Subgroups — C₃₇×#28768 #22650021

Order 9472.

780 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#496	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#3140	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#3138	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#2961	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2046	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2045	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1978	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1977	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1967	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1965	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1778	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
14	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic
16	C₃₇×#533	C₂²	1	1	yes	characteristic
17	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
19	C₃₇×#496	—	2	4	no	—
20	C₃₇×#490	—	2	2	no	—
21	C₃₇×#489	—	2	2	no	—
22	C₃₇×#488	—	2	2	no	—
23	C₃₇×#486	—	2	2	no	—
24	C₃₇×#446	—	2	4	no	—
25	C₂×#108×C₃₇	C₂²	1	2	yes	—
26	C₃₇×#424	C₂²	1	2	yes	—
27	C₃₇×#423	C₂²	1	1	yes	characteristic
28	C₃₇×#419	C₂²	1	2	yes	—
29	C₃₇×#418	C₂²	1	2	yes	—
30	C₃₇×#418	C₂²	1	2	yes	—
31	C₃₇×#418	C₂²	1	2	yes	—
32	C₂×#101×C₃₇	C₂²	1	2	yes	—
33	C₂×#100×C₃₇	C₂²	1	2	yes	—
34	C₂×#100×C₃₇	C₂²	1	2	yes	—
35	C₂×#100×C₃₇	C₂²	1	2	yes	—
36	C₃₇×#405	C₂²	1	2	yes	—
37	C₄×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
38	C₄×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
39	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
40	C₃₇×#341	C₂²	1	2	yes	—
41	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
42	C₂²×D₄×C₃₇	—	2	2	no	—
43	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
46	C₂×SD₁₆×C₃₇	—	2	2	no	—
47	C₂×SD₁₆×C₃₇	—	2	2	no	—
48	C₂×SD₁₆×C₃₇	—	2	4	no	—
49	C₂×SD₁₆×C₃₇	—	4	2	no	—
50	C₂×D₈×C₃₇	—	2	2	no	—
51	C₂×D₈×C₃₇	—	2	2	no	—
52	C₂×D₈×C₃₇	—	2	4	no	—
53	C₂×D₈×C₃₇	—	4	2	no	—
54	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
55	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
56	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
57	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
59	C₄⋊Q₈×C₃₇	D₄	1	2	yes	—
60	#127×C₃₇	—	2	1	no	—
61	#127×C₃₇	—	2	1	no	—
62	#127×C₃₇	—	2	2	no	—
63	#125×C₃₇	D₄	1	2	yes	—
64	#124×C₃₇	—	2	1	no	—
65	#124×C₃₇	—	2	1	no	—
66	#124×C₃₇	—	2	2	no	—
67	C₂²⋊Q₈×C₃₇	—	2	2	no	—
68	C₄×Q₈×C₃₇	—	2	2	no	—
69	#117×C₃₇	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
71	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
