₇	—	4	8	no	—
117	D₈×C₃₇	—	4	4	no	—
118	D₈×C₃₇	—	4	8	no	—
119	M₁₆×C₃₇	—	2	4	no	—
120	M₁₆×C₃₇	—	2	4	no	—
121	M₁₆×C₃₇	—	2	4	no	—
122	M₁₆×C₃₇	—	4	2	no	—
123	M₁₆×C₃₇	—	4	2	no	—
124	M₁₆×C₃₇	—	4	2	no	—
125	C₂×C₈×C₃₇	—	2	2	no	—
126	C₂×C₈×C₃₇	—	2	2	no	—
127	C₂×C₈×C₃₇	—	2	2	no	—
128	C₂×C₈×C₃₇	—	2	4	no	—
129	C₂×C₈×C₃₇	—	4	2	no	—
130	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
132	C₄⋊C₄×C₃₇	—	2	2	no	—
133	C₄⋊C₄×C₃₇	—	2	2	no	—
134	C₂²⋊C₄×C₃₇	—	4	2	no	—
135	C₂²⋊C₄×C₃₇	—	4	2	no	—
136	C₂³×C₃₇	—	2	2	no	—
137	C₂³×C₃₇	—	2	2	no	—
138	C₂³×C₃₇	—	4	2	no	—
139	C₂³×C₃₇	—	4	2	no	—
140	C₂³×C₃₇	—	4	2	no	—
141	C₂³×C₃₇	—	4	4	no	—
142	C₂³×C₃₇	—	8	2	no	—
143	C₂³×C₃₇	—	8	2	no	—
144	C₂³×C₃₇	—	8	2	no	—
145	C₂³×C₃₇	#121	1	1	yes	characteristic
146	C₂³×C₃₇	#121	1	1	yes	characteristic
147	C₂³×C₃₇	C₂×#41	1	1	yes	characteristic
148	Q₈×C₃₇	—	2	4	no	—
149	Q₈×C₃₇	—	4	2	no	—
150	D₄×C₃₇	—	2	4	no	—
151	D₄×C₃₇	—	4	2	no	—
152	D₄×C₃₇	—	4	4	no	—
153	D₄×C₃₇	—	4	4	no	—
154	D₄×C₃₇	—	4	2	no	—
155	D₄×C₃₇	—	4	4	no	—
156	D₄×C₃₇	—	4	2	no	—
157	D₄×C₃₇	—	8	4	no	—
158	D₄×C₃₇	—	8	4	no	—
159	C₂×C₄×C₃₇	—	2	2	no	—
160	C₂×C₄×C₃₇	—	2	1	no	—
161	C₂×C₄×C₃₇	—	2	1	no	—
162	C₂×C₄×C₃₇	—	2	2	no	—
163	C₂×C₄×C₃₇	—	2	2	no	—
164	C₂×C₄×C₃₇	—	2	1	no	—
165	C₂×C₄×C₃₇	—	2	1	no	—
166	C₂×C₄×C₃₇	—	2	2	no	—
167	C₂×C₄×C₃₇	—	4	4	no	—
168	C₂×C₄×C₃₇	—	4	2	no	—
169	C₂×C₄×C₃₇	—	4	2	no	—
170	C₂×C₄×C₃₇	—	4	2	no	—
171	C₂×C₄×C₃₇	—	4	2	no	—
172	C₂×C₄×C₃₇	—	8	2	no	—
173	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
174	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
175	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
178	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
179	C₈×C₃₇	—	2	2	no	—
180	C₈×C₃₇	—	2	2	no	—
181	C₈×C₃₇	—	4	4	no	—
182	C₈×C₃₇	—	4	2	no	—
183	#29751	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂²×C₃₇	—	2	2	no	—
185	C₂²×C₃₇	—	2	1	no	—
186	C₂²×C₃₇	—	2	1	no	—
187	C₂²×C₃₇	—	2	2	no	—
188	C₂²×C₃₇	—	2	2	no	—
189	C₂²×C₃₇	—	4	2	no	—
190	C₂²×C₃₇	—	4	4	no	—
191	C₂²×C₃₇	—	8	2	no	—
192	C₂²×C₃₇	—	8	4	no	—
193	C₂²×C₃₇	—	8	2	no	—
194	C₂²×C₃₇	—	8	2	no	—
195	C₂²×C₃₇	—	8	2	no	—
196	C₂²×C₃₇	—	16	4	no	—
197	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
198	C₂²×C₃₇	#538	1	2	yes	—
199	C₄×C₃₇	—	2	1	no	—
200	C₄×C₃₇	—	2	1	no	—
201	C₄×C₃₇	—	4	2	no	—
202	C₄×C₃₇	—	8	2	no	—
203	C₄×C₃₇	#534	1	1	yes	characteristic
204	C₄×C₃₇	#534	1	2	yes	—
205	C₄×C₃₇	#535	1	1	yes	characteristic
206	C₂×#469	C₂×C₃₇	1	1	yes	characteristic, complemented
207	#3006	C₂×C₃₇	1	2	yes	complemented
208	#2879	C₂×C₃₇	1	1	yes	characteristic, complemented
209	#2079	C₂×C₃₇	1	2	yes	complemented
210	#2051	C₂×C₃₇	1	4	yes	complemented
211	#2018	C₂×C₃₇	1	2	yes	complemented
212	#1900	C₂×C₃₇	1	2	yes	complemented
213	#1811	C₂×C₃₇	1	1	yes	characteristic, complemented
214	C₂×C₃₇	—	2	2	no	—
215	C₂×C₃₇	—	4	1	no	—
216	C₂×C₃₇	—	4	1	no	—
217	C₂×C₃₇	—	8	2	no	—
218	C₂×C₃₇	—	16	2	no	—
219	C₂×C₃₇	#2617	1	1	yes	characteristic
220	C₂×C₃₇	#3068	1	2	yes	—
221	C₂²×#41	C₂²×C₃₇	1	1	yes	characteristic
