Subgroups — C₃₇×#28502 #22649755

Order 9472.

1062 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3154	C₂	1	2	yes	maximal, complemented
2	C₂×C₃₇×#492	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#471	C₂	1	2	yes	maximal, complemented
4	C₃₇×#3057	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₇×#443	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2005	C₂	1	2	yes	maximal, complemented
7	C₃₇×#2002	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1977	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1772	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#137×C₃₇	C₂²	1	2	yes	—
11	C₂×AGL(1,ℤ/8)×C₃₇	C₂²	1	2	yes	—
12	C₂×#135×C₃₇	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	—
14	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	—
15	C₂×#131×C₃₇	C₂²	1	2	yes	—
16	C₃₇×#536	C₂²	1	2	yes	—
17	C₃₇×#535	C₂²	1	2	yes	—
18	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
19	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
20	C₃₇×#497	—	2	2	no	—
21	C₃₇×#496	—	2	2	no	—
22	C₃₇×#495	—	2	2	no	—
23	C₃₇×#492	—	2	2	no	—
24	C₃₇×#492	—	2	4	no	—
25	C₃₇×#471	—	2	8	no	—
26	C₃₇×#468	—	2	4	no	—
27	C₃₇×#465	—	2	4	no	—
28	C₃₇×#443	—	2	4	no	—
29	C₂×#108×C₃₇	C₂²	1	1	yes	characteristic
30	C₂×#108×C₃₇	C₂²	1	1	yes	characteristic
31	C₃₇×#427	C₂²	1	1	yes	characteristic
32	C₂×#104×C₃₇	C₂²	1	2	yes	—
33	C₃₇×#419	C₂²	1	2	yes	—
34	C₃₇×#418	C₂²	1	2	yes	—
35	C₂×#101×C₃₇	C₂²	1	2	yes	—
36	C₂×#100×C₃₇	C₂²	1	2	yes	—
37	C₃₇×#405	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
39	C₃₇×#339	C₂²	1	2	yes	—
40	C₂×#41×C₃₇	C₂³	1	2	yes	—
41	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
42	C₂²×D₄×C₃₇	—	4	1	no	—
43	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
44	#137×C₃₇	—	2	4	no	—
45	#137×C₃₇	—	4	2	no	—
46	AGL(1,ℤ/8)×C₃₇	—	2	4	no	—
47	AGL(1,ℤ/8)×C₃₇	—	4	2	no	—
48	#135×C₃₇	—	2	2	no	—
49	#135×C₃₇	—	2	2	no	—
50	C₂×Q₁₆×C₃₇	—	2	2	no	—
51	C₂×Q₁₆×C₃₇	D₄	1	1	yes	characteristic, complemented
52	C₂×SD₁₆×C₃₇	—	2	2	no	—
53	C₂×SD₁₆×C₃₇	—	2	2	no	—
54	C₂×SD₁₆×C₃₇	—	2	2	no	—
55	C₂×SD₁₆×C₃₇	—	2	2	no	—
56	C₂×SD₁₆×C₃₇	—	2	4	no	—
57	C₂×SD₁₆×C₃₇	—	2	4	no	—
58	C₂×SD₁₆×C₃₇	—	2	4	no	—
59	C₂×SD₁₆×C₃₇	—	2	2	no	—
60	C₂×SD₁₆×C₃₇	—	2	2	no	—
61	C₂×SD₁₆×C₃₇	—	2	4	no	—
62	C₂×SD₁₆×C₃₇	D₄	1	2	yes	complemented
63	C₂×D₈×C₃₇	—	2	2	no	—
64	C₂×D₈×C₃₇	D₄	1	1	yes	characteristic, complemented
65	#131×C₃₇	—	2	4	no	—
