Subgroups — C₃₇×#28592 #22649845

Order 9472.

846 conjugacy classes of subgroups.

The subgroup lattice has 538 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×#466	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#2929	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#2089	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2078	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	C₂×C₃₇×#341	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	C₂³×C₈×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×#468	—	2	2	no	—
21	C₃₇×#466	—	2	1	no	—
22	C₃₇×#466	—	2	1	no	—
23	C₃₇×#466	—	2	1	no	—
24	C₃₇×#466	—	2	1	no	—
25	C₃₇×#466	—	2	2	no	—
26	C₃₇×#465	—	2	2	no	—
27	C₃₇×#435	—	2	1	no	—
28	C₃₇×#435	—	2	1	no	—
29	C₈×D₄×C₃₇	—	2	1	no	—
30	C₈×D₄×C₃₇	—	2	1	no	—
31	C₃₇×#428	C₂²	1	2	yes	—
32	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
33	C₃₇×#424	C₂²	1	1	yes	characteristic
34	C₃₇×#418	C₂²	1	2	yes	—
35	C₃₇×#417	C₂²	1	2	yes	—
36	C₂×#102×C₃₇	C₂²	1	2	yes	—
37	C₂×#100×C₃₇	C₂²	1	2	yes	—
38	C₂×#100×C₃₇	C₂²	1	2	yes	—
39	C₃₇×#408	C₂²	1	1	yes	characteristic
40	C₃₇×#407	C₂²	1	1	yes	characteristic
41	C₃₇×#405	C₂²	1	1	yes	characteristic
42	C₃₇×#343	C₂²	1	2	yes	—
43	C₃₇×#343	C₂²	1	2	yes	—
44	C₃₇×#341	C₂²	1	2	yes	—
45	C₃₇×#341	C₂²	1	1	yes	characteristic
46	C₃₇×#341	C₂²	1	1	yes	characteristic
47	C₂×#41×C₃₇	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₃₇	—	2	2	no	—
49	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
50	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
51	AGL(1,ℤ/8)×C₃₇	—	2	4	no	—
52	AGL(1,ℤ/8)×C₃₇	—	4	2	no	—
53	C₂×SD₁₆×C₃₇	—	2	2	no	—
54	C₂×D₈×C₃₇	—	2	2	no	—
55	C₂×D₈×C₃₇	—	2	1	no	—
56	C₂×D₈×C₃₇	—	2	1	no	—
57	C₂×D₈×C₃₇	—	4	2	no	—
58	#131×C₃₇	—	4	2	no	—
59	C₂×M₁₆×C₃₇	—	2	2	no	—
60	C₂×M₁₆×C₃₇	—	2	1	no	—
61	C₂×M₁₆×C₃₇	—	2	4	no	—
62	C₂×M₁₆×C₃₇	—	4	2	no	—
63	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
64	C₂×M₁₆×C₃₇	C₂³	1	1	yes	characteristic
65	C₂×M₁₆×C₃₇	C₂³	1	1	yes	characteristic
66	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
67	C₂²×C₈×C₃₇	—	2	2	no	—
68	C₂²×C₈×C₃₇	—	2	1	no	—
69	C₂²×C₈×C₃₇	—	4	2	no	—
70	C₂²×C₈×C₃₇	D₄	1	1	yes	characteristic
71	C₂²×C₈×C₃₇	D₄	1	1	yes	characteristic
72	C₂²×C₈×C₃₇	D₄	1	1	yes	characteristic
73	C₂²×C₈×C₃₇	D₄	1	1	yes	characteristic
74	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
76	#123×C₃₇	—	2	1	no	—
77	C₂²⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
78	C₂²⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
79	#121×C₃₇	—	2	2	no	—
80	#121×C₃₇	—	2	2	no	—
81	#121×C₃₇	—	2	2	no	—
82	#121×C₃₇	—	2	2	no	—
