Subgroups — C₃₇×#18884 #22640137

Order 9472.

942 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×#3246	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
5	C₃₇×#1653	C₂	1	2	yes	maximal, complemented
6	C₃₇×#1651	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1627	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	Q₈²×C₃₇	—	2	1	no	—
14	C₃₇×#557	C₂²	1	2	yes	—
15	C₃₇×#554	—	2	1	no	—
16	C₃₇×#554	—	2	2	no	—
17	D₄×Q₈×C₃₇	—	2	2	no	—
18	D₄×Q₈×C₃₇	C₂²	1	2	yes	—
19	C₃₇×#544	—	2	2	no	—
20	C₃₇×#544	—	2	1	no	—
21	C₃₇×#533	—	2	1	no	—
22	C₃₇×#533	C₂²	1	1	yes	characteristic
23	C₃₇×#532	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₃₇	—	2	1	no	—
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×#476	—	2	1	no	—
33	C₃₇×#475	C₂²	1	2	yes	—
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	2	no	—
56	C₂²×Q₈×C₃₇	—	2	1	no	—
57	#135×C₃₇	—	4	4	no	—
58	C₂×Q₁₆×C₃₇	—	2	1	no	—
59	C₂×SD₁₆×C₃₇	—	2	1	no	—
60	C₂×SD₁₆×C₃₇	—	2	1	no	—
61	C₂×SD₁₆×C₃₇	—	2	2	no	—
62	C₂×D₈×C₃₇	—	2	1	no	—
63	C₂²×C₈×C₃₇	—	2	1	no	—
64	C₂²×C₈×C₃₇	—	2	1	no	—
65	C₄⋊Q₈×C₃₇	—	2	2	no	—
66	C₄⋊Q₈×C₃₇	—	2	2	no	—
67	C₄⋊Q₈×C₃₇	—	2	4	no	—
68	C₄⋊Q₈×C₃₇	—	2	2	no	—
69	C₄⋊Q₈×C₃₇	—	2	2	no	—
70	C₄⋊Q₈×C₃₇	—	2	1	no	—
71	C₄⋊Q₈×C₃₇	—	2	1	no	—
72	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
73	C₄⋊Q₈×C₃₇	D₄	1	2	yes	—
74	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
75	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
76	C₄⋊Q₈×C₃₇	C₂³	1	2	yes	—
77	#127×C₃₇	C₂³	1	1	yes	characteristic
78	#125×C₃₇	—	2	2	no	—
79	#125×C₃₇	—	2	4	no	—
80	#125×C₃₇	—	2	2	no	—
81	#125×C₃₇	—	2	1	no	—
82	#124×C₃₇	—	2	1	no	—
83	C₂²⋊Q₈×C₃₇	—	2	2	no	—
84	C₂²⋊Q₈×C₃₇	—	2	4	no	—
85	C₂²⋊Q₈×C₃₇	—	2	4	no	—
86	C₂²⋊Q₈×C₃₇	—	2	1	no	—
87	C₂²⋊Q₈×C₃₇	—	2	2	no	—
88	C₂²⋊Q₈×C₃₇	—	2	4	no	—
89	C₂²⋊Q₈×C₃₇	D₄	1	2	yes	—
90	#121×C₃₇	—	2	1	no	—
91	#121×C₃₇	—	2	1	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	1	no	—
96	C₄×Q₈×C₃₇	D₄	1	1	yes	characteristic
97	C₄×Q₈×C₃₇	C₂³	1	2	yes	—
98	C₄×Q₈×C₃₇	C₂³	1	1	yes	characteristic
99	C₄×D₄×C₃₇	—	2	4	no	—
100	C₄×D₄×C₃₇	—	2	2	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	1	yes	characteristic
107	#117×C₃₇	—	2	2	no	—
108	#117×C₃₇	—	2	1	no	—
109	#117×C₃₇	—	2	1	no	—
110	#117×C₃₇	D₄	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
112	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
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	#106×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	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	—	4	2	no	—
