Subgroups — C₃₇×#18886 #22640139

Order 9472.

908 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×#3246	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#3226	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#3035	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#1650	C₂	1	2	yes	maximal, complemented
6	C₃₇×#1648	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1628	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1626	C₂	1	2	yes	maximal, complemented
9	C₂×C₃₇×#332	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1481	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×#557	—	2	1	no	—
14	C₃₇×#557	C₂²	1	2	yes	—
15	C₃₇×#556	—	2	1	no	—
16	C₃₇×#556	C₂²	1	2	yes	—
17	C₃₇×#552	—	2	2	no	—
18	C₃₇×#552	—	2	2	no	—
19	C₃₇×#541	—	2	2	no	—
20	C₃₇×#536	—	2	1	no	—
21	C₃₇×#533	—	2	1	no	—
22	C₃₇×#533	—	2	1	no	—
23	C₃₇×#533	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×#519	—	2	1	no	—
27	C₄×#41×C₃₇	C₂²	1	1	yes	characteristic
28	C₃₇×#500	C₂²	1	2	yes	—
29	C₃₇×#486	C₂²	1	2	yes	—
30	C₃₇×#480	—	2	2	no	—
31	C₃₇×#476	—	2	1	no	—
32	C₃₇×#475	C₂²	1	2	yes	—
33	C₃₇×#474	—	2	2	no	—
34	C₃₇×#465	—	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	—	2	1	no	—
39	C₃₇×#461	C₂²	1	1	yes	characteristic
40	C₃₇×#460	C₂²	1	1	yes	characteristic
41	C₃₇×#460	C₂²	1	2	yes	—
42	C₃₇×#459	C₂²	1	1	yes	characteristic
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×Q₈⋊C₈	C₂²	1	2	yes	—
51	C₃₇×Q₈⋊C₈	C₂²	1	2	yes	—
52	C₃₇×D₄⋊C₈	C₂²	1	2	yes	—
53	C₂×#41×C₃₇	—	2	1	no	—
54	C₂×#41×C₃₇	D₄	1	1	yes	characteristic
55	C₂²×Q₈×C₃₇	—	2	1	no	—
56	#135×C₃₇	—	4	4	no	—
57	C₂×Q₁₆×C₃₇	—	2	1	no	—
58	C₂×SD₁₆×C₃₇	—	2	1	no	—
59	C₂×SD₁₆×C₃₇	—	2	1	no	—
60	C₂×SD₁₆×C₃₇	—	2	2	no	—
61	C₂×D₈×C₃₇	—	2	1	no	—
62	C₂²×C₈×C₃₇	—	2	1	no	—
63	C₂²×C₈×C₃₇	—	2	1	no	—
64	C₄⋊Q₈×C₃₇	—	2	2	no	—
65	C₄⋊Q₈×C₃₇	—	2	1	no	—
66	C₄⋊Q₈×C₃₇	—	2	1	no	—
67	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
73	#126×C₃₇	—	2	4	no	—
74	#126×C₃₇	—	2	4	no	—
75	#125×C₃₇	—	2	2	no	—
76	#125×C₃₇	—	2	4	no	—
77	#125×C₃₇	—	2	2	no	—
78	#125×C₃₇	—	2	4	no	—
79	#125×C₃₇	—	2	1	no	—
80	#124×C₃₇	—	2	2	no	—
81	#124×C₃₇	—	2	1	no	—
82	#123×C₃₇	—	2	4	no	—
83	C₂²⋊Q₈×C₃₇	—	2	2	no	—
84	C₂²⋊Q₈×C₃₇	—	2	2	no	—
85	C₂²⋊Q₈×C₃₇	—	2	2	no	—
86	C₂²⋊Q₈×C₃₇	—	2	2	no	—
87	C₂²⋊Q₈×C₃₇	—	2	1	no	—
88	C₂²⋊Q₈×C₃₇	D₄	1	2	yes	—
89	#121×C₃₇	—	2	1	no	—
90	#121×C₃₇	—	2	1	no	—
91	C₄×Q₈×C₃₇	—	2	2	no	—
92	C₄×Q₈×C₃₇	—	2	2	no	—
93	C₄×Q₈×C₃₇	—	2	2	no	—
94	C₄×Q₈×C₃₇	—	2	2	no	—
95	C₄×Q₈×C₃₇	—	2	2	no	—
96	C₄×Q₈×C₃₇	—	2	2	no	—
97	C₄×Q₈×C₃₇	—	2	1	no	—
98	C₄×Q₈×C₃₇	D₄	1	1	yes	characteristic
99	C₄×Q₈×C₃₇	C₂³	1	2	yes	—
100	C₄×Q₈×C₃₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
107	#117×C₃₇	—	2	4	no	—
