Subgroups — C₃₇×#28403 #22649656

Order 9472.

922 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#487	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#474	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₇×#462	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×SD₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#2568	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2547	C₂	1	1	yes	maximal, characteristic
7	C₃₇×#2097	C₂	1	2	yes	maximal, complemented
8	C₃₇×#2015	C₂	1	2	yes	maximal
9	C₃₇×#1969	C₂	1	2	yes	maximal, complemented
10	C₃₇×#1958	C₂	1	2	yes	maximal
11	C₈×C₄⋊C₄×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₃₇	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
16	C₂×#124×C₃₇	C₂²	1	2	yes	—
17	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
19	C₃₇×#487	—	2	4	no	—
20	C₃₇×#474	—	2	4	no	—
21	C₃₇×#462	—	2	4	no	—
22	C₄×SD₁₆×C₃₇	—	2	4	no	—
23	C₂×#107×C₃₇	C₂²	1	2	yes	—
24	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
26	C₂×#103×C₃₇	C₂²	1	2	yes	—
27	C₂×#103×C₃₇	C₂²	1	2	yes	—
28	C₂×#103×C₃₇	C₂²	1	2	yes	—
29	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
30	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
31	C₂×#102×C₃₇	C₂²	1	2	yes	—
32	C₂×C₄×C₈×C₃₇	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
34	C₃₇×#400	—	2	2	no	—
35	C₃₇×#397	—	2	2	no	—
36	C₃₇×#391	—	2	2	no	—
37	C₃₇×#391	C₂²	1	2	yes	—
38	C₃₇×#391	C₂²	1	2	yes	—
39	C₃₇×#382	C₂²	1	2	yes	—
40	C₃₇×#380	—	2	2	no	—
41	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
42	C₃₇×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₃₇	—	2	1	no	—
44	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
45	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₃₇	—	2	1	no	—
48	C₂×Q₁₆×C₃₇	—	2	4	no	—
49	C₂×Q₁₆×C₃₇	—	2	4	no	—
50	C₂×Q₁₆×C₃₇	—	4	2	no	—
51	C₂×SD₁₆×C₃₇	—	2	2	no	—
52	C₂×SD₁₆×C₃₇	—	2	2	no	—
53	C₂×SD₁₆×C₃₇	—	2	2	no	—
54	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
56	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
57	C₄⋊Q₈×C₃₇	—	2	2	no	—
58	C₄⋊Q₈×C₃₇	—	2	2	no	—
59	C₄⋊Q₈×C₃₇	—	2	2	no	—
60	C₄⋊Q₈×C₃₇	—	2	2	no	—
61	#124×C₃₇	—	2	4	no	—
62	#124×C₃₇	—	4	2	no	—
63	C₄×Q₈×C₃₇	—	2	2	no	—
64	C₄×Q₈×C₃₇	—	2	2	no	—
65	C₄×D₄×C₃₇	—	2	2	no	—
66	C₄×D₄×C₃₇	—	2	2	no	—
67	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
68	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
69	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
70	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
71	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
76	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
