Subgroups — C₃₇×#19564 #22640817

Order 9472.

626 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×#3255	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×#3208	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#3208	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#2986	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#1702	C₂	1	2	yes	maximal, complemented
6	C₃₇×#1686	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1682	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1666	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1574	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1545	C₂	1	1	yes	maximal, characteristic
11	C₃₇×#1544	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₇×#533	C₂²	1	1	yes	characteristic
13	C₃₇×#533	C₂²	1	1	yes	characteristic
14	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
15	C₃₇×#492	—	2	1	no	—
16	C₃₇×#492	C₂²	1	2	yes	—
17	C₃₇×#486	—	2	1	no	—
18	C₃₇×#486	C₂²	1	2	yes	—
19	C₃₇×#475	—	2	1	no	—
20	C₃₇×#475	C₂²	1	2	yes	complemented
21	C₃₇×#470	—	2	2	no	—
22	C₃₇×#462	—	2	1	no	—
23	C₃₇×#462	C₂²	1	2	yes	complemented
24	C₃₇×#460	—	2	1	no	—
25	C₃₇×#460	—	2	1	no	—
26	C₃₇×#460	C₂²	1	2	yes	—
27	C₃₇×#460	C₂²	1	2	yes	—
28	C₃₇×#450	—	2	2	no	—
29	C₃₇×#450	—	2	2	no	—
30	C₃₇×#446	—	2	1	no	—
31	C₃₇×#446	C₂²	1	2	yes	complemented
32	C₈×Q₈×C₃₇	—	2	1	no	—
33	C₈×Q₈×C₃₇	C₂²	1	2	yes	complemented
34	C₃₇×#433	—	2	2	no	—
35	C₃₇×#431	C₂²	1	1	yes	characteristic
36	C₃₇×#431	C₂²	1	1	yes	characteristic
37	C₃₇×#431	C₂²	1	1	yes	characteristic
38	C₃₇×#423	C₂²	1	1	yes	characteristic
39	C₃₇×#335	C₂²	1	2	yes	complemented
40	C₃₇×#334	C₂²	1	2	yes	complemented
41	C₃₇×#332	C₂²	1	1	yes	characteristic, complemented
42	C₃₇×#332	C₂²	1	1	yes	characteristic, complemented
43	C₃₇×#332	C₂²	1	1	yes	characteristic, complemented
44	C₃₇×#332	C₂²	1	1	yes	characteristic, complemented
45	C₃₇×#331	C₂²	1	2	yes	—
46	C₃₇×#331	C₂²	1	2	yes	—
47	C₂²×D₄×C₃₇	—	2	1	no	—
48	C₂²×D₄×C₃₇	—	2	1	no	—
49	C₂²×D₄×C₃₇	—	2	1	no	—
50	C₂×Q₁₆×C₃₇	—	2	2	no	—
51	C₂×SD₁₆×C₃₇	—	2	2	no	—
52	C₂×SD₁₆×C₃₇	—	2	2	no	—
53	C₂×SD₁₆×C₃₇	—	2	2	no	—
54	C₂×SD₁₆×C₃₇	—	2	2	no	—
55	C₂×M₁₆×C₃₇	—	2	1	no	—
56	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
57	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
58	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
59	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
60	#127×C₃₇	—	2	1	no	—
61	#127×C₃₇	—	2	1	no	—
62	#127×C₃₇	—	2	1	no	—
63	#127×C₃₇	C₂³	1	2	yes	—
64	#125×C₃₇	—	2	1	no	—
65	#125×C₃₇	—	2	1	no	—
66	C₂²⋊Q₈×C₃₇	—	2	1	no	—
67	C₂²⋊Q₈×C₃₇	—	2	1	no	—
68	C₂²⋊Q₈×C₃₇	—	2	1	no	—
69	C₂²⋊Q₈×C₃₇	D₄	1	2	yes	—
70	C₄×Q₈×C₃₇	—	2	1	no	—
71	C₄×Q₈×C₃₇	—	2	1	no	—
72	C₄×Q₈×C₃₇	—	2	1	no	—
73	C₄×Q₈×C₃₇	C₂³	1	2	yes	—
74	#117×C₃₇	—	2	1	no	—
75	#117×C₃₇	—	2	1	no	—
76	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
