Subgroups — C₃₇×#18889 #22640142

Order 9472.

910 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3511	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#3246	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#3230	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#1650	C₂	1	2	yes	maximal, complemented
6	C₃₇×#1647	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1638	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1635	C₂	1	2	yes	maximal, complemented
9	C₂×C₃₇×#332	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1480	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1477	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₇×#556	C₂²	1	2	yes	—
13	C₃₇×#555	—	2	1	no	—
14	C₃₇×#554	—	2	1	no	—
15	C₃₇×#553	—	2	2	no	—
16	C₃₇×#548	—	2	2	no	—
17	C₃₇×#547	C₂²	1	2	yes	—
18	C₃₇×#542	—	2	2	no	—
19	C₃₇×#537	—	2	1	no	—
20	C₃₇×#533	—	2	1	no	—
21	C₃₇×#533	C₂²	1	1	yes	characteristic
22	C₃₇×#532	—	2	1	no	—
23	C₃₇×#532	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
25	C₃₇×#520	—	2	1	no	—
26	C₄×#41×C₃₇	C₂²	1	1	yes	characteristic
27	C₃₇×#500	C₂²	1	2	yes	—
28	C₃₇×#487	C₂²	1	2	yes	—
29	C₃₇×#484	—	2	2	no	—
30	C₃₇×#479	—	2	1	no	—
31	C₃₇×#478	—	2	1	no	—
32	C₃₇×#477	—	2	2	no	—
33	C₃₇×#477	C₂²	1	1	yes	characteristic
34	C₃₇×#476	C₂²	1	1	yes	characteristic
35	C₃₇×#476	C₂²	1	2	yes	—
36	C₃₇×#475	—	2	1	no	—
37	C₃₇×#475	C₂²	1	1	yes	characteristic
38	C₃₇×#474	C₂²	1	1	yes	characteristic
39	C₃₇×#465	—	2	2	no	—
40	C₃₇×#461	C₂²	1	2	yes	—
41	C₃₇×#460	—	2	1	no	—
42	C₃₇×#431	C₂²	1	1	yes	characteristic
43	C₃₇×#427	—	2	1	no	—
44	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
46	C₃₇×#416	—	2	1	no	—
47	C₃₇×#332	C₂²	1	2	yes	—
48	C₃₇×#332	C₂²	1	2	yes	—
49	C₃₇×Q₈⋊C₈	C₂²	1	2	yes	—
50	C₃₇×D₄⋊C₈	C₂²	1	2	yes	—
51	C₃₇×D₄⋊C₈	C₂²	1	2	yes	—
52	C₃₇×D₄⋊C₈	C₂²	1	2	yes	—
53	C₂×#41×C₃₇	—	2	2	no	—
54	C₂×#41×C₃₇	—	2	1	no	—
55	C₂×#41×C₃₇	D₄	1	1	yes	characteristic
56	C₂²×Q₈×C₃₇	—	2	1	no	—
57	C₂×SD₁₆×C₃₇	—	2	2	no	—
58	C₂²×C₈×C₃₇	—	2	1	no	—
59	C₂²×C₈×C₃₇	—	2	1	no	—
60	C₄⋊Q₈×C₃₇	—	2	1	no	—
61	C₄⋊Q₈×C₃₇	—	2	1	no	—
62	C₄⋊Q₈×C₃₇	D₄	1	2	yes	—
63	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
64	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
65	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
66	C₄⋊Q₈×C₃₇	C₂³	1	2	yes	—
67	#127×C₃₇	D₄	1	1	yes	characteristic
68	#126×C₃₇	—	2	4	no	—
69	#125×C₃₇	—	2	2	no	—
70	#125×C₃₇	—	2	1	no	—
