Subgroups — C₃₇×#29823 #22651076

Order 9472.

782 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	C₂×C₃₇×#497	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×#3040	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#3039	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#2923	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#2047	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2046	C₂	1	2	yes	maximal, complemented
7	C₃₇×#2020	C₂	1	2	yes	maximal, complemented
8	C₃₇×#2019	C₂	1	2	yes	maximal
9	C₃₇×#1967	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1966	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1838	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₃₇	C₂²	1	2	yes	—
13	C₂×#137×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×AGL(1,ℤ/8)×C₃₇	C₂²	1	1	yes	characteristic
15	C₂²×Q₁₆×C₃₇	C₂²	1	2	yes	—
16	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	—
17	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
19	C₄×#41×C₃₇	C₂²	1	1	yes	characteristic
20	C₃₇×#497	—	2	2	no	—
21	C₃₇×#497	—	2	2	no	—
22	C₃₇×#464	—	2	2	no	—
23	C₃₇×#463	—	2	2	no	—
24	C₃₇×#462	—	2	2	no	—
25	C₃₇×#461	—	2	2	no	—
26	C₃₇×#433	—	2	2	no	—
27	C₃₇×#432	—	2	2	no	—
28	C₃₇×#424	C₂²	1	2	yes	—
29	C₃₇×#423	C₂²	1	1	yes	characteristic
30	C₃₇×#423	C₂²	1	1	yes	characteristic
31	C₃₇×#419	C₂²	1	2	yes	—
32	C₃₇×#419	C₂²	1	1	yes	characteristic
33	C₃₇×#418	C₂²	1	1	yes	characteristic
34	C₂×#101×C₃₇	C₂²	1	2	yes	—
35	C₂×#101×C₃₇	C₂²	1	2	yes	—
36	C₂×#101×C₃₇	C₂²	1	2	yes	—
37	C₂×#100×C₃₇	C₂²	1	2	yes	—
38	C₃₇×#408	C₂²	1	2	yes	—
39	C₄×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
40	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
41	C₃₇×#341	C₂²	1	2	yes	—
42	C₃₇×#341	C₂²	1	2	yes	—
43	C₂×#41×C₃₇	C₂³	1	1	yes	characteristic
44	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
46	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
47	#137×C₃₇	—	4	2	no	—
48	#137×C₃₇	—	4	2	no	—
49	#137×C₃₇	—	4	2	no	—
50	AGL(1,ℤ/8)×C₃₇	—	4	2	no	—
51	C₂×Q₁₆×C₃₇	—	2	2	no	—
52	C₂×Q₁₆×C₃₇	—	2	1	no	—
53	C₂×Q₁₆×C₃₇	—	2	4	no	—
54	C₂×Q₁₆×C₃₇	—	4	2	no	—
55	C₂×Q₁₆×C₃₇	—	4	2	no	—
56	C₂×SD₁₆×C₃₇	—	2	1	no	—
57	C₂×SD₁₆×C₃₇	—	2	2	no	—
58	C₂×SD₁₆×C₃₇	—	2	1	no	—
59	C₂×SD₁₆×C₃₇	—	2	4	no	—
60	C₂×SD₁₆×C₃₇	—	4	2	no	—
61	C₂×SD₁₆×C₃₇	—	4	2	no	—
62	C₂×D₈×C₃₇	—	2	1	no	—
63	C₂×M₁₆×C₃₇	C₂³	1	1	yes	characteristic
64	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
65	C₂×M₁₆×C₃₇	C₂³	1	1	yes	characteristic
66	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
67	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
68	C₄⋊Q₈×C₃₇	—	2	2	no	—
69	C₄⋊Q₈×C₃₇	—	2	1	no	—
