Subgroups — C₃₇×#22892 #22644145

Order 9472.

986 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#456	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#2947	C₂	1	2	yes	maximal, complemented
3	C₃₇×#2898	C₂	1	2	yes	maximal
4	C₃₇×#1960	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#1930	C₂	1	2	yes	maximal, complemented
6	C₃₇×#1908	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1886	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1860	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1765	C₂	1	2	yes	maximal, complemented
10	C₂×2₋¹⁺⁴×C₃₇	C₂²	1	1	yes	characteristic
11	C₂×#137×C₃₇	C₂²	1	2	yes	—
12	C₂×#131×C₃₇	C₂²	1	2	yes	—
13	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
14	C₃₇×#520	C₂²	1	2	yes	—
15	C₃₇×#519	C₂²	1	1	yes	characteristic
16	C₃₇×#456	C₄	1	8	yes	complemented
17	C₃₇×#441	—	2	2	no	—
18	C₃₇×#440	—	2	2	no	—
19	C₄×Q₁₆×C₃₇	—	2	2	no	—
20	C₄×SD₁₆×C₃₇	—	2	2	no	—
21	C₃₇×#428	C₂²	1	2	yes	—
22	C₂×#104×C₃₇	C₂²	1	2	yes	—
23	C₃₇×#419	—	2	2	no	—
24	C₃₇×#419	C₂²	1	2	yes	—
25	C₃₇×#417	—	2	2	no	—
26	C₃₇×#417	C₂²	1	2	yes	—
27	C₃₇×#416	—	2	2	no	—
28	C₃₇×#416	C₂²	1	2	yes	—
29	C₂×#103×C₃₇	—	2	2	no	—
30	C₂×#103×C₃₇	C₂²	1	2	yes	—
31	C₂×#103×C₃₇	C₂²	1	2	yes	—
32	C₂×#101×C₃₇	C₂²	1	1	yes	characteristic
33	C₂×#101×C₃₇	C₂²	1	1	yes	characteristic
34	C₃₇×#405	C₂²	1	2	yes	—
35	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
36	C₃₇×#382	C₂²	1	1	yes	characteristic
37	C₃₇×#343	C₂²	1	2	yes	—
38	C₃₇×#341	C₂²	1	2	yes	—
39	C₃₇×#339	C₂²	1	2	yes	—
40	2₋¹⁺⁴×C₃₇	—	2	4	no	—
41	2₋¹⁺⁴×C₃₇	—	4	1	no	—
42	2₋¹⁺⁴×C₃₇	C₂×C₄	1	4	yes	—
43	C₂×#41×C₃₇	—	2	2	no	—
44	C₂×#41×C₃₇	—	4	1	no	—
45	C₂×#41×C₃₇	C₂³	1	2	yes	—
46	C₂²×Q₈×C₃₇	—	2	2	no	—
47	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
48	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
49	#137×C₃₇	—	2	4	no	—
50	#137×C₃₇	C₂×C₄	1	8	yes	complemented
51	C₂×Q₁₆×C₃₇	—	2	2	no	—
52	C₂×SD₁₆×C₃₇	—	2	2	no	—
53	#131×C₃₇	—	2	4	no	—
54	#131×C₃₇	—	4	2	no	—
55	C₂×M₁₆×C₃₇	—	2	2	no	—
56	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
57	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
58	C₂²×C₈×C₃₇	—	2	2	no	—
59	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
60	C₄⋊Q₈×C₃₇	—	4	1	no	—
61	C₄⋊Q₈×C₃₇	C₂×C₄	1	4	yes	complemented
62	C₄×Q₈×C₃₇	—	2	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	—	4	2	no	—
67	#117×C₃₇	—	2	2	no	—
68	#117×C₃₇	—	4	1	no	—
69	#117×C₃₇	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
71	C₂×C₄⋊C₄×C₃₇	—	4	1	no	—
72	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
73	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
74	#107×C₃₇	—	2	2	no	—
