Subgroups — C₃₇×#18480 #22639733

Order 9472.

1082 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3481	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×#3147	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#3106	C₂	1	2	yes	maximal, complemented
4	C₃₇×#1632	C₂	1	2	yes	maximal, complemented
5	C₃₇×#1630	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#1629	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#1622	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1620	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1619	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1543	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1476	C₂	1	2	yes	maximal, complemented
12	C₂×#135×C₃₇	—	2	2	no	—
13	C₃₇×#559	C₂²	1	1	yes	characteristic
14	C₃₇×#554	C₂²	1	2	yes	—
15	C₃₇×#553	—	2	2	no	—
16	C₃₇×#551	—	2	2	no	—
17	C₃₇×#546	—	2	2	no	—
18	D₄²×C₃₇	C₂²	1	1	yes	characteristic
19	C₃₇×#532	C₂²	1	1	yes	characteristic
20	C₃₇×#532	C₂²	1	1	yes	characteristic, complemented
21	C₃₇×#529	—	2	2	no	—
22	C₃₇×#525	—	2	2	no	—
23	C₄×#41×C₃₇	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₃₇	—	2	2	no	—
25	C₃₇×#495	—	2	2	no	—
26	C₃₇×#494	C₂²	1	1	yes	characteristic, complemented
27	C₃₇×#493	C₂²	1	1	yes	characteristic
28	C₃₇×#492	C₂²	1	1	yes	characteristic
29	C₃₇×#492	C₂²	1	1	yes	characteristic, complemented
30	C₃₇×#482	—	2	2	no	—
31	C₃₇×#477	C₂²	1	2	yes	complemented
32	C₃₇×#476	C₂²	1	2	yes	—
33	C₃₇×#460	C₂²	1	2	yes	complemented
34	C₃₇×#459	C₂²	1	2	yes	—
35	C₃₇×#449	—	2	2	no	—
36	C₄×SD₁₆×C₃₇	—	2	2	no	—
37	C₄×D₈×C₃₇	—	2	2	no	—
38	C₃₇×#431	C₂²	1	2	yes	complemented
39	C₂×C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic, complemented
40	C₃₇×#333	C₂²	1	2	yes	complemented
41	C₃₇×#331	C₂²	1	1	yes	characteristic
42	C₃₇×#331	C₂²	1	1	yes	characteristic
43	C₃₇×Q₈⋊C₈	C₂²	1	2	yes	complemented
44	C₃₇×Q₈⋊C₈	C₂²	1	2	yes	complemented
45	C₃₇×D₄⋊C₈	C₂²	1	2	yes	—
46	C₃₇×D₄⋊C₈	C₂²	1	2	yes	—
47	C₂×#41×C₃₇	—	2	1	no	—
48	C₂×#41×C₃₇	D₄	1	2	yes	—
49	C₂×#41×C₃₇	D₄	1	2	yes	—
50	C₂²×D₄×C₃₇	—	2	2	no	—
51	C₂³×C₄×C₃₇	—	2	2	no	—
52	#135×C₃₇	—	4	8	no	—
53	C₂×Q₁₆×C₃₇	—	2	2	no	—
54	C₂×SD₁₆×C₃₇	—	2	2	no	—
55	C₂×SD₁₆×C₃₇	—	2	2	no	—
56	C₂×SD₁₆×C₃₇	—	2	2	no	—
57	C₂×D₈×C₃₇	—	2	2	no	—
58	C₂×D₈×C₃₇	—	2	2	no	—
59	C₂²×C₈×C₃₇	—	2	1	no	—
60	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
61	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
62	#127×C₃₇	C₂³	1	1	yes	characteristic
63	#127×C₃₇	C₂³	1	1	yes	characteristic
64	#126×C₃₇	—	2	4	no	—
65	#125×C₃₇	—	2	2	no	—
66	#124×C₃₇	—	2	2	no	—
67	#124×C₃₇	—	2	1	no	—
68	#124×C₃₇	D₄	1	2	yes	—
