Subgroups — C₃₇×#29902 #22651155

Order 9472.

772 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3008	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#2888	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#2081	C₂	1	2	yes	maximal, complemented
4	C₃₇×#2080	C₂	1	2	yes	maximal, complemented
5	C₃₇×#2048	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2045	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1914	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1910	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1868	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1858	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1795	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×H(5,𝔽₂)×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×AGL(1,ℤ/8)×C₃₇	C₂²	1	1	yes	characteristic
14	C₂²×D₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₃₇×#568	C₂²	1	1	yes	characteristic
16	C₃₇×#568	C₂²	1	1	yes	characteristic
17	C₃₇×#535	C₂²	1	1	yes	characteristic
18	C₃₇×#449	—	2	2	no	—
19	C₃₇×#447	—	2	2	no	—
20	C₃₇×#430	C₂²	1	2	yes	complemented
21	C₃₇×#424	C₂²	1	2	yes	complemented
22	C₃₇×#421	C₂²	1	2	yes	—
23	C₃₇×#418	C₂²	1	1	yes	characteristic
24	C₃₇×#418	C₂²	1	2	yes	—
25	C₃₇×#418	C₂²	1	2	yes	complemented
26	C₃₇×#416	C₂²	1	1	yes	characteristic
27	C₃₇×#413	—	2	2	no	—
28	C₃₇×#413	C₂²	1	1	yes	characteristic
29	C₃₇×#413	C₂²	1	2	yes	—
30	C₂×#100×C₃₇	—	2	2	no	—
31	C₂×#100×C₃₇	C₂²	1	2	yes	—
32	C₂×#100×C₃₇	C₂²	1	2	yes	complemented
33	C₃₇×#410	C₂²	1	1	yes	characteristic
34	C₃₇×#408	C₂²	1	1	yes	characteristic
35	C₃₇×#344	C₂²	1	2	yes	complemented
36	C₃₇×#344	C₂²	1	2	yes	complemented
37	C₃₇×#341	C₂²	1	2	yes	complemented
38	C₃₇×H(3,ℤ/4)	C₂²	1	2	yes	complemented
39	H(5,𝔽₂)×C₃₇	—	4	2	no	—
40	H(5,𝔽₂)×C₃₇	—	4	2	no	—
41	C₂×#41×C₃₇	—	2	1	no	—
42	C₂×#41×C₃₇	D₄	1	2	yes	—
43	C₂×#41×C₃₇	C₂³	1	1	yes	characteristic
44	C₂×#41×C₃₇	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₃₇	—	2	2	no	—
46	C₂²×D₄×C₃₇	—	2	1	no	—
47	C₂²×D₄×C₃₇	D₄	1	2	yes	—
48	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
50	AGL(1,ℤ/8)×C₃₇	—	4	2	no	—
51	C₂×SD₁₆×C₃₇	—	2	1	no	—
52	C₂×D₈×C₃₇	—	2	2	no	—
53	C₂×D₈×C₃₇	—	2	1	no	—
54	C₂×D₈×C₃₇	—	4	2	no	—
55	#131×C₃₇	—	4	2	no	—
56	#131×C₃₇	—	4	2	no	—
57	C₂×M₁₆×C₃₇	—	2	2	no	—
58	C₂×M₁₆×C₃₇	—	2	2	no	—