71	#124×C₃₇	—	2	4	no	—
72	#124×C₃₇	—	2	2	no	—
73	#124×C₃₇	—	2	1	no	—
74	#123×C₃₇	—	2	4	no	—
75	C₂²⋊Q₈×C₃₇	—	2	2	no	—
76	C₂²⋊Q₈×C₃₇	—	2	4	no	—
77	C₂²⋊Q₈×C₃₇	—	2	2	no	—
78	C₂²⋊Q₈×C₃₇	—	2	2	no	—
79	C₂²⋊Q₈×C₃₇	—	2	1	no	—
80	C₂²⋊Q₈×C₃₇	—	2	1	no	—
81	#121×C₃₇	—	2	2	no	—
82	#121×C₃₇	—	2	2	no	—
83	#121×C₃₇	—	2	4	no	—
84	#121×C₃₇	—	2	2	no	—
85	#121×C₃₇	—	2	1	no	—
86	#121×C₃₇	D₄	1	2	yes	—
87	C₄×Q₈×C₃₇	—	2	2	no	—
88	C₄×Q₈×C₃₇	—	2	2	no	—
89	C₄×Q₈×C₃₇	—	2	1	no	—
90	C₄×Q₈×C₃₇	—	2	1	no	—
91	C₄×Q₈×C₃₇	D₄	1	1	yes	characteristic
92	C₄×Q₈×C₃₇	C₂³	1	1	yes	characteristic
93	C₄×D₄×C₃₇	—	2	2	no	—
94	C₄×D₄×C₃₇	—	2	4	no	—
95	C₄×D₄×C₃₇	—	2	2	no	—
96	C₄×D₄×C₃₇	—	2	1	no	—
97	C₄×D₄×C₃₇	—	2	1	no	—
98	C₄×D₄×C₃₇	—	2	1	no	—
99	C₄×D₄×C₃₇	D₄	1	1	yes	characteristic
100	C₄×D₄×C₃₇	C₂³	1	2	yes	—
101	C₄×D₄×C₃₇	C₂³	1	1	yes	characteristic
102	#117×C₃₇	—	2	2	no	—
103	#117×C₃₇	—	2	2	no	—
104	#117×C₃₇	—	2	1	no	—
105	#117×C₃₇	—	2	1	no	—
106	#117×C₃₇	D₄	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
108	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
109	C₂×C₄⋊C₄×C₃₇	D₄	1	2	yes	—
110	C₂×C₄²×C₃₇	—	2	1	no	—
111	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
112	#107×C₃₇	—	2	1	no	—
113	#107×C₃₇	—	2	1	no	—
114	#107×C₃₇	—	2	4	no	—
115	#106×C₃₇	—	2	1	no	—
116	#106×C₃₇	—	2	1	no	—
117	#106×C₃₇	—	2	2	no	—
118	C₄⋊C₈×C₃₇	—	2	1	no	—
119	C₄⋊C₈×C₃₇	—	2	1	no	—
120	C₄⋊C₈×C₃₇	—	2	1	no	—
121	C₄⋊C₈×C₃₇	C₂³	1	1	yes	characteristic
122	C₄⋊C₈×C₃₇	C₂³	1	1	yes	characteristic
123	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
124	#103×C₃₇	—	2	1	no	—
125	#103×C₃₇	—	2	1	no	—
126	#103×C₃₇	—	2	2	no	—
127	#103×C₃₇	—	2	4	no	—
128	#102×C₃₇	—	2	1	no	—
129	#102×C₃₇	—	2	1	no	—
130	#102×C₃₇	—	2	2	no	—
131	C₂²⋊C₈×C₃₇	—	2	1	no	—
132	C₄×C₈×C₃₇	C₂³	1	2	yes	—
133	#41×C₃₇	—	2	2	no	—
134	#41×C₃₇	—	2	2	no	—
135	#41×C₃₇	—	4	2	no	—
136	#41×C₃₇	—	4	2	no	—
137	#41×C₃₇	—	8	2	no	—
138	#41×C₃₇	—	8	2	no	—
139	C₂×Q₈×C₃₇	—	2	1	no	—
140	C₂×Q₈×C₃₇	—	2	2	no	—
141	C₂×Q₈×C₃₇	—	2	2	no	—
142	C₂×Q₈×C₃₇	—	2	1	no	—
143	C₂×Q₈×C₃₇	—	2	1	no	—
144	C₂×Q₈×C₃₇	—	8	1	no	—
145	C₂×Q₈×C₃₇	—	8	1	no	—
146	C₂×Q₈×C₃₇	C₂×D₄	1	1	yes	characteristic
147	C₂×D₄×C₃₇	—	2	1	no	—
148	C₂×D₄×C₃₇	—	2	2	no	—
149	C₂×D₄×C₃₇	—	2	4	no	—
150	C₂×D₄×C₃₇	—	2	1	no	—
151	C₂×D₄×C₃₇	—	2	1	no	—
152	C₂×D₄×C₃₇	C₂×D₄	1	1	yes	characteristic
153	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₃₇	—	2	4	no	—
155	C₂²×C₄×C₃₇	—	2	2	no	—
