Subgroups — C₃₇×#18663 #22639916

Order 9472.

1206 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3496	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#3246	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#3167	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#3077	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#1654	C₂	1	2	yes	maximal, complemented
6	C₃₇×#1639	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1635	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1629	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1492	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃₇×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×H(5,𝔽₂)×C₃₇	—	2	1	no	—
13	C₃₇×#547	—	2	1	no	—
14	C₃₇×#547	C₂²	1	2	yes	—
15	C₃₇×#546	—	2	2	no	—
16	C₃₇×#546	—	2	2	no	—
17	D₄²×C₃₇	—	2	1	no	—
18	D₄²×C₃₇	C₂²	1	2	yes	—
19	C₃₇×#537	—	2	1	no	—
20	C₃₇×#534	—	2	2	no	—
21	C₃₇×#533	C₂²	1	1	yes	characteristic, complemented
22	C₃₇×#532	C₂²	1	1	yes	characteristic
23	C₃₇×#532	C₂²	1	1	yes	characteristic
24	C₂×#121×C₃₇	—	2	2	no	—
25	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
26	C₃₇×#498	C₂²	1	1	yes	characteristic, complemented
27	C₃₇×#492	C₂²	1	1	yes	characteristic, complemented
28	C₃₇×#487	C₂²	1	1	yes	characteristic, complemented
29	C₃₇×#486	C₂²	1	1	yes	characteristic, complemented
30	C₃₇×#478	—	2	2	no	—
31	C₃₇×#476	C₂²	1	2	yes	complemented
32	C₃₇×#476	C₂²	1	2	yes	complemented
33	C₃₇×#475	—	2	1	no	—
34	C₃₇×#474	C₂²	1	2	yes	complemented
35	C₃₇×#465	—	2	2	no	—
36	C₃₇×#465	—	2	2	no	—
37	C₃₇×#461	C₂²	1	2	yes	complemented
38	C₃₇×#460	—	2	1	no	—
39	C₄×SD₁₆×C₃₇	—	2	2	no	—
40	C₃₇×#428	—	2	1	no	—
41	C₃₇×#423	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic, complemented
43	C₃₇×#418	—	2	1	no	—
44	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic, complemented
45	C₃₇×#332	C₂²	1	2	yes	complemented
46	C₃₇×#331	C₂²	1	2	yes	complemented
47	C₃₇×D₄⋊C₈	C₂²	1	2	yes	complemented
48	C₃₇×D₄⋊C₈	C₂²	1	2	yes	complemented
49	C₃₇×D₄⋊C₈	C₂²	1	2	yes	complemented
50	C₃₇×D₄⋊C₈	C₂²	1	2	yes	complemented
51	H(5,𝔽₂)×C₃₇	—	4	4	no	—
52	H(5,𝔽₂)×C₃₇	—	4	4	no	—
53	C₂×#41×C₃₇	—	2	2	no	—
54	C₂×#41×C₃₇	—	2	2	no	—
55	C₂×#41×C₃₇	—	2	1	no	—
56	C₂×#41×C₃₇	—	2	1	no	—
57	C₂²×D₄×C₃₇	—	2	4	no	—
58	C₂²×D₄×C₃₇	—	2	2	no	—
59	C₂²×D₄×C₃₇	—	2	2	no	—
60	C₂²×D₄×C₃₇	—	2	2	no	—
61	C₂²×D₄×C₃₇	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₃₇	—	2	1	no	—
63	C₂×SD₁₆×C₃₇	—	2	2	no	—
64	C₂×SD₁₆×C₃₇	—	2	2	no	—
65	C₂×M₁₆×C₃₇	—	2	1	no	—
66	C₂²×C₈×C₃₇	—	2	1	no	—
67	C₂²×C₈×C₃₇	—	2	1	no	—
68	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
69	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
70	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
