Subgroups — C₃₇×#24279 #22645532

Order 9472.

1328 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#135×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#471	C₂	1	2	yes	maximal, complemented
3	C₃₇×#3005	C₂	1	2	yes	maximal, complemented
4	C₃₇×#2929	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2047	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2045	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#2020	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#2018	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1977	C₂	1	2	yes	maximal, complemented
10	C₃₇×#1810	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1785	C₂	1	2	yes	maximal, complemented
12	C₂²×#41×C₃₇	C₂²	1	2	yes	—
13	C₂×#137×C₃₇	C₂²	1	2	yes	—
14	C₂×AGL(1,ℤ/8)×C₃₇	C₂²	1	2	yes	—
15	C₂×#135×C₃₇	—	2	8	no	—
16	C₂×#135×C₃₇	—	2	2	no	—
17	C₂×#135×C₃₇	—	2	2	no	—
18	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	—
20	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic
21	C₂×#131×C₃₇	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₃₇	C₂²	1	1	yes	characteristic
23	C₃₇×#525	C₂²	1	1	yes	characteristic
24	C₃₇×#471	—	2	8	no	—
25	C₃₇×#452	—	2	4	no	—
26	C₃₇×#449	—	2	4	no	—
27	C₃₇×#435	—	2	2	no	—
28	C₈×D₄×C₃₇	—	2	2	no	—
29	C₂×#108×C₃₇	C₂²	1	2	yes	—
30	C₃₇×#424	C₂²	1	1	yes	characteristic
31	C₃₇×#419	C₂²	1	2	yes	—
32	C₃₇×#418	C₂²	1	2	yes	—
33	C₂×#101×C₃₇	C₂²	1	2	yes	—
34	C₂×#101×C₃₇	C₂²	1	2	yes	—
35	C₂×#100×C₃₇	C₂²	1	2	yes	—
36	C₂×#100×C₃₇	C₂²	1	2	yes	—
37	C₃₇×#408	C₂²	1	1	yes	characteristic
38	C₃₇×#407	C₂²	1	1	yes	characteristic
39	C₃₇×#407	C₂²	1	2	yes	—
40	C₃₇×#405	C₂²	1	1	yes	characteristic
41	C₃₇×#341	C₂²	1	1	yes	characteristic
42	C₃₇×#341	C₂²	1	1	yes	characteristic
43	C₂×#41×C₃₇	—	2	4	no	—
44	C₂×#41×C₃₇	—	2	4	no	—
45	C₂×#41×C₃₇	—	2	4	no	—
46	C₂×#41×C₃₇	—	2	4	no	—
47	C₂×#41×C₃₇	—	4	2	no	—
48	C₂×#41×C₃₇	—	4	2	no	—
49	C₂×#41×C₃₇	C₂³	1	1	yes	characteristic
50	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
51	C₂²×D₄×C₃₇	—	2	2	no	—
52	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
53	C₂³×C₄×C₃₇	—	2	2	no	—
54	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
55	#137×C₃₇	—	2	4	no	—
56	#137×C₃₇	—	4	2	no	—
57	AGL(1,ℤ/8)×C₃₇	—	2	4	no	—
58	AGL(1,ℤ/8)×C₃₇	—	4	2	no	—
59	#135×C₃₇	—	2	16	no	—
60	#135×C₃₇	—	2	16	no	—
61	C₂×Q₁₆×C₃₇	—	2	4	no	—
62	C₂×Q₁₆×C₃₇	—	2	2	no	—
63	C₂×Q₁₆×C₃₇	—	2	2	no	—
64	C₂×SD₁₆×C₃₇	—	2	2	no	—
65	C₂×SD₁₆×C₃₇	—	2	2	no	—
66	C₂×SD₁₆×C₃₇	—	2	2	no	—
67	C₂×SD₁₆×C₃₇	—	2	2	no	—
68	C₂×SD₁₆×C₃₇	—	2	4	no	—