77	#106×C₃₇	—	2	2	no	—
78	C₄⋊C₈×C₃₇	—	2	2	no	—
79	C₄⋊C₈×C₃₇	—	2	2	no	—
80	C₄⋊C₈×C₃₇	—	2	1	no	—
81	C₄⋊C₈×C₃₇	D₄	1	1	yes	characteristic
82	C₄⋊C₈×C₃₇	D₄	1	1	yes	characteristic
83	C₄⋊C₈×C₃₇	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₃₇	C₂³	1	1	yes	characteristic
85	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
86	C₄⋊C₈×C₃₇	C₂³	1	1	yes	characteristic
87	C₄⋊C₈×C₃₇	C₂³	1	1	yes	characteristic
88	#103×C₃₇	—	2	2	no	—
89	#103×C₃₇	—	2	2	no	—
90	#102×C₃₇	—	2	2	no	—
91	#102×C₃₇	—	2	2	no	—
92	#102×C₃₇	—	2	2	no	—
93	#102×C₃₇	—	2	2	no	—
94	C₂²⋊C₈×C₃₇	—	2	1	no	—
95	C₂²⋊C₈×C₃₇	—	2	1	no	—
96	C₂²⋊C₈×C₃₇	D₄	1	2	yes	—
97	#97×C₃₇	—	2	2	no	—
98	C₄×C₈×C₃₇	—	2	2	no	—
99	C₄×C₈×C₃₇	—	2	1	no	—
100	C₄×C₈×C₃₇	—	2	1	no	—
101	C₄×C₈×C₃₇	C₂³	1	2	yes	—
102	C₂⁴×C₃₇	—	4	1	no	—
103	C₂×Q₈×C₃₇	—	2	1	no	—
104	C₂×Q₈×C₃₇	—	2	1	no	—
105	C₂×Q₈×C₃₇	—	2	1	no	—
106	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
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	1	no	—
111	C₂×D₄×C₃₇	—	4	1	no	—
112	C₂×D₄×C₃₇	—	4	1	no	—
113	C₂×D₄×C₃₇	—	8	1	no	—
114	C₂×D₄×C₃₇	—	8	1	no	—
115	C₂×D₄×C₃₇	—	8	1	no	—
116	C₂×D₄×C₃₇	—	8	1	no	—
117	C₂×D₄×C₃₇	—	8	2	no	—
118	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₃₇	#41	1	1	yes	characteristic
121	Q₁₆×C₃₇	—	8	2	no	—
122	SD₁₆×C₃₇	—	8	2	no	—
123	SD₁₆×C₃₇	—	8	2	no	—
124	SD₁₆×C₃₇	—	8	2	no	—
125	SD₁₆×C₃₇	—	8	2	no	—
126	M₁₆×C₃₇	—	8	1	no	—
127	C₂×C₈×C₃₇	—	2	1	no	—
128	C₂×C₈×C₃₇	—	2	1	no	—
129	C₂×C₈×C₃₇	—	2	1	no	—
130	C₂×C₈×C₃₇	—	2	1	no	—
131	C₂×C₈×C₃₇	—	2	2	no	—
132	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
133	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
134	C₄⋊C₄×C₃₇	—	2	1	no	—
135	C₄⋊C₄×C₃₇	—	2	1	no	—
136	C₄⋊C₄×C₃₇	—	2	1	no	—
137	C₄⋊C₄×C₃₇	—	2	2	no	—
138	C₄⋊C₄×C₃₇	—	2	2	no	—
139	C₄⋊C₄×C₃₇	—	2	1	no	—
140	C₄⋊C₄×C₃₇	—	2	1	no	—
141	C₄⋊C₄×C₃₇	—	2	1	no	—
142	C₄⋊C₄×C₃₇	—	2	1	no	—
143	C₄⋊C₄×C₃₇	—	4	1	no	—
144	C₄⋊C₄×C₃₇	—	4	1	no	—
145	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
146	C₂²⋊C₄×C₃₇	—	2	2	no	—
147	C₂²⋊C₄×C₃₇	—	4	1	no	—
148	C₄²×C₃₇	—	2	2	no	—
149	C₄²×C₃₇	—	4	1	no	—
150	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₃₇	#41	1	1	yes	characteristic
153	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
154	C₂³×C₃₇	—	4	2	no	—
155	C₂³×C₃₇	—	8	2	no	—
156	C₂³×C₃₇	—	8	2	no	—
157	C₂³×C₃₇	—	8	2	no	—
158	C₂³×C₃₇	#121	1	1	yes	characteristic
159	Q₈×C₃₇	—	2	2	no	—
160	Q₈×C₃₇	—	2	2	no	—
161	Q₈×C₃₇	—	4	2	no	—
162	Q₈×C₃₇	—	4	1	no	—
163	Q₈×C₃₇	—	4	1	no	—
164	Q₈×C₃₇	—	4	1	no	—
165	Q₈×C₃₇	—	4	1	no	—
166	D₄×C₃₇	—	4	2	no	—
167	D₄×C₃₇	—	4	2	no	—
168	D₄×C₃₇	—	4	2	no	—
169	D₄×C₃₇	—	4	2	no	—
170	D₄×C₃₇	—	8	2	no	—
171	D₄×C₃₇	—	8	2	no	—
172	D₄×C₃₇	—	8	2	no	—
173	D₄×C₃₇	—	8	2	no	—
174	C₂×C₄×C₃₇	—	2	1	no	—
175	C₂×C₄×C₃₇	—	2	1	no	—
176	C₂×C₄×C₃₇	—	2	1	no	—
177	C₂×C₄×C₃₇	—	2	1	no	—
178	C₂×C₄×C₃₇	—	2	2	no	—
