Subgroups — C₃₇×#28670 #22649923

Order 9472.

698 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3165	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×#3138	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₇×#486	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2063	C₂	1	4	yes	maximal, complemented
6	C₃₇×#1997	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#1965	C₂	1	1	yes	maximal, characteristic
8	C₃₇×#1931	C₂	1	4	yes	maximal, complemented
9	C₄×#108×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#533	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
12	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
13	C₃₇×#501	—	2	2	no	—
14	C₃₇×#500	—	2	1	no	—
15	C₃₇×#498	—	2	1	no	—
16	C₃₇×#490	—	2	2	no	—
17	C₃₇×#486	—	2	1	no	—
18	C₃₇×#486	—	2	1	no	—
19	C₃₇×#486	—	2	1	no	—
20	C₃₇×#486	—	2	1	no	—
21	C₃₇×#486	—	2	1	no	—
22	C₃₇×#486	—	2	1	no	—
23	C₃₇×#446	—	2	1	no	—
24	C₃₇×#446	—	2	1	no	—
25	C₈×Q₈×C₃₇	—	2	1	no	—
26	C₈×Q₈×C₃₇	—	2	1	no	—
27	C₂×#108×C₃₇	C₂²	1	2	yes	—
28	C₃₇×#428	C₂²	1	4	yes	—
29	C₃₇×#424	C₂²	1	2	yes	—
30	C₃₇×#423	C₂²	1	1	yes	characteristic
31	C₃₇×#418	C₂²	1	4	yes	—
32	C₂×#102×C₃₇	C₂²	1	2	yes	—
33	C₂×#102×C₃₇	C₂²	1	2	yes	—
34	C₂×#100×C₃₇	C₂²	1	4	yes	—
35	C₃₇×#405	C₂²	1	2	yes	—
36	C₄×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
37	C₄×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
39	C₃₇×#343	C₂²	1	4	yes	—
40	C₃₇×#341	C₂²	1	2	yes	—
41	C₂²×Q₈×C₃₇	—	2	1	no	—
42	C₂²×D₄×C₃₇	—	2	1	no	—
43	C₂²×D₄×C₃₇	—	2	1	no	—
44	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
45	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
46	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
47	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
48	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
50	C₄⋊Q₈×C₃₇	—	2	1	no	—
51	C₄⋊Q₈×C₃₇	—	2	1	no	—
52	C₄⋊Q₈×C₃₇	—	2	1	no	—
53	C₄⋊Q₈×C₃₇	—	2	1	no	—
54	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
55	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
56	#127×C₃₇	—	2	1	no	—
57	#127×C₃₇	—	2	1	no	—
58	#127×C₃₇	—	2	1	no	—
59	#127×C₃₇	—	2	1	no	—
60	#125×C₃₇	D₄	1	2	yes	—
61	C₂²⋊Q₈×C₃₇	—	2	1	no	—
62	C₂²⋊Q₈×C₃₇	—	2	1	no	—
63	C₄×Q₈×C₃₇	—	2	1	no	—
64	C₄×Q₈×C₃₇	—	2	1	no	—
65	#117×C₃₇	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
67	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
68	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
69	#108×C₃₇	—	2	4	no	—
70	#107×C₃₇	—	2	4	no	—
71	#106×C₃₇	—	2	4	no	—
72	C₄⋊C₈×C₃₇	—	2	2	no	—
73	C₄⋊C₈×C₃₇	—	2	2	no	—
74	C₄⋊C₈×C₃₇	—	2	1	no	—
75	C₄⋊C₈×C₃₇	—	2	1	no	—
76	#102×C₃₇	—	2	2	no	—
77	#102×C₃₇	—	2	2	no	—
78	#102×C₃₇	—	2	2	no	—
79	#102×C₃₇	—	2	2	no	—
80	#102×C₃₇	—	2	4	no	—
81	#102×C₃₇	—	2	4	no	—
82	#100×C₃₇	—	2	8	no	—
83	#97×C₃₇	—	2	2	no	—
84	#97×C₃₇	—	2	1	no	—
85	#97×C₃₇	—	2	1	no	—
86	C₄×C₈×C₃₇	—	2	2	no	—
87	C₄×C₈×C₃₇	—	2	1	no	—
88	C₄×C₈×C₃₇	—	2	1	no	—
89	C₄×C₈×C₃₇	D₄	1	1	yes	characteristic
90	C₄×C₈×C₃₇	D₄	1	1	yes	characteristic
91	C₄×C₈×C₃₇	D₄	1	1	yes	characteristic
92	C₄×C₈×C₃₇	D₄	1	1	yes	characteristic
93	C₂⁴×C₃₇	—	2	2	no	—
94	C₂×Q₈×C₃₇	—	2	1	no	—
95	C₂×Q₈×C₃₇	—	2	1	no	—
96	C₂×Q₈×C₃₇	—	4	1	no	—