156	C₂²×C₄×C₃₇	—	2	1	no	—
157	C₂²×C₄×C₃₇	—	2	1	no	—
158	C₂²×C₄×C₃₇	—	2	1	no	—
159	C₂²×C₄×C₃₇	—	2	2	no	—
160	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
163	SD₁₆×C₃₇	—	8	2	no	—
164	C₂×C₈×C₃₇	—	2	2	no	—
165	C₂×C₈×C₃₇	—	2	1	no	—
166	C₂×C₈×C₃₇	—	2	2	no	—
167	C₂×C₈×C₃₇	—	2	1	no	—
168	C₂×C₈×C₃₇	—	4	2	no	—
169	C₂×C₈×C₃₇	—	8	1	no	—
170	C₄⋊C₄×C₃₇	—	2	4	no	—
171	C₄⋊C₄×C₃₇	—	2	4	no	—
172	C₄⋊C₄×C₃₇	—	2	2	no	—
173	C₄⋊C₄×C₃₇	—	2	2	no	—
174	C₄⋊C₄×C₃₇	—	2	1	no	—
175	C₄⋊C₄×C₃₇	—	2	1	no	—
176	C₄⋊C₄×C₃₇	—	2	2	no	—
177	C₄⋊C₄×C₃₇	—	2	1	no	—
178	C₄⋊C₄×C₃₇	—	2	1	no	—
179	C₄⋊C₄×C₃₇	—	2	1	no	—
180	C₄⋊C₄×C₃₇	—	2	1	no	—
181	C₄⋊C₄×C₃₇	—	2	1	no	—
182	C₄⋊C₄×C₃₇	—	4	1	no	—
183	C₄⋊C₄×C₃₇	—	4	1	no	—
184	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
185	C₄⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
186	C₄⋊C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
187	C₄⋊C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
188	C₂²⋊C₄×C₃₇	—	2	4	no	—
189	C₂²⋊C₄×C₃₇	—	2	4	no	—
190	C₂²⋊C₄×C₃₇	—	2	4	no	—
191	C₂²⋊C₄×C₃₇	—	2	1	no	—
192	C₂²⋊C₄×C₃₇	—	2	1	no	—
193	C₂²⋊C₄×C₃₇	—	2	2	no	—
194	C₂²⋊C₄×C₃₇	—	2	1	no	—
195	C₂²⋊C₄×C₃₇	—	2	2	no	—
196	C₂²⋊C₄×C₃₇	—	4	1	no	—
197	C₄²×C₃₇	—	2	4	no	—
198	C₄²×C₃₇	—	2	1	no	—
199	C₄²×C₃₇	—	2	1	no	—
200	C₄²×C₃₇	—	2	1	no	—
201	C₄²×C₃₇	—	4	1	no	—
202	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
206	C₂³×C₃₇	—	2	1	no	—
207	C₂³×C₃₇	—	2	2	no	—
208	C₂³×C₃₇	#120	1	1	yes	characteristic
209	Q₈×C₃₇	—	2	1	no	—
210	Q₈×C₃₇	—	2	1	no	—
211	Q₈×C₃₇	—	4	2	no	—
212	Q₈×C₃₇	—	4	2	no	—
213	Q₈×C₃₇	—	4	2	no	—
214	Q₈×C₃₇	—	4	2	no	—
215	Q₈×C₃₇	—	4	1	no	—
216	Q₈×C₃₇	—	4	1	no	—
217	Q₈×C₃₇	—	8	2	no	—
218	D₄×C₃₇	—	2	1	no	—
219	D₄×C₃₇	—	2	1	no	—
220	D₄×C₃₇	—	2	2	no	—
221	D₄×C₃₇	—	2	2	no	—
222	D₄×C₃₇	—	4	2	no	—
223	D₄×C₃₇	—	4	2	no	—
224	D₄×C₃₇	—	4	4	no	—
225	D₄×C₃₇	—	4	2	no	—
226	D₄×C₃₇	—	8	4	no	—
227	C₂×C₄×C₃₇	—	2	1	no	—
228	C₂×C₄×C₃₇	—	2	1	no	—
229	C₂×C₄×C₃₇	—	2	1	no	—
230	C₂×C₄×C₃₇	—	2	1	no	—
231	C₂×C₄×C₃₇	—	2	2	no	—
232	C₂×C₄×C₃₇	—	2	1	no	—
233	C₂×C₄×C₃₇	—	2	4	no	—
234	C₂×C₄×C₃₇	—	4	1	no	—
235	C₂×C₄×C₃₇	—	4	2	no	—
236	C₂×C₄×C₃₇	—	4	2	no	—
237	C₂×C₄×C₃₇	—	4	2	no	—
238	C₂×C₄×C₃₇	—	4	1	no	—
239	C₂×C₄×C₃₇	—	4	1	no	—
240	C₂×C₄×C₃₇	—	4	2	no	—
241	C₂×C₄×C₃₇	—	4	1	no	—
242	C₂×C₄×C₃₇	—	4	1	no	—
243	C₂×C₄×C₃₇	—	8	2	no	—
244	C₂×C₄×C₃₇	—	8	4	no	—
245	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
