Subgroups — C₃₇×#28564 #22649817

Order 9472.

876 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#467	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#435	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2415	C₂	1	2	yes	maximal
4	C₃₇×#2087	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2076	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2056	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#2001	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1935	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1894	C₂	1	2	yes	maximal, complemented
10	C₃₇×#1873	C₂	1	2	yes	maximal, complemented
11	C₃₇×#1735	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	2	yes	—
16	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×#117×C₃₇	C₂²	1	2	yes	—
19	C₃₇×#467	—	2	4	no	—
20	C₃₇×#435	—	2	4	no	—
21	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
23	C₂×#103×C₃₇	C₂²	1	2	yes	—
24	C₂×#103×C₃₇	C₂²	1	2	yes	—
25	C₂×#103×C₃₇	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
28	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
29	C₃₇×#397	—	2	2	no	—
30	C₃₇×#394	—	2	2	no	—
31	C₃₇×#391	C₂²	1	2	yes	—
32	C₃₇×#389	—	2	2	no	—
33	C₃₇×#389	C₂²	1	2	yes	—
34	C₃₇×#388	—	2	2	no	—
35	C₃₇×#380	C₂²	1	2	yes	—
36	C₃₇×#340	C₂²	1	2	yes	—
37	C₃₇×#340	C₂²	1	2	yes	—
38	C₃₇×#340	C₂²	1	2	yes	—
39	C₃₇×#340	C₂²	1	1	yes	characteristic
40	C₃₇×#340	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
42	C₂²×D₄×C₃₇	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
45	C₂×Q₁₆×C₃₇	—	2	2	no	—
46	C₂×Q₁₆×C₃₇	—	4	2	no	—
47	C₂×M₁₆×C₃₇	—	2	2	no	—
48	C₂×M₁₆×C₃₇	—	4	2	no	—
49	C₂²×C₈×C₃₇	—	4	2	no	—
50	C₂²×C₈×C₃₇	D₄	1	4	yes	—
51	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
55	C₂²⋊Q₈×C₃₇	—	2	4	no	—
56	C₂²⋊Q₈×C₃₇	—	2	4	no	—
57	C₂²⋊Q₈×C₃₇	—	2	4	no	—
58	C₂²⋊Q₈×C₃₇	—	4	2	no	—
59	C₄×D₄×C₃₇	—	2	2	no	—
60	C₄×D₄×C₃₇	—	2	2	no	—
61	#117×C₃₇	—	2	4	no	—
62	#117×C₃₇	—	4	2	no	—
63	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
64	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
65	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
66	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₃₇	D₄	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₃₇	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₃₇	—	2	2	no	—
77	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
78	#107×C₃₇	—	2	2	no	—
79	C₄⋊C₈×C₃₇	—	2	2	no	—
80	#103×C₃₇	—	2	4	no	—
81	#103×C₃₇	—	2	4	no	—
82	#103×C₃₇	—	4	2	no	—
83	C₂²⋊C₈×C₃₇	—	2	2	no	—
84	C₂²⋊C₈×C₃₇	—	2	2	no	—
