Subgroups — C₃₇×#28499 #22649752

Order 9472.

1004 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3153	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#3152	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#497	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₇×#473	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₇×#471	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2932	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#2020	C₂	1	2	yes	maximal, complemented
8	C₃₇×#2019	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1967	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1966	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1778	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₃₇	C₂²	1	2	yes	—
13	C₂×#137×C₃₇	C₂²	1	2	yes	—
14	C₂×#137×C₃₇	C₂²	1	2	yes	—
15	C₂×AGL(1,ℤ/8)×C₃₇	C₂²	1	2	yes	—
16	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
20	C₂×#131×C₃₇	C₂²	1	2	yes	—
21	C₃₇×#532	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
23	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
24	C₃₇×#497	—	2	1	no	—
25	C₃₇×#497	—	2	2	no	—
26	C₃₇×#497	—	2	4	no	—
27	C₃₇×#496	—	2	1	no	—
28	C₃₇×#495	—	2	2	no	—
29	C₃₇×#494	—	2	1	no	—
30	C₃₇×#492	—	2	1	no	—
31	C₃₇×#473	—	2	8	no	—
32	C₃₇×#471	—	2	8	no	—
33	C₃₇×#435	—	2	4	no	—
34	C₂×#108×C₃₇	C₂²	1	2	yes	—
35	C₃₇×#423	C₂²	1	1	yes	characteristic
36	C₂×#101×C₃₇	C₂²	1	2	yes	—
37	C₂×#101×C₃₇	C₂²	1	2	yes	—
38	C₂×#101×C₃₇	C₂²	1	2	yes	—
39	C₂×#100×C₃₇	C₂²	1	2	yes	—
40	C₃₇×#408	C₂²	1	2	yes	—
41	C₄×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
42	C₄×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
43	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
44	C₃₇×#341	C₂²	1	2	yes	—
45	C₂×#41×C₃₇	C₂³	1	2	yes	—
46	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
47	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
48	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
50	#137×C₃₇	—	2	4	no	—
51	#137×C₃₇	—	2	4	no	—
52	#137×C₃₇	—	2	4	no	—
53	#137×C₃₇	—	4	2	no	—
54	#137×C₃₇	—	4	2	no	—
55	#137×C₃₇	—	4	2	no	—
56	AGL(1,ℤ/8)×C₃₇	—	2	4	no	—
57	AGL(1,ℤ/8)×C₃₇	—	4	2	no	—
58	C₂×Q₁₆×C₃₇	—	2	2	no	—
59	C₂×Q₁₆×C₃₇	—	2	2	no	—
60	C₂×Q₁₆×C₃₇	—	2	2	no	—
61	C₂×Q₁₆×C₃₇	—	2	4	no	—
62	C₂×Q₁₆×C₃₇	—	2	2	no	—
63	C₂×Q₁₆×C₃₇	—	2	2	no	—
64	C₂×Q₁₆×C₃₇	—	4	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	2	no	—
69	C₂×SD₁₆×C₃₇	—	2	4	no	—
70	C₂×SD₁₆×C₃₇	—	2	2	no	—
71	C₂×SD₁₆×C₃₇	—	2	2	no	—
72	C₂×SD₁₆×C₃₇	—	4	2	no	—
73	C₂×D₈×C₃₇	—	2	2	no	—
74	#131×C₃₇	—	2	4	no	—
75	#131×C₃₇	—	2	4	no	—
76	C₂×M₁₆×C₃₇	—	2	2	no	—
77	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
78	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
79	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
80	C₂²×C₈×C₃₇	—	2	2	no	—
81	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
83	C₄⋊Q₈×C₃₇	—	2	1	no	—
84	C₄⋊Q₈×C₃₇	—	2	1	no	—
