Subgroups — C₃₇×#18625 #22639878

Order 9472.

1056 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3508	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#3230	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#492	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#3079	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#1631	C₂	1	4	yes	maximal, complemented
6	C₃₇×#1630	C₂	1	4	yes	maximal, complemented
7	C₃₇×#1545	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1493	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1476	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₃₇	—	2	2	no	—
11	C₃₇×#559	—	2	1	no	—
12	C₃₇×#559	C₂²	1	2	yes	—
13	C₃₇×#550	—	2	1	no	—
14	C₃₇×#550	C₂²	1	2	yes	—
15	C₃₇×#546	—	2	2	no	—
16	C₃₇×#546	—	2	2	no	—
17	C₃₇×#540	—	2	2	no	—
18	C₃₇×#535	—	2	1	no	—
19	C₃₇×#533	C₂²	1	1	yes	characteristic
20	C₃₇×#532	—	2	1	no	—
21	C₃₇×#532	—	2	1	no	—
22	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
23	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
24	C₃₇×#518	—	2	1	no	—
25	C₄×#41×C₃₇	C₂²	1	1	yes	characteristic
26	C₃₇×#500	—	2	1	no	—
27	C₃₇×#492	—	2	2	no	—
28	C₃₇×#492	C₂²	1	4	yes	—
29	C₃₇×#487	—	2	1	no	—
30	C₃₇×#484	—	2	2	no	—
31	C₃₇×#477	C₂²	1	2	yes	complemented
32	C₃₇×#477	C₂²	1	4	yes	complemented
33	C₃₇×#476	C₂²	1	2	yes	complemented
34	C₃₇×#475	—	2	1	no	—
35	C₃₇×#474	—	2	1	no	—
36	C₃₇×#431	C₂²	1	1	yes	characteristic
37	C₃₇×#428	—	2	1	no	—
38	C₃₇×#423	C₂²	1	1	yes	characteristic
39	C₃₇×#417	—	2	1	no	—
40	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
41	C₃₇×#331	C₂²	1	4	yes	—
42	C₃₇×Q₈⋊C₈	C₂²	1	2	yes	complemented
43	C₃₇×Q₈⋊C₈	C₂²	1	4	yes	complemented
44	C₃₇×D₄⋊C₈	C₂²	1	2	yes	complemented
45	C₂×#41×C₃₇	—	2	2	no	—
46	C₂×#41×C₃₇	—	2	2	no	—
47	C₂×#41×C₃₇	D₄	1	1	yes	characteristic
48	C₂²×Q₈×C₃₇	—	2	1	no	—
49	C₂²×D₄×C₃₇	—	2	1	no	—
50	C₂²×D₄×C₃₇	—	2	1	no	—
51	C₂²×D₄×C₃₇	D₄	1	2	yes	—
52	C₂×SD₁₆×C₃₇	—	2	8	no	—
53	C₂×SD₁₆×C₃₇	—	4	8	no	—
54	C₂×M₁₆×C₃₇	—	2	1	no	—
55	C₂²×C₈×C₃₇	—	2	1	no	—
56	C₄⋊Q₈×C₃₇	—	2	1	no	—
57	C₄⋊Q₈×C₃₇	—	2	1	no	—
58	C₄⋊Q₈×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	C₂³	1	2	yes	—
62	#127×C₃₇	—	2	2	no	—
63	#127×C₃₇	—	2	1	no	—
64	#127×C₃₇	—	2	1	no	—
65	#127×C₃₇	D₄	1	2	yes	—
66	#127×C₃₇	C₂³	1	2	yes	—
67	#125×C₃₇	—	2	1	no	—
68	#124×C₃₇	—	2	2	no	—
