Subgroups — C₃₇×#18934 #22640187

Order 9472.

1020 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3549	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×#3245	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#3214	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#3207	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#1646	C₂	1	2	yes	maximal, complemented
6	C₃₇×#1639	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1624	C₂	1	2	yes	maximal, complemented
8	C₃₇×#1619	C₂	1	2	yes	maximal, complemented
9	C₃₇×#1551	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1496	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1480	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₇×H(3,𝔽₄)	—	2	2	no	—
13	C₃₇×#555	—	2	1	no	—
14	C₃₇×#555	—	2	1	no	—
15	C₃₇×#555	C₂²	1	2	yes	—
16	D₄²×C₃₇	—	2	1	no	—
17	D₄²×C₃₇	—	2	1	no	—
18	D₄²×C₃₇	C₂²	1	2	yes	—
19	C₃₇×#535	—	2	2	no	—
20	C₃₇×#535	—	2	2	no	—
21	C₃₇×#535	—	2	2	no	—
22	C₃₇×#532	C₂²	1	1	yes	characteristic
23	C₃₇×#532	C₂²	1	1	yes	characteristic
24	C₃₇×#532	C₂²	1	1	yes	characteristic
25	C₃₇×#532	C₂²	1	1	yes	characteristic, complemented
26	C₃₇×#496	—	2	1	no	—
27	C₃₇×#493	C₂²	1	1	yes	characteristic
28	C₃₇×#492	C₂²	1	1	yes	characteristic, complemented
29	C₃₇×#489	—	2	1	no	—
30	C₃₇×#487	C₂²	1	1	yes	characteristic, complemented
31	C₃₇×#486	C₂²	1	1	yes	characteristic
32	C₃₇×#474	—	2	1	no	—
33	C₃₇×#474	C₂²	1	2	yes	complemented
34	C₃₇×#466	—	2	2	no	—
35	C₃₇×#463	—	2	2	no	—
36	C₃₇×#461	C₂²	1	2	yes	complemented
37	C₃₇×#459	—	2	1	no	—
38	C₃₇×#459	C₂²	1	2	yes	complemented
39	C₃₇×#459	C₂²	1	2	yes	complemented
40	C₃₇×#449	—	2	2	no	—
41	C₃₇×#449	—	2	2	no	—
42	C₃₇×#432	C₂²	1	1	yes	characteristic, complemented
43	C₃₇×#431	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic, complemented
45	C₃₇×#333	C₂²	1	2	yes	complemented
46	C₃₇×#331	C₂²	1	2	yes	—
47	C₃₇×D₄⋊C₈	C₂²	1	2	yes	complemented
48	C₃₇×D₄⋊C₈	C₂²	1	2	yes	complemented
49	C₃₇×D₄⋊C₈	C₂²	1	2	yes	complemented
50	C₃₇×D₄⋊C₈	C₂²	1	2	yes	complemented
51	C₂×#41×C₃₇	—	2	1	no	—
52	C₂×#41×C₃₇	—	2	1	no	—
53	C₂×#41×C₃₇	—	2	1	no	—
54	C₂×#41×C₃₇	D₄	1	2	yes	—
55	C₂²×D₄×C₃₇	—	2	2	no	—
56	C₂²×D₄×C₃₇	—	2	2	no	—
57	C₂²×D₄×C₃₇	—	2	2	no	—
58	C₂×SD₁₆×C₃₇	—	2	2	no	—
59	C₂×SD₁₆×C₃₇	—	2	2	no	—
