Subgroups — C₃₇×#24773 #22646026

Order 9472.

892 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#471	C₂	1	2	yes	maximal, complemented
2	C₃₇×#3038	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₇×#460	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#137×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2906	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2063	C₂	1	2	yes	maximal, complemented
7	C₃₇×#2046	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1965	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1950	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1907	C₂	1	2	yes	maximal, complemented
11	C₃₇×#1801	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×AGL(1,ℤ/8)×C₃₇	C₂²	1	2	yes	—
14	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	—
15	C₂×#131×C₃₇	C₂²	1	2	yes	—
16	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
17	C₄×#41×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
19	C₃₇×#471	—	2	8	no	—
20	C₃₇×#460	—	2	1	no	—
21	C₃₇×#460	—	2	1	no	—
22	C₃₇×#460	—	2	1	no	—
23	C₃₇×#460	—	2	1	no	—
24	C₃₇×#460	—	2	2	no	—
25	C₃₇×#459	—	2	1	no	—
26	C₃₇×#459	—	2	1	no	—
27	C₃₇×#441	—	2	1	no	—
28	C₃₇×#440	—	2	1	no	—
29	C₄×Q₁₆×C₃₇	—	2	1	no	—
30	C₄×SD₁₆×C₃₇	—	2	1	no	—
31	C₂×#108×C₃₇	C₂²	1	2	yes	—
32	C₃₇×#428	C₂²	1	1	yes	characteristic
33	C₃₇×#424	—	2	2	no	—
34	C₃₇×#424	C₂²	1	2	yes	—
35	C₃₇×#423	—	2	1	no	—
36	C₃₇×#423	C₂²	1	1	yes	characteristic
37	C₃₇×#423	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊C₈×C₃₇	—	2	1	no	—
39	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
40	C₃₇×#419	C₂²	1	1	yes	characteristic
41	C₃₇×#418	C₂²	1	2	yes	—
42	C₃₇×#417	C₂²	1	1	yes	characteristic
43	C₂×#102×C₃₇	C₂²	1	2	yes	—
44	C₂×#101×C₃₇	C₂²	1	2	yes	—
45	C₂×#100×C₃₇	C₂²	1	2	yes	—
46	C₂×#100×C₃₇	C₂²	1	2	yes	—
47	C₄×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
48	C₃₇×#343	C₂²	1	2	yes	—
49	C₃₇×#341	C₂²	1	2	yes	—
50	C₂×#41×C₃₇	C₂³	1	1	yes	characteristic
51	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₃₇	—	2	1	no	—
53	C₂²×D₄×C₃₇	—	2	1	no	—
54	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
55	#137×C₃₇	—	2	2	no	—
56	#137×C₃₇	D₄	1	4	yes	complemented
57	AGL(1,ℤ/8)×C₃₇	—	2	4	no	—
58	AGL(1,ℤ/8)×C₃₇	—	2	4	no	—
59	C₂×Q₁₆×C₃₇	—	2	1	no	—
60	C₂×SD₁₆×C₃₇	—	2	1	no	—
61	C₂×SD₁₆×C₃₇	—	2	4	no	—
62	C₂×SD₁₆×C₃₇	—	2	2	no	—
63	C₂×SD₁₆×C₃₇	—	2	2	no	—
64	C₂×SD₁₆×C₃₇	—	2	2	no	—
65	C₂×SD₁₆×C₃₇	—	4	2	no	—
66	C₂×D₈×C₃₇	—	2	2	no	—
67	#131×C₃₇	—	2	4	no	—
68	#131×C₃₇	—	4	2	no	—
69	C₂×M₁₆×C₃₇	—	2	2	no	—
70	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