222	C₂×AGL(1,ℤ/8)	C₂²×C₃₇	1	4	yes	—
223	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic, complemented
224	C₂²×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
225	C₂²×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
226	C₂×#121	C₂²×C₃₇	1	2	yes	—
227	#469	—	2	2	no	—
228	#469	—	2	2	no	—
229	#449	—	2	4	no	—
230	#448	—	2	2	no	—
231	#447	—	2	2	no	—
232	C₂×#108	C₂²×C₃₇	1	2	yes	complemented
233	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic, complemented
234	#417	C₂²×C₃₇	1	4	yes	—
235	C₂×#102	C₂²×C₃₇	1	2	yes	complemented
236	C₂×#100	C₂²×C₃₇	1	4	yes	complemented
237	#408	—	2	2	no	—
238	#408	C₂²×C₃₇	1	2	yes	—
239	#408	C₂²×C₃₇	1	2	yes	—
240	#407	—	2	2	no	—
241	#407	C₂²×C₃₇	1	2	yes	—
242	#343	C₂²×C₃₇	1	4	yes	complemented
243	#341	C₂²×C₃₇	1	2	yes	complemented
244	C₃₇	#29751	1	1	yes	characteristic, direct product factor, Sylow
245	C₂×#41	—	2	1	no	—
246	C₂×#41	—	2	1	no	—
247	C₂×#41	—	4	2	no	—
248	C₂×#41	—	4	2	no	—
249	C₂×#41	D₄×C₃₇	1	2	yes	—
250	C₂×#41	C₂³×C₃₇	1	2	yes	—
251	C₂²×Q₈	D₄×C₃₇	1	1	yes	characteristic
252	C₂²×D₄	—	2	1	no	—
253	C₂²×D₄	—	2	2	no	—
254	C₂²×D₄	D₄×C₃₇	1	1	yes	characteristic
255	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
256	C₂³×C₄	—	2	1	no	—
257	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
258	AGL(1,ℤ/8)	—	4	4	no	—
259	AGL(1,ℤ/8)	—	4	4	no	—
260	C₂×SD₁₆	—	2	4	no	—
261	C₂×D₈	—	2	4	no	—
262	C₂×D₈	—	2	2	no	—
263	C₂×D₈	—	4	2	no	—
264	C₂×M₁₆	—	2	1	no	—
265	C₂×M₁₆	—	4	2	no	—
266	C₂×M₁₆	—	4	2	no	—
267	C₂×M₁₆	D₄×C₃₇	1	2	yes	—
268	C₂×M₁₆	D₄×C₃₇	1	2	yes	—
269	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
270	C₂×M₁₆	C₂³×C₃₇	1	4	yes	—
271	C₂²×C₈	—	2	1	no	—
272	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
274	#121	—	2	2	no	—
275	#121	—	2	2	no	—
276	#121	—	2	2	no	—
277	#121	—	2	2	no	—
278	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	#108	—	4	2	no	—
281	#106	—	2	2	no	—
282	#103	—	2	4	no	—
283	#102	—	2	4	no	—
284	#102	—	2	4	no	—
285	#100	—	4	4	no	—
286	C₂²⋊C₈	—	2	2	no	—
287	C₂²⋊C₈	—	2	2	no	—
288	C₂²⋊C₈	—	2	4	no	—
289	C₂²⋊C₈	—	2	4	no	—
290	C₂⁴	—	2	1	no	—
291	C₂⁴	—	2	2	no	—
292	C₂⁴	#41×C₃₇	1	1	yes	characteristic
293	#41	—	2	4	no	—
294	#41	—	2	4	no	—
295	#41	—	4	4	no	—
296	#41	—	4	4	no	—
297	#41	—	4	2	no	—
298	#41	—	4	2	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	—	4	2	no	—
301	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	4	no	—
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	—	4	2	no	—
310	C₂×D₄	—	4	4	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	8	4	no	—
314	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
327	C₂²×C₄	#41×C₃₇	1	1	yes	characteristic
328	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
329	SD₁₆	—	4	8	no	—
330	D₈	—	4	4	no	—
331	D₈	—	4	8	no	—
332	M₁₆	—	2	4	no	—
333	M₁₆	—	2	4	no	—
334	M₁₆	—	2	4	no	—
335	M₁₆	—	4	2	no	—
336	M₁₆	—	4	2	no	—
337	M₁₆	—	4	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	4	no	—
342	C₂×C₈	—	4	2	no	—
343	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
