Subgroups — C₃₇×#28279 #22649532

Order 9472.

996 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#474	C₂	1	2	yes	maximal, complemented
2	C₄×C₄⋊Q₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#127×C₃₇	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#2067	C₂	1	4	yes	maximal, complemented
5	C₃₇×#1982	C₂	1	2	yes	maximal
6	C₃₇×#1947	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1842	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1802	C₂	1	2	yes	maximal, complemented
9	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
10	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₃₇	—	2	1	no	—
12	C₂×C₄×D₄×C₃₇	—	2	1	no	—
13	C₂×C₄×D₄×C₃₇	—	2	1	no	—
14	C₂×C₄×D₄×C₃₇	C₂²	1	2	yes	—
15	C₃₇×#474	—	2	8	no	—
16	C₂×#107×C₃₇	C₂²	1	4	yes	—
17	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
20	C₂×#102×C₃₇	C₂²	1	4	yes	—
21	C₂×#102×C₃₇	C₂²	1	4	yes	—
22	C₃₇×#391	—	2	1	no	—
23	C₃₇×#390	—	2	1	no	—
24	C₃₇×#390	—	2	1	no	—
25	C₃₇×#390	C₂²	1	2	yes	—
26	C₃₇×#389	—	2	1	no	—
27	C₃₇×#389	C₂²	1	2	yes	—
28	C₃₇×#384	C₂²	1	1	yes	characteristic
29	C₃₇×#384	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊C₄×C₃₇	—	2	1	no	—
31	C₄×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
32	C₄³×C₃₇	C₂²	1	1	yes	characteristic
33	C₃₇×#340	C₂²	1	4	yes	—
34	C₂²×Q₈×C₃₇	—	2	1	no	—
35	C₂²×D₄×C₃₇	—	2	1	no	—
36	C₂²×D₄×C₃₇	—	2	1	no	—
37	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
38	C₂³×C₄×C₃₇	—	2	2	no	—
39	C₂²×C₈×C₃₇	C₂³	1	4	yes	—
40	C₄⋊Q₈×C₃₇	—	2	2	no	—
41	C₄⋊Q₈×C₃₇	D₄	1	4	yes	complemented
42	#127×C₃₇	—	2	2	no	—
43	#127×C₃₇	Q₈	1	4	yes	complemented
44	C₄×Q₈×C₃₇	—	4	4	no	—
45	C₄×D₄×C₃₇	—	2	4	no	—
46	C₄×D₄×C₃₇	—	2	4	no	—
47	C₄×D₄×C₃₇	—	4	4	no	—
48	C₄×D₄×C₃₇	—	4	4	no	—
49	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
50	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
51	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
52	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
53	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
54	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
58	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
61	C₂×C₄²×C₃₇	—	2	2	no	—
62	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
69	#107×C₃₇	—	2	8	no	—
70	C₄⋊C₈×C₃₇	—	2	4	no	—
71	C₄⋊C₈×C₃₇	—	2	4	no	—
72	C₄⋊C₈×C₃₇	—	4	2	no	—
73	#102×C₃₇	—	2	8	no	—
74	#102×C₃₇	—	4	4	no	—
75	#95×C₃₇	—	2	2	no	—
76	#95×C₃₇	—	2	2	no	—
77	C₂⁴×C₃₇	—	2	2	no	—
78	C₂×Q₈×C₃₇	—	2	4	no	—
79	C₂×Q₈×C₃₇	—	4	2	no	—
80	C₂×Q₈×C₃₇	—	4	2	no	—
81	C₂×D₄×C₃₇	—	2	4	no	—
82	C₂×D₄×C₃₇	—	2	4	no	—
83	C₂×D₄×C₃₇	—	2	2	no	—
84	C₂×D₄×C₃₇	—	2	2	no	—
85	C₂×D₄×C₃₇	—	2	2	no	—