59	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
60	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
61	C₂×M₁₆×C₃₇	C₂³	1	1	yes	characteristic
62	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
63	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
64	#127×C₃₇	—	2	1	no	—
65	#124×C₃₇	—	2	1	no	—
66	#121×C₃₇	—	2	2	no	—
67	#120×C₃₇	—	2	2	no	—
68	#117×C₃₇	C₂³	1	1	yes	characteristic
69	#117×C₃₇	C₂³	1	2	yes	—
70	#108×C₃₇	—	4	2	no	—
71	C₄⋊C₈×C₃₇	—	4	2	no	—
72	#104×C₃₇	—	4	2	no	—
73	#103×C₃₇	—	2	1	no	—
74	#102×C₃₇	—	2	1	no	—
75	#102×C₃₇	—	2	2	no	—
76	#102×C₃₇	—	4	2	no	—
77	#102×C₃₇	—	4	2	no	—
78	#101×C₃₇	—	2	2	no	—
79	#101×C₃₇	—	2	1	no	—
80	#100×C₃₇	—	2	2	no	—
81	#100×C₃₇	—	2	4	no	—
82	#100×C₃₇	—	2	1	no	—
83	#100×C₃₇	—	4	2	no	—
84	#99×C₃₇	—	2	2	no	—
85	C₂²⋊C₈×C₃₇	—	2	2	no	—
86	C₂⁴×C₃₇	—	2	2	no	—
87	C₂⁴×C₃₇	—	2	1	no	—
88	C₂⁴×C₃₇	—	2	1	no	—
89	#41×C₃₇	—	2	2	no	—
90	#41×C₃₇	—	2	2	no	—
91	#41×C₃₇	—	2	2	no	—
92	#41×C₃₇	—	2	2	no	—
93	#41×C₃₇	—	4	2	no	—
94	#41×C₃₇	—	4	2	no	—
95	#41×C₃₇	—	4	4	no	—
96	C₂×Q₈×C₃₇	C₂×D₄	1	1	yes	characteristic
97	C₂×Q₈×C₃₇	#41	1	1	yes	characteristic
98	C₂×D₄×C₃₇	—	2	2	no	—
99	C₂×D₄×C₃₇	—	2	1	no	—
100	C₂×D₄×C₃₇	—	2	2	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	—	4	2	no	—
109	C₂×D₄×C₃₇	—	4	2	no	—
110	C₂×D₄×C₃₇	—	4	8	no	—
111	C₂×D₄×C₃₇	—	4	4	no	—
112	C₂×D₄×C₃₇	—	4	2	no	—
113	C₂×D₄×C₃₇	C₂×D₄	1	1	yes	characteristic
114	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
115	C₂×D₄×C₃₇	#41	1	2	yes	—
116	C₂×D₄×C₃₇	#41	1	1	yes	characteristic
117	C₂²×C₄×C₃₇	—	2	2	no	—
118	C₂²×C₄×C₃₇	—	2	1	no	—
119	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
121	SD₁₆×C₃₇	—	4	2	no	—
122	D₈×C₃₇	—	4	4	no	—
123	D₈×C₃₇	—	4	2	no	—
124	M₁₆×C₃₇	—	2	2	no	—
125	M₁₆×C₃₇	—	2	2	no	—
126	M₁₆×C₃₇	—	2	2	no	—
127	M₁₆×C₃₇	—	2	2	no	—
128	M₁₆×C₃₇	—	2	2	no	—
129	M₁₆×C₃₇	—	2	2	no	—
130	M₁₆×C₃₇	—	2	2	no	—
131	M₁₆×C₃₇	—	4	2	no	—
132	M₁₆×C₃₇	—	4	2	no	—
133	C₂×C₈×C₃₇	—	2	1	no	—
134	C₂×C₈×C₃₇	—	2	1	no	—
135	C₂×C₈×C₃₇	—	2	2	no	—
136	C₂×C₈×C₃₇	—	2	2	no	—
137	C₂×C₈×C₃₇	—	2	2	no	—
138	C₂×C₈×C₃₇	—	2	2	no	—
139	C₂×C₈×C₃₇	—	4	2	no	—
140	C₂×C₈×C₃₇	—	4	2	no	—
141	C₄⋊C₄×C₃₇	—	2	1	no	—
142	C₄⋊C₄×C₃₇	—	2	2	no	—
143	C₂²⋊C₄×C₃₇	—	2	2	no	—
144	C₂²⋊C₄×C₃₇	—	2	1	no	—
145	C₂²⋊C₄×C₃₇	—	4	2	no	—
146	C₄²×C₃₇	—	2	1	no	—
147	C₄²×C₃₇	—	2	2	no	—
148	C₂³×C₃₇	—	2	2	no	—
149	C₂³×C₃₇	—	2	1	no	—