72	#108×C₃₇	—	2	4	no	—
73	C₄⋊C₈×C₃₇	—	2	4	no	—
74	C₄⋊C₈×C₃₇	—	2	2	no	—
75	#103×C₃₇	—	2	4	no	—
76	#102×C₃₇	—	2	4	no	—
77	#102×C₃₇	—	2	4	no	—
78	#102×C₃₇	—	2	4	no	—
79	#101×C₃₇	—	4	2	no	—
80	#100×C₃₇	—	4	2	no	—
81	#100×C₃₇	—	4	2	no	—
82	#100×C₃₇	—	4	2	no	—
83	#97×C₃₇	—	2	2	no	—
84	#97×C₃₇	—	2	1	no	—
85	#97×C₃₇	—	2	1	no	—
86	#97×C₃₇	D₄	1	4	yes	—
87	C₄×C₈×C₃₇	—	2	2	no	—
88	C₄×C₈×C₃₇	—	2	1	no	—
89	C₄×C₈×C₃₇	—	2	1	no	—
90	C₂⁴×C₃₇	—	2	1	no	—
91	C₂⁴×C₃₇	—	2	1	no	—
92	C₂⁴×C₃₇	—	2	1	no	—
93	C₂×Q₈×C₃₇	—	2	2	no	—
94	C₂×Q₈×C₃₇	—	2	1	no	—
95	C₂×Q₈×C₃₇	—	2	1	no	—
96	C₂×Q₈×C₃₇	—	2	2	no	—
97	C₂×Q₈×C₃₇	—	2	2	no	—
98	C₂×D₄×C₃₇	—	2	1	no	—
99	C₂×D₄×C₃₇	—	2	1	no	—
100	C₂×D₄×C₃₇	—	2	1	no	—
101	C₂×D₄×C₃₇	—	2	1	no	—
102	C₂×D₄×C₃₇	—	2	1	no	—
103	C₂×D₄×C₃₇	—	2	1	no	—
104	C₂×D₄×C₃₇	—	2	2	no	—
105	C₂×D₄×C₃₇	—	2	2	no	—
106	C₂×D₄×C₃₇	—	2	2	no	—
107	C₂×D₄×C₃₇	—	2	2	no	—
108	C₂×D₄×C₃₇	—	2	2	no	—
109	C₂×D₄×C₃₇	—	2	2	no	—
110	C₂×D₄×C₃₇	—	4	2	no	—
111	C₂×D₄×C₃₇	—	4	2	no	—
112	C₂×D₄×C₃₇	—	8	4	no	—
113	C₂²×C₄×C₃₇	—	2	1	no	—
114	C₂²×C₄×C₃₇	#41	1	2	yes	—
115	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
116	SD₁₆×C₃₇	—	4	4	no	—
117	SD₁₆×C₃₇	—	4	4	no	—
118	D₈×C₃₇	—	4	4	no	—
119	D₈×C₃₇	—	4	4	no	—
120	M₁₆×C₃₇	—	2	2	no	—
121	M₁₆×C₃₇	—	2	2	no	—
122	M₁₆×C₃₇	—	2	2	no	—
123	M₁₆×C₃₇	—	2	2	no	—
124	M₁₆×C₃₇	—	2	2	no	—
125	M₁₆×C₃₇	—	2	2	no	—
126	C₂×C₈×C₃₇	—	2	2	no	—
127	C₂×C₈×C₃₇	—	2	2	no	—
128	C₂×C₈×C₃₇	—	2	2	no	—
129	C₂×C₈×C₃₇	—	2	2	no	—
130	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₃₇	#41	1	4	yes	—
133	C₄⋊C₄×C₃₇	—	2	4	no	—
134	C₄⋊C₄×C₃₇	—	2	2	no	—
135	C₄⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
136	C₂²⋊C₄×C₃₇	—	2	2	no	—
137	C₂²⋊C₄×C₃₇	—	4	2	no	—
138	C₂²⋊C₄×C₃₇	—	4	2	no	—
139	C₄²×C₃₇	—	2	2	no	—
140	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₃₇	C₂×D₄	1	2	yes	—
143	C₂³×C₃₇	—	4	1	no	—
144	C₂³×C₃₇	—	4	1	no	—
145	C₂³×C₃₇	—	4	1	no	—
146	C₂³×C₃₇	—	4	2	no	—
147	C₂³×C₃₇	—	4	2	no	—
148	C₂³×C₃₇	—	4	2	no	—
149	C₂³×C₃₇	—	8	2	no	—
150	C₂³×C₃₇	—	8	2	no	—
151	C₂³×C₃₇	—	8	2	no	—
152	C₂³×C₃₇	C₂×#41	1	1	yes	characteristic
153	Q₈×C₃₇	—	4	1	no	—
154	Q₈×C₃₇	—	4	1	no	—
155	Q₈×C₃₇	—	4	2	no	—
156	Q₈×C₃₇	—	8	2	no	—
157	D₄×C₃₇	—	4	1	no	—
158	D₄×C₃₇	—	4	1	no	—
159	D₄×C₃₇	—	4	1	no	—
160	D₄×C₃₇	—	4	1	no	—
161	D₄×C₃₇	—	4	1	no	—
162	D₄×C₃₇	—	4	1	no	—
163	D₄×C₃₇	—	4	2	no	—
164	D₄×C₃₇	—	4	2	no	—
165	D₄×C₃₇	—	4	2	no	—
166	D₄×C₃₇	—	8	4	no	—
167	D₄×C₃₇	—	8	4	no	—
168	C₂×C₄×C₃₇	—	2	4	no	—
169	C₂×C₄×C₃₇	—	4	2	no	—
170	C₂×C₄×C₃₇	—	4	1	no	—
171	C₂×C₄×C₃₇	—	4	2	no	—
172	C₂×C₄×C₃₇	#121	1	2	yes	—
173	C₂×C₄×C₃₇	#121	1	2	yes	—
