Subgroups — C₃₇×#18941 #22640194

Order 9472.

914 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3548	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#3249	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#3235	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#3210	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#1644	C₂	1	2	yes	maximal, complemented
6	C₃₇×#1641	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1632	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1631	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1551	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1497	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1480	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₇×#562	—	2	2	no	—
13	C₃₇×#554	—	2	1	no	—
14	C₃₇×#554	C₂²	1	2	yes	—
15	C₃₇×#550	—	2	1	no	—
16	C₃₇×#550	C₂²	1	2	yes	—
17	C₃₇×#547	—	2	1	no	—
18	C₃₇×#547	—	2	1	no	—
19	C₃₇×#540	—	2	2	no	—
20	C₃₇×#537	—	2	2	no	—
21	C₃₇×#537	—	2	2	no	—
22	C₃₇×#533	C₂²	1	1	yes	characteristic
23	C₃₇×#533	C₂²	1	1	yes	characteristic
24	C₃₇×#532	C₂²	1	1	yes	characteristic
25	C₃₇×#532	C₂²	1	1	yes	characteristic
26	C₃₇×#501	—	2	1	no	—
27	C₃₇×#494	C₂²	1	1	yes	characteristic
28	C₃₇×#492	C₂²	1	1	yes	characteristic
29	C₃₇×#490	—	2	1	no	—
30	C₃₇×#487	C₂²	1	1	yes	characteristic
31	C₃₇×#486	C₂²	1	1	yes	characteristic
32	C₃₇×#482	—	2	2	no	—
33	C₃₇×#477	—	2	1	no	—
34	C₃₇×#477	C₂²	1	2	yes	—
35	C₃₇×#476	C₂²	1	2	yes	—
36	C₃₇×#474	C₂²	1	2	yes	—
37	C₃₇×#467	—	2	2	no	—
38	C₃₇×#464	—	2	2	no	—
39	C₃₇×#462	—	2	1	no	—
40	C₃₇×#462	C₂²	1	2	yes	—
41	C₃₇×#452	—	2	2	no	—
42	C₃₇×#432	C₂²	1	1	yes	characteristic
43	C₃₇×#431	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
45	C₃₇×#333	C₂²	1	2	yes	—
46	C₃₇×#331	C₂²	1	2	yes	—
47	C₃₇×Q₈⋊C₈	C₂²	1	2	yes	—
48	C₃₇×Q₈⋊C₈	C₂²	1	2	yes	—
49	C₃₇×D₄⋊C₈	C₂²	1	2	yes	—
50	C₃₇×D₄⋊C₈	C₂²	1	2	yes	—
51	C₂×#41×C₃₇	—	2	2	no	—
52	C₂×#41×C₃₇	—	2	2	no	—
53	C₂×#41×C₃₇	—	2	1	no	—
54	C₂×#41×C₃₇	D₄	1	2	yes	—
55	C₂×Q₁₆×C₃₇	—	2	2	no	—
56	C₂×Q₁₆×C₃₇	—	2	2	no	—
57	C₂×SD₁₆×C₃₇	—	2	2	no	—
58	C₂²×C₈×C₃₇	—	2	1	no	—
59	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
60	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
61	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
62	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
63	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
64	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
65	#127×C₃₇	—	2	2	no	—
66	#127×C₃₇	D₄	1	1	yes	characteristic
67	#127×C₃₇	C₂³	1	1	yes	characteristic
68	#125×C₃₇	—	2	2	no	—
69	#125×C₃₇	—	2	1	no	—
70	#125×C₃₇	—	2	1	no	—
71	#124×C₃₇	—	2	1	no	—
72	#124×C₃₇	D₄	1	2	yes	—
73	#123×C₃₇	—	2	4	no	—
