Subgroups — C₃₇×#9179 #22630432

Order 9472.

620 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3036	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#2349	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#1517	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#1502	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#1478	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#1303	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#1286	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×AGL(1,ℤ/8)×C₃₇	—	2	1	no	—
9	C₃₇×#532	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₃₇	—	2	1	no	—
11	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
12	C₃₇×#463	—	2	2	no	—
13	C₃₇×#461	C₄	1	2	yes	complemented
14	C₃₇×#459	C₄	1	2	yes	complemented
15	C₃₇×#431	C₂²	1	1	yes	characteristic
16	C₃₇×#431	C₂²	1	1	yes	characteristic
17	C₃₇×#423	C₂²	1	1	yes	characteristic
18	C₃₇×#417	—	2	1	no	—
19	C₃₇×#389	—	2	1	no	—
20	C₃₇×#385	—	2	2	no	—
21	C₃₇×#382	C₂²	1	1	yes	characteristic
22	C₃₇×#380	—	2	1	no	—
23	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
24	C₂×#95×C₃₇	—	2	1	no	—
25	C₃₇×#327	—	2	1	no	—
26	C₃₇×#327	—	2	1	no	—
27	C₃₇×#327	—	2	2	no	—
28	C₃₇×D₄⋊C₈	—	2	2	no	—
29	C₂×#41×C₃₇	—	2	1	no	—
30	C₂²×D₄×C₃₇	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₃₇	—	2	1	no	—
32	C₂³×C₄×C₃₇	—	2	2	no	—
33	AGL(1,ℤ/8)×C₃₇	—	4	2	no	—
34	AGL(1,ℤ/8)×C₃₇	—	4	2	no	—
35	C₂×SD₁₆×C₃₇	—	2	2	no	—
36	C₂×D₈×C₃₇	—	2	2	no	—
37	C₂×M₁₆×C₃₇	—	2	1	no	—
38	C₄⋊Q₈×C₃₇	C₂×C₄	1	1	yes	characteristic, complemented
39	#127×C₃₇	C₂×C₄	1	1	yes	characteristic, complemented
40	#124×C₃₇	—	2	1	no	—
41	#121×C₃₇	—	2	1	no	—
42	#121×C₃₇	—	2	1	no	—
43	C₄×D₄×C₃₇	—	2	1	no	—
44	C₄×D₄×C₃₇	—	2	1	no	—
45	C₄×D₄×C₃₇	—	2	1	no	—
46	C₄×D₄×C₃₇	—	2	1	no	—
47	C₄×D₄×C₃₇	—	4	2	no	—
48	C₄×D₄×C₃₇	—	4	2	no	—
49	C₄×D₄×C₃₇	C₂×C₄	1	2	yes	—
50	C₄×D₄×C₃₇	D₄	1	2	yes	—
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	D₄	1	1	yes	characteristic
55	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
56	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
57	C₂×C₄²×C₃₇	—	2	1	no	—
58	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
59	C₄⋊C₈×C₃₇	—	2	1	no	—
60	C₄⋊C₈×C₃₇	—	2	1	no	—
61	C₄⋊C₈×C₃₇	—	2	1	no	—
62	C₄⋊C₈×C₃₇	C₂×C₄	1	2	yes	complemented
63	#103×C₃₇	—	2	2	no	—
64	#102×C₃₇	—	2	2	no	—
65	C₂²⋊C₈×C₃₇	—	2	1	no	—
66	C₂²⋊C₈×C₃₇	—	2	1	no	—
67	C₄×C₈×C₃₇	—	2	1	no	—
68	C₄×C₈×C₃₇	—	2	1	no	—
69	#95×C₃₇	—	2	2	no	—
70	#95×C₃₇	—	2	1	no	—
71	#95×C₃₇	D₄	1	1	yes	characteristic
72	#95×C₃₇	D₄	1	1	yes	characteristic
73	#95×C₃₇	D₄	1	2	yes	—
74	C₂⁴×C₃₇	—	2	1	no	—
