Subgroups — C₃₇×#18888 #22640141

Order 9472.

964 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×#3245	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#3227	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#3035	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#1654	C₂	1	2	yes	maximal, complemented
6	C₃₇×#1652	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1628	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1625	C₂	1	2	yes	maximal, complemented
9	C₂×C₃₇×#332	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1480	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1477	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₃₇	—	2	1	no	—
13	C₃₇×#556	C₂²	1	2	yes	—
14	C₃₇×#555	—	2	1	no	—
15	C₃₇×#554	—	2	1	no	—
16	C₃₇×#553	—	2	2	no	—
17	C₃₇×#548	—	2	2	no	—
18	C₃₇×#547	C₂²	1	2	yes	—
19	C₃₇×#542	—	2	2	no	—
20	C₃₇×#537	—	2	1	no	—
21	C₃₇×#533	—	2	1	no	—
22	C₃₇×#532	—	2	1	no	—
23	C₃₇×#532	C₂²	1	1	yes	characteristic
24	C₃₇×#532	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
26	C₃₇×#520	—	2	1	no	—
27	C₄×#41×C₃₇	C₂²	1	1	yes	characteristic
28	C₃₇×#498	C₂²	1	2	yes	—
29	C₃₇×#486	C₂²	1	2	yes	—
30	C₃₇×#481	—	2	2	no	—
31	C₃₇×#476	—	2	2	no	—
32	C₃₇×#474	—	2	1	no	—
33	C₃₇×#474	C₂²	1	2	yes	—
34	C₃₇×#466	—	2	2	no	—
35	C₃₇×#464	—	2	1	no	—
36	C₃₇×#463	—	2	1	no	—
37	C₃₇×#462	C₂²	1	1	yes	characteristic
38	C₃₇×#461	C₂²	1	1	yes	characteristic
39	C₃₇×#460	C₂²	1	1	yes	characteristic
40	C₃₇×#459	—	2	1	no	—
41	C₃₇×#459	C₂²	1	1	yes	characteristic
42	C₃₇×#459	C₂²	1	2	yes	—
43	C₃₇×#431	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
46	C₃₇×#416	—	2	1	no	—
47	C₃₇×#332	C₂²	1	2	yes	—
48	C₃₇×#332	C₂²	1	2	yes	—
49	C₃₇×Q₈⋊C₈	C₂²	1	2	yes	—
50	C₃₇×D₄⋊C₈	C₂²	1	2	yes	—
51	C₃₇×D₄⋊C₈	C₂²	1	2	yes	—
52	C₃₇×D₄⋊C₈	C₂²	1	2	yes	—
53	C₂×#41×C₃₇	—	2	2	no	—
54	C₂×#41×C₃₇	—	2	1	no	—
55	C₂×#41×C₃₇	—	2	1	no	—
56	C₂×#41×C₃₇	D₄	1	1	yes	characteristic
57	C₂²×Q₈×C₃₇	—	2	1	no	—
58	#135×C₃₇	—	4	4	no	—
59	C₂×Q₁₆×C₃₇	—	2	1	no	—
60	C₂×SD₁₆×C₃₇	—	2	1	no	—
61	C₂×SD₁₆×C₃₇	—	2	1	no	—
62	C₂×D₈×C₃₇	—	2	1	no	—
63	C₂×D₈×C₃₇	—	2	2	no	—
64	C₂²×C₈×C₃₇	—	2	1	no	—
65	C₂²×C₈×C₃₇	—	2	1	no	—
66	C₄⋊Q₈×C₃₇	—	2	1	no	—
67	C₄⋊Q₈×C₃₇	—	2	1	no	—
68	C₄⋊Q₈×C₃₇	D₄	1	2	yes	—
69	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
70	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
71	C₄⋊Q₈×C₃₇	C₂³	1	2	yes	—
72	#127×C₃₇	D₄	1	1	yes	characteristic
73	#127×C₃₇	C₂³	1	1	yes	characteristic
74	#126×C₃₇	—	2	4	no	—
75	#125×C₃₇	—	2	2	no	—
76	#124×C₃₇	—	2	4	no	—
77	#124×C₃₇	—	2	2	no	—