71	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
72	C₂×M₁₆×C₃₇	C₂³	1	1	yes	characteristic
73	C₂×M₁₆×C₃₇	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₃₇	—	2	2	no	—
75	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
76	#127×C₃₇	—	2	1	no	—
77	#127×C₃₇	—	2	1	no	—
78	#127×C₃₇	—	2	1	no	—
79	#127×C₃₇	—	2	1	no	—
80	C₄×Q₈×C₃₇	—	2	1	no	—
81	C₄×Q₈×C₃₇	—	2	1	no	—
82	C₄×Q₈×C₃₇	—	2	1	no	—
83	C₄×Q₈×C₃₇	—	2	1	no	—
84	C₄×Q₈×C₃₇	D₄	1	1	yes	characteristic
85	C₄×Q₈×C₃₇	D₄	1	1	yes	characteristic
86	C₄×D₄×C₃₇	—	2	1	no	—
87	C₄×D₄×C₃₇	—	2	1	no	—
88	C₄×D₄×C₃₇	D₄	1	1	yes	characteristic
89	C₄×D₄×C₃₇	D₄	1	1	yes	characteristic
90	#117×C₃₇	—	2	1	no	—
91	#117×C₃₇	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
93	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₃₇	—	2	1	no	—
95	C₂×C₄²×C₃₇	—	2	1	no	—
96	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
97	#108×C₃₇	—	2	4	no	—
98	#107×C₃₇	—	2	1	no	—
99	#106×C₃₇	—	2	1	no	—
100	C₄⋊C₈×C₃₇	—	2	2	no	—
101	C₄⋊C₈×C₃₇	—	2	2	no	—
102	C₄⋊C₈×C₃₇	—	2	1	no	—
103	C₄⋊C₈×C₃₇	—	2	1	no	—
104	C₄⋊C₈×C₃₇	—	2	1	no	—
105	C₄⋊C₈×C₃₇	—	2	1	no	—
106	C₄⋊C₈×C₃₇	D₄	1	1	yes	characteristic
107	C₄⋊C₈×C₃₇	D₄	1	1	yes	characteristic
108	C₄⋊C₈×C₃₇	D₄	1	2	yes	—
109	#103×C₃₇	—	2	1	no	—
110	#103×C₃₇	—	2	1	no	—
111	#103×C₃₇	—	2	1	no	—
112	#102×C₃₇	—	2	1	no	—
113	#102×C₃₇	—	2	2	no	—
114	#102×C₃₇	—	2	2	no	—
115	#102×C₃₇	—	2	2	no	—
116	#102×C₃₇	—	2	2	no	—
117	#101×C₃₇	—	2	4	no	—
118	#100×C₃₇	—	2	4	no	—
119	#100×C₃₇	—	4	2	no	—
120	#97×C₃₇	—	2	1	no	—
121	C₄×C₈×C₃₇	—	2	1	no	—
122	C₂⁴×C₃₇	—	2	2	no	—
123	#41×C₃₇	—	2	1	no	—
124	#41×C₃₇	—	2	1	no	—
125	#41×C₃₇	C₂×D₄	1	2	yes	—
126	#41×C₃₇	#41	1	2	yes	—
127	C₂×Q₈×C₃₇	—	2	1	no	—
128	C₂×Q₈×C₃₇	—	2	1	no	—
129	C₂×Q₈×C₃₇	—	2	1	no	—
130	C₂×Q₈×C₃₇	—	2	1	no	—
131	C₂×Q₈×C₃₇	—	2	1	no	—
132	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
133	C₂×Q₈×C₃₇	C₂×D₄	1	1	yes	characteristic
134	C₂×D₄×C₃₇	—	2	1	no	—
135	C₂×D₄×C₃₇	—	2	2	no	—
136	C₂×D₄×C₃₇	—	2	2	no	—
137	C₂×D₄×C₃₇	—	2	2	no	—
138	C₂×D₄×C₃₇	—	2	2	no	—
139	C₂×D₄×C₃₇	—	2	2	no	—
140	C₂×D₄×C₃₇	—	2	2	no	—
141	C₂×D₄×C₃₇	—	4	1	no	—
142	C₂×D₄×C₃₇	—	4	1	no	—
143	C₂×D₄×C₃₇	—	4	1	no	—
144	C₂×D₄×C₃₇	—	4	1	no	—
145	C₂×D₄×C₃₇	—	8	2	no	—
146	C₂×D₄×C₃₇	—	8	2	no	—
147	C₂×D₄×C₃₇	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₃₇	—	2	1	no	—
149	C₂²×C₄×C₃₇	—	2	1	no	—
150	C₂²×C₄×C₃₇	—	2	1	no	—
151	C₂²×C₄×C₃₇	—	2	1	no	—
152	C₂²×C₄×C₃₇	—	2	1	no	—
153	C₂²×C₄×C₃₇	#41	1	1	yes	characteristic
154	C₂²×C₄×C₃₇	#41	1	1	yes	characteristic