83	#121×C₃₇	D₄	1	1	yes	characteristic
84	#121×C₃₇	D₄	1	1	yes	characteristic
85	#120×C₃₇	—	2	1	no	—
86	C₄×D₄×C₃₇	—	2	1	no	—
87	C₄×D₄×C₃₇	—	2	1	no	—
88	#117×C₃₇	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
90	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
91	#107×C₃₇	—	2	1	no	—
92	#107×C₃₇	—	2	1	no	—
93	#107×C₃₇	—	2	2	no	—
94	#106×C₃₇	—	2	2	no	—
95	C₄⋊C₈×C₃₇	—	2	1	no	—
96	C₄⋊C₈×C₃₇	—	2	1	no	—
97	#103×C₃₇	—	2	2	no	—
98	#102×C₃₇	—	2	2	no	—
99	#102×C₃₇	—	2	2	no	—
100	#102×C₃₇	—	2	2	no	—
101	#102×C₃₇	—	2	2	no	—
102	#102×C₃₇	—	2	2	no	—
103	#100×C₃₇	—	2	4	no	—
104	#100×C₃₇	—	4	2	no	—
105	C₂²⋊C₈×C₃₇	—	2	1	no	—
106	C₂²⋊C₈×C₃₇	—	2	1	no	—
107	C₂²⋊C₈×C₃₇	—	2	1	no	—
108	C₂²⋊C₈×C₃₇	—	2	1	no	—
109	#97×C₃₇	—	2	1	no	—
110	C₄×C₈×C₃₇	—	2	1	no	—
111	C₂⁴×C₃₇	—	2	2	no	—
112	C₂⁴×C₃₇	#41	1	1	yes	characteristic
113	#41×C₃₇	—	2	2	no	—
114	#41×C₃₇	—	2	2	no	—
115	C₂×Q₈×C₃₇	C₂×D₄	1	1	yes	characteristic
116	C₂×D₄×C₃₇	—	2	1	no	—
117	C₂×D₄×C₃₇	—	2	1	no	—
118	C₂×D₄×C₃₇	—	2	1	no	—
119	C₂×D₄×C₃₇	—	2	2	no	—
120	C₂×D₄×C₃₇	—	2	2	no	—
121	C₂×D₄×C₃₇	—	2	2	no	—
122	C₂×D₄×C₃₇	—	2	2	no	—
123	C₂×D₄×C₃₇	—	2	2	no	—
124	C₂×D₄×C₃₇	—	2	2	no	—
125	C₂×D₄×C₃₇	—	4	2	no	—
126	C₂×D₄×C₃₇	—	4	2	no	—
127	C₂×D₄×C₃₇	—	8	4	no	—
128	C₂×D₄×C₃₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₃₇	—	2	2	no	—
130	C₂²×C₄×C₃₇	—	2	2	no	—
131	C₂²×C₄×C₃₇	—	2	1	no	—
132	C₂²×C₄×C₃₇	—	2	2	no	—
133	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₃₇	#41	1	1	yes	characteristic
138	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
139	SD₁₆×C₃₇	—	4	4	no	—
140	D₈×C₃₇	—	4	4	no	—
141	D₈×C₃₇	—	4	2	no	—
142	D₈×C₃₇	—	4	2	no	—
143	M₁₆×C₃₇	—	2	2	no	—
144	M₁₆×C₃₇	—	2	2	no	—
145	M₁₆×C₃₇	—	2	2	no	—
146	M₁₆×C₃₇	—	2	2	no	—
147	M₁₆×C₃₇	—	2	2	no	—
148	M₁₆×C₃₇	—	4	4	no	—
149	M₁₆×C₃₇	—	4	2	no	—
150	M₁₆×C₃₇	#41	1	4	yes	—
151	C₂×C₈×C₃₇	—	2	2	no	—
152	C₂×C₈×C₃₇	—	2	2	no	—
153	C₂×C₈×C₃₇	—	2	2	no	—
154	C₂×C₈×C₃₇	—	2	1	no	—
155	C₂×C₈×C₃₇	—	2	1	no	—
156	C₂×C₈×C₃₇	—	2	2	no	—
157	C₂×C₈×C₃₇	—	4	1	no	—
158	C₂×C₈×C₃₇	—	4	1	no	—
159	C₂×C₈×C₃₇	—	4	1	no	—
160	C₂×C₈×C₃₇	—	4	1	no	—
161	C₂×C₈×C₃₇	—	4	4	no	—
162	C₂×C₈×C₃₇	—	4	2	no	—
163	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
164	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
165	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
166	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
167	C₄⋊C₄×C₃₇	—	2	1	no	—
168	C₄⋊C₄×C₃₇	—	2	1	no	—
169	C₄⋊C₄×C₃₇	—	2	2	no	—
170	C₄⋊C₄×C₃₇	—	2	2	no	—
171	C₄⋊C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
172	C₄⋊C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
173	C₂²⋊C₄×C₃₇	—	2	1	no	—
