Subgroups — C₂×C₃₇×#1622 #22639729

Order 9472.

1170 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#492	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#460	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₇×#459	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#1622	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃₇×#333	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃₇×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₇×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×SD₁₆×C₃₇	—	2	2	no	—
10	C₂²×SD₁₆×C₃₇	—	2	1	no	—
11	C₂²×D₈×C₃₇	—	2	1	no	—
12	C₃₇×#554	—	2	2	no	—
13	C₃₇×#554	—	2	2	no	—
14	C₃₇×#554	—	2	2	no	—
15	C₃₇×#554	C₂²	1	4	yes	complemented
16	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
17	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×#125×C₃₇	—	2	1	no	—
19	C₂×C₂²⋊Q₈×C₃₇	—	2	1	no	—
20	C₂×C₂²⋊Q₈×C₃₇	—	2	2	no	—
21	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₃₇	—	2	1	no	—
23	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₃₇	—	2	1	no	—
25	C₃₇×#492	—	2	2	no	—
26	C₃₇×#492	C₂²	1	4	yes	complemented
27	C₃₇×#460	—	2	2	no	—
28	C₃₇×#460	C₂²	1	4	yes	complemented
29	C₃₇×#459	—	2	2	no	—
30	C₃₇×#459	C₂²	1	4	yes	—
31	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
33	C₂×#102×C₃₇	—	2	1	no	—
34	C₂×#102×C₃₇	—	2	1	no	—
35	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
36	C₃₇×#333	C₂²	1	4	yes	complemented
37	C₃₇×Q₈⋊C₈	C₂²	1	4	yes	complemented
38	C₃₇×D₄⋊C₈	C₂²	1	4	yes	complemented
39	C₂²×Q₈×C₃₇	D₄	1	1	yes	characteristic
40	C₂²×Q₈×C₃₇	D₄	1	2	yes	—
41	C₂²×D₄×C₃₇	—	2	1	no	—
42	C₂²×D₄×C₃₇	—	2	1	no	—
43	C₂²×D₄×C₃₇	—	2	1	no	—
44	C₂²×D₄×C₃₇	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₃₇	—	2	2	no	—
46	C₂³×C₄×C₃₇	—	2	1	no	—
47	C₂×SD₁₆×C₃₇	—	2	4	no	—
48	C₂×SD₁₆×C₃₇	—	2	8	no	—
49	C₂×SD₁₆×C₃₇	—	4	8	no	—
50	C₂×SD₁₆×C₃₇	—	4	4	no	—
51	C₂×D₈×C₃₇	—	2	4	no	—
52	C₂×D₈×C₃₇	—	4	4	no	—
53	C₂²×C₈×C₃₇	—	2	1	no	—
54	C₂²×C₈×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	D₄	1	2	yes	—
59	C₄⋊Q₈×C₃₇	C₂³	1	2	yes	—
60	#127×C₃₇	—	2	1	no	—
61	#127×C₃₇	—	2	1	no	—
62	#127×C₃₇	—	2	1	no	—
63	#127×C₃₇	C₂³	1	2	yes	—
64	#125×C₃₇	—	2	4	no	—
65	#125×C₃₇	—	2	4	no	—
66	C₂²⋊Q₈×C₃₇	—	2	4	no	—
67	C₂²⋊Q₈×C₃₇	—	2	8	no	—
68	C₂²⋊Q₈×C₃₇	—	2	4	no	—
69	C₂²⋊Q₈×C₃₇	—	2	8	no	—
70	C₄×Q₈×C₃₇	—	2	1	no	—
71	C₄×Q₈×C₃₇	—	2	1	no	—
72	C₄×Q₈×C₃₇	D₄	1	2	yes	—
73	C₄×Q₈×C₃₇	C₂³	1	2	yes	—
74	C₄×D₄×C₃₇	—	2	4	no	—
75	C₄×D₄×C₃₇	—	2	4	no	—
76	C₄×D₄×C₃₇	—	2	1	no	—
77	C₄×D₄×C₃₇	—	2	1	no	—
78	C₄×D₄×C₃₇	D₄	1	2	yes	—
79	C₄×D₄×C₃₇	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
