Subgroups — C₂×C₃₇×#3067 #22681719

Order 9472.

2650 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#575	C₂	1	2	yes	maximal, complemented
2	C₂²×#135×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#131×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#3067	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃₇×#473	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₇×#472	C₂	1	2	yes	maximal, complemented
7	C₂×C₃₇×#471	C₂	1	4	yes	maximal, complemented
8	C₂²×#108×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃₇×#413	C₂	1	2	yes	maximal, complemented
10	C₂²×#41×C₃₇	C₂²	1	1	yes	characteristic
11	C₂²×#41×C₃₇	C₂²	1	2	yes	—
12	C₃₇×#575	—	2	8	no	—
13	C₃₇×#575	C₂²	1	16	yes	complemented
14	C₂×#137×C₃₇	—	2	2	no	—
15	C₂×#137×C₃₇	C₂²	1	4	yes	—
16	C₂×AGL(1,ℤ/8)×C₃₇	—	2	2	no	—
17	C₂×AGL(1,ℤ/8)×C₃₇	C₂²	1	4	yes	—
18	C₂×#135×C₃₇	—	2	4	no	—
19	C₂×#135×C₃₇	—	2	1	no	—
20	C₂×#135×C₃₇	—	2	1	no	—
21	C₂×#135×C₃₇	—	2	1	no	—
22	C₂×#135×C₃₇	—	2	1	no	—
23	C₂×#135×C₃₇	—	2	4	no	—
24	C₂×#135×C₃₇	C₂²	1	8	yes	complemented
25	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic, complemented
26	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	complemented
27	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic, complemented
28	C₂×#131×C₃₇	—	2	1	no	—
29	C₂×#131×C₃₇	—	2	1	no	—
30	C₂×#131×C₃₇	—	2	4	no	—
31	C₂×#131×C₃₇	C₂²	1	2	yes	—
32	C₂×#131×C₃₇	C₂²	1	2	yes	—
33	C₂×#131×C₃₇	C₂²	1	8	yes	complemented
34	C₂²×M₁₆×C₃₇	—	2	1	no	—
35	C₂²×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
36	C₂²×M₁₆×C₃₇	C₂²	1	2	yes	—
37	C₂³×C₈×C₃₇	—	2	1	no	—
38	C₂³×C₈×C₃₇	C₂²	1	1	yes	characteristic
39	C₃₇×#473	C₂²	1	16	yes	complemented
40	C₃₇×#472	C₂²	1	16	yes	complemented
41	C₃₇×#471	C₂²	1	32	yes	complemented
42	C₂×#108×C₃₇	C₂²	1	2	yes	complemented
43	C₂×#108×C₃₇	C₂²	1	2	yes	complemented
44	C₂×#108×C₃₇	C₂²	1	8	yes	complemented
45	C₃₇×#413	C₂²	1	16	yes	complemented
46	C₂×#101×C₃₇	C₂²	1	4	yes	complemented
47	C₂×#100×C₃₇	C₂²	1	4	yes	complemented
48	C₂×#41×C₃₇	—	2	1	no	—
49	C₂×#41×C₃₇	—	2	2	no	—
50	C₂×#41×C₃₇	—	2	2	no	—
51	C₂×#41×C₃₇	—	2	1	no	—
52	C₂×#41×C₃₇	—	2	4	no	—
53	C₂×#41×C₃₇	—	2	2	no	—
54	C₂×#41×C₃₇	—	2	4	no	—
55	C₂×#41×C₃₇	—	2	2	no	—
56	C₂×#41×C₃₇	—	2	2	no	—
57	C₂×#41×C₃₇	—	2	2	no	—
58	C₂×#41×C₃₇	—	2	4	no	—
59	C₂×#41×C₃₇	D₄	1	2	yes	—
60	C₂×#41×C₃₇	D₄	1	4	yes	—
61	C₂×#41×C₃₇	C₂³	1	2	yes	—
62	C₂×#41×C₃₇	C₂³	1	4	yes	—
63	C₂×#41×C₃₇	C₂³	1	8	yes	—
64	C₂²×Q₈×C₃₇	D₄	1	1	yes	characteristic
65	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
66	C₂²×D₄×C₃₇	—	2	1	no	—
67	C₂²×D₄×C₃₇	—	2	2	no	—
68	C₂²×D₄×C₃₇	D₄	1	1	yes	characteristic
69	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
70	C₂³×C₄×C₃₇	—	2	1	no	—
71	C₂³×C₄×C₃₇	—	2	2	no	—
72	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
73	#137×C₃₇	—	2	8	no	—
74	#137×C₃₇	—	2	16	no	—
75	#137×C₃₇	C₂³	1	16	yes	—
76	AGL(1,ℤ/8)×C₃₇	—	2	8	no	—
77	AGL(1,ℤ/8)×C₃₇	—	2	16	no	—
78	AGL(1,ℤ/8)×C₃₇	C₂³	1	16	yes	—
79	#135×C₃₇	—	2	32	no	—