246	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
247	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
248	C₂×C₄×C₃₇	#135	1	2	yes	—
249	C₂×C₄×C₃₇	#137	1	2	yes	—
250	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
253	C₈×C₃₇	—	4	2	no	—
254	C₈×C₃₇	—	4	1	no	—
255	C₈×C₃₇	—	4	1	no	—
256	C₈×C₃₇	—	4	2	no	—
257	#18889	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
258	C₂²×C₃₇	—	2	1	no	—
259	C₂²×C₃₇	—	2	1	no	—
260	C₂²×C₃₇	—	4	1	no	—
261	C₂²×C₃₇	—	4	2	no	—
262	C₂²×C₃₇	—	4	1	no	—
263	C₂²×C₃₇	—	4	2	no	—
264	C₂²×C₃₇	—	4	1	no	—
265	C₂²×C₃₇	—	4	2	no	—
266	C₂²×C₃₇	#452	1	2	yes	—
267	C₂²×C₃₇	C₂×#120	1	1	yes	characteristic
268	C₄×C₃₇	—	2	1	no	—
269	C₄×C₃₇	—	2	1	no	—
270	C₄×C₃₇	—	2	1	no	—
271	C₄×C₃₇	—	4	1	no	—
272	C₄×C₃₇	—	4	2	no	—
273	C₄×C₃₇	—	4	1	no	—
274	C₄×C₃₇	—	4	4	no	—
275	C₄×C₃₇	—	4	1	no	—
276	C₄×C₃₇	—	8	1	no	—
277	C₄×C₃₇	—	8	1	no	—
278	C₄×C₃₇	#452	1	2	yes	—
279	C₄×C₃₇	C₂×#135	1	1	yes	characteristic
280	C₄×C₃₇	C₂×#137	1	1	yes	characteristic
281	C₄×C₃₇	#576	1	1	yes	characteristic
282	C₄×C₃₇	#577	1	1	yes	characteristic
283	#3511	C₂×C₃₇	1	1	yes	characteristic
284	#3246	C₂×C₃₇	1	1	yes	characteristic, complemented
285	#3230	C₂×C₃₇	1	1	yes	characteristic, complemented
286	#3076	C₂×C₃₇	1	1	yes	characteristic, complemented
287	#1650	C₂×C₃₇	1	2	yes	complemented
288	#1647	C₂×C₃₇	1	2	yes	complemented
289	#1638	C₂×C₃₇	1	2	yes	complemented
290	#1635	C₂×C₃₇	1	2	yes	complemented
291	C₂×#332	C₂×C₃₇	1	1	yes	characteristic, complemented
292	#1480	C₂×C₃₇	1	1	yes	characteristic, complemented
293	#1477	C₂×C₃₇	1	1	yes	characteristic, complemented
294	C₂×C₃₇	—	2	2	no	—
295	C₂×C₃₇	—	8	1	no	—
296	C₂×C₃₇	—	8	2	no	—
297	C₂×C₃₇	C₂×#452	1	1	yes	characteristic
298	C₂×C₃₇	#3012	1	1	yes	characteristic
299	C₂×C₃₇	#3020	1	1	yes	characteristic
300	#556	C₂²×C₃₇	1	2	yes	—
301	#555	—	2	1	no	—
302	#554	—	2	1	no	—
303	#553	—	2	2	no	—
304	#548	—	2	2	no	—
305	#547	C₂²×C₃₇	1	2	yes	—
306	#542	—	2	2	no	—
307	#537	—	2	1	no	—
308	#533	—	2	1	no	—
309	#533	C₂²×C₃₇	1	1	yes	characteristic
310	#532	—	2	1	no	—
311	#532	C₂²×C₃₇	1	1	yes	characteristic
312	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
313	#520	—	2	1	no	—
314	C₄×#41	C₂²×C₃₇	1	1	yes	characteristic
315	#500	C₂²×C₃₇	1	2	yes	—
316	#487	C₂²×C₃₇	1	2	yes	—
317	#484	—	2	2	no	—
318	#479	—	2	1	no	—
319	#478	—	2	1	no	—
320	#477	—	2	2	no	—
321	#477	C₂²×C₃₇	1	1	yes	characteristic