69	#124×C₃₇	—	2	2	no	—
70	#124×C₃₇	—	2	2	no	—
71	#123×C₃₇	—	2	4	no	—
72	#123×C₃₇	—	2	4	no	—
73	C₂²⋊Q₈×C₃₇	—	2	1	no	—
74	C₂²⋊Q₈×C₃₇	D₄	1	2	yes	—
75	#121×C₃₇	—	2	2	no	—
76	#121×C₃₇	—	2	2	no	—
77	#121×C₃₇	—	2	2	no	—
78	#121×C₃₇	—	2	4	no	—
79	#121×C₃₇	—	2	4	no	—
80	#121×C₃₇	—	2	2	no	—
81	#120×C₃₇	—	2	4	no	—
82	C₄×Q₈×C₃₇	—	2	1	no	—
83	C₄×Q₈×C₃₇	D₄	1	1	yes	characteristic
84	C₄×Q₈×C₃₇	C₂³	1	2	yes	—
85	C₄×Q₈×C₃₇	C₂³	1	1	yes	characteristic
86	C₄×D₄×C₃₇	—	2	2	no	—
87	C₄×D₄×C₃₇	—	2	2	no	—
88	C₄×D₄×C₃₇	—	2	2	no	—
89	C₄×D₄×C₃₇	—	2	1	no	—
90	C₄×D₄×C₃₇	—	2	1	no	—
91	C₄×D₄×C₃₇	—	2	2	no	—
92	C₄×D₄×C₃₇	—	2	2	no	—
93	C₄×D₄×C₃₇	—	2	2	no	—
94	C₄×D₄×C₃₇	D₄	1	1	yes	characteristic
95	C₄×D₄×C₃₇	C₂³	1	1	yes	characteristic
96	#117×C₃₇	—	2	1	no	—
97	#117×C₃₇	—	2	1	no	—
98	#117×C₃₇	D₄	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
100	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
102	C₂×C₄²×C₃₇	—	2	1	no	—
103	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
104	#107×C₃₇	—	2	2	no	—
105	#107×C₃₇	—	2	4	no	—
106	#106×C₃₇	—	2	2	no	—
107	C₄⋊C₈×C₃₇	—	2	1	no	—
108	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
109	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
110	#103×C₃₇	—	2	2	no	—
111	#103×C₃₇	—	2	4	no	—
112	#102×C₃₇	—	2	2	no	—
113	C₂²⋊C₈×C₃₇	—	2	1	no	—
114	C₄×C₈×C₃₇	—	2	1	no	—
115	C₄×C₈×C₃₇	—	2	1	no	—
116	C₄×C₈×C₃₇	C₂³	1	2	yes	—
117	C₂⁴×C₃₇	—	2	2	no	—
118	#41×C₃₇	—	2	2	no	—
119	#41×C₃₇	—	2	2	no	—
120	#41×C₃₇	—	8	4	no	—
121	#41×C₃₇	—	8	4	no	—
122	C₂×Q₈×C₃₇	—	2	1	no	—
123	C₂×Q₈×C₃₇	—	2	2	no	—
124	C₂×Q₈×C₃₇	—	4	4	no	—
125	C₂×Q₈×C₃₇	—	4	1	no	—
126	C₂×Q₈×C₃₇	C₂×D₄	1	1	yes	characteristic
127	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
128	C₂×D₄×C₃₇	—	2	1	no	—
129	C₂×D₄×C₃₇	—	2	4	no	—
130	C₂×D₄×C₃₇	—	2	4	no	—
131	C₂×D₄×C₃₇	—	2	2	no	—
132	C₂×D₄×C₃₇	—	2	2	no	—
133	C₂×D₄×C₃₇	—	2	2	no	—
134	C₂×D₄×C₃₇	—	2	2	no	—
135	C₂×D₄×C₃₇	—	2	2	no	—
136	C₂×D₄×C₃₇	—	4	4	no	—
137	C₂×D₄×C₃₇	—	4	2	no	—
138	C₂×D₄×C₃₇	—	4	2	no	—
139	C₂×D₄×C₃₇	—	8	2	no	—
140	C₂×D₄×C₃₇	C₂×D₄	1	1	yes	characteristic
141	C₂×D₄×C₃₇	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₃₇	—	2	4	no	—
143	C₂²×C₄×C₃₇	—	2	4	no	—
144	C₂²×C₄×C₃₇	—	2	1	no	—
145	C₂²×C₄×C₃₇	—	2	1	no	—
146	C₂²×C₄×C₃₇	—	2	1	no	—
147	C₂²×C₄×C₃₇	—	4	1	no	—