70	C₄⋊Q₈×C₃₇	—	2	1	no	—
71	#124×C₃₇	—	2	2	no	—
72	#124×C₃₇	—	2	1	no	—
73	#124×C₃₇	—	2	1	no	—
74	C₄×Q₈×C₃₇	D₄	1	2	yes	—
75	C₄×D₄×C₃₇	—	2	2	no	—
76	C₄×D₄×C₃₇	D₄	1	2	yes	—
77	#117×C₃₇	—	2	1	no	—
78	#117×C₃₇	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
81	C₂×C₄²×C₃₇	—	2	1	no	—
82	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₃₇	—	2	4	no	—
84	C₄⋊C₈×C₃₇	—	2	2	no	—
85	C₄⋊C₈×C₃₇	—	2	2	no	—
86	#103×C₃₇	—	2	4	no	—
87	#103×C₃₇	—	2	2	no	—
88	#102×C₃₇	—	2	2	no	—
89	#101×C₃₇	—	4	2	no	—
90	#101×C₃₇	—	4	2	no	—
91	#101×C₃₇	—	4	2	no	—
92	#100×C₃₇	—	4	2	no	—
93	C₂²⋊C₈×C₃₇	—	2	4	no	—
94	#97×C₃₇	—	2	1	no	—
95	#97×C₃₇	D₄	1	2	yes	—
96	#97×C₃₇	D₄	1	2	yes	—
97	C₄×C₈×C₃₇	—	2	1	no	—
98	C₂⁴×C₃₇	—	2	1	no	—
99	#41×C₃₇	—	2	2	no	—
100	#41×C₃₇	—	2	2	no	—
101	C₂×Q₈×C₃₇	—	2	1	no	—
102	C₂×Q₈×C₃₇	—	2	2	no	—
103	C₂×Q₈×C₃₇	—	2	1	no	—
104	C₂×Q₈×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	1	yes	characteristic
112	C₂×D₄×C₃₇	—	2	1	no	—
113	C₂×D₄×C₃₇	—	2	1	no	—
114	C₂×D₄×C₃₇	—	2	1	no	—
115	C₂×D₄×C₃₇	—	2	2	no	—
116	C₂×D₄×C₃₇	—	2	2	no	—
117	C₂×D₄×C₃₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₃₇	—	2	1	no	—
119	C₂²×C₄×C₃₇	—	2	2	no	—
120	C₂²×C₄×C₃₇	—	2	1	no	—
121	C₂²×C₄×C₃₇	—	2	2	no	—
122	C₂²×C₄×C₃₇	#41	1	2	yes	—
123	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
124	Q₁₆×C₃₇	—	4	8	no	—
125	Q₁₆×C₃₇	—	4	2	no	—
126	Q₁₆×C₃₇	—	4	4	no	—
127	SD₁₆×C₃₇	—	4	8	no	—
128	SD₁₆×C₃₇	—	4	2	no	—
129	SD₁₆×C₃₇	—	4	4	no	—
130	SD₁₆×C₃₇	—	4	2	no	—
131	D₈×C₃₇	—	4	2	no	—
132	M₁₆×C₃₇	—	2	2	no	—
133	M₁₆×C₃₇	—	2	2	no	—
134	M₁₆×C₃₇	—	2	2	no	—
135	M₁₆×C₃₇	—	2	2	no	—
136	M₁₆×C₃₇	—	2	2	no	—
137	M₁₆×C₃₇	—	2	2	no	—
138	C₂×C₈×C₃₇	—	2	2	no	—
139	C₂×C₈×C₃₇	—	2	2	no	—
140	C₂×C₈×C₃₇	—	2	2	no	—
141	C₂×C₈×C₃₇	—	2	1	no	—
142	C₂×C₈×C₃₇	—	2	1	no	—
143	C₂×C₈×C₃₇	—	2	2	no	—
144	C₂×C₈×C₃₇	C₂×D₄	1	4	yes	—
145	C₄⋊C₄×C₃₇	—	2	2	no	—
146	C₄⋊C₄×C₃₇	—	4	2	no	—
147	C₄⋊C₄×C₃₇	—	4	2	no	—
148	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
149	C₂²⋊C₄×C₃₇	—	2	1	no	—
150	C₂²⋊C₄×C₃₇	—	2	2	no	—
151	C₂²⋊C₄×C₃₇	—	4	2	no	—
152	C₂²⋊C₄×C₃₇	—	4	2	no	—
153	C₄²×C₃₇	—	2	2	no	—
154	C₄²×C₃₇	—	2	1	no	—
155	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₃₇	C₂×D₄	1	2	yes	—
158	C₂³×C₃₇	—	2	1	no	—
159	C₂³×C₃₇	—	4	1	no	—
160	C₂³×C₃₇	—	4	2	no	—
161	C₂³×C₃₇	—	8	2	no	—
162	C₂³×C₃₇	C₂×#41	1	1	yes	characteristic
163	Q₈×C₃₇	—	2	1	no	—
164	Q₈×C₃₇	—	2	1	no	—
165	Q₈×C₃₇	—	4	2	no	—
166	Q₈×C₃₇	—	4	1	no	—
167	Q₈×C₃₇	—	4	2	no	—
168	Q₈×C₃₇	—	4	2	no	—
169	Q₈×C₃₇	—	4	2	no	—
170	Q₈×C₃₇	—	4	1	no	—
171	Q₈×C₃₇	—	4	2	no	—
172	D₄×C₃₇	—	2	1	no	—
173	D₄×C₃₇	—	2	1	no	—
174	D₄×C₃₇	—	4	2	no	—
175	D₄×C₃₇	—	4	1	no	—
176	D₄×C₃₇	—	4	2	no	—