69	#123×C₃₇	—	2	2	no	—
70	#123×C₃₇	—	2	4	no	—
71	#123×C₃₇	—	2	2	no	—
72	C₂²⋊Q₈×C₃₇	—	2	4	no	—
73	C₂²⋊Q₈×C₃₇	—	2	2	no	—
74	#121×C₃₇	—	2	4	no	—
75	#121×C₃₇	—	2	2	no	—
76	#121×C₃₇	—	2	2	no	—
77	#121×C₃₇	—	2	2	no	—
78	#120×C₃₇	—	2	2	no	—
79	#120×C₃₇	—	2	2	no	—
80	C₄×Q₈×C₃₇	D₄	1	2	yes	—
81	C₄×Q₈×C₃₇	C₂³	1	2	yes	—
82	C₄×D₄×C₃₇	—	2	4	no	—
83	C₄×D₄×C₃₇	—	2	4	no	—
84	C₄×D₄×C₃₇	—	2	2	no	—
85	C₄×D₄×C₃₇	—	2	2	no	—
86	C₄×D₄×C₃₇	—	2	2	no	—
87	C₄×D₄×C₃₇	—	2	2	no	—
88	C₄×D₄×C₃₇	—	2	2	no	—
89	C₄×D₄×C₃₇	—	2	2	no	—
90	C₄×D₄×C₃₇	D₄	1	2	yes	—
91	C₄×D₄×C₃₇	C₂³	1	2	yes	—
92	#117×C₃₇	—	2	2	no	—
93	#117×C₃₇	—	2	2	no	—
94	#117×C₃₇	D₄	1	2	yes	—
95	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
97	C₂×C₄²×C₃₇	—	2	2	no	—
98	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
99	#107×C₃₇	—	2	2	no	—
100	#106×C₃₇	—	2	2	no	—
101	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
102	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
103	#103×C₃₇	—	2	2	no	—
104	#102×C₃₇	—	2	2	no	—
105	#102×C₃₇	—	2	2	no	—
106	#102×C₃₇	—	2	2	no	—
107	C₂²⋊C₈×C₃₇	—	2	2	no	—
108	C₄×C₈×C₃₇	—	2	1	no	—
109	C₄×C₈×C₃₇	—	2	2	no	—
110	C₄×C₈×C₃₇	C₂³	1	1	yes	characteristic
111	C₄×C₈×C₃₇	C₂³	1	1	yes	characteristic
112	C₂⁴×C₃₇	—	2	2	no	—
113	#41×C₃₇	—	2	4	no	—
114	#41×C₃₇	—	4	2	no	—
115	#41×C₃₇	—	4	4	no	—
116	#41×C₃₇	—	4	4	no	—
117	C₂×Q₈×C₃₇	—	2	1	no	—
118	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
119	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
120	C₂×D₄×C₃₇	—	2	4	no	—
121	C₂×D₄×C₃₇	—	2	2	no	—
122	C₂×D₄×C₃₇	—	2	2	no	—
123	C₂×D₄×C₃₇	—	2	2	no	—
124	C₂×D₄×C₃₇	—	2	2	no	—
125	C₂×D₄×C₃₇	—	2	1	no	—
126	C₂×D₄×C₃₇	—	4	4	no	—
127	C₂×D₄×C₃₇	—	4	4	no	—
128	C₂×D₄×C₃₇	—	4	1	no	—
129	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
130	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₃₇	—	2	4	no	—
132	C₂²×C₄×C₃₇	—	2	2	no	—
133	C₂²×C₄×C₃₇	—	2	2	no	—
134	C₂²×C₄×C₃₇	—	2	2	no	—
135	C₂²×C₄×C₃₇	—	2	2	no	—
136	C₂²×C₄×C₃₇	—	2	2	no	—
137	C₂²×C₄×C₃₇	—	4	1	no	—
138	C₂²×C₄×C₃₇	—	8	4	no	—
139	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
141	Q₁₆×C₃₇	—	4	4	no	—
142	SD₁₆×C₃₇	—	4	4	no	—
143	SD₁₆×C₃₇	—	4	4	no	—
144	SD₁₆×C₃₇	—	4	4	no	—
145	D₈×C₃₇	—	4	4	no	—
146	D₈×C₃₇	—	4	4	no	—
147	C₂×C₈×C₃₇	—	2	4	no	—
148	C₂×C₈×C₃₇	—	2	1	no	—
149	C₂×C₈×C₃₇	—	2	1	no	—
150	C₂×C₈×C₃₇	—	2	2	no	—
151	C₂×C₈×C₃₇	—	2	2	no	—
152	C₄⋊C₄×C₃₇	—	2	4	no	—
153	C₄⋊C₄×C₃₇	—	2	4	no	—
154	C₄⋊C₄×C₃₇	—	2	2	no	—
155	C₄⋊C₄×C₃₇	—	2	2	no	—
156	C₄⋊C₄×C₃₇	—	2	2	no	—
157	C₄⋊C₄×C₃₇	—	2	2	no	—
158	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
159	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
