Subgroups — C₃₇×#29750 #22651003

Order 9472.

930 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#465	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×#3007	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#3006	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃₇×#408	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2079	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2052	C₂	1	2	yes	maximal, complemented
7	C₃₇×#2051	C₂	1	2	yes	maximal, complemented
8	C₃₇×#2019	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1901	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1900	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1810	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×#137×C₃₇	C₂²	1	2	yes	—
14	C₂×AGL(1,ℤ/8)×C₃₇	C₂²	1	2	yes	—
15	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic, complemented
16	C₂²×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
19	C₂×#121×C₃₇	C₂²	1	1	yes	characteristic
20	C₃₇×#465	—	2	2	no	—
21	C₃₇×#465	—	2	2	no	—
22	C₃₇×#452	—	2	2	no	—
23	C₃₇×#451	—	2	1	no	—
24	C₃₇×#450	—	2	1	no	—
25	C₃₇×#449	—	2	2	no	—
26	C₃₇×#448	—	2	1	no	—
27	C₃₇×#447	—	2	1	no	—
28	C₂×#108×C₃₇	C₂²	1	2	yes	complemented
29	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic, complemented
30	C₃₇×#417	C₂²	1	2	yes	—
31	C₃₇×#417	C₂²	1	2	yes	—
32	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic, complemented
33	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic, complemented
34	C₂×#101×C₃₇	C₂²	1	2	yes	complemented
35	C₂×#100×C₃₇	C₂²	1	2	yes	complemented
36	C₃₇×#408	—	2	2	no	—
37	C₃₇×#408	C₂²	1	2	yes	—
38	C₃₇×#408	C₂²	1	2	yes	—
39	C₃₇×#407	C₂²	1	1	yes	characteristic
40	C₃₇×#407	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊C₈×C₃₇	—	2	2	no	—
42	C₃₇×#343	C₂²	1	2	yes	complemented
43	C₃₇×#343	C₂²	1	2	yes	complemented
44	C₃₇×#341	C₂²	1	2	yes	complemented
45	C₂×#41×C₃₇	—	2	1	no	—
46	C₂×#41×C₃₇	—	2	1	no	—
47	C₂×#41×C₃₇	—	4	2	no	—
48	C₂×#41×C₃₇	—	4	2	no	—
49	C₂×#41×C₃₇	D₄	1	2	yes	—
50	C₂×#41×C₃₇	C₂³	1	2	yes	—
51	C₂²×Q₈×C₃₇	D₄	1	1	yes	characteristic
52	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₃₇	—	2	1	no	—
54	C₂²×D₄×C₃₇	—	2	1	no	—
55	C₂²×D₄×C₃₇	D₄	1	1	yes	characteristic
56	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₃₇	—	2	1	no	—
58	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
59	#137×C₃₇	—	4	2	no	—
60	#137×C₃₇	—	4	2	no	—
61	AGL(1,ℤ/8)×C₃₇	—	4	2	no	—
62	AGL(1,ℤ/8)×C₃₇	—	4	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	—	4	2	no	—
68	C₂×D₈×C₃₇	—	2	2	no	—
69	C₂×M₁₆×C₃₇	—	2	1	no	—
70	C₂×M₁₆×C₃₇	—	4	2	no	—
71	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
72	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
73	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
74	C₂²×C₈×C₃₇	—	2	1	no	—
75	C₂²×C₈×C₃₇	—	4	2	no	—
76	C₂²×C₈×C₃₇	D₄	1	2	yes	—