177	D₄×C₃₇	—	4	1	no	—
178	C₂×C₄×C₃₇	—	2	2	no	—
179	C₂×C₄×C₃₇	—	2	1	no	—
180	C₂×C₄×C₃₇	—	4	2	no	—
181	C₂×C₄×C₃₇	—	4	2	no	—
182	C₂×C₄×C₃₇	—	4	1	no	—
183	C₂×C₄×C₃₇	—	4	2	no	—
184	C₂×C₄×C₃₇	—	4	2	no	—
185	C₂×C₄×C₃₇	—	4	2	no	—
186	C₂×C₄×C₃₇	—	4	2	no	—
187	C₂×C₄×C₃₇	—	8	2	no	—
188	C₂×C₄×C₃₇	#121	1	2	yes	—
189	C₂×C₄×C₃₇	#121	1	2	yes	—
190	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
193	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
194	C₈×C₃₇	—	2	4	no	—
195	C₈×C₃₇	—	4	2	no	—
196	C₈×C₃₇	—	4	1	no	—
197	C₈×C₃₇	—	4	1	no	—
198	C₈×C₃₇	—	4	2	no	—
199	#29823	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂²×C₃₇	—	2	2	no	—
201	C₂²×C₃₇	—	4	1	no	—
202	C₂²×C₃₇	—	4	2	no	—
203	C₂²×C₃₇	—	8	1	no	—
204	C₂²×C₃₇	—	8	2	no	—
205	C₂²×C₃₇	—	16	2	no	—
206	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
207	C₂²×C₃₇	#540	1	2	yes	—
208	C₄×C₃₇	—	2	2	no	—
209	C₄×C₃₇	—	2	2	no	—
210	C₄×C₃₇	—	4	1	no	—
211	C₄×C₃₇	—	4	2	no	—
212	C₄×C₃₇	—	8	1	no	—
213	C₄×C₃₇	—	8	2	no	—
214	C₄×C₃₇	#535	1	2	yes	—
215	C₄×C₃₇	#535	1	1	yes	characteristic
216	C₄×C₃₇	#535	1	1	yes	characteristic
217	C₂×#497	C₂×C₃₇	1	1	yes	characteristic, complemented
218	#3040	C₂×C₃₇	1	1	yes	characteristic
219	#3039	C₂×C₃₇	1	1	yes	characteristic, complemented
220	#2923	C₂×C₃₇	1	1	yes	characteristic, complemented
221	#2047	C₂×C₃₇	1	2	yes	complemented
222	#2046	C₂×C₃₇	1	2	yes	complemented
223	#2020	C₂×C₃₇	1	2	yes	complemented
224	#2019	C₂×C₃₇	1	2	yes	—
225	#1967	C₂×C₃₇	1	1	yes	characteristic, complemented
226	#1966	C₂×C₃₇	1	1	yes	characteristic, complemented
227	#1838	C₂×C₃₇	1	1	yes	characteristic, complemented
228	C₂×C₃₇	—	2	2	no	—
229	C₂×C₃₇	—	8	1	no	—
230	C₂×C₃₇	—	16	1	no	—
231	C₂×C₃₇	#2619	1	1	yes	characteristic
232	C₂×C₃₇	#3069	1	2	yes	—
233	C₂×#137	C₂²×C₃₇	1	2	yes	—
234	C₂×#137	C₂²×C₃₇	1	1	yes	characteristic
235	C₂×AGL(1,ℤ/8)	C₂²×C₃₇	1	1	yes	characteristic
236	C₂²×Q₁₆	C₂²×C₃₇	1	2	yes	—
237	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
238	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
239	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
240	C₄×#41	C₂²×C₃₇	1	1	yes	characteristic
241	#497	—	2	2	no	—
242	#497	—	2	2	no	—
243	#464	—	2	2	no	—
244	#463	—	2	2	no	—
245	#462	—	2	2	no	—
246	#461	—	2	2	no	—
247	#433	—	2	2	no	—
248	#432	—	2	2	no	—
249	#424	C₂²×C₃₇	1	2	yes	—
250	#423	C₂²×C₃₇	1	1	yes	characteristic
251	#423	C₂²×C₃₇	1	1	yes	characteristic
252	#419	C₂²×C₃₇	1	2	yes	—
253	#419	C₂²×C₃₇	1	1	yes	characteristic
254	#418	C₂²×C₃₇	1	1	yes	characteristic
255	C₂×#101	C₂²×C₃₇	1	2	yes	—
256	C₂×#101	C₂²×C₃₇	1	2	yes	—
257	C₂×#101	C₂²×C₃₇	1	2	yes	—
258	C₂×#100	C₂²×C₃₇	1	2	yes	—