155	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
156	Q₁₆×C₃₇	—	2	4	no	—
157	SD₁₆×C₃₇	—	2	4	no	—
158	SD₁₆×C₃₇	—	4	4	no	—
159	SD₁₆×C₃₇	—	4	4	no	—
160	SD₁₆×C₃₇	—	4	4	no	—
161	D₈×C₃₇	—	4	4	no	—
162	M₁₆×C₃₇	—	2	1	no	—
163	M₁₆×C₃₇	—	2	2	no	—
164	M₁₆×C₃₇	—	2	2	no	—
165	M₁₆×C₃₇	—	2	2	no	—
166	M₁₆×C₃₇	—	2	1	no	—
167	M₁₆×C₃₇	—	2	2	no	—
168	M₁₆×C₃₇	—	2	1	no	—
169	M₁₆×C₃₇	—	4	4	no	—
170	M₁₆×C₃₇	C₂×D₄	1	2	yes	—
171	C₂×C₈×C₃₇	—	2	1	no	—
172	C₂×C₈×C₃₇	—	2	2	no	—
173	C₂×C₈×C₃₇	—	2	2	no	—
174	C₂×C₈×C₃₇	—	2	1	no	—
175	C₂×C₈×C₃₇	—	2	2	no	—
176	C₂×C₈×C₃₇	—	2	2	no	—
177	C₂×C₈×C₃₇	—	4	4	no	—
178	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
179	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
180	C₄⋊C₄×C₃₇	—	2	1	no	—
181	C₄⋊C₄×C₃₇	—	2	1	no	—
182	C₄⋊C₄×C₃₇	—	2	1	no	—
183	C₄⋊C₄×C₃₇	—	2	1	no	—
184	C₄⋊C₄×C₃₇	—	4	1	no	—
185	C₄⋊C₄×C₃₇	—	4	1	no	—
186	C₄⋊C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
187	C₄⋊C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
188	C₂²⋊C₄×C₃₇	—	2	1	no	—
189	C₂²⋊C₄×C₃₇	—	2	1	no	—
190	C₂²⋊C₄×C₃₇	—	2	1	no	—
191	C₄²×C₃₇	—	2	1	no	—
192	C₄²×C₃₇	—	2	1	no	—
193	C₄²×C₃₇	—	2	1	no	—
194	C₄²×C₃₇	—	4	1	no	—
195	C₄²×C₃₇	—	4	1	no	—
196	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
197	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
198	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
199	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
200	C₂³×C₃₇	—	2	1	no	—
201	C₂³×C₃₇	—	4	2	no	—
202	C₂³×C₃₇	—	4	2	no	—
203	C₂³×C₃₇	—	4	2	no	—
204	C₂³×C₃₇	—	8	2	no	—
205	C₂³×C₃₇	—	8	2	no	—
206	C₂³×C₃₇	C₂×#41	1	1	yes	characteristic
207	Q₈×C₃₇	—	2	1	no	—
208	Q₈×C₃₇	—	2	2	no	—
209	Q₈×C₃₇	—	2	2	no	—
210	Q₈×C₃₇	—	4	1	no	—
211	Q₈×C₃₇	—	4	1	no	—
212	Q₈×C₃₇	#121	1	2	yes	—
213	D₄×C₃₇	—	2	2	no	—
214	D₄×C₃₇	—	2	2	no	—
215	D₄×C₃₇	—	2	1	no	—
216	D₄×C₃₇	—	4	2	no	—
217	D₄×C₃₇	—	4	2	no	—
218	D₄×C₃₇	—	4	2	no	—
219	D₄×C₃₇	—	4	2	no	—
220	D₄×C₃₇	—	8	2	no	—
221	D₄×C₃₇	—	8	2	no	—
222	D₄×C₃₇	—	8	2	no	—
223	D₄×C₃₇	—	8	2	no	—
224	D₄×C₃₇	#121	1	2	yes	—
225	C₂×C₄×C₃₇	—	2	1	no	—
226	C₂×C₄×C₃₇	—	2	2	no	—
227	C₂×C₄×C₃₇	—	2	2	no	—
228	C₂×C₄×C₃₇	—	2	2	no	—
229	C₂×C₄×C₃₇	—	2	1	no	—
230	C₂×C₄×C₃₇	—	2	1	no	—
231	C₂×C₄×C₃₇	—	2	2	no	—
232	C₂×C₄×C₃₇	—	4	1	no	—
233	C₂×C₄×C₃₇	—	4	1	no	—
234	C₂×C₄×C₃₇	—	4	1	no	—
235	C₂×C₄×C₃₇	—	4	2	no	—
236	C₂×C₄×C₃₇	—	4	1	no	—
237	C₂×C₄×C₃₇	—	8	1	no	—
238	C₂×C₄×C₃₇	—	8	1	no	—
239	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
240	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
241	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