136	#41×C₃₇	—	4	2	no	—
137	#41×C₃₇	SD₁₆	1	4	yes	complemented
138	C₂×Q₈×C₃₇	—	2	4	no	—
139	C₂×Q₈×C₃₇	—	2	1	no	—
140	C₂×Q₈×C₃₇	—	2	2	no	—
141	C₂×Q₈×C₃₇	—	2	2	no	—
142	C₂×Q₈×C₃₇	—	2	1	no	—
143	C₂×Q₈×C₃₇	—	8	1	no	—
144	C₂×Q₈×C₃₇	—	8	1	no	—
145	C₂×Q₈×C₃₇	—	8	2	no	—
146	C₂×Q₈×C₃₇	—	8	2	no	—
147	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
148	C₂×Q₈×C₃₇	C₂×D₄	1	1	yes	characteristic
149	C₂×D₄×C₃₇	—	2	1	no	—
150	C₂×D₄×C₃₇	—	2	1	no	—
151	C₂×D₄×C₃₇	—	2	1	no	—
152	C₂×D₄×C₃₇	—	2	1	no	—
153	C₂×D₄×C₃₇	—	4	1	no	—
154	C₂×D₄×C₃₇	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₃₇	—	2	1	no	—
156	C₂²×C₄×C₃₇	—	2	4	no	—
157	C₂²×C₄×C₃₇	—	2	2	no	—
158	C₂²×C₄×C₃₇	—	2	1	no	—
159	C₂²×C₄×C₃₇	—	2	1	no	—
160	C₂²×C₄×C₃₇	—	4	1	no	—
161	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
164	Q₁₆×C₃₇	—	4	2	no	—
165	SD₁₆×C₃₇	—	4	2	no	—
166	SD₁₆×C₃₇	—	4	2	no	—
167	SD₁₆×C₃₇	—	8	2	no	—
168	D₈×C₃₇	—	4	2	no	—
169	C₂×C₈×C₃₇	—	2	2	no	—
170	C₂×C₈×C₃₇	—	2	2	no	—
171	C₂×C₈×C₃₇	—	2	1	no	—
172	C₂×C₈×C₃₇	—	2	1	no	—
173	C₂×C₈×C₃₇	—	4	2	no	—
174	C₂×C₈×C₃₇	—	8	1	no	—
175	C₄⋊C₄×C₃₇	—	2	4	no	—
176	C₄⋊C₄×C₃₇	—	2	4	no	—
177	C₄⋊C₄×C₃₇	—	2	4	no	—
178	C₄⋊C₄×C₃₇	—	2	4	no	—
179	C₄⋊C₄×C₃₇	—	2	1	no	—
180	C₄⋊C₄×C₃₇	—	2	2	no	—
181	C₄⋊C₄×C₃₇	—	2	1	no	—
182	C₄⋊C₄×C₃₇	—	2	2	no	—
183	C₄⋊C₄×C₃₇	—	2	1	no	—
184	C₄⋊C₄×C₃₇	—	2	1	no	—
185	C₄⋊C₄×C₃₇	—	2	2	no	—
186	C₄⋊C₄×C₃₇	—	2	2	no	—
187	C₄⋊C₄×C₃₇	—	2	1	no	—
188	C₄⋊C₄×C₃₇	—	2	2	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	2	no	—
197	C₂²⋊C₄×C₃₇	—	2	1	no	—
198	C₂²⋊C₄×C₃₇	—	2	1	no	—
199	C₂²⋊C₄×C₃₇	—	2	1	no	—
200	C₂²⋊C₄×C₃₇	—	4	1	no	—
201	C₂²⋊C₄×C₃₇	—	4	1	no	—
202	C₄²×C₃₇	—	2	4	no	—
203	C₄²×C₃₇	—	2	1	no	—
204	C₄²×C₃₇	—	2	1	no	—
205	C₄²×C₃₇	—	2	1	no	—
206	C₄²×C₃₇	—	2	2	no	—
207	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
210	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
211	C₂³×C₃₇	—	2	1	no	—
212	C₂³×C₃₇	—	4	1	no	—
213	C₂³×C₃₇	#120	1	1	yes	characteristic
214	Q₈×C₃₇	—	2	1	no	—
215	Q₈×C₃₇	—	2	2	no	—
216	Q₈×C₃₇	—	2	2	no	—
217	Q₈×C₃₇	—	4	2	no	—
218	Q₈×C₃₇	—	4	2	no	—
219	Q₈×C₃₇	—	4	2	no	—
220	Q₈×C₃₇	—	4	1	no	—
221	Q₈×C₃₇	—	4	1	no	—
222	Q₈×C₃₇	—	8	2	no	—
223	Q₈×C₃₇	—	8	4	no	—
224	Q₈×C₃₇	C₂×SD₁₆	1	2	yes	—
225	D₄×C₃₇	—	2	4	no	—
226	D₄×C₃₇	—	2	1	no	—
227	D₄×C₃₇	—	4	2	no	—
228	D₄×C₃₇	—	4	1	no	—
229	D₄×C₃₇	—	4	1	no	—
230	D₄×C₃₇	—	4	1	no	—
231	D₄×C₃₇	—	4	1	no	—
232	D₄×C₃₇	—	8	2	no	—
233	D₄×C₃₇	C₂×SD₁₆	1	2	yes	—
234	C₂×C₄×C₃₇	—	2	1	no	—
235	C₂×C₄×C₃₇	—	2	1	no	—
236	C₂×C₄×C₃₇	—	2	1	no	—
237	C₂×C₄×C₃₇	—	2	4	no	—
238	C₂×C₄×C₃₇	—	2	2	no	—
239	C₂×C₄×C₃₇	—	2	1	no	—