71	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
72	#127×C₃₇	D₄	1	1	yes	characteristic
73	#127×C₃₇	C₂³	1	1	yes	characteristic
74	#125×C₃₇	—	2	1	no	—
75	#124×C₃₇	—	2	1	no	—
76	#124×C₃₇	—	2	1	no	—
77	#123×C₃₇	—	2	4	no	—
78	#123×C₃₇	—	2	4	no	—
79	C₂²⋊Q₈×C₃₇	—	2	2	no	—
80	C₂²⋊Q₈×C₃₇	—	2	2	no	—
81	C₂²⋊Q₈×C₃₇	—	2	1	no	—
82	C₂²⋊Q₈×C₃₇	—	2	1	no	—
83	#121×C₃₇	—	2	4	no	—
84	#121×C₃₇	—	2	4	no	—
85	#121×C₃₇	—	2	2	no	—
86	#121×C₃₇	—	2	2	no	—
87	#121×C₃₇	—	2	1	no	—
88	#121×C₃₇	—	2	1	no	—
89	#121×C₃₇	—	2	2	no	—
90	#121×C₃₇	—	2	2	no	—
91	#121×C₃₇	D₄	1	2	yes	—
92	#121×C₃₇	D₄	1	2	yes	—
93	#120×C₃₇	—	2	4	no	—
94	#120×C₃₇	—	2	4	no	—
95	C₄×Q₈×C₃₇	—	2	1	no	—
96	C₄×Q₈×C₃₇	—	2	1	no	—
97	C₄×D₄×C₃₇	—	2	1	no	—
98	C₄×D₄×C₃₇	—	2	1	no	—
99	C₄×D₄×C₃₇	—	2	1	no	—
100	C₄×D₄×C₃₇	—	2	1	no	—
101	C₄×D₄×C₃₇	D₄	1	2	yes	—
102	C₄×D₄×C₃₇	D₄	1	2	yes	—
103	C₄×D₄×C₃₇	C₂³	1	2	yes	—
104	C₄×D₄×C₃₇	C₂³	1	2	yes	—
105	#117×C₃₇	—	2	1	no	—
106	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
107	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
109	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
110	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
111	#107×C₃₇	—	2	2	no	—
112	#106×C₃₇	—	2	2	no	—
113	#106×C₃₇	—	2	2	no	—
114	#106×C₃₇	—	2	2	no	—
115	C₄⋊C₈×C₃₇	—	2	1	no	—
116	C₄⋊C₈×C₃₇	—	2	1	no	—
117	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
118	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
119	#103×C₃₇	—	2	2	no	—
120	#103×C₃₇	—	2	2	no	—
121	#102×C₃₇	—	2	2	no	—
122	#102×C₃₇	—	2	2	no	—
123	#102×C₃₇	—	2	2	no	—
124	#102×C₃₇	—	2	2	no	—
125	C₄×C₈×C₃₇	—	2	1	no	—
126	C₄×C₈×C₃₇	C₂³	1	1	yes	characteristic
127	C₄×C₈×C₃₇	C₂³	1	1	yes	characteristic
128	C₂⁴×C₃₇	—	2	1	no	—
129	C₂⁴×C₃₇	—	2	4	no	—
130	#41×C₃₇	—	4	4	no	—
131	#41×C₃₇	—	4	8	no	—
132	#41×C₃₇	—	4	4	no	—
133	#41×C₃₇	—	4	2	no	—
134	#41×C₃₇	—	4	2	no	—
135	#41×C₃₇	—	4	2	no	—
136	#41×C₃₇	—	4	2	no	—
137	C₂×Q₈×C₃₇	—	2	1	no	—
138	C₂×Q₈×C₃₇	—	2	1	no	—
139	C₂×Q₈×C₃₇	—	2	1	no	—
140	C₂×Q₈×C₃₇	—	2	1	no	—
141	C₂×D₄×C₃₇	—	2	4	no	—
142	C₂×D₄×C₃₇	—	2	4	no	—
143	C₂×D₄×C₃₇	—	2	2	no	—
144	C₂×D₄×C₃₇	—	2	2	no	—
145	C₂×D₄×C₃₇	—	2	4	no	—
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	2	no	—
150	C₂×D₄×C₃₇	—	2	1	no	—
151	C₂×D₄×C₃₇	—	2	1	no	—
152	C₂×D₄×C₃₇	—	4	4	no	—
153	C₂×D₄×C₃₇	—	4	8	no	—
154	C₂×D₄×C₃₇	—	4	16	no	—
155	C₂×D₄×C₃₇	—	4	4	no	—
156	C₂×D₄×C₃₇	—	8	2	no	—
157	C₂×D₄×C₃₇	—	8	2	no	—
158	C₂×D₄×C₃₇	SD₁₆	1	4	yes	complemented
159	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
160	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
161	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₃₇	—	2	4	no	—
163	C₂²×C₄×C₃₇	—	2	1	no	—
164	C₂²×C₄×C₃₇	—	2	2	no	—
