Subgroups — C₃₇×#28595 #22649848

Order 9472.

832 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3055	C₂	1	2	yes	maximal, complemented
2	C₂×C₃₇×#469	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#2930	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#2090	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2079	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2045	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#2018	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1931	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1907	C₂	1	2	yes	maximal, complemented
10	C₃₇×#1900	C₂	1	2	yes	maximal, complemented
11	C₃₇×#1738	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₃₇	C₂²	1	2	yes	—
13	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×#131×C₃₇	C₂²	1	1	yes	characteristic
15	C₂²×M₁₆×C₃₇	C₂²	1	2	yes	—
16	C₂²×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
17	C₃₇×#525	C₂²	1	1	yes	characteristic
18	C₂×#121×C₃₇	C₂²	1	2	yes	—
19	C₃₇×#469	—	2	2	no	—
20	C₃₇×#469	—	2	2	no	—
21	C₃₇×#469	—	2	2	no	—
22	C₃₇×#468	—	2	2	no	—
23	C₃₇×#466	—	2	2	no	—
24	C₃₇×#465	—	2	2	no	—
25	C₃₇×#436	—	2	2	no	—
26	C₃₇×#435	—	2	2	no	—
27	C₃₇×#428	C₂²	1	2	yes	—
28	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
29	C₃₇×#424	C₂²	1	1	yes	characteristic
30	C₃₇×#418	C₂²	1	2	yes	—
31	C₃₇×#417	C₂²	1	2	yes	—
32	C₂×#102×C₃₇	C₂²	1	2	yes	—
33	C₂×#100×C₃₇	C₂²	1	2	yes	—
34	C₂×#100×C₃₇	C₂²	1	2	yes	—
35	C₃₇×#408	C₂²	1	1	yes	characteristic
36	C₃₇×#407	C₂²	1	1	yes	characteristic
37	C₃₇×#405	C₂²	1	1	yes	characteristic
38	C₃₇×#343	C₂²	1	2	yes	—
39	C₃₇×#343	C₂²	1	2	yes	—
40	C₃₇×#341	C₂²	1	2	yes	—
41	C₃₇×#341	C₂²	1	1	yes	characteristic
42	C₃₇×#341	C₂²	1	1	yes	characteristic
43	C₂×#41×C₃₇	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₃₇	—	2	2	no	—
45	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
46	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
47	AGL(1,ℤ/8)×C₃₇	—	2	4	no	—
48	AGL(1,ℤ/8)×C₃₇	—	4	2	no	—
49	C₂×SD₁₆×C₃₇	—	2	2	no	—
50	C₂×D₈×C₃₇	—	2	2	no	—
51	C₂×D₈×C₃₇	—	2	2	no	—
52	C₂×D₈×C₃₇	—	4	2	no	—
53	#131×C₃₇	—	4	2	no	—
54	C₂×M₁₆×C₃₇	—	2	2	no	—
55	C₂×M₁₆×C₃₇	—	2	1	no	—
56	C₂×M₁₆×C₃₇	—	2	4	no	—
57	C₂×M₁₆×C₃₇	—	4	2	no	—
58	C₂×M₁₆×C₃₇	—	4	2	no	—
59	C₂×M₁₆×C₃₇	D₄	1	2	yes	—
60	C₂×M₁₆×C₃₇	D₄	1	2	yes	—
61	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
62	C₂×M₁₆×C₃₇	C₂³	1	1	yes	characteristic
63	C₂×M₁₆×C₃₇	C₂³	1	1	yes	characteristic
64	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
65	C₂²×C₈×C₃₇	—	2	2	no	—
66	C₂²×C₈×C₃₇	—	2	1	no	—
67	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
69	#123×C₃₇	—	2	1	no	—