66	#131×C₃₇	—	2	4	no	—
67	C₂×M₁₆×C₃₇	—	2	2	no	—
68	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
69	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
70	C₂²×C₈×C₃₇	—	2	2	no	—
71	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
73	C₄⋊Q₈×C₃₇	—	2	2	no	—
74	C₄⋊Q₈×C₃₇	—	2	2	no	—
75	C₄⋊Q₈×C₃₇	—	4	1	no	—
76	#127×C₃₇	—	2	2	no	—
77	#127×C₃₇	—	2	2	no	—
78	#127×C₃₇	—	4	1	no	—
79	#124×C₃₇	—	2	2	no	—
80	#124×C₃₇	—	2	2	no	—
81	#123×C₃₇	—	4	2	no	—
82	C₂²⋊Q₈×C₃₇	—	2	4	no	—
83	#121×C₃₇	—	2	4	no	—
84	#120×C₃₇	—	4	2	no	—
85	#117×C₃₇	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₃₇	—	4	1	no	—
87	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
88	#108×C₃₇	—	2	2	no	—
89	#108×C₃₇	D₄	1	4	yes	complemented
90	#107×C₃₇	D₄	1	2	yes	complemented
91	#106×C₃₇	D₄	1	2	yes	complemented
92	#104×C₃₇	—	2	4	no	—
93	#103×C₃₇	—	2	4	no	—
94	#102×C₃₇	—	2	4	no	—
95	#101×C₃₇	—	2	4	no	—
96	#100×C₃₇	—	2	4	no	—
97	#97×C₃₇	—	2	2	no	—
98	C₄×C₈×C₃₇	—	2	2	no	—
99	C₄×C₈×C₃₇	D₄	1	4	yes	complemented
100	C₂⁴×C₃₇	—	2	2	no	—
101	#41×C₃₇	—	2	2	no	—
102	#41×C₃₇	—	2	2	no	—
103	#41×C₃₇	—	2	2	no	—
104	#41×C₃₇	—	2	2	no	—
105	C₂×Q₈×C₃₇	—	2	2	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	—	2	2	no	—
111	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
112	C₂×D₄×C₃₇	—	2	2	no	—
113	C₂×D₄×C₃₇	—	2	2	no	—
114	C₂×D₄×C₃₇	—	2	2	no	—
115	C₂×D₄×C₃₇	—	2	2	no	—
116	C₂×D₄×C₃₇	—	2	2	no	—
117	C₂×D₄×C₃₇	—	2	2	no	—
118	C₂×D₄×C₃₇	—	2	2	no	—
119	C₂×D₄×C₃₇	—	4	4	no	—
120	C₂×D₄×C₃₇	—	4	4	no	—
121	C₂×D₄×C₃₇	—	8	4	no	—
122	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₃₇	—	2	1	no	—
124	C₂²×C₄×C₃₇	—	2	2	no	—
125	C₂²×C₄×C₃₇	—	2	2	no	—
126	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
127	Q₁₆×C₃₇	—	2	2	no	—
128	Q₁₆×C₃₇	—	4	4	no	—
129	SD₁₆×C₃₇	—	2	4	no	—
130	SD₁₆×C₃₇	—	4	4	no	—
131	SD₁₆×C₃₇	—	4	4	no	—
132	SD₁₆×C₃₇	—	4	4	no	—
133	SD₁₆×C₃₇	—	4	4	no	—
134	SD₁₆×C₃₇	—	4	4	no	—
135	SD₁₆×C₃₇	—	4	4	no	—
136	D₈×C₃₇	—	2	2	no	—
137	D₈×C₃₇	—	4	4	no	—
138	M₁₆×C₃₇	—	2	2	no	—
139	M₁₆×C₃₇	—	2	2	no	—
140	M₁₆×C₃₇	—	2	2	no	—
141	M₁₆×C₃₇	—	4	4	no	—
142	M₁₆×C₃₇	C₂×D₄	1	4	yes	—
143	C₂×C₈×C₃₇	—	2	2	no	—
144	C₂×C₈×C₃₇	—	2	2	no	—
145	C₂×C₈×C₃₇	—	4	4	no	—
146	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
148	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
150	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₃₇	#41	1	2	yes	—
154	C₄⋊C₄×C₃₇	—	4	4	no	—