69	C₂×SD₁₆×C₃₇	D₄	1	8	yes	complemented
70	C₂×D₈×C₃₇	—	2	4	no	—
71	C₂×D₈×C₃₇	—	2	2	no	—
72	C₂×D₈×C₃₇	—	2	2	no	—
73	#131×C₃₇	—	2	4	no	—
74	C₂×M₁₆×C₃₇	—	2	1	no	—
75	C₂×M₁₆×C₃₇	C₂³	1	1	yes	characteristic
76	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
77	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
78	C₂×M₁₆×C₃₇	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₃₇	—	2	4	no	—
80	C₂²×C₈×C₃₇	—	2	1	no	—
81	C₂²×C₈×C₃₇	D₄	1	2	yes	—
82	C₂²×C₈×C₃₇	D₄	1	2	yes	—
83	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
85	#123×C₃₇	—	2	1	no	—
86	C₂²⋊Q₈×C₃₇	D₄	1	2	yes	—
87	#121×C₃₇	D₄	1	2	yes	—
88	#120×C₃₇	—	2	1	no	—
89	C₄×D₄×C₃₇	—	2	2	no	—
90	#117×C₃₇	C₂³	1	1	yes	characteristic
91	#108×C₃₇	—	2	4	no	—
92	C₄⋊C₈×C₃₇	—	2	2	no	—
93	#103×C₃₇	—	2	4	no	—
94	#102×C₃₇	—	2	4	no	—
95	#101×C₃₇	—	2	4	no	—
96	#101×C₃₇	—	4	2	no	—
97	#100×C₃₇	—	2	4	no	—
98	#100×C₃₇	—	4	2	no	—
99	C₂²⋊C₈×C₃₇	—	2	2	no	—
100	C₂²⋊C₈×C₃₇	—	2	4	no	—
101	C₂²⋊C₈×C₃₇	—	2	2	no	—
102	#97×C₃₇	—	2	1	no	—
103	C₄×C₈×C₃₇	—	2	1	no	—
104	C₂⁴×C₃₇	—	2	2	no	—
105	C₂⁴×C₃₇	#41	1	1	yes	characteristic
106	#41×C₃₇	—	2	16	no	—
107	#41×C₃₇	—	2	2	no	—
108	#41×C₃₇	—	2	2	no	—
109	#41×C₃₇	—	4	8	no	—
110	#41×C₃₇	—	4	8	no	—
111	#41×C₃₇	—	4	8	no	—
112	C₂×Q₈×C₃₇	—	2	2	no	—
113	C₂×Q₈×C₃₇	—	2	2	no	—
114	C₂×Q₈×C₃₇	—	2	2	no	—
115	C₂×Q₈×C₃₇	—	2	2	no	—
116	C₂×Q₈×C₃₇	—	2	2	no	—
117	C₂×Q₈×C₃₇	C₂×D₄	1	4	yes	—
118	C₂×Q₈×C₃₇	C₂×D₄	1	1	yes	characteristic
119	C₂×D₄×C₃₇	—	2	2	no	—
120	C₂×D₄×C₃₇	—	2	1	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	—	2	2	no	—
126	C₂×D₄×C₃₇	—	4	4	no	—
127	C₂×D₄×C₃₇	—	4	4	no	—
128	C₂×D₄×C₃₇	—	4	4	no	—
129	C₂×D₄×C₃₇	C₂×D₄	1	4	yes	—
130	C₂×D₄×C₃₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₃₇	—	2	2	no	—
132	C₂²×C₄×C₃₇	—	2	2	no	—
133	C₂²×C₄×C₃₇	—	2	2	no	—
134	C₂²×C₄×C₃₇	—	2	1	no	—
135	C₂²×C₄×C₃₇	—	4	4	no	—
136	C₂²×C₄×C₃₇	—	4	4	no	—
137	C₂²×C₄×C₃₇	—	4	4	no	—
138	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₃₇	#41	1	1	yes	characteristic
141	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
142	Q₁₆×C₃₇	—	2	8	no	—
143	Q₁₆×C₃₇	—	4	4	no	—
144	SD₁₆×C₃₇	—	2	8	no	—
145	SD₁₆×C₃₇	—	2	8	no	—
146	SD₁₆×C₃₇	—	4	4	no	—
147	SD₁₆×C₃₇	—	4	4	no	—
148	D₈×C₃₇	—	2	8	no	—
149	D₈×C₃₇	—	4	4	no	—
150	M₁₆×C₃₇	—	2	2	no	—
151	M₁₆×C₃₇	—	2	2	no	—
152	M₁₆×C₃₇	—	2	2	no	—
153	M₁₆×C₃₇	—	2	2	no	—
154	M₁₆×C₃₇	—	2	2	no	—
155	M₁₆×C₃₇	—	2	2	no	—
156	M₁₆×C₃₇	—	4	2	no	—
157	C₂×C₈×C₃₇	—	2	2	no	—
158	C₂×C₈×C₃₇	—	2	4	no	—
159	C₂×C₈×C₃₇	—	2	4	no	—
160	C₂×C₈×C₃₇	—	2	1	no	—