150	C₂³×C₃₇	—	4	4	no	—
151	C₂³×C₃₇	—	4	2	no	—
152	C₂³×C₃₇	—	4	1	no	—
153	C₂³×C₃₇	—	4	2	no	—
154	C₂³×C₃₇	—	16	1	no	—
155	C₂³×C₃₇	—	16	1	no	—
156	C₂³×C₃₇	—	16	2	no	—
157	C₂³×C₃₇	#123	1	2	yes	—
158	C₂³×C₃₇	C₂×#41	1	1	yes	characteristic
159	Q₈×C₃₇	—	2	2	no	—
160	Q₈×C₃₇	—	2	1	no	—
161	Q₈×C₃₇	—	2	1	no	—
162	D₄×C₃₇	—	2	4	no	—
163	D₄×C₃₇	—	2	2	no	—
164	D₄×C₃₇	—	2	1	no	—
165	D₄×C₃₇	—	2	2	no	—
166	D₄×C₃₇	—	2	1	no	—
167	D₄×C₃₇	—	2	2	no	—
168	D₄×C₃₇	—	4	4	no	—
169	D₄×C₃₇	—	4	4	no	—
170	D₄×C₃₇	—	4	2	no	—
171	D₄×C₃₇	—	4	1	no	—
172	D₄×C₃₇	—	4	1	no	—
173	D₄×C₃₇	—	4	2	no	—
174	D₄×C₃₇	—	4	2	no	—
175	D₄×C₃₇	—	16	2	no	—
176	C₂×C₄×C₃₇	—	2	2	no	—
177	C₂×C₄×C₃₇	—	2	2	no	—
178	C₂×C₄×C₃₇	—	2	1	no	—
179	C₂×C₄×C₃₇	—	4	4	no	—
180	C₂×C₄×C₃₇	—	4	2	no	—
181	C₂×C₄×C₃₇	—	4	1	no	—
182	C₂×C₄×C₃₇	—	4	2	no	—
183	C₂×C₄×C₃₇	#123	1	2	yes	—
184	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
187	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
188	C₈×C₃₇	—	4	1	no	—
189	C₈×C₃₇	—	4	2	no	—
190	C₈×C₃₇	—	4	2	no	—
191	C₈×C₃₇	—	4	1	no	—
192	C₈×C₃₇	—	4	2	no	—
193	#29902	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂²×C₃₇	—	2	2	no	—
195	C₂²×C₃₇	—	4	1	no	—
196	C₂²×C₃₇	—	4	2	no	—
197	C₂²×C₃₇	—	4	2	no	—
198	C₂²×C₃₇	—	4	1	no	—
199	C₂²×C₃₇	—	8	2	no	—
200	C₂²×C₃₇	—	8	1	no	—
201	C₂²×C₃₇	—	8	2	no	—
202	C₂²×C₃₇	—	8	1	no	—
203	C₂²×C₃₇	—	16	2	no	—
204	C₂²×C₃₇	—	16	2	no	—
205	C₂²×C₃₇	—	16	4	no	—
206	C₂²×C₃₇	C₂×#123	1	1	yes	characteristic
207	C₂²×C₃₇	#538	1	2	yes	—
208	C₄×C₃₇	—	2	2	no	—
209	C₄×C₃₇	—	4	1	no	—
210	C₄×C₃₇	—	8	2	no	—
211	C₄×C₃₇	—	8	1	no	—
212	C₄×C₃₇	#534	1	1	yes	characteristic
213	C₄×C₃₇	#534	1	1	yes	characteristic
214	C₄×C₃₇	#538	1	2	yes	—
215	#3008	C₂×C₃₇	1	1	yes	characteristic
216	#2888	C₂×C₃₇	1	1	yes	characteristic, complemented
217	#2081	C₂×C₃₇	1	2	yes	complemented
218	#2080	C₂×C₃₇	1	2	yes	complemented
219	#2048	C₂×C₃₇	1	2	yes	complemented
220	#2045	C₂×C₃₇	1	2	yes	complemented
221	#1914	C₂×C₃₇	1	1	yes	characteristic, complemented
222	#1910	C₂×C₃₇	1	1	yes	characteristic, complemented
223	#1868	C₂×C₃₇	1	1	yes	characteristic, complemented
224	#1858	C₂×C₃₇	1	1	yes	characteristic, complemented
225	#1795	C₂×C₃₇	1	1	yes	characteristic, complemented
226	C₂×C₃₇	—	2	1	no	—
227	C₂×C₃₇	—	2	2	no	—
228	C₂×C₃₇	—	4	2	no	—
229	C₂×C₃₇	—	8	2	no	—
230	C₂×C₃₇	—	8	1	no	—
231	C₂×C₃₇	—	16	1	no	—