179	C₂×C₄×C₃₇	—	2	2	no	—
180	C₂×C₄×C₃₇	—	2	2	no	—
181	C₂×C₄×C₃₇	—	4	1	no	—
182	C₂×C₄×C₃₇	—	4	1	no	—
183	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
184	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
185	C₂×C₄×C₃₇	#121	1	1	yes	characteristic
186	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
189	C₈×C₃₇	—	2	2	no	—
190	C₈×C₃₇	—	2	2	no	—
191	C₈×C₃₇	—	4	2	no	—
192	C₈×C₃₇	—	4	1	no	—
193	C₈×C₃₇	—	4	1	no	—
194	C₈×C₃₇	—	4	1	no	—
195	C₈×C₃₇	—	4	1	no	—
196	#19564	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂²×C₃₇	—	2	1	no	—
198	C₂²×C₃₇	—	2	1	no	—
199	C₂²×C₃₇	—	2	1	no	—
200	C₂²×C₃₇	—	8	2	no	—
201	C₂²×C₃₇	—	8	2	no	—
202	C₂²×C₃₇	—	8	2	no	—
203	C₂²×C₃₇	—	16	4	no	—
204	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
205	C₄×C₃₇	—	2	1	no	—
206	C₄×C₃₇	—	2	1	no	—
207	C₄×C₃₇	—	2	1	no	—
208	C₄×C₃₇	—	4	2	no	—
209	C₄×C₃₇	—	4	2	no	—
210	C₄×C₃₇	—	8	1	no	—
211	C₄×C₃₇	—	8	1	no	—
212	C₄×C₃₇	#471	1	2	yes	—
213	C₄×C₃₇	#576	1	1	yes	characteristic
214	C₄×C₃₇	#577	1	1	yes	characteristic
215	C₄×C₃₇	#577	1	1	yes	characteristic
216	C₄×C₃₇	#577	1	1	yes	characteristic
217	#3255	C₂×C₃₇	1	1	yes	characteristic, complemented
218	#3208	C₂×C₃₇	1	1	yes	characteristic
219	#3208	C₂×C₃₇	1	1	yes	characteristic
220	#2986	C₂×C₃₇	1	1	yes	characteristic, complemented
221	#1702	C₂×C₃₇	1	2	yes	complemented
222	#1686	C₂×C₃₇	1	2	yes	complemented
223	#1682	C₂×C₃₇	1	2	yes	complemented
224	#1666	C₂×C₃₇	1	2	yes	complemented
225	#1574	C₂×C₃₇	1	1	yes	characteristic, complemented
226	#1545	C₂×C₃₇	1	1	yes	characteristic
227	#1544	C₂×C₃₇	1	1	yes	characteristic, complemented
228	C₂×C₃₇	—	4	1	no	—
229	C₂×C₃₇	—	16	2	no	—
230	C₂×C₃₇	#3043	1	1	yes	characteristic
231	C₂×C₃₇	#3062	1	1	yes	characteristic
232	C₂×C₃₇	C₂×#471	1	1	yes	characteristic
233	#533	C₂²×C₃₇	1	1	yes	characteristic
234	#533	C₂²×C₃₇	1	1	yes	characteristic
235	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
236	#492	—	2	1	no	—
237	#492	C₂²×C₃₇	1	2	yes	—
238	#486	—	2	1	no	—
239	#486	C₂²×C₃₇	1	2	yes	—
240	#475	—	2	1	no	—
241	#475	C₂²×C₃₇	1	2	yes	complemented
242	#470	—	2	2	no	—
243	#462	—	2	1	no	—
244	#462	C₂²×C₃₇	1	2	yes	complemented
245	#460	—	2	1	no	—
246	#460	—	2	1	no	—
247	#460	C₂²×C₃₇	1	2	yes	—
248	#460	C₂²×C₃₇	1	2	yes	—
249	#450	—	2	2	no	—
250	#450	—	2	2	no	—
251	#446	—	2	1	no	—
252	#446	C₂²×C₃₇	1	2	yes	complemented
253	C₈×Q₈	—	2	1	no	—
254	C₈×Q₈	C₂²×C₃₇	1	2	yes	complemented
255	#433	—	2	2	no	—
256	#431	C₂²×C₃₇	1	1	yes	characteristic
257	#431	C₂²×C₃₇	1	1	yes	characteristic
258	#431	C₂²×C₃₇	1	1	yes	characteristic
259	#423	C₂²×C₃₇	1	1	yes	characteristic
260	#335	C₂²×C₃₇	1	2	yes	complemented
261	#334	C₂²×C₃₇	1	2	yes	complemented
262	#332	C₂²×C₃₇	1	1	yes	characteristic, complemented
263	#332	C₂²×C₃₇	1	1	yes	characteristic, complemented
264	#332	C₂²×C₃₇	1	1	yes	characteristic, complemented