160	C₂²⋊C₄×C₃₇	—	2	4	no	—
161	C₂²⋊C₄×C₃₇	—	2	4	no	—
162	C₂²⋊C₄×C₃₇	—	2	2	no	—
163	C₂²⋊C₄×C₃₇	—	2	2	no	—
164	C₂²⋊C₄×C₃₇	—	2	2	no	—
165	C₂²⋊C₄×C₃₇	—	2	2	no	—
166	C₂²⋊C₄×C₃₇	—	2	4	no	—
167	C₂²⋊C₄×C₃₇	—	2	2	no	—
168	C₂²⋊C₄×C₃₇	—	4	2	no	—
169	C₄²×C₃₇	—	2	2	no	—
170	C₄²×C₃₇	—	2	2	no	—
171	C₄²×C₃₇	—	2	2	no	—
172	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₃₇	C₂×D₄	1	2	yes	—
174	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
175	C₂³×C₃₇	—	2	2	no	—
176	C₂³×C₃₇	—	2	2	no	—
177	C₂³×C₃₇	—	4	8	no	—
178	C₂³×C₃₇	—	4	1	no	—
179	C₂³×C₃₇	—	8	2	no	—
180	C₂³×C₃₇	#120	1	1	yes	characteristic
181	Q₈×C₃₇	—	2	2	no	—
182	Q₈×C₃₇	—	2	2	no	—
183	Q₈×C₃₇	—	4	2	no	—
184	Q₈×C₃₇	—	4	2	no	—
185	D₄×C₃₇	—	2	2	no	—
186	D₄×C₃₇	—	4	2	no	—
187	D₄×C₃₇	—	4	2	no	—
188	D₄×C₃₇	—	4	4	no	—
189	D₄×C₃₇	—	4	8	no	—
190	D₄×C₃₇	—	4	2	no	—
191	D₄×C₃₇	—	4	2	no	—
192	D₄×C₃₇	—	4	2	no	—
193	D₄×C₃₇	—	4	2	no	—
194	D₄×C₃₇	—	8	2	no	—
195	D₄×C₃₇	—	8	2	no	—
196	D₄×C₃₇	#135	1	4	yes	complemented
197	C₂×C₄×C₃₇	—	2	2	no	—
198	C₂×C₄×C₃₇	—	2	2	no	—
199	C₂×C₄×C₃₇	—	2	2	no	—
200	C₂×C₄×C₃₇	—	2	2	no	—
201	C₂×C₄×C₃₇	—	2	2	no	—
202	C₂×C₄×C₃₇	—	2	2	no	—
203	C₂×C₄×C₃₇	—	2	2	no	—
204	C₂×C₄×C₃₇	—	4	4	no	—
205	C₂×C₄×C₃₇	—	4	2	no	—
206	C₂×C₄×C₃₇	—	4	2	no	—
207	C₂×C₄×C₃₇	—	4	4	no	—
208	C₂×C₄×C₃₇	—	4	4	no	—
209	C₂×C₄×C₃₇	—	4	1	no	—
210	C₂×C₄×C₃₇	—	8	2	no	—
211	C₂×C₄×C₃₇	—	8	4	no	—
212	C₂×C₄×C₃₇	—	8	2	no	—
213	C₂×C₄×C₃₇	#120	1	2	yes	—
214	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
215	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
217	C₈×C₃₇	—	2	2	no	—
218	C₈×C₃₇	—	2	2	no	—
219	C₈×C₃₇	—	4	2	no	—
220	C₈×C₃₇	—	4	2	no	—
221	#18480	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₂²×C₃₇	—	2	2	no	—
223	C₂²×C₃₇	—	2	4	no	—
224	C₂²×C₃₇	—	2	1	no	—
225	C₂²×C₃₇	—	4	2	no	—
226	C₂²×C₃₇	—	4	2	no	—
227	C₂²×C₃₇	—	4	4	no	—
228	C₂²×C₃₇	—	4	2	no	—
229	C₂²×C₃₇	—	8	8	no	—
230	C₂²×C₃₇	—	8	2	no	—
231	C₂²×C₃₇	—	8	1	no	—
232	C₂²×C₃₇	C₂×#120	1	1	yes	characteristic
233	C₄×C₃₇	—	2	2	no	—
234	C₄×C₃₇	—	2	1	no	—
235	C₄×C₃₇	—	4	2	no	—
236	C₄×C₃₇	—	4	2	no	—
237	C₄×C₃₇	—	4	2	no	—
238	C₄×C₃₇	—	4	2	no	—
239	C₄×C₃₇	—	8	1	no	—
240	C₄×C₃₇	#453	1	2	yes	—
241	C₄×C₃₇	C₂×#135	1	2	yes	—
242	C₄×C₃₇	#575	1	2	yes	—
243	#3481	C₂×C₃₇	1	1	yes	characteristic, complemented
244	#3147	C₂×C₃₇	1	1	yes	characteristic, complemented
245	#3106	C₂×C₃₇	1	2	yes	complemented
246	#1632	C₂×C₃₇	1	2	yes	complemented
247	#1630	C₂×C₃₇	1	1	yes	characteristic, complemented
248	#1629	C₂×C₃₇	1	1	yes	characteristic, complemented
249	#1622	C₂×C₃₇	1	2	yes	complemented
