Subgroups — C₃₇×#24410 #22645663

Order 9472.

1322 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3586	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×#3043	C₂	1	2	yes	maximal, complemented
3	C₃₇×#3027	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#3010	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2884	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2053	C₂	1	2	yes	maximal, complemented
7	C₃₇×#2008	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1910	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1905	C₂	1	2	yes	maximal, complemented
10	C₃₇×#1868	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1794	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₇×#585	C₂²	1	1	yes	characteristic
13	C₂×2₋¹⁺⁴×C₃₇	C₂²	1	1	yes	characteristic
14	C₃₇×#578	—	2	4	no	—
15	C₃₇×#577	—	2	4	no	—
16	C₃₇×#575	—	2	2	no	—
17	C₃₇×#575	C₂²	1	2	yes	—
18	C₂×#137×C₃₇	—	2	2	no	—
19	C₂×#137×C₃₇	C₂²	1	2	yes	—
20	C₂×AGL(1,ℤ/8)×C₃₇	C₂²	1	1	yes	characteristic, complemented
21	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic, complemented
22	C₃₇×#568	C₂²	1	1	yes	characteristic
23	C₃₇×#535	C₂²	1	1	yes	characteristic
24	C₃₇×#535	C₂²	1	2	yes	—
25	C₃₇×#519	C₂²	1	2	yes	complemented
26	C₃₇×#464	—	2	4	no	—
27	C₃₇×#460	—	2	4	no	—
28	C₃₇×B(4,𝔽₂)	—	2	4	no	—
29	C₃₇×#449	—	2	2	no	—
30	C₃₇×#448	—	2	2	no	—
31	C₃₇×#424	C₂²	1	2	yes	complemented
32	C₃₇×#421	C₂²	1	2	yes	—
33	C₃₇×#419	C₂²	1	1	yes	characteristic, complemented
34	C₃₇×#418	C₂²	1	2	yes	complemented
35	C₃₇×#416	C₂²	1	2	yes	—
36	C₃₇×#416	C₂²	1	1	yes	characteristic, complemented
37	C₃₇×#410	—	2	4	no	—
38	C₃₇×#410	C₂²	1	1	yes	characteristic
39	C₃₇×#410	C₂²	1	2	yes	—
40	C₃₇×#410	C₂²	1	1	yes	characteristic
41	C₃₇×#410	C₂²	1	2	yes	complemented
42	C₃₇×#408	C₂²	1	1	yes	characteristic
43	C₃₇×#344	C₂²	1	2	yes	complemented
44	C₃₇×H(3,ℤ/4)	C₂²	1	2	yes	complemented
45	2₋¹⁺⁴×C₃₇	—	2	4	no	—
46	2₋¹⁺⁴×C₃₇	—	2	2	no	—
47	2₋¹⁺⁴×C₃₇	—	2	1	no	—
48	2₋¹⁺⁴×C₃₇	—	4	2	no	—
49	H(5,𝔽₂)×C₃₇	—	2	2	no	—
50	H(5,𝔽₂)×C₃₇	—	2	2	no	—
51	H(5,𝔽₂)×C₃₇	—	2	1	no	—
52	C₂×#41×C₃₇	—	2	2	no	—
53	C₂×#41×C₃₇	—	2	1	no	—
54	C₂×#41×C₃₇	—	2	2	no	—
55	C₂×#41×C₃₇	—	4	2	no	—
56	C₂×#41×C₃₇	D₄	1	2	yes	complemented
57	C₂×#41×C₃₇	C₂³	1	2	yes	—
58	C₂×#41×C₃₇	C₂³	1	1	yes	characteristic