74	#123×C₃₇	—	2	4	no	—
75	C₂²⋊Q₈×C₃₇	—	2	2	no	—
76	C₂²⋊Q₈×C₃₇	—	2	4	no	—
77	C₂²⋊Q₈×C₃₇	—	2	2	no	—
78	C₂²⋊Q₈×C₃₇	—	2	4	no	—
79	C₂²⋊Q₈×C₃₇	—	2	1	no	—
80	C₂²⋊Q₈×C₃₇	—	2	1	no	—
81	C₂²⋊Q₈×C₃₇	—	2	1	no	—
82	C₂²⋊Q₈×C₃₇	D₄	1	2	yes	—
83	#121×C₃₇	—	2	4	no	—
84	#121×C₃₇	—	2	4	no	—
85	#121×C₃₇	—	2	2	no	—
86	#121×C₃₇	—	2	4	no	—
87	#121×C₃₇	—	2	4	no	—
88	#121×C₃₇	—	2	1	no	—
89	#121×C₃₇	—	2	1	no	—
90	#121×C₃₇	—	2	1	no	—
91	#121×C₃₇	—	2	2	no	—
92	#121×C₃₇	D₄	1	2	yes	—
93	C₄×Q₈×C₃₇	—	2	1	no	—
94	C₄×Q₈×C₃₇	—	2	1	no	—
95	C₄×Q₈×C₃₇	—	2	1	no	—
96	C₄×Q₈×C₃₇	C₂³	1	2	yes	—
97	C₄×D₄×C₃₇	—	2	2	no	—
98	C₄×D₄×C₃₇	—	2	2	no	—
99	C₄×D₄×C₃₇	—	2	1	no	—
100	C₄×D₄×C₃₇	—	2	1	no	—
101	C₄×D₄×C₃₇	—	2	1	no	—
102	C₄×D₄×C₃₇	C₂³	1	2	yes	—
103	#117×C₃₇	—	2	1	no	—
104	#117×C₃₇	—	2	1	no	—
105	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
106	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
107	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
108	#107×C₃₇	—	2	2	no	—
109	#107×C₃₇	—	2	2	no	—
110	#106×C₃₇	—	2	2	no	—
111	C₄⋊C₈×C₃₇	—	2	1	no	—
112	C₄⋊C₈×C₃₇	—	2	1	no	—
113	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
114	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
115	#103×C₃₇	—	2	2	no	—
116	#103×C₃₇	—	2	2	no	—
117	#103×C₃₇	—	2	2	no	—
118	#102×C₃₇	—	2	2	no	—
119	#102×C₃₇	—	2	2	no	—
120	#102×C₃₇	—	2	2	no	—
121	C₂²⋊C₈×C₃₇	—	2	1	no	—
122	C₂²⋊C₈×C₃₇	—	2	1	no	—
123	#97×C₃₇	—	2	1	no	—
124	C₄×C₈×C₃₇	C₂³	1	1	yes	characteristic
125	C₄×C₈×C₃₇	C₂³	1	1	yes	characteristic
126	#41×C₃₇	—	8	1	no	—
127	#41×C₃₇	—	8	1	no	—
128	#41×C₃₇	—	8	2	no	—
129	#41×C₃₇	—	8	2	no	—
130	#41×C₃₇	—	8	2	no	—
131	#41×C₃₇	—	8	4	no	—
132	C₂×Q₈×C₃₇	—	2	1	no	—
133	C₂×Q₈×C₃₇	—	2	1	no	—
134	C₂×Q₈×C₃₇	—	2	1	no	—
135	C₂×Q₈×C₃₇	—	2	1	no	—
136	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
137	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
138	C₂×D₄×C₃₇	—	2	4	no	—
139	C₂×D₄×C₃₇	—	2	4	no	—
140	C₂×D₄×C₃₇	—	2	2	no	—
141	C₂×D₄×C₃₇	—	2	2	no	—
142	C₂×D₄×C₃₇	—	2	1	no	—
143	C₂×D₄×C₃₇	—	2	1	no	—
144	C₂×D₄×C₃₇	—	2	1	no	—
145	C₂×D₄×C₃₇	—	2	1	no	—
146	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
147	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₃₇	—	2	4	no	—
149	C₂²×C₄×C₃₇	—	2	4	no	—
150	C₂²×C₄×C₃₇	—	2	2	no	—
151	C₂²×C₄×C₃₇	—	2	2	no	—
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	Q₁₆×C₃₇	—	8	2	no	—
156	Q₁₆×C₃₇	—	8	2	no	—
157	SD₁₆×C₃₇	—	8	2	no	—
158	C₂×C₈×C₃₇	—	2	1	no	—
159	C₂×C₈×C₃₇	—	2	1	no	—
160	C₂×C₈×C₃₇	—	2	2	no	—
161	C₂×C₈×C₃₇	—	2	2	no	—
162	C₂×C₈×C₃₇	—	8	1	no	—
163	C₄⋊C₄×C₃₇	—	2	4	no	—
164	C₄⋊C₄×C₃₇	—	2	4	no	—
165	C₄⋊C₄×C₃₇	—	2	1	no	—
166	C₄⋊C₄×C₃₇	—	2	1	no	—
167	C₄⋊C₄×C₃₇	—	2	1	no	—
168	C₄⋊C₄×C₃₇	—	2	1	no	—