77	C₂×C₄²×C₃₇	—	2	1	no	—
78	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
79	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
80	#107×C₃₇	—	2	4	no	—
81	#106×C₃₇	—	2	2	no	—
82	C₄⋊C₈×C₃₇	D₄	1	4	yes	—
83	#103×C₃₇	—	2	2	no	—
84	#103×C₃₇	—	2	4	no	—
85	#103×C₃₇	—	2	4	no	—
86	#103×C₃₇	—	2	4	no	—
87	#102×C₃₇	—	2	2	no	—
88	#102×C₃₇	—	2	4	no	—
89	C₄×C₈×C₃₇	—	4	2	no	—
90	C₄×C₈×C₃₇	D₄	1	4	yes	—
91	#95×C₃₇	—	2	4	no	—
92	#95×C₃₇	—	2	4	no	—
93	#95×C₃₇	—	2	4	no	—
94	#95×C₃₇	D₄	1	2	yes	—
95	C₂⁴×C₃₇	—	2	1	no	—
96	C₂×Q₈×C₃₇	—	2	1	no	—
97	C₂×Q₈×C₃₇	—	2	1	no	—
98	C₂×Q₈×C₃₇	—	2	1	no	—
99	C₂×Q₈×C₃₇	—	2	2	no	—
100	C₂×Q₈×C₃₇	—	2	2	no	—
101	C₂×Q₈×C₃₇	—	2	1	no	—
102	C₂×Q₈×C₃₇	—	2	2	no	—
103	C₂×Q₈×C₃₇	—	2	2	no	—
104	C₂×Q₈×C₃₇	—	2	1	no	—
105	C₂×Q₈×C₃₇	—	2	2	no	—
106	C₂×Q₈×C₃₇	—	2	2	no	—
107	C₂×Q₈×C₃₇	—	4	2	no	—
108	C₂×Q₈×C₃₇	—	4	4	no	—
109	C₂×Q₈×C₃₇	#41	1	2	yes	—
110	C₂×D₄×C₃₇	—	2	1	no	—
111	C₂×D₄×C₃₇	—	2	1	no	—
112	C₂×D₄×C₃₇	—	2	1	no	—
113	C₂×D₄×C₃₇	—	2	1	no	—
114	C₂×D₄×C₃₇	—	2	1	no	—
115	C₂×D₄×C₃₇	#41	1	2	yes	—
116	C₂²×C₄×C₃₇	—	2	1	no	—
117	C₂²×C₄×C₃₇	—	2	1	no	—
118	C₂²×C₄×C₃₇	—	2	1	no	—
119	C₂²×C₄×C₃₇	—	2	2	no	—
120	C₂²×C₄×C₃₇	—	2	2	no	—
121	C₂²×C₄×C₃₇	—	4	2	no	—
122	C₂²×C₄×C₃₇	—	4	4	no	—
123	C₂²×C₄×C₃₇	C₂×D₄	1	4	yes	—
124	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
127	Q₁₆×C₃₇	—	4	8	no	—
128	SD₁₆×C₃₇	—	2	8	no	—
129	C₂×C₈×C₃₇	—	2	1	no	—
130	C₂×C₈×C₃₇	—	2	1	no	—
131	C₂×C₈×C₃₇	—	2	2	no	—
132	C₂×C₈×C₃₇	—	2	1	no	—
133	C₂×C₈×C₃₇	—	2	2	no	—
134	C₂×C₈×C₃₇	—	2	1	no	—
135	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₃₇	C₂×D₄	1	4	yes	—
138	C₄⋊C₄×C₃₇	—	2	4	no	—
139	C₄⋊C₄×C₃₇	—	2	1	no	—
140	C₄⋊C₄×C₃₇	—	2	2	no	—
141	C₄⋊C₄×C₃₇	—	2	1	no	—
142	C₄⋊C₄×C₃₇	—	2	2	no	—
143	C₄⋊C₄×C₃₇	—	2	1	no	—
144	C₄⋊C₄×C₃₇	—	2	1	no	—
145	C₄⋊C₄×C₃₇	—	4	2	no	—
146	C₄⋊C₄×C₃₇	—	4	2	no	—
147	C₄⋊C₄×C₃₇	—	4	2	no	—
148	C₄⋊C₄×C₃₇	—	4	2	no	—
149	C₂²⋊C₄×C₃₇	—	4	8	no	—
150	C₂²⋊C₄×C₃₇	—	4	2	no	—
151	C₄²×C₃₇	—	2	2	no	—
152	C₄²×C₃₇	—	2	2	no	—
153	C₄²×C₃₇	—	4	2	no	—
154	C₄²×C₃₇	C₂×D₄	1	2	yes	—
155	C₄²×C₃₇	C₂×D₄	1	2	yes	—
156	C₂³×C₃₇	—	2	2	no	—
157	C₂³×C₃₇	—	4	1	no	—
158	C₂³×C₃₇	—	4	1	no	—
159	C₂³×C₃₇	—	4	2	no	—
160	C₂³×C₃₇	—	4	2	no	—
161	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
162	Q₈×C₃₇	—	2	2	no	—
163	Q₈×C₃₇	—	2	2	no	—
164	Q₈×C₃₇	—	4	1	no	—
165	Q₈×C₃₇	—	4	1	no	—
166	Q₈×C₃₇	—	4	2	no	—
167	Q₈×C₃₇	—	4	2	no	—
168	Q₈×C₃₇	—	4	2	no	—
169	Q₈×C₃₇	—	4	2	no	—
170	Q₈×C₃₇	—	8	4	no	—
171	D₄×C₃₇	—	2	2	no	—
172	D₄×C₃₇	—	2	2	no	—
173	D₄×C₃₇	—	4	1	no	—
174	D₄×C₃₇	—	4	1	no	—
175	C₂×C₄×C₃₇	—	2	2	no	—
176	C₂×C₄×C₃₇	—	2	4	no	—
177	C₂×C₄×C₃₇	—	2	2	no	—
178	C₂×C₄×C₃₇	—	2	4	no	—