85	#97×C₃₇	—	2	2	no	—
86	#95×C₃₇	—	2	2	no	—
87	#95×C₃₇	—	2	2	no	—
88	#95×C₃₇	—	2	2	no	—
89	#95×C₃₇	—	2	2	no	—
90	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
91	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
92	C₂×Q₈×C₃₇	—	2	2	no	—
93	C₂×Q₈×C₃₇	—	2	2	no	—
94	C₂×Q₈×C₃₇	—	2	2	no	—
95	C₂×Q₈×C₃₇	—	2	2	no	—
96	C₂×Q₈×C₃₇	—	2	2	no	—
97	C₂×Q₈×C₃₇	—	2	2	no	—
98	C₂×D₄×C₃₇	—	2	2	no	—
99	C₂×D₄×C₃₇	—	4	2	no	—
100	C₂²×C₄×C₃₇	—	2	2	no	—
101	C₂²×C₄×C₃₇	—	2	2	no	—
102	C₂²×C₄×C₃₇	—	2	2	no	—
103	C₂²×C₄×C₃₇	—	2	1	no	—
104	C₂²×C₄×C₃₇	—	2	1	no	—
105	C₂²×C₄×C₃₇	—	2	2	no	—
106	C₂²×C₄×C₃₇	—	2	2	no	—
107	C₂²×C₄×C₃₇	—	2	2	no	—
108	C₂²×C₄×C₃₇	—	2	2	no	—
109	C₂²×C₄×C₃₇	—	2	2	no	—
110	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₃₇	#41	1	2	yes	—
116	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
117	Q₁₆×C₃₇	—	4	4	no	—
118	M₁₆×C₃₇	—	4	4	no	—
119	C₂×C₈×C₃₇	—	2	2	no	—
120	C₂×C₈×C₃₇	—	2	2	no	—
121	C₂×C₈×C₃₇	—	2	1	no	—
122	C₂×C₈×C₃₇	—	2	1	no	—
123	C₂×C₈×C₃₇	—	2	2	no	—
124	C₂×C₈×C₃₇	—	2	2	no	—
125	C₂×C₈×C₃₇	—	4	4	no	—
126	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
128	C₄⋊C₄×C₃₇	—	2	2	no	—
129	C₄⋊C₄×C₃₇	—	2	2	no	—
130	C₄⋊C₄×C₃₇	—	2	2	no	—
131	C₄⋊C₄×C₃₇	—	2	2	no	—
132	C₄⋊C₄×C₃₇	—	2	2	no	—
133	C₄⋊C₄×C₃₇	—	2	2	no	—
134	C₄⋊C₄×C₃₇	—	4	4	no	—
135	C₄⋊C₄×C₃₇	—	4	4	no	—
136	C₄⋊C₄×C₃₇	—	4	4	no	—
137	C₄⋊C₄×C₃₇	#41	1	4	yes	—
138	C₂²⋊C₄×C₃₇	—	2	2	no	—
139	C₂²⋊C₄×C₃₇	—	2	2	no	—
140	C₂²⋊C₄×C₃₇	—	4	4	no	—
141	C₂²⋊C₄×C₃₇	—	4	4	no	—
142	C₂²⋊C₄×C₃₇	—	4	4	no	—
143	C₂²⋊C₄×C₃₇	—	4	4	no	—
144	C₄²×C₃₇	—	2	1	no	—
145	C₄²×C₃₇	—	2	1	no	—
146	C₄²×C₃₇	—	4	4	no	—
147	C₂³×C₃₇	—	2	2	no	—
148	C₂³×C₃₇	—	2	2	no	—
149	C₂³×C₃₇	—	2	1	no	—
150	C₂³×C₃₇	—	2	1	no	—
151	C₂³×C₃₇	—	2	1	no	—
152	C₂³×C₃₇	—	2	2	no	—
153	C₂³×C₃₇	—	2	2	no	—
154	C₂³×C₃₇	—	2	1	no	—
155	C₂³×C₃₇	—	2	1	no	—
156	C₂³×C₃₇	#121	1	2	yes	—
157	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
158	Q₈×C₃₇	—	4	2	no	—
159	Q₈×C₃₇	—	4	2	no	—
160	Q₈×C₃₇	—	4	2	no	—
161	Q₈×C₃₇	—	4	2	no	—
162	D₄×C₃₇	—	4	4	no	—
163	C₂×C₄×C₃₇	—	2	2	no	—
164	C₂×C₄×C₃₇	—	2	2	no	—
165	C₂×C₄×C₃₇	—	2	2	no	—
166	C₂×C₄×C₃₇	—	2	4	no	—
167	C₂×C₄×C₃₇	—	2	1	no	—
168	C₂×C₄×C₃₇	—	2	1	no	—
169	C₂×C₄×C₃₇	—	2	1	no	—
170	C₂×C₄×C₃₇	—	2	4	no	—
171	C₂×C₄×C₃₇	—	2	2	no	—
172	C₂×C₄×C₃₇	—	2	2	no	—
173	C₂×C₄×C₃₇	—	2	1	no	—
174	C₂×C₄×C₃₇	—	2	1	no	—
175	C₂×C₄×C₃₇	—	4	2	no	—
176	C₂×C₄×C₃₇	—	4	2	no	—
177	C₂×C₄×C₃₇	—	4	1	no	—
178	C₂×C₄×C₃₇	—	4	1	no	—
179	C₂×C₄×C₃₇	—	4	2	no	—
180	C₂×C₄×C₃₇	—	4	2	no	—
181	C₂×C₄×C₃₇	—	4	2	no	—