59	C₂×#41×C₃₇	C₂³	1	1	yes	characteristic
60	C₂²×Q₈×C₃₇	—	2	1	no	—
61	C₂²×Q₈×C₃₇	D₄	1	2	yes	complemented
62	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
64	#137×C₃₇	—	2	8	no	—
65	#137×C₃₇	—	2	4	no	—
66	#137×C₃₇	—	2	2	no	—
67	#137×C₃₇	—	2	4	no	—
68	#137×C₃₇	—	2	4	no	—
69	#137×C₃₇	—	2	2	no	—
70	AGL(1,ℤ/8)×C₃₇	—	2	4	no	—
71	AGL(1,ℤ/8)×C₃₇	—	2	2	no	—
72	AGL(1,ℤ/8)×C₃₇	—	2	2	no	—
73	AGL(1,ℤ/8)×C₃₇	—	4	2	no	—
74	#135×C₃₇	—	2	8	no	—
75	#135×C₃₇	—	2	4	no	—
76	C₂×Q₁₆×C₃₇	—	2	4	no	—
77	C₂×Q₁₆×C₃₇	D₄	1	4	yes	complemented
78	C₂×SD₁₆×C₃₇	—	2	4	no	—
79	C₂×SD₁₆×C₃₇	—	2	2	no	—
80	C₂×SD₁₆×C₃₇	—	2	4	no	—
81	C₂×SD₁₆×C₃₇	—	2	1	no	—
82	C₂×SD₁₆×C₃₇	D₄	1	4	yes	complemented
83	C₂×D₈×C₃₇	—	2	1	no	—
84	#131×C₃₇	—	2	4	no	—
85	C₂×M₁₆×C₃₇	—	2	2	no	—
86	C₂×M₁₆×C₃₇	C₂³	1	1	yes	characteristic
87	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
88	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
89	#127×C₃₇	—	2	2	no	—
90	#127×C₃₇	—	2	1	no	—
91	#124×C₃₇	—	2	2	no	—
92	#124×C₃₇	—	2	1	no	—
93	#121×C₃₇	—	2	2	no	—
94	#121×C₃₇	—	4	2	no	—
95	#120×C₃₇	—	2	2	no	—
96	#120×C₃₇	—	2	4	no	—
97	C₄×Q₈×C₃₇	—	2	4	no	—
98	C₄×Q₈×C₃₇	—	4	2	no	—
99	#117×C₃₇	—	2	4	no	—
100	#117×C₃₇	C₂³	1	2	yes	—
101	#117×C₃₇	C₂³	1	1	yes	characteristic
102	#117×C₃₇	C₂³	1	2	yes	—
103	C₄⋊C₈×C₃₇	—	2	4	no	—
104	#104×C₃₇	—	4	2	no	—
105	#103×C₃₇	—	2	2	no	—
106	#103×C₃₇	—	2	1	no	—
107	#103×C₃₇	—	2	2	no	—
108	#102×C₃₇	—	2	2	no	—
109	#102×C₃₇	—	2	1	no	—
110	#102×C₃₇	—	2	4	no	—
111	#99×C₃₇	—	2	2	no	—
112	#99×C₃₇	—	2	4	no	—
113	#99×C₃₇	—	2	4	no	—
114	#99×C₃₇	D₄	1	4	yes	—
115	C₂²⋊C₈×C₃₇	—	2	2	no	—
116	C₂⁴×C₃₇	—	2	1	no	—
117	#41×C₃₇	—	2	2	no	—
118	#41×C₃₇	—	2	2	no	—
119	#41×C₃₇	—	2	4	no	—
120	#41×C₃₇	—	2	4	no	—
121	#41×C₃₇	—	2	2	no	—
122	#41×C₃₇	—	2	2	no	—
123	#41×C₃₇	—	2	2	no	—
124	#41×C₃₇	—	2	2	no	—
125	#41×C₃₇	—	2	2	no	—
126	#41×C₃₇	—	2	2	no	—
127	#41×C₃₇	—	4	2	no	—
128	#41×C₃₇	—	4	8	no	—
129	#41×C₃₇	—	4	4	no	—
130	#41×C₃₇	—	4	2	no	—
131	#41×C₃₇	—	4	4	no	—
132	#41×C₃₇	—	4	2	no	—
133	#41×C₃₇	—	4	2	no	—
134	#41×C₃₇	—	4	2	no	—
135	C₂×Q₈×C₃₇	—	2	2	no	—
136	C₂×Q₈×C₃₇	—	2	1	no	—
137	C₂×Q₈×C₃₇	—	2	2	no	—
138	C₂×Q₈×C₃₇	—	2	2	no	—
139	C₂×Q₈×C₃₇	—	2	4	no	—
140	C₂×Q₈×C₃₇	—	4	2	no	—
141	C₂×Q₈×C₃₇	—	4	4	no	—
142	C₂×Q₈×C₃₇	—	4	2	no	—