179	C₂×C₄×C₃₇	—	2	4	no	—
180	C₂×C₄×C₃₇	—	4	1	no	—
181	C₂×C₄×C₃₇	—	4	1	no	—
182	C₂×C₄×C₃₇	—	4	1	no	—
183	C₂×C₄×C₃₇	—	4	1	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	—	4	4	no	—
190	C₂×C₄×C₃₇	—	4	2	no	—
191	C₂×C₄×C₃₇	—	8	4	no	—
192	C₂×C₄×C₃₇	#127	1	2	yes	—
193	C₂×C₄×C₃₇	#127	1	2	yes	—
194	C₂×C₄×C₃₇	#135	1	4	yes	—
195	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
200	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
201	C₈×C₃₇	—	2	2	no	—
202	C₈×C₃₇	—	2	2	no	—
203	C₈×C₃₇	—	2	4	no	—
204	#28403	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂²×C₃₇	—	4	4	no	—
206	C₂²×C₃₇	—	4	2	no	—
207	C₂²×C₃₇	—	8	2	no	—
208	C₂²×C₃₇	—	8	1	no	—
209	C₂²×C₃₇	—	8	1	no	—
210	C₂²×C₃₇	C₂×#127	1	1	yes	characteristic
211	C₂²×C₃₇	#546	1	1	yes	characteristic
212	C₂²×C₃₇	#548	1	1	yes	characteristic
213	C₂²×C₃₇	C₂×#135	1	2	yes	—
214	C₂²×C₃₇	#578	1	2	yes	—
215	C₄×C₃₇	—	2	2	no	—
216	C₄×C₃₇	—	4	4	no	—
217	C₄×C₃₇	—	4	2	no	—
218	C₄×C₃₇	—	8	1	no	—
219	C₄×C₃₇	—	8	2	no	—
220	C₄×C₃₇	—	8	1	no	—
221	C₄×C₃₇	—	8	2	no	—
222	C₄×C₃₇	#495	1	4	yes	—
223	C₄×C₃₇	#525	1	1	yes	characteristic
224	C₄×C₃₇	#537	1	1	yes	characteristic
225	C₄×C₃₇	#546	1	1	yes	characteristic
226	C₄×C₃₇	#548	1	1	yes	characteristic
227	C₂×#487	C₂×C₃₇	1	1	yes	characteristic, complemented
228	C₂×#474	C₂×C₃₇	1	1	yes	characteristic
229	C₂×#462	C₂×C₃₇	1	1	yes	characteristic, complemented
230	C₂×C₄×SD₁₆	C₂×C₃₇	1	1	yes	characteristic
231	#2568	C₂×C₃₇	1	1	yes	characteristic, complemented
232	#2547	C₂×C₃₇	1	1	yes	characteristic
233	#2097	C₂×C₃₇	1	2	yes	complemented
234	#2015	C₂×C₃₇	1	2	yes	—
235	#1969	C₂×C₃₇	1	2	yes	complemented
236	#1958	C₂×C₃₇	1	2	yes	—
237	C₈×C₄⋊C₄	C₂×C₃₇	1	1	yes	characteristic, complemented
238	C₂×C₃₇	—	8	2	no	—
239	C₂×C₃₇	#2540	1	1	yes	characteristic
240	C₂×C₃₇	C₂×#495	1	1	yes	characteristic
241	C₂×C₃₇	#3156	1	1	yes	characteristic
242	C₂×C₃₇	#3302	1	2	yes	—
243	C₂×C₃₇	#3364	1	2	yes	—
244	C₂²×Q₁₆	C₂²×C₃₇	1	2	yes	—
245	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
246	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
247	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
248	C₂×#124	C₂²×C₃₇	1	2	yes	—
249	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
250	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
251	#487	—	2	4	no	—
252	#474	—	2	4	no	—
253	#462	—	2	4	no	—
254	C₄×SD₁₆	—	2	4	no	—
255	C₂×#107	C₂²×C₃₇	1	2	yes	—
256	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
257	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
258	C₂×#103	C₂²×C₃₇	1	2	yes	—
259	C₂×#103	C₂²×C₃₇	1	2	yes	—
260	C₂×#103	C₂²×C₃₇	1	2	yes	—