80	#135×C₃₇	—	2	8	no	—
81	#135×C₃₇	—	2	8	no	—
82	#135×C₃₇	—	2	8	no	—
83	#135×C₃₇	—	2	8	no	—
84	C₂×Q₁₆×C₃₇	—	2	4	no	—
85	C₂×Q₁₆×C₃₇	—	2	1	no	—
86	C₂×Q₁₆×C₃₇	—	2	1	no	—
87	C₂×Q₁₆×C₃₇	—	2	2	no	—
88	C₂×Q₁₆×C₃₇	C₂³	1	4	yes	complemented
89	C₂×SD₁₆×C₃₇	—	2	4	no	—
90	C₂×SD₁₆×C₃₇	—	2	4	no	—
91	C₂×SD₁₆×C₃₇	—	2	2	no	—
92	C₂×SD₁₆×C₃₇	—	2	2	no	—
93	C₂×SD₁₆×C₃₇	—	2	4	no	—
94	C₂×SD₁₆×C₃₇	C₂³	1	8	yes	complemented
95	C₂×D₈×C₃₇	—	2	4	no	—
96	C₂×D₈×C₃₇	—	2	1	no	—
97	C₂×D₈×C₃₇	—	2	1	no	—
98	C₂×D₈×C₃₇	—	2	2	no	—
99	C₂×D₈×C₃₇	C₂³	1	4	yes	complemented
100	#131×C₃₇	—	2	4	no	—
101	#131×C₃₇	—	2	4	no	—
102	#131×C₃₇	—	2	8	no	—
103	#131×C₃₇	—	2	8	no	—
104	#131×C₃₇	C₂³	1	8	yes	—
105	#131×C₃₇	C₂³	1	8	yes	—
106	C₂×M₁₆×C₃₇	—	2	1	no	—
107	C₂×M₁₆×C₃₇	—	2	2	no	—
108	C₂×M₁₆×C₃₇	—	2	2	no	—
109	C₂×M₁₆×C₃₇	—	2	4	no	—
110	C₂×M₁₆×C₃₇	—	2	2	no	—
111	C₂×M₁₆×C₃₇	—	2	2	no	—
112	C₂×M₁₆×C₃₇	—	2	8	no	—
113	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
114	C₂×M₁₆×C₃₇	C₂³	1	4	yes	—
115	C₂×M₁₆×C₃₇	C₂³	1	4	yes	—
116	C₂×M₁₆×C₃₇	C₂³	1	8	yes	—
117	C₂²×C₈×C₃₇	—	2	1	no	—
118	C₂²×C₈×C₃₇	—	2	2	no	—
119	C₂²×C₈×C₃₇	—	2	2	no	—
120	C₂²×C₈×C₃₇	—	2	2	no	—
121	C₂²×C₈×C₃₇	—	2	8	no	—
122	C₂²×C₈×C₃₇	D₄	1	1	yes	characteristic
123	C₂²×C₈×C₃₇	D₄	1	1	yes	characteristic
124	C₂²×C₈×C₃₇	D₄	1	1	yes	characteristic
125	C₂²×C₈×C₃₇	D₄	1	1	yes	characteristic
126	C₂²×C₈×C₃₇	D₄	1	4	yes	—
127	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
128	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
129	C₂²×C₈×C₃₇	C₂³	1	4	yes	—
130	#108×C₃₇	C₂³	1	8	yes	complemented
131	#108×C₃₇	C₂³	1	8	yes	complemented
132	#101×C₃₇	C₂³	1	16	yes	complemented
133	#100×C₃₇	C₂³	1	16	yes	complemented
134	C₂⁴×C₃₇	—	2	1	no	—
135	C₂⁴×C₃₇	—	2	2	no	—
136	C₂⁴×C₃₇	#41	1	1	yes	characteristic
137	#41×C₃₇	—	2	4	no	—
138	#41×C₃₇	—	2	4	no	—
139	#41×C₃₇	—	2	4	no	—
140	#41×C₃₇	—	2	2	no	—
141	#41×C₃₇	—	2	4	no	—
142	#41×C₃₇	—	2	4	no	—
143	#41×C₃₇	—	2	2	no	—
144	#41×C₃₇	—	2	8	no	—
145	#41×C₃₇	—	2	8	no	—
146	#41×C₃₇	—	2	8	no	—
147	#41×C₃₇	—	2	8	no	—
148	#41×C₃₇	—	4	4	no	—
149	#41×C₃₇	—	4	4	no	—
150	#41×C₃₇	—	4	4	no	—
151	#41×C₃₇	—	4	4	no	—
152	#41×C₃₇	C₂×D₄	1	8	yes	—
153	#41×C₃₇	C₂×D₄	1	4	yes	—
154	#41×C₃₇	C₂⁴	1	4	yes	—
155	C₂×Q₈×C₃₇	—	2	1	no	—
156	C₂×Q₈×C₃₇	—	2	2	no	—
157	C₂×Q₈×C₃₇	—	2	2	no	—
158	C₂×Q₈×C₃₇	—	2	2	no	—
159	C₂×Q₈×C₃₇	—	2	2	no	—
160	C₂×Q₈×C₃₇	—	2	2	no	—
161	C₂×Q₈×C₃₇	—	2	2	no	—
162	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
163	C₂×Q₈×C₃₇	C₂×D₄	1	4	yes	—
164	C₂×Q₈×C₃₇	C₂⁴	1	4	yes	—
165	C₂×D₄×C₃₇	—	2	2	no	—
166	C₂×D₄×C₃₇	—	2	4	no	—
167	C₂×D₄×C₃₇	—	2	2	no	—
168	C₂×D₄×C₃₇	—	2	4	no	—
169	C₂×D₄×C₃₇	—	2	8	no	—
170	C₂×D₄×C₃₇	—	2	1	no	—
171	C₂×D₄×C₃₇	—	2	2	no	—
172	C₂×D₄×C₃₇	—	2	2	no	—
173	C₂×D₄×C₃₇	—	2	2	no	—
174	C₂×D₄×C₃₇	—	2	2	no	—
175	C₂×D₄×C₃₇	—	2	2	no	—
176	C₂×D₄×C₃₇	—	2	2	no	—
177	C₂×D₄×C₃₇	—	4	2	no	—
178	C₂×D₄×C₃₇	—	4	2	no	—
179	C₂×D₄×C₃₇	—	4	4	no	—
180	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
181	C₂×D₄×C₃₇	C₂×D₄	1	4	yes	—