344	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₂²⋊C₄	—	4	2	no	—
348	C₂²⋊C₄	—	4	2	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	4	4	no	—
355	C₂³	—	8	2	no	—
356	C₂³	—	8	2	no	—
357	C₂³	—	8	2	no	—
358	C₂³	#121×C₃₇	1	1	yes	characteristic
359	C₂³	#121×C₃₇	1	1	yes	characteristic
360	C₂³	C₂×#41×C₃₇	1	1	yes	characteristic
361	Q₈	—	2	4	no	—
362	Q₈	—	4	2	no	—
363	D₄	—	2	4	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	4	no	—
366	D₄	—	4	4	no	—
367	D₄	—	4	2	no	—
368	D₄	—	4	4	no	—
369	D₄	—	4	2	no	—
370	D₄	—	8	4	no	—
371	D₄	—	8	4	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	8	2	no	—
386	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
387	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
388	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
389	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
390	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
391	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
392	C₈	—	2	2	no	—
393	C₈	—	2	2	no	—
394	C₈	—	4	4	no	—
395	C₈	—	4	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	4	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	4	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	8	2	no	—
407	C₂²	—	8	2	no	—
408	C₂²	—	16	4	no	—
409	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
410	C₂²	C₃₇×#538	1	2	yes	—
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	4	2	no	—
414	C₄	—	8	2	no	—
415	C₄	C₃₇×#534	1	1	yes	characteristic
416	C₄	C₃₇×#534	1	2	yes	—
417	C₄	C₃₇×#535	1	1	yes	characteristic
418	C₂	—	2	2	no	—
419	C₂	—	4	1	no	—
420	C₂	—	4	1	no	—
421	C₂	—	8	2	no	—
422	C₂	—	16	2	no	—
423	C₂	C₃₇×#2617	1	1	yes	characteristic
424	C₂	C₃₇×#3068	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂³×C₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#469	C₂	semidirect
2. C₃₇×#3006	C₂	semidirect
3. C₃₇×#2879	C₂	semidirect
4. C₃₇×#2079	C₂	semidirect
5. C₃₇×#2051	C₂	semidirect
6. C₃₇×#2018	C₂	semidirect
7. C₃₇×#1900	C₂	semidirect
8. C₃₇×#1811	C₂	semidirect
11. C₂²×D₈×C₃₇	C₂²	semidirect
20. C₂×#108×C₃₇	C₂²	semidirect
21. C₂×#106×C₃₇	C₂²	semidirect
23. C₂×#102×C₃₇	C₂²	semidirect
24. C₂×#100×C₃₇	C₂²	semidirect
30. C₃₇×#343	C₂²	semidirect
31. C₃₇×#341	C₂²	semidirect
183. #29751	C₃₇	direct (N × H)
206. C₂×#469	C₂×C₃₇	semidirect
207. #3006	C₂×C₃₇	semidirect
208. #2879	C₂×C₃₇	semidirect
209. #2079	C₂×C₃₇	semidirect
210. #2051	C₂×C₃₇	semidirect
211. #2018	C₂×C₃₇	semidirect
212. #1900	C₂×C₃₇	semidirect
213. #1811	C₂×C₃₇	semidirect
223. C₂²×D₈	C₂²×C₃₇	semidirect
232. C₂×#108	C₂²×C₃₇	semidirect
233. C₂×#106	C₂²×C₃₇	semidirect
235. C₂×#102	C₂²×C₃₇	semidirect
236. C₂×#100	C₂²×C₃₇	semidirect
242. #343	C₂²×C₃₇	semidirect
243. #341	C₂²×C₃₇	semidirect
244. C₃₇	#29751	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×#469	2
C₃₇×#3006	2
C₃₇×#2879	2
C₃₇×#2079	2
C₃₇×#2051	2
C₃₇×#2018	2
C₃₇×#1900	2
C₃₇×#1811	2
#29751	37

Subgroups — C37×#29751 #22651004

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#29751 #22651004