Subgroups — C₃₇×#29995 #22651248

Order 9472.

738 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#2859	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×#2293	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2088	C₂	1	2	yes	maximal, complemented
4	C₃₇×#2087	C₂	1	2	yes	maximal, complemented
5	C₃₇×#2067	C₂	1	2	yes	maximal
6	C₃₇×#2065	C₂	1	2	yes	maximal
7	C₃₇×#1948	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1947	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1842	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1802	C₂	1	1	yes	maximal, characteristic
11	C₃₇×#1802	C₂	1	1	yes	maximal, characteristic
12	C₂×#125×C₃₇	—	2	1	no	—
13	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×#117×C₃₇	—	2	1	no	—
15	C₂×#107×C₃₇	C₂²	1	2	yes	—
16	C₂×#106×C₃₇	C₂²	1	2	yes	—
17	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
20	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
21	C₂×#102×C₃₇	C₂²	1	2	yes	—
22	C₂×#102×C₃₇	C₂²	1	2	yes	—
23	C₃₇×#390	C₂²	1	1	yes	characteristic
24	C₃₇×#390	C₂²	1	1	yes	characteristic
25	C₃₇×#389	—	2	1	no	—
26	C₃₇×#389	—	2	1	no	—
27	C₃₇×#389	C₂²	1	1	yes	characteristic
28	C₃₇×#389	C₂²	1	1	yes	characteristic
29	C₃₇×#389	C₂²	1	2	yes	—
30	C₃₇×#389	C₂²	1	2	yes	—
31	C₃₇×#388	—	2	1	no	—
32	C₃₇×#388	—	2	1	no	—
33	C₃₇×#384	C₂²	1	1	yes	characteristic
34	C₃₇×#384	C₂²	1	1	yes	characteristic
35	C₃₇×#382	—	2	1	no	—
36	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊C₄×C₃₇	—	2	1	no	—
38	C₄³×C₃₇	C₂²	1	1	yes	characteristic
39	C₃₇×#340	C₂²	1	2	yes	—
40	C₃₇×#340	C₂²	1	2	yes	—
41	C₃₇×#340	C₂²	1	2	yes	—
42	C₃₇×#340	C₂²	1	2	yes	—
43	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₃₇	—	2	1	no	—
45	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
46	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
47	#125×C₃₇	—	4	4	no	—
48	C₄×D₄×C₃₇	—	2	2	no	—
49	C₄×D₄×C₃₇	Q₈	1	4	yes	—
50	#117×C₃₇	—	4	4	no	—
51	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
52	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
53	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
56	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
57	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
58	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
59	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
69	C₂×C₄²×C₃₇	—	2	1	no	—
70	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
77	#107×C₃₇	—	4	2	no	—
78	#106×C₃₇	—	4	2	no	—
79	C₄⋊C₈×C₃₇	—	2	2	no	—
80	C₄⋊C₈×C₃₇	—	2	2	no	—
81	C₄⋊C₈×C₃₇	—	4	2	no	—
82	C₄⋊C₈×C₃₇	—	4	2	no	—
83	#102×C₃₇	—	4	2	no	—
84	#102×C₃₇	—	4	2	no	—
85	#95×C₃₇	—	2	1	no	—
86	#95×C₃₇	—	2	1	no	—
87	#95×C₃₇	—	2	1	no	—
88	#95×C₃₇	—	2	2	no	—