242	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
243	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
247	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
248	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
249	C₈×C₃₇	—	2	2	no	—
250	C₈×C₃₇	—	2	2	no	—
251	C₈×C₃₇	—	2	2	no	—
252	C₈×C₃₇	—	4	2	no	—
253	C₈×C₃₇	—	4	1	no	—
254	C₈×C₃₇	—	4	2	no	—
255	#24773	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₂²×C₃₇	—	2	1	no	—
257	C₂²×C₃₇	—	2	1	no	—
258	C₂²×C₃₇	—	2	2	no	—
259	C₂²×C₃₇	—	4	1	no	—
260	C₂²×C₃₇	—	4	1	no	—
261	C₂²×C₃₇	—	8	2	no	—
262	C₂²×C₃₇	—	8	2	no	—
263	C₂²×C₃₇	—	8	2	no	—
264	C₂²×C₃₇	—	16	2	no	—
265	C₂²×C₃₇	—	16	2	no	—
266	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
267	C₂²×C₃₇	#547	1	1	yes	characteristic
268	C₂²×C₃₇	#553	1	1	yes	characteristic
269	C₄×C₃₇	—	2	2	no	—
270	C₄×C₃₇	—	2	1	no	—
271	C₄×C₃₇	—	2	1	no	—
272	C₄×C₃₇	—	2	1	no	—
273	C₄×C₃₇	—	4	2	no	—
274	C₄×C₃₇	—	4	1	no	—
275	C₄×C₃₇	—	4	1	no	—
276	C₄×C₃₇	—	8	1	no	—
277	C₄×C₃₇	#471	1	2	yes	complemented
278	C₄×C₃₇	C₂×#121	1	1	yes	characteristic
279	C₄×C₃₇	#537	1	1	yes	characteristic
280	C₄×C₃₇	D₄²	1	1	yes	characteristic
281	C₄×C₃₇	#548	1	1	yes	characteristic
282	C₂×#471	C₂×C₃₇	1	2	yes	complemented
283	#3038	C₂×C₃₇	1	1	yes	characteristic
284	C₂×#460	C₂×C₃₇	1	1	yes	characteristic, complemented
285	C₄×#137	C₂×C₃₇	1	1	yes	characteristic, complemented
286	#2906	C₂×C₃₇	1	1	yes	characteristic, complemented
287	#2063	C₂×C₃₇	1	2	yes	complemented
288	#2046	C₂×C₃₇	1	2	yes	complemented
289	#1965	C₂×C₃₇	1	1	yes	characteristic, complemented
290	#1950	C₂×C₃₇	1	1	yes	characteristic, complemented
291	#1907	C₂×C₃₇	1	2	yes	complemented
292	#1801	C₂×C₃₇	1	1	yes	characteristic, complemented
293	C₂×C₃₇	—	2	1	no	—
294	C₂×C₃₇	—	2	1	no	—
295	C₂×C₃₇	—	4	2	no	—
296	C₂×C₃₇	—	16	2	no	—
297	C₂×C₃₇	#2416	1	1	yes	characteristic
298	C₂×C₃₇	C₂×#471	1	1	yes	characteristic
299	C₂×C₃₇	#3068	1	1	yes	characteristic
300	C₂×#137	C₂²×C₃₇	1	1	yes	characteristic
301	C₂×AGL(1,ℤ/8)	C₂²×C₃₇	1	2	yes	—
302	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
303	C₂×#131	C₂²×C₃₇	1	2	yes	—
304	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
305	C₄×#41	C₂²×C₃₇	1	1	yes	characteristic
306	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
307	#471	—	2	8	no	—
308	#460	—	2	1	no	—
309	#460	—	2	1	no	—
310	#460	—	2	1	no	—
311	#460	—	2	1	no	—
312	#460	—	2	2	no	—
313	#459	—	2	1	no	—
314	#459	—	2	1	no	—
315	#441	—	2	1	no	—
316	#440	—	2	1	no	—
317	C₄×Q₁₆	—	2	1	no	—
318	C₄×SD₁₆	—	2	1	no	—
319	C₂×#108	C₂²×C₃₇	1	2	yes	—