81	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
82	C₂×C₄⋊C₄×C₃₇	—	2	4	no	—
83	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
84	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
85	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
86	C₂×C₄⋊C₄×C₃₇	—	2	4	no	—
87	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
89	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
91	C₂×C₄²×C₃₇	—	2	1	no	—
92	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₃₇	—	2	1	no	—
94	C₄⋊C₈×C₃₇	—	2	1	no	—
95	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
96	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
97	#102×C₃₇	—	2	4	no	—
98	#102×C₃₇	—	2	4	no	—
99	C₄×C₈×C₃₇	—	2	1	no	—
100	C₄×C₈×C₃₇	C₂³	1	2	yes	—
101	C₂⁴×C₃₇	—	2	1	no	—
102	C₂⁴×C₃₇	—	4	1	no	—
103	C₂×Q₈×C₃₇	—	2	1	no	—
104	C₂×Q₈×C₃₇	—	2	2	no	—
105	C₂×Q₈×C₃₇	—	2	2	no	—
106	C₂×Q₈×C₃₇	—	2	2	no	—
107	C₂×Q₈×C₃₇	—	4	4	no	—
108	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
109	C₂×Q₈×C₃₇	C₂×D₄	1	4	yes	—
110	C₂×D₄×C₃₇	—	2	1	no	—
111	C₂×D₄×C₃₇	—	2	2	no	—
112	C₂×D₄×C₃₇	—	2	2	no	—
113	C₂×D₄×C₃₇	—	2	2	no	—
114	C₂×D₄×C₃₇	—	2	2	no	—
115	C₂×D₄×C₃₇	—	4	4	no	—
116	C₂×D₄×C₃₇	—	4	1	no	—
117	C₂×D₄×C₃₇	—	4	1	no	—
118	C₂×D₄×C₃₇	—	4	1	no	—
119	C₂×D₄×C₃₇	—	4	2	no	—
120	C₂×D₄×C₃₇	—	4	2	no	—
121	C₂×D₄×C₃₇	—	4	2	no	—
122	C₂×D₄×C₃₇	—	4	2	no	—
123	C₂×D₄×C₃₇	SD₁₆	1	4	yes	complemented
124	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₃₇	—	2	1	no	—
126	C₂²×C₄×C₃₇	—	2	1	no	—
127	C₂²×C₄×C₃₇	—	2	1	no	—
128	C₂²×C₄×C₃₇	—	2	2	no	—
129	C₂²×C₄×C₃₇	—	2	8	no	—
130	C₂²×C₄×C₃₇	—	2	2	no	—
131	C₂²×C₄×C₃₇	—	2	2	no	—
132	C₂²×C₄×C₃₇	—	4	2	no	—
133	C₂²×C₄×C₃₇	—	4	2	no	—
134	C₂²×C₄×C₃₇	—	8	4	no	—
135	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
138	SD₁₆×C₃₇	—	4	16	no	—
139	SD₁₆×C₃₇	—	4	8	no	—
140	D₈×C₃₇	—	4	8	no	—
141	C₂×C₈×C₃₇	—	2	4	no	—
142	C₂×C₈×C₃₇	—	2	2	no	—
143	C₂×C₈×C₃₇	—	2	2	no	—
144	C₂×C₈×C₃₇	—	2	2	no	—
145	C₂×C₈×C₃₇	—	4	2	no	—
146	C₂×C₈×C₃₇	—	4	2	no	—
147	C₄⋊C₄×C₃₇	—	2	8	no	—
148	C₄⋊C₄×C₃₇	—	2	8	no	—
149	C₄⋊C₄×C₃₇	—	2	1	no	—
150	C₄⋊C₄×C₃₇	—	2	2	no	—
151	C₄⋊C₄×C₃₇	—	2	2	no	—
152	C₄⋊C₄×C₃₇	—	2	2	no	—
153	C₄⋊C₄×C₃₇	—	2	1	no	—
154	C₄⋊C₄×C₃₇	—	2	2	no	—
155	C₄⋊C₄×C₃₇	—	2	2	no	—
156	C₄⋊C₄×C₃₇	—	2	2	no	—
157	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
158	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
159	C₂²⋊C₄×C₃₇	—	2	8	no	—
160	C₂²⋊C₄×C₃₇	—	2	2	no	—
161	C₂²⋊C₄×C₃₇	—	2	2	no	—
162	C₄²×C₃₇	—	2	2	no	—
163	C₄²×C₃₇	—	2	2	no	—
164	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
168	C₂³×C₃₇	—	2	2	no	—