108	#117×C₃₇	—	2	2	no	—
109	#117×C₃₇	—	2	1	no	—
110	#117×C₃₇	—	2	2	no	—
111	#117×C₃₇	—	2	1	no	—
112	#117×C₃₇	D₄	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₃₇	—	2	1	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	4	no	—
118	#106×C₃₇	—	2	2	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	2	yes	—
123	C₄⋊C₈×C₃₇	C₂³	1	1	yes	characteristic
124	C₄⋊C₈×C₃₇	C₂³	1	1	yes	characteristic
125	#103×C₃₇	—	2	2	no	—
126	#103×C₃₇	—	2	1	no	—
127	#103×C₃₇	—	2	1	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	C₂×Q₈×C₃₇	—	2	1	no	—
139	C₂×Q₈×C₃₇	—	2	2	no	—
140	C₂×Q₈×C₃₇	—	2	2	no	—
141	C₂×Q₈×C₃₇	—	2	1	no	—
142	C₂×Q₈×C₃₇	—	4	2	no	—
143	C₂×Q₈×C₃₇	—	4	2	no	—
144	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
145	C₂×Q₈×C₃₇	C₂×D₄	1	1	yes	characteristic
146	C₂×D₄×C₃₇	—	2	1	no	—
147	C₂×D₄×C₃₇	—	2	1	no	—
148	C₂×D₄×C₃₇	—	2	1	no	—
149	C₂×D₄×C₃₇	—	2	1	no	—
150	C₂×D₄×C₃₇	—	4	1	no	—
151	C₂×D₄×C₃₇	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₃₇	—	2	2	no	—
153	C₂²×C₄×C₃₇	—	2	1	no	—
154	C₂²×C₄×C₃₇	—	2	1	no	—
155	C₂²×C₄×C₃₇	—	2	1	no	—
156	C₂²×C₄×C₃₇	—	4	1	no	—
157	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
160	Q₁₆×C₃₇	—	4	2	no	—
161	SD₁₆×C₃₇	—	4	2	no	—
162	SD₁₆×C₃₇	—	4	2	no	—
163	SD₁₆×C₃₇	—	8	2	no	—
164	D₈×C₃₇	—	4	2	no	—
165	C₂×C₈×C₃₇	—	2	2	no	—
166	C₂×C₈×C₃₇	—	2	2	no	—
167	C₂×C₈×C₃₇	—	2	1	no	—
168	C₂×C₈×C₃₇	—	2	1	no	—
169	C₂×C₈×C₃₇	—	4	2	no	—
170	C₂×C₈×C₃₇	—	8	1	no	—
171	C₄⋊C₄×C₃₇	—	2	4	no	—
172	C₄⋊C₄×C₃₇	—	2	4	no	—
173	C₄⋊C₄×C₃₇	—	2	4	no	—
174	C₄⋊C₄×C₃₇	—	2	4	no	—
175	C₄⋊C₄×C₃₇	—	2	2	no	—
176	C₄⋊C₄×C₃₇	—	2	2	no	—
177	C₄⋊C₄×C₃₇	—	2	1	no	—
178	C₄⋊C₄×C₃₇	—	2	1	no	—
179	C₄⋊C₄×C₃₇	—	2	1	no	—
180	C₄⋊C₄×C₃₇	—	2	1	no	—
181	C₄⋊C₄×C₃₇	—	2	2	no	—
182	C₄⋊C₄×C₃₇	—	2	2	no	—
183	C₄⋊C₄×C₃₇	—	2	1	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	C₂×D₄	1	1	yes	characteristic
188	C₄⋊C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
189	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
190	C₄⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
191	C₂²⋊C₄×C₃₇	—	2	4	no	—
192	C₂²⋊C₄×C₃₇	—	2	4	no	—
193	C₂²⋊C₄×C₃₇	—	2	1	no	—
194	C₂²⋊C₄×C₃₇	—	2	2	no	—
195	C₂²⋊C₄×C₃₇	—	2	1	no	—
196	C₂²⋊C₄×C₃₇	—	2	1	no	—
197	C₂²⋊C₄×C₃₇	—	4	1	no	—
198	C₂²⋊C₄×C₃₇	—	4	1	no	—
199	C₄²×C₃₇	—	2	4	no	—
200	C₄²×C₃₇	—	2	4	no	—
201	C₄²×C₃₇	—	2	1	no	—
202	C₄²×C₃₇	—	2	1	no	—
203	C₄²×C₃₇	—	2	1	no	—
204	C₄²×C₃₇	—	2	2	no	—
205	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
209	C₂³×C₃₇	—	2	1	no	—
210	C₂³×C₃₇	—	4	1	no	—
211	C₂³×C₃₇	#120	1	1	yes	characteristic
212	Q₈×C₃₇	—	2	1	no	—
213	Q₈×C₃₇	—	2	1	no	—
214	Q₈×C₃₇	—	2	2	no	—
215	Q₈×C₃₇	—	2	2	no	—
216	Q₈×C₃₇	—	4	2	no	—
217	Q₈×C₃₇	—	4	2	no	—