174	C₂²⋊C₄×C₃₇	—	2	1	no	—
175	C₂²⋊C₄×C₃₇	—	2	1	no	—
176	C₂²⋊C₄×C₃₇	—	2	1	no	—
177	C₂²⋊C₄×C₃₇	—	2	1	no	—
178	C₂²⋊C₄×C₃₇	—	4	2	no	—
179	C₂²⋊C₄×C₃₇	—	4	2	no	—
180	C₄²×C₃₇	—	2	1	no	—
181	C₂³×C₃₇	—	2	2	no	—
182	C₂³×C₃₇	—	2	2	no	—
183	C₂³×C₃₇	—	2	1	no	—
184	C₂³×C₃₇	—	4	1	no	—
185	C₂³×C₃₇	—	4	2	no	—
186	C₂³×C₃₇	—	4	2	no	—
187	C₂³×C₃₇	—	4	2	no	—
188	C₂³×C₃₇	—	8	2	no	—
189	C₂³×C₃₇	—	8	2	no	—
190	C₂³×C₃₇	#121	1	1	yes	characteristic
191	C₂³×C₃₇	#121	1	1	yes	characteristic
192	C₂³×C₃₇	C₂×#41	1	1	yes	characteristic
193	Q₈×C₃₇	—	2	2	no	—
194	D₄×C₃₇	—	2	2	no	—
195	D₄×C₃₇	—	4	2	no	—
196	D₄×C₃₇	—	4	2	no	—
197	D₄×C₃₇	—	4	2	no	—
198	D₄×C₃₇	—	4	2	no	—
199	D₄×C₃₇	—	4	2	no	—
200	D₄×C₃₇	—	4	2	no	—
201	D₄×C₃₇	—	4	2	no	—
202	D₄×C₃₇	—	8	4	no	—
203	D₄×C₃₇	—	8	4	no	—
204	C₂×C₄×C₃₇	—	2	2	no	—
205	C₂×C₄×C₃₇	—	2	1	no	—
206	C₂×C₄×C₃₇	—	2	1	no	—
207	C₂×C₄×C₃₇	—	2	1	no	—
208	C₂×C₄×C₃₇	—	2	1	no	—
209	C₂×C₄×C₃₇	—	2	2	no	—
210	C₂×C₄×C₃₇	—	2	2	no	—
211	C₂×C₄×C₃₇	—	2	1	no	—
212	C₂×C₄×C₃₇	—	2	1	no	—
213	C₂×C₄×C₃₇	—	2	1	no	—
214	C₂×C₄×C₃₇	—	4	1	no	—
215	C₂×C₄×C₃₇	—	4	1	no	—
216	C₂×C₄×C₃₇	—	4	2	no	—
217	C₂×C₄×C₃₇	—	8	2	no	—
218	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
219	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
220	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
223	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
224	C₈×C₃₇	—	2	1	no	—
225	C₈×C₃₇	—	2	1	no	—
226	C₈×C₃₇	—	2	1	no	—
227	C₈×C₃₇	—	2	1	no	—
228	C₈×C₃₇	—	2	4	no	—
229	C₈×C₃₇	—	4	1	no	—
230	C₈×C₃₇	—	4	1	no	—
231	C₈×C₃₇	—	4	2	no	—
232	#28592	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
233	C₂²×C₃₇	—	2	1	no	—
234	C₂²×C₃₇	—	2	1	no	—
235	C₂²×C₃₇	—	2	1	no	—
236	C₂²×C₃₇	—	2	1	no	—
237	C₂²×C₃₇	—	2	1	no	—
238	C₂²×C₃₇	—	2	1	no	—
239	C₂²×C₃₇	—	2	1	no	—
240	C₂²×C₃₇	—	4	4	no	—
241	C₂²×C₃₇	—	4	1	no	—
242	C₂²×C₃₇	—	4	1	no	—
243	C₂²×C₃₇	—	4	1	no	—
244	C₂²×C₃₇	—	8	2	no	—
245	C₂²×C₃₇	—	8	2	no	—
246	C₂²×C₃₇	—	8	2	no	—
247	C₂²×C₃₇	—	16	2	no	—
248	C₂²×C₃₇	—	16	2	no	—
249	C₂²×C₃₇	#472	1	2	yes	—
250	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
251	C₂²×C₃₇	#553	1	2	yes	—
252	C₄×C₃₇	—	2	1	no	—
253	C₄×C₃₇	—	2	1	no	—
254	C₄×C₃₇	—	4	1	no	—
255	C₄×C₃₇	—	4	1	no	—
256	C₄×C₃₇	—	4	1	no	—
257	C₄×C₃₇	—	8	2	no	—
258	C₄×C₃₇	#532	1	1	yes	characteristic
259	C₄×C₃₇	#534	1	1	yes	characteristic
260	C₄×C₃₇	#546	1	2	yes	—
261	#3055	C₂×C₃₇	1	2	yes	complemented
262	C₂×#466	C₂×C₃₇	1	1	yes	characteristic, complemented
263	#2929	C₂×C₃₇	1	1	yes	characteristic, complemented
264	#2089	C₂×C₃₇	1	1	yes	characteristic, complemented
265	#2078	C₂×C₃₇	1	1	yes	characteristic, complemented