161	C₂×C₈×C₃₇	—	2	2	no	—
162	C₂×C₈×C₃₇	—	2	2	no	—
163	C₂×C₈×C₃₇	—	2	1	no	—
164	C₂×C₈×C₃₇	—	4	2	no	—
165	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
166	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
167	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
168	C₂×C₈×C₃₇	C₂×D₄	1	4	yes	—
169	C₄⋊C₄×C₃₇	—	2	2	no	—
170	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
171	C₂²⋊C₄×C₃₇	—	2	2	no	—
172	C₂²⋊C₄×C₃₇	—	2	1	no	—
173	C₂²⋊C₄×C₃₇	—	2	2	no	—
174	C₄²×C₃₇	—	2	1	no	—
175	C₂³×C₃₇	—	2	2	no	—
176	C₂³×C₃₇	—	2	1	no	—
177	C₂³×C₃₇	—	2	4	no	—
178	C₂³×C₃₇	—	4	2	no	—
179	C₂³×C₃₇	—	4	2	no	—
180	C₂³×C₃₇	—	4	2	no	—
181	C₂³×C₃₇	—	8	4	no	—
182	C₂³×C₃₇	#121	1	2	yes	—
183	C₂³×C₃₇	C₂×#41	1	1	yes	characteristic
184	Q₈×C₃₇	—	2	4	no	—
185	Q₈×C₃₇	—	2	2	no	—
186	Q₈×C₃₇	—	2	4	no	—
187	Q₈×C₃₇	—	4	2	no	—
188	Q₈×C₃₇	—	4	2	no	—
189	D₄×C₃₇	—	2	4	no	—
190	D₄×C₃₇	—	2	2	no	—
191	D₄×C₃₇	—	2	4	no	—
192	D₄×C₃₇	—	4	4	no	—
193	D₄×C₃₇	—	4	16	no	—
194	D₄×C₃₇	—	4	2	no	—
195	D₄×C₃₇	—	4	2	no	—
196	D₄×C₃₇	—	4	2	no	—
197	C₂×C₄×C₃₇	—	2	2	no	—
198	C₂×C₄×C₃₇	—	2	2	no	—
199	C₂×C₄×C₃₇	—	2	2	no	—
200	C₂×C₄×C₃₇	—	2	4	no	—
201	C₂×C₄×C₃₇	—	2	2	no	—
202	C₂×C₄×C₃₇	—	2	1	no	—
203	C₂×C₄×C₃₇	—	2	4	no	—
204	C₂×C₄×C₃₇	—	4	16	no	—
205	C₂×C₄×C₃₇	—	4	2	no	—
206	C₂×C₄×C₃₇	—	4	2	no	—
207	C₂×C₄×C₃₇	—	4	1	no	—
208	C₂×C₄×C₃₇	—	4	1	no	—
209	C₂×C₄×C₃₇	#121	1	2	yes	—
210	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
212	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
214	C₈×C₃₇	—	2	2	no	—
215	C₈×C₃₇	—	4	1	no	—
216	C₈×C₃₇	—	4	1	no	—
217	C₈×C₃₇	—	4	2	no	—
218	C₈×C₃₇	—	4	2	no	—
219	C₈×C₃₇	#120	1	2	yes	—
220	C₈×C₃₇	#120	1	2	yes	—
221	#24279	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₂²×C₃₇	—	2	2	no	—
223	C₂²×C₃₇	—	2	2	no	—
224	C₂²×C₃₇	—	2	2	no	—
225	C₂²×C₃₇	—	2	2	no	—
226	C₂²×C₃₇	—	4	4	no	—
227	C₂²×C₃₇	—	4	4	no	—
228	C₂²×C₃₇	—	4	1	no	—
229	C₂²×C₃₇	—	4	2	no	—
230	C₂²×C₃₇	—	8	4	no	—
231	C₂²×C₃₇	—	8	4	no	—
232	C₂²×C₃₇	—	8	4	no	—
233	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
234	C₂²×C₃₇	#546	1	2	yes	—
235	C₄×C₃₇	—	2	2	no	—
236	C₄×C₃₇	—	4	4	no	—
237	C₄×C₃₇	—	4	1	no	—
238	C₄×C₃₇	—	4	2	no	—
239	C₄×C₃₇	C₂×#120	1	1	yes	characteristic
240	C₄×C₃₇	#535	1	1	yes	characteristic
241	C₄×C₃₇	D₄²	1	2	yes	—
242	C₂²×#135	C₂×C₃₇	1	1	yes	characteristic, complemented
243	C₂×#471	C₂×C₃₇	1	2	yes	complemented
244	#3005	C₂×C₃₇	1	2	yes	complemented
245	#2929	C₂×C₃₇	1	1	yes	characteristic, complemented
246	#2047	C₂×C₃₇	1	1	yes	characteristic, complemented