240	C₂×C₄×C₃₇	—	2	1	no	—
241	C₂×C₄×C₃₇	—	2	2	no	—
242	C₂×C₄×C₃₇	—	2	4	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	—	4	1	no	—
247	C₂×C₄×C₃₇	—	4	1	no	—
248	C₂×C₄×C₃₇	—	8	2	no	—
249	C₂×C₄×C₃₇	—	8	4	no	—
250	C₂×C₄×C₃₇	—	8	2	no	—
251	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
252	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
253	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
254	C₂×C₄×C₃₇	C₂×SD₁₆	1	2	yes	—
255	C₂×C₄×C₃₇	#137	1	2	yes	—
256	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
259	C₈×C₃₇	—	4	2	no	—
260	C₈×C₃₇	—	4	1	no	—
261	C₈×C₃₇	—	4	1	no	—
262	C₈×C₃₇	—	4	2	no	—
263	#18884	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
264	C₂²×C₃₇	—	2	1	no	—
265	C₂²×C₃₇	—	2	1	no	—
266	C₂²×C₃₇	—	2	2	no	—
267	C₂²×C₃₇	—	4	1	no	—
268	C₂²×C₃₇	—	4	1	no	—
269	C₂²×C₃₇	—	8	1	no	—
270	C₂²×C₃₇	—	8	1	no	—
271	C₂²×C₃₇	—	8	1	no	—
272	C₂²×C₃₇	#448	1	2	yes	—
273	C₂²×C₃₇	C₂×#120	1	1	yes	characteristic
274	C₄×C₃₇	—	2	2	no	—
275	C₄×C₃₇	—	2	1	no	—
276	C₄×C₃₇	—	2	1	no	—
277	C₄×C₃₇	—	2	1	no	—
278	C₄×C₃₇	—	4	1	no	—
279	C₄×C₃₇	—	4	2	no	—
280	C₄×C₃₇	—	4	4	no	—
281	C₄×C₃₇	—	4	1	no	—
282	C₄×C₃₇	—	4	2	no	—
283	C₄×C₃₇	—	8	1	no	—
284	C₄×C₃₇	#448	1	2	yes	—
285	C₄×C₃₇	C₂²×SD₁₆	1	1	yes	characteristic
286	C₄×C₃₇	C₂×#137	1	1	yes	characteristic
287	C₄×C₃₇	#576	1	1	yes	characteristic
288	C₄×C₃₇	#577	1	1	yes	characteristic
289	#3503	C₂×C₃₇	1	1	yes	characteristic, complemented
290	#3246	C₂×C₃₇	1	1	yes	characteristic, complemented
291	#3227	C₂×C₃₇	1	1	yes	characteristic, complemented
292	#3035	C₂×C₃₇	1	1	yes	characteristic
293	#1653	C₂×C₃₇	1	2	yes	complemented
294	#1651	C₂×C₃₇	1	2	yes	complemented
295	#1627	C₂×C₃₇	1	2	yes	complemented
296	#1626	C₂×C₃₇	1	2	yes	complemented
297	C₂×#332	C₂×C₃₇	1	1	yes	characteristic, complemented
298	#1481	C₂×C₃₇	1	1	yes	characteristic, complemented
299	#1477	C₂×C₃₇	1	1	yes	characteristic, complemented
300	C₂×C₃₇	—	2	2	no	—
301	C₂×C₃₇	—	4	2	no	—
302	C₂×C₃₇	—	16	1	no	—
303	C₂×C₃₇	C₂×#448	1	1	yes	characteristic
304	C₂×C₃₇	#3012	1	1	yes	characteristic
305	C₂×C₃₇	#3020	1	1	yes	characteristic
306	C₂×#135	—	2	1	no	—
307	Q₈²	—	2	1	no	—
308	#557	C₂²×C₃₇	1	2	yes	—
309	#554	—	2	1	no	—
310	#554	—	2	2	no	—
311	D₄×Q₈	—	2	2	no	—
312	D₄×Q₈	C₂²×C₃₇	1	2	yes	—
313	#544	—	2	2	no	—
314	#544	—	2	1	no	—
315	#533	—	2	1	no	—
316	#533	C₂²×C₃₇	1	1	yes	characteristic
317	#532	C₂²×C₃₇	1	1	yes	characteristic
318	C₂×C₄⋊Q₈	—	2	1	no	—
319	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
320	#520	—	2	1	no	—
321	C₄×#41	C₂²×C₃₇	1	1	yes	characteristic