77	C₂²×C₈×C₃₇	D₄	1	2	yes	—
78	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
80	C₂²⋊Q₈×C₃₇	—	2	1	no	—
81	C₂²⋊Q₈×C₃₇	—	2	1	no	—
82	C₂²⋊Q₈×C₃₇	—	2	1	no	—
83	C₂²⋊Q₈×C₃₇	—	2	1	no	—
84	#121×C₃₇	—	2	1	no	—
85	#121×C₃₇	—	2	1	no	—
86	#121×C₃₇	—	2	1	no	—
87	#121×C₃₇	—	2	1	no	—
88	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
89	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
93	#108×C₃₇	—	4	2	no	—
94	#106×C₃₇	—	2	2	no	—
95	#103×C₃₇	—	2	2	no	—
96	#103×C₃₇	—	2	2	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	#101×C₃₇	—	4	2	no	—
102	#100×C₃₇	—	4	2	no	—
103	C₂²⋊C₈×C₃₇	—	2	1	no	—
104	C₂²⋊C₈×C₃₇	—	2	1	no	—
105	C₂²⋊C₈×C₃₇	—	2	1	no	—
106	C₂²⋊C₈×C₃₇	—	2	1	no	—
107	C₂²⋊C₈×C₃₇	—	2	4	no	—
108	C₂²⋊C₈×C₃₇	—	2	4	no	—
109	C₂⁴×C₃₇	—	2	1	no	—
110	C₂⁴×C₃₇	—	2	1	no	—
111	C₂⁴×C₃₇	#41	1	1	yes	characteristic
112	#41×C₃₇	—	2	2	no	—
113	#41×C₃₇	—	2	2	no	—
114	#41×C₃₇	—	2	2	no	—
115	#41×C₃₇	—	2	2	no	—
116	#41×C₃₇	—	4	2	no	—
117	#41×C₃₇	—	4	2	no	—
118	#41×C₃₇	—	4	4	no	—
119	#41×C₃₇	—	4	2	no	—
120	#41×C₃₇	—	4	2	no	—
121	C₂×Q₈×C₃₇	—	2	1	no	—
122	C₂×Q₈×C₃₇	—	2	1	no	—
123	C₂×Q₈×C₃₇	—	2	1	no	—
124	C₂×Q₈×C₃₇	—	2	2	no	—
125	C₂×Q₈×C₃₇	—	2	2	no	—
126	C₂×Q₈×C₃₇	—	4	2	no	—
127	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
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	1	no	—
133	C₂×D₄×C₃₇	—	2	2	no	—
134	C₂×D₄×C₃₇	—	2	2	no	—
135	C₂×D₄×C₃₇	—	4	2	no	—
136	C₂×D₄×C₃₇	—	4	4	no	—
137	C₂×D₄×C₃₇	—	4	1	no	—
138	C₂×D₄×C₃₇	—	4	1	no	—
139	C₂×D₄×C₃₇	—	8	2	no	—
140	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₃₇	—	2	2	no	—
142	C₂²×C₄×C₃₇	—	2	2	no	—
143	C₂²×C₄×C₃₇	—	2	1	no	—
144	C₂²×C₄×C₃₇	—	2	2	no	—
145	C₂²×C₄×C₃₇	—	2	2	no	—
146	C₂²×C₄×C₃₇	—	2	1	no	—
147	C₂²×C₄×C₃₇	—	2	1	no	—
148	C₂²×C₄×C₃₇	—	2	1	no	—
149	C₂²×C₄×C₃₇	—	4	2	no	—
150	C₂²×C₄×C₃₇	—	4	2	no	—
151	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₃₇	#41	1	1	yes	characteristic
156	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
157	Q₁₆×C₃₇	—	4	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	2	no	—
163	M₁₆×C₃₇	—	2	2	no	—
164	M₁₆×C₃₇	—	2	2	no	—
165	M₁₆×C₃₇	—	2	2	no	—
166	M₁₆×C₃₇	—	2	2	no	—
167	M₁₆×C₃₇	—	2	2	no	—
168	M₁₆×C₃₇	—	4	2	no	—
169	C₂×C₈×C₃₇	—	2	2	no	—
170	C₂×C₈×C₃₇	—	2	2	no	—
171	C₂×C₈×C₃₇	—	2	2	no	—
172	C₂×C₈×C₃₇	—	2	2	no	—
173	C₂×C₈×C₃₇	—	2	2	no	—
174	C₂×C₈×C₃₇	—	4	2	no	—
175	C₂×C₈×C₃₇	—	4	2	no	—
176	C₂×C₈×C₃₇	—	4	2	no	—
177	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
178	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
179	C₄⋊C₄×C₃₇	—	2	1	no	—
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	—	4	1	no	—
184	C₄⋊C₄×C₃₇	—	4	1	no	—
185	C₂²⋊C₄×C₃₇	—	4	1	no	—
186	C₂²⋊C₄×C₃₇	—	4	1	no	—
187	C₂²⋊C₄×C₃₇	—	4	1	no	—
188	C₂²⋊C₄×C₃₇	—	4	1	no	—
189	C₂³×C₃₇	—	2	2	no	—
190	C₂³×C₃₇	—	2	2	no	—
191	C₂³×C₃₇	—	2	2	no	—
192	C₂³×C₃₇	—	4	1	no	—