148	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
151	SD₁₆×C₃₇	—	4	16	no	—
152	M₁₆×C₃₇	—	4	2	no	—
153	C₂×C₈×C₃₇	—	2	4	no	—
154	C₂×C₈×C₃₇	—	2	2	no	—
155	C₂×C₈×C₃₇	—	2	2	no	—
156	C₂×C₈×C₃₇	—	2	2	no	—
157	C₄⋊C₄×C₃₇	—	2	1	no	—
158	C₄⋊C₄×C₃₇	—	2	1	no	—
159	C₄⋊C₄×C₃₇	—	2	1	no	—
160	C₄⋊C₄×C₃₇	—	2	1	no	—
161	C₄⋊C₄×C₃₇	—	2	2	no	—
162	C₄⋊C₄×C₃₇	—	2	1	no	—
163	C₄⋊C₄×C₃₇	—	2	2	no	—
164	C₄⋊C₄×C₃₇	—	2	2	no	—
165	C₄⋊C₄×C₃₇	—	2	2	no	—
166	C₄⋊C₄×C₃₇	—	4	1	no	—
167	C₄⋊C₄×C₃₇	—	4	1	no	—
168	C₄⋊C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
169	C₄⋊C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
170	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
171	C₂²⋊C₄×C₃₇	—	2	4	no	—
172	C₂²⋊C₄×C₃₇	—	2	4	no	—
173	C₂²⋊C₄×C₃₇	—	2	4	no	—
174	C₂²⋊C₄×C₃₇	—	2	4	no	—
175	C₂²⋊C₄×C₃₇	—	2	1	no	—
176	C₂²⋊C₄×C₃₇	—	2	2	no	—
177	C₂²⋊C₄×C₃₇	—	2	1	no	—
178	C₂²⋊C₄×C₃₇	—	2	1	no	—
179	C₄²×C₃₇	—	2	1	no	—
180	C₄²×C₃₇	—	2	1	no	—
181	C₄²×C₃₇	—	2	1	no	—
182	C₄²×C₃₇	—	2	2	no	—
183	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
186	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
187	C₂³×C₃₇	—	2	4	no	—
188	C₂³×C₃₇	—	2	1	no	—
189	C₂³×C₃₇	—	4	4	no	—
190	C₂³×C₃₇	—	8	2	no	—
191	C₂³×C₃₇	—	8	2	no	—
192	C₂³×C₃₇	#120	1	1	yes	characteristic
193	Q₈×C₃₇	—	2	1	no	—
194	Q₈×C₃₇	—	2	1	no	—
195	Q₈×C₃₇	—	2	4	no	—
196	Q₈×C₃₇	—	4	4	no	—
197	Q₈×C₃₇	—	4	2	no	—
198	Q₈×C₃₇	—	8	2	no	—
199	D₄×C₃₇	—	2	1	no	—
200	D₄×C₃₇	—	2	1	no	—
201	D₄×C₃₇	—	4	4	no	—
202	D₄×C₃₇	—	4	2	no	—
203	D₄×C₃₇	—	4	2	no	—
204	D₄×C₃₇	—	4	2	no	—
205	D₄×C₃₇	—	4	4	no	—
206	D₄×C₃₇	—	4	4	no	—
207	D₄×C₃₇	—	4	4	no	—
208	D₄×C₃₇	—	8	2	no	—
209	D₄×C₃₇	—	8	4	no	—
210	D₄×C₃₇	—	8	4	no	—
211	C₂×C₄×C₃₇	—	2	2	no	—
212	C₂×C₄×C₃₇	—	2	2	no	—
213	C₂×C₄×C₃₇	—	2	1	no	—
214	C₂×C₄×C₃₇	—	2	1	no	—
215	C₂×C₄×C₃₇	—	2	1	no	—
216	C₂×C₄×C₃₇	—	2	2	no	—
217	C₂×C₄×C₃₇	—	2	2	no	—
218	C₂×C₄×C₃₇	—	4	2	no	—
219	C₂×C₄×C₃₇	—	4	2	no	—
220	C₂×C₄×C₃₇	—	4	2	no	—
221	C₂×C₄×C₃₇	—	4	2	no	—
222	C₂×C₄×C₃₇	—	8	4	no	—
223	C₂×C₄×C₃₇	—	8	4	no	—
224	C₂×C₄×C₃₇	—	8	2	no	—
225	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
226	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
227	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
228	C₂×C₄×C₃₇	#135	1	2	yes	—
229	C₂×C₄×C₃₇	#137	1	2	yes	—
230	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