70	C₂²⋊Q₈×C₃₇	D₄	1	2	yes	—
71	#121×C₃₇	—	2	2	no	—
72	#121×C₃₇	—	2	2	no	—
73	#121×C₃₇	—	2	2	no	—
74	#121×C₃₇	—	2	2	no	—
75	#121×C₃₇	D₄	1	2	yes	—
76	#120×C₃₇	—	2	1	no	—
77	C₄×D₄×C₃₇	—	2	2	no	—
78	#117×C₃₇	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
80	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
81	#107×C₃₇	—	2	2	no	—
82	#106×C₃₇	—	2	2	no	—
83	#106×C₃₇	—	2	2	no	—
84	C₄⋊C₈×C₃₇	—	2	2	no	—
85	#103×C₃₇	—	2	2	no	—
86	#102×C₃₇	—	2	2	no	—
87	#102×C₃₇	—	2	2	no	—
88	#102×C₃₇	—	2	2	no	—
89	#102×C₃₇	—	2	2	no	—
90	#102×C₃₇	—	2	2	no	—
91	#100×C₃₇	—	2	4	no	—
92	#100×C₃₇	—	4	2	no	—
93	C₂²⋊C₈×C₃₇	—	2	2	no	—
94	C₂²⋊C₈×C₃₇	—	2	2	no	—
95	#97×C₃₇	—	2	1	no	—
96	C₄×C₈×C₃₇	—	2	1	no	—
97	C₂⁴×C₃₇	—	2	2	no	—
98	C₂⁴×C₃₇	#41	1	1	yes	characteristic
99	#41×C₃₇	—	2	2	no	—
100	#41×C₃₇	—	2	2	no	—
101	C₂×Q₈×C₃₇	C₂×D₄	1	1	yes	characteristic
102	C₂×D₄×C₃₇	—	2	1	no	—
103	C₂×D₄×C₃₇	—	2	2	no	—
104	C₂×D₄×C₃₇	—	2	2	no	—
105	C₂×D₄×C₃₇	—	2	2	no	—
106	C₂×D₄×C₃₇	—	2	2	no	—
107	C₂×D₄×C₃₇	—	2	2	no	—
108	C₂×D₄×C₃₇	—	2	2	no	—
109	C₂×D₄×C₃₇	—	2	2	no	—
110	C₂×D₄×C₃₇	—	4	2	no	—
111	C₂×D₄×C₃₇	—	4	2	no	—
112	C₂×D₄×C₃₇	—	8	4	no	—
113	C₂×D₄×C₃₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₃₇	—	2	2	no	—
115	C₂²×C₄×C₃₇	—	2	2	no	—
116	C₂²×C₄×C₃₇	—	2	1	no	—
117	C₂²×C₄×C₃₇	—	2	2	no	—
118	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₃₇	#41	1	1	yes	characteristic
121	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
122	SD₁₆×C₃₇	—	4	4	no	—
123	D₈×C₃₇	—	4	4	no	—
124	D₈×C₃₇	—	4	4	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	M₁₆×C₃₇	—	4	4	no	—
133	M₁₆×C₃₇	—	4	2	no	—
134	M₁₆×C₃₇	#41	1	4	yes	—
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	—	2	1	no	—
139	C₂×C₈×C₃₇	—	2	1	no	—
140	C₂×C₈×C₃₇	—	2	2	no	—
141	C₂×C₈×C₃₇	—	4	4	no	—
142	C₂×C₈×C₃₇	—	4	2	no	—
143	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
146	C₄⋊C₄×C₃₇	—	2	2	no	—
147	C₄⋊C₄×C₃₇	—	2	2	no	—
148	C₄⋊C₄×C₃₇	—	2	2	no	—
149	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
150	C₂²⋊C₄×C₃₇	—	2	2	no	—
151	C₂²⋊C₄×C₃₇	—	2	1	no	—
152	C₂²⋊C₄×C₃₇	—	2	2	no	—
153	C₂²⋊C₄×C₃₇	—	4	2	no	—
154	C₂²⋊C₄×C₃₇	—	4	2	no	—
155	C₄²×C₃₇	—	2	1	no	—
156	C₂³×C₃₇	—	2	2	no	—
157	C₂³×C₃₇	—	2	1	no	—
158	C₂³×C₃₇	—	4	2	no	—
159	C₂³×C₃₇	—	4	2	no	—
160	C₂³×C₃₇	—	4	2	no	—
161	C₂³×C₃₇	—	4	2	no	—
162	C₂³×C₃₇	—	8	2	no	—
163	C₂³×C₃₇	—	8	2	no	—
164	C₂³×C₃₇	#121	1	2	yes	—
165	C₂³×C₃₇	C₂×#41	1	1	yes	characteristic
166	Q₈×C₃₇	—	2	2	no	—
167	D₄×C₃₇	—	2	2	no	—
168	D₄×C₃₇	—	4	2	no	—
169	D₄×C₃₇	—	4	2	no	—
170	D₄×C₃₇	—	4	2	no	—
171	D₄×C₃₇	—	4	2	no	—
172	D₄×C₃₇	—	4	2	no	—
173	D₄×C₃₇	—	8	2	no	—
174	D₄×C₃₇	—	8	4	no	—