89	#95×C₃₇	—	2	2	no	—
90	C₂⁴×C₃₇	—	2	1	no	—
91	C₂×D₄×C₃₇	—	2	1	no	—
92	C₂×D₄×C₃₇	—	2	1	no	—
93	C₂×D₄×C₃₇	—	2	1	no	—
94	C₂×D₄×C₃₇	—	2	1	no	—
95	C₂×D₄×C₃₇	—	2	1	no	—
96	C₂×D₄×C₃₇	C₂×Q₈	1	2	yes	—
97	C₂²×C₄×C₃₇	—	2	1	no	—
98	C₂²×C₄×C₃₇	—	2	4	no	—
99	C₂²×C₄×C₃₇	—	2	1	no	—
100	C₂²×C₄×C₃₇	—	2	1	no	—
101	C₂²×C₄×C₃₇	—	2	2	no	—
102	C₂²×C₄×C₃₇	—	2	2	no	—
103	C₂²×C₄×C₃₇	—	4	2	no	—
104	C₂²×C₄×C₃₇	—	4	2	no	—
105	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
112	C₂×C₈×C₃₇	—	2	2	no	—
113	C₂×C₈×C₃₇	—	2	2	no	—
114	C₂×C₈×C₃₇	—	2	2	no	—
115	C₂×C₈×C₃₇	—	2	2	no	—
116	C₂×C₈×C₃₇	—	2	2	no	—
117	C₂×C₈×C₃₇	—	2	2	no	—
118	C₄⋊C₄×C₃₇	—	2	1	no	—
119	C₄⋊C₄×C₃₇	—	2	2	no	—
120	C₄⋊C₄×C₃₇	—	2	2	no	—
121	C₄⋊C₄×C₃₇	—	2	1	no	—
122	C₄⋊C₄×C₃₇	—	2	1	no	—
123	C₄⋊C₄×C₃₇	—	2	1	no	—
124	C₄⋊C₄×C₃₇	—	2	1	no	—
125	C₄⋊C₄×C₃₇	—	2	2	no	—
126	C₄⋊C₄×C₃₇	—	2	2	no	—
127	C₄⋊C₄×C₃₇	—	4	2	no	—
128	C₄⋊C₄×C₃₇	—	4	2	no	—
129	C₄⋊C₄×C₃₇	—	4	2	no	—
130	C₄⋊C₄×C₃₇	—	4	2	no	—
131	C₄⋊C₄×C₃₇	—	4	4	no	—
132	C₄⋊C₄×C₃₇	—	4	2	no	—
133	C₄⋊C₄×C₃₇	—	4	2	no	—
134	C₄⋊C₄×C₃₇	—	4	4	no	—
135	C₄⋊C₄×C₃₇	C₂×Q₈	1	2	yes	—
136	C₂²⋊C₄×C₃₇	—	2	4	no	—
137	C₂²⋊C₄×C₃₇	—	4	2	no	—
138	C₂²⋊C₄×C₃₇	—	4	2	no	—
139	C₂²⋊C₄×C₃₇	—	4	2	no	—
140	C₂²⋊C₄×C₃₇	—	4	2	no	—
141	C₄²×C₃₇	—	2	2	no	—
142	C₄²×C₃₇	—	2	2	no	—
143	C₄²×C₃₇	—	2	2	no	—
144	C₄²×C₃₇	—	2	2	no	—
145	C₄²×C₃₇	—	2	1	no	—
146	C₄²×C₃₇	—	2	1	no	—
147	C₄²×C₃₇	—	2	1	no	—
148	C₄²×C₃₇	—	2	1	no	—
149	C₄²×C₃₇	—	4	2	no	—
150	C₄²×C₃₇	C₂×Q₈	1	2	yes	—
151	C₄²×C₃₇	#41	1	2	yes	—
152	C₂³×C₃₇	—	2	2	no	—
153	C₂³×C₃₇	—	4	1	no	—
154	C₂³×C₃₇	—	4	1	no	—
155	C₂³×C₃₇	—	4	1	no	—
156	C₂³×C₃₇	—	4	1	no	—
157	C₂³×C₃₇	—	4	1	no	—
158	C₂³×C₃₇	—	4	1	no	—
159	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
160	D₄×C₃₇	—	2	2	no	—
161	D₄×C₃₇	—	2	2	no	—
162	D₄×C₃₇	—	4	1	no	—
163	D₄×C₃₇	—	4	1	no	—
164	C₂×C₄×C₃₇	—	2	1	no	—
165	C₂×C₄×C₃₇	—	2	1	no	—
166	C₂×C₄×C₃₇	—	2	1	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	2	no	—
171	C₂×C₄×C₃₇	—	2	1	no	—
172	C₂×C₄×C₃₇	—	2	1	no	—
173	C₂×C₄×C₃₇	—	2	1	no	—
174	C₂×C₄×C₃₇	—	2	1	no	—
175	C₂×C₄×C₃₇	—	2	1	no	—
176	C₂×C₄×C₃₇	—	2	1	no	—
177	C₂×C₄×C₃₇	—	4	1	no	—
178	C₂×C₄×C₃₇	—	4	1	no	—
179	C₂×C₄×C₃₇	—	4	8	no	—
180	C₂×C₄×C₃₇	—	4	2	no	—
181	C₂×C₄×C₃₇	—	4	2	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	1	no	—
186	C₂×C₄×C₃₇	—	4	1	no	—
187	C₂×C₄×C₃₇	—	4	1	no	—
188	C₂×C₄×C₃₇	—	4	2	no	—
189	C₂×C₄×C₃₇	—	4	2	no	—
190	C₂×C₄×C₃₇	—	4	2	no	—
191	C₂×C₄×C₃₇	—	4	1	no	—
192	C₂×C₄×C₃₇	C₂²⋊Q₈	1	2	yes	—
193	C₂×C₄×C₃₇	C₂²⋊Q₈	1	2	yes	—
194	C₂×C₄×C₃₇	#135	1	2	yes	—
195	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
196	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
197	C₂×C₄×C₃₇	#137	1	2	yes	—
198	C₂×C₄×C₃₇	C₂²×Q₈	1	1	yes	characteristic