165	C₂²×C₄×C₃₇	—	2	2	no	—
166	C₂²×C₄×C₃₇	—	2	2	no	—
167	C₂²×C₄×C₃₇	—	2	2	no	—
168	C₂²×C₄×C₃₇	—	8	1	no	—
169	C₂²×C₄×C₃₇	—	8	1	no	—
170	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
173	SD₁₆×C₃₇	—	4	4	no	—
174	SD₁₆×C₃₇	—	8	2	no	—
175	M₁₆×C₃₇	—	4	2	no	—
176	C₂×C₈×C₃₇	—	2	1	no	—
177	C₂×C₈×C₃₇	—	2	1	no	—
178	C₂×C₈×C₃₇	—	2	2	no	—
179	C₂×C₈×C₃₇	—	2	2	no	—
180	C₂×C₈×C₃₇	—	4	2	no	—
181	C₂×C₈×C₃₇	—	8	1	no	—
182	C₄⋊C₄×C₃₇	—	2	4	no	—
183	C₄⋊C₄×C₃₇	—	2	1	no	—
184	C₄⋊C₄×C₃₇	—	2	1	no	—
185	C₄⋊C₄×C₃₇	—	2	1	no	—
186	C₄⋊C₄×C₃₇	—	2	1	no	—
187	C₄⋊C₄×C₃₇	—	2	1	no	—
188	C₄⋊C₄×C₃₇	—	2	1	no	—
189	C₄⋊C₄×C₃₇	—	2	1	no	—
190	C₄⋊C₄×C₃₇	—	4	1	no	—
191	C₄⋊C₄×C₃₇	—	4	1	no	—
192	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
193	C₄⋊C₄×C₃₇	C₂×D₄	1	2	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	2	no	—
198	C₂²⋊C₄×C₃₇	—	2	2	no	—
199	C₂²⋊C₄×C₃₇	—	2	2	no	—
200	C₂²⋊C₄×C₃₇	—	2	2	no	—
201	C₂²⋊C₄×C₃₇	—	2	2	no	—
202	C₂²⋊C₄×C₃₇	—	2	2	no	—
203	C₂²⋊C₄×C₃₇	—	4	1	no	—
204	C₄²×C₃₇	—	4	1	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	2	no	—
210	C₂³×C₃₇	—	2	4	no	—
211	C₂³×C₃₇	—	2	2	no	—
212	C₂³×C₃₇	—	2	2	no	—
213	C₂³×C₃₇	—	4	8	no	—
214	C₂³×C₃₇	—	8	1	no	—
215	C₂³×C₃₇	—	8	1	no	—
216	C₂³×C₃₇	—	8	4	no	—
217	C₂³×C₃₇	—	8	4	no	—
218	C₂³×C₃₇	#120	1	1	yes	characteristic
219	Q₈×C₃₇	—	4	2	no	—
220	Q₈×C₃₇	—	4	1	no	—
221	Q₈×C₃₇	—	4	1	no	—
222	Q₈×C₃₇	—	4	2	no	—
223	Q₈×C₃₇	—	4	1	no	—
224	Q₈×C₃₇	—	4	1	no	—
225	D₄×C₃₇	—	2	2	no	—
226	D₄×C₃₇	—	2	2	no	—
227	D₄×C₃₇	—	2	2	no	—
228	D₄×C₃₇	—	2	4	no	—
229	D₄×C₃₇	—	4	2	no	—
230	D₄×C₃₇	—	4	8	no	—
231	D₄×C₃₇	—	4	8	no	—
232	D₄×C₃₇	—	4	4	no	—
233	D₄×C₃₇	—	4	4	no	—
234	D₄×C₃₇	—	4	1	no	—
235	D₄×C₃₇	—	4	1	no	—
236	D₄×C₃₇	—	4	1	no	—
237	D₄×C₃₇	—	4	1	no	—
238	D₄×C₃₇	—	4	2	no	—
239	D₄×C₃₇	—	8	1	no	—
240	D₄×C₃₇	—	8	4	no	—
241	D₄×C₃₇	C₂×SD₁₆	1	4	yes	—
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	2	no	—
246	C₂×C₄×C₃₇	—	2	2	no	—
247	C₂×C₄×C₃₇	—	4	1	no	—
248	C₂×C₄×C₃₇	—	4	8	no	—
249	C₂×C₄×C₃₇	—	4	2	no	—
250	C₂×C₄×C₃₇	—	4	2	no	—
251	C₂×C₄×C₃₇	—	4	2	no	—
252	C₂×C₄×C₃₇	—	4	2	no	—
253	C₂×C₄×C₃₇	—	4	4	no	—
254	C₂×C₄×C₃₇	—	4	1	no	—
255	C₂×C₄×C₃₇	—	4	1	no	—
256	C₂×C₄×C₃₇	—	8	2	no	—
257	C₂×C₄×C₃₇	—	8	1	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	C₂×SD₁₆	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	—	2	2	no	—
267	C₈×C₃₇	—	4	1	no	—
268	C₈×C₃₇	—	4	2	no	—
269	C₈×C₃₇	—	4	2	no	—
270	#18663	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	—	2	4	no	—
274	C₂²×C₃₇	—	4	2	no	—
275	C₂²×C₃₇	—	4	2	no	—
276	C₂²×C₃₇	—	4	2	no	—
277	C₂²×C₃₇	—	4	2	no	—
278	C₂²×C₃₇	—	4	2	no	—
279	C₂²×C₃₇	—	4	2	no	—
280	C₂²×C₃₇	—	4	2	no	—
281	C₂²×C₃₇	—	4	2	no	—
282	C₂²×C₃₇	—	8	4	no	—
283	C₂²×C₃₇	—	16	8	no	—