320	#428	C₂²×C₃₇	1	1	yes	characteristic
321	#424	—	2	2	no	—
322	#424	C₂²×C₃₇	1	2	yes	—
323	#423	—	2	1	no	—
324	#423	C₂²×C₃₇	1	1	yes	characteristic
325	#423	C₂²×C₃₇	1	1	yes	characteristic
326	C₂×C₄⋊C₈	—	2	1	no	—
327	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
328	#419	C₂²×C₃₇	1	1	yes	characteristic
329	#418	C₂²×C₃₇	1	2	yes	—
330	#417	C₂²×C₃₇	1	1	yes	characteristic
331	C₂×#102	C₂²×C₃₇	1	2	yes	—
332	C₂×#101	C₂²×C₃₇	1	2	yes	—
333	C₂×#100	C₂²×C₃₇	1	2	yes	—
334	C₂×#100	C₂²×C₃₇	1	2	yes	—
335	C₄×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
336	#343	C₂²×C₃₇	1	2	yes	—
337	#341	C₂²×C₃₇	1	2	yes	—
338	C₃₇	#24773	1	1	yes	characteristic, direct product factor, Sylow
339	C₂×#41	C₂³×C₃₇	1	1	yes	characteristic
340	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
341	C₂²×D₄	—	2	1	no	—
342	C₂²×D₄	—	2	1	no	—
343	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
344	#137	—	2	2	no	—
345	#137	D₄×C₃₇	1	4	yes	complemented
346	AGL(1,ℤ/8)	—	2	4	no	—
347	AGL(1,ℤ/8)	—	2	4	no	—
348	C₂×Q₁₆	—	2	1	no	—
349	C₂×SD₁₆	—	2	1	no	—
350	C₂×SD₁₆	—	2	4	no	—
351	C₂×SD₁₆	—	2	2	no	—
352	C₂×SD₁₆	—	2	2	no	—
353	C₂×SD₁₆	—	2	2	no	—
354	C₂×SD₁₆	—	4	2	no	—
355	C₂×D₈	—	2	2	no	—
356	#131	—	2	4	no	—
357	#131	—	4	2	no	—
358	C₂×M₁₆	—	2	2	no	—
359	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
360	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
361	C₂×M₁₆	C₂³×C₃₇	1	1	yes	characteristic
362	C₂×M₁₆	C₂³×C₃₇	1	1	yes	characteristic
363	C₂²×C₈	—	2	2	no	—
364	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
365	#127	—	2	1	no	—
366	#127	—	2	1	no	—
367	#127	—	2	1	no	—
368	#127	—	2	1	no	—
369	C₄×Q₈	—	2	1	no	—
370	C₄×Q₈	—	2	1	no	—
371	C₄×Q₈	—	2	1	no	—
372	C₄×Q₈	—	2	1	no	—
373	C₄×Q₈	D₄×C₃₇	1	1	yes	characteristic
374	C₄×Q₈	D₄×C₃₇	1	1	yes	characteristic
375	C₄×D₄	—	2	1	no	—
376	C₄×D₄	—	2	1	no	—
377	C₄×D₄	D₄×C₃₇	1	1	yes	characteristic
378	C₄×D₄	D₄×C₃₇	1	1	yes	characteristic
379	#117	—	2	1	no	—
380	#117	C₂³×C₃₇	1	1	yes	characteristic
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
383	C₂×C₄²	—	2	1	no	—
384	C₂×C₄²	—	2	1	no	—
385	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
386	#108	—	2	4	no	—
387	#107	—	2	1	no	—
388	#106	—	2	1	no	—
389	C₄⋊C₈	—	2	2	no	—
390	C₄⋊C₈	—	2	2	no	—
391	C₄⋊C₈	—	2	1	no	—
392	C₄⋊C₈	—	2	1	no	—
393	C₄⋊C₈	—	2	1	no	—
394	C₄⋊C₈	—	2	1	no	—
395	C₄⋊C₈	D₄×C₃₇	1	1	yes	characteristic
396	C₄⋊C₈	D₄×C₃₇	1	1	yes	characteristic
397	C₄⋊C₈	D₄×C₃₇	1	2	yes	—
398	#103	—	2	1	no	—
399	#103	—	2	1	no	—
400	#103	—	2	1	no	—
401	#102	—	2	1	no	—
402	#102	—	2	2	no	—
403	#102	—	2	2	no	—