97	C₂×Q₈×C₃₇	—	4	1	no	—
98	C₂×Q₈×C₃₇	—	8	2	no	—
99	C₂×D₄×C₃₇	—	2	2	no	—
100	C₂×D₄×C₃₇	—	2	2	no	—
101	C₂×D₄×C₃₇	—	2	4	no	—
102	C₂×D₄×C₃₇	—	2	4	no	—
103	C₂×D₄×C₃₇	—	4	1	no	—
104	C₂×D₄×C₃₇	—	4	1	no	—
105	C₂×D₄×C₃₇	—	4	1	no	—
106	C₂×D₄×C₃₇	—	4	1	no	—
107	C₂×D₄×C₃₇	—	8	2	no	—
108	C₂×D₄×C₃₇	—	8	2	no	—
109	C₂²×C₄×C₃₇	—	2	2	no	—
110	C₂²×C₄×C₃₇	#41	1	1	yes	characteristic
111	C₂²×C₄×C₃₇	#41	1	1	yes	characteristic
112	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
113	M₁₆×C₃₇	—	2	2	no	—
114	M₁₆×C₃₇	—	2	4	no	—
115	M₁₆×C₃₇	—	2	2	no	—
116	M₁₆×C₃₇	—	2	2	no	—
117	M₁₆×C₃₇	#41	1	4	yes	—
118	C₂×C₈×C₃₇	—	2	2	no	—
119	C₂×C₈×C₃₇	—	2	2	no	—
120	C₂×C₈×C₃₇	—	2	2	no	—
121	C₂×C₈×C₃₇	—	2	2	no	—
122	C₂×C₈×C₃₇	—	2	2	no	—
123	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
127	C₄⋊C₄×C₃₇	—	2	2	no	—
128	C₄⋊C₄×C₃₇	—	2	2	no	—
129	C₄⋊C₄×C₃₇	—	2	1	no	—
130	C₄⋊C₄×C₃₇	—	2	1	no	—
131	C₄⋊C₄×C₃₇	—	2	2	no	—
132	C₄⋊C₄×C₃₇	—	2	2	no	—
133	C₄⋊C₄×C₃₇	—	4	1	no	—
134	C₄⋊C₄×C₃₇	—	4	1	no	—
135	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
136	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
137	C₂²⋊C₄×C₃₇	—	2	2	no	—
138	C₄²×C₃₇	—	2	2	no	—
139	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
143	C₂³×C₃₇	—	4	2	no	—
144	C₂³×C₃₇	—	4	4	no	—
145	C₂³×C₃₇	—	8	2	no	—
146	C₂³×C₃₇	—	8	2	no	—
147	C₂³×C₃₇	C₂×#41	1	1	yes	characteristic
148	Q₈×C₃₇	—	4	2	no	—
149	Q₈×C₃₇	—	4	2	no	—
150	Q₈×C₃₇	—	8	2	no	—
151	Q₈×C₃₇	—	8	2	no	—
152	D₄×C₃₇	—	4	2	no	—
153	D₄×C₃₇	—	4	2	no	—
154	D₄×C₃₇	—	4	4	no	—
155	D₄×C₃₇	—	8	2	no	—
156	D₄×C₃₇	—	8	2	no	—
157	D₄×C₃₇	—	8	2	no	—
158	D₄×C₃₇	—	8	2	no	—
159	C₂×C₄×C₃₇	—	2	2	no	—
160	C₂×C₄×C₃₇	—	2	2	no	—
161	C₂×C₄×C₃₇	—	2	2	no	—
162	C₂×C₄×C₃₇	—	2	2	no	—
163	C₂×C₄×C₃₇	—	4	2	no	—
164	C₂×C₄×C₃₇	—	8	2	no	—
165	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
166	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
167	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
168	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
169	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
172	C₂×C₄×C₃₇	2₋¹⁺⁴	1	2	yes	—
173	C₈×C₃₇	—	2	1	no	—
174	C₈×C₃₇	—	2	1	no	—
175	C₈×C₃₇	—	2	1	no	—
176	C₈×C₃₇	—	2	1	no	—
177	C₈×C₃₇	—	2	4	no	—
178	C₈×C₃₇	—	4	2	no	—
179	C₈×C₃₇	—	4	2	no	—
180	#28670	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂²×C₃₇	—	2	1	no	—
182	C₂²×C₃₇	—	2	1	no	—
183	C₂²×C₃₇	—	8	2	no	—
184	C₂²×C₃₇	—	8	2	no	—
185	C₂²×C₃₇	—	8	2	no	—
186	C₂²×C₃₇	—	16	4	no	—
187	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
188	C₂²×C₃₇	#556	1	2	yes	—
189	C₄×C₃₇	—	2	1	no	—
190	C₄×C₃₇	—	2	1	no	—
191	C₄×C₃₇	—	4	2	no	—
192	C₄×C₃₇	—	4	2	no	—
193	C₄×C₃₇	—	8	2	no	—
194	C₄×C₃₇	#471	1	2	yes	—
195	C₄×C₃₇	#472	1	2	yes	—
196	C₄×C₃₇	#532	1	1	yes	characteristic
197	C₄×C₃₇	#536	1	1	yes	characteristic
198	C₄×C₃₇	#548	1	2	yes	—
199	#3165	C₂×C₃₇	1	1	yes	characteristic, complemented
200	#3138	C₂×C₃₇	1	1	yes	characteristic
201	C₂×#486	C₂×C₃₇	1	1	yes	characteristic
202	#2960	C₂×C₃₇	1	1	yes	characteristic, complemented
203	#2063	C₂×C₃₇	1	4	yes	complemented
204	#1997	C₂×C₃₇	1	1	yes	characteristic, complemented
205	#1965	C₂×C₃₇	1	1	yes	characteristic