284	C₂²×C₃₇	#450	1	2	yes	—
285	C₂²×C₃₇	C₂×#120	1	1	yes	characteristic
286	C₄×C₃₇	—	2	1	no	—
287	C₄×C₃₇	—	2	1	no	—
288	C₄×C₃₇	—	2	1	no	—
289	C₄×C₃₇	—	4	2	no	—
290	C₄×C₃₇	—	4	2	no	—
291	C₄×C₃₇	—	4	2	no	—
292	C₄×C₃₇	—	8	1	no	—
293	C₄×C₃₇	—	8	1	no	—
294	C₄×C₃₇	#450	1	2	yes	—
295	C₄×C₃₇	C₂²×SD₁₆	1	1	yes	characteristic
296	C₄×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
297	C₄×C₃₇	#576	1	1	yes	characteristic
298	C₄×C₃₇	#577	1	1	yes	characteristic
299	#3496	C₂×C₃₇	1	1	yes	characteristic
300	#3246	C₂×C₃₇	1	1	yes	characteristic, complemented
301	#3167	C₂×C₃₇	1	1	yes	characteristic, complemented
302	#3077	C₂×C₃₇	1	1	yes	characteristic, complemented
303	#1654	C₂×C₃₇	1	2	yes	complemented
304	#1639	C₂×C₃₇	1	2	yes	complemented
305	#1635	C₂×C₃₇	1	2	yes	complemented
306	#1629	C₂×C₃₇	1	2	yes	complemented
307	#1547	C₂×C₃₇	1	1	yes	characteristic, complemented
308	#1492	C₂×C₃₇	1	1	yes	characteristic, complemented
309	C₂×D₄⋊C₈	C₂×C₃₇	1	1	yes	characteristic, complemented
310	C₂×C₃₇	—	2	2	no	—
311	C₂×C₃₇	—	4	4	no	—
312	C₂×C₃₇	—	8	2	no	—
313	C₂×C₃₇	—	8	2	no	—
314	C₂×C₃₇	C₂×#450	1	1	yes	characteristic
315	C₂×C₃₇	#3012	1	1	yes	characteristic
316	C₂×C₃₇	#3018	1	1	yes	characteristic
317	C₂×H(5,𝔽₂)	—	2	1	no	—
318	#547	—	2	1	no	—
319	#547	C₂²×C₃₇	1	2	yes	—
320	#546	—	2	2	no	—
321	#546	—	2	2	no	—
322	D₄²	—	2	1	no	—
323	D₄²	C₂²×C₃₇	1	2	yes	—
324	#537	—	2	1	no	—
325	#534	—	2	2	no	—
326	#533	C₂²×C₃₇	1	1	yes	characteristic, complemented
327	#532	C₂²×C₃₇	1	1	yes	characteristic
328	#532	C₂²×C₃₇	1	1	yes	characteristic
329	C₂×#121	—	2	2	no	—
330	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
331	#498	C₂²×C₃₇	1	1	yes	characteristic, complemented
332	#492	C₂²×C₃₇	1	1	yes	characteristic, complemented
333	#487	C₂²×C₃₇	1	1	yes	characteristic, complemented
334	#486	C₂²×C₃₇	1	1	yes	characteristic, complemented
335	#478	—	2	2	no	—
336	#476	C₂²×C₃₇	1	2	yes	complemented
337	#476	C₂²×C₃₇	1	2	yes	complemented
338	#475	—	2	1	no	—
339	#474	C₂²×C₃₇	1	2	yes	complemented
340	#465	—	2	2	no	—
341	#465	—	2	2	no	—
342	#461	C₂²×C₃₇	1	2	yes	complemented
343	#460	—	2	1	no	—
344	C₄×SD₁₆	—	2	2	no	—
345	#428	—	2	1	no	—
346	#423	C₂²×C₃₇	1	1	yes	characteristic, complemented
347	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic, complemented
348	#418	—	2	1	no	—
349	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic, complemented
350	#332	C₂²×C₃₇	1	2	yes	complemented
351	#331	C₂²×C₃₇	1	2	yes	complemented
352	D₄⋊C₈	C₂²×C₃₇	1	2	yes	complemented
353	D₄⋊C₈	C₂²×C₃₇	1	2	yes	complemented
354	D₄⋊C₈	C₂²×C₃₇	1	2	yes	complemented
355	D₄⋊C₈	C₂²×C₃₇	1	2	yes	complemented
356	C₃₇	#18663	1	1	yes	characteristic, direct product factor, Sylow