175	D₄×C₃₇	—	8	4	no	—
176	C₂×C₄×C₃₇	—	2	2	no	—
177	C₂×C₄×C₃₇	—	2	2	no	—
178	C₂×C₄×C₃₇	—	2	2	no	—
179	C₂×C₄×C₃₇	—	2	2	no	—
180	C₂×C₄×C₃₇	—	2	2	no	—
181	C₂×C₄×C₃₇	—	2	2	no	—
182	C₂×C₄×C₃₇	—	2	1	no	—
183	C₂×C₄×C₃₇	—	4	1	no	—
184	C₂×C₄×C₃₇	—	4	1	no	—
185	C₂×C₄×C₃₇	—	4	2	no	—
186	C₂×C₄×C₃₇	—	8	2	no	—
187	C₂×C₄×C₃₇	#121	1	2	yes	—
188	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
191	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
192	C₈×C₃₇	—	2	1	no	—
193	C₈×C₃₇	—	2	1	no	—
194	C₈×C₃₇	—	2	2	no	—
195	C₈×C₃₇	—	2	4	no	—
196	C₈×C₃₇	—	4	1	no	—
197	C₈×C₃₇	—	4	1	no	—
198	C₈×C₃₇	—	4	2	no	—
199	#28595	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂²×C₃₇	—	2	2	no	—
201	C₂²×C₃₇	—	2	2	no	—
202	C₂²×C₃₇	—	2	2	no	—
203	C₂²×C₃₇	—	2	2	no	—
204	C₂²×C₃₇	—	4	1	no	—
205	C₂²×C₃₇	—	4	2	no	—
206	C₂²×C₃₇	—	8	2	no	—
207	C₂²×C₃₇	—	8	2	no	—
208	C₂²×C₃₇	—	8	2	no	—
209	C₂²×C₃₇	—	8	2	no	—
210	C₂²×C₃₇	—	16	2	no	—
211	C₂²×C₃₇	—	16	2	no	—
212	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
213	C₂²×C₃₇	#553	1	2	yes	—
214	C₄×C₃₇	—	2	2	no	—
215	C₄×C₃₇	—	4	1	no	—
216	C₄×C₃₇	—	4	2	no	—
217	C₄×C₃₇	—	8	2	no	—
218	C₄×C₃₇	#532	1	1	yes	characteristic
219	C₄×C₃₇	#534	1	1	yes	characteristic
220	C₄×C₃₇	#546	1	2	yes	—
221	#3055	C₂×C₃₇	1	2	yes	complemented
222	C₂×#469	C₂×C₃₇	1	1	yes	characteristic, complemented
223	#2930	C₂×C₃₇	1	1	yes	characteristic, complemented
224	#2090	C₂×C₃₇	1	1	yes	characteristic, complemented
225	#2079	C₂×C₃₇	1	1	yes	characteristic, complemented
226	#2045	C₂×C₃₇	1	1	yes	characteristic, complemented
227	#2018	C₂×C₃₇	1	1	yes	characteristic, complemented
228	#1931	C₂×C₃₇	1	2	yes	complemented
229	#1907	C₂×C₃₇	1	2	yes	complemented
230	#1900	C₂×C₃₇	1	2	yes	complemented
231	#1738	C₂×C₃₇	1	1	yes	characteristic, complemented
232	C₂×C₃₇	—	2	2	no	—
233	C₂×C₃₇	—	4	2	no	—
234	C₂×C₃₇	—	8	1	no	—
235	C₂×C₃₇	—	16	2	no	—
236	C₂×C₃₇	#2543	1	1	yes	characteristic
237	C₂×C₃₇	#3068	1	2	yes	—
238	C₂×AGL(1,ℤ/8)	C₂²×C₃₇	1	2	yes	—
239	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
240	C₂×#131	C₂²×C₃₇	1	1	yes	characteristic
241	C₂²×M₁₆	C₂²×C₃₇	1	2	yes	—
242	C₂²×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
243	#525	C₂²×C₃₇	1	1	yes	characteristic
244	C₂×#121	C₂²×C₃₇	1	2	yes	—
245	#469	—	2	2	no	—
246	#469	—	2	2	no	—
247	#469	—	2	2	no	—
248	#468	—	2	2	no	—
249	#466	—	2	2	no	—
250	#465	—	2	2	no	—
251	#436	—	2	2	no	—
252	#435	—	2	2	no	—
253	#428	C₂²×C₃₇	1	2	yes	—
254	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
255	#424	C₂²×C₃₇	1	1	yes	characteristic
256	#418	C₂²×C₃₇	1	2	yes	—
257	#417	C₂²×C₃₇	1	2	yes	—
258	C₂×#102	C₂²×C₃₇	1	2	yes	—
259	C₂×#100	C₂²×C₃₇	1	2	yes	—