250	#1620	C₂×C₃₇	1	1	yes	characteristic, complemented
251	#1619	C₂×C₃₇	1	1	yes	characteristic, complemented
252	#1543	C₂×C₃₇	1	1	yes	characteristic, complemented
253	#1476	C₂×C₃₇	1	2	yes	complemented
254	C₂×C₃₇	—	4	1	no	—
255	C₂×C₃₇	—	4	4	no	—
256	C₂×C₃₇	—	8	2	no	—
257	C₂×C₃₇	—	16	1	no	—
258	C₂×C₃₇	#3002	1	2	yes	—
259	C₂×C₃₇	C₂×#453	1	1	yes	characteristic
260	C₂×#135	—	2	2	no	—
261	#559	C₂²×C₃₇	1	1	yes	characteristic
262	#554	C₂²×C₃₇	1	2	yes	—
263	#553	—	2	2	no	—
264	#551	—	2	2	no	—
265	#546	—	2	2	no	—
266	D₄²	C₂²×C₃₇	1	1	yes	characteristic
267	#532	C₂²×C₃₇	1	1	yes	characteristic
268	#532	C₂²×C₃₇	1	1	yes	characteristic, complemented
269	#529	—	2	2	no	—
270	#525	—	2	2	no	—
271	C₄×#41	C₂²×C₃₇	1	2	yes	—
272	C₂×C₄×D₄	—	2	2	no	—
273	#495	—	2	2	no	—
274	#494	C₂²×C₃₇	1	1	yes	characteristic, complemented
275	#493	C₂²×C₃₇	1	1	yes	characteristic
276	#492	C₂²×C₃₇	1	1	yes	characteristic
277	#492	C₂²×C₃₇	1	1	yes	characteristic, complemented
278	#482	—	2	2	no	—
279	#477	C₂²×C₃₇	1	2	yes	complemented
280	#476	C₂²×C₃₇	1	2	yes	—
281	#460	C₂²×C₃₇	1	2	yes	complemented
282	#459	C₂²×C₃₇	1	2	yes	—
283	#449	—	2	2	no	—
284	C₄×SD₁₆	—	2	2	no	—
285	C₄×D₈	—	2	2	no	—
286	#431	C₂²×C₃₇	1	2	yes	complemented
287	C₂×C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic, complemented
288	#333	C₂²×C₃₇	1	2	yes	complemented
289	#331	C₂²×C₃₇	1	1	yes	characteristic
290	#331	C₂²×C₃₇	1	1	yes	characteristic
291	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	complemented
292	Q₈⋊C₈	C₂²×C₃₇	1	2	yes	complemented
293	D₄⋊C₈	C₂²×C₃₇	1	2	yes	—
294	D₄⋊C₈	C₂²×C₃₇	1	2	yes	—
295	C₃₇	#18480	1	1	yes	characteristic, direct product factor, Sylow
296	C₂×#41	—	2	1	no	—
297	C₂×#41	D₄×C₃₇	1	2	yes	—
298	C₂×#41	D₄×C₃₇	1	2	yes	—
299	C₂²×D₄	—	2	2	no	—
300	C₂³×C₄	—	2	2	no	—
301	#135	—	4	8	no	—
302	C₂×Q₁₆	—	2	2	no	—
303	C₂×SD₁₆	—	2	2	no	—
304	C₂×SD₁₆	—	2	2	no	—
305	C₂×SD₁₆	—	2	2	no	—
306	C₂×D₈	—	2	2	no	—
307	C₂×D₈	—	2	2	no	—
308	C₂²×C₈	—	2	1	no	—
309	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
310	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
311	#127	C₂³×C₃₇	1	1	yes	characteristic
312	#127	C₂³×C₃₇	1	1	yes	characteristic
313	#126	—	2	4	no	—
314	#125	—	2	2	no	—
315	#124	—	2	2	no	—
316	#124	—	2	1	no	—
317	#124	D₄×C₃₇	1	2	yes	—
318	#123	—	2	2	no	—
319	#123	—	2	4	no	—
320	#123	—	2	2	no	—
321	C₂²⋊Q₈	—	2	4	no	—
322	C₂²⋊Q₈	—	2	2	no	—
323	#121	—	2	4	no	—
324	#121	—	2	2	no	—
325	#121	—	2	2	no	—
326	#121	—	2	2	no	—
327	#120	—	2	2	no	—
328	#120	—	2	2	no	—
329	C₄×Q₈	D₄×C₃₇	1	2	yes	—
330	C₄×Q₈	C₂³×C₃₇	1	2	yes	—
331	C₄×D₄	—	2	4	no	—
332	C₄×D₄	—	2	4	no	—
333	C₄×D₄	—	2	2	no	—