247	#2045	C₂×C₃₇	1	1	yes	characteristic, complemented
248	#2020	C₂×C₃₇	1	1	yes	characteristic, complemented
249	#2018	C₂×C₃₇	1	1	yes	characteristic, complemented
250	#1977	C₂×C₃₇	1	2	yes	complemented
251	#1810	C₂×C₃₇	1	1	yes	characteristic, complemented
252	#1785	C₂×C₃₇	1	2	yes	complemented
253	C₂×C₃₇	—	2	2	no	—
254	C₂×C₃₇	—	4	2	no	—
255	C₂×C₃₇	—	8	1	no	—
256	C₂×C₃₇	—	8	4	no	—
257	C₂×C₃₇	#2408	1	1	yes	characteristic
258	C₂×C₃₇	#3067	1	2	yes	—
259	C₂²×#41	C₂²×C₃₇	1	2	yes	—
260	C₂×#137	C₂²×C₃₇	1	2	yes	—
261	C₂×AGL(1,ℤ/8)	C₂²×C₃₇	1	2	yes	—
262	C₂×#135	—	2	8	no	—
263	C₂×#135	—	2	2	no	—
264	C₂×#135	—	2	2	no	—
265	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
266	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
267	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
268	C₂×#131	C₂²×C₃₇	1	1	yes	characteristic
269	C₂³×C₈	C₂²×C₃₇	1	1	yes	characteristic
270	#525	C₂²×C₃₇	1	1	yes	characteristic
271	#471	—	2	8	no	—
272	#452	—	2	4	no	—
273	#449	—	2	4	no	—
274	#435	—	2	2	no	—
275	C₈×D₄	—	2	2	no	—
276	C₂×#108	C₂²×C₃₇	1	2	yes	—
277	#424	C₂²×C₃₇	1	1	yes	characteristic
278	#419	C₂²×C₃₇	1	2	yes	—
279	#418	C₂²×C₃₇	1	2	yes	—
280	C₂×#101	C₂²×C₃₇	1	2	yes	—
281	C₂×#101	C₂²×C₃₇	1	2	yes	—
282	C₂×#100	C₂²×C₃₇	1	2	yes	—
283	C₂×#100	C₂²×C₃₇	1	2	yes	—
284	#408	C₂²×C₃₇	1	1	yes	characteristic
285	#407	C₂²×C₃₇	1	2	yes	—
286	#407	C₂²×C₃₇	1	1	yes	characteristic
287	#405	C₂²×C₃₇	1	1	yes	characteristic
288	#341	C₂²×C₃₇	1	1	yes	characteristic
289	#341	C₂²×C₃₇	1	1	yes	characteristic
290	C₃₇	#24279	1	1	yes	characteristic, direct product factor, Sylow
291	C₂×#41	—	2	4	no	—
292	C₂×#41	—	2	4	no	—
293	C₂×#41	—	2	4	no	—
294	C₂×#41	—	2	4	no	—
295	C₂×#41	—	4	2	no	—
296	C₂×#41	—	4	2	no	—
297	C₂×#41	C₂³×C₃₇	1	1	yes	characteristic
298	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
299	C₂²×D₄	—	2	2	no	—
300	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
301	C₂³×C₄	—	2	2	no	—
302	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
303	#137	—	2	4	no	—
304	#137	—	4	2	no	—
305	AGL(1,ℤ/8)	—	2	4	no	—
306	AGL(1,ℤ/8)	—	4	2	no	—
307	#135	—	2	16	no	—
308	#135	—	2	16	no	—
309	C₂×Q₁₆	—	2	4	no	—
310	C₂×Q₁₆	—	2	2	no	—
311	C₂×Q₁₆	—	2	2	no	—
312	C₂×SD₁₆	—	2	2	no	—
313	C₂×SD₁₆	—	2	2	no	—
314	C₂×SD₁₆	—	2	2	no	—
315	C₂×SD₁₆	—	2	2	no	—
316	C₂×SD₁₆	—	2	4	no	—
317	C₂×SD₁₆	D₄×C₃₇	1	8	yes	complemented
318	C₂×D₈	—	2	4	no	—
319	C₂×D₈	—	2	2	no	—
320	C₂×D₈	—	2	2	no	—
321	#131	—	2	4	no	—
322	C₂×M₁₆	—	2	1	no	—
323	C₂×M₁₆	C₂³×C₃₇	1	1	yes	characteristic