143	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
144	C₂×Q₈×C₃₇	C₂×D₄	1	1	yes	characteristic
145	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
146	C₂×Q₈×C₃₇	C₂×D₄	1	4	yes	—
147	C₂×Q₈×C₃₇	#41	1	1	yes	characteristic
148	C₂×D₄×C₃₇	—	2	2	no	—
149	C₂×D₄×C₃₇	—	2	2	no	—
150	C₂×D₄×C₃₇	—	2	1	no	—
151	C₂×D₄×C₃₇	—	2	2	no	—
152	C₂×D₄×C₃₇	—	2	2	no	—
153	C₂×D₄×C₃₇	—	2	1	no	—
154	C₂×D₄×C₃₇	—	2	1	no	—
155	C₂×D₄×C₃₇	—	2	2	no	—
156	C₂×D₄×C₃₇	—	4	4	no	—
157	C₂×D₄×C₃₇	—	4	2	no	—
158	C₂×D₄×C₃₇	—	4	4	no	—
159	C₂×D₄×C₃₇	—	4	2	no	—
160	C₂×D₄×C₃₇	—	4	2	no	—
161	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
162	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
163	C₂×D₄×C₃₇	C₂×D₄	1	1	yes	characteristic
164	C₂×D₄×C₃₇	#41	1	1	yes	characteristic
165	C₂²×C₄×C₃₇	—	2	1	no	—
166	C₂²×C₄×C₃₇	—	2	2	no	—
167	C₂²×C₄×C₃₇	—	2	2	no	—
168	C₂²×C₄×C₃₇	—	2	1	no	—
169	C₂²×C₄×C₃₇	—	2	2	no	—
170	C₂²×C₄×C₃₇	—	4	2	no	—
171	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
173	Q₁₆×C₃₇	—	2	4	no	—
174	Q₁₆×C₃₇	—	2	8	no	—
175	SD₁₆×C₃₇	—	2	4	no	—
176	SD₁₆×C₃₇	—	2	4	no	—
177	SD₁₆×C₃₇	—	2	8	no	—
178	SD₁₆×C₃₇	—	4	2	no	—
179	SD₁₆×C₃₇	—	4	4	no	—
180	D₈×C₃₇	—	2	4	no	—
181	D₈×C₃₇	—	4	2	no	—
182	M₁₆×C₃₇	—	2	4	no	—
183	M₁₆×C₃₇	—	2	2	no	—
184	M₁₆×C₃₇	—	2	2	no	—
185	M₁₆×C₃₇	—	2	2	no	—
186	C₂×C₈×C₃₇	—	2	4	no	—
187	C₂×C₈×C₃₇	—	2	1	no	—
188	C₂×C₈×C₃₇	—	2	1	no	—
189	C₂×C₈×C₃₇	—	2	2	no	—
190	C₂×C₈×C₃₇	C₂×D₄	1	4	yes	—
191	C₄⋊C₄×C₃₇	—	2	2	no	—
192	C₄⋊C₄×C₃₇	—	2	2	no	—
193	C₄⋊C₄×C₃₇	—	2	1	no	—
194	C₄⋊C₄×C₃₇	—	4	4	no	—
195	C₂²⋊C₄×C₃₇	—	2	2	no	—
196	C₂²⋊C₄×C₃₇	—	2	1	no	—
197	C₂²⋊C₄×C₃₇	—	4	4	no	—
198	C₂²⋊C₄×C₃₇	—	4	2	no	—
199	C₂²⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
200	C₄²×C₃₇	—	2	2	no	—
201	C₄²×C₃₇	—	2	1	no	—
202	C₄²×C₃₇	—	2	2	no	—
203	C₄²×C₃₇	—	4	4	no	—
204	C₂³×C₃₇	—	2	1	no	—
205	C₂³×C₃₇	—	2	2	no	—
206	C₂³×C₃₇	—	4	2	no	—
207	C₂³×C₃₇	—	4	1	no	—
208	C₂³×C₃₇	—	4	2	no	—
209	C₂³×C₃₇	—	16	1	no	—
210	C₂³×C₃₇	#121	1	2	yes	—
211	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
212	Q₈×C₃₇	—	2	2	no	—
213	Q₈×C₃₇	—	2	4	no	—
214	Q₈×C₃₇	—	2	2	no	—
215	Q₈×C₃₇	—	2	1	no	—
216	Q₈×C₃₇	—	2	2	no	—
217	Q₈×C₃₇	—	2	1	no	—
218	Q₈×C₃₇	—	2	2	no	—
219	Q₈×C₃₇	—	4	4	no	—
220	Q₈×C₃₇	—	4	2	no	—
221	Q₈×C₃₇	#120	1	4	yes	—
222	D₄×C₃₇	—	2	4	no	—
223	D₄×C₃₇	—	2	1	no	—