75	#106×C₃₇	—	2	2	no	—
76	#104×C₃₇	C₂×C₄	1	8	yes	complemented
77	#103×C₃₇	—	2	2	no	—
78	#103×C₃₇	—	2	2	no	—
79	#103×C₃₇	—	2	2	no	—
80	#103×C₃₇	—	2	2	no	—
81	#103×C₃₇	—	2	2	no	—
82	#103×C₃₇	—	2	2	no	—
83	#103×C₃₇	—	2	2	no	—
84	#103×C₃₇	D₄	1	2	yes	—
85	#103×C₃₇	D₄	1	2	yes	—
86	#102×C₃₇	—	2	2	no	—
87	#102×C₃₇	D₄	1	2	yes	—
88	#102×C₃₇	D₄	1	2	yes	—
89	#101×C₃₇	—	4	1	no	—
90	#101×C₃₇	C₂×C₄	1	4	yes	complemented
91	#97×C₃₇	—	2	2	no	—
92	#97×C₃₇	—	4	1	no	—
93	C₄×C₈×C₃₇	—	2	2	no	—
94	#95×C₃₇	—	4	1	no	—
95	#41×C₃₇	—	2	2	no	—
96	#41×C₃₇	—	2	2	no	—
97	#41×C₃₇	—	2	8	no	—
98	#41×C₃₇	—	4	4	no	—
99	#41×C₃₇	—	4	4	no	—
100	#41×C₃₇	—	4	4	no	—
101	#41×C₃₇	C₂²×C₄	1	4	yes	—
102	#41×C₃₇	#41	1	4	yes	—
103	C₂×Q₈×C₃₇	—	2	1	no	—
104	C₂×Q₈×C₃₇	—	2	1	no	—
105	C₂×Q₈×C₃₇	—	2	8	no	—
106	C₂×Q₈×C₃₇	—	2	2	no	—
107	C₂×Q₈×C₃₇	—	2	2	no	—
108	C₂×Q₈×C₃₇	—	2	2	no	—
109	C₂×Q₈×C₃₇	—	2	2	no	—
110	C₂×Q₈×C₃₇	—	4	1	no	—
111	C₂×Q₈×C₃₇	—	4	4	no	—
112	C₂×Q₈×C₃₇	C₂²×C₄	1	2	yes	—
113	C₂×Q₈×C₃₇	C₂²×C₄	1	2	yes	—
114	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
115	C₂×D₄×C₃₇	—	2	2	no	—
116	C₂×D₄×C₃₇	—	4	1	no	—
117	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₃₇	—	2	2	no	—
119	C₂²×C₄×C₃₇	—	2	1	no	—
120	C₂²×C₄×C₃₇	—	2	1	no	—
121	C₂²×C₄×C₃₇	—	2	1	no	—
122	C₂²×C₄×C₃₇	—	2	2	no	—
123	C₂²×C₄×C₃₇	—	4	2	no	—
124	C₂²×C₄×C₃₇	—	4	2	no	—
125	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
126	Q₁₆×C₃₇	—	2	8	no	—
127	SD₁₆×C₃₇	—	2	8	no	—
128	M₁₆×C₃₇	—	2	2	no	—
129	M₁₆×C₃₇	—	2	2	no	—
130	M₁₆×C₃₇	—	2	2	no	—
131	M₁₆×C₃₇	—	4	4	no	—
132	M₁₆×C₃₇	C₂²×C₄	1	4	yes	—
133	C₂×C₈×C₃₇	—	2	2	no	—
134	C₂×C₈×C₃₇	—	2	2	no	—
135	C₂×C₈×C₃₇	—	2	2	no	—
136	C₂×C₈×C₃₇	—	2	2	no	—
137	C₂×C₈×C₃₇	—	4	4	no	—
138	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
140	C₄⋊C₄×C₃₇	—	2	2	no	—
141	C₄⋊C₄×C₃₇	—	2	2	no	—
142	C₄⋊C₄×C₃₇	—	4	4	no	—
143	C₄⋊C₄×C₃₇	—	4	2	no	—
144	C₄⋊C₄×C₃₇	—	4	2	no	—
145	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
146	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
147	C₂²⋊C₄×C₃₇	—	2	2	no	—
148	C₂²⋊C₄×C₃₇	—	4	2	no	—
149	C₄²×C₃₇	—	2	2	no	—
150	C₄²×C₃₇	—	2	1	no	—
151	C₄²×C₃₇	—	4	2	no	—
152	C₄²×C₃₇	—	4	1	no	—
153	C₄²×C₃₇	—	4	1	no	—
154	C₄²×C₃₇	C₂²×C₄	1	2	yes	—
155	C₂³×C₃₇	—	2	2	no	—
156	C₂³×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
157	Q₈×C₃₇	—	2	2	no	—
158	Q₈×C₃₇	—	2	4	no	—
159	Q₈×C₃₇	—	2	4	no	—
160	Q₈×C₃₇	—	4	4	no	—
161	Q₈×C₃₇	—	4	2	no	—
162	Q₈×C₃₇	—	4	2	no	—
163	Q₈×C₃₇	C₄×D₄	1	4	yes	—
164	D₄×C₃₇	—	2	4	no	—
165	D₄×C₃₇	—	2	4	no	—
166	D₄×C₃₇	—	2	2	no	—
167	D₄×C₃₇	—	4	4	no	—
168	D₄×C₃₇	C₄×D₄	1	4	yes	—
169	C₂×C₄×C₃₇	—	2	2	no	—
170	C₂×C₄×C₃₇	—	2	4	no	—
171	C₂×C₄×C₃₇	—	2	4	no	—