193	C₂³×C₃₇	—	4	2	no	—
194	C₂³×C₃₇	—	4	2	no	—
195	C₂³×C₃₇	—	4	2	no	—
196	C₂³×C₃₇	—	4	1	no	—
197	C₂³×C₃₇	—	4	2	no	—
198	C₂³×C₃₇	—	8	1	no	—
199	C₂³×C₃₇	—	8	1	no	—
200	C₂³×C₃₇	#121	1	1	yes	characteristic
201	C₂³×C₃₇	#121	1	1	yes	characteristic
202	C₂³×C₃₇	C₂×#41	1	1	yes	characteristic
203	Q₈×C₃₇	—	2	2	no	—
204	Q₈×C₃₇	—	2	2	no	—
205	Q₈×C₃₇	—	4	2	no	—
206	Q₈×C₃₇	—	4	1	no	—
207	Q₈×C₃₇	—	4	2	no	—
208	Q₈×C₃₇	—	4	1	no	—
209	D₄×C₃₇	—	2	2	no	—
210	D₄×C₃₇	—	2	2	no	—
211	D₄×C₃₇	—	4	2	no	—
212	D₄×C₃₇	—	4	4	no	—
213	D₄×C₃₇	—	4	2	no	—
214	D₄×C₃₇	—	4	2	no	—
215	D₄×C₃₇	—	4	2	no	—
216	D₄×C₃₇	—	4	1	no	—
217	D₄×C₃₇	—	4	1	no	—
218	D₄×C₃₇	—	8	2	no	—
219	D₄×C₃₇	—	8	2	no	—
220	C₂×C₄×C₃₇	—	2	2	no	—
221	C₂×C₄×C₃₇	—	2	1	no	—
222	C₂×C₄×C₃₇	—	2	1	no	—
223	C₂×C₄×C₃₇	—	2	2	no	—
224	C₂×C₄×C₃₇	—	2	2	no	—
225	C₂×C₄×C₃₇	—	2	1	no	—
226	C₂×C₄×C₃₇	—	2	1	no	—
227	C₂×C₄×C₃₇	—	2	2	no	—
228	C₂×C₄×C₃₇	—	4	4	no	—
229	C₂×C₄×C₃₇	—	4	2	no	—
230	C₂×C₄×C₃₇	—	4	2	no	—
231	C₂×C₄×C₃₇	—	4	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	—	8	1	no	—
237	C₂×C₄×C₃₇	—	8	1	no	—
238	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
239	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
240	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
243	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
244	C₈×C₃₇	—	2	2	no	—
245	C₈×C₃₇	—	2	2	no	—
246	C₈×C₃₇	—	4	2	no	—
247	C₈×C₃₇	—	4	2	no	—
248	C₈×C₃₇	—	4	2	no	—
249	#29750	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
250	C₂²×C₃₇	—	2	1	no	—
251	C₂²×C₃₇	—	2	1	no	—
252	C₂²×C₃₇	—	2	1	no	—
253	C₂²×C₃₇	—	2	1	no	—
254	C₂²×C₃₇	—	2	1	no	—
255	C₂²×C₃₇	—	2	1	no	—
256	C₂²×C₃₇	—	2	1	no	—
257	C₂²×C₃₇	—	4	4	no	—
258	C₂²×C₃₇	—	4	2	no	—
259	C₂²×C₃₇	—	4	2	no	—
260	C₂²×C₃₇	—	4	2	no	—
261	C₂²×C₃₇	—	8	4	no	—
262	C₂²×C₃₇	—	8	1	no	—
263	C₂²×C₃₇	—	8	1	no	—
264	C₂²×C₃₇	—	8	1	no	—
265	C₂²×C₃₇	—	16	2	no	—
266	C₂²×C₃₇	#471	1	2	yes	—
267	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
268	C₂²×C₃₇	#538	1	2	yes	—
269	C₄×C₃₇	—	2	1	no	—
270	C₄×C₃₇	—	2	1	no	—
271	C₄×C₃₇	—	4	2	no	—
272	C₄×C₃₇	—	8	1	no	—
273	C₄×C₃₇	—	8	1	no	—
274	C₄×C₃₇	—	8	1	no	—
275	C₄×C₃₇	#534	1	1	yes	characteristic
276	C₄×C₃₇	#534	1	2	yes	—
277	C₄×C₃₇	#535	1	1	yes	characteristic
278	C₂×#465	C₂×C₃₇	1	1	yes	characteristic, complemented
279	#3007	C₂×C₃₇	1	1	yes	characteristic, complemented
280	#3006	C₂×C₃₇	1	1	yes	characteristic
281	C₂×#408	C₂×C₃₇	1	1	yes	characteristic, complemented
282	#2079	C₂×C₃₇	1	2	yes	complemented
283	#2052	C₂×C₃₇	1	2	yes	complemented
284	#2051	C₂×C₃₇	1	2	yes	complemented
285	#2019	C₂×C₃₇	1	2	yes	complemented
286	#1901	C₂×C₃₇	1	1	yes	characteristic, complemented
287	#1900	C₂×C₃₇	1	1	yes	characteristic, complemented
288	#1810	C₂×C₃₇	1	1	yes	characteristic, complemented
289	C₂×C₃₇	—	2	2	no	—
290	C₂×C₃₇	—	2	2	no	—
291	C₂×C₃₇	—	4	1	no	—
292	C₂×C₃₇	—	8	2	no	—
293	C₂×C₃₇	—	16	1	no	—