182	C₂×D₄×C₃₇	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₃₇	—	2	1	no	—
184	C₂²×C₄×C₃₇	—	2	4	no	—
185	C₂²×C₄×C₃₇	—	2	2	no	—
186	C₂²×C₄×C₃₇	—	2	2	no	—
187	C₂²×C₄×C₃₇	—	2	4	no	—
188	C₂²×C₄×C₃₇	—	2	2	no	—
189	C₂²×C₄×C₃₇	—	2	8	no	—
190	C₂²×C₄×C₃₇	—	4	2	no	—
191	C₂²×C₄×C₃₇	—	4	4	no	—
192	C₂²×C₄×C₃₇	—	4	2	no	—
193	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
195	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
197	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₃₇	#41	1	2	yes	—
200	C₂²×C₄×C₃₇	#41	1	1	yes	characteristic
201	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
203	Q₁₆×C₃₇	—	2	16	no	—
204	Q₁₆×C₃₇	—	2	4	no	—
205	Q₁₆×C₃₇	—	2	4	no	—
206	SD₁₆×C₃₇	—	2	16	no	—
207	SD₁₆×C₃₇	—	2	16	no	—
208	SD₁₆×C₃₇	—	2	8	no	—
209	SD₁₆×C₃₇	—	2	8	no	—
210	D₈×C₃₇	—	2	16	no	—
211	D₈×C₃₇	—	2	4	no	—
212	D₈×C₃₇	—	2	4	no	—
213	M₁₆×C₃₇	—	2	2	no	—
214	M₁₆×C₃₇	—	2	4	no	—
215	M₁₆×C₃₇	—	2	4	no	—
216	M₁₆×C₃₇	—	2	8	no	—
217	M₁₆×C₃₇	—	2	8	no	—
218	M₁₆×C₃₇	—	2	8	no	—
219	M₁₆×C₃₇	C₂⁴	1	4	yes	—
220	M₁₆×C₃₇	C₂⁴	1	8	yes	—
221	C₂×C₈×C₃₇	—	2	2	no	—
222	C₂×C₈×C₃₇	—	2	4	no	—
223	C₂×C₈×C₃₇	—	2	4	no	—
224	C₂×C₈×C₃₇	—	2	8	no	—
225	C₂×C₈×C₃₇	—	2	8	no	—
226	C₂×C₈×C₃₇	—	2	8	no	—
227	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
228	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
229	C₂×C₈×C₃₇	C₂×D₄	1	4	yes	—
230	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
231	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
232	C₂×C₈×C₃₇	C₂×D₄	1	4	yes	—
233	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
234	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
235	C₂×C₈×C₃₇	C₂×D₄	1	4	yes	—
236	C₂×C₈×C₃₇	C₂×D₄	1	4	yes	—
237	C₂×C₈×C₃₇	C₂⁴	1	2	yes	—
238	C₂×C₈×C₃₇	C₂⁴	1	2	yes	—
239	C₂³×C₃₇	—	2	4	no	—
240	C₂³×C₃₇	—	2	2	no	—
241	C₂³×C₃₇	—	2	4	no	—
242	C₂³×C₃₇	—	4	2	no	—
243	C₂³×C₃₇	—	4	4	no	—
244	C₂³×C₃₇	—	4	2	no	—
245	C₂³×C₃₇	—	4	2	no	—
246	C₂³×C₃₇	—	8	4	no	—
247	C₂³×C₃₇	#121	1	1	yes	characteristic
248	C₂³×C₃₇	#121	1	1	yes	characteristic
249	C₂³×C₃₇	#121	1	2	yes	—
250	C₂³×C₃₇	C₂×#41	1	1	yes	characteristic
251	C₂³×C₃₇	C₂×#41	1	2	yes	—
252	Q₈×C₃₇	—	2	4	no	—
253	Q₈×C₃₇	—	2	2	no	—
254	Q₈×C₃₇	—	2	4	no	—
255	Q₈×C₃₇	—	2	4	no	—
256	Q₈×C₃₇	—	4	2	no	—
257	Q₈×C₃₇	—	4	2	no	—
258	Q₈×C₃₇	C₂²×D₄	1	4	yes	—
259	D₄×C₃₇	—	2	4	no	—
260	D₄×C₃₇	—	2	8	no	—
261	D₄×C₃₇	—	2	4	no	—
262	D₄×C₃₇	—	2	4	no	—
263	D₄×C₃₇	—	2	2	no	—
264	D₄×C₃₇	—	2	4	no	—
265	D₄×C₃₇	—	2	4	no	—
266	D₄×C₃₇	—	4	8	no	—
267	D₄×C₃₇	—	4	8	no	—
268	D₄×C₃₇	—	4	2	no	—
269	D₄×C₃₇	—	4	2	no	—
270	D₄×C₃₇	C₂²×D₄	1	4	yes	—
271	C₂×C₄×C₃₇	—	2	4	no	—
272	C₂×C₄×C₃₇	—	2	2	no	—
273	C₂×C₄×C₃₇	—	2	8	no	—
274	C₂×C₄×C₃₇	—	2	4	no	—
275	C₂×C₄×C₃₇	—	2	4	no	—
276	C₂×C₄×C₃₇	—	2	4	no	—
277	C₂×C₄×C₃₇	—	4	2	no	—
278	C₂×C₄×C₃₇	—	4	2	no	—
279	C₂×C₄×C₃₇	—	4	8	no	—
280	C₂×C₄×C₃₇	—	4	8	no	—
281	C₂×C₄×C₃₇	#121	1	2	yes	—
282	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
283	C₂×C₄×C₃₇	#121	1	2	yes	—
284	C₂×C₄×C₃₇	#121	1	2	yes	—
285	C₂×C₄×C₃₇	#121	1	2	yes	—