259	#408	C₂²×C₃₇	1	2	yes	—
260	C₄×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
261	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
262	#341	C₂²×C₃₇	1	2	yes	—
263	#341	C₂²×C₃₇	1	2	yes	—
264	C₃₇	#29823	1	1	yes	characteristic, direct product factor, Sylow
265	C₂×#41	C₂³×C₃₇	1	1	yes	characteristic
266	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
267	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
268	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
269	#137	—	4	2	no	—
270	#137	—	4	2	no	—
271	#137	—	4	2	no	—
272	AGL(1,ℤ/8)	—	4	2	no	—
273	C₂×Q₁₆	—	2	2	no	—
274	C₂×Q₁₆	—	2	1	no	—
275	C₂×Q₁₆	—	2	4	no	—
276	C₂×Q₁₆	—	4	2	no	—
277	C₂×Q₁₆	—	4	2	no	—
278	C₂×SD₁₆	—	2	1	no	—
279	C₂×SD₁₆	—	2	2	no	—
280	C₂×SD₁₆	—	2	1	no	—
281	C₂×SD₁₆	—	2	4	no	—
282	C₂×SD₁₆	—	4	2	no	—
283	C₂×SD₁₆	—	4	2	no	—
284	C₂×D₈	—	2	1	no	—
285	C₂×M₁₆	C₂³×C₃₇	1	1	yes	characteristic
286	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
287	C₂×M₁₆	C₂³×C₃₇	1	1	yes	characteristic
288	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
289	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
290	C₄⋊Q₈	—	2	2	no	—
291	C₄⋊Q₈	—	2	1	no	—
292	C₄⋊Q₈	—	2	1	no	—
293	#124	—	2	2	no	—
294	#124	—	2	1	no	—
295	#124	—	2	1	no	—
296	C₄×Q₈	D₄×C₃₇	1	2	yes	—
297	C₄×D₄	—	2	2	no	—
298	C₄×D₄	D₄×C₃₇	1	2	yes	—
299	#117	—	2	1	no	—
300	#117	C₂³×C₃₇	1	1	yes	characteristic
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₂²⋊C₄	—	2	2	no	—
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
305	C₄⋊C₈	—	2	4	no	—
306	C₄⋊C₈	—	2	2	no	—
307	C₄⋊C₈	—	2	2	no	—
308	#103	—	2	4	no	—
309	#103	—	2	2	no	—
310	#102	—	2	2	no	—
311	#101	—	4	2	no	—
312	#101	—	4	2	no	—
313	#101	—	4	2	no	—
314	#100	—	4	2	no	—
315	C₂²⋊C₈	—	2	4	no	—
316	#97	—	2	1	no	—
317	#97	D₄×C₃₇	1	2	yes	—
318	#97	D₄×C₃₇	1	2	yes	—
319	C₄×C₈	—	2	1	no	—
320	C₂⁴	—	2	1	no	—
321	#41	—	2	2	no	—
322	#41	—	2	2	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	C₂×D₄×C₃₇	1	1	yes	characteristic
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	C₂×D₄×C₃₇	1	1	yes	characteristic
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	#41×C₃₇	1	2	yes	—
345	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
346	Q₁₆	—	4	8	no	—
347	Q₁₆	—	4	2	no	—
348	Q₁₆	—	4	4	no	—
349	SD₁₆	—	4	8	no	—
350	SD₁₆	—	4	2	no	—
351	SD₁₆	—	4	4	no	—
352	SD₁₆	—	4	2	no	—
353	D₈	—	4	2	no	—
354	M₁₆	—	2	2	no	—
355	M₁₆	—	2	2	no	—
356	M₁₆	—	2	2	no	—
357	M₁₆	—	2	2	no	—
358	M₁₆	—	2	2	no	—
359	M₁₆	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	C₂×D₄×C₃₇	1	4	yes	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	4	2	no	—
369	C₄⋊C₄	—	4	2	no	—