155	C₄⋊C₄×C₃₇	—	4	4	no	—
156	C₄⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
157	C₂²⋊C₄×C₃₇	—	2	2	no	—
158	C₂²⋊C₄×C₃₇	—	4	4	no	—
159	C₂²⋊C₄×C₃₇	—	4	4	no	—
160	C₄²×C₃₇	—	2	2	no	—
161	C₄²×C₃₇	—	2	1	no	—
162	C₄²×C₃₇	C₂×D₄	1	2	yes	—
163	C₂³×C₃₇	—	2	2	no	—
164	C₂³×C₃₇	—	4	2	no	—
165	C₂³×C₃₇	—	4	2	no	—
166	C₂³×C₃₇	—	4	2	no	—
167	C₂³×C₃₇	—	8	4	no	—
168	C₂³×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
169	Q₈×C₃₇	—	2	2	no	—
170	Q₈×C₃₇	—	2	2	no	—
171	Q₈×C₃₇	—	4	2	no	—
172	Q₈×C₃₇	—	4	2	no	—
173	Q₈×C₃₇	—	4	2	no	—
174	Q₈×C₃₇	—	4	2	no	—
175	D₄×C₃₇	—	2	2	no	—
176	D₄×C₃₇	—	2	2	no	—
177	D₄×C₃₇	—	4	2	no	—
178	D₄×C₃₇	—	4	2	no	—
179	D₄×C₃₇	—	4	2	no	—
180	D₄×C₃₇	—	4	2	no	—
181	D₄×C₃₇	—	4	2	no	—
182	D₄×C₃₇	—	4	2	no	—
183	D₄×C₃₇	—	8	8	no	—
184	D₄×C₃₇	—	16	4	no	—
185	C₂×C₄×C₃₇	—	2	4	no	—
186	C₂×C₄×C₃₇	—	2	2	no	—
187	C₂×C₄×C₃₇	—	2	4	no	—
188	C₂×C₄×C₃₇	—	2	2	no	—
189	C₂×C₄×C₃₇	—	4	2	no	—
190	C₂×C₄×C₃₇	—	4	2	no	—
191	C₂×C₄×C₃₇	—	4	2	no	—
192	C₂×C₄×C₃₇	—	4	2	no	—
193	C₂×C₄×C₃₇	—	4	2	no	—
194	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
200	C₈×C₃₇	—	2	4	no	—
201	C₈×C₃₇	—	4	2	no	—
202	C₈×C₃₇	#121	1	2	yes	—
203	C₈×C₃₇	#121	1	2	yes	—
204	C₈×C₃₇	#127	1	2	yes	—
205	C₈×C₃₇	#127	1	2	yes	—
206	#28502	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂²×C₃₇	—	2	2	no	—
208	C₂²×C₃₇	—	4	4	no	—
209	C₂²×C₃₇	—	4	2	no	—
210	C₂²×C₃₇	—	8	4	no	—
211	C₂²×C₃₇	—	8	4	no	—
212	C₂²×C₃₇	—	8	2	no	—
213	C₂²×C₃₇	—	16	2	no	—
214	C₂²×C₃₇	#535	1	1	yes	characteristic
215	C₂²×C₃₇	D₄²	1	1	yes	characteristic
216	C₂²×C₃₇	#550	1	1	yes	characteristic
217	C₄×C₃₇	—	2	4	no	—
218	C₄×C₃₇	—	4	4	no	—
219	C₄×C₃₇	—	4	2	no	—
220	C₄×C₃₇	—	8	2	no	—
221	C₄×C₃₇	C₂×#121	1	1	yes	characteristic
222	C₄×C₃₇	C₂×#127	1	1	yes	characteristic
223	C₄×C₃₇	D₄²	1	1	yes	characteristic
224	C₄×C₃₇	#550	1	1	yes	characteristic
225	#3154	C₂×C₃₇	1	2	yes	complemented
226	C₂×#492	C₂×C₃₇	1	1	yes	characteristic, complemented
227	C₂×#471	C₂×C₃₇	1	2	yes	complemented
228	#3057	C₂×C₃₇	1	2	yes	complemented
229	C₂×#443	C₂×C₃₇	1	1	yes	characteristic, complemented
230	#2005	C₂×C₃₇	1	2	yes	complemented
231	#2002	C₂×C₃₇	1	2	yes	complemented
232	#1977	C₂×C₃₇	1	2	yes	complemented
233	#1772	C₂×C₃₇	1	1	yes	characteristic, complemented
234	C₂×C₃₇	—	2	1	no	—
235	C₂×C₃₇	—	2	1	no	—
236	C₂×C₃₇	—	8	2	no	—
237	C₂×C₃₇	—	16	2	no	—
238	C₂×C₃₇	#2541	1	1	yes	characteristic
239	C₂×C₃₇	#3291	1	2	yes	—