182	C₂×C₄×C₃₇	—	4	2	no	—
183	C₂×C₄×C₃₇	—	4	2	no	—
184	C₂×C₄×C₃₇	—	4	2	no	—
185	C₂×C₄×C₃₇	—	4	2	no	—
186	C₂×C₄×C₃₇	—	4	2	no	—
187	C₂×C₄×C₃₇	—	4	2	no	—
188	C₂×C₄×C₃₇	—	4	2	no	—
189	C₂×C₄×C₃₇	#121	1	2	yes	—
190	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
192	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
194	C₈×C₃₇	—	2	2	no	—
195	C₈×C₃₇	—	2	2	no	—
196	C₈×C₃₇	—	4	1	no	—
197	C₈×C₃₇	—	4	1	no	—
198	#28564	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂²×C₃₇	—	2	2	no	—
200	C₂²×C₃₇	—	2	2	no	—
201	C₂²×C₃₇	—	2	2	no	—
202	C₂²×C₃₇	—	4	2	no	—
203	C₂²×C₃₇	—	4	2	no	—
204	C₂²×C₃₇	—	4	1	no	—
205	C₂²×C₃₇	—	4	1	no	—
206	C₂²×C₃₇	—	4	2	no	—
207	C₂²×C₃₇	—	4	1	no	—
208	C₂²×C₃₇	—	4	2	no	—
209	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
210	C₂²×C₃₇	#546	1	2	yes	—
211	C₂²×C₃₇	#575	1	2	yes	—
212	C₂²×C₃₇	#578	1	1	yes	characteristic
213	C₂²×C₃₇	#578	1	1	yes	characteristic
214	C₄×C₃₇	—	2	2	no	—
215	C₄×C₃₇	—	4	1	no	—
216	C₄×C₃₇	—	4	1	no	—
217	C₄×C₃₇	—	4	1	no	—
218	C₄×C₃₇	—	4	4	no	—
219	C₄×C₃₇	—	8	2	no	—
220	C₄×C₃₇	—	8	2	no	—
221	C₄×C₃₇	—	8	2	no	—
222	C₄×C₃₇	#532	1	1	yes	characteristic
223	C₄×C₃₇	#534	1	1	yes	characteristic
224	C₄×C₃₇	#553	1	2	yes	—
225	C₂×#467	C₂×C₃₇	1	1	yes	characteristic, complemented
226	C₂×#435	C₂×C₃₇	1	1	yes	characteristic
227	#2415	C₂×C₃₇	1	2	yes	—
228	#2087	C₂×C₃₇	1	1	yes	characteristic, complemented
229	#2076	C₂×C₃₇	1	1	yes	characteristic, complemented
230	#2056	C₂×C₃₇	1	1	yes	characteristic, complemented
231	#2001	C₂×C₃₇	1	1	yes	characteristic, complemented
232	#1935	C₂×C₃₇	1	2	yes	complemented
233	#1894	C₂×C₃₇	1	2	yes	complemented
234	#1873	C₂×C₃₇	1	2	yes	complemented
235	#1735	C₂×C₃₇	1	1	yes	characteristic, complemented
236	C₂×C₃₇	—	4	2	no	—
237	C₂×C₃₇	—	8	1	no	—
238	C₂×C₃₇	#2543	1	1	yes	characteristic
239	C₂×C₃₇	#3054	1	1	yes	characteristic
240	C₂×C₃₇	#3059	1	1	yes	characteristic
241	C₂×C₃₇	#3313	1	2	yes	—
242	C₂×C₃₇	#3315	1	2	yes	—
243	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
244	C₂²×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
245	C₂³×C₈	C₂²×C₃₇	1	1	yes	characteristic
246	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	2	yes	—
247	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	2	yes	—
248	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
249	C₂×#117	C₂²×C₃₇	1	2	yes	—
250	#467	—	2	4	no	—
251	#435	—	2	4	no	—
252	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
253	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
254	C₂×#103	C₂²×C₃₇	1	2	yes	—