261	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
262	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
263	C₂×#102	C₂²×C₃₇	1	2	yes	—
264	C₂×C₄×C₈	C₂²×C₃₇	1	2	yes	—
265	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
266	#400	—	2	2	no	—
267	#397	—	2	2	no	—
268	#391	—	2	2	no	—
269	#391	C₂²×C₃₇	1	2	yes	—
270	#391	C₂²×C₃₇	1	2	yes	—
271	#382	C₂²×C₃₇	1	2	yes	—
272	#380	—	2	2	no	—
273	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
274	#336	C₂²×C₃₇	1	2	yes	—
275	C₃₇	#28403	1	1	yes	characteristic, direct product factor, Sylow
276	C₂²×Q₈	—	2	1	no	—
277	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
278	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
279	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
280	C₂³×C₄	—	2	1	no	—
281	C₂×Q₁₆	—	2	4	no	—
282	C₂×Q₁₆	—	2	4	no	—
283	C₂×Q₁₆	—	4	2	no	—
284	C₂×SD₁₆	—	2	2	no	—
285	C₂×SD₁₆	—	2	2	no	—
286	C₂×SD₁₆	—	2	2	no	—
287	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
288	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
289	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
290	C₄⋊Q₈	—	2	2	no	—
291	C₄⋊Q₈	—	2	2	no	—
292	C₄⋊Q₈	—	2	2	no	—
293	C₄⋊Q₈	—	2	2	no	—
294	#124	—	2	4	no	—
295	#124	—	4	2	no	—
296	C₄×Q₈	—	2	2	no	—
297	C₄×Q₈	—	2	2	no	—
298	C₄×D₄	—	2	2	no	—
299	C₄×D₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
305	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₂²⋊C₄	—	2	4	no	—
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
312	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
313	#107	—	2	4	no	—
314	#106	—	2	2	no	—
315	C₄⋊C₈	D₄×C₃₇	1	4	yes	—
316	#103	—	2	2	no	—
317	#103	—	2	4	no	—
318	#103	—	2	4	no	—
319	#103	—	2	4	no	—
320	#102	—	2	2	no	—
321	#102	—	2	4	no	—
322	C₄×C₈	—	4	2	no	—
323	C₄×C₈	D₄×C₃₇	1	4	yes	—
324	#95	—	2	4	no	—
325	#95	—	2	4	no	—
326	#95	—	2	4	no	—
327	#95	D₄×C₃₇	1	2	yes	—
328	C₂⁴	—	2	1	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	4	2	no	—
341	C₂×Q₈	—	4	4	no	—
342	C₂×Q₈	#41×C₃₇	1	2	yes	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	#41×C₃₇	1	2	yes	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	4	2	no	—
355	C₂²×C₄	—	4	4	no	—
356	C₂²×C₄	C₂×D₄×C₃₇	1	4	yes	—
357	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
359	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
360	Q₁₆	—	4	8	no	—
361	SD₁₆	—	2	8	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
369	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
370	C₂×C₈	C₂×D₄×C₃₇	1	4	yes	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	4	2	no	—
379	C₄⋊C₄	—	4	2	no	—
380	C₄⋊C₄	—	4	2	no	—
381	C₄⋊C₄	—	4	2	no	—
382	C₂²⋊C₄	—	4	8	no	—