233	C₈×C₃₇	—	2	4	no	—
234	C₈×C₃₇	—	4	2	no	—
235	C₈×C₃₇	—	4	2	no	—
236	#18625	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₂²×C₃₇	—	2	1	no	—
238	C₂²×C₃₇	—	2	1	no	—
239	C₂²×C₃₇	—	4	1	no	—
240	C₂²×C₃₇	—	4	4	no	—
241	C₂²×C₃₇	—	4	1	no	—
242	C₂²×C₃₇	—	4	4	no	—
243	C₂²×C₃₇	—	4	1	no	—
244	C₂²×C₃₇	—	4	4	no	—
245	C₂²×C₃₇	—	16	4	no	—
246	C₂²×C₃₇	#452	1	2	yes	—
247	C₂²×C₃₇	C₂×#120	1	1	yes	characteristic
248	C₄×C₃₇	—	2	1	no	—
249	C₄×C₃₇	—	2	1	no	—
250	C₄×C₃₇	—	4	1	no	—
251	C₄×C₃₇	—	4	1	no	—
252	C₄×C₃₇	—	4	2	no	—
253	C₄×C₃₇	—	4	1	no	—
254	C₄×C₃₇	—	4	2	no	—
255	C₄×C₃₇	—	8	2	no	—
256	C₄×C₃₇	#452	1	2	yes	—
257	C₄×C₃₇	#453	1	2	yes	—
258	C₄×C₃₇	C₂×#135	1	1	yes	characteristic
259	C₄×C₃₇	C₂×#137	1	1	yes	characteristic
260	C₄×C₃₇	#577	1	2	yes	—
261	#3508	C₂×C₃₇	1	1	yes	characteristic
262	#3230	C₂×C₃₇	1	1	yes	characteristic, complemented
263	C₂×#492	C₂×C₃₇	1	1	yes	characteristic, complemented
264	#3079	C₂×C₃₇	1	1	yes	characteristic, complemented
265	#1631	C₂×C₃₇	1	4	yes	complemented
266	#1630	C₂×C₃₇	1	4	yes	complemented
267	#1545	C₂×C₃₇	1	1	yes	characteristic, complemented
268	#1493	C₂×C₃₇	1	1	yes	characteristic, complemented
269	#1476	C₂×C₃₇	1	1	yes	characteristic, complemented
270	C₂×C₃₇	—	2	2	no	—
271	C₂×C₃₇	—	8	1	no	—
272	C₂×C₃₇	—	8	4	no	—
273	C₂×C₃₇	C₂×#452	1	1	yes	characteristic
274	C₂×C₃₇	#3009	1	1	yes	characteristic
275	C₂×C₃₇	C₂×#453	1	1	yes	characteristic
276	C₂²×SD₁₆	—	2	2	no	—
277	#559	—	2	1	no	—
278	#559	C₂²×C₃₇	1	2	yes	—
279	#550	—	2	1	no	—
280	#550	C₂²×C₃₇	1	2	yes	—
281	#546	—	2	2	no	—
282	#546	—	2	2	no	—
283	#540	—	2	2	no	—
284	#535	—	2	1	no	—
285	#533	C₂²×C₃₇	1	1	yes	characteristic
286	#532	—	2	1	no	—
287	#532	—	2	1	no	—
288	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
289	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
290	#518	—	2	1	no	—
291	C₄×#41	C₂²×C₃₇	1	1	yes	characteristic
292	#500	—	2	1	no	—
293	#492	—	2	2	no	—
294	#492	C₂²×C₃₇	1	4	yes	—
295	#487	—	2	1	no	—
296	#484	—	2	2	no	—
297	#477	C₂²×C₃₇	1	2	yes	complemented
298	#477	C₂²×C₃₇	1	4	yes	complemented
299	#476	C₂²×C₃₇	1	2	yes	complemented
300	#475	—	2	1	no	—
301	#474	—	2	1	no	—
302	#431	C₂²×C₃₇	1	1	yes	characteristic
303	#428	—	2	1	no	—
304	#423	C₂²×C₃₇	1	1	yes	characteristic
305	#417	—	2	1	no	—
306	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