322	#498	C₂²×C₃₇	1	2	yes	—
323	#486	C₂²×C₃₇	1	2	yes	—
324	#481	—	2	2	no	—
325	#476	—	2	2	no	—
326	#476	—	2	1	no	—
327	#475	C₂²×C₃₇	1	2	yes	—
328	#465	—	2	2	no	—
329	#464	—	2	1	no	—
330	#463	—	2	1	no	—
331	#462	C₂²×C₃₇	1	1	yes	characteristic
332	#461	—	2	1	no	—
333	#461	C₂²×C₃₇	1	1	yes	characteristic
334	#460	C₂²×C₃₇	1	1	yes	characteristic
335	#460	C₂²×C₃₇	1	2	yes	—
336	#459	C₂²×C₃₇	1	1	yes	characteristic
337	#431	C₂²×C₃₇	1	1	yes	characteristic
338	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
339	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
340	#416	—	2	1	no	—
341	#332	C₂²×C₃₇	1	2	yes	—
342	#332	C₂²×C₃₇	1	2	yes	—
343	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	—
344	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	—
345	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	—
346	D₄⋊C₈	C₂²×C₃₇	1	2	yes	—
347	C₃₇	#18884	1	1	yes	characteristic, direct product factor, Sylow
348	C₂×#41	—	2	1	no	—
349	C₂×#41	D₄×C₃₇	1	1	yes	characteristic
350	C₂²×Q₈	—	2	2	no	—
351	C₂²×Q₈	—	2	1	no	—
352	#135	—	4	4	no	—
353	C₂×Q₁₆	—	2	1	no	—
354	C₂×SD₁₆	—	2	1	no	—
355	C₂×SD₁₆	—	2	1	no	—
356	C₂×SD₁₆	—	2	2	no	—
357	C₂×D₈	—	2	1	no	—
358	C₂²×C₈	—	2	1	no	—
359	C₂²×C₈	—	2	1	no	—
360	C₄⋊Q₈	—	2	2	no	—
361	C₄⋊Q₈	—	2	2	no	—
362	C₄⋊Q₈	—	2	4	no	—
363	C₄⋊Q₈	—	2	2	no	—
364	C₄⋊Q₈	—	2	2	no	—
365	C₄⋊Q₈	—	2	1	no	—
366	C₄⋊Q₈	—	2	1	no	—
367	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
368	C₄⋊Q₈	D₄×C₃₇	1	2	yes	—
369	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
370	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
371	C₄⋊Q₈	C₂³×C₃₇	1	2	yes	—
372	#127	C₂³×C₃₇	1	1	yes	characteristic
373	#125	—	2	2	no	—
374	#125	—	2	4	no	—
375	#125	—	2	2	no	—
376	#125	—	2	1	no	—
377	#124	—	2	1	no	—
378	C₂²⋊Q₈	—	2	2	no	—
379	C₂²⋊Q₈	—	2	4	no	—
380	C₂²⋊Q₈	—	2	4	no	—
381	C₂²⋊Q₈	—	2	1	no	—
382	C₂²⋊Q₈	—	2	2	no	—
383	C₂²⋊Q₈	—	2	4	no	—
384	C₂²⋊Q₈	D₄×C₃₇	1	2	yes	—
385	#121	—	2	1	no	—
386	#121	—	2	1	no	—
387	C₄×Q₈	—	2	2	no	—
388	C₄×Q₈	—	2	2	no	—
389	C₄×Q₈	—	2	2	no	—
390	C₄×Q₈	—	2	1	no	—
391	C₄×Q₈	D₄×C₃₇	1	1	yes	characteristic
392	C₄×Q₈	C₂³×C₃₇	1	1	yes	characteristic
393	C₄×Q₈	C₂³×C₃₇	1	2	yes	—
394	C₄×D₄	—	2	4	no	—
395	C₄×D₄	—	2	2	no	—
396	C₄×D₄	—	2	1	no	—
397	C₄×D₄	—	2	1	no	—
398	C₄×D₄	—	2	1	no	—
399	C₄×D₄	—	2	1	no	—
400	C₄×D₄	D₄×C₃₇	1	1	yes	characteristic
401	C₄×D₄	C₂³×C₃₇	1	1	yes	characteristic
402	#117	—	2	2	no	—
403	#117	—	2	1	no	—
404	#117	—	2	1	no	—
405	#117	D₄×C₃₇	1	1	yes	characteristic
406	C₂×C₄⋊C₄	—	2	2	no	—