334	C₄×D₄	—	2	2	no	—
335	C₄×D₄	—	2	2	no	—
336	C₄×D₄	—	2	2	no	—
337	C₄×D₄	—	2	2	no	—
338	C₄×D₄	—	2	2	no	—
339	C₄×D₄	D₄×C₃₇	1	2	yes	—
340	C₄×D₄	C₂³×C₃₇	1	2	yes	—
341	#117	—	2	2	no	—
342	#117	—	2	2	no	—
343	#117	D₄×C₃₇	1	2	yes	—
344	C₂×C₄⋊C₄	—	2	2	no	—
345	C₂×C₂²⋊C₄	—	2	4	no	—
346	C₂×C₄²	—	2	2	no	—
347	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
348	#107	—	2	2	no	—
349	#106	—	2	2	no	—
350	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
351	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
352	#103	—	2	2	no	—
353	#102	—	2	2	no	—
354	#102	—	2	2	no	—
355	#102	—	2	2	no	—
356	C₂²⋊C₈	—	2	2	no	—
357	C₄×C₈	—	2	1	no	—
358	C₄×C₈	—	2	2	no	—
359	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
360	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
361	C₂⁴	—	2	2	no	—
362	#41	—	2	4	no	—
363	#41	—	4	2	no	—
364	#41	—	4	4	no	—
365	#41	—	4	4	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
368	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	4	4	no	—
376	C₂×D₄	—	4	4	no	—
377	C₂×D₄	—	4	1	no	—
378	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
379	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	4	1	no	—
387	C₂²×C₄	—	8	4	no	—
388	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
389	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
390	Q₁₆	—	4	4	no	—
391	SD₁₆	—	4	4	no	—
392	SD₁₆	—	4	4	no	—
393	SD₁₆	—	4	4	no	—
394	D₈	—	4	4	no	—
395	D₈	—	4	4	no	—
396	C₂×C₈	—	2	4	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
408	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
409	C₂²⋊C₄	—	2	4	no	—
410	C₂²⋊C₄	—	2	4	no	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	4	2	no	—
418	C₄²	—	2	2	no	—
419	C₄²	—	2	2	no	—
420	C₄²	—	2	2	no	—
421	C₄²	C₂×D₄×C₃₇	1	2	yes	—
422	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
423	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	4	8	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	8	2	no	—
429	C₂³	#120×C₃₇	1	1	yes	characteristic
430	Q₈	—	2	2	no	—
431	Q₈	—	2	2	no	—
432	Q₈	—	4	2	no	—
433	Q₈	—	4	2	no	—
434	D₄	—	2	2	no	—
435	D₄	—	4	2	no	—
436	D₄	—	4	2	no	—
437	D₄	—	4	4	no	—
438	D₄	—	4	8	no	—
439	D₄	—	4	2	no	—
440	D₄	—	4	2	no	—
441	D₄	—	4	2	no	—
442	D₄	—	4	2	no	—
443	D₄	—	8	2	no	—
444	D₄	—	8	2	no	—
445	D₄	#135×C₃₇	1	4	yes	complemented
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	4	no	—
457	C₂×C₄	—	4	4	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	8	2	no	—
460	C₂×C₄	—	8	4	no	—
461	C₂×C₄	—	8	2	no	—
462	C₂×C₄	#120×C₃₇	1	2	yes	—
463	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