174	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
177	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
178	C₈×C₃₇	—	2	2	no	—
179	C₈×C₃₇	—	4	2	no	—
180	C₈×C₃₇	—	4	2	no	—
181	C₈×C₃₇	—	4	2	no	—
182	C₈×C₃₇	#124	1	4	yes	—
183	#28768	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂²×C₃₇	—	2	2	no	—
185	C₂²×C₃₇	—	8	1	no	—
186	C₂²×C₃₇	—	8	1	no	—
187	C₂²×C₃₇	—	8	1	no	—
188	C₂²×C₃₇	—	8	2	no	—
189	C₂²×C₃₇	—	8	2	no	—
190	C₂²×C₃₇	—	8	2	no	—
191	C₂²×C₃₇	—	16	2	no	—
192	C₂²×C₃₇	—	16	2	no	—
193	C₂²×C₃₇	—	16	2	no	—
194	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
195	C₂²×C₃₇	#559	1	2	yes	—
196	C₄×C₃₇	—	2	2	no	—
197	C₄×C₃₇	—	2	2	no	—
198	C₄×C₃₇	—	4	4	no	—
199	C₄×C₃₇	—	8	1	no	—
200	C₄×C₃₇	C₂×#124	1	1	yes	characteristic
201	C₄×C₃₇	#535	1	1	yes	characteristic
202	C₄×C₃₇	#550	1	2	yes	—
203	C₂×#496	C₂×C₃₇	1	1	yes	characteristic
204	#3140	C₂×C₃₇	1	1	yes	characteristic, complemented
205	#3138	C₂×C₃₇	1	1	yes	characteristic, complemented
206	#2961	C₂×C₃₇	1	1	yes	characteristic, complemented
207	#2046	C₂×C₃₇	1	2	yes	complemented
208	#2045	C₂×C₃₇	1	2	yes	complemented
209	#1978	C₂×C₃₇	1	2	yes	complemented
210	#1977	C₂×C₃₇	1	2	yes	complemented
211	#1967	C₂×C₃₇	1	1	yes	characteristic, complemented
212	#1965	C₂×C₃₇	1	1	yes	characteristic, complemented
213	#1778	C₂×C₃₇	1	1	yes	characteristic, complemented
214	C₂×C₃₇	—	2	2	no	—
215	C₂×C₃₇	—	16	1	no	—
216	C₂×C₃₇	—	16	1	no	—
217	C₂×C₃₇	—	16	1	no	—
218	C₂×C₃₇	#2548	1	1	yes	characteristic
219	C₂×C₃₇	#3068	1	2	yes	—
220	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
221	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
222	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
223	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
224	#533	C₂²×C₃₇	1	1	yes	characteristic
225	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
226	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
227	#496	—	2	4	no	—
228	#490	—	2	2	no	—
229	#489	—	2	2	no	—
230	#488	—	2	2	no	—
231	#486	—	2	2	no	—
232	#446	—	2	4	no	—
233	C₂×#108	C₂²×C₃₇	1	2	yes	—
234	#424	C₂²×C₃₇	1	2	yes	—
235	#423	C₂²×C₃₇	1	1	yes	characteristic
236	#419	C₂²×C₃₇	1	2	yes	—
237	#418	C₂²×C₃₇	1	2	yes	—
238	#418	C₂²×C₃₇	1	2	yes	—
239	#418	C₂²×C₃₇	1	2	yes	—
240	C₂×#101	C₂²×C₃₇	1	2	yes	—
241	C₂×#100	C₂²×C₃₇	1	2	yes	—
242	C₂×#100	C₂²×C₃₇	1	2	yes	—
243	C₂×#100	C₂²×C₃₇	1	2	yes	—
244	#405	C₂²×C₃₇	1	2	yes	—
245	C₄×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
246	C₄×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
247	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