324	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
325	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
326	C₂×M₁₆	C₂³×C₃₇	1	1	yes	characteristic
327	C₂²×C₈	—	2	4	no	—
328	C₂²×C₈	—	2	1	no	—
329	C₂²×C₈	D₄×C₃₇	1	2	yes	—
330	C₂²×C₈	D₄×C₃₇	1	2	yes	—
331	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
332	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
333	#123	—	2	1	no	—
334	C₂²⋊Q₈	D₄×C₃₇	1	2	yes	—
335	#121	D₄×C₃₇	1	2	yes	—
336	#120	—	2	1	no	—
337	C₄×D₄	—	2	2	no	—
338	#117	C₂³×C₃₇	1	1	yes	characteristic
339	#108	—	2	4	no	—
340	C₄⋊C₈	—	2	2	no	—
341	#103	—	2	4	no	—
342	#102	—	2	4	no	—
343	#101	—	2	4	no	—
344	#101	—	4	2	no	—
345	#100	—	2	4	no	—
346	#100	—	4	2	no	—
347	C₂²⋊C₈	—	2	2	no	—
348	C₂²⋊C₈	—	2	4	no	—
349	C₂²⋊C₈	—	2	2	no	—
350	#97	—	2	1	no	—
351	C₄×C₈	—	2	1	no	—
352	C₂⁴	—	2	2	no	—
353	C₂⁴	#41×C₃₇	1	1	yes	characteristic
354	#41	—	2	16	no	—
355	#41	—	2	2	no	—
356	#41	—	2	2	no	—
357	#41	—	4	8	no	—
358	#41	—	4	8	no	—
359	#41	—	4	8	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	C₂×D₄×C₃₇	1	4	yes	—
366	C₂×Q₈	C₂×D₄×C₃₇	1	1	yes	characteristic
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	4	4	no	—
375	C₂×D₄	—	4	4	no	—
376	C₂×D₄	—	4	4	no	—
377	C₂×D₄	C₂×D₄×C₃₇	1	4	yes	—
378	C₂×D₄	C₂×D₄×C₃₇	1	1	yes	characteristic
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	4	4	no	—
384	C₂²×C₄	—	4	4	no	—
385	C₂²×C₄	—	4	4	no	—
386	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
387	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
388	C₂²×C₄	#41×C₃₇	1	1	yes	characteristic
389	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
390	Q₁₆	—	2	8	no	—
391	Q₁₆	—	4	4	no	—
392	SD₁₆	—	2	8	no	—
393	SD₁₆	—	2	8	no	—
394	SD₁₆	—	4	4	no	—
395	SD₁₆	—	4	4	no	—
396	D₈	—	2	8	no	—
397	D₈	—	4	4	no	—
398	M₁₆	—	2	2	no	—
399	M₁₆	—	2	2	no	—
400	M₁₆	—	2	2	no	—
401	M₁₆	—	2	2	no	—
402	M₁₆	—	2	2	no	—
403	M₁₆	—	2	2	no	—
404	M₁₆	—	4	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	4	no	—
407	C₂×C₈	—	2	4	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	4	2	no	—
413	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
414	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
415	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
416	C₂×C₈	C₂×D₄×C₃₇	1	4	yes	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	1	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₄²	—	2	1	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	1	no	—
425	C₂³	—	2	4	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	8	4	no	—