407	C₂×C₄⋊C₄	—	2	2	no	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
410	C₂×C₄²	—	2	1	no	—
411	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
412	#106	—	2	2	no	—
413	#106	—	2	4	no	—
414	C₄⋊C₈	—	2	1	no	—
415	C₄⋊C₈	—	2	1	no	—
416	C₄⋊C₈	—	2	1	no	—
417	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
418	C₄⋊C₈	C₂³×C₃₇	1	1	yes	characteristic
419	C₄⋊C₈	C₂³×C₃₇	1	1	yes	characteristic
420	#103	—	2	2	no	—
421	#103	—	2	1	no	—
422	#103	—	2	1	no	—
423	#102	—	2	1	no	—
424	#102	—	2	1	no	—
425	#102	—	2	2	no	—
426	#102	—	2	4	no	—
427	C₂²⋊C₈	—	2	1	no	—
428	C₄×C₈	C₂³×C₃₇	1	2	yes	—
429	#41	—	2	2	no	—
430	#41	—	4	2	no	—
431	#41	—	4	2	no	—
432	#41	SD₁₆×C₃₇	1	4	yes	complemented
433	C₂×Q₈	—	2	4	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	2	no	—
436	C₂×Q₈	—	2	2	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	8	1	no	—
439	C₂×Q₈	—	8	1	no	—
440	C₂×Q₈	—	8	2	no	—
441	C₂×Q₈	—	8	2	no	—
442	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
443	C₂×Q₈	C₂×D₄×C₃₇	1	1	yes	characteristic
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	4	1	no	—
449	C₂×D₄	C₂×D₄×C₃₇	1	1	yes	characteristic
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	4	1	no	—
456	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
459	Q₁₆	—	4	2	no	—
460	SD₁₆	—	4	2	no	—
461	SD₁₆	—	4	2	no	—
462	SD₁₆	—	8	2	no	—
463	D₈	—	4	2	no	—
464	C₂×C₈	—	2	2	no	—
465	C₂×C₈	—	2	2	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	4	2	no	—
469	C₂×C₈	—	8	1	no	—
470	C₄⋊C₄	—	2	4	no	—
471	C₄⋊C₄	—	2	4	no	—
472	C₄⋊C₄	—	2	4	no	—
473	C₄⋊C₄	—	2	4	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
487	C₄⋊C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
488	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
489	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
490	C₂²⋊C₄	—	2	4	no	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	—	2	1	no	—
495	C₂²⋊C₄	—	4	1	no	—
496	C₂²⋊C₄	—	4	1	no	—
497	C₄²	—	2	4	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	2	2	no	—
502	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
503	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
504	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
505	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
506	C₂³	—	2	1	no	—
507	C₂³	—	4	1	no	—
508	C₂³	#120×C₃₇	1	1	yes	characteristic
509	Q₈	—	2	1	no	—
510	Q₈	—	2	2	no	—
511	Q₈	—	2	2	no	—
512	Q₈	—	4	2	no	—
513	Q₈	—	4	2	no	—
514	Q₈	—	4	2	no	—
515	Q₈	—	4	1	no	—
516	Q₈	—	4	1	no	—
517	Q₈	—	8	2	no	—
518	Q₈	—	8	4	no	—
519	Q₈	C₂×SD₁₆×C₃₇	1	2	yes	—
520	D₄	—	2	4	no	—
521	D₄	—	2	1	no	—