232	C₂×C₃₇	#2622	1	1	yes	characteristic
233	C₂×H(5,𝔽₂)	C₂²×C₃₇	1	1	yes	characteristic
234	C₂×AGL(1,ℤ/8)	C₂²×C₃₇	1	1	yes	characteristic
235	C₂²×D₈	C₂²×C₃₇	1	1	yes	characteristic
236	#568	C₂²×C₃₇	1	1	yes	characteristic
237	#568	C₂²×C₃₇	1	1	yes	characteristic
238	#535	C₂²×C₃₇	1	1	yes	characteristic
239	#449	—	2	2	no	—
240	#447	—	2	2	no	—
241	#430	C₂²×C₃₇	1	2	yes	complemented
242	#424	C₂²×C₃₇	1	2	yes	complemented
243	#421	C₂²×C₃₇	1	2	yes	—
244	#418	C₂²×C₃₇	1	1	yes	characteristic
245	#418	C₂²×C₃₇	1	2	yes	—
246	#418	C₂²×C₃₇	1	2	yes	complemented
247	#416	C₂²×C₃₇	1	1	yes	characteristic
248	#413	—	2	2	no	—
249	#413	C₂²×C₃₇	1	2	yes	—
250	#413	C₂²×C₃₇	1	1	yes	characteristic
251	C₂×#100	—	2	2	no	—
252	C₂×#100	C₂²×C₃₇	1	2	yes	—
253	C₂×#100	C₂²×C₃₇	1	2	yes	complemented
254	#410	C₂²×C₃₇	1	1	yes	characteristic
255	#408	C₂²×C₃₇	1	1	yes	characteristic
256	#344	C₂²×C₃₇	1	2	yes	complemented
257	#344	C₂²×C₃₇	1	2	yes	complemented
258	#341	C₂²×C₃₇	1	2	yes	complemented
259	H(3,ℤ/4)	C₂²×C₃₇	1	2	yes	complemented
260	C₃₇	#29902	1	1	yes	characteristic, direct product factor, Sylow
261	H(5,𝔽₂)	—	4	2	no	—
262	H(5,𝔽₂)	—	4	2	no	—
263	C₂×#41	—	2	1	no	—
264	C₂×#41	D₄×C₃₇	1	2	yes	—
265	C₂×#41	C₂³×C₃₇	1	1	yes	characteristic
266	C₂×#41	C₂³×C₃₇	1	1	yes	characteristic
267	C₂²×D₄	—	2	2	no	—
268	C₂²×D₄	—	2	1	no	—
269	C₂²×D₄	D₄×C₃₇	1	2	yes	—
270	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
271	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
272	AGL(1,ℤ/8)	—	4	2	no	—
273	C₂×SD₁₆	—	2	1	no	—
274	C₂×D₈	—	2	2	no	—
275	C₂×D₈	—	2	1	no	—
276	C₂×D₈	—	4	2	no	—
277	#131	—	4	2	no	—
278	#131	—	4	2	no	—
279	C₂×M₁₆	—	2	2	no	—
280	C₂×M₁₆	—	2	2	no	—
281	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
282	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
283	C₂×M₁₆	C₂³×C₃₇	1	1	yes	characteristic
284	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
285	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
286	#127	—	2	1	no	—
287	#124	—	2	1	no	—
288	#121	—	2	2	no	—
289	#120	—	2	2	no	—
290	#117	C₂³×C₃₇	1	1	yes	characteristic
291	#117	C₂³×C₃₇	1	2	yes	—
292	#108	—	4	2	no	—
293	C₄⋊C₈	—	4	2	no	—
294	#104	—	4	2	no	—
295	#103	—	2	1	no	—
296	#102	—	2	1	no	—
297	#102	—	2	2	no	—
298	#102	—	4	2	no	—
299	#102	—	4	2	no	—
300	#101	—	2	2	no	—
301	#101	—	2	1	no	—
302	#100	—	2	2	no	—