404	#102	—	2	2	no	—
405	#102	—	2	2	no	—
406	#101	—	2	4	no	—
407	#100	—	2	4	no	—
408	#100	—	4	2	no	—
409	#97	—	2	1	no	—
410	C₄×C₈	—	2	1	no	—
411	C₂⁴	—	2	2	no	—
412	#41	—	2	1	no	—
413	#41	—	2	1	no	—
414	#41	C₂×D₄×C₃₇	1	2	yes	—
415	#41	#41×C₃₇	1	2	yes	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	—	2	1	no	—
421	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
422	C₂×Q₈	C₂×D₄×C₃₇	1	1	yes	characteristic
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	4	1	no	—
431	C₂×D₄	—	4	1	no	—
432	C₂×D₄	—	4	1	no	—
433	C₂×D₄	—	4	1	no	—
434	C₂×D₄	—	8	2	no	—
435	C₂×D₄	—	8	2	no	—
436	C₂×D₄	C₂×D₄×C₃₇	1	1	yes	characteristic
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	#41×C₃₇	1	1	yes	characteristic
443	C₂²×C₄	#41×C₃₇	1	1	yes	characteristic
444	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
445	Q₁₆	—	2	4	no	—
446	SD₁₆	—	2	4	no	—
447	SD₁₆	—	4	4	no	—
448	SD₁₆	—	4	4	no	—
449	SD₁₆	—	4	4	no	—
450	D₈	—	4	4	no	—
451	M₁₆	—	2	1	no	—
452	M₁₆	—	2	2	no	—
453	M₁₆	—	2	2	no	—
454	M₁₆	—	2	2	no	—
455	M₁₆	—	2	1	no	—
456	M₁₆	—	2	2	no	—
457	M₁₆	—	2	1	no	—
458	M₁₆	—	4	4	no	—
459	M₁₆	C₂×D₄×C₃₇	1	2	yes	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	2	no	—
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	2	no	—
465	C₂×C₈	—	2	2	no	—
466	C₂×C₈	—	4	4	no	—
467	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
468	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	4	1	no	—
474	C₄⋊C₄	—	4	1	no	—
475	C₄⋊C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
476	C₄⋊C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	4	1	no	—
484	C₄²	—	4	1	no	—
485	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
486	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
487	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
488	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
489	C₂³	—	2	1	no	—
490	C₂³	—	4	2	no	—
491	C₂³	—	4	2	no	—
492	C₂³	—	4	2	no	—
493	C₂³	—	8	2	no	—
494	C₂³	—	8	2	no	—
495	C₂³	C₂×#41×C₃₇	1	1	yes	characteristic
496	Q₈	—	2	1	no	—
497	Q₈	—	2	2	no	—
498	Q₈	—	2	2	no	—
499	Q₈	—	4	1	no	—
500	Q₈	—	4	1	no	—
501	Q₈	#121×C₃₇	1	2	yes	—
502	D₄	—	2	2	no	—
503	D₄	—	2	2	no	—
504	D₄	—	2	1	no	—
505	D₄	—	4	2	no	—
506	D₄	—	4	2	no	—
507	D₄	—	4	2	no	—
508	D₄	—	4	2	no	—
509	D₄	—	8	2	no	—
510	D₄	—	8	2	no	—
511	D₄	—	8	2	no	—
512	D₄	—	8	2	no	—
513	D₄	#121×C₃₇	1	2	yes	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	8	1	no	—
527	C₂×C₄	—	8	1	no	—
528	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
529	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