430	C₂³	#121×C₃₇	1	2	yes	—
431	C₂³	C₂×#41×C₃₇	1	1	yes	characteristic
432	Q₈	—	2	4	no	—
433	Q₈	—	2	2	no	—
434	Q₈	—	2	4	no	—
435	Q₈	—	4	2	no	—
436	Q₈	—	4	2	no	—
437	D₄	—	2	4	no	—
438	D₄	—	2	2	no	—
439	D₄	—	2	4	no	—
440	D₄	—	4	4	no	—
441	D₄	—	4	16	no	—
442	D₄	—	4	2	no	—
443	D₄	—	4	2	no	—
444	D₄	—	4	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	4	16	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	#121×C₃₇	1	2	yes	—
458	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
459	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
460	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
461	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
462	C₈	—	2	2	no	—
463	C₈	—	4	1	no	—
464	C₈	—	4	1	no	—
465	C₈	—	4	2	no	—
466	C₈	—	4	2	no	—
467	C₈	#120×C₃₇	1	2	yes	—
468	C₈	#120×C₃₇	1	2	yes	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	4	4	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	8	4	no	—
478	C₂²	—	8	4	no	—
479	C₂²	—	8	4	no	—
480	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
481	C₂²	C₃₇×#546	1	2	yes	—
482	C₄	—	2	2	no	—
483	C₄	—	4	4	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	2	no	—
486	C₄	C₂×#120×C₃₇	1	1	yes	characteristic
487	C₄	C₃₇×#535	1	1	yes	characteristic
488	C₄	D₄²×C₃₇	1	2	yes	—
489	C₂	—	2	2	no	—
490	C₂	—	4	2	no	—
491	C₂	—	8	1	no	—
492	C₂	—	8	4	no	—
493	C₂	C₃₇×#2408	1	1	yes	characteristic
494	C₂	C₃₇×#3067	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. C₂²×#135×C₃₇	C₂	semidirect
2. C₂×C₃₇×#471	C₂	semidirect
3. C₃₇×#3005	C₂	semidirect
4. C₃₇×#2929	C₂	semidirect
5. C₃₇×#2047	C₂	semidirect
6. C₃₇×#2045	C₂	semidirect
7. C₃₇×#2020	C₂	semidirect
8. C₃₇×#2018	C₂	semidirect
9. C₃₇×#1977	C₂	semidirect
10. C₃₇×#1810	C₂	semidirect
11. C₃₇×#1785	C₂	semidirect
69. C₂×SD₁₆×C₃₇	D₄	semidirect
221. #24279	C₃₇	direct (N × H)
242. C₂²×#135	C₂×C₃₇	semidirect
243. C₂×#471	C₂×C₃₇	semidirect
244. #3005	C₂×C₃₇	semidirect
245. #2929	C₂×C₃₇	semidirect
246. #2047	C₂×C₃₇	semidirect
247. #2045	C₂×C₃₇	semidirect
248. #2020	C₂×C₃₇	semidirect
249. #2018	C₂×C₃₇	semidirect
250. #1977	C₂×C₃₇	semidirect
251. #1810	C₂×C₃₇	semidirect
252. #1785	C₂×C₃₇	semidirect
290. C₃₇	#24279	direct (N × H)
317. C₂×SD₁₆	D₄×C₃₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#135×C₃₇	2
C₂×C₃₇×#471	2
C₃₇×#3005	2
C₃₇×#2929	2
C₃₇×#2047	2
C₃₇×#2045	2
C₃₇×#2020	2
C₃₇×#2018	2
C₃₇×#1977	2
C₃₇×#1810	2
C₃₇×#1785	2
#24279	37

Subgroups — C37×#24279 #22645532

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#24279 #22645532