286	C₂×C₄×C₃₇	#121	1	2	yes	—
287	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
288	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
289	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
290	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
291	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
292	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
293	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
294	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
295	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
296	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
297	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
298	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
299	C₈×C₃₇	—	2	4	no	—
300	C₈×C₃₇	—	2	8	no	—
301	C₈×C₃₇	C₂²×D₄	1	2	yes	—
302	C₈×C₃₇	C₂²×D₄	1	2	yes	—
303	C₈×C₃₇	C₂²×D₄	1	2	yes	—
304	C₈×C₃₇	C₂²×D₄	1	2	yes	—
305	C₂×#3067	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
306	C₂²×C₃₇	—	2	2	no	—
307	C₂²×C₃₇	—	2	2	no	—
308	C₂²×C₃₇	—	2	2	no	—
309	C₂²×C₃₇	—	2	4	no	—
310	C₂²×C₃₇	—	4	2	no	—
311	C₂²×C₃₇	—	4	2	no	—
312	C₂²×C₃₇	—	4	8	no	—
313	C₂²×C₃₇	—	4	4	no	—
314	C₂²×C₃₇	—	4	4	no	—
315	C₂²×C₃₇	—	8	4	no	—
316	C₂²×C₃₇	—	8	4	no	—
317	C₂²×C₃₇	—	8	4	no	—
318	C₂²×C₃₇	C₂×#121	1	2	yes	—
319	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
320	C₂²×C₃₇	C₂×#121	1	2	yes	—
321	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
322	C₂²×C₃₇	C₂²×#41	1	1	yes	characteristic
323	C₄×C₃₇	—	2	4	no	—
324	C₄×C₃₇	—	4	4	no	—
325	C₄×C₃₇	C₂×#121	1	2	yes	—
326	C₄×C₃₇	C₂×#121	1	1	yes	characteristic
327	C₄×C₃₇	C₂×#121	1	2	yes	—
328	C₄×C₃₇	C₂×#121	1	1	yes	characteristic
329	C₄×C₃₇	C₂³×D₄	1	1	yes	characteristic
330	C₄×C₃₇	C₂³×D₄	1	1	yes	characteristic
331	C₂×#575	C₂×C₃₇	1	2	yes	complemented
332	C₂²×#135	C₂×C₃₇	1	1	yes	characteristic, complemented
333	C₂²×#131	C₂×C₃₇	1	1	yes	characteristic, complemented
334	#3067	C₂×C₃₇	1	16	yes	direct product factor
335	C₂×#473	C₂×C₃₇	1	2	yes	complemented
336	C₂×#472	C₂×C₃₇	1	2	yes	complemented
337	C₂×#471	C₂×C₃₇	1	4	yes	complemented
338	C₂²×#108	C₂×C₃₇	1	1	yes	characteristic, complemented
339	C₂×#413	C₂×C₃₇	1	2	yes	complemented
340	C₂×C₃₇	—	2	2	no	—
341	C₂×C₃₇	—	2	1	no	—
342	C₂×C₃₇	—	2	1	no	—
343	C₂×C₃₇	—	2	2	no	—
344	C₂×C₃₇	—	4	4	no	—
345	C₂×C₃₇	—	8	4	no	—
346	C₂×C₃₇	#3067	1	2	yes	direct product factor
347	C₂×C₃₇	C₂²×#121	1	1	yes	characteristic
348	C₂²×#41	C₂²×C₃₇	1	1	yes	characteristic
349	C₂²×#41	C₂²×C₃₇	1	2	yes	—
350	#575	—	2	8	no	—
351	#575	C₂²×C₃₇	1	16	yes	complemented
352	C₂×#137	—	2	2	no	—
353	C₂×#137	C₂²×C₃₇	1	4	yes	—
354	C₂×AGL(1,ℤ/8)	—	2	2	no	—
355	C₂×AGL(1,ℤ/8)	C₂²×C₃₇	1	4	yes	—
356	C₂×#135	—	2	4	no	—
357	C₂×#135	—	2	1	no	—
358	C₂×#135	—	2	1	no	—
359	C₂×#135	—	2	1	no	—
360	C₂×#135	—	2	1	no	—
361	C₂×#135	—	2	4	no	—
362	C₂×#135	C₂²×C₃₇	1	8	yes	complemented
363	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic, complemented
364	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	complemented