240	C₂×#137	C₂²×C₃₇	1	2	yes	—
241	C₂×AGL(1,ℤ/8)	C₂²×C₃₇	1	2	yes	—
242	C₂×#135	C₂²×C₃₇	1	1	yes	characteristic
243	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
244	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
245	C₂×#131	C₂²×C₃₇	1	2	yes	—
246	#536	C₂²×C₃₇	1	2	yes	—
247	#535	C₂²×C₃₇	1	2	yes	—
248	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
249	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
250	#497	—	2	2	no	—
251	#496	—	2	2	no	—
252	#495	—	2	2	no	—
253	#492	—	2	2	no	—
254	#492	—	2	4	no	—
255	#471	—	2	8	no	—
256	#468	—	2	4	no	—
257	#465	—	2	4	no	—
258	#443	—	2	4	no	—
259	C₂×#108	C₂²×C₃₇	1	1	yes	characteristic
260	C₂×#108	C₂²×C₃₇	1	1	yes	characteristic
261	#427	C₂²×C₃₇	1	1	yes	characteristic
262	C₂×#104	C₂²×C₃₇	1	2	yes	—
263	#419	C₂²×C₃₇	1	2	yes	—
264	#418	C₂²×C₃₇	1	2	yes	—
265	C₂×#101	C₂²×C₃₇	1	2	yes	—
266	C₂×#100	C₂²×C₃₇	1	2	yes	—
267	#405	C₂²×C₃₇	1	2	yes	—
268	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
269	#339	C₂²×C₃₇	1	2	yes	—
270	C₃₇	#28502	1	1	yes	characteristic, direct product factor, Sylow
271	C₂×#41	C₂³×C₃₇	1	2	yes	—
272	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
273	C₂²×D₄	—	4	1	no	—
274	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
275	#137	—	2	4	no	—
276	#137	—	4	2	no	—
277	AGL(1,ℤ/8)	—	2	4	no	—
278	AGL(1,ℤ/8)	—	4	2	no	—
279	#135	—	2	2	no	—
280	#135	—	2	2	no	—
281	C₂×Q₁₆	—	2	2	no	—
282	C₂×Q₁₆	D₄×C₃₇	1	1	yes	characteristic, complemented
283	C₂×SD₁₆	—	2	2	no	—
284	C₂×SD₁₆	—	2	2	no	—
285	C₂×SD₁₆	—	2	2	no	—
286	C₂×SD₁₆	—	2	2	no	—
287	C₂×SD₁₆	—	2	4	no	—
288	C₂×SD₁₆	—	2	4	no	—
289	C₂×SD₁₆	—	2	4	no	—
290	C₂×SD₁₆	—	2	2	no	—
291	C₂×SD₁₆	—	2	2	no	—
292	C₂×SD₁₆	—	2	4	no	—
293	C₂×SD₁₆	D₄×C₃₇	1	2	yes	complemented
294	C₂×D₈	—	2	2	no	—
295	C₂×D₈	D₄×C₃₇	1	1	yes	characteristic, complemented
296	#131	—	2	4	no	—
297	#131	—	2	4	no	—
298	C₂×M₁₆	—	2	2	no	—
299	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
300	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
301	C₂²×C₈	—	2	2	no	—
302	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
303	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
304	C₄⋊Q₈	—	2	2	no	—
305	C₄⋊Q₈	—	2	2	no	—
306	C₄⋊Q₈	—	4	1	no	—
307	#127	—	2	2	no	—
308	#127	—	2	2	no	—
309	#127	—	4	1	no	—
310	#124	—	2	2	no	—
311	#124	—	2	2	no	—
312	#123	—	4	2	no	—
313	C₂²⋊Q₈	—	2	4	no	—
314	#121	—	2	4	no	—
315	#120	—	4	2	no	—