85	C₄⋊Q₈×C₃₇	—	2	2	no	—
86	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
87	#127×C₃₇	D₄	1	1	yes	characteristic
88	#124×C₃₇	—	2	1	no	—
89	#124×C₃₇	—	2	1	no	—
90	#124×C₃₇	—	2	2	no	—
91	#124×C₃₇	D₄	1	2	yes	—
92	#121×C₃₇	—	2	2	no	—
93	C₄×D₄×C₃₇	—	2	2	no	—
94	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
96	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
97	#108×C₃₇	D₄	1	8	yes	complemented
98	C₄⋊C₈×C₃₇	—	2	2	no	—
99	#101×C₃₇	—	2	4	no	—
100	#101×C₃₇	—	2	4	no	—
101	#101×C₃₇	—	2	4	no	—
102	#100×C₃₇	—	2	4	no	—
103	C₂²⋊C₈×C₃₇	—	2	4	no	—
104	#97×C₃₇	—	2	1	no	—
105	#97×C₃₇	—	2	1	no	—
106	#97×C₃₇	D₄	1	4	yes	—
107	C₄×C₈×C₃₇	—	2	1	no	—
108	C₄×C₈×C₃₇	—	2	1	no	—
109	C₂⁴×C₃₇	—	2	1	no	—
110	#41×C₃₇	—	2	2	no	—
111	#41×C₃₇	—	2	2	no	—
112	#41×C₃₇	—	2	2	no	—
113	#41×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	—	2	1	no	—
118	C₂×Q₈×C₃₇	—	2	1	no	—
119	C₂×Q₈×C₃₇	—	2	1	no	—
120	C₂×Q₈×C₃₇	—	2	1	no	—
121	C₂×Q₈×C₃₇	—	2	1	no	—
122	C₂×Q₈×C₃₇	—	2	1	no	—
123	C₂×Q₈×C₃₇	—	2	2	no	—
124	C₂×Q₈×C₃₇	—	2	2	no	—
125	C₂×Q₈×C₃₇	—	2	2	no	—
126	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
127	C₂×D₄×C₃₇	—	2	2	no	—
128	C₂×D₄×C₃₇	—	2	2	no	—
129	C₂×D₄×C₃₇	—	2	2	no	—
130	C₂×D₄×C₃₇	—	2	1	no	—
131	C₂×D₄×C₃₇	—	2	1	no	—
132	C₂×D₄×C₃₇	—	2	2	no	—
133	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₃₇	—	2	2	no	—
135	C₂²×C₄×C₃₇	—	2	1	no	—
136	C₂²×C₄×C₃₇	—	2	1	no	—
137	C₂²×C₄×C₃₇	—	2	1	no	—
138	C₂²×C₄×C₃₇	#41	1	2	yes	—
139	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
140	Q₁₆×C₃₇	—	4	4	no	—
141	Q₁₆×C₃₇	—	4	4	no	—
142	Q₁₆×C₃₇	—	4	4	no	—
143	Q₁₆×C₃₇	—	4	4	no	—
144	Q₁₆×C₃₇	—	4	4	no	—
145	SD₁₆×C₃₇	—	4	4	no	—
146	SD₁₆×C₃₇	—	4	4	no	—
147	SD₁₆×C₃₇	—	4	4	no	—
148	SD₁₆×C₃₇	—	4	4	no	—
149	SD₁₆×C₃₇	—	4	4	no	—
150	SD₁₆×C₃₇	—	4	4	no	—
151	D₈×C₃₇	—	4	4	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	4	no	—
157	M₁₆×C₃₇	C₂×D₄	1	4	yes	—
158	M₁₆×C₃₇	C₂×D₄	1	4	yes	—
159	C₂×C₈×C₃₇	—	2	2	no	—
160	C₂×C₈×C₃₇	—	2	2	no	—
161	C₂×C₈×C₃₇	—	2	2	no	—
162	C₂×C₈×C₃₇	—	2	2	no	—
163	C₂×C₈×C₃₇	—	4	4	no	—
164	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
165	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
166	C₂×C₈×C₃₇	C₂×D₄	1	4	yes	—
167	C₄⋊C₄×C₃₇	—	2	2	no	—
168	C₄⋊C₄×C₃₇	—	4	2	no	—
169	C₄⋊C₄×C₃₇	—	4	2	no	—
170	C₂²⋊C₄×C₃₇	—	2	4	no	—
171	C₂²⋊C₄×C₃₇	—	4	2	no	—
172	C₂²⋊C₄×C₃₇	—	4	2	no	—
173	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₃₇	C₂×D₄	1	2	yes	—
176	C₂³×C₃₇	—	2	2	no	—
177	C₂³×C₃₇	—	4	1	no	—
178	C₂³×C₃₇	—	4	2	no	—
179	C₂³×C₃₇	—	8	2	no	—
180	C₂³×C₃₇	C₂×#41	1	1	yes	characteristic
181	Q₈×C₃₇	—	2	2	no	—
182	Q₈×C₃₇	—	2	2	no	—
183	Q₈×C₃₇	—	4	1	no	—
184	Q₈×C₃₇	—	4	1	no	—
185	Q₈×C₃₇	—	4	1	no	—
186	Q₈×C₃₇	—	4	1	no	—
187	Q₈×C₃₇	—	4	1	no	—
188	Q₈×C₃₇	—	4	1	no	—
189	Q₈×C₃₇	—	4	2	no	—
190	Q₈×C₃₇	—	4	2	no	—
191	Q₈×C₃₇	—	4	2	no	—
192	D₄×C₃₇	—	2	2	no	—
193	D₄×C₃₇	—	2	2	no	—
194	D₄×C₃₇	—	4	2	no	—
195	D₄×C₃₇	—	4	2	no	—