303	#100	—	2	4	no	—
304	#100	—	2	1	no	—
305	#100	—	4	2	no	—
306	#99	—	2	2	no	—
307	C₂²⋊C₈	—	2	2	no	—
308	C₂⁴	—	2	2	no	—
309	C₂⁴	—	2	1	no	—
310	C₂⁴	—	2	1	no	—
311	#41	—	2	2	no	—
312	#41	—	2	2	no	—
313	#41	—	2	2	no	—
314	#41	—	2	2	no	—
315	#41	—	4	2	no	—
316	#41	—	4	2	no	—
317	#41	—	4	4	no	—
318	C₂×Q₈	C₂×D₄×C₃₇	1	1	yes	characteristic
319	C₂×Q₈	#41×C₃₇	1	1	yes	characteristic
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	4	2	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	—	4	8	no	—
333	C₂×D₄	—	4	4	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	C₂×D₄×C₃₇	1	1	yes	characteristic
336	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
337	C₂×D₄	#41×C₃₇	1	2	yes	—
338	C₂×D₄	#41×C₃₇	1	1	yes	characteristic
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
342	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
343	SD₁₆	—	4	2	no	—
344	D₈	—	4	4	no	—
345	D₈	—	4	2	no	—
346	M₁₆	—	2	2	no	—
347	M₁₆	—	2	2	no	—
348	M₁₆	—	2	2	no	—
349	M₁₆	—	2	2	no	—
350	M₁₆	—	2	2	no	—
351	M₁₆	—	2	2	no	—
352	M₁₆	—	2	2	no	—
353	M₁₆	—	4	2	no	—
354	M₁₆	—	4	2	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	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	—	4	2	no	—
362	C₂×C₈	—	4	2	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₂²⋊C₄	—	2	2	no	—
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	4	2	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	2	no	—
370	C₂³	—	2	2	no	—
371	C₂³	—	2	1	no	—
372	C₂³	—	4	4	no	—
373	C₂³	—	4	2	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	16	1	no	—
377	C₂³	—	16	1	no	—
378	C₂³	—	16	2	no	—
379	C₂³	#123×C₃₇	1	2	yes	—
380	C₂³	C₂×#41×C₃₇	1	1	yes	characteristic
381	Q₈	—	2	2	no	—
382	Q₈	—	2	1	no	—
383	Q₈	—	2	1	no	—
384	D₄	—	2	4	no	—
385	D₄	—	2	2	no	—
386	D₄	—	2	1	no	—
387	D₄	—	2	2	no	—
388	D₄	—	2	1	no	—
389	D₄	—	2	2	no	—
390	D₄	—	4	4	no	—
391	D₄	—	4	4	no	—
392	D₄	—	4	2	no	—
393	D₄	—	4	1	no	—
394	D₄	—	4	1	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	16	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	#123×C₃₇	1	2	yes	—
406	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
407	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
408	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
409	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
410	C₈	—	4	1	no	—
411	C₈	—	4	2	no	—