224	D₄×C₃₇	—	2	2	no	—
225	D₄×C₃₇	—	2	1	no	—
226	D₄×C₃₇	—	2	2	no	—
227	D₄×C₃₇	—	2	2	no	—
228	D₄×C₃₇	—	4	4	no	—
229	D₄×C₃₇	—	4	2	no	—
230	D₄×C₃₇	—	4	4	no	—
231	D₄×C₃₇	—	4	2	no	—
232	D₄×C₃₇	—	4	2	no	—
233	D₄×C₃₇	—	4	2	no	—
234	D₄×C₃₇	—	4	1	no	—
235	D₄×C₃₇	—	4	1	no	—
236	D₄×C₃₇	—	4	2	no	—
237	D₄×C₃₇	—	16	4	no	—
238	D₄×C₃₇	—	16	2	no	—
239	C₂×C₄×C₃₇	—	2	2	no	—
240	C₂×C₄×C₃₇	—	2	4	no	—
241	C₂×C₄×C₃₇	—	2	2	no	—
242	C₂×C₄×C₃₇	—	2	2	no	—
243	C₂×C₄×C₃₇	—	2	1	no	—
244	C₂×C₄×C₃₇	—	2	4	no	—
245	C₂×C₄×C₃₇	—	2	2	no	—
246	C₂×C₄×C₃₇	—	4	4	no	—
247	C₂×C₄×C₃₇	—	4	4	no	—
248	C₂×C₄×C₃₇	—	4	4	no	—
249	C₂×C₄×C₃₇	—	4	2	no	—
250	C₂×C₄×C₃₇	—	4	2	no	—
251	C₂×C₄×C₃₇	—	4	2	no	—
252	C₂×C₄×C₃₇	—	4	2	no	—
253	C₂×C₄×C₃₇	—	4	1	no	—
254	C₂×C₄×C₃₇	—	4	2	no	—
255	C₂×C₄×C₃₇	#121	1	2	yes	—
256	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
258	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
259	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
260	C₈×C₃₇	—	2	4	no	—
261	C₈×C₃₇	—	4	1	no	—
262	C₈×C₃₇	—	4	1	no	—
263	#24410	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
264	C₂²×C₃₇	—	2	2	no	—
265	C₂²×C₃₇	—	4	1	no	—
266	C₂²×C₃₇	—	4	2	no	—
267	C₂²×C₃₇	—	4	1	no	—
268	C₂²×C₃₇	—	4	2	no	—
269	C₂²×C₃₇	—	8	2	no	—
270	C₂²×C₃₇	—	8	1	no	—
271	C₂²×C₃₇	—	8	4	no	—
272	C₂²×C₃₇	—	8	2	no	—
273	C₂²×C₃₇	—	8	1	no	—
274	C₂²×C₃₇	—	16	2	no	—
275	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
276	C₂²×C₃₇	D₄²	1	2	yes	—
277	C₄×C₃₇	—	2	4	no	—
278	C₄×C₃₇	—	2	2	no	—
279	C₄×C₃₇	—	4	4	no	—
280	C₄×C₃₇	—	4	2	no	—
281	C₄×C₃₇	—	4	1	no	—
282	C₄×C₃₇	—	8	2	no	—
283	C₄×C₃₇	—	8	1	no	—
284	C₄×C₃₇	C₂×#120	1	1	yes	characteristic
285	C₄×C₃₇	#534	1	1	yes	characteristic
286	C₄×C₃₇	#546	1	2	yes	—
287	#3586	C₂×C₃₇	1	1	yes	characteristic, complemented
288	#3043	C₂×C₃₇	1	2	yes	complemented
289	#3027	C₂×C₃₇	1	1	yes	characteristic, complemented
290	#3010	C₂×C₃₇	1	1	yes	characteristic, complemented
291	#2884	C₂×C₃₇	1	1	yes	characteristic, complemented
292	#2053	C₂×C₃₇	1	2	yes	complemented
293	#2008	C₂×C₃₇	1	2	yes	complemented
294	#1910	C₂×C₃₇	1	1	yes	characteristic, complemented
295	#1905	C₂×C₃₇	1	2	yes	complemented
296	#1868	C₂×C₃₇	1	1	yes	characteristic, complemented
297	#1794	C₂×C₃₇	1	1	yes	characteristic, complemented
298	C₂×C₃₇	—	2	2	no	—