218	Q₈×C₃₇	—	4	2	no	—
219	Q₈×C₃₇	—	4	4	no	—
220	Q₈×C₃₇	—	4	1	no	—
221	Q₈×C₃₇	—	4	1	no	—
222	D₄×C₃₇	—	2	1	no	—
223	D₄×C₃₇	—	2	1	no	—
224	D₄×C₃₇	—	4	2	no	—
225	D₄×C₃₇	—	4	2	no	—
226	D₄×C₃₇	—	4	1	no	—
227	D₄×C₃₇	—	4	1	no	—
228	D₄×C₃₇	—	4	1	no	—
229	D₄×C₃₇	—	4	1	no	—
230	D₄×C₃₇	—	8	2	no	—
231	C₂×C₄×C₃₇	—	2	1	no	—
232	C₂×C₄×C₃₇	—	2	1	no	—
233	C₂×C₄×C₃₇	—	2	1	no	—
234	C₂×C₄×C₃₇	—	2	1	no	—
235	C₂×C₄×C₃₇	—	2	2	no	—
236	C₂×C₄×C₃₇	—	2	2	no	—
237	C₂×C₄×C₃₇	—	2	4	no	—
238	C₂×C₄×C₃₇	—	2	1	no	—
239	C₂×C₄×C₃₇	—	4	1	no	—
240	C₂×C₄×C₃₇	—	4	2	no	—
241	C₂×C₄×C₃₇	—	4	4	no	—
242	C₂×C₄×C₃₇	—	4	1	no	—
243	C₂×C₄×C₃₇	—	4	1	no	—
244	C₂×C₄×C₃₇	—	4	2	no	—
245	C₂×C₄×C₃₇	—	4	1	no	—
246	C₂×C₄×C₃₇	—	8	2	no	—
247	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
248	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
249	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
250	C₂×C₄×C₃₇	#135	1	2	yes	—
251	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
252	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
255	C₈×C₃₇	—	4	2	no	—
256	C₈×C₃₇	—	4	1	no	—
257	C₈×C₃₇	—	4	1	no	—
258	C₈×C₃₇	—	4	2	no	—
259	#18886	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
260	C₂²×C₃₇	—	2	1	no	—
261	C₂²×C₃₇	—	2	1	no	—
262	C₂²×C₃₇	—	4	1	no	—
263	C₂²×C₃₇	—	4	1	no	—
264	C₂²×C₃₇	—	4	1	no	—
265	C₂²×C₃₇	—	8	1	no	—
266	C₂²×C₃₇	—	8	1	no	—
267	C₂²×C₃₇	—	8	1	no	—
268	C₂²×C₃₇	#449	1	2	yes	—
269	C₂²×C₃₇	C₂×#120	1	1	yes	characteristic
270	C₄×C₃₇	—	2	1	no	—
271	C₄×C₃₇	—	2	1	no	—
272	C₄×C₃₇	—	2	1	no	—
273	C₄×C₃₇	—	4	1	no	—
274	C₄×C₃₇	—	4	4	no	—
275	C₄×C₃₇	—	4	1	no	—
276	C₄×C₃₇	—	4	2	no	—
277	C₄×C₃₇	—	4	1	no	—
278	C₄×C₃₇	—	4	2	no	—
279	C₄×C₃₇	—	8	1	no	—
280	C₄×C₃₇	#449	1	2	yes	—
281	C₄×C₃₇	C₂×#135	1	1	yes	characteristic
282	C₄×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
283	C₄×C₃₇	#577	1	1	yes	characteristic
284	C₄×C₃₇	#578	1	1	yes	characteristic
285	#3509	C₂×C₃₇	1	1	yes	characteristic, complemented
286	#3246	C₂×C₃₇	1	1	yes	characteristic, complemented
287	#3226	C₂×C₃₇	1	1	yes	characteristic, complemented
288	#3035	C₂×C₃₇	1	1	yes	characteristic
289	#1650	C₂×C₃₇	1	2	yes	complemented
290	#1648	C₂×C₃₇	1	2	yes	complemented
291	#1628	C₂×C₃₇	1	2	yes	complemented
292	#1626	C₂×C₃₇	1	2	yes	complemented
293	C₂×#332	C₂×C₃₇	1	1	yes	characteristic, complemented
294	#1481	C₂×C₃₇	1	1	yes	characteristic, complemented
295	#1477	C₂×C₃₇	1	1	yes	characteristic, complemented
296	C₂×C₃₇	—	2	2	no	—
297	C₂×C₃₇	—	8	1	no	—
298	C₂×C₃₇	—	16	1	no	—
299	C₂×C₃₇	C₂×#449	1	1	yes	characteristic
300	C₂×C₃₇	#3013	1	1	yes	characteristic
301	C₂×C₃₇	#3020	1	1	yes	characteristic
302	C₂×#135	—	2	1	no	—
303	#557	—	2	1	no	—
304	#557	C₂²×C₃₇	1	2	yes	—
305	#556	—	2	1	no	—