530	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
531	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
532	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
533	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
534	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
535	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
536	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
537	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
538	C₈	—	2	2	no	—
539	C₈	—	2	2	no	—
540	C₈	—	2	2	no	—
541	C₈	—	4	2	no	—
542	C₈	—	4	1	no	—
543	C₈	—	4	2	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	4	1	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	8	2	no	—
550	C₂²	—	8	2	no	—
551	C₂²	—	8	2	no	—
552	C₂²	—	16	2	no	—
553	C₂²	—	16	2	no	—
554	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
555	C₂²	C₃₇×#547	1	1	yes	characteristic
556	C₂²	C₃₇×#553	1	1	yes	characteristic
557	C₄	—	2	2	no	—
558	C₄	—	2	1	no	—
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	8	1	no	—
565	C₄	C₃₇×#471	1	2	yes	complemented
566	C₄	C₂×#121×C₃₇	1	1	yes	characteristic
567	C₄	C₃₇×#537	1	1	yes	characteristic
568	C₄	D₄²×C₃₇	1	1	yes	characteristic
569	C₄	C₃₇×#548	1	1	yes	characteristic
570	C₂	—	2	1	no	—
571	C₂	—	2	1	no	—
572	C₂	—	4	2	no	—
573	C₂	—	16	2	no	—
574	C₂	C₃₇×#2416	1	1	yes	characteristic
575	C₂	C₂×C₃₇×#471	1	1	yes	characteristic
576	C₂	C₃₇×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₃₇×#3038	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#471	C₂	semidirect
3. C₂×C₃₇×#460	C₂	semidirect
4. C₄×#137×C₃₇	C₂	semidirect
5. C₃₇×#2906	C₂	semidirect
6. C₃₇×#2063	C₂	semidirect
7. C₃₇×#2046	C₂	semidirect
8. C₃₇×#1965	C₂	semidirect
9. C₃₇×#1950	C₂	semidirect
10. C₃₇×#1907	C₂	semidirect
11. C₃₇×#1801	C₂	semidirect
56. #137×C₃₇	D₄	semidirect
255. #24773	C₃₇	direct (N × H)
277. C₄×C₃₇	#471	semidirect
282. C₂×#471	C₂×C₃₇	semidirect
284. C₂×#460	C₂×C₃₇	semidirect
285. C₄×#137	C₂×C₃₇	semidirect
286. #2906	C₂×C₃₇	semidirect
287. #2063	C₂×C₃₇	semidirect
288. #2046	C₂×C₃₇	semidirect
289. #1965	C₂×C₃₇	semidirect
290. #1950	C₂×C₃₇	semidirect
291. #1907	C₂×C₃₇	semidirect
292. #1801	C₂×C₃₇	semidirect
338. C₃₇	#24773	direct (N × H)
345. #137	D₄×C₃₇	semidirect
565. C₄	C₃₇×#471	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₇×#471	2
C₃₇×#3038	2
C₂×C₃₇×#460	2
C₄×#137×C₃₇	2
C₃₇×#2906	2
C₃₇×#2063	2
C₃₇×#2046	2
C₃₇×#1965	2
C₃₇×#1950	2
C₃₇×#1907	2
C₃₇×#1801	2
#24773	37

Subgroups — C37×#24773 #22646026

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#24773 #22646026