299	C₂×C₃₇	—	2	1	no	—
300	C₂×C₃₇	—	4	2	no	—
301	C₂×C₃₇	—	8	1	no	—
302	C₂×C₃₇	—	8	2	no	—
303	C₂×C₃₇	—	16	1	no	—
304	C₂×C₃₇	#2410	1	1	yes	characteristic
305	#585	C₂²×C₃₇	1	1	yes	characteristic
306	C₂×2₋¹⁺⁴	C₂²×C₃₇	1	1	yes	characteristic
307	#578	—	2	4	no	—
308	#577	—	2	4	no	—
309	#575	—	2	2	no	—
310	#575	C₂²×C₃₇	1	2	yes	—
311	C₂×#137	—	2	2	no	—
312	C₂×#137	C₂²×C₃₇	1	2	yes	—
313	C₂×AGL(1,ℤ/8)	C₂²×C₃₇	1	1	yes	characteristic, complemented
314	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic, complemented
315	#568	C₂²×C₃₇	1	1	yes	characteristic
316	#535	C₂²×C₃₇	1	1	yes	characteristic
317	#535	C₂²×C₃₇	1	2	yes	—
318	#519	C₂²×C₃₇	1	2	yes	complemented
319	#464	—	2	4	no	—
320	#460	—	2	4	no	—
321	B(4,𝔽₂)	—	2	4	no	—
322	#449	—	2	2	no	—
323	#448	—	2	2	no	—
324	#424	C₂²×C₃₇	1	2	yes	complemented
325	#421	C₂²×C₃₇	1	2	yes	—
326	#419	C₂²×C₃₇	1	1	yes	characteristic, complemented
327	#418	C₂²×C₃₇	1	2	yes	complemented
328	#416	C₂²×C₃₇	1	2	yes	—
329	#416	C₂²×C₃₇	1	1	yes	characteristic, complemented
330	#410	—	2	4	no	—
331	#410	C₂²×C₃₇	1	1	yes	characteristic
332	#410	C₂²×C₃₇	1	2	yes	—
333	#410	C₂²×C₃₇	1	1	yes	characteristic
334	#410	C₂²×C₃₇	1	2	yes	complemented
335	#408	C₂²×C₃₇	1	1	yes	characteristic
336	#344	C₂²×C₃₇	1	2	yes	complemented
337	H(3,ℤ/4)	C₂²×C₃₇	1	2	yes	complemented
338	C₃₇	#24410	1	1	yes	characteristic, direct product factor, Sylow
339	2₋¹⁺⁴	—	2	4	no	—
340	2₋¹⁺⁴	—	2	2	no	—
341	2₋¹⁺⁴	—	2	1	no	—
342	2₋¹⁺⁴	—	4	2	no	—
343	H(5,𝔽₂)	—	2	2	no	—
344	H(5,𝔽₂)	—	2	2	no	—
345	H(5,𝔽₂)	—	2	1	no	—
346	C₂×#41	—	2	2	no	—
347	C₂×#41	—	2	1	no	—
348	C₂×#41	—	2	2	no	—
349	C₂×#41	—	4	2	no	—
350	C₂×#41	D₄×C₃₇	1	2	yes	complemented
351	C₂×#41	C₂³×C₃₇	1	2	yes	—
352	C₂×#41	C₂³×C₃₇	1	1	yes	characteristic
353	C₂×#41	C₂³×C₃₇	1	1	yes	characteristic
354	C₂²×Q₈	—	2	1	no	—
355	C₂²×Q₈	D₄×C₃₇	1	2	yes	complemented
356	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
357	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
358	#137	—	2	8	no	—
359	#137	—	2	4	no	—
360	#137	—	2	2	no	—
361	#137	—	2	4	no	—
362	#137	—	2	4	no	—
363	#137	—	2	2	no	—
364	AGL(1,ℤ/8)	—	2	4	no	—
365	AGL(1,ℤ/8)	—	2	2	no	—
366	AGL(1,ℤ/8)	—	2	2	no	—
367	AGL(1,ℤ/8)	—	4	2	no	—
368	#135	—	2	8	no	—
369	#135	—	2	4	no	—
370	C₂×Q₁₆	—	2	4	no	—