307	#331	C₂²×C₃₇	1	4	yes	—
308	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	complemented
309	Q₈⋊C₈	C₂²×C₃₇	1	4	yes	complemented
310	D₄⋊C₈	C₂²×C₃₇	1	2	yes	complemented
311	C₃₇	#18625	1	1	yes	characteristic, direct product factor, Sylow
312	C₂×#41	—	2	2	no	—
313	C₂×#41	—	2	2	no	—
314	C₂×#41	D₄×C₃₇	1	1	yes	characteristic
315	C₂²×Q₈	—	2	1	no	—
316	C₂²×D₄	—	2	1	no	—
317	C₂²×D₄	—	2	1	no	—
318	C₂²×D₄	D₄×C₃₇	1	2	yes	—
319	C₂×SD₁₆	—	2	8	no	—
320	C₂×SD₁₆	—	4	8	no	—
321	C₂×M₁₆	—	2	1	no	—
322	C₂²×C₈	—	2	1	no	—
323	C₄⋊Q₈	—	2	1	no	—
324	C₄⋊Q₈	—	2	1	no	—
325	C₄⋊Q₈	—	2	1	no	—
326	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
327	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
328	C₄⋊Q₈	C₂³×C₃₇	1	2	yes	—
329	#127	—	2	2	no	—
330	#127	—	2	1	no	—
331	#127	—	2	1	no	—
332	#127	D₄×C₃₇	1	2	yes	—
333	#127	C₂³×C₃₇	1	2	yes	—
334	#125	—	2	1	no	—
335	#124	—	2	2	no	—
336	#124	—	2	2	no	—
337	#124	—	2	2	no	—
338	#123	—	2	4	no	—
339	#123	—	2	4	no	—
340	C₂²⋊Q₈	—	2	1	no	—
341	C₂²⋊Q₈	D₄×C₃₇	1	2	yes	—
342	#121	—	2	2	no	—
343	#121	—	2	2	no	—
344	#121	—	2	2	no	—
345	#121	—	2	4	no	—
346	#121	—	2	4	no	—
347	#121	—	2	2	no	—
348	#120	—	2	4	no	—
349	C₄×Q₈	—	2	1	no	—
350	C₄×Q₈	D₄×C₃₇	1	1	yes	characteristic
351	C₄×Q₈	C₂³×C₃₇	1	1	yes	characteristic
352	C₄×Q₈	C₂³×C₃₇	1	2	yes	—
353	C₄×D₄	—	2	2	no	—
354	C₄×D₄	—	2	2	no	—
355	C₄×D₄	—	2	2	no	—
356	C₄×D₄	—	2	1	no	—
357	C₄×D₄	—	2	1	no	—
358	C₄×D₄	—	2	2	no	—
359	C₄×D₄	—	2	2	no	—
360	C₄×D₄	—	2	2	no	—
361	C₄×D₄	D₄×C₃₇	1	1	yes	characteristic
362	C₄×D₄	C₂³×C₃₇	1	1	yes	characteristic
363	#117	—	2	1	no	—
364	#117	—	2	1	no	—
365	#117	D₄×C₃₇	1	1	yes	characteristic
366	C₂×C₄⋊C₄	—	2	1	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	4	no	—
369	C₂×C₄²	—	2	1	no	—
370	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
371	#107	—	2	2	no	—
372	#107	—	2	4	no	—
373	#106	—	2	2	no	—
374	C₄⋊C₈	—	2	1	no	—
375	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
376	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
377	#103	—	2	2	no	—
378	#103	—	2	4	no	—
379	#102	—	2	2	no	—
380	C₂²⋊C₈	—	2	1	no	—
381	C₄×C₈	—	2	1	no	—
382	C₄×C₈	—	2	1	no	—
383	C₄×C₈	C₂³×C₃₇	1	2	yes	—
384	C₂⁴	—	2	2	no	—
385	#41	—	2	2	no	—
386	#41	—	2	2	no	—
387	#41	—	8	4	no	—
388	#41	—	8	4	no	—