260	C₂×#100	C₂²×C₃₇	1	2	yes	—
261	#408	C₂²×C₃₇	1	1	yes	characteristic
262	#407	C₂²×C₃₇	1	1	yes	characteristic
263	#405	C₂²×C₃₇	1	1	yes	characteristic
264	#343	C₂²×C₃₇	1	2	yes	—
265	#343	C₂²×C₃₇	1	2	yes	—
266	#341	C₂²×C₃₇	1	1	yes	characteristic
267	#341	C₂²×C₃₇	1	1	yes	characteristic
268	#341	C₂²×C₃₇	1	2	yes	—
269	C₃₇	#28595	1	1	yes	characteristic, direct product factor, Sylow
270	C₂×#41	C₂³×C₃₇	1	1	yes	characteristic
271	C₂²×D₄	—	2	2	no	—
272	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
273	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
274	AGL(1,ℤ/8)	—	2	4	no	—
275	AGL(1,ℤ/8)	—	4	2	no	—
276	C₂×SD₁₆	—	2	2	no	—
277	C₂×D₈	—	2	2	no	—
278	C₂×D₈	—	2	2	no	—
279	C₂×D₈	—	4	2	no	—
280	#131	—	4	2	no	—
281	C₂×M₁₆	—	2	2	no	—
282	C₂×M₁₆	—	2	1	no	—
283	C₂×M₁₆	—	2	4	no	—
284	C₂×M₁₆	—	4	2	no	—
285	C₂×M₁₆	—	4	2	no	—
286	C₂×M₁₆	D₄×C₃₇	1	2	yes	—
287	C₂×M₁₆	D₄×C₃₇	1	2	yes	—
288	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
289	C₂×M₁₆	C₂³×C₃₇	1	1	yes	characteristic
290	C₂×M₁₆	C₂³×C₃₇	1	1	yes	characteristic
291	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
292	C₂²×C₈	—	2	2	no	—
293	C₂²×C₈	—	2	1	no	—
294	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
295	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
296	#123	—	2	1	no	—
297	C₂²⋊Q₈	D₄×C₃₇	1	2	yes	—
298	#121	—	2	2	no	—
299	#121	—	2	2	no	—
300	#121	—	2	2	no	—
301	#121	—	2	2	no	—
302	#121	D₄×C₃₇	1	2	yes	—
303	#120	—	2	1	no	—
304	C₄×D₄	—	2	2	no	—
305	#117	C₂³×C₃₇	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	#107	—	2	2	no	—
309	#106	—	2	2	no	—
310	#106	—	2	2	no	—
311	C₄⋊C₈	—	2	2	no	—
312	#103	—	2	2	no	—
313	#102	—	2	2	no	—
314	#102	—	2	2	no	—
315	#102	—	2	2	no	—
316	#102	—	2	2	no	—
317	#102	—	2	2	no	—
318	#100	—	2	4	no	—
319	#100	—	4	2	no	—
320	C₂²⋊C₈	—	2	2	no	—
321	C₂²⋊C₈	—	2	2	no	—
322	#97	—	2	1	no	—
323	C₄×C₈	—	2	1	no	—
324	C₂⁴	—	2	2	no	—
325	C₂⁴	#41×C₃₇	1	1	yes	characteristic
326	#41	—	2	2	no	—
327	#41	—	2	2	no	—
328	C₂×Q₈	C₂×D₄×C₃₇	1	1	yes	characteristic
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	8	4	no	—
340	C₂×D₄	C₂×D₄×C₃₇	1	1	yes	characteristic
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
346	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
347	C₂²×C₄	#41×C₃₇	1	1	yes	characteristic
348	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
349	SD₁₆	—	4	4	no	—
350	D₈	—	4	4	no	—
351	D₈	—	4	4	no	—
352	M₁₆	—	2	2	no	—
353	M₁₆	—	2	2	no	—
354	M₁₆	—	2	2	no	—
355	M₁₆	—	2	2	no	—
356	M₁₆	—	2	2	no	—
357	M₁₆	—	4	2	no	—
358	M₁₆	—	4	2	no	—
359	M₁₆	—	4	4	no	—
360	M₁₆	—	4	2	no	—