412	C₈	—	4	2	no	—
413	C₈	—	4	1	no	—
414	C₈	—	4	2	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	4	1	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	8	2	no	—
421	C₂²	—	8	1	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	8	1	no	—
424	C₂²	—	16	2	no	—
425	C₂²	—	16	2	no	—
426	C₂²	—	16	4	no	—
427	C₂²	C₂×#123×C₃₇	1	1	yes	characteristic
428	C₂²	C₃₇×#538	1	2	yes	—
429	C₄	—	2	2	no	—
430	C₄	—	4	1	no	—
431	C₄	—	8	1	no	—
432	C₄	—	8	2	no	—
433	C₄	C₃₇×#534	1	1	yes	characteristic
434	C₄	C₃₇×#534	1	1	yes	characteristic
435	C₄	C₃₇×#538	1	2	yes	—
436	C₂	—	2	1	no	—
437	C₂	—	2	2	no	—
438	C₂	—	4	2	no	—
439	C₂	—	8	2	no	—
440	C₂	—	8	1	no	—
441	C₂	—	16	1	no	—
442	C₂	C₃₇×#2622	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃₇	#2622
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₃₇×#3008	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₇ ◁ C₂²×C₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₇×#2888	C₂	semidirect
3. C₃₇×#2081	C₂	semidirect
4. C₃₇×#2080	C₂	semidirect
5. C₃₇×#2048	C₂	semidirect
6. C₃₇×#2045	C₂	semidirect
7. C₃₇×#1914	C₂	semidirect
8. C₃₇×#1910	C₂	semidirect
9. C₃₇×#1868	C₂	semidirect
10. C₃₇×#1858	C₂	semidirect
11. C₃₇×#1795	C₂	semidirect
20. C₃₇×#430	C₂²	semidirect
21. C₃₇×#424	C₂²	semidirect
25. C₃₇×#418	C₂²	semidirect
32. C₂×#100×C₃₇	C₂²	semidirect
35. C₃₇×#344	C₂²	semidirect
36. C₃₇×#344	C₂²	semidirect
37. C₃₇×#341	C₂²	semidirect
38. C₃₇×H(3,ℤ/4)	C₂²	semidirect
193. #29902	C₃₇	direct (N × H)
216. #2888	C₂×C₃₇	semidirect
217. #2081	C₂×C₃₇	semidirect
218. #2080	C₂×C₃₇	semidirect
219. #2048	C₂×C₃₇	semidirect
220. #2045	C₂×C₃₇	semidirect
221. #1914	C₂×C₃₇	semidirect
222. #1910	C₂×C₃₇	semidirect
223. #1868	C₂×C₃₇	semidirect
224. #1858	C₂×C₃₇	semidirect
225. #1795	C₂×C₃₇	semidirect
241. #430	C₂²×C₃₇	semidirect
242. #424	C₂²×C₃₇	semidirect
246. #418	C₂²×C₃₇	semidirect
253. C₂×#100	C₂²×C₃₇	semidirect
256. #344	C₂²×C₃₇	semidirect
257. #344	C₂²×C₃₇	semidirect
258. #341	C₂²×C₃₇	semidirect
259. H(3,ℤ/4)	C₂²×C₃₇	semidirect
260. C₃₇	#29902	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×#3008	2
C₃₇×#2888	2
C₃₇×#2081	2
C₃₇×#2080	2
C₃₇×#2048	2
C₃₇×#2045	2
C₃₇×#1914	2
C₃₇×#1910	2
C₃₇×#1868	2
C₃₇×#1858	2
C₃₇×#1795	2
#29902	37

Subgroups — C37×#29902 #22651155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#29902 #22651155