266	#2045	C₂×C₃₇	1	1	yes	characteristic, complemented
267	#2018	C₂×C₃₇	1	1	yes	characteristic, complemented
268	#1931	C₂×C₃₇	1	2	yes	complemented
269	#1907	C₂×C₃₇	1	2	yes	complemented
270	#1900	C₂×C₃₇	1	2	yes	complemented
271	C₂×#341	C₂×C₃₇	1	1	yes	characteristic, complemented
272	C₂×C₃₇	—	2	2	no	—
273	C₂×C₃₇	—	2	2	no	—
274	C₂×C₃₇	—	4	1	no	—
275	C₂×C₃₇	—	8	1	no	—
276	C₂×C₃₇	—	16	2	no	—
277	C₂×C₃₇	#2543	1	1	yes	characteristic
278	C₂×C₃₇	C₂×#472	1	1	yes	characteristic
279	C₂×C₃₇	#3067	1	1	yes	characteristic
280	C₂×AGL(1,ℤ/8)	C₂²×C₃₇	1	2	yes	—
281	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
282	C₂×#131	C₂²×C₃₇	1	1	yes	characteristic
283	C₂²×M₁₆	C₂²×C₃₇	1	2	yes	—
284	C₂³×C₈	C₂²×C₃₇	1	1	yes	characteristic
285	#525	C₂²×C₃₇	1	1	yes	characteristic
286	C₂×#121	C₂²×C₃₇	1	2	yes	—
287	#469	—	2	2	no	—
288	#468	—	2	2	no	—
289	#466	—	2	1	no	—
290	#466	—	2	1	no	—
291	#466	—	2	1	no	—
292	#466	—	2	1	no	—
293	#466	—	2	2	no	—
294	#465	—	2	2	no	—
295	#435	—	2	1	no	—
296	#435	—	2	1	no	—
297	C₈×D₄	—	2	1	no	—
298	C₈×D₄	—	2	1	no	—
299	#428	C₂²×C₃₇	1	2	yes	—
300	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
301	#424	C₂²×C₃₇	1	1	yes	characteristic
302	#418	C₂²×C₃₇	1	2	yes	—
303	#417	C₂²×C₃₇	1	2	yes	—
304	C₂×#102	C₂²×C₃₇	1	2	yes	—
305	C₂×#100	C₂²×C₃₇	1	2	yes	—
306	C₂×#100	C₂²×C₃₇	1	2	yes	—
307	#408	C₂²×C₃₇	1	1	yes	characteristic
308	#407	C₂²×C₃₇	1	1	yes	characteristic
309	#405	C₂²×C₃₇	1	1	yes	characteristic
310	#343	C₂²×C₃₇	1	2	yes	—
311	#343	C₂²×C₃₇	1	2	yes	—
312	#341	C₂²×C₃₇	1	1	yes	characteristic
313	#341	C₂²×C₃₇	1	1	yes	characteristic
314	#341	C₂²×C₃₇	1	2	yes	—
315	C₃₇	#28592	1	1	yes	characteristic, direct product factor, Sylow
316	C₂×#41	C₂³×C₃₇	1	1	yes	characteristic
317	C₂²×D₄	—	2	2	no	—
318	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
319	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
320	AGL(1,ℤ/8)	—	2	4	no	—
321	AGL(1,ℤ/8)	—	4	2	no	—
322	C₂×SD₁₆	—	2	2	no	—
323	C₂×D₈	—	2	2	no	—
324	C₂×D₈	—	2	1	no	—
325	C₂×D₈	—	2	1	no	—
326	C₂×D₈	—	4	2	no	—
327	#131	—	4	2	no	—
328	C₂×M₁₆	—	2	2	no	—
329	C₂×M₁₆	—	2	1	no	—
330	C₂×M₁₆	—	2	4	no	—
331	C₂×M₁₆	—	4	2	no	—
332	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
333	C₂×M₁₆	C₂³×C₃₇	1	1	yes	characteristic
334	C₂×M₁₆	C₂³×C₃₇	1	1	yes	characteristic
335	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
336	C₂²×C₈	—	2	2	no	—
337	C₂²×C₈	—	2	1	no	—
338	C₂²×C₈	—	4	2	no	—
339	C₂²×C₈	D₄×C₃₇	1	1	yes	characteristic
340	C₂²×C₈	D₄×C₃₇	1	1	yes	characteristic
341	C₂²×C₈	D₄×C₃₇	1	1	yes	characteristic
342	C₂²×C₈	D₄×C₃₇	1	1	yes	characteristic