169	C₂³×C₃₇	—	2	4	no	—
170	C₂³×C₃₇	—	4	2	no	—
171	C₂³×C₃₇	—	4	2	no	—
172	C₂³×C₃₇	—	4	2	no	—
173	C₂³×C₃₇	—	8	2	no	—
174	C₂³×C₃₇	—	8	2	no	—
175	C₂³×C₃₇	—	8	2	no	—
176	C₂³×C₃₇	#120	1	1	yes	characteristic
177	Q₈×C₃₇	—	2	2	no	—
178	Q₈×C₃₇	—	2	2	no	—
179	Q₈×C₃₇	—	4	4	no	—
180	Q₈×C₃₇	—	4	2	no	—
181	Q₈×C₃₇	—	8	2	no	—
182	D₄×C₃₇	—	2	2	no	—
183	D₄×C₃₇	—	2	4	no	—
184	D₄×C₃₇	—	4	4	no	—
185	D₄×C₃₇	—	4	2	no	—
186	D₄×C₃₇	—	4	2	no	—
187	D₄×C₃₇	—	4	2	no	—
188	D₄×C₃₇	—	4	2	no	—
189	D₄×C₃₇	—	8	2	no	—
190	D₄×C₃₇	—	8	2	no	—
191	D₄×C₃₇	—	8	2	no	—
192	D₄×C₃₇	C₂×SD₁₆	1	4	yes	complemented
193	C₂×C₄×C₃₇	—	2	2	no	—
194	C₂×C₄×C₃₇	—	2	2	no	—
195	C₂×C₄×C₃₇	—	2	2	no	—
196	C₂×C₄×C₃₇	—	2	2	no	—
197	C₂×C₄×C₃₇	—	2	4	no	—
198	C₂×C₄×C₃₇	—	4	2	no	—
199	C₂×C₄×C₃₇	—	4	2	no	—
200	C₂×C₄×C₃₇	—	4	2	no	—
201	C₂×C₄×C₃₇	—	4	4	no	—
202	C₂×C₄×C₃₇	—	4	2	no	—
203	C₂×C₄×C₃₇	—	4	2	no	—
204	C₂×C₄×C₃₇	—	4	4	no	—
205	C₂×C₄×C₃₇	—	8	8	no	—
206	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
207	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
208	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
209	C₂×C₄×C₃₇	C₂×SD₁₆	1	2	yes	—
210	C₂×C₄×C₃₇	#135	1	2	yes	—
211	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
212	C₂×C₄×C₃₇	#137	1	2	yes	—
213	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
216	C₈×C₃₇	—	2	4	no	—
217	C₈×C₃₇	—	4	2	no	—
218	C₈×C₃₇	—	4	2	no	—
219	C₂×#1622	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂²×C₃₇	—	2	4	no	—
221	C₂²×C₃₇	—	4	8	no	—
222	C₂²×C₃₇	—	4	2	no	—
223	C₂²×C₃₇	—	4	2	no	—
224	C₂²×C₃₇	—	8	2	no	—
225	C₂²×C₃₇	—	8	2	no	—
226	C₂²×C₃₇	—	8	2	no	—
227	C₂²×C₃₇	—	16	4	no	—
228	C₂²×C₃₇	#448	1	2	yes	—
229	C₂²×C₃₇	#449	1	2	yes	—
230	C₂²×C₃₇	#453	1	2	yes	—
231	C₂²×C₃₇	C₂×#120	1	1	yes	characteristic
232	C₄×C₃₇	—	2	1	no	—
233	C₄×C₃₇	—	2	1	no	—
234	C₄×C₃₇	—	4	2	no	—
235	C₄×C₃₇	—	4	2	no	—
236	C₄×C₃₇	—	4	2	no	—
237	C₄×C₃₇	—	4	4	no	—
238	C₄×C₃₇	#448	1	2	yes	—
239	C₄×C₃₇	#449	1	2	yes	—
240	C₄×C₃₇	C₂²×SD₁₆	1	1	yes	characteristic
241	C₄×C₃₇	C₂×#135	1	1	yes	characteristic
242	C₄×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
243	C₄×C₃₇	C₂×#137	1	1	yes	characteristic
244	C₂×#554	C₂×C₃₇	1	1	yes	characteristic, complemented
245	C₂×#492	C₂×C₃₇	1	1	yes	characteristic, complemented
246	C₂×#460	C₂×C₃₇	1	1	yes	characteristic, complemented
247	C₂×#459	C₂×C₃₇	1	1	yes	characteristic
248	#1622	C₂×C₃₇	1	8	yes	direct product factor
249	C₂×#333	C₂×C₃₇	1	1	yes	characteristic, complemented
250	C₂×Q₈⋊C₈	C₂×C₃₇	1	1	yes	characteristic, complemented
251	C₂×D₄⋊C₈	C₂×C₃₇	1	1	yes	characteristic, complemented
252	C₂×C₃₇	—	4	4	no	—