357	H(5,𝔽₂)	—	4	4	no	—
358	H(5,𝔽₂)	—	4	4	no	—
359	C₂×#41	—	2	2	no	—
360	C₂×#41	—	2	2	no	—
361	C₂×#41	—	2	1	no	—
362	C₂×#41	—	2	1	no	—
363	C₂²×D₄	—	2	4	no	—
364	C₂²×D₄	—	2	2	no	—
365	C₂²×D₄	—	2	2	no	—
366	C₂²×D₄	—	2	2	no	—
367	C₂²×D₄	D₄×C₃₇	1	1	yes	characteristic
368	C₂³×C₄	—	2	1	no	—
369	C₂×SD₁₆	—	2	2	no	—
370	C₂×SD₁₆	—	2	2	no	—
371	C₂×M₁₆	—	2	1	no	—
372	C₂²×C₈	—	2	1	no	—
373	C₂²×C₈	—	2	1	no	—
374	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
375	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
376	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
377	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
378	#127	D₄×C₃₇	1	1	yes	characteristic
379	#127	C₂³×C₃₇	1	1	yes	characteristic
380	#125	—	2	1	no	—
381	#124	—	2	1	no	—
382	#124	—	2	1	no	—
383	#123	—	2	4	no	—
384	#123	—	2	4	no	—
385	C₂²⋊Q₈	—	2	2	no	—
386	C₂²⋊Q₈	—	2	2	no	—
387	C₂²⋊Q₈	—	2	1	no	—
388	C₂²⋊Q₈	—	2	1	no	—
389	#121	—	2	4	no	—
390	#121	—	2	4	no	—
391	#121	—	2	2	no	—
392	#121	—	2	2	no	—
393	#121	—	2	1	no	—
394	#121	—	2	1	no	—
395	#121	—	2	2	no	—
396	#121	—	2	2	no	—
397	#121	D₄×C₃₇	1	2	yes	—
398	#121	D₄×C₃₇	1	2	yes	—
399	#120	—	2	4	no	—
400	#120	—	2	4	no	—
401	C₄×Q₈	—	2	1	no	—
402	C₄×Q₈	—	2	1	no	—
403	C₄×D₄	—	2	1	no	—
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	D₄×C₃₇	1	2	yes	—
408	C₄×D₄	D₄×C₃₇	1	2	yes	—
409	C₄×D₄	C₂³×C₃₇	1	2	yes	—
410	C₄×D₄	C₂³×C₃₇	1	2	yes	—
411	#117	—	2	1	no	—
412	C₂×C₄⋊C₄	—	2	2	no	—
413	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
414	C₂×C₂²⋊C₄	—	2	4	no	—
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
417	#107	—	2	2	no	—
418	#106	—	2	2	no	—
419	#106	—	2	2	no	—
420	#106	—	2	2	no	—
421	C₄⋊C₈	—	2	1	no	—
422	C₄⋊C₈	—	2	1	no	—
423	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
424	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
425	#103	—	2	2	no	—
426	#103	—	2	2	no	—
427	#102	—	2	2	no	—
428	#102	—	2	2	no	—
429	#102	—	2	2	no	—
430	#102	—	2	2	no	—
431	C₄×C₈	—	2	1	no	—
432	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
433	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
434	C₂⁴	—	2	1	no	—
435	C₂⁴	—	2	4	no	—
436	#41	—	4	4	no	—
437	#41	—	4	8	no	—
438	#41	—	4	4	no	—
439	#41	—	4	2	no	—
440	#41	—	4	2	no	—
441	#41	—	4	2	no	—
442	#41	—	4	2	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×D₄	—	2	4	no	—
448	C₂×D₄	—	2	4	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	4	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	4	4	no	—
459	C₂×D₄	—	4	8	no	—
460	C₂×D₄	—	4	16	no	—
461	C₂×D₄	—	4	4	no	—
462	C₂×D₄	—	8	2	no	—
463	C₂×D₄	—	8	2	no	—
464	C₂×D₄	SD₁₆×C₃₇	1	4	yes	complemented
465	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