78	#124×C₃₇	—	2	1	no	—
79	#124×C₃₇	—	2	1	no	—
80	#123×C₃₇	—	2	4	no	—
81	C₂²⋊Q₈×C₃₇	—	2	2	no	—
82	C₂²⋊Q₈×C₃₇	—	2	4	no	—
83	C₂²⋊Q₈×C₃₇	—	2	2	no	—
84	C₂²⋊Q₈×C₃₇	—	2	2	no	—
85	#121×C₃₇	—	2	2	no	—
86	#121×C₃₇	—	2	2	no	—
87	#121×C₃₇	—	2	4	no	—
88	#121×C₃₇	—	2	2	no	—
89	#121×C₃₇	—	2	1	no	—
90	#121×C₃₇	—	2	1	no	—
91	#121×C₃₇	—	2	1	no	—
92	#121×C₃₇	D₄	1	2	yes	—
93	C₄×Q₈×C₃₇	—	2	2	no	—
94	C₄×Q₈×C₃₇	—	2	2	no	—
95	C₄×Q₈×C₃₇	D₄	1	1	yes	characteristic
96	C₄×Q₈×C₃₇	C₂³	1	1	yes	characteristic
97	C₄×D₄×C₃₇	—	2	2	no	—
98	C₄×D₄×C₃₇	—	2	4	no	—
99	C₄×D₄×C₃₇	—	2	2	no	—
100	C₄×D₄×C₃₇	—	2	1	no	—
101	C₄×D₄×C₃₇	—	2	1	no	—
102	C₄×D₄×C₃₇	—	2	1	no	—
103	C₄×D₄×C₃₇	—	2	1	no	—
104	C₄×D₄×C₃₇	—	2	1	no	—
105	C₄×D₄×C₃₇	D₄	1	1	yes	characteristic
106	C₄×D₄×C₃₇	C₂³	1	2	yes	—
107	C₄×D₄×C₃₇	C₂³	1	1	yes	characteristic
108	#117×C₃₇	—	2	2	no	—
109	#117×C₃₇	—	2	2	no	—
110	#117×C₃₇	—	2	1	no	—
111	#117×C₃₇	D₄	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
113	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
114	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
115	C₂×C₄²×C₃₇	—	2	1	no	—
116	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
117	#107×C₃₇	—	2	2	no	—
118	#106×C₃₇	—	2	4	no	—
119	C₄⋊C₈×C₃₇	—	2	1	no	—
120	C₄⋊C₈×C₃₇	—	2	1	no	—
121	C₄⋊C₈×C₃₇	—	2	1	no	—
122	C₄⋊C₈×C₃₇	C₂³	1	1	yes	characteristic
123	C₄⋊C₈×C₃₇	C₂³	1	1	yes	characteristic
124	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
125	#103×C₃₇	—	2	1	no	—
126	#103×C₃₇	—	2	1	no	—
127	#102×C₃₇	—	2	2	no	—
128	#102×C₃₇	—	2	1	no	—
129	#102×C₃₇	—	2	1	no	—
130	#102×C₃₇	—	2	2	no	—
131	#102×C₃₇	—	2	4	no	—
132	C₂²⋊C₈×C₃₇	—	2	1	no	—
133	C₄×C₈×C₃₇	C₂³	1	2	yes	—
134	#41×C₃₇	—	2	2	no	—
135	#41×C₃₇	—	2	2	no	—
136	#41×C₃₇	—	4	2	no	—
137	#41×C₃₇	—	4	2	no	—
138	#41×C₃₇	—	4	2	no	—
139	#41×C₃₇	—	4	2	no	—
140	#41×C₃₇	—	8	2	no	—
141	#41×C₃₇	—	8	2	no	—
142	C₂×Q₈×C₃₇	—	2	1	no	—
143	C₂×Q₈×C₃₇	—	2	2	no	—
144	C₂×Q₈×C₃₇	—	2	2	no	—
145	C₂×Q₈×C₃₇	—	2	1	no	—
146	C₂×Q₈×C₃₇	—	8	1	no	—
147	C₂×Q₈×C₃₇	—	8	1	no	—
148	C₂×Q₈×C₃₇	C₂×D₄	1	1	yes	characteristic
149	C₂×D₄×C₃₇	—	2	1	no	—
150	C₂×D₄×C₃₇	—	2	2	no	—
151	C₂×D₄×C₃₇	—	2	4	no	—
152	C₂×D₄×C₃₇	—	2	1	no	—
153	C₂×D₄×C₃₇	—	2	1	no	—
154	C₂×D₄×C₃₇	—	2	1	no	—
155	C₂×D₄×C₃₇	—	2	1	no	—
156	C₂×D₄×C₃₇	—	2	1	no	—
157	C₂×D₄×C₃₇	—	4	1	no	—
158	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
159	C₂×D₄×C₃₇	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₃₇	—	2	4	no	—
161	C₂²×C₄×C₃₇	—	2	2	no	—
162	C₂²×C₄×C₃₇	—	2	1	no	—
163	C₂²×C₄×C₃₇	—	2	1	no	—
164	C₂²×C₄×C₃₇	—	2	1	no	—
165	C₂²×C₄×C₃₇	—	2	2	no	—