75	#41×C₃₇	—	4	1	no	—
76	#41×C₃₇	—	4	1	no	—
77	#41×C₃₇	—	4	1	no	—
78	#41×C₃₇	—	4	1	no	—
79	C₂×Q₈×C₃₇	—	2	1	no	—
80	C₂×D₄×C₃₇	—	2	1	no	—
81	C₂×D₄×C₃₇	—	2	1	no	—
82	C₂×D₄×C₃₇	—	2	1	no	—
83	C₂×D₄×C₃₇	—	2	1	no	—
84	C₂×D₄×C₃₇	—	2	1	no	—
85	C₂×D₄×C₃₇	—	2	1	no	—
86	C₂×D₄×C₃₇	—	4	1	no	—
87	C₂×D₄×C₃₇	C₂²⋊C₄	1	2	yes	—
88	C₂×D₄×C₃₇	D₈	1	2	yes	—
89	C₂×D₄×C₃₇	SD₁₆	1	2	yes	—
90	C₂²×C₄×C₃₇	—	2	1	no	—
91	C₂²×C₄×C₃₇	—	2	1	no	—
92	C₂²×C₄×C₃₇	—	2	2	no	—
93	C₂²×C₄×C₃₇	—	2	2	no	—
94	C₂²×C₄×C₃₇	—	2	2	no	—
95	C₂²×C₄×C₃₇	—	2	1	no	—
96	C₂²×C₄×C₃₇	—	4	4	no	—
97	C₂²×C₄×C₃₇	—	4	4	no	—
98	C₂²×C₄×C₃₇	—	4	1	no	—
99	C₂²×C₄×C₃₇	—	8	2	no	—
100	C₂²×C₄×C₃₇	—	8	2	no	—
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	SD₁₆×C₃₇	—	4	4	no	—
105	D₈×C₃₇	—	4	4	no	—
106	M₁₆×C₃₇	—	4	1	no	—
107	M₁₆×C₃₇	—	4	1	no	—
108	C₂×C₈×C₃₇	—	2	2	no	—
109	C₂×C₈×C₃₇	—	4	1	no	—
110	C₂×C₈×C₃₇	—	4	1	no	—
111	C₄⋊C₄×C₃₇	—	2	1	no	—
112	C₄⋊C₄×C₃₇	—	2	1	no	—
113	C₄⋊C₄×C₃₇	—	2	1	no	—
114	C₄⋊C₄×C₃₇	—	4	2	no	—
115	C₄⋊C₄×C₃₇	—	4	1	no	—
116	C₄⋊C₄×C₃₇	—	4	1	no	—
117	C₄⋊C₄×C₃₇	—	8	2	no	—
118	C₄⋊C₄×C₃₇	C₂²⋊C₄	1	2	yes	—
119	C₂²⋊C₄×C₃₇	—	2	2	no	—
120	C₂²⋊C₄×C₃₇	—	2	2	no	—
121	C₂²⋊C₄×C₃₇	—	4	4	no	—
122	C₂²⋊C₄×C₃₇	—	4	1	no	—
123	C₂²⋊C₄×C₃₇	—	4	1	no	—
124	C₄²×C₃₇	—	4	1	no	—
125	C₄²×C₃₇	—	4	1	no	—
126	C₄²×C₃₇	C₂²×C₄	1	1	yes	characteristic
127	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₃₇	#41	1	1	yes	characteristic
129	C₄²×C₃₇	#41	1	1	yes	characteristic
130	C₂³×C₃₇	—	2	2	no	—
131	C₂³×C₃₇	—	2	2	no	—
132	C₂³×C₃₇	—	2	2	no	—
133	C₂³×C₃₇	—	4	2	no	—
134	C₂³×C₃₇	—	4	2	no	—
135	C₂³×C₃₇	—	4	1	no	—
136	C₂³×C₃₇	#120	1	1	yes	characteristic
137	Q₈×C₃₇	—	4	1	no	—
138	Q₈×C₃₇	—	4	1	no	—
139	D₄×C₃₇	—	2	2	no	—
140	D₄×C₃₇	—	2	2	no	—
141	D₄×C₃₇	—	2	2	no	—
142	D₄×C₃₇	—	4	1	no	—
143	D₄×C₃₇	—	4	1	no	—
144	D₄×C₃₇	—	8	1	no	—
145	D₄×C₃₇	—	8	1	no	—
146	D₄×C₃₇	—	8	1	no	—
147	D₄×C₃₇	—	8	1	no	—
148	D₄×C₃₇	#102	1	4	yes	—
149	C₂×C₄×C₃₇	—	2	2	no	—
150	C₂×C₄×C₃₇	—	2	2	no	—
151	C₂×C₄×C₃₇	—	4	1	no	—
152	C₂×C₄×C₃₇	—	4	1	no	—
153	C₂×C₄×C₃₇	—	4	2	no	—
154	C₂×C₄×C₃₇	—	4	1	no	—
155	C₂×C₄×C₃₇	—	4	1	no	—
156	C₂×C₄×C₃₇	—	4	1	no	—
157	C₂×C₄×C₃₇	—	4	1	no	—
158	C₂×C₄×C₃₇	—	4	2	no	—
159	C₂×C₄×C₃₇	—	4	2	no	—
160	C₂×C₄×C₃₇	—	4	1	no	—
161	C₂×C₄×C₃₇	—	4	1	no	—
162	C₂×C₄×C₃₇	—	4	2	no	—
163	C₂×C₄×C₃₇	—	8	2	no	—
164	C₂×C₄×C₃₇	—	8	2	no	—
165	C₂×C₄×C₃₇	—	8	8	no	—
166	C₂×C₄×C₃₇	—	8	1	no	—
167	C₂×C₄×C₃₇	—	8	1	no	—
168	C₂×C₄×C₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₃₇	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₃₇	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