294	C₂×C₃₇	#2617	1	1	yes	characteristic
295	C₂×C₃₇	C₂×#471	1	1	yes	characteristic
296	C₂×C₃₇	#3067	1	1	yes	characteristic
297	C₂²×#41	C₂²×C₃₇	1	1	yes	characteristic
298	C₂×#137	C₂²×C₃₇	1	2	yes	—
299	C₂×AGL(1,ℤ/8)	C₂²×C₃₇	1	2	yes	—
300	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic, complemented
301	C₂²×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
302	C₂³×C₈	C₂²×C₃₇	1	1	yes	characteristic
303	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
304	C₂×#121	C₂²×C₃₇	1	1	yes	characteristic
305	#465	—	2	2	no	—
306	#465	—	2	2	no	—
307	#452	—	2	2	no	—
308	#451	—	2	1	no	—
309	#450	—	2	1	no	—
310	#449	—	2	2	no	—
311	#448	—	2	1	no	—
312	#447	—	2	1	no	—
313	C₂×#108	C₂²×C₃₇	1	2	yes	complemented
314	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic, complemented
315	#417	C₂²×C₃₇	1	2	yes	—
316	#417	C₂²×C₃₇	1	2	yes	—
317	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic, complemented
318	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic, complemented
319	C₂×#101	C₂²×C₃₇	1	2	yes	complemented
320	C₂×#100	C₂²×C₃₇	1	2	yes	complemented
321	#408	—	2	2	no	—
322	#408	C₂²×C₃₇	1	2	yes	—
323	#408	C₂²×C₃₇	1	2	yes	—
324	#407	C₂²×C₃₇	1	1	yes	characteristic
325	#407	C₂²×C₃₇	1	1	yes	characteristic
326	C₂×C₂²⋊C₈	—	2	2	no	—
327	#343	C₂²×C₃₇	1	2	yes	complemented
328	#343	C₂²×C₃₇	1	2	yes	complemented
329	#341	C₂²×C₃₇	1	2	yes	complemented
330	C₃₇	#29750	1	1	yes	characteristic, direct product factor, Sylow
331	C₂×#41	—	2	1	no	—
332	C₂×#41	—	2	1	no	—
333	C₂×#41	—	4	2	no	—
334	C₂×#41	—	4	2	no	—
335	C₂×#41	D₄×C₃₇	1	2	yes	—
336	C₂×#41	C₂³×C₃₇	1	2	yes	—
337	C₂²×Q₈	D₄×C₃₇	1	1	yes	characteristic
338	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
339	C₂²×D₄	—	2	1	no	—
340	C₂²×D₄	—	2	1	no	—
341	C₂²×D₄	D₄×C₃₇	1	1	yes	characteristic
342	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
343	C₂³×C₄	—	2	1	no	—
344	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
345	#137	—	4	2	no	—
346	#137	—	4	2	no	—
347	AGL(1,ℤ/8)	—	4	2	no	—
348	AGL(1,ℤ/8)	—	4	2	no	—
349	C₂×Q₁₆	—	2	2	no	—
350	C₂×SD₁₆	—	2	2	no	—
351	C₂×SD₁₆	—	2	2	no	—
352	C₂×SD₁₆	—	2	2	no	—
353	C₂×SD₁₆	—	4	2	no	—
354	C₂×D₈	—	2	2	no	—
355	C₂×M₁₆	—	2	1	no	—
356	C₂×M₁₆	—	4	2	no	—
357	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
358	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
359	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
360	C₂²×C₈	—	2	1	no	—
361	C₂²×C₈	—	4	2	no	—
362	C₂²×C₈	D₄×C₃₇	1	2	yes	—
363	C₂²×C₈	D₄×C₃₇	1	2	yes	—
364	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
365	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
366	C₂²⋊Q₈	—	2	1	no	—
367	C₂²⋊Q₈	—	2	1	no	—
368	C₂²⋊Q₈	—	2	1	no	—
369	C₂²⋊Q₈	—	2	1	no	—
370	#121	—	2	1	no	—
371	#121	—	2	1	no	—
372	#121	—	2	1	no	—
373	#121	—	2	1	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