166	C₂²×C₄×C₃₇	—	4	1	no	—
167	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
170	Q₁₆×C₃₇	—	4	2	no	—
171	SD₁₆×C₃₇	—	4	2	no	—
172	SD₁₆×C₃₇	—	4	2	no	—
173	D₈×C₃₇	—	4	2	no	—
174	D₈×C₃₇	—	8	2	no	—
175	C₂×C₈×C₃₇	—	2	2	no	—
176	C₂×C₈×C₃₇	—	2	2	no	—
177	C₂×C₈×C₃₇	—	2	1	no	—
178	C₂×C₈×C₃₇	—	2	1	no	—
179	C₂×C₈×C₃₇	—	4	2	no	—
180	C₂×C₈×C₃₇	—	8	1	no	—
181	C₄⋊C₄×C₃₇	—	2	4	no	—
182	C₄⋊C₄×C₃₇	—	2	4	no	—
183	C₄⋊C₄×C₃₇	—	2	2	no	—
184	C₄⋊C₄×C₃₇	—	2	2	no	—
185	C₄⋊C₄×C₃₇	—	2	1	no	—
186	C₄⋊C₄×C₃₇	—	2	1	no	—
187	C₄⋊C₄×C₃₇	—	2	2	no	—
188	C₄⋊C₄×C₃₇	—	2	1	no	—
189	C₄⋊C₄×C₃₇	—	2	1	no	—
190	C₄⋊C₄×C₃₇	—	2	1	no	—
191	C₄⋊C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
192	C₄⋊C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
193	C₄⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
194	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
195	C₂²⋊C₄×C₃₇	—	2	4	no	—
196	C₂²⋊C₄×C₃₇	—	2	4	no	—
197	C₂²⋊C₄×C₃₇	—	2	4	no	—
198	C₂²⋊C₄×C₃₇	—	2	1	no	—
199	C₂²⋊C₄×C₃₇	—	2	1	no	—
200	C₂²⋊C₄×C₃₇	—	2	2	no	—
201	C₂²⋊C₄×C₃₇	—	2	1	no	—
202	C₂²⋊C₄×C₃₇	—	2	2	no	—
203	C₂²⋊C₄×C₃₇	—	4	1	no	—
204	C₂²⋊C₄×C₃₇	—	4	1	no	—
205	C₄²×C₃₇	—	2	4	no	—
206	C₄²×C₃₇	—	2	1	no	—
207	C₄²×C₃₇	—	2	1	no	—
208	C₄²×C₃₇	—	2	1	no	—
209	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
210	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
211	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
212	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
213	C₂³×C₃₇	—	2	1	no	—
214	C₂³×C₃₇	—	2	2	no	—
215	C₂³×C₃₇	—	4	1	no	—
216	C₂³×C₃₇	#120	1	1	yes	characteristic
217	Q₈×C₃₇	—	2	1	no	—
218	Q₈×C₃₇	—	2	1	no	—
219	Q₈×C₃₇	—	4	2	no	—
220	Q₈×C₃₇	—	4	2	no	—
221	Q₈×C₃₇	—	4	2	no	—
222	Q₈×C₃₇	—	4	1	no	—
223	Q₈×C₃₇	—	4	1	no	—
224	Q₈×C₃₇	—	8	2	no	—
225	D₄×C₃₇	—	2	1	no	—
226	D₄×C₃₇	—	2	1	no	—
227	D₄×C₃₇	—	2	2	no	—
228	D₄×C₃₇	—	2	2	no	—
229	D₄×C₃₇	—	4	2	no	—
230	D₄×C₃₇	—	4	2	no	—
231	D₄×C₃₇	—	4	2	no	—
232	D₄×C₃₇	—	4	4	no	—
233	D₄×C₃₇	—	4	1	no	—
234	D₄×C₃₇	—	4	1	no	—
235	D₄×C₃₇	—	4	1	no	—
236	D₄×C₃₇	—	4	1	no	—
237	D₄×C₃₇	—	4	2	no	—
238	D₄×C₃₇	—	8	4	no	—
239	D₄×C₃₇	—	8	2	no	—
240	C₂×C₄×C₃₇	—	2	1	no	—
241	C₂×C₄×C₃₇	—	2	1	no	—
242	C₂×C₄×C₃₇	—	2	1	no	—
243	C₂×C₄×C₃₇	—	2	1	no	—
244	C₂×C₄×C₃₇	—	2	2	no	—
245	C₂×C₄×C₃₇	—	2	1	no	—
246	C₂×C₄×C₃₇	—	2	4	no	—
247	C₂×C₄×C₃₇	—	4	1	no	—
248	C₂×C₄×C₃₇	—	4	2	no	—
249	C₂×C₄×C₃₇	—	4	2	no	—
250	C₂×C₄×C₃₇	—	4	2	no	—
251	C₂×C₄×C₃₇	—	4	1	no	—
252	C₂×C₄×C₃₇	—	4	1	no	—
253	C₂×C₄×C₃₇	—	4	2	no	—
254	C₂×C₄×C₃₇	—	4	1	no	—
255	C₂×C₄×C₃₇	—	8	2	no	—
256	C₂×C₄×C₃₇	—	8	4	no	—
257	C₂×C₄×C₃₇	—	8	2	no	—