343	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
344	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
345	#123	—	2	1	no	—
346	C₂²⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
347	C₂²⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
348	#121	—	2	2	no	—
349	#121	—	2	2	no	—
350	#121	—	2	2	no	—
351	#121	—	2	2	no	—
352	#121	D₄×C₃₇	1	1	yes	characteristic
353	#121	D₄×C₃₇	1	1	yes	characteristic
354	#120	—	2	1	no	—
355	C₄×D₄	—	2	1	no	—
356	C₄×D₄	—	2	1	no	—
357	#117	C₂³×C₃₇	1	1	yes	characteristic
358	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
359	C₂×C₂²⋊C₄	—	2	2	no	—
360	#107	—	2	1	no	—
361	#107	—	2	1	no	—
362	#107	—	2	2	no	—
363	#106	—	2	2	no	—
364	C₄⋊C₈	—	2	1	no	—
365	C₄⋊C₈	—	2	1	no	—
366	#103	—	2	2	no	—
367	#102	—	2	2	no	—
368	#102	—	2	2	no	—
369	#102	—	2	2	no	—
370	#102	—	2	2	no	—
371	#102	—	2	2	no	—
372	#100	—	2	4	no	—
373	#100	—	4	2	no	—
374	C₂²⋊C₈	—	2	1	no	—
375	C₂²⋊C₈	—	2	1	no	—
376	C₂²⋊C₈	—	2	1	no	—
377	C₂²⋊C₈	—	2	1	no	—
378	#97	—	2	1	no	—
379	C₄×C₈	—	2	1	no	—
380	C₂⁴	—	2	2	no	—
381	C₂⁴	#41×C₃₇	1	1	yes	characteristic
382	#41	—	2	2	no	—
383	#41	—	2	2	no	—
384	C₂×Q₈	C₂×D₄×C₃₇	1	1	yes	characteristic
385	C₂×D₄	—	2	1	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	4	2	no	—
395	C₂×D₄	—	4	2	no	—
396	C₂×D₄	—	8	4	no	—
397	C₂×D₄	C₂×D₄×C₃₇	1	1	yes	characteristic
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
405	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
406	C₂²×C₄	#41×C₃₇	1	1	yes	characteristic
407	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
408	SD₁₆	—	4	4	no	—
409	D₈	—	4	4	no	—
410	D₈	—	4	2	no	—
411	D₈	—	4	2	no	—
412	M₁₆	—	2	2	no	—
413	M₁₆	—	2	2	no	—
414	M₁₆	—	2	2	no	—
415	M₁₆	—	2	2	no	—
416	M₁₆	—	2	2	no	—
417	M₁₆	—	4	4	no	—
418	M₁₆	—	4	2	no	—
419	M₁₆	#41×C₃₇	1	4	yes	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	4	1	no	—
427	C₂×C₈	—	4	1	no	—
428	C₂×C₈	—	4	1	no	—
429	C₂×C₈	—	4	1	no	—
430	C₂×C₈	—	4	4	no	—
431	C₂×C₈	—	4	2	no	—
432	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
433	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
434	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
435	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
441	C₄⋊C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
442	C₂²⋊C₄	—	2	1	no	—
443	C₂²⋊C₄	—	2	1	no	—
444	C₂²⋊C₄	—	2	1	no	—
445	C₂²⋊C₄	—	2	1	no	—
446	C₂²⋊C₄	—	2	1	no	—
447	C₂²⋊C₄	—	4	2	no	—
448	C₂²⋊C₄	—	4	2	no	—
449	C₄²	—	2	1	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	1	no	—
453	C₂³	—	4	1	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	4	2	no	—
456	C₂³	—	4	2	no	—