464	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
465	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
466	C₈	—	2	2	no	—
467	C₈	—	2	2	no	—
468	C₈	—	4	2	no	—
469	C₈	—	4	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	4	no	—
472	C₂²	—	2	1	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	4	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	8	8	no	—
478	C₂²	—	8	2	no	—
479	C₂²	—	8	1	no	—
480	C₂²	C₂×#120×C₃₇	1	1	yes	characteristic
481	C₄	—	2	2	no	—
482	C₄	—	2	1	no	—
483	C₄	—	4	2	no	—
484	C₄	—	4	2	no	—
485	C₄	—	4	2	no	—
486	C₄	—	4	2	no	—
487	C₄	—	8	1	no	—
488	C₄	C₃₇×#453	1	2	yes	—
489	C₄	C₂×#135×C₃₇	1	2	yes	—
490	C₄	C₃₇×#575	1	2	yes	—
491	C₂	—	4	1	no	—
492	C₂	—	4	4	no	—
493	C₂	—	8	2	no	—
494	C₂	—	16	1	no	—
495	C₂	C₃₇×#3002	1	2	yes	—
496	C₂	C₂×C₃₇×#453	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₇	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₇
socle	C₂²×C₃₇	C₂×#120
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×#3481	C₂	semidirect
2. C₃₇×#3147	C₂	semidirect
3. C₃₇×#3106	C₂	semidirect
4. C₃₇×#1632	C₂	semidirect
5. C₃₇×#1630	C₂	semidirect
6. C₃₇×#1629	C₂	semidirect
7. C₃₇×#1622	C₂	semidirect
8. C₃₇×#1620	C₂	semidirect
9. C₃₇×#1619	C₂	semidirect
10. C₃₇×#1543	C₂	semidirect
11. C₃₇×#1476	C₂	semidirect
20. C₃₇×#532	C₂²	semidirect
26. C₃₇×#494	C₂²	semidirect
29. C₃₇×#492	C₂²	semidirect
31. C₃₇×#477	C₂²	semidirect
33. C₃₇×#460	C₂²	semidirect
38. C₃₇×#431	C₂²	semidirect
39. C₂×C₄×C₈×C₃₇	C₂²	semidirect
40. C₃₇×#333	C₂²	semidirect
43. C₃₇×Q₈⋊C₈	C₂²	semidirect
44. C₃₇×Q₈⋊C₈	C₂²	semidirect
196. D₄×C₃₇	#135	semidirect
221. #18480	C₃₇	direct (N × H)
243. #3481	C₂×C₃₇	semidirect
244. #3147	C₂×C₃₇	semidirect
245. #3106	C₂×C₃₇	semidirect
246. #1632	C₂×C₃₇	semidirect
247. #1630	C₂×C₃₇	semidirect
248. #1629	C₂×C₃₇	semidirect
249. #1622	C₂×C₃₇	semidirect
250. #1620	C₂×C₃₇	semidirect
251. #1619	C₂×C₃₇	semidirect
252. #1543	C₂×C₃₇	semidirect
253. #1476	C₂×C₃₇	semidirect
268. #532	C₂²×C₃₇	semidirect
274. #494	C₂²×C₃₇	semidirect
277. #492	C₂²×C₃₇	semidirect
279. #477	C₂²×C₃₇	semidirect
281. #460	C₂²×C₃₇	semidirect
286. #431	C₂²×C₃₇	semidirect
287. C₂×C₄×C₈	C₂²×C₃₇	semidirect
288. #333	C₂²×C₃₇	semidirect
291. Q₈⋊C₈	C₂²×C₃₇	semidirect
292. Q₈⋊C₈	C₂²×C₃₇	semidirect
295. C₃₇	#18480	direct (N × H)
445. D₄	#135×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₃₇×#3481	2
C₃₇×#3147	2
C₃₇×#3106	2
C₃₇×#1632	2
C₃₇×#1630	2
C₃₇×#1629	2
C₃₇×#1622	2
C₃₇×#1620	2
C₃₇×#1619	2
C₃₇×#1543	2
C₃₇×#1476	2
#18480	37

Subgroups — C37×#18480 #22639733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#18480 #22639733