371	C₂×Q₁₆	D₄×C₃₇	1	4	yes	complemented
372	C₂×SD₁₆	—	2	4	no	—
373	C₂×SD₁₆	—	2	2	no	—
374	C₂×SD₁₆	—	2	4	no	—
375	C₂×SD₁₆	—	2	1	no	—
376	C₂×SD₁₆	D₄×C₃₇	1	4	yes	complemented
377	C₂×D₈	—	2	1	no	—
378	#131	—	2	4	no	—
379	C₂×M₁₆	—	2	2	no	—
380	C₂×M₁₆	C₂³×C₃₇	1	1	yes	characteristic
381	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
382	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
383	#127	—	2	2	no	—
384	#127	—	2	1	no	—
385	#124	—	2	2	no	—
386	#124	—	2	1	no	—
387	#121	—	2	2	no	—
388	#121	—	4	2	no	—
389	#120	—	2	2	no	—
390	#120	—	2	4	no	—
391	C₄×Q₈	—	2	4	no	—
392	C₄×Q₈	—	4	2	no	—
393	#117	—	2	4	no	—
394	#117	C₂³×C₃₇	1	2	yes	—
395	#117	C₂³×C₃₇	1	1	yes	characteristic
396	#117	C₂³×C₃₇	1	2	yes	—
397	C₄⋊C₈	—	2	4	no	—
398	#104	—	4	2	no	—
399	#103	—	2	2	no	—
400	#103	—	2	1	no	—
401	#103	—	2	2	no	—
402	#102	—	2	2	no	—
403	#102	—	2	1	no	—
404	#102	—	2	4	no	—
405	#99	—	2	2	no	—
406	#99	—	2	4	no	—
407	#99	—	2	4	no	—
408	#99	D₄×C₃₇	1	4	yes	—
409	C₂²⋊C₈	—	2	2	no	—
410	C₂⁴	—	2	1	no	—
411	#41	—	2	2	no	—
412	#41	—	2	2	no	—
413	#41	—	2	4	no	—
414	#41	—	2	4	no	—
415	#41	—	2	2	no	—
416	#41	—	2	2	no	—
417	#41	—	2	2	no	—
418	#41	—	2	2	no	—
419	#41	—	2	2	no	—
420	#41	—	2	2	no	—
421	#41	—	4	2	no	—
422	#41	—	4	8	no	—
423	#41	—	4	4	no	—
424	#41	—	4	2	no	—
425	#41	—	4	4	no	—
426	#41	—	4	2	no	—
427	#41	—	4	2	no	—
428	#41	—	4	2	no	—
429	C₂×Q₈	—	2	2	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	2	2	no	—
432	C₂×Q₈	—	2	2	no	—
433	C₂×Q₈	—	2	4	no	—
434	C₂×Q₈	—	4	2	no	—
435	C₂×Q₈	—	4	4	no	—
436	C₂×Q₈	—	4	2	no	—
437	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
438	C₂×Q₈	C₂×D₄×C₃₇	1	1	yes	characteristic
439	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
440	C₂×Q₈	C₂×D₄×C₃₇	1	4	yes	—
441	C₂×Q₈	#41×C₃₇	1	1	yes	characteristic
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	4	4	no	—
451	C₂×D₄	—	4	2	no	—
452	C₂×D₄	—	4	4	no	—
453	C₂×D₄	—	4	2	no	—
454	C₂×D₄	—	4	2	no	—
455	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
456	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
457	C₂×D₄	C₂×D₄×C₃₇	1	1	yes	characteristic
458	C₂×D₄	#41×C₃₇	1	1	yes	characteristic
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	4	2	no	—
465	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