265	#332	C₂²×C₃₇	1	1	yes	characteristic, complemented
266	#331	C₂²×C₃₇	1	2	yes	—
267	#331	C₂²×C₃₇	1	2	yes	—
268	C₃₇	#19564	1	1	yes	characteristic, direct product factor, Sylow
269	C₂²×D₄	—	2	1	no	—
270	C₂²×D₄	—	2	1	no	—
271	C₂²×D₄	—	2	1	no	—
272	C₂×Q₁₆	—	2	2	no	—
273	C₂×SD₁₆	—	2	2	no	—
274	C₂×SD₁₆	—	2	2	no	—
275	C₂×SD₁₆	—	2	2	no	—
276	C₂×SD₁₆	—	2	2	no	—
277	C₂×M₁₆	—	2	1	no	—
278	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
279	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
280	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
281	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
282	#127	—	2	1	no	—
283	#127	—	2	1	no	—
284	#127	—	2	1	no	—
285	#127	C₂³×C₃₇	1	2	yes	—
286	#125	—	2	1	no	—
287	#125	—	2	1	no	—
288	C₂²⋊Q₈	—	2	1	no	—
289	C₂²⋊Q₈	—	2	1	no	—
290	C₂²⋊Q₈	—	2	1	no	—
291	C₂²⋊Q₈	D₄×C₃₇	1	2	yes	—
292	C₄×Q₈	—	2	1	no	—
293	C₄×Q₈	—	2	1	no	—
294	C₄×Q₈	—	2	1	no	—
295	C₄×Q₈	C₂³×C₃₇	1	2	yes	—
296	#117	—	2	1	no	—
297	#117	—	2	1	no	—
298	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
299	#106	—	2	2	no	—
300	C₄⋊C₈	—	2	2	no	—
301	C₄⋊C₈	—	2	2	no	—
302	C₄⋊C₈	—	2	1	no	—
303	C₄⋊C₈	D₄×C₃₇	1	1	yes	characteristic
304	C₄⋊C₈	D₄×C₃₇	1	1	yes	characteristic
305	C₄⋊C₈	C₂³×C₃₇	1	1	yes	characteristic
306	C₄⋊C₈	C₂³×C₃₇	1	1	yes	characteristic
307	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
308	C₄⋊C₈	C₂³×C₃₇	1	1	yes	characteristic
309	C₄⋊C₈	C₂³×C₃₇	1	1	yes	characteristic
310	#103	—	2	2	no	—
311	#103	—	2	2	no	—
312	#102	—	2	2	no	—
313	#102	—	2	2	no	—
314	#102	—	2	2	no	—
315	#102	—	2	2	no	—
316	C₂²⋊C₈	—	2	1	no	—
317	C₂²⋊C₈	—	2	1	no	—
318	C₂²⋊C₈	D₄×C₃₇	1	2	yes	—
319	#97	—	2	2	no	—
320	C₄×C₈	—	2	2	no	—
321	C₄×C₈	—	2	1	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	C₂³×C₃₇	1	2	yes	—
324	C₂⁴	—	4	1	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	4	1	no	—
333	C₂×D₄	—	4	1	no	—
334	C₂×D₄	—	4	1	no	—
335	C₂×D₄	—	8	1	no	—
336	C₂×D₄	—	8	1	no	—
337	C₂×D₄	—	8	1	no	—
338	C₂×D₄	—	8	1	no	—
339	C₂×D₄	—	8	2	no	—
340	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
342	C₂²×C₄	#41×C₃₇	1	1	yes	characteristic
343	Q₁₆	—	8	2	no	—
344	SD₁₆	—	8	2	no	—
345	SD₁₆	—	8	2	no	—
346	SD₁₆	—	8	2	no	—
347	SD₁₆	—	8	2	no	—
348	M₁₆	—	8	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
355	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	4	1	no	—
366	C₄⋊C₄	—	4	1	no	—
367	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	4	1	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	4	1	no	—
372	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
373	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
374	C₄²	#41×C₃₇	1	1	yes	characteristic
375	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
376	C₂³	—	4	2	no	—
377	C₂³	—	8	2	no	—
378	C₂³	—	8	2	no	—
379	C₂³	—	8	2	no	—
380	C₂³	#121×C₃₇	1	1	yes	characteristic