322	#476	C₂²×C₃₇	1	1	yes	characteristic
323	#476	C₂²×C₃₇	1	2	yes	—
324	#475	—	2	1	no	—
325	#475	C₂²×C₃₇	1	1	yes	characteristic
326	#474	C₂²×C₃₇	1	1	yes	characteristic
327	#465	—	2	2	no	—
328	#461	C₂²×C₃₇	1	2	yes	—
329	#460	—	2	1	no	—
330	#431	C₂²×C₃₇	1	1	yes	characteristic
331	#427	—	2	1	no	—
332	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
333	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
334	#416	—	2	1	no	—
335	#332	C₂²×C₃₇	1	2	yes	—
336	#332	C₂²×C₃₇	1	2	yes	—
337	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	—
338	D₄⋊C₈	C₂²×C₃₇	1	2	yes	—
339	D₄⋊C₈	C₂²×C₃₇	1	2	yes	—
340	D₄⋊C₈	C₂²×C₃₇	1	2	yes	—
341	C₃₇	#18889	1	1	yes	characteristic, direct product factor, Sylow
342	C₂×#41	—	2	2	no	—
343	C₂×#41	—	2	1	no	—
344	C₂×#41	D₄×C₃₇	1	1	yes	characteristic
345	C₂²×Q₈	—	2	1	no	—
346	C₂×SD₁₆	—	2	2	no	—
347	C₂²×C₈	—	2	1	no	—
348	C₂²×C₈	—	2	1	no	—
349	C₄⋊Q₈	—	2	1	no	—
350	C₄⋊Q₈	—	2	1	no	—
351	C₄⋊Q₈	D₄×C₃₇	1	2	yes	—
352	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
353	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
354	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
355	C₄⋊Q₈	C₂³×C₃₇	1	2	yes	—
356	#127	D₄×C₃₇	1	1	yes	characteristic
357	#126	—	2	4	no	—
358	#125	—	2	2	no	—
359	#125	—	2	1	no	—
360	#124	—	2	4	no	—
361	#124	—	2	2	no	—
362	#124	—	2	1	no	—
363	#123	—	2	4	no	—
364	C₂²⋊Q₈	—	2	2	no	—
365	C₂²⋊Q₈	—	2	4	no	—
366	C₂²⋊Q₈	—	2	2	no	—
367	C₂²⋊Q₈	—	2	2	no	—
368	C₂²⋊Q₈	—	2	1	no	—
369	C₂²⋊Q₈	—	2	1	no	—
370	#121	—	2	2	no	—
371	#121	—	2	2	no	—
372	#121	—	2	4	no	—
373	#121	—	2	2	no	—
374	#121	—	2	1	no	—
375	#121	D₄×C₃₇	1	2	yes	—
376	C₄×Q₈	—	2	2	no	—
377	C₄×Q₈	—	2	2	no	—
378	C₄×Q₈	—	2	1	no	—
379	C₄×Q₈	—	2	1	no	—
380	C₄×Q₈	D₄×C₃₇	1	1	yes	characteristic
381	C₄×Q₈	C₂³×C₃₇	1	1	yes	characteristic
382	C₄×D₄	—	2	2	no	—
383	C₄×D₄	—	2	4	no	—
384	C₄×D₄	—	2	2	no	—
385	C₄×D₄	—	2	1	no	—
386	C₄×D₄	—	2	1	no	—
387	C₄×D₄	—	2	1	no	—
388	C₄×D₄	D₄×C₃₇	1	1	yes	characteristic
389	C₄×D₄	C₂³×C₃₇	1	1	yes	characteristic
390	C₄×D₄	C₂³×C₃₇	1	2	yes	—
391	#117	—	2	2	no	—
392	#117	—	2	2	no	—
393	#117	—	2	1	no	—
394	#117	—	2	1	no	—
395	#117	D₄×C₃₇	1	1	yes	characteristic
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	2	no	—
398	C₂×C₄⋊C₄	D₄×C₃₇	1	2	yes	—
399	C₂×C₄²	—	2	1	no	—
400	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
401	#107	—	2	1	no	—
402	#107	—	2	1	no	—
403	#107	—	2	4	no	—
404	#106	—	2	1	no	—
405	#106	—	2	1	no	—