306	#556	C₂²×C₃₇	1	2	yes	—
307	#552	—	2	2	no	—
308	#552	—	2	2	no	—
309	#541	—	2	2	no	—
310	#536	—	2	1	no	—
311	#533	—	2	1	no	—
312	#533	—	2	1	no	—
313	#533	C₂²×C₃₇	1	1	yes	characteristic
314	#532	C₂²×C₃₇	1	1	yes	characteristic
315	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
316	#519	—	2	1	no	—
317	C₄×#41	C₂²×C₃₇	1	1	yes	characteristic
318	#500	C₂²×C₃₇	1	2	yes	—
319	#486	C₂²×C₃₇	1	2	yes	—
320	#480	—	2	2	no	—
321	#476	—	2	1	no	—
322	#475	C₂²×C₃₇	1	2	yes	—
323	#474	—	2	2	no	—
324	#465	—	2	2	no	—
325	#464	—	2	1	no	—
326	#463	—	2	1	no	—
327	#462	C₂²×C₃₇	1	1	yes	characteristic
328	#461	—	2	1	no	—
329	#461	C₂²×C₃₇	1	1	yes	characteristic
330	#460	C₂²×C₃₇	1	1	yes	characteristic
331	#460	C₂²×C₃₇	1	2	yes	—
332	#459	C₂²×C₃₇	1	1	yes	characteristic
333	#431	C₂²×C₃₇	1	1	yes	characteristic
334	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
335	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
336	#416	—	2	1	no	—
337	#332	C₂²×C₃₇	1	2	yes	—
338	#332	C₂²×C₃₇	1	2	yes	—
339	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	—
340	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	—
341	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	—
342	D₄⋊C₈	C₂²×C₃₇	1	2	yes	—
343	C₃₇	#18886	1	1	yes	characteristic, direct product factor, Sylow
344	C₂×#41	—	2	1	no	—
345	C₂×#41	D₄×C₃₇	1	1	yes	characteristic
346	C₂²×Q₈	—	2	1	no	—
347	#135	—	4	4	no	—
348	C₂×Q₁₆	—	2	1	no	—
349	C₂×SD₁₆	—	2	1	no	—
350	C₂×SD₁₆	—	2	1	no	—
351	C₂×SD₁₆	—	2	2	no	—
352	C₂×D₈	—	2	1	no	—
353	C₂²×C₈	—	2	1	no	—
354	C₂²×C₈	—	2	1	no	—
355	C₄⋊Q₈	—	2	2	no	—
356	C₄⋊Q₈	—	2	1	no	—
357	C₄⋊Q₈	—	2	1	no	—
358	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
359	C₄⋊Q₈	D₄×C₃₇	1	2	yes	—
360	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
361	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
362	C₄⋊Q₈	C₂³×C₃₇	1	2	yes	—
363	#127	C₂³×C₃₇	1	1	yes	characteristic
364	#126	—	2	4	no	—
365	#126	—	2	4	no	—
366	#125	—	2	2	no	—
367	#125	—	2	4	no	—
368	#125	—	2	2	no	—
369	#125	—	2	4	no	—
370	#125	—	2	1	no	—
371	#124	—	2	2	no	—
372	#124	—	2	1	no	—
373	#123	—	2	4	no	—
374	C₂²⋊Q₈	—	2	2	no	—
375	C₂²⋊Q₈	—	2	2	no	—
376	C₂²⋊Q₈	—	2	2	no	—
377	C₂²⋊Q₈	—	2	2	no	—
378	C₂²⋊Q₈	—	2	1	no	—
379	C₂²⋊Q₈	D₄×C₃₇	1	2	yes	—
380	#121	—	2	1	no	—
381	#121	—	2	1	no	—
382	C₄×Q₈	—	2	2	no	—
383	C₄×Q₈	—	2	2	no	—
384	C₄×Q₈	—	2	2	no	—
385	C₄×Q₈	—	2	2	no	—
386	C₄×Q₈	—	2	2	no	—
387	C₄×Q₈	—	2	2	no	—
388	C₄×Q₈	—	2	1	no	—
389	C₄×Q₈	D₄×C₃₇	1	1	yes	characteristic
390	C₄×Q₈	C₂³×C₃₇	1	1	yes	characteristic
391	C₄×Q₈	C₂³×C₃₇	1	2	yes	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	—	2	1	no	—
394	C₄×D₄	—	2	1	no	—
395	C₄×D₄	—	2	1	no	—
396	C₄×D₄	D₄×C₃₇	1	1	yes	characteristic