457	C₂³	—	8	2	no	—
458	C₂³	—	8	2	no	—
459	C₂³	#121×C₃₇	1	1	yes	characteristic
460	C₂³	#121×C₃₇	1	1	yes	characteristic
461	C₂³	C₂×#41×C₃₇	1	1	yes	characteristic
462	Q₈	—	2	2	no	—
463	D₄	—	2	2	no	—
464	D₄	—	4	2	no	—
465	D₄	—	4	2	no	—
466	D₄	—	4	2	no	—
467	D₄	—	4	2	no	—
468	D₄	—	4	2	no	—
469	D₄	—	4	2	no	—
470	D₄	—	4	2	no	—
471	D₄	—	8	4	no	—
472	D₄	—	8	4	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	8	2	no	—
487	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
488	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
489	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
490	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
491	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
492	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
493	C₈	—	2	1	no	—
494	C₈	—	2	1	no	—
495	C₈	—	2	1	no	—
496	C₈	—	2	1	no	—
497	C₈	—	2	4	no	—
498	C₈	—	4	1	no	—
499	C₈	—	4	1	no	—
500	C₈	—	4	2	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	2	1	no	—
508	C₂²	—	4	4	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	1	no	—
512	C₂²	—	8	2	no	—
513	C₂²	—	8	2	no	—
514	C₂²	—	8	2	no	—
515	C₂²	—	16	2	no	—
516	C₂²	—	16	2	no	—
517	C₂²	C₃₇×#472	1	2	yes	—
518	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
519	C₂²	C₃₇×#553	1	2	yes	—
520	C₄	—	2	1	no	—
521	C₄	—	2	1	no	—
522	C₄	—	4	1	no	—
523	C₄	—	4	1	no	—
524	C₄	—	4	1	no	—
525	C₄	—	8	2	no	—
526	C₄	C₃₇×#532	1	1	yes	characteristic
527	C₄	C₃₇×#534	1	1	yes	characteristic
528	C₄	C₃₇×#546	1	2	yes	—
529	C₂	—	2	2	no	—
530	C₂	—	2	2	no	—
531	C₂	—	4	1	no	—
532	C₂	—	8	1	no	—
533	C₂	—	16	2	no	—
534	C₂	C₃₇×#2543	1	1	yes	characteristic
535	C₂	C₂×C₃₇×#472	1	1	yes	characteristic
536	C₂	C₃₇×#3067	1	1	yes	characteristic

	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×#466	C₂	semidirect
3. C₃₇×#2929	C₂	semidirect
4. C₃₇×#2089	C₂	semidirect
5. C₃₇×#2078	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. C₂×C₃₇×#341	C₂	semidirect
232. #28592	C₃₇	direct (N × H)
261. #3055	C₂×C₃₇	semidirect
262. C₂×#466	C₂×C₃₇	semidirect
263. #2929	C₂×C₃₇	semidirect
264. #2089	C₂×C₃₇	semidirect
265. #2078	C₂×C₃₇	semidirect
266. #2045	C₂×C₃₇	semidirect
267. #2018	C₂×C₃₇	semidirect
268. #1931	C₂×C₃₇	semidirect
269. #1907	C₂×C₃₇	semidirect
270. #1900	C₂×C₃₇	semidirect
271. C₂×#341	C₂×C₃₇	semidirect
315. C₃₇	#28592	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×#466	2
C₃₇×#2929	2
C₃₇×#2089	2
C₃₇×#2078	2
C₃₇×#2045	2
C₃₇×#2018	2
C₃₇×#1931	2
C₃₇×#1907	2
C₃₇×#1900	2
C₂×C₃₇×#341	2
#28592	37

Subgroups — C37×#28592 #22649845

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28592 #22649845