248	#341	C₂²×C₃₇	1	2	yes	—
249	C₃₇	#28768	1	1	yes	characteristic, direct product factor, Sylow
250	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
251	C₂²×D₄	—	2	2	no	—
252	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
253	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
254	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
255	C₂×SD₁₆	—	2	2	no	—
256	C₂×SD₁₆	—	2	2	no	—
257	C₂×SD₁₆	—	2	4	no	—
258	C₂×SD₁₆	—	4	2	no	—
259	C₂×D₈	—	2	2	no	—
260	C₂×D₈	—	2	2	no	—
261	C₂×D₈	—	2	4	no	—
262	C₂×D₈	—	4	2	no	—
263	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
264	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
265	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
266	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
267	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
268	C₄⋊Q₈	D₄×C₃₇	1	2	yes	—
269	#127	—	2	1	no	—
270	#127	—	2	1	no	—
271	#127	—	2	2	no	—
272	#125	D₄×C₃₇	1	2	yes	—
273	#124	—	2	1	no	—
274	#124	—	2	1	no	—
275	#124	—	2	2	no	—
276	C₂²⋊Q₈	—	2	2	no	—
277	C₄×Q₈	—	2	2	no	—
278	#117	C₂³×C₃₇	1	2	yes	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
281	#108	—	2	4	no	—
282	C₄⋊C₈	—	2	4	no	—
283	C₄⋊C₈	—	2	2	no	—
284	#103	—	2	4	no	—
285	#102	—	2	4	no	—
286	#102	—	2	4	no	—
287	#102	—	2	4	no	—
288	#101	—	4	2	no	—
289	#100	—	4	2	no	—
290	#100	—	4	2	no	—
291	#100	—	4	2	no	—
292	#97	—	2	2	no	—
293	#97	—	2	1	no	—
294	#97	—	2	1	no	—
295	#97	D₄×C₃₇	1	4	yes	—
296	C₄×C₈	—	2	2	no	—
297	C₄×C₈	—	2	1	no	—
298	C₄×C₈	—	2	1	no	—
299	C₂⁴	—	2	1	no	—
300	C₂⁴	—	2	1	no	—
301	C₂⁴	—	2	1	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	1	no	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	4	2	no	—
320	C₂×D₄	—	4	2	no	—
321	C₂×D₄	—	8	4	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	#41×C₃₇	1	2	yes	—
324	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
325	SD₁₆	—	4	4	no	—
326	SD₁₆	—	4	4	no	—
327	D₈	—	4	4	no	—
328	D₈	—	4	4	no	—
329	M₁₆	—	2	2	no	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	2	2	no	—
332	M₁₆	—	2	2	no	—
333	M₁₆	—	2	2	no	—
334	M₁₆	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
340	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
341	C₂×C₈	#41×C₃₇	1	4	yes	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
345	C₂²⋊C₄	—	2	2	no	—
346	C₂²⋊C₄	—	4	2	no	—
347	C₂²⋊C₄	—	4	2	no	—
348	C₄²	—	2	2	no	—
349	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
350	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
351	C₄²	C₂×D₄×C₃₇	1	2	yes	—
352	C₂³	—	4	1	no	—
353	C₂³	—	4	1	no	—