376	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	#108	—	4	2	no	—
380	#106	—	2	2	no	—
381	#103	—	2	2	no	—
382	#103	—	2	2	no	—
383	#103	—	2	2	no	—
384	#102	—	2	2	no	—
385	#102	—	2	2	no	—
386	#102	—	2	2	no	—
387	#101	—	4	2	no	—
388	#100	—	4	2	no	—
389	C₂²⋊C₈	—	2	1	no	—
390	C₂²⋊C₈	—	2	1	no	—
391	C₂²⋊C₈	—	2	1	no	—
392	C₂²⋊C₈	—	2	1	no	—
393	C₂²⋊C₈	—	2	4	no	—
394	C₂²⋊C₈	—	2	4	no	—
395	C₂⁴	—	2	1	no	—
396	C₂⁴	—	2	1	no	—
397	C₂⁴	#41×C₃₇	1	1	yes	characteristic
398	#41	—	2	2	no	—
399	#41	—	2	2	no	—
400	#41	—	2	2	no	—
401	#41	—	2	2	no	—
402	#41	—	4	2	no	—
403	#41	—	4	2	no	—
404	#41	—	4	4	no	—
405	#41	—	4	2	no	—
406	#41	—	4	2	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	1	no	—
409	C₂×Q₈	—	2	1	no	—
410	C₂×Q₈	—	2	2	no	—
411	C₂×Q₈	—	2	2	no	—
412	C₂×Q₈	—	4	2	no	—
413	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	—	2	1	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	4	2	no	—
422	C₂×D₄	—	4	4	no	—
423	C₂×D₄	—	4	1	no	—
424	C₂×D₄	—	4	1	no	—
425	C₂×D₄	—	8	2	no	—
426	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	4	2	no	—
436	C₂²×C₄	—	4	2	no	—
437	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
440	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
441	C₂²×C₄	#41×C₃₇	1	1	yes	characteristic
442	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
443	Q₁₆	—	4	4	no	—
444	SD₁₆	—	4	4	no	—
445	SD₁₆	—	4	4	no	—
446	SD₁₆	—	4	4	no	—
447	D₈	—	4	4	no	—
448	M₁₆	—	2	2	no	—
449	M₁₆	—	2	2	no	—
450	M₁₆	—	2	2	no	—
451	M₁₆	—	2	2	no	—
452	M₁₆	—	2	2	no	—
453	M₁₆	—	2	2	no	—
454	M₁₆	—	4	2	no	—
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	—	2	2	no	—
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	—	2	2	no	—
459	C₂×C₈	—	2	2	no	—
460	C₂×C₈	—	4	2	no	—
461	C₂×C₈	—	4	2	no	—
462	C₂×C₈	—	4	2	no	—
463	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
464	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	4	1	no	—
470	C₄⋊C₄	—	4	1	no	—
471	C₂²⋊C₄	—	4	1	no	—
472	C₂²⋊C₄	—	4	1	no	—
473	C₂²⋊C₄	—	4	1	no	—
474	C₂²⋊C₄	—	4	1	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	4	1	no	—
479	C₂³	—	4	2	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	1	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	8	1	no	—
485	C₂³	—	8	1	no	—
486	C₂³	#121×C₃₇	1	1	yes	characteristic
487	C₂³	#121×C₃₇	1	1	yes	characteristic
488	C₂³	C₂×#41×C₃₇	1	1	yes	characteristic
489	Q₈	—	2	2	no	—
490	Q₈	—	2	2	no	—
491	Q₈	—	4	2	no	—
492	Q₈	—	4	1	no	—
493	Q₈	—	4	2	no	—
494	Q₈	—	4	1	no	—
495	D₄	—	2	2	no	—
496	D₄	—	2	2	no	—
497	D₄	—	4	2	no	—
498	D₄	—	4	4	no	—
499	D₄	—	4	2	no	—
500	D₄	—	4	2	no	—
501	D₄	—	4	2	no	—
502	D₄	—	4	1	no	—
503	D₄	—	4	1	no	—
504	D₄	—	8	2	no	—
505	D₄	—	8	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	4	4	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	8	1	no	—
523	C₂×C₄	—	8	1	no	—