169	C₄⋊C₄×C₃₇	—	2	2	no	—
170	C₄⋊C₄×C₃₇	—	2	1	no	—
171	C₄⋊C₄×C₃₇	—	2	1	no	—
172	C₄⋊C₄×C₃₇	—	2	2	no	—
173	C₄⋊C₄×C₃₇	—	2	1	no	—
174	C₄⋊C₄×C₃₇	—	2	1	no	—
175	C₄⋊C₄×C₃₇	—	2	1	no	—
176	C₄⋊C₄×C₃₇	—	2	1	no	—
177	C₄⋊C₄×C₃₇	—	4	1	no	—
178	C₄⋊C₄×C₃₇	—	4	1	no	—
179	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
180	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
181	C₂²⋊C₄×C₃₇	—	2	4	no	—
182	C₂²⋊C₄×C₃₇	—	2	4	no	—
183	C₂²⋊C₄×C₃₇	—	2	2	no	—
184	C₂²⋊C₄×C₃₇	—	2	2	no	—
185	C₂²⋊C₄×C₃₇	—	2	2	no	—
186	C₂²⋊C₄×C₃₇	—	2	2	no	—
187	C₂²⋊C₄×C₃₇	—	2	2	no	—
188	C₂²⋊C₄×C₃₇	—	4	1	no	—
189	C₄²×C₃₇	—	2	2	no	—
190	C₄²×C₃₇	—	4	1	no	—
191	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
193	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
195	C₂³×C₃₇	—	2	2	no	—
196	C₂³×C₃₇	—	2	2	no	—
197	C₂³×C₃₇	#120	1	1	yes	characteristic
198	Q₈×C₃₇	—	2	2	no	—
199	Q₈×C₃₇	—	2	2	no	—
200	Q₈×C₃₇	—	4	2	no	—
201	Q₈×C₃₇	—	4	2	no	—
202	Q₈×C₃₇	—	4	2	no	—
203	Q₈×C₃₇	—	4	1	no	—
204	Q₈×C₃₇	—	4	1	no	—
205	Q₈×C₃₇	—	8	1	no	—
206	D₄×C₃₇	—	2	4	no	—
207	D₄×C₃₇	—	4	2	no	—
208	D₄×C₃₇	—	4	2	no	—
209	D₄×C₃₇	—	4	1	no	—
210	D₄×C₃₇	—	4	1	no	—
211	D₄×C₃₇	—	4	2	no	—
212	D₄×C₃₇	—	8	1	no	—
213	D₄×C₃₇	—	8	2	no	—
214	D₄×C₃₇	—	8	2	no	—
215	D₄×C₃₇	—	8	4	no	—
216	D₄×C₃₇	—	8	4	no	—
217	C₂×C₄×C₃₇	—	2	1	no	—
218	C₂×C₄×C₃₇	—	2	1	no	—
219	C₂×C₄×C₃₇	—	2	2	no	—
220	C₂×C₄×C₃₇	—	2	2	no	—
221	C₂×C₄×C₃₇	—	2	2	no	—
222	C₂×C₄×C₃₇	—	2	2	no	—
223	C₂×C₄×C₃₇	—	2	2	no	—
224	C₂×C₄×C₃₇	—	4	1	no	—
225	C₂×C₄×C₃₇	—	4	4	no	—
226	C₂×C₄×C₃₇	—	4	2	no	—
227	C₂×C₄×C₃₇	—	4	2	no	—
228	C₂×C₄×C₃₇	—	4	1	no	—
229	C₂×C₄×C₃₇	—	4	1	no	—
230	C₂×C₄×C₃₇	—	8	4	no	—
231	C₂×C₄×C₃₇	—	8	4	no	—
232	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
233	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
234	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
235	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
238	C₈×C₃₇	—	4	1	no	—
239	C₈×C₃₇	—	4	1	no	—
240	C₈×C₃₇	—	4	2	no	—
241	C₈×C₃₇	—	4	2	no	—
242	#18941	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
243	C₂²×C₃₇	—	2	1	no	—
244	C₂²×C₃₇	—	2	1	no	—
245	C₂²×C₃₇	—	2	1	no	—
246	C₂²×C₃₇	—	4	2	no	—
247	C₂²×C₃₇	—	4	2	no	—
248	C₂²×C₃₇	—	4	2	no	—
249	C₂²×C₃₇	—	4	2	no	—
250	C₂²×C₃₇	—	4	2	no	—
251	C₂²×C₃₇	—	4	2	no	—
252	C₂²×C₃₇	C₂×#120	1	1	yes	characteristic
253	C₄×C₃₇	—	2	1	no	—
254	C₄×C₃₇	—	2	1	no	—
255	C₄×C₃₇	—	2	1	no	—
256	C₄×C₃₇	—	2	1	no	—
257	C₄×C₃₇	—	4	2	no	—
258	C₄×C₃₇	—	4	2	no	—
259	C₄×C₃₇	—	4	2	no	—
260	C₄×C₃₇	—	4	2	no	—
261	C₄×C₃₇	—	8	1	no	—
262	C₄×C₃₇	—	8	1	no	—
263	C₄×C₃₇	#576	1	1	yes	characteristic
264	C₄×C₃₇	#577	1	1	yes	characteristic
265	C₄×C₃₇	#578	1	2	yes	—
266	#3548	C₂×C₃₇	1	1	yes	characteristic