258	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
259	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
260	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
261	C₂×C₄×C₃₇	#135	1	2	yes	—
262	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
263	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
266	C₈×C₃₇	—	4	2	no	—
267	C₈×C₃₇	—	4	1	no	—
268	C₈×C₃₇	—	4	1	no	—
269	C₈×C₃₇	—	4	2	no	—
270	#18888	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
271	C₂²×C₃₇	—	2	1	no	—
272	C₂²×C₃₇	—	2	1	no	—
273	C₂²×C₃₇	—	4	1	no	—
274	C₂²×C₃₇	—	4	2	no	—
275	C₂²×C₃₇	—	4	1	no	—
276	C₂²×C₃₇	—	4	2	no	—
277	C₂²×C₃₇	—	4	1	no	—
278	C₂²×C₃₇	—	4	2	no	—
279	C₂²×C₃₇	—	8	1	no	—
280	C₂²×C₃₇	—	8	1	no	—
281	C₂²×C₃₇	—	8	1	no	—
282	C₂²×C₃₇	#449	1	2	yes	—
283	C₂²×C₃₇	C₂×#120	1	1	yes	characteristic
284	C₄×C₃₇	—	2	1	no	—
285	C₄×C₃₇	—	2	1	no	—
286	C₄×C₃₇	—	2	1	no	—
287	C₄×C₃₇	—	4	1	no	—
288	C₄×C₃₇	—	4	2	no	—
289	C₄×C₃₇	—	4	1	no	—
290	C₄×C₃₇	—	4	4	no	—
291	C₄×C₃₇	—	4	1	no	—
292	C₄×C₃₇	—	8	1	no	—
293	C₄×C₃₇	#449	1	2	yes	—
294	C₄×C₃₇	C₂×#135	1	1	yes	characteristic
295	C₄×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
296	C₄×C₃₇	#576	1	1	yes	characteristic
297	C₄×C₃₇	#577	1	1	yes	characteristic
298	#3511	C₂×C₃₇	1	1	yes	characteristic, complemented
299	#3245	C₂×C₃₇	1	1	yes	characteristic, complemented
300	#3227	C₂×C₃₇	1	1	yes	characteristic, complemented
301	#3035	C₂×C₃₇	1	1	yes	characteristic, complemented
302	#1654	C₂×C₃₇	1	2	yes	complemented
303	#1652	C₂×C₃₇	1	2	yes	complemented
304	#1628	C₂×C₃₇	1	2	yes	complemented
305	#1625	C₂×C₃₇	1	2	yes	complemented
306	C₂×#332	C₂×C₃₇	1	1	yes	characteristic, complemented
307	#1480	C₂×C₃₇	1	1	yes	characteristic, complemented
308	#1477	C₂×C₃₇	1	1	yes	characteristic, complemented
309	C₂×C₃₇	—	2	2	no	—
310	C₂×C₃₇	—	8	1	no	—
311	C₂×C₃₇	—	8	2	no	—
312	C₂×C₃₇	—	16	1	no	—
313	C₂×C₃₇	C₂×#449	1	1	yes	characteristic
314	C₂×C₃₇	#3012	1	1	yes	characteristic
315	C₂×C₃₇	#3020	1	1	yes	characteristic
316	C₂×#135	—	2	1	no	—
317	#556	C₂²×C₃₇	1	2	yes	—
318	#555	—	2	1	no	—
319	#554	—	2	1	no	—
320	#553	—	2	2	no	—
321	#548	—	2	2	no	—
322	#547	C₂²×C₃₇	1	2	yes	—
323	#542	—	2	2	no	—
324	#537	—	2	1	no	—
325	#533	—	2	1	no	—
326	#532	—	2	1	no	—
327	#532	C₂²×C₃₇	1	1	yes	characteristic
328	#532	C₂²×C₃₇	1	1	yes	characteristic
329	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
330	#520	—	2	1	no	—
331	C₄×#41	C₂²×C₃₇	1	1	yes	characteristic
332	#498	C₂²×C₃₇	1	2	yes	—
333	#486	C₂²×C₃₇	1	2	yes	—
334	#481	—	2	2	no	—
335	#476	—	2	2	no	—