199	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
201	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
202	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
203	C₂×C₄×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
204	C₈×C₃₇	—	4	2	no	—
205	C₈×C₃₇	—	4	2	no	—
206	#29995	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂²×C₃₇	—	4	2	no	—
208	C₂²×C₃₇	—	4	2	no	—
209	C₂²×C₃₇	—	4	2	no	—
210	C₂²×C₃₇	—	8	1	no	—
211	C₂²×C₃₇	—	8	1	no	—
212	C₂²×C₃₇	—	8	1	no	—
213	C₂²×C₃₇	—	8	1	no	—
214	C₂²×C₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
215	C₂²×C₃₇	#537	1	1	yes	characteristic
216	C₂²×C₃₇	#537	1	1	yes	characteristic
217	C₂²×C₃₇	C₂×#135	1	1	yes	characteristic
218	C₂²×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
219	C₂²×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
220	C₂²×C₃₇	C₂×#137	1	1	yes	characteristic
221	C₄×C₃₇	—	2	2	no	—
222	C₄×C₃₇	—	2	2	no	—
223	C₄×C₃₇	—	2	2	no	—
224	C₄×C₃₇	—	4	2	no	—
225	C₄×C₃₇	—	4	1	no	—
226	C₄×C₃₇	—	4	1	no	—
227	C₄×C₃₇	—	8	2	no	—
228	C₄×C₃₇	—	8	1	no	—
229	C₄×C₃₇	—	8	2	no	—
230	C₄×C₃₇	—	8	1	no	—
231	C₄×C₃₇	#478	1	4	yes	—
232	C₄×C₃₇	#540	1	1	yes	characteristic
233	C₄×C₃₇	#541	1	1	yes	characteristic
234	C₄×C₃₇	#544	1	1	yes	characteristic
235	C₄×C₃₇	#544	1	1	yes	characteristic
236	#2859	C₂×C₃₇	1	1	yes	characteristic, complemented
237	#2293	C₂×C₃₇	1	1	yes	characteristic
238	#2088	C₂×C₃₇	1	2	yes	complemented
239	#2087	C₂×C₃₇	1	2	yes	complemented
240	#2067	C₂×C₃₇	1	2	yes	—
241	#2065	C₂×C₃₇	1	2	yes	—
242	#1948	C₂×C₃₇	1	1	yes	characteristic, complemented
243	#1947	C₂×C₃₇	1	1	yes	characteristic, complemented
244	#1842	C₂×C₃₇	1	1	yes	characteristic, complemented
245	#1802	C₂×C₃₇	1	1	yes	characteristic
246	#1802	C₂×C₃₇	1	1	yes	characteristic
247	C₂×C₃₇	—	8	2	no	—
248	C₂×C₃₇	#2629	1	1	yes	characteristic
249	C₂×C₃₇	C₂×#478	1	1	yes	characteristic
250	C₂×C₃₇	#3079	1	1	yes	characteristic
251	C₂×C₃₇	#3247	1	1	yes	characteristic
252	C₂×C₃₇	#3248	1	1	yes	characteristic
253	C₂×C₃₇	#3253	1	1	yes	characteristic
254	C₂×C₃₇	#3254	1	1	yes	characteristic
255	C₂×#125	—	2	1	no	—
256	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
257	C₂×#117	—	2	1	no	—
258	C₂×#107	C₂²×C₃₇	1	2	yes	—
259	C₂×#106	C₂²×C₃₇	1	2	yes	—
260	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
261	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
262	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
263	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
264	C₂×#102	C₂²×C₃₇	1	2	yes	—
265	C₂×#102	C₂²×C₃₇	1	2	yes	—
266	#390	C₂²×C₃₇	1	1	yes	characteristic
267	#390	C₂²×C₃₇	1	1	yes	characteristic
268	#389	—	2	1	no	—
269	#389	—	2	1	no	—
270	#389	C₂²×C₃₇	1	2	yes	—