267	#3249	C₂×C₃₇	1	1	yes	characteristic, complemented
268	#3235	C₂×C₃₇	1	1	yes	characteristic, complemented
269	#3210	C₂×C₃₇	1	1	yes	characteristic, complemented
270	#1644	C₂×C₃₇	1	2	yes	complemented
271	#1641	C₂×C₃₇	1	2	yes	complemented
272	#1632	C₂×C₃₇	1	2	yes	complemented
273	#1631	C₂×C₃₇	1	2	yes	complemented
274	#1551	C₂×C₃₇	1	1	yes	characteristic, complemented
275	#1497	C₂×C₃₇	1	1	yes	characteristic, complemented
276	#1480	C₂×C₃₇	1	1	yes	characteristic, complemented
277	C₂×C₃₇	—	4	1	no	—
278	C₂×C₃₇	—	8	2	no	—
279	C₂×C₃₇	—	8	2	no	—
280	C₂×C₃₇	#3011	1	1	yes	characteristic
281	C₂×C₃₇	#3012	1	1	yes	characteristic
282	C₂×C₃₇	#3019	1	1	yes	characteristic
283	#562	—	2	2	no	—
284	#554	—	2	1	no	—
285	#554	C₂²×C₃₇	1	2	yes	—
286	#550	—	2	1	no	—
287	#550	C₂²×C₃₇	1	2	yes	—
288	#547	—	2	1	no	—
289	#547	—	2	1	no	—
290	#540	—	2	2	no	—
291	#537	—	2	2	no	—
292	#537	—	2	2	no	—
293	#533	C₂²×C₃₇	1	1	yes	characteristic
294	#533	C₂²×C₃₇	1	1	yes	characteristic
295	#532	C₂²×C₃₇	1	1	yes	characteristic
296	#532	C₂²×C₃₇	1	1	yes	characteristic
297	#501	—	2	1	no	—
298	#494	C₂²×C₃₇	1	1	yes	characteristic
299	#492	C₂²×C₃₇	1	1	yes	characteristic
300	#490	—	2	1	no	—
301	#487	C₂²×C₃₇	1	1	yes	characteristic
302	#486	C₂²×C₃₇	1	1	yes	characteristic
303	#482	—	2	2	no	—
304	#477	—	2	1	no	—
305	#477	C₂²×C₃₇	1	2	yes	—
306	#476	C₂²×C₃₇	1	2	yes	—
307	#474	C₂²×C₃₇	1	2	yes	—
308	#467	—	2	2	no	—
309	#464	—	2	2	no	—
310	#462	—	2	1	no	—
311	#462	C₂²×C₃₇	1	2	yes	—
312	#452	—	2	2	no	—
313	#432	C₂²×C₃₇	1	1	yes	characteristic
314	#431	C₂²×C₃₇	1	1	yes	characteristic
315	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
316	#333	C₂²×C₃₇	1	2	yes	—
317	#331	C₂²×C₃₇	1	2	yes	—
318	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	—
319	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	—
320	D₄⋊C₈	C₂²×C₃₇	1	2	yes	—
321	D₄⋊C₈	C₂²×C₃₇	1	2	yes	—
322	C₃₇	#18941	1	1	yes	characteristic, direct product factor, Sylow
323	C₂×#41	—	2	2	no	—
324	C₂×#41	—	2	2	no	—
325	C₂×#41	—	2	1	no	—
326	C₂×#41	D₄×C₃₇	1	2	yes	—
327	C₂×Q₁₆	—	2	2	no	—
328	C₂×Q₁₆	—	2	2	no	—
329	C₂×SD₁₆	—	2	2	no	—
330	C₂²×C₈	—	2	1	no	—
331	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
332	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
333	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
334	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
335	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
336	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
337	#127	—	2	2	no	—
338	#127	D₄×C₃₇	1	1	yes	characteristic
339	#127	C₂³×C₃₇	1	1	yes	characteristic
340	#125	—	2	2	no	—
341	#125	—	2	1	no	—
342	#125	—	2	1	no	—
343	#124	—	2	1	no	—