466	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
467	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
468	C₂²×C₄	—	2	4	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	8	1	no	—
475	C₂²×C₄	—	8	1	no	—
476	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
479	SD₁₆	—	4	4	no	—
480	SD₁₆	—	8	2	no	—
481	M₁₆	—	4	2	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	2	no	—
485	C₂×C₈	—	2	2	no	—
486	C₂×C₈	—	4	2	no	—
487	C₂×C₈	—	8	1	no	—
488	C₄⋊C₄	—	2	4	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	4	1	no	—
497	C₄⋊C₄	—	4	1	no	—
498	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
499	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
500	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
501	C₂²⋊C₄	—	2	4	no	—
502	C₂²⋊C₄	—	2	4	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	4	1	no	—
510	C₄²	—	4	1	no	—
511	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
512	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
513	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
514	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
515	C₂³	—	2	2	no	—
516	C₂³	—	2	4	no	—
517	C₂³	—	2	2	no	—
518	C₂³	—	2	2	no	—
519	C₂³	—	4	8	no	—
520	C₂³	—	8	1	no	—
521	C₂³	—	8	1	no	—
522	C₂³	—	8	4	no	—
523	C₂³	—	8	4	no	—
524	C₂³	#120×C₃₇	1	1	yes	characteristic
525	Q₈	—	4	2	no	—
526	Q₈	—	4	1	no	—
527	Q₈	—	4	1	no	—
528	Q₈	—	4	2	no	—
529	Q₈	—	4	1	no	—
530	Q₈	—	4	1	no	—
531	D₄	—	2	2	no	—
532	D₄	—	2	2	no	—
533	D₄	—	2	2	no	—
534	D₄	—	2	4	no	—
535	D₄	—	4	2	no	—
536	D₄	—	4	8	no	—
537	D₄	—	4	8	no	—
538	D₄	—	4	4	no	—
539	D₄	—	4	4	no	—
540	D₄	—	4	1	no	—
541	D₄	—	4	1	no	—
542	D₄	—	4	1	no	—
543	D₄	—	4	1	no	—
544	D₄	—	4	2	no	—
545	D₄	—	8	1	no	—
546	D₄	—	8	4	no	—
547	D₄	C₂×SD₁₆×C₃₇	1	4	yes	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	8	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	4	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	8	2	no	—
563	C₂×C₄	—	8	1	no	—
564	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
565	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
566	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
567	C₂×C₄	C₂×SD₁₆×C₃₇	1	2	yes	—
568	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
569	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
570	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
571	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
572	C₈	—	2	2	no	—
573	C₈	—	4	1	no	—
574	C₈	—	4	2	no	—
575	C₈	—	4	2	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	4	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	2	no	—
587	C₂²	—	8	4	no	—
588	C₂²	—	16	8	no	—
589	C₂²	C₃₇×#450	1	2	yes	—
590	C₂²	C₂×#120×C₃₇	1	1	yes	characteristic