397	C₄×D₄	C₂³×C₃₇	1	1	yes	characteristic
398	#117	—	2	4	no	—
399	#117	—	2	2	no	—
400	#117	—	2	1	no	—
401	#117	—	2	2	no	—
402	#117	—	2	1	no	—
403	#117	D₄×C₃₇	1	1	yes	characteristic
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
406	C₂×C₄²	—	2	1	no	—
407	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
408	#107	—	2	4	no	—
409	#106	—	2	2	no	—
410	C₄⋊C₈	—	2	1	no	—
411	C₄⋊C₈	—	2	1	no	—
412	C₄⋊C₈	—	2	1	no	—
413	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
414	C₄⋊C₈	C₂³×C₃₇	1	1	yes	characteristic
415	C₄⋊C₈	C₂³×C₃₇	1	1	yes	characteristic
416	#103	—	2	2	no	—
417	#103	—	2	1	no	—
418	#103	—	2	1	no	—
419	#102	—	2	1	no	—
420	#102	—	2	1	no	—
421	#102	—	2	2	no	—
422	#102	—	2	4	no	—
423	C₂²⋊C₈	—	2	1	no	—
424	C₄×C₈	C₂³×C₃₇	1	2	yes	—
425	#41	—	2	2	no	—
426	#41	—	2	2	no	—
427	#41	—	4	2	no	—
428	#41	—	4	2	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	2	no	—
431	C₂×Q₈	—	2	2	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	4	2	no	—
434	C₂×Q₈	—	4	2	no	—
435	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
436	C₂×Q₈	C₂×D₄×C₃₇	1	1	yes	characteristic
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	4	1	no	—
442	C₂×D₄	C₂×D₄×C₃₇	1	1	yes	characteristic
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	4	1	no	—
448	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
449	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
450	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
451	Q₁₆	—	4	2	no	—
452	SD₁₆	—	4	2	no	—
453	SD₁₆	—	4	2	no	—
454	SD₁₆	—	8	2	no	—
455	D₈	—	4	2	no	—
456	C₂×C₈	—	2	2	no	—
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	4	2	no	—
461	C₂×C₈	—	8	1	no	—
462	C₄⋊C₄	—	2	4	no	—
463	C₄⋊C₄	—	2	4	no	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	4	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
479	C₄⋊C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
480	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
481	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
482	C₂²⋊C₄	—	2	4	no	—
483	C₂²⋊C₄	—	2	4	no	—
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	1	no	—
488	C₂²⋊C₄	—	4	1	no	—
489	C₂²⋊C₄	—	4	1	no	—
490	C₄²	—	2	4	no	—
491	C₄²	—	2	4	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	—	2	2	no	—
496	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
497	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
498	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
499	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
500	C₂³	—	2	1	no	—
501	C₂³	—	4	1	no	—
502	C₂³	#120×C₃₇	1	1	yes	characteristic
503	Q₈	—	2	1	no	—
504	Q₈	—	2	1	no	—
505	Q₈	—	2	2	no	—
506	Q₈	—	2	2	no	—
507	Q₈	—	4	2	no	—