370	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
371	C₂²⋊C₄	—	2	1	no	—
372	C₂²⋊C₄	—	2	2	no	—
373	C₂²⋊C₄	—	4	2	no	—
374	C₂²⋊C₄	—	4	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	1	no	—
377	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
378	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
379	C₄²	C₂×D₄×C₃₇	1	2	yes	—
380	C₂³	—	2	1	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	2	no	—
383	C₂³	—	8	2	no	—
384	C₂³	C₂×#41×C₃₇	1	1	yes	characteristic
385	Q₈	—	2	1	no	—
386	Q₈	—	2	1	no	—
387	Q₈	—	4	2	no	—
388	Q₈	—	4	1	no	—
389	Q₈	—	4	2	no	—
390	Q₈	—	4	2	no	—
391	Q₈	—	4	2	no	—
392	Q₈	—	4	1	no	—
393	Q₈	—	4	2	no	—
394	D₄	—	2	1	no	—
395	D₄	—	2	1	no	—
396	D₄	—	4	2	no	—
397	D₄	—	4	1	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	8	2	no	—
410	C₂×C₄	#121×C₃₇	1	2	yes	—
411	C₂×C₄	#121×C₃₇	1	2	yes	—
412	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
414	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
415	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
416	C₈	—	2	4	no	—
417	C₈	—	4	1	no	—
418	C₈	—	4	1	no	—
419	C₈	—	4	2	no	—
420	C₈	—	4	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	8	1	no	—
425	C₂²	—	8	2	no	—
426	C₂²	—	16	2	no	—
427	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
428	C₂²	C₃₇×#540	1	2	yes	—
429	C₄	—	2	2	no	—
430	C₄	—	2	2	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	2	no	—
433	C₄	—	8	1	no	—
434	C₄	—	8	2	no	—
435	C₄	C₃₇×#535	1	2	yes	—
436	C₄	C₃₇×#535	1	1	yes	characteristic
437	C₄	C₃₇×#535	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	8	1	no	—
440	C₂	—	16	1	no	—
441	C₂	C₃₇×#2619	1	1	yes	characteristic
442	C₂	C₃₇×#3069	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂×AGL(1,ℤ/8)×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. C₂×C₃₇×#497	C₂	semidirect
3. C₃₇×#3039	C₂	semidirect
4. C₃₇×#2923	C₂	semidirect
5. C₃₇×#2047	C₂	semidirect
6. C₃₇×#2046	C₂	semidirect
7. C₃₇×#2020	C₂	semidirect
9. C₃₇×#1967	C₂	semidirect
10. C₃₇×#1966	C₂	semidirect
11. C₃₇×#1838	C₂	semidirect
199. #29823	C₃₇	direct (N × H)
217. C₂×#497	C₂×C₃₇	semidirect
219. #3039	C₂×C₃₇	semidirect
220. #2923	C₂×C₃₇	semidirect
221. #2047	C₂×C₃₇	semidirect
222. #2046	C₂×C₃₇	semidirect
223. #2020	C₂×C₃₇	semidirect
225. #1967	C₂×C₃₇	semidirect
226. #1966	C₂×C₃₇	semidirect
227. #1838	C₂×C₃₇	semidirect
264. C₃₇	#29823	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×#497	2
C₃₇×#3040	2
C₃₇×#3039	2
C₃₇×#2923	2
C₃₇×#2047	2
C₃₇×#2046	2
C₃₇×#2020	2
C₃₇×#2019	2
C₃₇×#1967	2
C₃₇×#1966	2
C₃₇×#1838	2
#29823	37

Subgroups — C37×#29823 #22651076

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#29823 #22651076