60	C₂×D₈×C₃₇	—	2	2	no	—
61	C₂×D₈×C₃₇	—	2	2	no	—
62	C₂×D₈×C₃₇	—	2	2	no	—
63	C₂²×C₈×C₃₇	—	2	1	no	—
64	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
65	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
66	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
67	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
68	#127×C₃₇	—	2	4	no	—
69	#127×C₃₇	D₄	1	1	yes	characteristic
70	#127×C₃₇	D₄	1	1	yes	characteristic
71	#127×C₃₇	C₂³	1	1	yes	characteristic
72	#127×C₃₇	C₂³	1	1	yes	characteristic
73	#124×C₃₇	—	2	4	no	—
74	#124×C₃₇	—	2	4	no	—
75	#124×C₃₇	—	2	4	no	—
76	#124×C₃₇	—	2	1	no	—
77	#124×C₃₇	—	2	1	no	—
78	#124×C₃₇	—	2	1	no	—
79	#124×C₃₇	D₄	1	2	yes	—
80	#121×C₃₇	—	2	2	no	—
81	#121×C₃₇	—	2	2	no	—
82	#121×C₃₇	—	2	2	no	—
83	#121×C₃₇	—	2	2	no	—
84	#121×C₃₇	—	2	1	no	—
85	#121×C₃₇	—	2	1	no	—
86	#121×C₃₇	—	2	1	no	—
87	#121×C₃₇	—	2	1	no	—
88	#121×C₃₇	—	2	2	no	—
89	#121×C₃₇	—	2	2	no	—
90	#121×C₃₇	—	2	1	no	—
91	#121×C₃₇	—	2	1	no	—
92	#121×C₃₇	D₄	1	2	yes	—
93	#121×C₃₇	D₄	1	2	yes	—
94	#120×C₃₇	—	2	4	no	—
95	#120×C₃₇	—	2	4	no	—
96	#120×C₃₇	—	2	4	no	—
97	#120×C₃₇	—	2	4	no	—
98	C₄×D₄×C₃₇	—	2	1	no	—
99	C₄×D₄×C₃₇	—	2	1	no	—
100	C₄×D₄×C₃₇	—	2	1	no	—
101	C₄×D₄×C₃₇	—	2	1	no	—
102	C₄×D₄×C₃₇	—	2	1	no	—
103	C₄×D₄×C₃₇	—	2	1	no	—
104	C₄×D₄×C₃₇	C₂³	1	2	yes	—
105	C₄×D₄×C₃₇	C₂³	1	2	yes	—
106	#117×C₃₇	—	2	2	no	—
107	#117×C₃₇	—	2	2	no	—
108	#117×C₃₇	—	2	2	no	—
109	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
110	#107×C₃₇	—	2	2	no	—
111	C₄⋊C₈×C₃₇	—	2	1	no	—
112	C₄⋊C₈×C₃₇	—	2	1	no	—
113	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
114	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
115	#103×C₃₇	—	2	2	no	—
116	#103×C₃₇	—	2	2	no	—
117	#102×C₃₇	—	2	2	no	—
118	#102×C₃₇	—	2	2	no	—
119	#102×C₃₇	—	2	2	no	—
120	#102×C₃₇	—	2	2	no	—
121	C₂²⋊C₈×C₃₇	—	2	1	no	—
122	C₂²⋊C₈×C₃₇	—	2	1	no	—
123	#97×C₃₇	—	2	1	no	—
124	C₄×C₈×C₃₇	C₂³	1	1	yes	characteristic
125	C₄×C₈×C₃₇	C₂³	1	1	yes	characteristic
126	C₂⁴×C₃₇	—	2	4	no	—
127	#41×C₃₇	—	8	1	no	—
128	#41×C₃₇	—	8	2	no	—
129	#41×C₃₇	—	8	1	no	—
130	#41×C₃₇	—	8	2	no	—
131	#41×C₃₇	—	8	2	no	—
132	C₂×Q₈×C₃₇	—	2	1	no	—
133	C₂×Q₈×C₃₇	—	2	1	no	—
134	C₂×Q₈×C₃₇	—	2	1	no	—
135	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
136	C₂×D₄×C₃₇	—	2	4	no	—