361	M₁₆	#41×C₃₇	1	4	yes	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	4	4	no	—
369	C₂×C₈	—	4	2	no	—
370	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
371	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
372	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	1	no	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	4	2	no	—
381	C₂²⋊C₄	—	4	2	no	—
382	C₄²	—	2	1	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	4	2	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	8	2	no	—
390	C₂³	—	8	2	no	—
391	C₂³	#121×C₃₇	1	2	yes	—
392	C₂³	C₂×#41×C₃₇	1	1	yes	characteristic
393	Q₈	—	2	2	no	—
394	D₄	—	2	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	8	2	no	—
401	D₄	—	8	4	no	—
402	D₄	—	8	4	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	8	2	no	—
414	C₂×C₄	#121×C₃₇	1	2	yes	—
415	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
417	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
418	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	2	2	no	—
422	C₈	—	2	4	no	—
423	C₈	—	4	1	no	—
424	C₈	—	4	1	no	—
425	C₈	—	4	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	8	2	no	—
433	C₂²	—	8	2	no	—
434	C₂²	—	8	2	no	—
435	C₂²	—	8	2	no	—
436	C₂²	—	16	2	no	—
437	C₂²	—	16	2	no	—
438	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
439	C₂²	C₃₇×#553	1	2	yes	—
440	C₄	—	2	2	no	—
441	C₄	—	4	1	no	—
442	C₄	—	4	2	no	—
443	C₄	—	8	2	no	—
444	C₄	C₃₇×#532	1	1	yes	characteristic
445	C₄	C₃₇×#534	1	1	yes	characteristic
446	C₄	C₃₇×#546	1	2	yes	—
447	C₂	—	2	2	no	—
448	C₂	—	4	2	no	—
449	C₂	—	8	1	no	—
450	C₂	—	16	2	no	—
451	C₂	C₃₇×#2543	1	1	yes	characteristic
452	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. C₃₇×#3055	C₂	semidirect
2. C₂×C₃₇×#469	C₂	semidirect
3. C₃₇×#2930	C₂	semidirect
4. C₃₇×#2090	C₂	semidirect
5. C₃₇×#2079	C₂	semidirect
6. C₃₇×#2045	C₂	semidirect
7. C₃₇×#2018	C₂	semidirect
8. C₃₇×#1931	C₂	semidirect
9. C₃₇×#1907	C₂	semidirect
10. C₃₇×#1900	C₂	semidirect
11. C₃₇×#1738	C₂	semidirect
199. #28595	C₃₇	direct (N × H)
221. #3055	C₂×C₃₇	semidirect
222. C₂×#469	C₂×C₃₇	semidirect
223. #2930	C₂×C₃₇	semidirect
224. #2090	C₂×C₃₇	semidirect
225. #2079	C₂×C₃₇	semidirect
226. #2045	C₂×C₃₇	semidirect
227. #2018	C₂×C₃₇	semidirect
228. #1931	C₂×C₃₇	semidirect
229. #1907	C₂×C₃₇	semidirect
230. #1900	C₂×C₃₇	semidirect
231. #1738	C₂×C₃₇	semidirect
269. C₃₇	#28595	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×#3055	2
C₂×C₃₇×#469	2
C₃₇×#2930	2
C₃₇×#2090	2
C₃₇×#2079	2
C₃₇×#2045	2
C₃₇×#2018	2
C₃₇×#1931	2
C₃₇×#1907	2
C₃₇×#1900	2
C₃₇×#1738	2
#28595	37

Subgroups — C37×#28595 #22649848

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28595 #22649848