466	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
467	Q₁₆	—	2	4	no	—
468	Q₁₆	—	2	8	no	—
469	SD₁₆	—	2	4	no	—
470	SD₁₆	—	2	4	no	—
471	SD₁₆	—	2	8	no	—
472	SD₁₆	—	4	2	no	—
473	SD₁₆	—	4	4	no	—
474	D₈	—	2	4	no	—
475	D₈	—	4	2	no	—
476	M₁₆	—	2	4	no	—
477	M₁₆	—	2	2	no	—
478	M₁₆	—	2	2	no	—
479	M₁₆	—	2	2	no	—
480	C₂×C₈	—	2	4	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	2	no	—
484	C₂×C₈	C₂×D₄×C₃₇	1	4	yes	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	4	4	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	2	1	no	—
491	C₂²⋊C₄	—	4	4	no	—
492	C₂²⋊C₄	—	4	2	no	—
493	C₂²⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
494	C₄²	—	2	2	no	—
495	C₄²	—	2	1	no	—
496	C₄²	—	2	2	no	—
497	C₄²	—	4	4	no	—
498	C₂³	—	2	1	no	—
499	C₂³	—	2	2	no	—
500	C₂³	—	4	2	no	—
501	C₂³	—	4	1	no	—
502	C₂³	—	4	2	no	—
503	C₂³	—	16	1	no	—
504	C₂³	#121×C₃₇	1	2	yes	—
505	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
506	Q₈	—	2	2	no	—
507	Q₈	—	2	4	no	—
508	Q₈	—	2	2	no	—
509	Q₈	—	2	1	no	—
510	Q₈	—	2	2	no	—
511	Q₈	—	2	1	no	—
512	Q₈	—	2	2	no	—
513	Q₈	—	4	4	no	—
514	Q₈	—	4	2	no	—
515	Q₈	#120×C₃₇	1	4	yes	—
516	D₄	—	2	4	no	—
517	D₄	—	2	1	no	—
518	D₄	—	2	2	no	—
519	D₄	—	2	1	no	—
520	D₄	—	2	2	no	—
521	D₄	—	2	2	no	—
522	D₄	—	4	4	no	—
523	D₄	—	4	2	no	—
524	D₄	—	4	4	no	—
525	D₄	—	4	2	no	—
526	D₄	—	4	2	no	—
527	D₄	—	4	2	no	—
528	D₄	—	4	1	no	—
529	D₄	—	4	1	no	—
530	D₄	—	4	2	no	—
531	D₄	—	16	4	no	—
532	D₄	—	16	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	4	4	no	—
541	C₂×C₄	—	4	4	no	—
542	C₂×C₄	—	4	4	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	#121×C₃₇	1	2	yes	—
550	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
551	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
552	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
553	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
554	C₈	—	2	4	no	—
555	C₈	—	4	1	no	—
556	C₈	—	4	1	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	2	no	—
562	C₂²	—	8	2	no	—
563	C₂²	—	8	1	no	—
564	C₂²	—	8	4	no	—
565	C₂²	—	8	2	no	—
566	C₂²	—	8	1	no	—
567	C₂²	—	16	2	no	—
568	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
569	C₂²	D₄²×C₃₇	1	2	yes	—
570	C₄	—	2	4	no	—
571	C₄	—	2	2	no	—
572	C₄	—	4	4	no	—
573	C₄	—	4	2	no	—
574	C₄	—	4	1	no	—
575	C₄	—	8	1	no	—