86	C₂×D₄×C₃₇	—	2	2	no	—
87	C₂×D₄×C₃₇	—	2	2	no	—
88	C₂×D₄×C₃₇	—	4	2	no	—
89	C₂×D₄×C₃₇	—	4	2	no	—
90	C₂×D₄×C₃₇	—	4	2	no	—
91	C₂×D₄×C₃₇	—	4	2	no	—
92	C₂×D₄×C₃₇	C₂×Q₈	1	4	yes	—
93	C₂²×C₄×C₃₇	—	2	2	no	—
94	C₂²×C₄×C₃₇	—	2	2	no	—
95	C₂²×C₄×C₃₇	—	2	2	no	—
96	C₂²×C₄×C₃₇	—	4	4	no	—
97	C₂²×C₄×C₃₇	—	4	4	no	—
98	C₂²×C₄×C₃₇	—	4	4	no	—
99	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
106	C₂×C₈×C₃₇	—	2	4	no	—
107	C₂×C₈×C₃₇	—	2	4	no	—
108	C₂×C₈×C₃₇	—	2	4	no	—
109	C₄⋊C₄×C₃₇	—	2	4	no	—
110	C₄⋊C₄×C₃₇	—	2	2	no	—
111	C₄⋊C₄×C₃₇	—	2	2	no	—
112	C₄⋊C₄×C₃₇	—	2	2	no	—
113	C₄⋊C₄×C₃₇	—	2	2	no	—
114	C₄⋊C₄×C₃₇	—	2	2	no	—
115	C₄⋊C₄×C₃₇	—	4	2	no	—
116	C₄⋊C₄×C₃₇	—	4	2	no	—
117	C₄⋊C₄×C₃₇	—	4	2	no	—
118	C₄⋊C₄×C₃₇	—	4	4	no	—
119	C₄⋊C₄×C₃₇	—	4	2	no	—
120	C₄⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
121	C₂²⋊C₄×C₃₇	—	4	4	no	—
122	C₂²⋊C₄×C₃₇	—	4	4	no	—
123	C₂²⋊C₄×C₃₇	—	4	4	no	—
124	C₄²×C₃₇	—	2	2	no	—
125	C₄²×C₃₇	—	2	2	no	—
126	C₄²×C₃₇	—	2	1	no	—
127	C₄²×C₃₇	—	2	1	no	—
128	C₄²×C₃₇	—	4	1	no	—
129	C₄²×C₃₇	—	4	4	no	—
130	C₄²×C₃₇	D₈	1	4	yes	—
131	C₄²×C₃₇	C₂×D₄	1	2	yes	—
132	C₄²×C₃₇	C₂×Q₈	1	2	yes	—
133	C₄²×C₃₇	#41	1	2	yes	—
134	C₄²×C₃₇	#41	1	2	yes	—
135	C₂³×C₃₇	—	2	4	no	—
136	C₂³×C₃₇	—	4	2	no	—
137	C₂³×C₃₇	—	4	2	no	—
138	C₂³×C₃₇	—	4	2	no	—
139	C₂³×C₃₇	—	4	2	no	—
140	C₂³×C₃₇	—	4	2	no	—
141	C₂³×C₃₇	—	4	2	no	—
142	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
143	Q₈×C₃₇	—	4	8	no	—
144	D₄×C₃₇	—	2	4	no	—
145	D₄×C₃₇	—	2	4	no	—
146	D₄×C₃₇	—	4	8	no	—
147	D₄×C₃₇	—	4	2	no	—
148	D₄×C₃₇	—	4	2	no	—
149	D₄×C₃₇	—	4	8	no	—
150	C₂×C₄×C₃₇	—	2	1	no	—
151	C₂×C₄×C₃₇	—	2	1	no	—
152	C₂×C₄×C₃₇	—	2	1	no	—
153	C₂×C₄×C₃₇	—	2	1	no	—
154	C₂×C₄×C₃₇	—	2	1	no	—
155	C₂×C₄×C₃₇	—	2	1	no	—
156	C₂×C₄×C₃₇	—	2	4	no	—
157	C₂×C₄×C₃₇	—	2	1	no	—
158	C₂×C₄×C₃₇	—	2	1	no	—
159	C₂×C₄×C₃₇	—	2	1	no	—
160	C₂×C₄×C₃₇	—	4	2	no	—
161	C₂×C₄×C₃₇	—	4	2	no	—
162	C₂×C₄×C₃₇	—	4	2	no	—
163	C₂×C₄×C₃₇	—	4	2	no	—
164	C₂×C₄×C₃₇	—	4	2	no	—
165	C₂×C₄×C₃₇	—	4	2	no	—
166	C₂×C₄×C₃₇	—	4	2	no	—
167	C₂×C₄×C₃₇	—	4	2	no	—
168	C₂×C₄×C₃₇	—	8	8	no	—
169	C₂×C₄×C₃₇	#121	1	2	yes	—
170	C₂×C₄×C₃₇	#121	1	2	yes	—
171	C₂×C₄×C₃₇	C₂²⋊Q₈	1	2	yes	—
172	C₂×C₄×C₃₇	C₂²⋊Q₈	1	2	yes	—
173	C₂×C₄×C₃₇	C₂×D₈	1	2	yes	—
174	C₂×C₄×C₃₇	C₂×D₈	1	2	yes	—
175	C₂×C₄×C₃₇	C₂×D₈	1	2	yes	—
176	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
177	C₂×C₄×C₃₇	#137	1	2	yes	—
178	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₃₇	C₂²×Q₈	1	1	yes	characteristic
180	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
183	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
184	C₈×C₃₇	—	4	4	no	—
185	#28279	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂²×C₃₇	—	4	4	no	—