336	#474	—	2	1	no	—
337	#474	C₂²×C₃₇	1	2	yes	—
338	#466	—	2	2	no	—
339	#464	—	2	1	no	—
340	#463	—	2	1	no	—
341	#462	C₂²×C₃₇	1	1	yes	characteristic
342	#461	C₂²×C₃₇	1	1	yes	characteristic
343	#460	C₂²×C₃₇	1	1	yes	characteristic
344	#459	—	2	1	no	—
345	#459	C₂²×C₃₇	1	1	yes	characteristic
346	#459	C₂²×C₃₇	1	2	yes	—
347	#431	C₂²×C₃₇	1	1	yes	characteristic
348	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
349	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
350	#416	—	2	1	no	—
351	#332	C₂²×C₃₇	1	2	yes	—
352	#332	C₂²×C₃₇	1	2	yes	—
353	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	—
354	D₄⋊C₈	C₂²×C₃₇	1	2	yes	—
355	D₄⋊C₈	C₂²×C₃₇	1	2	yes	—
356	D₄⋊C₈	C₂²×C₃₇	1	2	yes	—
357	C₃₇	#18888	1	1	yes	characteristic, direct product factor, Sylow
358	C₂×#41	—	2	2	no	—
359	C₂×#41	—	2	1	no	—
360	C₂×#41	—	2	1	no	—
361	C₂×#41	D₄×C₃₇	1	1	yes	characteristic
362	C₂²×Q₈	—	2	1	no	—
363	#135	—	4	4	no	—
364	C₂×Q₁₆	—	2	1	no	—
365	C₂×SD₁₆	—	2	1	no	—
366	C₂×SD₁₆	—	2	1	no	—
367	C₂×D₈	—	2	1	no	—
368	C₂×D₈	—	2	2	no	—
369	C₂²×C₈	—	2	1	no	—
370	C₂²×C₈	—	2	1	no	—
371	C₄⋊Q₈	—	2	1	no	—
372	C₄⋊Q₈	—	2	1	no	—
373	C₄⋊Q₈	D₄×C₃₇	1	2	yes	—
374	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
375	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
376	C₄⋊Q₈	C₂³×C₃₇	1	2	yes	—
377	#127	D₄×C₃₇	1	1	yes	characteristic
378	#127	C₂³×C₃₇	1	1	yes	characteristic
379	#126	—	2	4	no	—
380	#125	—	2	2	no	—
381	#124	—	2	4	no	—
382	#124	—	2	2	no	—
383	#124	—	2	1	no	—
384	#124	—	2	1	no	—
385	#123	—	2	4	no	—
386	C₂²⋊Q₈	—	2	2	no	—
387	C₂²⋊Q₈	—	2	4	no	—
388	C₂²⋊Q₈	—	2	2	no	—
389	C₂²⋊Q₈	—	2	2	no	—
390	#121	—	2	2	no	—
391	#121	—	2	2	no	—
392	#121	—	2	4	no	—
393	#121	—	2	2	no	—
394	#121	—	2	1	no	—
395	#121	—	2	1	no	—
396	#121	—	2	1	no	—
397	#121	D₄×C₃₇	1	2	yes	—
398	C₄×Q₈	—	2	2	no	—
399	C₄×Q₈	—	2	2	no	—
400	C₄×Q₈	D₄×C₃₇	1	1	yes	characteristic
401	C₄×Q₈	C₂³×C₃₇	1	1	yes	characteristic
402	C₄×D₄	—	2	2	no	—
403	C₄×D₄	—	2	4	no	—
404	C₄×D₄	—	2	2	no	—
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	—	2	1	no	—
408	C₄×D₄	—	2	1	no	—
409	C₄×D₄	—	2	1	no	—
410	C₄×D₄	D₄×C₃₇	1	1	yes	characteristic
411	C₄×D₄	C₂³×C₃₇	1	1	yes	characteristic
412	C₄×D₄	C₂³×C₃₇	1	2	yes	—
413	#117	—	2	2	no	—
414	#117	—	2	2	no	—
415	#117	—	2	1	no	—
416	#117	D₄×C₃₇	1	1	yes	characteristic
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	—	2	2	no	—
419	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
420	C₂×C₄²	—	2	1	no	—
421	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
422	#107	—	2	2	no	—
423	#106	—	2	4	no	—