172	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
173	C₂×C₄×C₃₇	#123	1	1	yes	characteristic
174	C₂×C₄×C₃₇	C₂×D₈	1	1	yes	characteristic
175	C₂×C₄×C₃₇	C₂×SD₁₆	1	1	yes	characteristic
176	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	1	yes	characteristic
177	C₂×C₄×C₃₇	#137	1	1	yes	characteristic
178	C₈×C₃₇	—	4	2	no	—
179	C₈×C₃₇	—	8	1	no	—
180	C₈×C₃₇	—	8	1	no	—
181	#9179	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂²×C₃₇	—	2	1	no	—
183	C₂²×C₃₇	—	2	1	no	—
184	C₂²×C₃₇	—	2	4	no	—
185	C₂²×C₃₇	—	4	4	no	—
186	C₂²×C₃₇	—	4	4	no	—
187	C₂²×C₃₇	—	4	2	no	—
188	C₂²×C₃₇	—	4	2	no	—
189	C₂²×C₃₇	—	8	1	no	—
190	C₂²×C₃₇	—	8	1	no	—
191	C₂²×C₃₇	—	8	1	no	—
192	C₂²×C₃₇	#386	1	1	yes	characteristic
193	C₂²×C₃₇	#447	1	1	yes	characteristic
194	C₂²×C₃₇	#448	1	1	yes	characteristic
195	C₄×C₃₇	—	2	1	no	—
196	C₄×C₃₇	—	2	1	no	—
197	C₄×C₃₇	—	2	1	no	—
198	C₄×C₃₇	—	2	1	no	—
199	C₄×C₃₇	—	4	2	no	—
200	C₄×C₃₇	—	4	2	no	—
201	C₄×C₃₇	—	8	1	no	—
202	C₄×C₃₇	—	8	2	no	—
203	C₄×C₃₇	—	8	1	no	—
204	C₄×C₃₇	C₂×#102	1	1	yes	characteristic
205	C₄×C₃₇	#417	1	1	yes	characteristic
206	C₄×C₃₇	#480	1	1	yes	characteristic
207	C₄×C₃₇	#481	1	1	yes	characteristic
208	#3036	C₂×C₃₇	1	1	yes	characteristic
209	#2349	C₂×C₃₇	1	1	yes	characteristic, complemented
210	#1517	C₂×C₃₇	1	1	yes	characteristic, complemented
211	#1502	C₂×C₃₇	1	1	yes	characteristic, complemented
212	#1478	C₂×C₃₇	1	1	yes	characteristic, complemented
213	#1303	C₂×C₃₇	1	1	yes	characteristic, complemented
214	#1286	C₂×C₃₇	1	1	yes	characteristic, complemented
215	C₂×C₃₇	—	2	1	no	—
216	C₂×C₃₇	—	2	1	no	—
217	C₂×C₃₇	—	4	4	no	—
218	C₂×C₃₇	—	16	1	no	—
219	C₂×C₃₇	#1874	1	1	yes	characteristic
220	C₂×C₃₇	#1904	1	1	yes	characteristic
221	C₂×C₃₇	#1906	1	1	yes	characteristic
222	C₂×AGL(1,ℤ/8)	—	2	1	no	—
223	#532	C₂²×C₃₇	1	1	yes	characteristic
224	C₂×C₄×D₄	—	2	1	no	—
225	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
226	#463	—	2	2	no	—
227	#461	C₄×C₃₇	1	2	yes	complemented
228	#459	C₄×C₃₇	1	2	yes	complemented
229	#431	C₂²×C₃₇	1	1	yes	characteristic
230	#431	C₂²×C₃₇	1	1	yes	characteristic
231	#423	C₂²×C₃₇	1	1	yes	characteristic
232	#417	—	2	1	no	—
233	#389	—	2	1	no	—
234	#385	—	2	2	no	—
235	#382	C₂²×C₃₇	1	1	yes	characteristic
236	#380	—	2	1	no	—
237	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
238	C₂×#95	—	2	1	no	—
239	#327	—	2	1	no	—
240	#327	—	2	1	no	—
241	#327	—	2	2	no	—
242	D₄⋊C₈	—	2	2	no	—
243	C₃₇	#9179	1	1	yes	characteristic, direct product factor, Sylow
244	C₂×#41	—	2	1	no	—
245	C₂²×D₄	D₄×C₃₇	1	1	yes	characteristic
246	C₂³×C₄	—	2	1	no	—
247	C₂³×C₄	—	2	2	no	—