344	#124	D₄×C₃₇	1	2	yes	—
345	#123	—	2	4	no	—
346	#123	—	2	4	no	—
347	C₂²⋊Q₈	—	2	2	no	—
348	C₂²⋊Q₈	—	2	4	no	—
349	C₂²⋊Q₈	—	2	2	no	—
350	C₂²⋊Q₈	—	2	4	no	—
351	C₂²⋊Q₈	—	2	1	no	—
352	C₂²⋊Q₈	—	2	1	no	—
353	C₂²⋊Q₈	—	2	1	no	—
354	C₂²⋊Q₈	D₄×C₃₇	1	2	yes	—
355	#121	—	2	4	no	—
356	#121	—	2	4	no	—
357	#121	—	2	2	no	—
358	#121	—	2	4	no	—
359	#121	—	2	4	no	—
360	#121	—	2	1	no	—
361	#121	—	2	1	no	—
362	#121	—	2	1	no	—
363	#121	—	2	2	no	—
364	#121	D₄×C₃₇	1	2	yes	—
365	C₄×Q₈	—	2	1	no	—
366	C₄×Q₈	—	2	1	no	—
367	C₄×Q₈	—	2	1	no	—
368	C₄×Q₈	C₂³×C₃₇	1	2	yes	—
369	C₄×D₄	—	2	2	no	—
370	C₄×D₄	—	2	2	no	—
371	C₄×D₄	—	2	1	no	—
372	C₄×D₄	—	2	1	no	—
373	C₄×D₄	—	2	1	no	—
374	C₄×D₄	C₂³×C₃₇	1	2	yes	—
375	#117	—	2	1	no	—
376	#117	—	2	1	no	—
377	C₂×C₄⋊C₄	—	2	2	no	—
378	C₂×C₄⋊C₄	—	2	2	no	—
379	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
380	#107	—	2	2	no	—
381	#107	—	2	2	no	—
382	#106	—	2	2	no	—
383	C₄⋊C₈	—	2	1	no	—
384	C₄⋊C₈	—	2	1	no	—
385	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
386	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
387	#103	—	2	2	no	—
388	#103	—	2	2	no	—
389	#103	—	2	2	no	—
390	#102	—	2	2	no	—
391	#102	—	2	2	no	—
392	#102	—	2	2	no	—
393	C₂²⋊C₈	—	2	1	no	—
394	C₂²⋊C₈	—	2	1	no	—
395	#97	—	2	1	no	—
396	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
397	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
398	#41	—	8	1	no	—
399	#41	—	8	1	no	—
400	#41	—	8	2	no	—
401	#41	—	8	2	no	—
402	#41	—	8	2	no	—
403	#41	—	8	4	no	—
404	C₂×Q₈	—	2	1	no	—
405	C₂×Q₈	—	2	1	no	—
406	C₂×Q₈	—	2	1	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
409	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
410	C₂×D₄	—	2	4	no	—
411	C₂×D₄	—	2	4	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
419	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
427	Q₁₆	—	8	2	no	—
428	Q₁₆	—	8	2	no	—
429	SD₁₆	—	8	2	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	8	1	no	—
435	C₄⋊C₄	—	2	4	no	—
436	C₄⋊C₄	—	2	4	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	4	1	no	—
450	C₄⋊C₄	—	4	1	no	—
451	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
452	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
453	C₂²⋊C₄	—	2	4	no	—
454	C₂²⋊C₄	—	2	4	no	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₂²⋊C₄	—	2	2	no	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₂²⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	4	1	no	—
461	C₄²	—	2	2	no	—
462	C₄²	—	4	1	no	—
463	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
464	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
465	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
466	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