524	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
525	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
526	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
527	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
528	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
529	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
530	C₈	—	2	2	no	—
531	C₈	—	2	2	no	—
532	C₈	—	4	2	no	—
533	C₈	—	4	2	no	—
534	C₈	—	4	2	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	4	4	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	2	no	—
546	C₂²	—	8	4	no	—
547	C₂²	—	8	1	no	—
548	C₂²	—	8	1	no	—
549	C₂²	—	8	1	no	—
550	C₂²	—	16	2	no	—
551	C₂²	C₃₇×#471	1	2	yes	—
552	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
553	C₂²	C₃₇×#538	1	2	yes	—
554	C₄	—	2	1	no	—
555	C₄	—	2	1	no	—
556	C₄	—	4	2	no	—
557	C₄	—	8	1	no	—
558	C₄	—	8	1	no	—
559	C₄	—	8	1	no	—
560	C₄	C₃₇×#534	1	1	yes	characteristic
561	C₄	C₃₇×#534	1	2	yes	—
562	C₄	C₃₇×#535	1	1	yes	characteristic
563	C₂	—	2	2	no	—
564	C₂	—	2	2	no	—
565	C₂	—	4	1	no	—
566	C₂	—	8	2	no	—
567	C₂	—	16	1	no	—
568	C₂	C₃₇×#2617	1	1	yes	characteristic
569	C₂	C₂×C₃₇×#471	1	1	yes	characteristic
570	C₂	C₃₇×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₃₇×#3006	C₂
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. C₂×C₃₇×#465	C₂	semidirect
2. C₃₇×#3007	C₂	semidirect
4. C₂×C₃₇×#408	C₂	semidirect
5. C₃₇×#2079	C₂	semidirect
6. C₃₇×#2052	C₂	semidirect
7. C₃₇×#2051	C₂	semidirect
8. C₃₇×#2019	C₂	semidirect
9. C₃₇×#1901	C₂	semidirect
10. C₃₇×#1900	C₂	semidirect
11. C₃₇×#1810	C₂	semidirect
15. C₂²×SD₁₆×C₃₇	C₂²	semidirect
28. C₂×#108×C₃₇	C₂²	semidirect
29. C₂×#106×C₃₇	C₂²	semidirect
32. C₂×#103×C₃₇	C₂²	semidirect
33. C₂×#102×C₃₇	C₂²	semidirect
34. C₂×#101×C₃₇	C₂²	semidirect
35. C₂×#100×C₃₇	C₂²	semidirect
42. C₃₇×#343	C₂²	semidirect
43. C₃₇×#343	C₂²	semidirect
44. C₃₇×#341	C₂²	semidirect
249. #29750	C₃₇	direct (N × H)
278. C₂×#465	C₂×C₃₇	semidirect
279. #3007	C₂×C₃₇	semidirect
281. C₂×#408	C₂×C₃₇	semidirect
282. #2079	C₂×C₃₇	semidirect
283. #2052	C₂×C₃₇	semidirect
284. #2051	C₂×C₃₇	semidirect
285. #2019	C₂×C₃₇	semidirect
286. #1901	C₂×C₃₇	semidirect
287. #1900	C₂×C₃₇	semidirect
288. #1810	C₂×C₃₇	semidirect
300. C₂²×SD₁₆	C₂²×C₃₇	semidirect
313. C₂×#108	C₂²×C₃₇	semidirect
314. C₂×#106	C₂²×C₃₇	semidirect
317. C₂×#103	C₂²×C₃₇	semidirect
318. C₂×#102	C₂²×C₃₇	semidirect
319. C₂×#101	C₂²×C₃₇	semidirect
320. C₂×#100	C₂²×C₃₇	semidirect
327. #343	C₂²×C₃₇	semidirect
328. #343	C₂²×C₃₇	semidirect
329. #341	C₂²×C₃₇	semidirect
330. C₃₇	#29750	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₇×#465	2
C₃₇×#3007	2
C₃₇×#3006	2
C₂×C₃₇×#408	2
C₃₇×#2079	2
C₃₇×#2052	2
C₃₇×#2051	2
C₃₇×#2019	2
C₃₇×#1901	2
C₃₇×#1900	2
C₃₇×#1810	2
#29750	37

Subgroups — C37×#29750 #22651003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#29750 #22651003