271	#389	C₂²×C₃₇	1	2	yes	—
272	#389	C₂²×C₃₇	1	1	yes	characteristic
273	#389	C₂²×C₃₇	1	1	yes	characteristic
274	#388	—	2	1	no	—
275	#388	—	2	1	no	—
276	#384	C₂²×C₃₇	1	1	yes	characteristic
277	#384	C₂²×C₃₇	1	1	yes	characteristic
278	#382	—	2	1	no	—
279	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
280	C₄×C₂²⋊C₄	—	2	1	no	—
281	C₄³	C₂²×C₃₇	1	1	yes	characteristic
282	#340	C₂²×C₃₇	1	2	yes	—
283	#340	C₂²×C₃₇	1	2	yes	—
284	#340	C₂²×C₃₇	1	2	yes	—
285	#340	C₂²×C₃₇	1	2	yes	—
286	C₃₇	#29995	1	1	yes	characteristic, direct product factor, Sylow
287	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
288	C₂³×C₄	—	2	1	no	—
289	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
290	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
291	#125	—	4	4	no	—
292	C₄×D₄	—	2	2	no	—
293	C₄×D₄	Q₈×C₃₇	1	4	yes	—
294	#117	—	4	4	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
306	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
307	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₂²⋊C₄	—	2	1	no	—
312	C₂×C₂²⋊C₄	—	2	1	no	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
315	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
316	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
317	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
318	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
319	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
320	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
321	#107	—	4	2	no	—
322	#106	—	4	2	no	—
323	C₄⋊C₈	—	2	2	no	—
324	C₄⋊C₈	—	2	2	no	—
325	C₄⋊C₈	—	4	2	no	—
326	C₄⋊C₈	—	4	2	no	—
327	#102	—	4	2	no	—
328	#102	—	4	2	no	—
329	#95	—	2	1	no	—
330	#95	—	2	1	no	—
331	#95	—	2	1	no	—
332	#95	—	2	2	no	—
333	#95	—	2	2	no	—
334	C₂⁴	—	2	1	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	C₂×Q₈×C₃₇	1	2	yes	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
355	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	4	2	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	—	4	2	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	—	4	4	no	—
376	C₄⋊C₄	—	4	2	no	—
377	C₄⋊C₄	—	4	2	no	—
378	C₄⋊C₄	—	4	4	no	—
379	C₄⋊C₄	C₂×Q₈×C₃₇	1	2	yes	—
380	C₂²⋊C₄	—	2	4	no	—
381	C₂²⋊C₄	—	4	2	no	—
382	C₂²⋊C₄	—	4	2	no	—
383	C₂²⋊C₄	—	4	2	no	—
384	C₂²⋊C₄	—	4	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	1	no	—
390	C₄²	—	2	1	no	—
391	C₄²	—	2	1	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	4	2	no	—
394	C₄²	C₂×Q₈×C₃₇	1	2	yes	—
395	C₄²	#41×C₃₇	1	2	yes	—
396	C₂³	—	2	2	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	1	no	—
400	C₂³	—	4	1	no	—
401	C₂³	—	4	1	no	—
402	C₂³	—	4	1	no	—
403	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