137	C₂×D₄×C₃₇	—	2	4	no	—
138	C₂×D₄×C₃₇	—	2	4	no	—
139	C₂×D₄×C₃₇	—	2	2	no	—
140	C₂×D₄×C₃₇	—	2	2	no	—
141	C₂×D₄×C₃₇	—	2	2	no	—
142	C₂×D₄×C₃₇	—	2	1	no	—
143	C₂×D₄×C₃₇	—	2	1	no	—
144	C₂×D₄×C₃₇	—	2	1	no	—
145	C₂×D₄×C₃₇	—	2	1	no	—
146	C₂×D₄×C₃₇	—	2	1	no	—
147	C₂×D₄×C₃₇	—	2	1	no	—
148	C₂×D₄×C₃₇	—	2	1	no	—
149	C₂×D₄×C₃₇	—	2	1	no	—
150	C₂×D₄×C₃₇	—	2	1	no	—
151	C₂×D₄×C₃₇	—	4	1	no	—
152	C₂×D₄×C₃₇	—	8	2	no	—
153	C₂×D₄×C₃₇	—	8	2	no	—
154	C₂×D₄×C₃₇	—	8	2	no	—
155	C₂×D₄×C₃₇	—	8	2	no	—
156	C₂×D₄×C₃₇	—	8	4	no	—
157	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
158	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
159	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₃₇	—	2	2	no	—
161	C₂²×C₄×C₃₇	—	2	2	no	—
162	C₂²×C₄×C₃₇	—	2	2	no	—
163	C₂²×C₄×C₃₇	—	4	1	no	—
164	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
167	SD₁₆×C₃₇	—	8	2	no	—
168	SD₁₆×C₃₇	—	8	2	no	—
169	D₈×C₃₇	—	8	2	no	—
170	D₈×C₃₇	—	8	2	no	—
171	D₈×C₃₇	—	8	2	no	—
172	C₂×C₈×C₃₇	—	2	1	no	—
173	C₂×C₈×C₃₇	—	2	1	no	—
174	C₂×C₈×C₃₇	—	2	2	no	—
175	C₂×C₈×C₃₇	—	2	2	no	—
176	C₂×C₈×C₃₇	—	8	1	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	—	2	1	no	—
183	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
184	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
185	C₂²⋊C₄×C₃₇	—	2	4	no	—
186	C₂²⋊C₄×C₃₇	—	2	4	no	—
187	C₂²⋊C₄×C₃₇	—	2	4	no	—
188	C₂²⋊C₄×C₃₇	—	2	2	no	—
189	C₂²⋊C₄×C₃₇	—	2	2	no	—
190	C₂²⋊C₄×C₃₇	—	2	2	no	—
191	C₂²⋊C₄×C₃₇	—	2	2	no	—
192	C₂²⋊C₄×C₃₇	—	2	2	no	—
193	C₂²⋊C₄×C₃₇	—	2	2	no	—
194	C₂²⋊C₄×C₃₇	—	4	1	no	—
195	C₂²⋊C₄×C₃₇	—	4	1	no	—
196	C₄²×C₃₇	—	2	4	no	—
197	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
198	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
199	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
200	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
201	C₂³×C₃₇	—	2	2	no	—
202	C₂³×C₃₇	—	2	2	no	—
203	C₂³×C₃₇	—	2	2	no	—
204	C₂³×C₃₇	—	4	1	no	—
205	C₂³×C₃₇	—	8	4	no	—
206	C₂³×C₃₇	—	8	4	no	—
207	C₂³×C₃₇	—	8	4	no	—
208	C₂³×C₃₇	#120	1	1	yes	characteristic
209	Q₈×C₃₇	—	4	2	no	—
210	Q₈×C₃₇	—	4	2	no	—
211	Q₈×C₃₇	—	8	1	no	—
212	Q₈×C₃₇	—	8	1	no	—
213	D₄×C₃₇	—	2	2	no	—
214	D₄×C₃₇	—	2	2	no	—
215	D₄×C₃₇	—	2	2	no	—
216	D₄×C₃₇	—	2	2	no	—
217	D₄×C₃₇	—	4	2	no	—
218	D₄×C₃₇	—	4	2	no	—