316	#117	C₂³×C₃₇	1	2	yes	—
317	C₂×C₄⋊C₄	—	4	1	no	—
318	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
319	#108	—	2	2	no	—
320	#108	D₄×C₃₇	1	4	yes	complemented
321	#107	D₄×C₃₇	1	2	yes	complemented
322	#106	D₄×C₃₇	1	2	yes	complemented
323	#104	—	2	4	no	—
324	#103	—	2	4	no	—
325	#102	—	2	4	no	—
326	#101	—	2	4	no	—
327	#100	—	2	4	no	—
328	#97	—	2	2	no	—
329	C₄×C₈	—	2	2	no	—
330	C₄×C₈	D₄×C₃₇	1	4	yes	complemented
331	C₂⁴	—	2	2	no	—
332	#41	—	2	2	no	—
333	#41	—	2	2	no	—
334	#41	—	2	2	no	—
335	#41	—	2	2	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	4	4	no	—
351	C₂×D₄	—	4	4	no	—
352	C₂×D₄	—	8	4	no	—
353	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
358	Q₁₆	—	2	2	no	—
359	Q₁₆	—	4	4	no	—
360	SD₁₆	—	2	4	no	—
361	SD₁₆	—	4	4	no	—
362	SD₁₆	—	4	4	no	—
363	SD₁₆	—	4	4	no	—
364	SD₁₆	—	4	4	no	—
365	SD₁₆	—	4	4	no	—
366	SD₁₆	—	4	4	no	—
367	D₈	—	2	2	no	—
368	D₈	—	4	4	no	—
369	M₁₆	—	2	2	no	—
370	M₁₆	—	2	2	no	—
371	M₁₆	—	2	2	no	—
372	M₁₆	—	4	4	no	—
373	M₁₆	C₂×D₄×C₃₇	1	4	yes	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	4	4	no	—
377	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
378	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
379	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
380	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
381	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
382	C₂×C₈	C₂×D₄×C₃₇	1	1	yes	characteristic
383	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
384	C₂×C₈	#41×C₃₇	1	2	yes	—
385	C₄⋊C₄	—	4	4	no	—
386	C₄⋊C₄	—	4	4	no	—
387	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
388	C₂²⋊C₄	—	2	2	no	—
389	C₂²⋊C₄	—	4	4	no	—
390	C₂²⋊C₄	—	4	4	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	2	1	no	—
393	C₄²	C₂×D₄×C₃₇	1	2	yes	—
394	C₂³	—	2	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	4	2	no	—
398	C₂³	—	8	4	no	—
399	C₂³	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
400	Q₈	—	2	2	no	—
401	Q₈	—	2	2	no	—
402	Q₈	—	4	2	no	—
403	Q₈	—	4	2	no	—
404	Q₈	—	4	2	no	—
405	Q₈	—	4	2	no	—
406	D₄	—	2	2	no	—
407	D₄	—	2	2	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	4	2	no	—
411	D₄	—	4	2	no	—
412	D₄	—	4	2	no	—
413	D₄	—	4	2	no	—
414	D₄	—	8	8	no	—
415	D₄	—	16	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
426	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
427	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