196	D₄×C₃₇	—	4	1	no	—
197	D₄×C₃₇	—	4	1	no	—
198	D₄×C₃₇	—	4	2	no	—
199	D₄×C₃₇	—	8	2	no	—
200	C₂×C₄×C₃₇	—	2	2	no	—
201	C₂×C₄×C₃₇	—	4	2	no	—
202	C₂×C₄×C₃₇	—	4	2	no	—
203	C₂×C₄×C₃₇	—	4	2	no	—
204	C₂×C₄×C₃₇	—	4	1	no	—
205	C₂×C₄×C₃₇	—	4	1	no	—
206	C₂×C₄×C₃₇	—	4	1	no	—
207	C₂×C₄×C₃₇	—	4	2	no	—
208	C₂×C₄×C₃₇	—	4	2	no	—
209	C₂×C₄×C₃₇	—	4	2	no	—
210	C₂×C₄×C₃₇	#121	1	2	yes	—
211	C₂×C₄×C₃₇	#121	1	2	yes	—
212	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
214	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
216	C₈×C₃₇	—	2	2	no	—
217	C₈×C₃₇	—	2	4	no	—
218	C₈×C₃₇	—	2	4	no	—
219	C₈×C₃₇	—	4	2	no	—
220	C₈×C₃₇	#127	1	4	yes	—
221	#28499	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₂²×C₃₇	—	2	2	no	—
223	C₂²×C₃₇	—	4	2	no	—
224	C₂²×C₃₇	—	4	4	no	—
225	C₂²×C₃₇	—	8	1	no	—
226	C₂²×C₃₇	—	8	2	no	—
227	C₂²×C₃₇	—	16	2	no	—
228	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
229	C₂²×C₃₇	#550	1	2	yes	—
230	C₄×C₃₇	—	2	2	no	—
231	C₄×C₃₇	—	2	2	no	—
232	C₄×C₃₇	—	4	2	no	—
233	C₄×C₃₇	—	8	1	no	—
234	C₄×C₃₇	—	8	1	no	—
235	C₄×C₃₇	—	8	1	no	—
236	C₄×C₃₇	C₂×#127	1	1	yes	characteristic
237	C₄×C₃₇	#535	1	1	yes	characteristic
238	C₄×C₃₇	D₄²	1	2	yes	—
239	#3153	C₂×C₃₇	1	1	yes	characteristic
240	#3152	C₂×C₃₇	1	1	yes	characteristic, complemented
241	C₂×#497	C₂×C₃₇	1	1	yes	characteristic, complemented
242	C₂×#473	C₂×C₃₇	1	2	yes	complemented
243	C₂×#471	C₂×C₃₇	1	2	yes	complemented
244	#2932	C₂×C₃₇	1	1	yes	characteristic, complemented
245	#2020	C₂×C₃₇	1	2	yes	complemented
246	#2019	C₂×C₃₇	1	2	yes	complemented
247	#1967	C₂×C₃₇	1	1	yes	characteristic, complemented
248	#1966	C₂×C₃₇	1	1	yes	characteristic, complemented
249	#1778	C₂×C₃₇	1	1	yes	characteristic, complemented
250	C₂×C₃₇	—	2	2	no	—
251	C₂×C₃₇	—	8	2	no	—
252	C₂×C₃₇	—	16	1	no	—
253	C₂×C₃₇	#2541	1	1	yes	characteristic
254	C₂×C₃₇	#3069	1	2	yes	—
255	C₂×#137	C₂²×C₃₇	1	2	yes	—
256	C₂×#137	C₂²×C₃₇	1	2	yes	—
257	C₂×#137	C₂²×C₃₇	1	2	yes	—
258	C₂×AGL(1,ℤ/8)	C₂²×C₃₇	1	2	yes	—
259	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
260	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
261	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
262	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
263	C₂×#131	C₂²×C₃₇	1	2	yes	—
264	#532	C₂²×C₃₇	1	1	yes	characteristic
265	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
266	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
267	#497	—	2	1	no	—
268	#497	—	2	2	no	—
269	#497	—	2	4	no	—
270	#496	—	2	1	no	—
271	#495	—	2	2	no	—
272	#494	—	2	1	no	—
273	#492	—	2	1	no	—
274	#473	—	2	8	no	—
275	#471	—	2	8	no	—
276	#435	—	2	4	no	—
277	C₂×#108	C₂²×C₃₇	1	2	yes	—
278	#423	C₂²×C₃₇	1	1	yes	characteristic
279	C₂×#101	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	#408	C₂²×C₃₇	1	2	yes	—
284	C₄×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
285	C₄×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