381	Q₈	—	2	2	no	—
382	Q₈	—	2	2	no	—
383	Q₈	—	4	2	no	—
384	Q₈	—	4	1	no	—
385	Q₈	—	4	1	no	—
386	Q₈	—	4	1	no	—
387	Q₈	—	4	1	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	8	2	no	—
393	D₄	—	8	2	no	—
394	D₄	—	8	2	no	—
395	D₄	—	8	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
406	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
407	C₂×C₄	#121×C₃₇	1	1	yes	characteristic
408	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
409	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
410	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
411	C₈	—	2	2	no	—
412	C₈	—	2	2	no	—
413	C₈	—	4	2	no	—
414	C₈	—	4	1	no	—
415	C₈	—	4	1	no	—
416	C₈	—	4	1	no	—
417	C₈	—	4	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	8	2	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	8	2	no	—
424	C₂²	—	16	4	no	—
425	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	2	no	—
431	C₄	—	8	1	no	—
432	C₄	—	8	1	no	—
433	C₄	C₃₇×#471	1	2	yes	—
434	C₄	C₃₇×#576	1	1	yes	characteristic
435	C₄	C₃₇×#577	1	1	yes	characteristic
436	C₄	C₃₇×#577	1	1	yes	characteristic
437	C₄	C₃₇×#577	1	1	yes	characteristic
438	C₂	—	4	1	no	—
439	C₂	—	16	2	no	—
440	C₂	C₃₇×#3043	1	1	yes	characteristic
441	C₂	C₃₇×#3062	1	1	yes	characteristic
442	C₂	C₂×C₃₇×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₇
prime radical	C₂×#127×C₃₇	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ 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×#3255	C₂	semidirect
4. C₃₇×#2986	C₂	semidirect
5. C₃₇×#1702	C₂	semidirect
6. C₃₇×#1686	C₂	semidirect
7. C₃₇×#1682	C₂	semidirect
8. C₃₇×#1666	C₂	semidirect
9. C₃₇×#1574	C₂	semidirect
11. C₃₇×#1544	C₂	semidirect
20. C₃₇×#475	C₂²	semidirect
23. C₃₇×#462	C₂²	semidirect
31. C₃₇×#446	C₂²	semidirect
33. C₈×Q₈×C₃₇	C₂²	semidirect
39. C₃₇×#335	C₂²	semidirect
40. C₃₇×#334	C₂²	semidirect
41. C₃₇×#332	C₂²	semidirect
42. C₃₇×#332	C₂²	semidirect
43. C₃₇×#332	C₂²	semidirect
44. C₃₇×#332	C₂²	semidirect
196. #19564	C₃₇	direct (N × H)
217. #3255	C₂×C₃₇	semidirect
220. #2986	C₂×C₃₇	semidirect
221. #1702	C₂×C₃₇	semidirect
222. #1686	C₂×C₃₇	semidirect
223. #1682	C₂×C₃₇	semidirect
224. #1666	C₂×C₃₇	semidirect
225. #1574	C₂×C₃₇	semidirect
227. #1544	C₂×C₃₇	semidirect
241. #475	C₂²×C₃₇	semidirect
244. #462	C₂²×C₃₇	semidirect
252. #446	C₂²×C₃₇	semidirect
254. C₈×Q₈	C₂²×C₃₇	semidirect
260. #335	C₂²×C₃₇	semidirect
261. #334	C₂²×C₃₇	semidirect
262. #332	C₂²×C₃₇	semidirect
263. #332	C₂²×C₃₇	semidirect
264. #332	C₂²×C₃₇	semidirect
265. #332	C₂²×C₃₇	semidirect
268. C₃₇	#19564	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×#3255	2
C₃₇×#3208	2
C₃₇×#2986	2
C₃₇×#1702	2
C₃₇×#1686	2
C₃₇×#1682	2
C₃₇×#1666	2
C₃₇×#1574	2
C₃₇×#1545	2
C₃₇×#1544	2
#19564	37

Subgroups — C37×#19564 #22640817

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#19564 #22640817