206	#1931	C₂×C₃₇	1	4	yes	complemented
207	C₄×#108	C₂×C₃₇	1	1	yes	characteristic, complemented
208	C₂×C₃₇	—	2	2	no	—
209	C₂×C₃₇	—	16	2	no	—
210	C₂×C₃₇	#2545	1	1	yes	characteristic
211	C₂×C₃₇	C₂×#471	1	1	yes	characteristic
212	C₂×C₃₇	C₂×#472	1	1	yes	characteristic
213	#533	C₂²×C₃₇	1	1	yes	characteristic
214	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
215	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
216	#501	—	2	2	no	—
217	#500	—	2	1	no	—
218	#498	—	2	1	no	—
219	#490	—	2	2	no	—
220	#486	—	2	1	no	—
221	#486	—	2	1	no	—
222	#486	—	2	1	no	—
223	#486	—	2	1	no	—
224	#486	—	2	1	no	—
225	#486	—	2	1	no	—
226	#446	—	2	1	no	—
227	#446	—	2	1	no	—
228	C₈×Q₈	—	2	1	no	—
229	C₈×Q₈	—	2	1	no	—
230	C₂×#108	C₂²×C₃₇	1	2	yes	—
231	#428	C₂²×C₃₇	1	4	yes	—
232	#424	C₂²×C₃₇	1	2	yes	—
233	#423	C₂²×C₃₇	1	1	yes	characteristic
234	#418	C₂²×C₃₇	1	4	yes	—
235	C₂×#102	C₂²×C₃₇	1	2	yes	—
236	C₂×#102	C₂²×C₃₇	1	2	yes	—
237	C₂×#100	C₂²×C₃₇	1	4	yes	—
238	#405	C₂²×C₃₇	1	2	yes	—
239	C₄×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
240	C₄×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
241	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
242	#343	C₂²×C₃₇	1	4	yes	—
243	#341	C₂²×C₃₇	1	2	yes	—
244	C₃₇	#28670	1	1	yes	characteristic, direct product factor, Sylow
245	C₂²×Q₈	—	2	1	no	—
246	C₂²×D₄	—	2	1	no	—
247	C₂²×D₄	—	2	1	no	—
248	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
249	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
250	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
251	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
252	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
253	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
254	C₄⋊Q₈	—	2	1	no	—
255	C₄⋊Q₈	—	2	1	no	—
256	C₄⋊Q₈	—	2	1	no	—
257	C₄⋊Q₈	—	2	1	no	—
258	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
259	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
260	#127	—	2	1	no	—
261	#127	—	2	1	no	—
262	#127	—	2	1	no	—
263	#127	—	2	1	no	—
264	#125	D₄×C₃₇	1	2	yes	—
265	C₂²⋊Q₈	—	2	1	no	—
266	C₂²⋊Q₈	—	2	1	no	—
267	C₄×Q₈	—	2	1	no	—
268	C₄×Q₈	—	2	1	no	—
269	#117	C₂³×C₃₇	1	2	yes	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
272	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
273	#108	—	2	4	no	—
274	#107	—	2	4	no	—
275	#106	—	2	4	no	—
276	C₄⋊C₈	—	2	2	no	—
277	C₄⋊C₈	—	2	2	no	—
278	C₄⋊C₈	—	2	1	no	—
279	C₄⋊C₈	—	2	1	no	—
280	#102	—	2	2	no	—
281	#102	—	2	2	no	—
282	#102	—	2	2	no	—
283	#102	—	2	2	no	—
284	#102	—	2	4	no	—
285	#102	—	2	4	no	—
286	#100	—	2	8	no	—
287	#97	—	2	2	no	—
288	#97	—	2	1	no	—
289	#97	—	2	1	no	—
290	C₄×C₈	—	2	2	no	—
291	C₄×C₈	—	2	1	no	—
292	C₄×C₈	—	2	1	no	—
293	C₄×C₈	D₄×C₃₇	1	1	yes	characteristic
294	C₄×C₈	D₄×C₃₇	1	1	yes	characteristic
295	C₄×C₈	D₄×C₃₇	1	1	yes	characteristic
296	C₄×C₈	D₄×C₃₇	1	1	yes	characteristic
297	C₂⁴	—	2	2	no	—
298	C₂×Q₈	—	2	1	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	—	4	1	no	—
301	C₂×Q₈	—	4	1	no	—
302	C₂×Q₈	—	8	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	2	4	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂×D₄	—	4	1	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	8	2	no	—