424	C₄⋊C₈	—	2	1	no	—
425	C₄⋊C₈	—	2	1	no	—
426	C₄⋊C₈	—	2	1	no	—
427	C₄⋊C₈	C₂³×C₃₇	1	1	yes	characteristic
428	C₄⋊C₈	C₂³×C₃₇	1	1	yes	characteristic
429	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
430	#103	—	2	1	no	—
431	#103	—	2	1	no	—
432	#102	—	2	2	no	—
433	#102	—	2	1	no	—
434	#102	—	2	1	no	—
435	#102	—	2	2	no	—
436	#102	—	2	4	no	—
437	C₂²⋊C₈	—	2	1	no	—
438	C₄×C₈	C₂³×C₃₇	1	2	yes	—
439	#41	—	2	2	no	—
440	#41	—	2	2	no	—
441	#41	—	4	2	no	—
442	#41	—	4	2	no	—
443	#41	—	4	2	no	—
444	#41	—	4	2	no	—
445	#41	—	8	2	no	—
446	#41	—	8	2	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	2	no	—
449	C₂×Q₈	—	2	2	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	8	1	no	—
452	C₂×Q₈	—	8	1	no	—
453	C₂×Q₈	C₂×D₄×C₃₇	1	1	yes	characteristic
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	4	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	4	1	no	—
463	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
464	C₂×D₄	C₂×D₄×C₃₇	1	1	yes	characteristic
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	4	1	no	—
472	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
473	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
475	Q₁₆	—	4	2	no	—
476	SD₁₆	—	4	2	no	—
477	SD₁₆	—	4	2	no	—
478	D₈	—	4	2	no	—
479	D₈	—	8	2	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	4	2	no	—
485	C₂×C₈	—	8	1	no	—
486	C₄⋊C₄	—	2	4	no	—
487	C₄⋊C₄	—	2	4	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
497	C₄⋊C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
498	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
499	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
500	C₂²⋊C₄	—	2	4	no	—
501	C₂²⋊C₄	—	2	4	no	—
502	C₂²⋊C₄	—	2	4	no	—
503	C₂²⋊C₄	—	2	1	no	—
504	C₂²⋊C₄	—	2	1	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	4	1	no	—
509	C₂²⋊C₄	—	4	1	no	—
510	C₄²	—	2	4	no	—
511	C₄²	—	2	1	no	—
512	C₄²	—	2	1	no	—
513	C₄²	—	2	1	no	—
514	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
515	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
516	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
517	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
518	C₂³	—	2	1	no	—
519	C₂³	—	2	2	no	—
520	C₂³	—	4	1	no	—
521	C₂³	#120×C₃₇	1	1	yes	characteristic
522	Q₈	—	2	1	no	—
523	Q₈	—	2	1	no	—
524	Q₈	—	4	2	no	—
525	Q₈	—	4	2	no	—
526	Q₈	—	4	2	no	—
527	Q₈	—	4	1	no	—
528	Q₈	—	4	1	no	—
529	Q₈	—	8	2	no	—
530	D₄	—	2	1	no	—
531	D₄	—	2	1	no	—
532	D₄	—	2	2	no	—
533	D₄	—	2	2	no	—
534	D₄	—	4	2	no	—
535	D₄	—	4	2	no	—
536	D₄	—	4	2	no	—
537	D₄	—	4	4	no	—
538	D₄	—	4	1	no	—