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	4	2	no	—
595	C₄	—	4	2	no	—
596	C₄	—	4	2	no	—
597	C₄	—	8	1	no	—
598	C₄	—	8	1	no	—
599	C₄	C₃₇×#450	1	2	yes	—
600	C₄	C₂²×SD₁₆×C₃₇	1	1	yes	characteristic
601	C₄	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
602	C₄	C₃₇×#576	1	1	yes	characteristic
603	C₄	C₃₇×#577	1	1	yes	characteristic
604	C₂	—	2	2	no	—
605	C₂	—	4	4	no	—
606	C₂	—	8	2	no	—
607	C₂	—	8	2	no	—
608	C₂	C₂×C₃₇×#450	1	1	yes	characteristic
609	C₂	C₃₇×#3012	1	1	yes	characteristic
610	C₂	C₃₇×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₇
prime radical	C₃₇×#3496	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×#3246	C₂	semidirect
3. C₃₇×#3167	C₂	semidirect
4. C₃₇×#3077	C₂	semidirect
5. C₃₇×#1654	C₂	semidirect
6. C₃₇×#1639	C₂	semidirect
7. C₃₇×#1635	C₂	semidirect
8. C₃₇×#1629	C₂	semidirect
9. C₃₇×#1547	C₂	semidirect
10. C₃₇×#1492	C₂	semidirect
11. C₂×C₃₇×D₄⋊C₈	C₂	semidirect
21. C₃₇×#533	C₂²	semidirect
26. C₃₇×#498	C₂²	semidirect
27. C₃₇×#492	C₂²	semidirect
28. C₃₇×#487	C₂²	semidirect
29. C₃₇×#486	C₂²	semidirect
31. C₃₇×#476	C₂²	semidirect
32. C₃₇×#476	C₂²	semidirect
34. C₃₇×#474	C₂²	semidirect
37. C₃₇×#461	C₂²	semidirect
41. C₃₇×#423	C₂²	semidirect
42. C₂×C₄⋊C₈×C₃₇	C₂²	semidirect
44. C₂×C₄×C₈×C₃₇	C₂²	semidirect
45. C₃₇×#332	C₂²	semidirect
46. C₃₇×#331	C₂²	semidirect
47. C₃₇×D₄⋊C₈	C₂²	semidirect
48. C₃₇×D₄⋊C₈	C₂²	semidirect
49. C₃₇×D₄⋊C₈	C₂²	semidirect
50. C₃₇×D₄⋊C₈	C₂²	semidirect
158. C₂×D₄×C₃₇	SD₁₆	semidirect
270. #18663	C₃₇	direct (N × H)
300. #3246	C₂×C₃₇	semidirect
301. #3167	C₂×C₃₇	semidirect
302. #3077	C₂×C₃₇	semidirect
303. #1654	C₂×C₃₇	semidirect
304. #1639	C₂×C₃₇	semidirect
305. #1635	C₂×C₃₇	semidirect
306. #1629	C₂×C₃₇	semidirect
307. #1547	C₂×C₃₇	semidirect
308. #1492	C₂×C₃₇	semidirect
309. C₂×D₄⋊C₈	C₂×C₃₇	semidirect
326. #533	C₂²×C₃₇	semidirect
331. #498	C₂²×C₃₇	semidirect
332. #492	C₂²×C₃₇	semidirect
333. #487	C₂²×C₃₇	semidirect
334. #486	C₂²×C₃₇	semidirect
336. #476	C₂²×C₃₇	semidirect
337. #476	C₂²×C₃₇	semidirect
339. #474	C₂²×C₃₇	semidirect
342. #461	C₂²×C₃₇	semidirect
346. #423	C₂²×C₃₇	semidirect
347. C₂×C₄⋊C₈	C₂²×C₃₇	semidirect
349. C₂×C₄×C₈	C₂²×C₃₇	semidirect
350. #332	C₂²×C₃₇	semidirect
351. #331	C₂²×C₃₇	semidirect
352. D₄⋊C₈	C₂²×C₃₇	semidirect
353. D₄⋊C₈	C₂²×C₃₇	semidirect
354. D₄⋊C₈	C₂²×C₃₇	semidirect
355. D₄⋊C₈	C₂²×C₃₇	semidirect
356. C₃₇	#18663	direct (N × H)
464. C₂×D₄	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×#3496	2
C₃₇×#3246	2
C₃₇×#3167	2
C₃₇×#3077	2
C₃₇×#1654	2
C₃₇×#1639	2
C₃₇×#1635	2
C₃₇×#1629	2
C₃₇×#1547	2
C₃₇×#1492	2
C₂×C₃₇×D₄⋊C₈	2
#18663	37

Subgroups — C37×#18663 #22639916

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#18663 #22639916