253	C₂×C₃₇	—	16	2	no	—
254	C₂×C₃₇	#1622	1	4	yes	direct product factor
255	C₂×C₃₇	C₂×#448	1	1	yes	characteristic
256	C₂×C₃₇	C₂×#449	1	1	yes	characteristic
257	C₂×C₃₇	C₂×#453	1	1	yes	characteristic
258	C₂²×SD₁₆	—	2	2	no	—
259	C₂²×SD₁₆	—	2	1	no	—
260	C₂²×D₈	—	2	1	no	—
261	#554	—	2	2	no	—
262	#554	—	2	2	no	—
263	#554	—	2	2	no	—
264	#554	C₂²×C₃₇	1	4	yes	complemented
265	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
266	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
267	C₂×#125	—	2	1	no	—
268	C₂×C₂²⋊Q₈	—	2	1	no	—
269	C₂×C₂²⋊Q₈	—	2	2	no	—
270	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
271	C₂×C₄×D₄	—	2	1	no	—
272	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
273	C₂²×C₄⋊C₄	—	2	1	no	—
274	#492	—	2	2	no	—
275	#492	C₂²×C₃₇	1	4	yes	complemented
276	#460	—	2	2	no	—
277	#460	C₂²×C₃₇	1	4	yes	complemented
278	#459	—	2	2	no	—
279	#459	C₂²×C₃₇	1	4	yes	—
280	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
281	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
282	C₂×#102	—	2	1	no	—
283	C₂×#102	—	2	1	no	—
284	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
285	#333	C₂²×C₃₇	1	4	yes	complemented
286	Q₈⋊C₈	C₂²×C₃₇	1	4	yes	complemented
287	D₄⋊C₈	C₂²×C₃₇	1	4	yes	complemented
288	C₃₇	C₂×#1622	1	1	yes	characteristic, direct product factor, Sylow
289	C₂²×Q₈	D₄×C₃₇	1	1	yes	characteristic
290	C₂²×Q₈	D₄×C₃₇	1	2	yes	—
291	C₂²×D₄	—	2	1	no	—
292	C₂²×D₄	—	2	1	no	—
293	C₂²×D₄	—	2	1	no	—
294	C₂²×D₄	D₄×C₃₇	1	1	yes	characteristic
295	C₂³×C₄	—	2	2	no	—
296	C₂³×C₄	—	2	1	no	—
297	C₂×SD₁₆	—	2	4	no	—
298	C₂×SD₁₆	—	2	8	no	—
299	C₂×SD₁₆	—	4	8	no	—
300	C₂×SD₁₆	—	4	4	no	—
301	C₂×D₈	—	2	4	no	—
302	C₂×D₈	—	4	4	no	—
303	C₂²×C₈	—	2	1	no	—
304	C₂²×C₈	—	2	1	no	—
305	C₂²×C₈	—	2	1	no	—
306	C₄⋊Q₈	—	2	1	no	—
307	C₄⋊Q₈	—	2	1	no	—
308	C₄⋊Q₈	D₄×C₃₇	1	2	yes	—
309	C₄⋊Q₈	C₂³×C₃₇	1	2	yes	—
310	#127	—	2	1	no	—
311	#127	—	2	1	no	—
312	#127	—	2	1	no	—
313	#127	C₂³×C₃₇	1	2	yes	—
314	#125	—	2	4	no	—
315	#125	—	2	4	no	—
316	C₂²⋊Q₈	—	2	4	no	—
317	C₂²⋊Q₈	—	2	8	no	—
318	C₂²⋊Q₈	—	2	4	no	—
319	C₂²⋊Q₈	—	2	8	no	—
320	C₄×Q₈	—	2	1	no	—
321	C₄×Q₈	—	2	1	no	—
322	C₄×Q₈	D₄×C₃₇	1	2	yes	—
323	C₄×Q₈	C₂³×C₃₇	1	2	yes	—
324	C₄×D₄	—	2	4	no	—
325	C₄×D₄	—	2	4	no	—
326	C₄×D₄	—	2	1	no	—
327	C₄×D₄	—	2	1	no	—
328	C₄×D₄	D₄×C₃₇	1	2	yes	—
329	C₄×D₄	C₂³×C₃₇	1	2	yes	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	—	2	4	no	—
332	C₂×C₄⋊C₄	—	2	2	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	4	no	—
337	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
338	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