255	C₂×#103	C₂²×C₃₇	1	2	yes	—
256	C₂×#103	C₂²×C₃₇	1	2	yes	—
257	C₂×C₂²⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
258	C₂×C₂²⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
259	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
260	#397	—	2	2	no	—
261	#394	—	2	2	no	—
262	#391	C₂²×C₃₇	1	2	yes	—
263	#389	—	2	2	no	—
264	#389	C₂²×C₃₇	1	2	yes	—
265	#388	—	2	2	no	—
266	#380	C₂²×C₃₇	1	2	yes	—
267	#340	C₂²×C₃₇	1	1	yes	characteristic
268	#340	C₂²×C₃₇	1	2	yes	—
269	#340	C₂²×C₃₇	1	2	yes	—
270	#340	C₂²×C₃₇	1	1	yes	characteristic
271	#340	C₂²×C₃₇	1	2	yes	—
272	C₃₇	#28564	1	1	yes	characteristic, direct product factor, Sylow
273	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
274	C₂²×D₄	D₄×C₃₇	1	1	yes	characteristic
275	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
276	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
277	C₂×Q₁₆	—	2	2	no	—
278	C₂×Q₁₆	—	4	2	no	—
279	C₂×M₁₆	—	2	2	no	—
280	C₂×M₁₆	—	4	2	no	—
281	C₂²×C₈	—	4	2	no	—
282	C₂²×C₈	D₄×C₃₇	1	4	yes	—
283	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
284	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
285	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
287	C₂²⋊Q₈	—	2	4	no	—
288	C₂²⋊Q₈	—	2	4	no	—
289	C₂²⋊Q₈	—	2	4	no	—
290	C₂²⋊Q₈	—	4	2	no	—
291	C₄×D₄	—	2	2	no	—
292	C₄×D₄	—	2	2	no	—
293	#117	—	2	4	no	—
294	#117	—	4	2	no	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
302	C₂×C₂²⋊C₄	—	2	2	no	—
303	C₂×C₂²⋊C₄	—	2	2	no	—
304	C₂×C₂²⋊C₄	—	2	2	no	—
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₂²⋊C₄	D₄×C₃₇	1	1	yes	characteristic
307	C₂×C₂²⋊C₄	D₄×C₃₇	1	1	yes	characteristic
308	C₂×C₄²	—	2	2	no	—
309	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
310	#107	—	2	2	no	—
311	C₄⋊C₈	—	2	2	no	—
312	#103	—	2	4	no	—
313	#103	—	2	4	no	—
314	#103	—	4	2	no	—
315	C₂²⋊C₈	—	2	2	no	—
316	C₂²⋊C₈	—	2	2	no	—
317	#97	—	2	2	no	—
318	#95	—	2	2	no	—
319	#95	—	2	2	no	—
320	#95	—	2	2	no	—
321	#95	—	2	2	no	—
322	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
323	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
347	C₂²×C₄	#41×C₃₇	1	2	yes	—
348	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
349	Q₁₆	—	4	4	no	—
350	M₁₆	—	4	4	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	4	4	no	—
358	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
359	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	4	4	no	—
367	C₄⋊C₄	—	4	4	no	—
368	C₄⋊C₄	—	4	4	no	—
369	C₄⋊C₄	#41×C₃₇	1	4	yes	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	4	4	no	—