187	C₂²×C₃₇	—	4	4	no	—
188	C₂²×C₃₇	—	4	4	no	—
189	C₂²×C₃₇	—	8	2	no	—
190	C₂²×C₃₇	—	8	2	no	—
191	C₂²×C₃₇	—	8	2	no	—
192	C₂²×C₃₇	—	8	2	no	—
193	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
194	C₂²×C₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
195	C₂²×C₃₇	#537	1	1	yes	characteristic
196	C₂²×C₃₇	C₂²×D₈	1	1	yes	characteristic
197	C₂²×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
198	C₂²×C₃₇	C₂×#137	1	1	yes	characteristic
199	C₂²×C₃₇	#575	1	1	yes	characteristic
200	C₄×C₃₇	—	2	2	no	—
201	C₄×C₃₇	—	2	2	no	—
202	C₄×C₃₇	—	2	2	no	—
203	C₄×C₃₇	—	4	1	no	—
204	C₄×C₃₇	—	4	4	no	—
205	C₄×C₃₇	—	8	2	no	—
206	C₄×C₃₇	—	8	2	no	—
207	C₄×C₃₇	#459	1	4	yes	—
208	C₄×C₃₇	#474	1	4	yes	complemented
209	C₄×C₃₇	D₄×Q₈	1	1	yes	characteristic
210	C₄×C₃₇	#550	1	1	yes	characteristic
211	C₄×C₃₇	#554	1	1	yes	characteristic
212	C₄×C₃₇	#556	1	1	yes	characteristic
213	C₂×#474	C₂×C₃₇	1	2	yes	complemented
214	C₄×C₄⋊Q₈	C₂×C₃₇	1	1	yes	characteristic, complemented
215	C₄×#127	C₂×C₃₇	1	1	yes	characteristic
216	#2067	C₂×C₃₇	1	4	yes	complemented
217	#1982	C₂×C₃₇	1	2	yes	—
218	#1947	C₂×C₃₇	1	2	yes	complemented
219	#1842	C₂×C₃₇	1	1	yes	characteristic, complemented
220	#1802	C₂×C₃₇	1	2	yes	complemented
221	C₂×C₃₇	—	8	4	no	—
222	C₂×C₃₇	#2538	1	1	yes	characteristic
223	C₂×C₃₇	C₂×#459	1	1	yes	characteristic
224	C₂×C₃₇	#3037	1	1	yes	characteristic
225	C₂×C₃₇	C₂×#474	1	1	yes	characteristic
226	C₂×C₃₇	#3077	1	1	yes	characteristic
227	C₂×C₃₇	#3245	1	1	yes	characteristic
228	C₂×C₃₇	#3254	1	1	yes	characteristic
229	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
230	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
231	C₂×C₄×Q₈	—	2	1	no	—
232	C₂×C₄×D₄	—	2	1	no	—
233	C₂×C₄×D₄	—	2	1	no	—
234	C₂×C₄×D₄	C₂²×C₃₇	1	2	yes	—
235	#474	—	2	8	no	—
236	C₂×#107	C₂²×C₃₇	1	4	yes	—
237	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
238	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
239	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
240	C₂×#102	C₂²×C₃₇	1	4	yes	—
241	C₂×#102	C₂²×C₃₇	1	4	yes	—
242	#391	—	2	1	no	—
243	#390	—	2	1	no	—
244	#390	—	2	1	no	—
245	#390	C₂²×C₃₇	1	2	yes	—
246	#389	—	2	1	no	—
247	#389	C₂²×C₃₇	1	2	yes	—
248	#384	C₂²×C₃₇	1	1	yes	characteristic
249	#384	C₂²×C₃₇	1	1	yes	characteristic
250	C₄×C₄⋊C₄	—	2	1	no	—
251	C₄×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
252	C₄³	C₂²×C₃₇	1	1	yes	characteristic
253	#340	C₂²×C₃₇	1	4	yes	—
254	C₃₇	#28279	1	1	yes	characteristic, direct product factor, Sylow
255	C₂²×Q₈	—	2	1	no	—
256	C₂²×D₄	—	2	1	no	—
257	C₂²×D₄	—	2	1	no	—
258	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