339	C₂×C₂²⋊C₄	—	2	2	no	—
340	C₂×C₂²⋊C₄	—	2	1	no	—
341	C₂×C₄²	—	2	1	no	—
342	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
343	C₄⋊C₈	—	2	1	no	—
344	C₄⋊C₈	—	2	1	no	—
345	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
346	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
347	#102	—	2	4	no	—
348	#102	—	2	4	no	—
349	C₄×C₈	—	2	1	no	—
350	C₄×C₈	C₂³×C₃₇	1	2	yes	—
351	C₂⁴	—	2	1	no	—
352	C₂⁴	—	4	1	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	—	4	4	no	—
358	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
359	C₂×Q₈	C₂×D₄×C₃₇	1	4	yes	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	4	4	no	—
366	C₂×D₄	—	4	1	no	—
367	C₂×D₄	—	4	1	no	—
368	C₂×D₄	—	4	1	no	—
369	C₂×D₄	—	4	2	no	—
370	C₂×D₄	—	4	2	no	—
371	C₂×D₄	—	4	2	no	—
372	C₂×D₄	—	4	2	no	—
373	C₂×D₄	SD₁₆×C₃₇	1	4	yes	complemented
374	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	8	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	4	2	no	—
383	C₂²×C₄	—	4	2	no	—
384	C₂²×C₄	—	8	4	no	—
385	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
388	SD₁₆	—	4	16	no	—
389	SD₁₆	—	4	8	no	—
390	D₈	—	4	8	no	—
391	C₂×C₈	—	2	4	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	4	2	no	—
396	C₂×C₈	—	4	2	no	—
397	C₄⋊C₄	—	2	8	no	—
398	C₄⋊C₄	—	2	8	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
408	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
409	C₂²⋊C₄	—	2	8	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
415	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
416	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
417	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
418	C₂³	—	2	2	no	—
419	C₂³	—	2	4	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	8	2	no	—
424	C₂³	—	8	2	no	—
425	C₂³	—	8	2	no	—
426	C₂³	#120×C₃₇	1	1	yes	characteristic
427	Q₈	—	2	2	no	—
428	Q₈	—	2	2	no	—
429	Q₈	—	4	4	no	—
430	Q₈	—	4	2	no	—
431	Q₈	—	8	2	no	—
432	D₄	—	2	2	no	—
433	D₄	—	2	4	no	—
434	D₄	—	4	4	no	—
435	D₄	—	4	2	no	—
436	D₄	—	4	2	no	—
437	D₄	—	4	2	no	—
438	D₄	—	4	2	no	—
439	D₄	—	8	2	no	—
440	D₄	—	8	2	no	—
441	D₄	—	8	2	no	—
442	D₄	C₂×SD₁₆×C₃₇	1	4	yes	complemented
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	4	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	4	no	—
455	C₂×C₄	—	8	8	no	—
456	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
457	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
458	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
459	C₂×C₄	C₂×SD₁₆×C₃₇	1	2	yes	—
460	C₂×C₄	#135×C₃₇	1	2	yes	—
461	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
462	C₂×C₄	#137×C₃₇	1	2	yes	—