406	#106	—	2	2	no	—
407	C₄⋊C₈	—	2	1	no	—
408	C₄⋊C₈	—	2	1	no	—
409	C₄⋊C₈	—	2	1	no	—
410	C₄⋊C₈	C₂³×C₃₇	1	1	yes	characteristic
411	C₄⋊C₈	C₂³×C₃₇	1	1	yes	characteristic
412	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
413	#103	—	2	1	no	—
414	#103	—	2	1	no	—
415	#103	—	2	2	no	—
416	#103	—	2	4	no	—
417	#102	—	2	1	no	—
418	#102	—	2	1	no	—
419	#102	—	2	2	no	—
420	C₂²⋊C₈	—	2	1	no	—
421	C₄×C₈	C₂³×C₃₇	1	2	yes	—
422	#41	—	2	2	no	—
423	#41	—	2	2	no	—
424	#41	—	4	2	no	—
425	#41	—	4	2	no	—
426	#41	—	8	2	no	—
427	#41	—	8	2	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	2	2	no	—
430	C₂×Q₈	—	2	2	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	8	1	no	—
434	C₂×Q₈	—	8	1	no	—
435	C₂×Q₈	C₂×D₄×C₃₇	1	1	yes	characteristic
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	4	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	C₂×D₄×C₃₇	1	1	yes	characteristic
442	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
450	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
452	SD₁₆	—	8	2	no	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	4	2	no	—
458	C₂×C₈	—	8	1	no	—
459	C₄⋊C₄	—	2	4	no	—
460	C₄⋊C₄	—	2	4	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	4	1	no	—
472	C₄⋊C₄	—	4	1	no	—
473	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
474	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
475	C₄⋊C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
476	C₄⋊C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
477	C₂²⋊C₄	—	2	4	no	—
478	C₂²⋊C₄	—	2	4	no	—
479	C₂²⋊C₄	—	2	4	no	—
480	C₂²⋊C₄	—	2	1	no	—
481	C₂²⋊C₄	—	2	1	no	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	2	1	no	—
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	4	1	no	—
486	C₄²	—	2	4	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	4	1	no	—
491	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
492	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
493	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
494	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
495	C₂³	—	2	1	no	—
496	C₂³	—	2	2	no	—
497	C₂³	#120×C₃₇	1	1	yes	characteristic
498	Q₈	—	2	1	no	—
499	Q₈	—	2	1	no	—
500	Q₈	—	4	2	no	—
501	Q₈	—	4	2	no	—
502	Q₈	—	4	2	no	—
503	Q₈	—	4	2	no	—
504	Q₈	—	4	1	no	—
505	Q₈	—	4	1	no	—
506	Q₈	—	8	2	no	—
507	D₄	—	2	1	no	—
508	D₄	—	2	1	no	—
509	D₄	—	2	2	no	—
510	D₄	—	2	2	no	—
511	D₄	—	4	2	no	—
512	D₄	—	4	2	no	—