373	C₂²⋊C₄	—	4	4	no	—
374	C₂²⋊C₄	—	4	4	no	—
375	C₂²⋊C₄	—	4	4	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	2	1	no	—
378	C₄²	—	4	4	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	1	no	—
388	C₂³	#121×C₃₇	1	2	yes	—
389	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
390	Q₈	—	4	2	no	—
391	Q₈	—	4	2	no	—
392	Q₈	—	4	2	no	—
393	Q₈	—	4	2	no	—
394	D₄	—	4	4	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	#121×C₃₇	1	2	yes	—
422	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
423	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
424	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
425	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
426	C₈	—	2	2	no	—
427	C₈	—	2	2	no	—
428	C₈	—	4	1	no	—
429	C₈	—	4	1	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	2	no	—
440	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
441	C₂²	C₃₇×#546	1	2	yes	—
442	C₂²	C₃₇×#575	1	2	yes	—
443	C₂²	C₃₇×#578	1	1	yes	characteristic
444	C₂²	C₃₇×#578	1	1	yes	characteristic
445	C₄	—	2	2	no	—
446	C₄	—	4	1	no	—
447	C₄	—	4	1	no	—
448	C₄	—	4	1	no	—
449	C₄	—	4	4	no	—
450	C₄	—	8	2	no	—
451	C₄	—	8	2	no	—
452	C₄	—	8	2	no	—
453	C₄	C₃₇×#532	1	1	yes	characteristic
454	C₄	C₃₇×#534	1	1	yes	characteristic
455	C₄	C₃₇×#553	1	2	yes	—
456	C₂	—	4	2	no	—
457	C₂	—	8	1	no	—
458	C₂	C₃₇×#2543	1	1	yes	characteristic
459	C₂	C₃₇×#3054	1	1	yes	characteristic
460	C₂	C₃₇×#3059	1	1	yes	characteristic
461	C₂	C₃₇×#3313	1	2	yes	—
462	C₂	C₃₇×#3315	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂²×D₄×C₃₇	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₂×C₄×D₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#467	C₂	semidirect
4. C₃₇×#2087	C₂	semidirect
5. C₃₇×#2076	C₂	semidirect
6. C₃₇×#2056	C₂	semidirect
7. C₃₇×#2001	C₂	semidirect
8. C₃₇×#1935	C₂	semidirect
9. C₃₇×#1894	C₂	semidirect
10. C₃₇×#1873	C₂	semidirect
11. C₃₇×#1735	C₂	semidirect
198. #28564	C₃₇	direct (N × H)
225. C₂×#467	C₂×C₃₇	semidirect
228. #2087	C₂×C₃₇	semidirect
229. #2076	C₂×C₃₇	semidirect
230. #2056	C₂×C₃₇	semidirect
231. #2001	C₂×C₃₇	semidirect
232. #1935	C₂×C₃₇	semidirect
233. #1894	C₂×C₃₇	semidirect
234. #1873	C₂×C₃₇	semidirect
235. #1735	C₂×C₃₇	semidirect
272. C₃₇	#28564	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×#467	2
C₂×C₃₇×#435	2
C₃₇×#2415	2
C₃₇×#2087	2
C₃₇×#2076	2
C₃₇×#2056	2
C₃₇×#2001	2
C₃₇×#1935	2
C₃₇×#1894	2
C₃₇×#1873	2
C₃₇×#1735	2
#28564	37

Subgroups — C37×#28564 #22649817

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28564 #22649817