404	D₄	—	2	2	no	—
405	D₄	—	2	2	no	—
406	D₄	—	4	1	no	—
407	D₄	—	4	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	8	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	C₂²⋊Q₈×C₃₇	1	2	yes	—
437	C₂×C₄	C₂²⋊Q₈×C₃₇	1	2	yes	—
438	C₂×C₄	#135×C₃₇	1	2	yes	—
439	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
440	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
441	C₂×C₄	#137×C₃₇	1	2	yes	—
442	C₂×C₄	C₂²×Q₈×C₃₇	1	1	yes	characteristic
443	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
444	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
445	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
446	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
447	C₂×C₄	2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
448	C₈	—	4	2	no	—
449	C₈	—	4	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	8	1	no	—
454	C₂²	—	8	1	no	—
455	C₂²	—	8	1	no	—
456	C₂²	—	8	1	no	—
457	C₂²	C₂×C₂²⋊Q₈×C₃₇	1	1	yes	characteristic
458	C₂²	C₃₇×#537	1	1	yes	characteristic
459	C₂²	C₃₇×#537	1	1	yes	characteristic
460	C₂²	C₂×#135×C₃₇	1	1	yes	characteristic
461	C₂²	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
462	C₂²	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
463	C₂²	C₂×#137×C₃₇	1	1	yes	characteristic
464	C₄	—	2	2	no	—
465	C₄	—	2	2	no	—
466	C₄	—	2	2	no	—
467	C₄	—	4	1	no	—
468	C₄	—	4	1	no	—
469	C₄	—	4	2	no	—
470	C₄	—	8	2	no	—
471	C₄	—	8	1	no	—
472	C₄	—	8	2	no	—
473	C₄	—	8	1	no	—
474	C₄	C₃₇×#478	1	4	yes	—
475	C₄	C₃₇×#540	1	1	yes	characteristic
476	C₄	C₃₇×#541	1	1	yes	characteristic
477	C₄	C₃₇×#544	1	1	yes	characteristic
478	C₄	C₃₇×#544	1	1	yes	characteristic
479	C₂	—	8	2	no	—
480	C₂	C₃₇×#2629	1	1	yes	characteristic
481	C₂	C₂×C₃₇×#478	1	1	yes	characteristic
482	C₂	C₃₇×#3079	1	1	yes	characteristic
483	C₂	C₃₇×#3247	1	1	yes	characteristic
484	C₂	C₃₇×#3248	1	1	yes	characteristic
485	C₂	C₃₇×#3253	1	1	yes	characteristic
486	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	C₂²×D₄×C₃₇	C₂³
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. C₃₇×#2859	C₂	semidirect
3. C₃₇×#2088	C₂	semidirect
4. C₃₇×#2087	C₂	semidirect
7. C₃₇×#1948	C₂	semidirect
8. C₃₇×#1947	C₂	semidirect
9. C₃₇×#1842	C₂	semidirect
206. #29995	C₃₇	direct (N × H)
236. #2859	C₂×C₃₇	semidirect
238. #2088	C₂×C₃₇	semidirect
239. #2087	C₂×C₃₇	semidirect
242. #1948	C₂×C₃₇	semidirect
243. #1947	C₂×C₃₇	semidirect
244. #1842	C₂×C₃₇	semidirect
286. C₃₇	#29995	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₇×#2859	2
C₃₇×#2293	2
C₃₇×#2088	2
C₃₇×#2087	2
C₃₇×#2067	2
C₃₇×#2065	2
C₃₇×#1948	2
C₃₇×#1947	2
C₃₇×#1842	2
C₃₇×#1802	2
#29995	37

Subgroups — C37×#29995 #22651248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#29995 #22651248