365	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic, complemented
366	C₂×#131	—	2	1	no	—
367	C₂×#131	—	2	1	no	—
368	C₂×#131	—	2	4	no	—
369	C₂×#131	C₂²×C₃₇	1	2	yes	—
370	C₂×#131	C₂²×C₃₇	1	2	yes	—
371	C₂×#131	C₂²×C₃₇	1	8	yes	complemented
372	C₂²×M₁₆	—	2	1	no	—
373	C₂²×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
374	C₂²×M₁₆	C₂²×C₃₇	1	2	yes	—
375	C₂³×C₈	—	2	1	no	—
376	C₂³×C₈	C₂²×C₃₇	1	1	yes	characteristic
377	#473	C₂²×C₃₇	1	16	yes	complemented
378	#472	C₂²×C₃₇	1	16	yes	complemented
379	#471	C₂²×C₃₇	1	32	yes	complemented
380	C₂×#108	C₂²×C₃₇	1	2	yes	complemented
381	C₂×#108	C₂²×C₃₇	1	2	yes	complemented
382	C₂×#108	C₂²×C₃₇	1	8	yes	complemented
383	#413	C₂²×C₃₇	1	16	yes	complemented
384	C₂×#101	C₂²×C₃₇	1	4	yes	complemented
385	C₂×#100	C₂²×C₃₇	1	4	yes	complemented
386	C₃₇	C₂×#3067	1	1	yes	characteristic, direct product factor, Sylow
387	C₂×#41	—	2	1	no	—
388	C₂×#41	—	2	2	no	—
389	C₂×#41	—	2	1	no	—
390	C₂×#41	—	2	2	no	—
391	C₂×#41	—	2	4	no	—
392	C₂×#41	—	2	2	no	—
393	C₂×#41	—	2	2	no	—
394	C₂×#41	—	2	2	no	—
395	C₂×#41	—	2	4	no	—
396	C₂×#41	—	2	2	no	—
397	C₂×#41	—	2	4	no	—
398	C₂×#41	D₄×C₃₇	1	2	yes	—
399	C₂×#41	D₄×C₃₇	1	4	yes	—
400	C₂×#41	C₂³×C₃₇	1	2	yes	—
401	C₂×#41	C₂³×C₃₇	1	4	yes	—
402	C₂×#41	C₂³×C₃₇	1	8	yes	—
403	C₂²×Q₈	D₄×C₃₇	1	1	yes	characteristic
404	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
405	C₂²×D₄	—	2	1	no	—
406	C₂²×D₄	—	2	2	no	—
407	C₂²×D₄	D₄×C₃₇	1	1	yes	characteristic
408	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
409	C₂³×C₄	—	2	1	no	—
410	C₂³×C₄	—	2	2	no	—
411	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
412	#137	—	2	8	no	—
413	#137	—	2	16	no	—
414	#137	C₂³×C₃₇	1	16	yes	—
415	AGL(1,ℤ/8)	—	2	8	no	—
416	AGL(1,ℤ/8)	—	2	16	no	—
417	AGL(1,ℤ/8)	C₂³×C₃₇	1	16	yes	—
418	#135	—	2	32	no	—
419	#135	—	2	8	no	—
420	#135	—	2	8	no	—
421	#135	—	2	8	no	—
422	#135	—	2	8	no	—
423	C₂×Q₁₆	—	2	4	no	—
424	C₂×Q₁₆	—	2	1	no	—
425	C₂×Q₁₆	—	2	1	no	—
426	C₂×Q₁₆	—	2	2	no	—
427	C₂×Q₁₆	C₂³×C₃₇	1	4	yes	complemented
428	C₂×SD₁₆	—	2	4	no	—
429	C₂×SD₁₆	—	2	4	no	—
430	C₂×SD₁₆	—	2	2	no	—
431	C₂×SD₁₆	—	2	2	no	—
432	C₂×SD₁₆	—	2	4	no	—
433	C₂×SD₁₆	C₂³×C₃₇	1	8	yes	complemented
434	C₂×D₈	—	2	4	no	—
435	C₂×D₈	—	2	1	no	—
436	C₂×D₈	—	2	1	no	—
437	C₂×D₈	—	2	2	no	—
438	C₂×D₈	C₂³×C₃₇	1	4	yes	complemented
439	#131	—	2	4	no	—
440	#131	—	2	4	no	—
441	#131	—	2	8	no	—
442	#131	—	2	8	no	—
443	#131	C₂³×C₃₇	1	8	yes	—
444	#131	C₂³×C₃₇	1	8	yes	—
445	C₂×M₁₆	—	2	1	no	—
446	C₂×M₁₆	—	2	2	no	—
447	C₂×M₁₆	—	2	2	no	—
448	C₂×M₁₆	—	2	4	no	—
449	C₂×M₁₆	—	2	2	no	—
450	C₂×M₁₆	—	2	2	no	—
451	C₂×M₁₆	—	2	8	no	—
452	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
453	C₂×M₁₆	C₂³×C₃₇	1	4	yes	—
454	C₂×M₁₆	C₂³×C₃₇	1	4	yes	—
455	C₂×M₁₆	C₂³×C₃₇	1	8	yes	—
456	C₂²×C₈	—	2	1	no	—
457	C₂²×C₈	—	2	2	no	—
458	C₂²×C₈	—	2	2	no	—
459	C₂²×C₈	—	2	2	no	—
460	C₂²×C₈	—	2	8	no	—
461	C₂²×C₈	D₄×C₃₇	1	1	yes	characteristic
462	C₂²×C₈	D₄×C₃₇	1	1	yes	characteristic