383	C₂²⋊C₄	—	4	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	4	2	no	—
387	C₄²	C₂×D₄×C₃₇	1	2	yes	—
388	C₄²	C₂×D₄×C₃₇	1	2	yes	—
389	C₂³	—	2	2	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
395	Q₈	—	2	2	no	—
396	Q₈	—	2	2	no	—
397	Q₈	—	4	1	no	—
398	Q₈	—	4	1	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	4	2	no	—
401	Q₈	—	4	2	no	—
402	Q₈	—	4	2	no	—
403	Q₈	—	8	4	no	—
404	D₄	—	2	2	no	—
405	D₄	—	2	2	no	—
406	D₄	—	4	1	no	—
407	D₄	—	4	1	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	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	—	4	2	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	8	4	no	—
425	C₂×C₄	#127×C₃₇	1	2	yes	—
426	C₂×C₄	#127×C₃₇	1	2	yes	—
427	C₂×C₄	#135×C₃₇	1	4	yes	—
428	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
430	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
431	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
432	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
433	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
434	C₈	—	2	2	no	—
435	C₈	—	2	2	no	—
436	C₈	—	2	4	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	8	1	no	—
440	C₂²	—	8	1	no	—
441	C₂²	—	8	2	no	—
442	C₂²	C₂×#127×C₃₇	1	1	yes	characteristic
443	C₂²	C₃₇×#546	1	1	yes	characteristic
444	C₂²	C₃₇×#548	1	1	yes	characteristic
445	C₂²	C₂×#135×C₃₇	1	2	yes	—
446	C₂²	C₃₇×#578	1	2	yes	—
447	C₄	—	2	2	no	—
448	C₄	—	4	4	no	—
449	C₄	—	4	2	no	—
450	C₄	—	8	1	no	—
451	C₄	—	8	2	no	—
452	C₄	—	8	1	no	—
453	C₄	—	8	2	no	—
454	C₄	C₃₇×#495	1	4	yes	—
455	C₄	C₃₇×#525	1	1	yes	characteristic
456	C₄	C₃₇×#537	1	1	yes	characteristic
457	C₄	C₃₇×#546	1	1	yes	characteristic
458	C₄	C₃₇×#548	1	1	yes	characteristic
459	C₂	—	8	2	no	—
460	C₂	C₃₇×#2540	1	1	yes	characteristic
461	C₂	C₂×C₃₇×#495	1	1	yes	characteristic
462	C₂	C₃₇×#3156	1	1	yes	characteristic
463	C₂	C₃₇×#3302	1	2	yes	—
464	C₂	C₃₇×#3364	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#487	C₂	semidirect
3. C₂×C₃₇×#462	C₂	semidirect
5. C₃₇×#2568	C₂	semidirect
7. C₃₇×#2097	C₂	semidirect
9. C₃₇×#1969	C₂	semidirect
11. C₈×C₄⋊C₄×C₃₇	C₂	semidirect
204. #28403	C₃₇	direct (N × H)
227. C₂×#487	C₂×C₃₇	semidirect
229. C₂×#462	C₂×C₃₇	semidirect
231. #2568	C₂×C₃₇	semidirect
233. #2097	C₂×C₃₇	semidirect
235. #1969	C₂×C₃₇	semidirect
237. C₈×C₄⋊C₄	C₂×C₃₇	semidirect
275. C₃₇	#28403	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×#487	2
C₂×C₃₇×#474	2
C₂×C₃₇×#462	2
C₂×C₄×SD₁₆×C₃₇	2
C₃₇×#2568	2
C₃₇×#2547	2
C₃₇×#2097	2
C₃₇×#2015	2
C₃₇×#1969	2
C₃₇×#1958	2
C₈×C₄⋊C₄×C₃₇	2
#28403	37

Subgroups — C37×#28403 #22649656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28403 #22649656