354	C₂³	—	4	1	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	8	2	no	—
359	C₂³	—	8	2	no	—
360	C₂³	—	8	2	no	—
361	C₂³	C₂×#41×C₃₇	1	1	yes	characteristic
362	Q₈	—	4	1	no	—
363	Q₈	—	4	1	no	—
364	Q₈	—	4	2	no	—
365	Q₈	—	8	2	no	—
366	D₄	—	4	1	no	—
367	D₄	—	4	1	no	—
368	D₄	—	4	1	no	—
369	D₄	—	4	1	no	—
370	D₄	—	4	1	no	—
371	D₄	—	4	1	no	—
372	D₄	—	4	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	2	no	—
375	D₄	—	8	4	no	—
376	D₄	—	8	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	#121×C₃₇	1	2	yes	—
382	C₂×C₄	#121×C₃₇	1	2	yes	—
383	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
384	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
385	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
386	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
387	C₈	—	2	2	no	—
388	C₈	—	4	2	no	—
389	C₈	—	4	2	no	—
390	C₈	—	4	2	no	—
391	C₈	#124×C₃₇	1	4	yes	—
392	C₂²	—	2	2	no	—
393	C₂²	—	8	1	no	—
394	C₂²	—	8	1	no	—
395	C₂²	—	8	1	no	—
396	C₂²	—	8	2	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	16	2	no	—
400	C₂²	—	16	2	no	—
401	C₂²	—	16	2	no	—
402	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
403	C₂²	C₃₇×#559	1	2	yes	—
404	C₄	—	2	2	no	—
405	C₄	—	2	2	no	—
406	C₄	—	4	4	no	—
407	C₄	—	8	1	no	—
408	C₄	C₂×#124×C₃₇	1	1	yes	characteristic
409	C₄	C₃₇×#535	1	1	yes	characteristic
410	C₄	C₃₇×#550	1	2	yes	—
411	C₂	—	2	2	no	—
412	C₂	—	16	1	no	—
413	C₂	—	16	1	no	—
414	C₂	—	16	1	no	—
415	C₂	C₃₇×#2548	1	1	yes	characteristic
416	C₂	C₃₇×#3068	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂×C₃₇×#496	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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×#3140	C₂	semidirect
3. C₃₇×#3138	C₂	semidirect
4. C₃₇×#2961	C₂	semidirect
5. C₃₇×#2046	C₂	semidirect
6. C₃₇×#2045	C₂	semidirect
7. C₃₇×#1978	C₂	semidirect
8. C₃₇×#1977	C₂	semidirect
9. C₃₇×#1967	C₂	semidirect
10. C₃₇×#1965	C₂	semidirect
11. C₃₇×#1778	C₂	semidirect
183. #28768	C₃₇	direct (N × H)
204. #3140	C₂×C₃₇	semidirect
205. #3138	C₂×C₃₇	semidirect
206. #2961	C₂×C₃₇	semidirect
207. #2046	C₂×C₃₇	semidirect
208. #2045	C₂×C₃₇	semidirect
209. #1978	C₂×C₃₇	semidirect
210. #1977	C₂×C₃₇	semidirect
211. #1967	C₂×C₃₇	semidirect
212. #1965	C₂×C₃₇	semidirect
213. #1778	C₂×C₃₇	semidirect
249. C₃₇	#28768	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×#496	2
C₃₇×#3140	2
C₃₇×#3138	2
C₃₇×#2961	2
C₃₇×#2046	2
C₃₇×#2045	2
C₃₇×#1978	2
C₃₇×#1977	2
C₃₇×#1967	2
C₃₇×#1965	2
C₃₇×#1778	2
#28768	37

Subgroups — C37×#28768 #22650021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28768 #22650021