248	AGL(1,ℤ/8)	—	4	2	no	—
249	AGL(1,ℤ/8)	—	4	2	no	—
250	C₂×SD₁₆	—	2	2	no	—
251	C₂×D₈	—	2	2	no	—
252	C₂×M₁₆	—	2	1	no	—
253	C₄⋊Q₈	C₂×C₄×C₃₇	1	1	yes	characteristic, complemented
254	#127	C₂×C₄×C₃₇	1	1	yes	characteristic, complemented
255	#124	—	2	1	no	—
256	#121	—	2	1	no	—
257	#121	—	2	1	no	—
258	C₄×D₄	—	2	1	no	—
259	C₄×D₄	—	2	1	no	—
260	C₄×D₄	—	2	1	no	—
261	C₄×D₄	—	2	1	no	—
262	C₄×D₄	—	4	2	no	—
263	C₄×D₄	—	4	2	no	—
264	C₄×D₄	C₂×C₄×C₃₇	1	2	yes	—
265	C₄×D₄	D₄×C₃₇	1	2	yes	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	—	2	1	no	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₄²	—	2	1	no	—
273	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
274	C₄⋊C₈	—	2	1	no	—
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	C₂×C₄×C₃₇	1	2	yes	complemented
278	#103	—	2	2	no	—
279	#102	—	2	2	no	—
280	C₂²⋊C₈	—	2	1	no	—
281	C₂²⋊C₈	—	2	1	no	—
282	C₄×C₈	—	2	1	no	—
283	C₄×C₈	—	2	1	no	—
284	#95	—	2	2	no	—
285	#95	—	2	1	no	—
286	#95	D₄×C₃₇	1	1	yes	characteristic
287	#95	D₄×C₃₇	1	1	yes	characteristic
288	#95	D₄×C₃₇	1	2	yes	—
289	C₂⁴	—	2	1	no	—
290	#41	—	4	1	no	—
291	#41	—	4	1	no	—
292	#41	—	4	1	no	—
293	#41	—	4	1	no	—
294	C₂×Q₈	—	2	1	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	4	1	no	—
302	C₂×D₄	C₂²⋊C₄×C₃₇	1	2	yes	—
303	C₂×D₄	D₈×C₃₇	1	2	yes	—
304	C₂×D₄	SD₁₆×C₃₇	1	2	yes	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	4	4	no	—
312	C₂²×C₄	—	4	4	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	—	8	2	no	—
315	C₂²×C₄	—	8	2	no	—
316	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
319	SD₁₆	—	4	4	no	—
320	D₈	—	4	4	no	—
321	M₁₆	—	4	1	no	—
322	M₁₆	—	4	1	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	4	1	no	—
325	C₂×C₈	—	4	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	4	2	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₄⋊C₄	—	4	1	no	—
332	C₄⋊C₄	—	8	2	no	—
333	C₄⋊C₄	C₂²⋊C₄×C₃₇	1	2	yes	—
334	C₂²⋊C₄	—	2	2	no	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	4	4	no	—
337	C₂²⋊C₄	—	4	1	no	—
338	C₂²⋊C₄	—	4	1	no	—
339	C₄²	—	4	1	no	—
340	C₄²	—	4	1	no	—
341	C₄²	C₂²×C₄×C₃₇	1	1	yes	characteristic
342	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
343	C₄²	#41×C₃₇	1	1	yes	characteristic
344	C₄²	#41×C₃₇	1	1	yes	characteristic
345	C₂³	—	2	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	1	no	—
351	C₂³	#120×C₃₇	1	1	yes	characteristic
352	Q₈	—	4	1	no	—
353	Q₈	—	4	1	no	—
354	D₄	—	2	2	no	—
355	D₄	—	2	2	no	—
356	D₄	—	2	2	no	—
357	D₄	—	4	1	no	—
358	D₄	—	4	1	no	—
359	D₄	—	8	1	no	—
360	D₄	—	8	1	no	—
361	D₄	—	8	1	no	—
362	D₄	—	8	1	no	—