286	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
287	#341	C₂²×C₃₇	1	2	yes	—
288	C₃₇	#28499	1	1	yes	characteristic, direct product factor, Sylow
289	C₂×#41	C₂³×C₃₇	1	2	yes	—
290	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
291	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
292	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
293	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
294	#137	—	2	4	no	—
295	#137	—	2	4	no	—
296	#137	—	2	4	no	—
297	#137	—	4	2	no	—
298	#137	—	4	2	no	—
299	#137	—	4	2	no	—
300	AGL(1,ℤ/8)	—	2	4	no	—
301	AGL(1,ℤ/8)	—	4	2	no	—
302	C₂×Q₁₆	—	2	2	no	—
303	C₂×Q₁₆	—	2	2	no	—
304	C₂×Q₁₆	—	2	2	no	—
305	C₂×Q₁₆	—	2	4	no	—
306	C₂×Q₁₆	—	2	2	no	—
307	C₂×Q₁₆	—	2	2	no	—
308	C₂×Q₁₆	—	4	2	no	—
309	C₂×SD₁₆	—	2	2	no	—
310	C₂×SD₁₆	—	2	2	no	—
311	C₂×SD₁₆	—	2	2	no	—
312	C₂×SD₁₆	—	2	2	no	—
313	C₂×SD₁₆	—	2	4	no	—
314	C₂×SD₁₆	—	2	2	no	—
315	C₂×SD₁₆	—	2	2	no	—
316	C₂×SD₁₆	—	4	2	no	—
317	C₂×D₈	—	2	2	no	—
318	#131	—	2	4	no	—
319	#131	—	2	4	no	—
320	C₂×M₁₆	—	2	2	no	—
321	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
322	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
323	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
324	C₂²×C₈	—	2	2	no	—
325	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
326	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
327	C₄⋊Q₈	—	2	1	no	—
328	C₄⋊Q₈	—	2	1	no	—
329	C₄⋊Q₈	—	2	2	no	—
330	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
331	#127	D₄×C₃₇	1	1	yes	characteristic
332	#124	—	2	1	no	—
333	#124	—	2	1	no	—
334	#124	—	2	2	no	—
335	#124	D₄×C₃₇	1	2	yes	—
336	#121	—	2	2	no	—
337	C₄×D₄	—	2	2	no	—
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₂²⋊C₄	—	2	2	no	—
340	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
341	#108	D₄×C₃₇	1	8	yes	complemented
342	C₄⋊C₈	—	2	2	no	—
343	#101	—	2	4	no	—
344	#101	—	2	4	no	—
345	#101	—	2	4	no	—
346	#100	—	2	4	no	—
347	C₂²⋊C₈	—	2	4	no	—
348	#97	—	2	1	no	—
349	#97	—	2	1	no	—
350	#97	D₄×C₃₇	1	4	yes	—
351	C₄×C₈	—	2	1	no	—
352	C₄×C₈	—	2	1	no	—
353	C₂⁴	—	2	1	no	—
354	#41	—	2	2	no	—
355	#41	—	2	2	no	—
356	#41	—	2	2	no	—
357	#41	—	2	2	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	#41×C₃₇	1	2	yes	—
383	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
384	Q₁₆	—	4	4	no	—
385	Q₁₆	—	4	4	no	—
386	Q₁₆	—	4	4	no	—
387	Q₁₆	—	4	4	no	—
388	Q₁₆	—	4	4	no	—
389	SD₁₆	—	4	4	no	—
390	SD₁₆	—	4	4	no	—
391	SD₁₆	—	4	4	no	—
392	SD₁₆	—	4	4	no	—
393	SD₁₆	—	4	4	no	—
394	SD₁₆	—	4	4	no	—
395	D₈	—	4	4	no	—
396	M₁₆	—	2	2	no	—
397	M₁₆	—	2	2	no	—
398	M₁₆	—	2	2	no	—
399	M₁₆	—	2	2	no	—
400	M₁₆	—	4	4	no	—
401	M₁₆	C₂×D₄×C₃₇	1	4	yes	—
402	M₁₆	C₂×D₄×C₃₇	1	4	yes	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	4	4	no	—
408	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
409	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
410	C₂×C₈	C₂×D₄×C₃₇	1	4	yes	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	4	2	no	—