463	C₂²×C₈	D₄×C₃₇	1	1	yes	characteristic
464	C₂²×C₈	D₄×C₃₇	1	1	yes	characteristic
465	C₂²×C₈	D₄×C₃₇	1	4	yes	—
466	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
467	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
468	C₂²×C₈	C₂³×C₃₇	1	4	yes	—
469	#108	C₂³×C₃₇	1	8	yes	complemented
470	#108	C₂³×C₃₇	1	8	yes	complemented
471	#101	C₂³×C₃₇	1	16	yes	complemented
472	#100	C₂³×C₃₇	1	16	yes	complemented
473	C₂⁴	—	2	1	no	—
474	C₂⁴	—	2	2	no	—
475	C₂⁴	#41×C₃₇	1	1	yes	characteristic
476	#41	—	2	4	no	—
477	#41	—	2	4	no	—
478	#41	—	2	4	no	—
479	#41	—	2	2	no	—
480	#41	—	2	4	no	—
481	#41	—	2	4	no	—
482	#41	—	2	2	no	—
483	#41	—	2	8	no	—
484	#41	—	2	8	no	—
485	#41	—	2	8	no	—
486	#41	—	2	8	no	—
487	#41	—	4	4	no	—
488	#41	—	4	4	no	—
489	#41	—	4	4	no	—
490	#41	—	4	4	no	—
491	#41	C₂×D₄×C₃₇	1	8	yes	—
492	#41	C₂×D₄×C₃₇	1	4	yes	—
493	#41	C₂⁴×C₃₇	1	4	yes	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	—	2	2	no	—
496	C₂×Q₈	—	2	2	no	—
497	C₂×Q₈	—	2	2	no	—
498	C₂×Q₈	—	2	2	no	—
499	C₂×Q₈	—	2	2	no	—
500	C₂×Q₈	—	2	2	no	—
501	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
502	C₂×Q₈	C₂×D₄×C₃₇	1	4	yes	—
503	C₂×Q₈	C₂⁴×C₃₇	1	4	yes	—
504	C₂×D₄	—	2	2	no	—
505	C₂×D₄	—	2	4	no	—
506	C₂×D₄	—	2	2	no	—
507	C₂×D₄	—	2	4	no	—
508	C₂×D₄	—	2	8	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	2	no	—
511	C₂×D₄	—	2	2	no	—
512	C₂×D₄	—	2	2	no	—
513	C₂×D₄	—	2	2	no	—
514	C₂×D₄	—	2	2	no	—
515	C₂×D₄	—	2	2	no	—
516	C₂×D₄	—	4	2	no	—
517	C₂×D₄	—	4	2	no	—
518	C₂×D₄	—	4	4	no	—
519	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
520	C₂×D₄	C₂×D₄×C₃₇	1	4	yes	—
521	C₂×D₄	C₂⁴×C₃₇	1	4	yes	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	2	no	—
524	C₂²×C₄	—	2	4	no	—
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	2	4	no	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	8	no	—
529	C₂²×C₄	—	4	2	no	—
530	C₂²×C₄	—	4	2	no	—
531	C₂²×C₄	—	4	4	no	—
532	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
533	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
534	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
535	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
536	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
537	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
538	C₂²×C₄	#41×C₃₇	1	1	yes	characteristic
539	C₂²×C₄	#41×C₃₇	1	2	yes	—
540	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
541	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
542	Q₁₆	—	2	16	no	—
543	Q₁₆	—	2	4	no	—
544	Q₁₆	—	2	4	no	—
545	SD₁₆	—	2	16	no	—
546	SD₁₆	—	2	16	no	—
547	SD₁₆	—	2	8	no	—
548	SD₁₆	—	2	8	no	—
549	D₈	—	2	16	no	—
550	D₈	—	2	4	no	—
551	D₈	—	2	4	no	—
552	M₁₆	—	2	2	no	—
553	M₁₆	—	2	4	no	—
554	M₁₆	—	2	4	no	—
555	M₁₆	—	2	8	no	—
556	M₁₆	—	2	8	no	—
557	M₁₆	—	2	8	no	—
558	M₁₆	C₂⁴×C₃₇	1	4	yes	—
559	M₁₆	C₂⁴×C₃₇	1	8	yes	—
560	C₂×C₈	—	2	2	no	—
561	C₂×C₈	—	2	4	no	—
562	C₂×C₈	—	2	4	no	—
563	C₂×C₈	—	2	8	no	—
564	C₂×C₈	—	2	8	no	—
565	C₂×C₈	—	2	8	no	—
566	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