513	D₄	—	4	4	no	—
514	D₄	—	4	2	no	—
515	D₄	—	8	4	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	8	2	no	—
533	C₂×C₄	—	8	4	no	—
534	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
535	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
536	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
537	C₂×C₄	#135×C₃₇	1	2	yes	—
538	C₂×C₄	#137×C₃₇	1	2	yes	—
539	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
540	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
541	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
542	C₈	—	4	2	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₈	—	4	2	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	2	no	—
554	C₂²	C₃₇×#452	1	2	yes	—
555	C₂²	C₂×#120×C₃₇	1	1	yes	characteristic
556	C₄	—	2	1	no	—
557	C₄	—	2	1	no	—
558	C₄	—	2	1	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	2	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	4	no	—
563	C₄	—	4	1	no	—
564	C₄	—	8	1	no	—
565	C₄	—	8	1	no	—
566	C₄	C₃₇×#452	1	2	yes	—
567	C₄	C₂×#135×C₃₇	1	1	yes	characteristic
568	C₄	C₂×#137×C₃₇	1	1	yes	characteristic
569	C₄	C₃₇×#576	1	1	yes	characteristic
570	C₄	C₃₇×#577	1	1	yes	characteristic
571	C₂	—	2	2	no	—
572	C₂	—	8	1	no	—
573	C₂	—	8	2	no	—
574	C₂	C₂×C₃₇×#452	1	1	yes	characteristic
575	C₂	C₃₇×#3012	1	1	yes	characteristic
576	C₂	C₃₇×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₇
prime radical	C₃₇×#3511	C₂
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
2. C₃₇×#3246	C₂	semidirect
3. C₃₇×#3230	C₂	semidirect
4. C₃₇×#3076	C₂	semidirect
5. C₃₇×#1650	C₂	semidirect
6. C₃₇×#1647	C₂	semidirect
7. C₃₇×#1638	C₂	semidirect
8. C₃₇×#1635	C₂	semidirect
9. C₂×C₃₇×#332	C₂	semidirect
10. C₃₇×#1480	C₂	semidirect
11. C₃₇×#1477	C₂	semidirect
257. #18889	C₃₇	direct (N × H)
284. #3246	C₂×C₃₇	semidirect
285. #3230	C₂×C₃₇	semidirect
286. #3076	C₂×C₃₇	semidirect
287. #1650	C₂×C₃₇	semidirect
288. #1647	C₂×C₃₇	semidirect
289. #1638	C₂×C₃₇	semidirect
290. #1635	C₂×C₃₇	semidirect
291. C₂×#332	C₂×C₃₇	semidirect
292. #1480	C₂×C₃₇	semidirect
293. #1477	C₂×C₃₇	semidirect
341. C₃₇	#18889	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×#3511	2
C₃₇×#3246	2
C₃₇×#3230	2
C₃₇×#3076	2
C₃₇×#1650	2
C₃₇×#1647	2
C₃₇×#1638	2
C₃₇×#1635	2
C₂×C₃₇×#332	2
C₃₇×#1480	2
C₃₇×#1477	2
#18889	37

Subgroups — C37×#18889 #22640142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#18889 #22640142