172	C₂×C₄×C₃₇	—	2	2	no	—
173	C₂×C₄×C₃₇	—	2	2	no	—
174	C₂×C₄×C₃₇	—	2	2	no	—
175	C₂×C₄×C₃₇	—	2	2	no	—
176	C₂×C₄×C₃₇	—	2	2	no	—
177	C₂×C₄×C₃₇	—	4	8	no	—
178	C₂×C₄×C₃₇	—	4	2	no	—
179	C₂×C₄×C₃₇	—	4	1	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	2	no	—
184	C₂×C₄×C₃₇	—	8	2	no	—
185	C₂×C₄×C₃₇	—	16	2	no	—
186	C₂×C₄×C₃₇	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
188	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
189	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
190	C₈×C₃₇	—	2	4	no	—
191	C₈×C₃₇	—	2	2	no	—
192	C₈×C₃₇	—	2	2	no	—
193	C₈×C₃₇	—	4	2	no	—
194	#22892	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂²×C₃₇	—	2	2	no	—
196	C₂²×C₃₇	—	2	4	no	—
197	C₂²×C₃₇	—	4	2	no	—
198	C₂²×C₃₇	—	4	2	no	—
199	C₂²×C₃₇	#518	1	1	yes	characteristic
200	C₂²×C₃₇	D₄²	1	1	yes	characteristic
201	C₂²×C₃₇	#551	1	1	yes	characteristic
202	C₄×C₃₇	—	2	4	no	—
203	C₄×C₃₇	—	4	2	no	—
204	C₄×C₃₇	—	4	2	no	—
205	C₄×C₃₇	—	4	2	no	—
206	C₄×C₃₇	—	4	2	no	—
207	C₄×C₃₇	—	4	2	no	—
208	C₄×C₃₇	—	8	2	no	—
209	C₄×C₃₇	C₂×C₄×D₄	1	2	yes	—
210	C₄×C₃₇	#546	1	2	yes	—
211	C₂×#456	C₂×C₃₇	1	1	yes	characteristic
212	#2947	C₂×C₃₇	1	2	yes	complemented
213	#2898	C₂×C₃₇	1	2	yes	—
214	#1960	C₂×C₃₇	1	1	yes	characteristic, complemented
215	#1930	C₂×C₃₇	1	2	yes	complemented
216	#1908	C₂×C₃₇	1	2	yes	complemented
217	#1886	C₂×C₃₇	1	1	yes	characteristic, complemented
218	#1860	C₂×C₃₇	1	2	yes	complemented
219	#1765	C₂×C₃₇	1	2	yes	complemented
220	C₂×C₃₇	—	2	1	no	—
221	C₂×C₃₇	—	2	1	no	—
222	C₂×C₃₇	—	4	4	no	—
223	C₂×C₃₇	#2358	1	1	yes	characteristic
224	C₂×C₃₇	#3289	1	2	yes	—
225	C₂×2₋¹⁺⁴	C₂²×C₃₇	1	1	yes	characteristic
226	C₂×#137	C₂²×C₃₇	1	2	yes	—
227	C₂×#131	C₂²×C₃₇	1	2	yes	—
228	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
229	#520	C₂²×C₃₇	1	2	yes	—
230	#519	C₂²×C₃₇	1	1	yes	characteristic
231	#456	C₄×C₃₇	1	8	yes	complemented
232	#441	—	2	2	no	—
233	#440	—	2	2	no	—
234	C₄×Q₁₆	—	2	2	no	—
235	C₄×SD₁₆	—	2	2	no	—
236	#428	C₂²×C₃₇	1	2	yes	—
237	C₂×#104	C₂²×C₃₇	1	2	yes	—
238	#419	—	2	2	no	—
239	#419	C₂²×C₃₇	1	2	yes	—
240	#417	—	2	2	no	—
241	#417	C₂²×C₃₇	1	2	yes	—
242	#416	—	2	2	no	—
243	#416	C₂²×C₃₇	1	2	yes	—
244	C₂×#103	—	2	2	no	—
245	C₂×#103	C₂²×C₃₇	1	2	yes	—
246	C₂×#103	C₂²×C₃₇	1	2	yes	—
247	C₂×#101	C₂²×C₃₇	1	1	yes	characteristic
248	C₂×#101	C₂²×C₃₇	1	1	yes	characteristic
249	#405	C₂²×C₃₇	1	2	yes	—
250	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
251	#382	C₂²×C₃₇	1	1	yes	characteristic
252	#343	C₂²×C₃₇	1	2	yes	—
253	#341	C₂²×C₃₇	1	2	yes	—
254	#339	C₂²×C₃₇	1	2	yes	—
255	C₃₇	#22892	1	1	yes	characteristic, direct product factor, Sylow
256	2₋¹⁺⁴	—	2	4	no	—