463	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
464	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
465	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
466	C₈	—	2	4	no	—
467	C₈	—	4	2	no	—
468	C₈	—	4	2	no	—
469	C₂²	—	2	4	no	—
470	C₂²	—	4	8	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	8	2	no	—
474	C₂²	—	8	2	no	—
475	C₂²	—	8	2	no	—
476	C₂²	—	16	4	no	—
477	C₂²	C₃₇×#448	1	2	yes	—
478	C₂²	C₃₇×#449	1	2	yes	—
479	C₂²	C₃₇×#453	1	2	yes	—
480	C₂²	C₂×#120×C₃₇	1	1	yes	characteristic
481	C₄	—	2	1	no	—
482	C₄	—	2	1	no	—
483	C₄	—	4	2	no	—
484	C₄	—	4	2	no	—
485	C₄	—	4	2	no	—
486	C₄	—	4	4	no	—
487	C₄	C₃₇×#448	1	2	yes	—
488	C₄	C₃₇×#449	1	2	yes	—
489	C₄	C₂²×SD₁₆×C₃₇	1	1	yes	characteristic
490	C₄	C₂×#135×C₃₇	1	1	yes	characteristic
491	C₄	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
492	C₄	C₂×#137×C₃₇	1	1	yes	characteristic
493	C₂	—	4	4	no	—
494	C₂	—	16	2	no	—
495	C₂	C₃₇×#1622	1	4	yes	direct product factor
496	C₂	C₂×C₃₇×#448	1	1	yes	characteristic
497	C₂	C₂×C₃₇×#449	1	1	yes	characteristic
498	C₂	C₂×C₃₇×#453	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₇	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₇
prime radical	C₂×C₃₇×#459	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#554	C₂	semidirect
2. C₂×C₃₇×#492	C₂	semidirect
3. C₂×C₃₇×#460	C₂	semidirect
5. C₃₇×#1622	C₂	direct (N × H)
6. C₂×C₃₇×#333	C₂	semidirect
7. C₂×C₃₇×Q₈⋊C₈	C₂	semidirect
8. C₂×C₃₇×D₄⋊C₈	C₂	semidirect
15. C₃₇×#554	C₂²	semidirect
26. C₃₇×#492	C₂²	semidirect
28. C₃₇×#460	C₂²	semidirect
36. C₃₇×#333	C₂²	semidirect
37. C₃₇×Q₈⋊C₈	C₂²	semidirect
38. C₃₇×D₄⋊C₈	C₂²	semidirect
123. C₂×D₄×C₃₇	SD₁₆	semidirect
192. D₄×C₃₇	C₂×SD₁₆	semidirect
219. C₂×#1622	C₃₇	direct (N × H)
244. C₂×#554	C₂×C₃₇	semidirect
245. C₂×#492	C₂×C₃₇	semidirect
246. C₂×#460	C₂×C₃₇	semidirect
248. #1622	C₂×C₃₇	direct (N × H)
249. C₂×#333	C₂×C₃₇	semidirect
250. C₂×Q₈⋊C₈	C₂×C₃₇	semidirect
251. C₂×D₄⋊C₈	C₂×C₃₇	semidirect
254. C₂×C₃₇	#1622	direct (N × H)
264. #554	C₂²×C₃₇	semidirect
275. #492	C₂²×C₃₇	semidirect
277. #460	C₂²×C₃₇	semidirect
285. #333	C₂²×C₃₇	semidirect
286. Q₈⋊C₈	C₂²×C₃₇	semidirect
287. D₄⋊C₈	C₂²×C₃₇	semidirect
288. C₃₇	C₂×#1622	direct (N × H)
373. C₂×D₄	SD₁₆×C₃₇	semidirect
442. D₄	C₂×SD₁₆×C₃₇	semidirect
495. C₂	C₃₇×#1622	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×#554	2
C₂×C₃₇×#492	2
C₂×C₃₇×#460	2
C₂×C₃₇×#459	2
C₃₇×#1622	2
C₂×C₃₇×#333	2
C₂×C₃₇×Q₈⋊C₈	2
C₂×C₃₇×D₄⋊C₈	2
C₂×#1622	37

Subgroups — C2×C37×#1622 #22639729

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₇×#1622 #22639729