259	C₂³×C₄	—	2	2	no	—
260	C₂²×C₈	C₂³×C₃₇	1	4	yes	—
261	C₄⋊Q₈	—	2	2	no	—
262	C₄⋊Q₈	D₄×C₃₇	1	4	yes	complemented
263	#127	—	2	2	no	—
264	#127	Q₈×C₃₇	1	4	yes	complemented
265	C₄×Q₈	—	4	4	no	—
266	C₄×D₄	—	2	4	no	—
267	C₄×D₄	—	2	4	no	—
268	C₄×D₄	—	4	4	no	—
269	C₄×D₄	—	4	4	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
277	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
278	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₄²	—	2	2	no	—
283	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
284	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
285	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
286	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
287	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
288	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
289	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
290	#107	—	2	8	no	—
291	C₄⋊C₈	—	2	4	no	—
292	C₄⋊C₈	—	2	4	no	—
293	C₄⋊C₈	—	4	2	no	—
294	#102	—	2	8	no	—
295	#102	—	4	4	no	—
296	#95	—	2	2	no	—
297	#95	—	2	2	no	—
298	C₂⁴	—	2	2	no	—
299	C₂×Q₈	—	2	4	no	—
300	C₂×Q₈	—	4	2	no	—
301	C₂×Q₈	—	4	2	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	4	2	no	—
310	C₂×D₄	—	4	2	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	C₂×Q₈×C₃₇	1	4	yes	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	4	4	no	—
318	C₂²×C₄	—	4	4	no	—
319	C₂²×C₄	—	4	4	no	—
320	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
323	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
326	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
327	C₂×C₈	—	2	4	no	—
328	C₂×C₈	—	2	4	no	—
329	C₂×C₈	—	2	4	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	4	2	no	—
337	C₄⋊C₄	—	4	2	no	—
338	C₄⋊C₄	—	4	2	no	—
339	C₄⋊C₄	—	4	4	no	—
340	C₄⋊C₄	—	4	2	no	—
341	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
342	C₂²⋊C₄	—	4	4	no	—
343	C₂²⋊C₄	—	4	4	no	—
344	C₂²⋊C₄	—	4	4	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	2	1	no	—
348	C₄²	—	2	1	no	—
349	C₄²	—	4	1	no	—
350	C₄²	—	4	4	no	—
351	C₄²	D₈×C₃₇	1	4	yes	—
352	C₄²	C₂×D₄×C₃₇	1	2	yes	—
353	C₄²	C₂×Q₈×C₃₇	1	2	yes	—
354	C₄²	#41×C₃₇	1	2	yes	—
355	C₄²	#41×C₃₇	1	2	yes	—
356	C₂³	—	2	4	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	2	no	—
363	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
364	Q₈	—	4	8	no	—
365	D₄	—	2	4	no	—
366	D₄	—	2	4	no	—
367	D₄	—	4	8	no	—
368	D₄	—	4	2	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	8	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	8	8	no	—
390	C₂×C₄	#121×C₃₇	1	2	yes	—
391	C₂×C₄	#121×C₃₇	1	2	yes	—
392	C₂×C₄	C₂²⋊Q₈×C₃₇	1	2	yes	—
393	C₂×C₄	C₂²⋊Q₈×C₃₇	1	2	yes	—
394	C₂×C₄	C₂×D₈×C₃₇	1	2	yes	—