567	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
568	C₂×C₈	C₂×D₄×C₃₇	1	4	yes	—
569	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
570	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
571	C₂×C₈	C₂×D₄×C₃₇	1	4	yes	—
572	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
573	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
574	C₂×C₈	C₂×D₄×C₃₇	1	4	yes	—
575	C₂×C₈	C₂×D₄×C₃₇	1	4	yes	—
576	C₂×C₈	C₂⁴×C₃₇	1	2	yes	—
577	C₂×C₈	C₂⁴×C₃₇	1	2	yes	—
578	C₂³	—	2	4	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	2	4	no	—
581	C₂³	—	4	2	no	—
582	C₂³	—	4	4	no	—
583	C₂³	—	4	2	no	—
584	C₂³	—	4	2	no	—
585	C₂³	—	8	4	no	—
586	C₂³	#121×C₃₇	1	1	yes	characteristic
587	C₂³	#121×C₃₇	1	1	yes	characteristic
588	C₂³	#121×C₃₇	1	2	yes	—
589	C₂³	C₂×#41×C₃₇	1	1	yes	characteristic
590	C₂³	C₂×#41×C₃₇	1	2	yes	—
591	Q₈	—	2	4	no	—
592	Q₈	—	2	2	no	—
593	Q₈	—	2	4	no	—
594	Q₈	—	2	4	no	—
595	Q₈	—	4	2	no	—
596	Q₈	—	4	2	no	—
597	Q₈	C₂²×D₄×C₃₇	1	4	yes	—
598	D₄	—	2	4	no	—
599	D₄	—	2	8	no	—
600	D₄	—	2	4	no	—
601	D₄	—	2	4	no	—
602	D₄	—	2	2	no	—
603	D₄	—	2	4	no	—
604	D₄	—	2	4	no	—
605	D₄	—	4	8	no	—
606	D₄	—	4	8	no	—
607	D₄	—	4	2	no	—
608	D₄	—	4	2	no	—
609	D₄	C₂²×D₄×C₃₇	1	4	yes	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	8	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	4	2	no	—
617	C₂×C₄	—	4	2	no	—
618	C₂×C₄	—	4	8	no	—
619	C₂×C₄	—	4	8	no	—
620	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
621	C₂×C₄	#121×C₃₇	1	2	yes	—
622	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
623	C₂×C₄	#121×C₃₇	1	2	yes	—
624	C₂×C₄	#121×C₃₇	1	2	yes	—
625	C₂×C₄	#121×C₃₇	1	2	yes	—
626	C₂×C₄	#121×C₃₇	1	2	yes	—
627	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
628	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
629	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
630	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
631	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
632	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
633	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
634	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
635	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
636	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
637	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
638	C₈	—	2	4	no	—
639	C₈	—	2	8	no	—
640	C₈	C₂²×D₄×C₃₇	1	2	yes	—
641	C₈	C₂²×D₄×C₃₇	1	2	yes	—
642	C₈	C₂²×D₄×C₃₇	1	2	yes	—
643	C₈	C₂²×D₄×C₃₇	1	2	yes	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	4	no	—
648	C₂²	—	4	2	no	—
649	C₂²	—	4	2	no	—
650	C₂²	—	4	8	no	—
651	C₂²	—	4	4	no	—
652	C₂²	—	4	4	no	—
653	C₂²	—	8	4	no	—
654	C₂²	—	8	4	no	—
655	C₂²	—	8	4	no	—
656	C₂²	C₂×#121×C₃₇	1	2	yes	—
657	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
658	C₂²	C₂×#121×C₃₇	1	2	yes	—
659	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
660	C₂²	C₂²×#41×C₃₇	1	1	yes	characteristic
661	C₄	—	2	4	no	—
662	C₄	—	4	4	no	—
663	C₄	C₂×#121×C₃₇	1	2	yes	—