257	2₋¹⁺⁴	—	4	1	no	—
258	2₋¹⁺⁴	C₂×C₄×C₃₇	1	4	yes	—
259	C₂×#41	—	2	2	no	—
260	C₂×#41	—	4	1	no	—
261	C₂×#41	C₂³×C₃₇	1	2	yes	—
262	C₂²×Q₈	—	2	2	no	—
263	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
264	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
265	#137	—	2	4	no	—
266	#137	C₂×C₄×C₃₇	1	8	yes	complemented
267	C₂×Q₁₆	—	2	2	no	—
268	C₂×SD₁₆	—	2	2	no	—
269	#131	—	2	4	no	—
270	#131	—	4	2	no	—
271	C₂×M₁₆	—	2	2	no	—
272	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
273	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
274	C₂²×C₈	—	2	2	no	—
275	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
276	C₄⋊Q₈	—	4	1	no	—
277	C₄⋊Q₈	C₂×C₄×C₃₇	1	4	yes	complemented
278	C₄×Q₈	—	2	2	no	—
279	C₄×Q₈	—	2	2	no	—
280	C₄×Q₈	—	2	2	no	—
281	C₄×D₄	—	2	2	no	—
282	C₄×D₄	—	4	2	no	—
283	#117	—	2	2	no	—
284	#117	—	4	1	no	—
285	#117	C₂³×C₃₇	1	2	yes	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	4	1	no	—
288	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
289	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
290	#107	—	2	2	no	—
291	#106	—	2	2	no	—
292	#104	C₂×C₄×C₃₇	1	8	yes	complemented
293	#103	—	2	2	no	—
294	#103	—	2	2	no	—
295	#103	—	2	2	no	—
296	#103	—	2	2	no	—
297	#103	—	2	2	no	—
298	#103	—	2	2	no	—
299	#103	—	2	2	no	—
300	#103	D₄×C₃₇	1	2	yes	—
301	#103	D₄×C₃₇	1	2	yes	—
302	#102	—	2	2	no	—
303	#102	D₄×C₃₇	1	2	yes	—
304	#102	D₄×C₃₇	1	2	yes	—
305	#101	—	4	1	no	—
306	#101	C₂×C₄×C₃₇	1	4	yes	complemented
307	#97	—	2	2	no	—
308	#97	—	4	1	no	—
309	C₄×C₈	—	2	2	no	—
310	#95	—	4	1	no	—
311	#41	—	2	2	no	—
312	#41	—	2	2	no	—
313	#41	—	2	8	no	—
314	#41	—	4	4	no	—
315	#41	—	4	4	no	—
316	#41	—	4	4	no	—
317	#41	C₂²×C₄×C₃₇	1	4	yes	—
318	#41	#41×C₃₇	1	4	yes	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	8	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	4	1	no	—
327	C₂×Q₈	—	4	4	no	—
328	C₂×Q₈	C₂²×C₄×C₃₇	1	2	yes	—
329	C₂×Q₈	C₂²×C₄×C₃₇	1	2	yes	—
330	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	4	1	no	—
333	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
342	Q₁₆	—	2	8	no	—
343	SD₁₆	—	2	8	no	—
344	M₁₆	—	2	2	no	—
345	M₁₆	—	2	2	no	—
346	M₁₆	—	2	2	no	—
347	M₁₆	—	4	4	no	—
348	M₁₆	C₂²×C₄×C₃₇	1	4	yes	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	4	4	no	—
354	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
355	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	4	4	no	—
359	C₄⋊C₄	—	4	2	no	—
360	C₄⋊C₄	—	4	2	no	—
361	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
362	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
363	C₂²⋊C₄	—	2	2	no	—
364	C₂²⋊C₄	—	4	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	4	2	no	—