363	D₄	#102×C₃₇	1	4	yes	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	8	2	no	—
379	C₂×C₄	—	8	2	no	—
380	C₂×C₄	—	8	8	no	—
381	C₂×C₄	—	8	1	no	—
382	C₂×C₄	—	8	1	no	—
383	C₂×C₄	C₂×C₂²⋊C₄×C₃₇	1	1	yes	characteristic
384	C₂×C₄	C₄×D₄×C₃₇	1	1	yes	characteristic
385	C₂×C₄	C₄×D₄×C₃₇	1	1	yes	characteristic
386	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
387	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
388	C₂×C₄	#123×C₃₇	1	1	yes	characteristic
389	C₂×C₄	C₂×D₈×C₃₇	1	1	yes	characteristic
390	C₂×C₄	C₂×SD₁₆×C₃₇	1	1	yes	characteristic
391	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
392	C₂×C₄	#137×C₃₇	1	1	yes	characteristic
393	C₈	—	4	2	no	—
394	C₈	—	8	1	no	—
395	C₈	—	8	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	4	no	—
399	C₂²	—	4	4	no	—
400	C₂²	—	4	4	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	8	1	no	—
405	C₂²	—	8	1	no	—
406	C₂²	C₃₇×#386	1	1	yes	characteristic
407	C₂²	C₃₇×#447	1	1	yes	characteristic
408	C₂²	C₃₇×#448	1	1	yes	characteristic
409	C₄	—	2	1	no	—
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	2	no	—
415	C₄	—	8	2	no	—
416	C₄	—	8	1	no	—
417	C₄	—	8	1	no	—
418	C₄	C₂×#102×C₃₇	1	1	yes	characteristic
419	C₄	C₃₇×#417	1	1	yes	characteristic
420	C₄	C₃₇×#480	1	1	yes	characteristic
421	C₄	C₃₇×#481	1	1	yes	characteristic
422	C₂	—	2	1	no	—
423	C₂	—	2	1	no	—
424	C₂	—	4	4	no	—
425	C₂	—	16	1	no	—
426	C₂	C₃₇×#1874	1	1	yes	characteristic
427	C₂	C₃₇×#1904	1	1	yes	characteristic
428	C₂	C₃₇×#1906	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	#386
commutator	C₄²	C₂²×C₄×C₃₇
Frattini, cosocle	C₂×C₄²	C₂³×C₃₇
prime radical	C₃₇×#3036	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₇×#2349	C₂	semidirect
3. C₃₇×#1517	C₂	semidirect
4. C₃₇×#1502	C₂	semidirect
5. C₃₇×#1478	C₂	semidirect
6. C₃₇×#1303	C₂	semidirect
7. C₃₇×#1286	C₂	semidirect
13. C₃₇×#461	C₄	semidirect
14. C₃₇×#459	C₄	semidirect
38. C₄⋊Q₈×C₃₇	C₂×C₄	semidirect
39. #127×C₃₇	C₂×C₄	semidirect
62. C₄⋊C₈×C₃₇	C₂×C₄	semidirect
181. #9179	C₃₇	direct (N × H)
209. #2349	C₂×C₃₇	semidirect
210. #1517	C₂×C₃₇	semidirect
211. #1502	C₂×C₃₇	semidirect
212. #1478	C₂×C₃₇	semidirect
213. #1303	C₂×C₃₇	semidirect
214. #1286	C₂×C₃₇	semidirect
227. #461	C₄×C₃₇	semidirect
228. #459	C₄×C₃₇	semidirect
243. C₃₇	#9179	direct (N × H)
253. C₄⋊Q₈	C₂×C₄×C₃₇	semidirect
254. #127	C₂×C₄×C₃₇	semidirect
277. C₄⋊C₈	C₂×C₄×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₃₇×#3036	2
C₃₇×#2349	2
C₃₇×#1517	2
C₃₇×#1502	2
C₃₇×#1478	2
C₃₇×#1303	2
C₃₇×#1286	2
#9179	37

Subgroups — C37×#9179 #22630432

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#9179 #22630432