395	C₂×C₄	C₂×D₈×C₃₇	1	2	yes	—
396	C₂×C₄	C₂×D₈×C₃₇	1	2	yes	—
397	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
398	C₂×C₄	#137×C₃₇	1	2	yes	—
399	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
400	C₂×C₄	C₂²×Q₈×C₃₇	1	1	yes	characteristic
401	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
402	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
403	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
404	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
405	C₈	—	4	4	no	—
406	C₂²	—	4	4	no	—
407	C₂²	—	4	4	no	—
408	C₂²	—	4	4	no	—
409	C₂²	—	8	2	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	8	2	no	—
413	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
414	C₂²	C₂×C₂²⋊Q₈×C₃₇	1	1	yes	characteristic
415	C₂²	C₃₇×#537	1	1	yes	characteristic
416	C₂²	C₂²×D₈×C₃₇	1	1	yes	characteristic
417	C₂²	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
418	C₂²	C₂×#137×C₃₇	1	1	yes	characteristic
419	C₂²	C₃₇×#575	1	1	yes	characteristic
420	C₄	—	2	2	no	—
421	C₄	—	2	2	no	—
422	C₄	—	2	2	no	—
423	C₄	—	4	1	no	—
424	C₄	—	4	4	no	—
425	C₄	—	8	2	no	—
426	C₄	—	8	2	no	—
427	C₄	C₃₇×#459	1	4	yes	—
428	C₄	C₃₇×#474	1	4	yes	complemented
429	C₄	D₄×Q₈×C₃₇	1	1	yes	characteristic
430	C₄	C₃₇×#550	1	1	yes	characteristic
431	C₄	C₃₇×#554	1	1	yes	characteristic
432	C₄	C₃₇×#556	1	1	yes	characteristic
433	C₂	—	8	4	no	—
434	C₂	C₃₇×#2538	1	1	yes	characteristic
435	C₂	C₂×C₃₇×#459	1	1	yes	characteristic
436	C₂	C₃₇×#3037	1	1	yes	characteristic
437	C₂	C₂×C₃₇×#474	1	1	yes	characteristic
438	C₂	C₃₇×#3077	1	1	yes	characteristic
439	C₂	C₃₇×#3245	1	1	yes	characteristic
440	C₂	C₃₇×#3254	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂×#127×C₃₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₄³×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#474	C₂	semidirect
2. C₄×C₄⋊Q₈×C₃₇	C₂	semidirect
4. C₃₇×#2067	C₂	semidirect
6. C₃₇×#1947	C₂	semidirect
7. C₃₇×#1842	C₂	semidirect
8. C₃₇×#1802	C₂	semidirect
41. C₄⋊Q₈×C₃₇	D₄	semidirect
43. #127×C₃₇	Q₈	semidirect
185. #28279	C₃₇	direct (N × H)
208. C₄×C₃₇	#474	semidirect
213. C₂×#474	C₂×C₃₇	semidirect
214. C₄×C₄⋊Q₈	C₂×C₃₇	semidirect
216. #2067	C₂×C₃₇	semidirect
218. #1947	C₂×C₃₇	semidirect
219. #1842	C₂×C₃₇	semidirect
220. #1802	C₂×C₃₇	semidirect
254. C₃₇	#28279	direct (N × H)
262. C₄⋊Q₈	D₄×C₃₇	semidirect
264. #127	Q₈×C₃₇	semidirect
428. C₄	C₃₇×#474	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₇×#474	2
C₄×C₄⋊Q₈×C₃₇	2
C₄×#127×C₃₇	2
C₃₇×#2067	2
C₃₇×#1982	2
C₃₇×#1947	2
C₃₇×#1842	2
C₃₇×#1802	2
#28279	37

Subgroups — C37×#28279 #22649532

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28279 #22649532