522	D₄	—	4	2	no	—
523	D₄	—	4	1	no	—
524	D₄	—	4	1	no	—
525	D₄	—	4	1	no	—
526	D₄	—	4	1	no	—
527	D₄	—	8	2	no	—
528	D₄	C₂×SD₁₆×C₃₇	1	2	yes	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	8	2	no	—
544	C₂×C₄	—	8	4	no	—
545	C₂×C₄	—	8	2	no	—
546	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
547	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
548	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
549	C₂×C₄	C₂×SD₁₆×C₃₇	1	2	yes	—
550	C₂×C₄	#137×C₃₇	1	2	yes	—
551	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
552	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
553	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
554	C₈	—	4	2	no	—
555	C₈	—	4	1	no	—
556	C₈	—	4	1	no	—
557	C₈	—	4	2	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	2	2	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	—	8	1	no	—
564	C₂²	—	8	1	no	—
565	C₂²	—	8	1	no	—
566	C₂²	C₃₇×#448	1	2	yes	—
567	C₂²	C₂×#120×C₃₇	1	1	yes	characteristic
568	C₄	—	2	2	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	1	no	—
572	C₄	—	4	1	no	—
573	C₄	—	4	2	no	—
574	C₄	—	4	4	no	—
575	C₄	—	4	1	no	—
576	C₄	—	4	2	no	—
577	C₄	—	8	1	no	—
578	C₄	C₃₇×#448	1	2	yes	—
579	C₄	C₂²×SD₁₆×C₃₇	1	1	yes	characteristic
580	C₄	C₂×#137×C₃₇	1	1	yes	characteristic
581	C₄	C₃₇×#576	1	1	yes	characteristic
582	C₄	C₃₇×#577	1	1	yes	characteristic
583	C₂	—	2	2	no	—
584	C₂	—	4	2	no	—
585	C₂	—	16	1	no	—
586	C₂	C₂×C₃₇×#448	1	1	yes	characteristic
587	C₂	C₃₇×#3012	1	1	yes	characteristic
588	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×#3503	C₂	semidirect
2. C₃₇×#3246	C₂	semidirect
3. C₃₇×#3227	C₂	semidirect
5. C₃₇×#1653	C₂	semidirect
6. C₃₇×#1651	C₂	semidirect
7. C₃₇×#1627	C₂	semidirect
8. C₃₇×#1626	C₂	semidirect
9. C₂×C₃₇×#332	C₂	semidirect
10. C₃₇×#1481	C₂	semidirect
11. C₃₇×#1477	C₂	semidirect
137. #41×C₃₇	SD₁₆	semidirect
263. #18884	C₃₇	direct (N × H)
289. #3503	C₂×C₃₇	semidirect
290. #3246	C₂×C₃₇	semidirect
291. #3227	C₂×C₃₇	semidirect
293. #1653	C₂×C₃₇	semidirect
294. #1651	C₂×C₃₇	semidirect
295. #1627	C₂×C₃₇	semidirect
296. #1626	C₂×C₃₇	semidirect
297. C₂×#332	C₂×C₃₇	semidirect
298. #1481	C₂×C₃₇	semidirect
299. #1477	C₂×C₃₇	semidirect
347. C₃₇	#18884	direct (N × H)
432. #41	SD₁₆×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₃₇×#3503	2
C₃₇×#3246	2
C₃₇×#3227	2
C₃₇×#3035	2
C₃₇×#1653	2
C₃₇×#1651	2
C₃₇×#1627	2
C₃₇×#1626	2
C₂×C₃₇×#332	2
C₃₇×#1481	2
C₃₇×#1477	2
#18884	37

Subgroups — C37×#18884 #22640137

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#18884 #22640137