368	C₄²	—	4	1	no	—
369	C₄²	—	4	1	no	—
370	C₄²	C₂²×C₄×C₃₇	1	2	yes	—
371	C₂³	—	2	2	no	—
372	C₂³	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
373	Q₈	—	2	2	no	—
374	Q₈	—	2	4	no	—
375	Q₈	—	2	4	no	—
376	Q₈	—	4	4	no	—
377	Q₈	—	4	2	no	—
378	Q₈	—	4	2	no	—
379	Q₈	C₄×D₄×C₃₇	1	4	yes	—
380	D₄	—	2	4	no	—
381	D₄	—	2	4	no	—
382	D₄	—	2	2	no	—
383	D₄	—	4	4	no	—
384	D₄	C₄×D₄×C₃₇	1	4	yes	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	4	8	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	8	2	no	—
401	C₂×C₄	—	16	2	no	—
402	C₂×C₄	C₂³×C₄×C₃₇	1	1	yes	characteristic
403	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
404	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
405	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	2	2	no	—
408	C₈	—	2	4	no	—
409	C₈	—	4	2	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	2	4	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	4	2	no	—
414	C₂²	C₃₇×#518	1	1	yes	characteristic
415	C₂²	D₄²×C₃₇	1	1	yes	characteristic
416	C₂²	C₃₇×#551	1	1	yes	characteristic
417	C₄	—	2	4	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	4	2	no	—
422	C₄	—	4	2	no	—
423	C₄	—	8	2	no	—
424	C₄	C₂×C₄×D₄×C₃₇	1	2	yes	—
425	C₄	C₃₇×#546	1	2	yes	—
426	C₂	—	2	1	no	—
427	C₂	—	2	1	no	—
428	C₂	—	4	4	no	—
429	C₂	C₃₇×#2358	1	1	yes	characteristic
430	C₂	C₃₇×#3289	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₇	D₄²
commutator	C₂×C₄	C₂³×C₄×C₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂×2₋¹⁺⁴×C₃₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂²×C₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₇×#2947	C₂	semidirect
4. C₃₇×#1960	C₂	semidirect
5. C₃₇×#1930	C₂	semidirect
6. C₃₇×#1908	C₂	semidirect
7. C₃₇×#1886	C₂	semidirect
8. C₃₇×#1860	C₂	semidirect
9. C₃₇×#1765	C₂	semidirect
16. C₃₇×#456	C₄	semidirect
50. #137×C₃₇	C₂×C₄	semidirect
61. C₄⋊Q₈×C₃₇	C₂×C₄	semidirect
76. #104×C₃₇	C₂×C₄	semidirect
90. #101×C₃₇	C₂×C₄	semidirect
194. #22892	C₃₇	direct (N × H)
212. #2947	C₂×C₃₇	semidirect
214. #1960	C₂×C₃₇	semidirect
215. #1930	C₂×C₃₇	semidirect
216. #1908	C₂×C₃₇	semidirect
217. #1886	C₂×C₃₇	semidirect
218. #1860	C₂×C₃₇	semidirect
219. #1765	C₂×C₃₇	semidirect
231. #456	C₄×C₃₇	semidirect
255. C₃₇	#22892	direct (N × H)
266. #137	C₂×C₄×C₃₇	semidirect
277. C₄⋊Q₈	C₂×C₄×C₃₇	semidirect
292. #104	C₂×C₄×C₃₇	semidirect
306. #101	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
C₂×C₃₇×#456	2
C₃₇×#2947	2
C₃₇×#2898	2
C₃₇×#1960	2
C₃₇×#1930	2
C₃₇×#1908	2
C₃₇×#1886	2
C₃₇×#1860	2
C₃₇×#1765	2
#22892	37

Subgroups — C37×#22892 #22644145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#22892 #22644145