312	C₂×D₄	—	8	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	#41×C₃₇	1	1	yes	characteristic
315	C₂²×C₄	#41×C₃₇	1	1	yes	characteristic
316	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
317	M₁₆	—	2	2	no	—
318	M₁₆	—	2	4	no	—
319	M₁₆	—	2	2	no	—
320	M₁₆	—	2	2	no	—
321	M₁₆	#41×C₃₇	1	4	yes	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
328	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
329	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
330	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
340	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₄²	—	2	2	no	—
343	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
344	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
345	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
346	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
347	C₂³	—	4	2	no	—
348	C₂³	—	4	4	no	—
349	C₂³	—	8	2	no	—
350	C₂³	—	8	2	no	—
351	C₂³	C₂×#41×C₃₇	1	1	yes	characteristic
352	Q₈	—	4	2	no	—
353	Q₈	—	4	2	no	—
354	Q₈	—	8	2	no	—
355	Q₈	—	8	2	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	2	no	—
358	D₄	—	4	4	no	—
359	D₄	—	8	2	no	—
360	D₄	—	8	2	no	—
361	D₄	—	8	2	no	—
362	D₄	—	8	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	8	2	no	—
369	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
370	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
371	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
372	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
373	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
375	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
376	C₂×C₄	2₋¹⁺⁴×C₃₇	1	2	yes	—
377	C₈	—	2	1	no	—
378	C₈	—	2	1	no	—
379	C₈	—	2	1	no	—
380	C₈	—	2	1	no	—
381	C₈	—	2	4	no	—
382	C₈	—	4	2	no	—
383	C₈	—	4	2	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	16	4	no	—
390	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
391	C₂²	C₃₇×#556	1	2	yes	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	4	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	8	2	no	—
397	C₄	C₃₇×#471	1	2	yes	—
398	C₄	C₃₇×#472	1	2	yes	—
399	C₄	C₃₇×#532	1	1	yes	characteristic
400	C₄	C₃₇×#536	1	1	yes	characteristic
401	C₄	C₃₇×#548	1	2	yes	—
402	C₂	—	2	2	no	—
403	C₂	—	16	2	no	—
404	C₂	C₃₇×#2545	1	1	yes	characteristic
405	C₂	C₂×C₃₇×#471	1	1	yes	characteristic
406	C₂	C₂×C₃₇×#472	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂×#127×C₃₇	C₂²
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
1. C₃₇×#3165	C₂	semidirect
4. C₃₇×#2960	C₂	semidirect
5. C₃₇×#2063	C₂	semidirect
6. C₃₇×#1997	C₂	semidirect
8. C₃₇×#1931	C₂	semidirect
9. C₄×#108×C₃₇	C₂	semidirect
180. #28670	C₃₇	direct (N × H)
199. #3165	C₂×C₃₇	semidirect
202. #2960	C₂×C₃₇	semidirect
203. #2063	C₂×C₃₇	semidirect
204. #1997	C₂×C₃₇	semidirect
206. #1931	C₂×C₃₇	semidirect
207. C₄×#108	C₂×C₃₇	semidirect
244. C₃₇	#28670	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×#3165	2
C₃₇×#3138	2
C₂×C₃₇×#486	2
C₃₇×#2960	2
C₃₇×#2063	2
C₃₇×#1997	2
C₃₇×#1965	2
C₃₇×#1931	2
C₄×#108×C₃₇	2
#28670	37

Subgroups — C37×#28670 #22649923

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28670 #22649923