467	C₂³	—	2	2	no	—
468	C₂³	—	2	2	no	—
469	C₂³	#120×C₃₇	1	1	yes	characteristic
470	Q₈	—	2	2	no	—
471	Q₈	—	2	2	no	—
472	Q₈	—	4	2	no	—
473	Q₈	—	4	2	no	—
474	Q₈	—	4	2	no	—
475	Q₈	—	4	1	no	—
476	Q₈	—	4	1	no	—
477	Q₈	—	8	1	no	—
478	D₄	—	2	4	no	—
479	D₄	—	4	2	no	—
480	D₄	—	4	2	no	—
481	D₄	—	4	1	no	—
482	D₄	—	4	1	no	—
483	D₄	—	4	2	no	—
484	D₄	—	8	1	no	—
485	D₄	—	8	2	no	—
486	D₄	—	8	2	no	—
487	D₄	—	8	4	no	—
488	D₄	—	8	4	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	4	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	8	4	no	—
503	C₂×C₄	—	8	4	no	—
504	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
505	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
506	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
507	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
508	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
509	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
510	C₈	—	4	1	no	—
511	C₈	—	4	1	no	—
512	C₈	—	4	2	no	—
513	C₈	—	4	2	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	2	1	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	2	no	—
523	C₂²	C₂×#120×C₃₇	1	1	yes	characteristic
524	C₄	—	2	1	no	—
525	C₄	—	2	1	no	—
526	C₄	—	2	1	no	—
527	C₄	—	2	1	no	—
528	C₄	—	4	2	no	—
529	C₄	—	4	2	no	—
530	C₄	—	4	2	no	—
531	C₄	—	4	2	no	—
532	C₄	—	8	1	no	—
533	C₄	—	8	1	no	—
534	C₄	C₃₇×#576	1	1	yes	characteristic
535	C₄	C₃₇×#577	1	1	yes	characteristic
536	C₄	C₃₇×#578	1	2	yes	—
537	C₂	—	4	1	no	—
538	C₂	—	8	2	no	—
539	C₂	—	8	2	no	—
540	C₂	C₃₇×#3011	1	1	yes	characteristic
541	C₂	C₃₇×#3012	1	1	yes	characteristic
542	C₂	C₃₇×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₇
prime radical	C₃₇×#3548	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
2. C₃₇×#3249	C₂	semidirect
3. C₃₇×#3235	C₂	semidirect
4. C₃₇×#3210	C₂	semidirect
5. C₃₇×#1644	C₂	semidirect
6. C₃₇×#1641	C₂	semidirect
7. C₃₇×#1632	C₂	semidirect
8. C₃₇×#1631	C₂	semidirect
9. C₃₇×#1551	C₂	semidirect
10. C₃₇×#1497	C₂	semidirect
11. C₃₇×#1480	C₂	semidirect
242. #18941	C₃₇	direct (N × H)
267. #3249	C₂×C₃₇	semidirect
268. #3235	C₂×C₃₇	semidirect
269. #3210	C₂×C₃₇	semidirect
270. #1644	C₂×C₃₇	semidirect
271. #1641	C₂×C₃₇	semidirect
272. #1632	C₂×C₃₇	semidirect
273. #1631	C₂×C₃₇	semidirect
274. #1551	C₂×C₃₇	semidirect
275. #1497	C₂×C₃₇	semidirect
276. #1480	C₂×C₃₇	semidirect
322. C₃₇	#18941	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×#3548	2
C₃₇×#3249	2
C₃₇×#3235	2
C₃₇×#3210	2
C₃₇×#1644	2
C₃₇×#1641	2
C₃₇×#1632	2
C₃₇×#1631	2
C₃₇×#1551	2
C₃₇×#1497	2
C₃₇×#1480	2
#18941	37

Subgroups — C37×#18941 #22640194

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#18941 #22640194