428	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
429	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
430	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
431	C₈	—	2	4	no	—
432	C₈	—	4	2	no	—
433	C₈	#121×C₃₇	1	2	yes	—
434	C₈	#121×C₃₇	1	2	yes	—
435	C₈	#127×C₃₇	1	2	yes	—
436	C₈	#127×C₃₇	1	2	yes	—
437	C₂²	—	2	2	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	8	4	no	—
441	C₂²	—	8	4	no	—
442	C₂²	—	8	2	no	—
443	C₂²	—	16	2	no	—
444	C₂²	C₃₇×#535	1	1	yes	characteristic
445	C₂²	D₄²×C₃₇	1	1	yes	characteristic
446	C₂²	C₃₇×#550	1	1	yes	characteristic
447	C₄	—	2	4	no	—
448	C₄	—	4	4	no	—
449	C₄	—	4	2	no	—
450	C₄	—	8	2	no	—
451	C₄	C₂×#121×C₃₇	1	1	yes	characteristic
452	C₄	C₂×#127×C₃₇	1	1	yes	characteristic
453	C₄	D₄²×C₃₇	1	1	yes	characteristic
454	C₄	C₃₇×#550	1	1	yes	characteristic
455	C₂	—	2	1	no	—
456	C₂	—	2	1	no	—
457	C₂	—	8	2	no	—
458	C₂	—	16	2	no	—
459	C₂	C₃₇×#2541	1	1	yes	characteristic
460	C₂	C₃₇×#3291	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₇	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
LCS	G ▷ C₂²×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
1. C₃₇×#3154	C₂	semidirect
2. C₂×C₃₇×#492	C₂	semidirect
3. C₂×C₃₇×#471	C₂	semidirect
4. C₃₇×#3057	C₂	semidirect
5. C₂×C₃₇×#443	C₂	semidirect
6. C₃₇×#2005	C₂	semidirect
7. C₃₇×#2002	C₂	semidirect
8. C₃₇×#1977	C₂	semidirect
9. C₃₇×#1772	C₂	semidirect
51. C₂×Q₁₆×C₃₇	D₄	semidirect
62. C₂×SD₁₆×C₃₇	D₄	semidirect
64. C₂×D₈×C₃₇	D₄	semidirect
89. #108×C₃₇	D₄	semidirect
90. #107×C₃₇	D₄	semidirect
91. #106×C₃₇	D₄	semidirect
99. C₄×C₈×C₃₇	D₄	semidirect
206. #28502	C₃₇	direct (N × H)
225. #3154	C₂×C₃₇	semidirect
226. C₂×#492	C₂×C₃₇	semidirect
227. C₂×#471	C₂×C₃₇	semidirect
228. #3057	C₂×C₃₇	semidirect
229. C₂×#443	C₂×C₃₇	semidirect
230. #2005	C₂×C₃₇	semidirect
231. #2002	C₂×C₃₇	semidirect
232. #1977	C₂×C₃₇	semidirect
233. #1772	C₂×C₃₇	semidirect
270. C₃₇	#28502	direct (N × H)
282. C₂×Q₁₆	D₄×C₃₇	semidirect
293. C₂×SD₁₆	D₄×C₃₇	semidirect
295. C₂×D₈	D₄×C₃₇	semidirect
320. #108	D₄×C₃₇	semidirect
321. #107	D₄×C₃₇	semidirect
322. #106	D₄×C₃₇	semidirect
330. C₄×C₈	D₄×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₃₇×#3154	2
C₂×C₃₇×#492	2
C₂×C₃₇×#471	2
C₃₇×#3057	2
C₂×C₃₇×#443	2
C₃₇×#2005	2
C₃₇×#2002	2
C₃₇×#1977	2
C₃₇×#1772	2
#28502	37

Subgroups — C37×#28502 #22649755

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28502 #22649755