576	C₄	—	8	2	no	—
577	C₄	C₂×#120×C₃₇	1	1	yes	characteristic
578	C₄	C₃₇×#534	1	1	yes	characteristic
579	C₄	C₃₇×#546	1	2	yes	—
580	C₂	—	2	2	no	—
581	C₂	—	2	1	no	—
582	C₂	—	4	2	no	—
583	C₂	—	8	2	no	—
584	C₂	—	8	1	no	—
585	C₂	—	16	1	no	—
586	C₂	C₃₇×#2410	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃₇	#2410
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₇ ◁ C₂²×C₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×#3586	C₂	semidirect
2. C₃₇×#3043	C₂	semidirect
3. C₃₇×#3027	C₂	semidirect
4. C₃₇×#3010	C₂	semidirect
5. C₃₇×#2884	C₂	semidirect
6. C₃₇×#2053	C₂	semidirect
7. C₃₇×#2008	C₂	semidirect
8. C₃₇×#1910	C₂	semidirect
9. C₃₇×#1905	C₂	semidirect
10. C₃₇×#1868	C₂	semidirect
11. C₃₇×#1794	C₂	semidirect
20. C₂×AGL(1,ℤ/8)×C₃₇	C₂²	semidirect
21. C₂²×SD₁₆×C₃₇	C₂²	semidirect
25. C₃₇×#519	C₂²	semidirect
31. C₃₇×#424	C₂²	semidirect
33. C₃₇×#419	C₂²	semidirect
34. C₃₇×#418	C₂²	semidirect
36. C₃₇×#416	C₂²	semidirect
41. C₃₇×#410	C₂²	semidirect
43. C₃₇×#344	C₂²	semidirect
44. C₃₇×H(3,ℤ/4)	C₂²	semidirect
56. C₂×#41×C₃₇	D₄	semidirect
61. C₂²×Q₈×C₃₇	D₄	semidirect
77. C₂×Q₁₆×C₃₇	D₄	semidirect
82. C₂×SD₁₆×C₃₇	D₄	semidirect
263. #24410	C₃₇	direct (N × H)
287. #3586	C₂×C₃₇	semidirect
288. #3043	C₂×C₃₇	semidirect
289. #3027	C₂×C₃₇	semidirect
290. #3010	C₂×C₃₇	semidirect
291. #2884	C₂×C₃₇	semidirect
292. #2053	C₂×C₃₇	semidirect
293. #2008	C₂×C₃₇	semidirect
294. #1910	C₂×C₃₇	semidirect
295. #1905	C₂×C₃₇	semidirect
296. #1868	C₂×C₃₇	semidirect
297. #1794	C₂×C₃₇	semidirect
313. C₂×AGL(1,ℤ/8)	C₂²×C₃₇	semidirect
314. C₂²×SD₁₆	C₂²×C₃₇	semidirect
318. #519	C₂²×C₃₇	semidirect
324. #424	C₂²×C₃₇	semidirect
326. #419	C₂²×C₃₇	semidirect
327. #418	C₂²×C₃₇	semidirect
329. #416	C₂²×C₃₇	semidirect
334. #410	C₂²×C₃₇	semidirect
336. #344	C₂²×C₃₇	semidirect
337. H(3,ℤ/4)	C₂²×C₃₇	semidirect
338. C₃₇	#24410	direct (N × H)
350. C₂×#41	D₄×C₃₇	semidirect
355. C₂²×Q₈	D₄×C₃₇	semidirect
371. C₂×Q₁₆	D₄×C₃₇	semidirect
376. 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
C₃₇×#3586	2
C₃₇×#3043	2
C₃₇×#3027	2
C₃₇×#3010	2
C₃₇×#2884	2
C₃₇×#2053	2
C₃₇×#2008	2
C₃₇×#1910	2
C₃₇×#1905	2
C₃₇×#1868	2
C₃₇×#1794	2
#24410	37

Subgroups — C37×#24410 #22645663

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#24410 #22645663