508	Q₈	—	4	2	no	—
509	Q₈	—	4	2	no	—
510	Q₈	—	4	4	no	—
511	Q₈	—	4	1	no	—
512	Q₈	—	4	1	no	—
513	D₄	—	2	1	no	—
514	D₄	—	2	1	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	1	no	—
518	D₄	—	4	1	no	—
519	D₄	—	4	1	no	—
520	D₄	—	4	1	no	—
521	D₄	—	8	2	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	4	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	8	2	no	—
538	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
539	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
540	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
541	C₂×C₄	#135×C₃₇	1	2	yes	—
542	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
543	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
544	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
545	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
546	C₈	—	4	2	no	—
547	C₈	—	4	1	no	—
548	C₈	—	4	1	no	—
549	C₈	—	4	2	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	8	1	no	—
556	C₂²	—	8	1	no	—
557	C₂²	—	8	1	no	—
558	C₂²	C₃₇×#449	1	2	yes	—
559	C₂²	C₂×#120×C₃₇	1	1	yes	characteristic
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	4	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	2	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	2	no	—
569	C₄	—	8	1	no	—
570	C₄	C₃₇×#449	1	2	yes	—
571	C₄	C₂×#135×C₃₇	1	1	yes	characteristic
572	C₄	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
573	C₄	C₃₇×#577	1	1	yes	characteristic
574	C₄	C₃₇×#578	1	1	yes	characteristic
575	C₂	—	2	2	no	—
576	C₂	—	8	1	no	—
577	C₂	—	16	1	no	—
578	C₂	C₂×C₃₇×#449	1	1	yes	characteristic
579	C₂	C₃₇×#3013	1	1	yes	characteristic
580	C₂	C₃₇×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₇
prime radical	C₃₇×#3035	C₂
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×#3509	C₂	semidirect
2. C₃₇×#3246	C₂	semidirect
3. C₃₇×#3226	C₂	semidirect
5. C₃₇×#1650	C₂	semidirect
6. C₃₇×#1648	C₂	semidirect
7. C₃₇×#1628	C₂	semidirect
8. C₃₇×#1626	C₂	semidirect
9. C₂×C₃₇×#332	C₂	semidirect
10. C₃₇×#1481	C₂	semidirect
11. C₃₇×#1477	C₂	semidirect
259. #18886	C₃₇	direct (N × H)
285. #3509	C₂×C₃₇	semidirect
286. #3246	C₂×C₃₇	semidirect
287. #3226	C₂×C₃₇	semidirect
289. #1650	C₂×C₃₇	semidirect
290. #1648	C₂×C₃₇	semidirect
291. #1628	C₂×C₃₇	semidirect
292. #1626	C₂×C₃₇	semidirect
293. C₂×#332	C₂×C₃₇	semidirect
294. #1481	C₂×C₃₇	semidirect
295. #1477	C₂×C₃₇	semidirect
343. C₃₇	#18886	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×#3509	2
C₃₇×#3246	2
C₃₇×#3226	2
C₃₇×#3035	2
C₃₇×#1650	2
C₃₇×#1648	2
C₃₇×#1628	2
C₃₇×#1626	2
C₂×C₃₇×#332	2
C₃₇×#1481	2
C₃₇×#1477	2
#18886	37

Subgroups — C37×#18886 #22640139

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#18886 #22640139