664	C₄	C₂×#121×C₃₇	1	1	yes	characteristic
665	C₄	C₂×#121×C₃₇	1	2	yes	—
666	C₄	C₂×#121×C₃₇	1	1	yes	characteristic
667	C₄	C₂³×D₄×C₃₇	1	1	yes	characteristic
668	C₄	C₂³×D₄×C₃₇	1	1	yes	characteristic
669	C₂	—	2	2	no	—
670	C₂	—	2	1	no	—
671	C₂	—	2	1	no	—
672	C₂	—	2	2	no	—
673	C₂	—	4	4	no	—
674	C₂	—	8	4	no	—
675	C₂	C₃₇×#3067	1	2	yes	direct product factor
676	C₂	C₂²×#121×C₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₇	#121
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₇
socle	C₂²×C₃₇	C₂×#121
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇ ◁ C₂³×C₄×C₃₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₃₇×#575	C₂	semidirect
2. C₂²×#135×C₃₇	C₂	semidirect
3. C₂²×#131×C₃₇	C₂	semidirect
4. C₃₇×#3067	C₂	direct (N × H)
5. C₂×C₃₇×#473	C₂	semidirect
6. C₂×C₃₇×#472	C₂	semidirect
7. C₂×C₃₇×#471	C₂	semidirect
8. C₂²×#108×C₃₇	C₂	semidirect
9. C₂×C₃₇×#413	C₂	semidirect
13. C₃₇×#575	C₂²	semidirect
24. C₂×#135×C₃₇	C₂²	semidirect
25. C₂²×Q₁₆×C₃₇	C₂²	semidirect
26. C₂²×SD₁₆×C₃₇	C₂²	semidirect
27. C₂²×D₈×C₃₇	C₂²	semidirect
33. C₂×#131×C₃₇	C₂²	semidirect
39. C₃₇×#473	C₂²	semidirect
40. C₃₇×#472	C₂²	semidirect
41. C₃₇×#471	C₂²	semidirect
42. C₂×#108×C₃₇	C₂²	semidirect
43. C₂×#108×C₃₇	C₂²	semidirect
44. C₂×#108×C₃₇	C₂²	semidirect
45. C₃₇×#413	C₂²	semidirect
46. C₂×#101×C₃₇	C₂²	semidirect
47. C₂×#100×C₃₇	C₂²	semidirect
88. C₂×Q₁₆×C₃₇	C₂³	semidirect
94. C₂×SD₁₆×C₃₇	C₂³	semidirect
99. C₂×D₈×C₃₇	C₂³	semidirect
130. #108×C₃₇	C₂³	semidirect
131. #108×C₃₇	C₂³	semidirect
132. #101×C₃₇	C₂³	semidirect
133. #100×C₃₇	C₂³	semidirect
305. C₂×#3067	C₃₇	direct (N × H)
331. C₂×#575	C₂×C₃₇	semidirect
332. C₂²×#135	C₂×C₃₇	semidirect
333. C₂²×#131	C₂×C₃₇	semidirect
334. #3067	C₂×C₃₇	direct (N × H)
335. C₂×#473	C₂×C₃₇	semidirect
336. C₂×#472	C₂×C₃₇	semidirect
337. C₂×#471	C₂×C₃₇	semidirect
338. C₂²×#108	C₂×C₃₇	semidirect
339. C₂×#413	C₂×C₃₇	semidirect
346. C₂×C₃₇	#3067	direct (N × H)
351. #575	C₂²×C₃₇	semidirect
362. C₂×#135	C₂²×C₃₇	semidirect
363. C₂²×Q₁₆	C₂²×C₃₇	semidirect
364. C₂²×SD₁₆	C₂²×C₃₇	semidirect
365. C₂²×D₈	C₂²×C₃₇	semidirect
371. C₂×#131	C₂²×C₃₇	semidirect
377. #473	C₂²×C₃₇	semidirect
378. #472	C₂²×C₃₇	semidirect
379. #471	C₂²×C₃₇	semidirect
380. C₂×#108	C₂²×C₃₇	semidirect
381. C₂×#108	C₂²×C₃₇	semidirect
382. C₂×#108	C₂²×C₃₇	semidirect
383. #413	C₂²×C₃₇	semidirect
384. C₂×#101	C₂²×C₃₇	semidirect
385. C₂×#100	C₂²×C₃₇	semidirect
386. C₃₇	C₂×#3067	direct (N × H)
427. C₂×Q₁₆	C₂³×C₃₇	semidirect
433. C₂×SD₁₆	C₂³×C₃₇	semidirect
438. C₂×D₈	C₂³×C₃₇	semidirect
469. #108	C₂³×C₃₇	semidirect
470. #108	C₂³×C₃₇	semidirect
471. #101	C₂³×C₃₇	semidirect
472. #100	C₂³×C₃₇	semidirect
675. C₂	C₃₇×#3067	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₇×#575	2
C₂²×#135×C₃₇	2
C₂²×#131×C₃₇	2
C₃₇×#3067	2
C₂×C₃₇×#473	2
C₂×C₃₇×#472	2
C₂×C₃₇×#471	2
C₂²×#108×C₃₇	2
C₂×C₃₇×#413	2
C₂×#3067	37

Subgroups — C2×C37×#3067 #22681719

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₇×#3067 #22681719