413	C₄⋊C₄	—	4	2	no	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	—	4	2	no	—
416	C₂²⋊C₄	—	4	2	no	—
417	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
418	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
419	C₄²	C₂×D₄×C₃₇	1	2	yes	—
420	C₂³	—	2	2	no	—
421	C₂³	—	4	1	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	8	2	no	—
424	C₂³	C₂×#41×C₃₇	1	1	yes	characteristic
425	Q₈	—	2	2	no	—
426	Q₈	—	2	2	no	—
427	Q₈	—	4	1	no	—
428	Q₈	—	4	1	no	—
429	Q₈	—	4	1	no	—
430	Q₈	—	4	1	no	—
431	Q₈	—	4	1	no	—
432	Q₈	—	4	1	no	—
433	Q₈	—	4	2	no	—
434	Q₈	—	4	2	no	—
435	Q₈	—	4	2	no	—
436	D₄	—	2	2	no	—
437	D₄	—	2	2	no	—
438	D₄	—	4	2	no	—
439	D₄	—	4	2	no	—
440	D₄	—	4	1	no	—
441	D₄	—	4	1	no	—
442	D₄	—	4	2	no	—
443	D₄	—	8	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	#121×C₃₇	1	2	yes	—
455	C₂×C₄	#121×C₃₇	1	2	yes	—
456	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
457	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
458	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
459	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
460	C₈	—	2	2	no	—
461	C₈	—	2	4	no	—
462	C₈	—	2	4	no	—
463	C₈	—	4	2	no	—
464	C₈	#127×C₃₇	1	4	yes	—
465	C₂²	—	2	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	4	no	—
468	C₂²	—	8	1	no	—
469	C₂²	—	8	2	no	—
470	C₂²	—	16	2	no	—
471	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
472	C₂²	C₃₇×#550	1	2	yes	—
473	C₄	—	2	2	no	—
474	C₄	—	2	2	no	—
475	C₄	—	4	2	no	—
476	C₄	—	8	1	no	—
477	C₄	—	8	1	no	—
478	C₄	—	8	1	no	—
479	C₄	C₂×#127×C₃₇	1	1	yes	characteristic
480	C₄	C₃₇×#535	1	1	yes	characteristic
481	C₄	D₄²×C₃₇	1	2	yes	—
482	C₂	—	2	2	no	—
483	C₂	—	8	2	no	—
484	C₂	—	16	1	no	—
485	C₂	C₃₇×#2541	1	1	yes	characteristic
486	C₂	C₃₇×#3069	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₃₇×#3153	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
2. C₃₇×#3152	C₂	semidirect
3. C₂×C₃₇×#497	C₂	semidirect
4. C₂×C₃₇×#473	C₂	semidirect
5. C₂×C₃₇×#471	C₂	semidirect
6. C₃₇×#2932	C₂	semidirect
7. C₃₇×#2020	C₂	semidirect
8. C₃₇×#2019	C₂	semidirect
9. C₃₇×#1967	C₂	semidirect
10. C₃₇×#1966	C₂	semidirect
11. C₃₇×#1778	C₂	semidirect
97. #108×C₃₇	D₄	semidirect
221. #28499	C₃₇	direct (N × H)
240. #3152	C₂×C₃₇	semidirect
241. C₂×#497	C₂×C₃₇	semidirect
242. C₂×#473	C₂×C₃₇	semidirect
243. C₂×#471	C₂×C₃₇	semidirect
244. #2932	C₂×C₃₇	semidirect
245. #2020	C₂×C₃₇	semidirect
246. #2019	C₂×C₃₇	semidirect
247. #1967	C₂×C₃₇	semidirect
248. #1966	C₂×C₃₇	semidirect
249. #1778	C₂×C₃₇	semidirect
288. C₃₇	#28499	direct (N × H)
341. #108	D₄×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₃₇×#3153	2
C₃₇×#3152	2
C₂×C₃₇×#497	2
C₂×C₃₇×#473	2
C₂×C₃₇×#471	2
C₃₇×#2932	2
C₃₇×#2020	2
C₃₇×#2019	2
C₃₇×#1967	2
C₃₇×#1966	2
C₃₇×#1778	2
#28499	37

Subgroups — C37×#28499 #22649752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28499 #22649752