389	C₂×Q₈	—	2	1	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	4	4	no	—
392	C₂×Q₈	—	4	1	no	—
393	C₂×Q₈	C₂×D₄×C₃₇	1	1	yes	characteristic
394	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	4	no	—
397	C₂×D₄	—	2	4	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	4	4	no	—
404	C₂×D₄	—	4	2	no	—
405	C₂×D₄	—	4	2	no	—
406	C₂×D₄	—	8	2	no	—
407	C₂×D₄	C₂×D₄×C₃₇	1	1	yes	characteristic
408	C₂×D₄	C₂×D₄×C₃₇	1	4	yes	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	4	1	no	—
415	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
416	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
417	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
418	SD₁₆	—	4	16	no	—
419	M₁₆	—	4	2	no	—
420	C₂×C₈	—	2	4	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	4	1	no	—
434	C₄⋊C₄	—	4	1	no	—
435	C₄⋊C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
436	C₄⋊C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
437	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
438	C₂²⋊C₄	—	2	4	no	—
439	C₂²⋊C₄	—	2	4	no	—
440	C₂²⋊C₄	—	2	4	no	—
441	C₂²⋊C₄	—	2	4	no	—
442	C₂²⋊C₄	—	2	1	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	2	1	no	—
445	C₂²⋊C₄	—	2	1	no	—
446	C₄²	—	2	1	no	—
447	C₄²	—	2	1	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	2	2	no	—
450	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
451	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
452	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
453	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
454	C₂³	—	2	4	no	—
455	C₂³	—	2	1	no	—
456	C₂³	—	4	4	no	—
457	C₂³	—	8	2	no	—
458	C₂³	—	8	2	no	—
459	C₂³	#120×C₃₇	1	1	yes	characteristic
460	Q₈	—	2	1	no	—
461	Q₈	—	2	1	no	—
462	Q₈	—	2	4	no	—
463	Q₈	—	4	4	no	—
464	Q₈	—	4	2	no	—
465	Q₈	—	8	2	no	—
466	D₄	—	2	1	no	—
467	D₄	—	2	1	no	—
468	D₄	—	4	4	no	—
469	D₄	—	4	2	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	2	no	—
472	D₄	—	4	4	no	—
473	D₄	—	4	4	no	—
474	D₄	—	4	4	no	—
475	D₄	—	8	2	no	—
476	D₄	—	8	4	no	—
477	D₄	—	8	4	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	8	4	no	—
490	C₂×C₄	—	8	4	no	—
491	C₂×C₄	—	8	2	no	—
492	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
493	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
494	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
495	C₂×C₄	#135×C₃₇	1	2	yes	—