539	D₄	—	4	1	no	—
540	D₄	—	4	1	no	—
541	D₄	—	4	1	no	—
542	D₄	—	4	2	no	—
543	D₄	—	8	4	no	—
544	D₄	—	8	2	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	8	2	no	—
561	C₂×C₄	—	8	4	no	—
562	C₂×C₄	—	8	2	no	—
563	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
564	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
565	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
566	C₂×C₄	#135×C₃₇	1	2	yes	—
567	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
568	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
569	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
570	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
571	C₈	—	4	2	no	—
572	C₈	—	4	1	no	—
573	C₈	—	4	1	no	—
574	C₈	—	4	2	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	8	1	no	—
584	C₂²	—	8	1	no	—
585	C₂²	—	8	1	no	—
586	C₂²	C₃₇×#449	1	2	yes	—
587	C₂²	C₂×#120×C₃₇	1	1	yes	characteristic
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	2	no	—
593	C₄	—	4	1	no	—
594	C₄	—	4	4	no	—
595	C₄	—	4	1	no	—
596	C₄	—	8	1	no	—
597	C₄	C₃₇×#449	1	2	yes	—
598	C₄	C₂×#135×C₃₇	1	1	yes	characteristic
599	C₄	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
600	C₄	C₃₇×#576	1	1	yes	characteristic
601	C₄	C₃₇×#577	1	1	yes	characteristic
602	C₂	—	2	2	no	—
603	C₂	—	8	1	no	—
604	C₂	—	8	2	no	—
605	C₂	—	16	1	no	—
606	C₂	C₂×C₃₇×#449	1	1	yes	characteristic
607	C₂	C₃₇×#3012	1	1	yes	characteristic
608	C₂	C₃₇×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₇
LCS	G ▷ C₄² ▷ C₂² ▷ 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. C₃₇×#3511	C₂	semidirect
2. C₃₇×#3245	C₂	semidirect
3. C₃₇×#3227	C₂	semidirect
4. C₃₇×#3035	C₂	semidirect
5. C₃₇×#1654	C₂	semidirect
6. C₃₇×#1652	C₂	semidirect
7. C₃₇×#1628	C₂	semidirect
8. C₃₇×#1625	C₂	semidirect
9. C₂×C₃₇×#332	C₂	semidirect
10. C₃₇×#1480	C₂	semidirect
11. C₃₇×#1477	C₂	semidirect
270. #18888	C₃₇	direct (N × H)
298. #3511	C₂×C₃₇	semidirect
299. #3245	C₂×C₃₇	semidirect
300. #3227	C₂×C₃₇	semidirect
301. #3035	C₂×C₃₇	semidirect
302. #1654	C₂×C₃₇	semidirect
303. #1652	C₂×C₃₇	semidirect
304. #1628	C₂×C₃₇	semidirect
305. #1625	C₂×C₃₇	semidirect
306. C₂×#332	C₂×C₃₇	semidirect
307. #1480	C₂×C₃₇	semidirect
308. #1477	C₂×C₃₇	semidirect
357. C₃₇	#18888	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₇×#3511	2
C₃₇×#3245	2
C₃₇×#3227	2
C₃₇×#3035	2
C₃₇×#1654	2
C₃₇×#1652	2
C₃₇×#1628	2
C₃₇×#1625	2
C₂×C₃₇×#332	2
C₃₇×#1480	2
C₃₇×#1477	2
#18888	37

Subgroups — C37×#18888 #22640141

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#18888 #22640141