496	C₂×C₄	#137×C₃₇	1	2	yes	—
497	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
498	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
499	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
500	C₈	—	2	4	no	—
501	C₈	—	4	2	no	—
502	C₈	—	4	2	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	4	1	no	—
506	C₂²	—	4	4	no	—
507	C₂²	—	4	1	no	—
508	C₂²	—	4	4	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	4	4	no	—
511	C₂²	—	16	4	no	—
512	C₂²	C₃₇×#452	1	2	yes	—
513	C₂²	C₂×#120×C₃₇	1	1	yes	characteristic
514	C₄	—	2	1	no	—
515	C₄	—	2	1	no	—
516	C₄	—	4	1	no	—
517	C₄	—	4	1	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	1	no	—
520	C₄	—	4	2	no	—
521	C₄	—	8	2	no	—
522	C₄	C₃₇×#452	1	2	yes	—
523	C₄	C₃₇×#453	1	2	yes	—
524	C₄	C₂×#135×C₃₇	1	1	yes	characteristic
525	C₄	C₂×#137×C₃₇	1	1	yes	characteristic
526	C₄	C₃₇×#577	1	2	yes	—
527	C₂	—	2	2	no	—
528	C₂	—	8	4	no	—
529	C₂	—	8	1	no	—
530	C₂	C₂×C₃₇×#452	1	1	yes	characteristic
531	C₂	C₃₇×#3009	1	1	yes	characteristic
532	C₂	C₂×C₃₇×#453	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₇
prime radical	C₃₇×#3508	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×#3230	C₂	semidirect
3. C₂×C₃₇×#492	C₂	semidirect
4. C₃₇×#3079	C₂	semidirect
5. C₃₇×#1631	C₂	semidirect
6. C₃₇×#1630	C₂	semidirect
7. C₃₇×#1545	C₂	semidirect
8. C₃₇×#1493	C₂	semidirect
9. C₃₇×#1476	C₂	semidirect
31. C₃₇×#477	C₂²	semidirect
32. C₃₇×#477	C₂²	semidirect
33. C₃₇×#476	C₂²	semidirect
42. C₃₇×Q₈⋊C₈	C₂²	semidirect
43. C₃₇×Q₈⋊C₈	C₂²	semidirect
44. C₃₇×D₄⋊C₈	C₂²	semidirect
236. #18625	C₃₇	direct (N × H)
262. #3230	C₂×C₃₇	semidirect
263. C₂×#492	C₂×C₃₇	semidirect
264. #3079	C₂×C₃₇	semidirect
265. #1631	C₂×C₃₇	semidirect
266. #1630	C₂×C₃₇	semidirect
267. #1545	C₂×C₃₇	semidirect
268. #1493	C₂×C₃₇	semidirect
269. #1476	C₂×C₃₇	semidirect
297. #477	C₂²×C₃₇	semidirect
298. #477	C₂²×C₃₇	semidirect
299. #476	C₂²×C₃₇	semidirect
308. Q₈⋊C₈	C₂²×C₃₇	semidirect
309. Q₈⋊C₈	C₂²×C₃₇	semidirect
310. D₄⋊C₈	C₂²×C₃₇	semidirect
311. C₃₇	#18625	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×#3508	2
C₃₇×#3230	2
C₂×C₃₇×#492	2
C₃₇×#3079	2
C₃₇×#1631	2
C₃₇×#1630	2
C₃₇×#1545	2
C₃₇×#1493	2
C₃₇×#1476	2
#18625	37

Subgroups — C37×#18625 #22639878

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#18625 #22639878