219	D₄×C₃₇	—	4	2	no	—
220	D₄×C₃₇	—	4	2	no	—
221	D₄×C₃₇	—	4	2	no	—
222	D₄×C₃₇	—	4	1	no	—
223	D₄×C₃₇	—	4	1	no	—
224	D₄×C₃₇	—	4	2	no	—
225	D₄×C₃₇	—	4	1	no	—
226	D₄×C₃₇	—	4	1	no	—
227	D₄×C₃₇	—	8	1	no	—
228	D₄×C₃₇	—	8	1	no	—
229	D₄×C₃₇	—	8	2	no	—
230	D₄×C₃₇	—	8	2	no	—
231	D₄×C₃₇	—	8	2	no	—
232	D₄×C₃₇	—	8	4	no	—
233	D₄×C₃₇	—	8	4	no	—
234	D₄×C₃₇	—	8	4	no	—
235	D₄×C₃₇	—	8	2	no	—
236	C₂×C₄×C₃₇	—	2	1	no	—
237	C₂×C₄×C₃₇	—	2	2	no	—
238	C₂×C₄×C₃₇	—	2	1	no	—
239	C₂×C₄×C₃₇	—	2	2	no	—
240	C₂×C₄×C₃₇	—	2	2	no	—
241	C₂×C₄×C₃₇	—	2	2	no	—
242	C₂×C₄×C₃₇	—	4	1	no	—
243	C₂×C₄×C₃₇	—	4	4	no	—
244	C₂×C₄×C₃₇	—	4	2	no	—
245	C₂×C₄×C₃₇	—	4	2	no	—
246	C₂×C₄×C₃₇	—	4	2	no	—
247	C₂×C₄×C₃₇	—	4	2	no	—
248	C₂×C₄×C₃₇	—	4	1	no	—
249	C₂×C₄×C₃₇	—	8	2	no	—
250	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
251	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
252	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
253	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
256	C₈×C₃₇	—	4	1	no	—
257	C₈×C₃₇	—	4	1	no	—
258	C₈×C₃₇	—	4	2	no	—
259	C₈×C₃₇	—	4	2	no	—
260	#18934	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
261	C₂²×C₃₇	—	2	1	no	—
262	C₂²×C₃₇	—	2	1	no	—
263	C₂²×C₃₇	—	2	1	no	—
264	C₂²×C₃₇	—	4	2	no	—
265	C₂²×C₃₇	—	4	2	no	—
266	C₂²×C₃₇	—	4	2	no	—
267	C₂²×C₃₇	—	4	2	no	—
268	C₂²×C₃₇	—	4	2	no	—
269	C₂²×C₃₇	—	4	2	no	—
270	C₂²×C₃₇	—	4	2	no	—
271	C₂²×C₃₇	—	4	2	no	—
272	C₂²×C₃₇	—	4	2	no	—
273	C₂²×C₃₇	—	8	1	no	—
274	C₂²×C₃₇	—	8	1	no	—
275	C₂²×C₃₇	—	8	1	no	—
276	C₂²×C₃₇	—	16	8	no	—
277	C₂²×C₃₇	C₂×#120	1	1	yes	characteristic
278	C₄×C₃₇	—	2	1	no	—
279	C₄×C₃₇	—	2	1	no	—
280	C₄×C₃₇	—	2	1	no	—
281	C₄×C₃₇	—	2	1	no	—
282	C₄×C₃₇	—	4	2	no	—
283	C₄×C₃₇	—	4	2	no	—
284	C₄×C₃₇	—	4	2	no	—
285	C₄×C₃₇	—	8	1	no	—
286	C₄×C₃₇	#576	1	2	yes	—
287	C₄×C₃₇	#576	1	1	yes	characteristic
288	C₄×C₃₇	#577	1	1	yes	characteristic
289	#3549	C₂×C₃₇	1	1	yes	characteristic, complemented
290	#3245	C₂×C₃₇	1	1	yes	characteristic, complemented
291	#3214	C₂×C₃₇	1	1	yes	characteristic, complemented
292	#3207	C₂×C₃₇	1	1	yes	characteristic, complemented
293	#1646	C₂×C₃₇	1	2	yes	complemented
294	#1639	C₂×C₃₇	1	2	yes	complemented
295	#1624	C₂×C₃₇	1	2	yes	complemented
296	#1619	C₂×C₃₇	1	2	yes	complemented
297	#1551	C₂×C₃₇	1	1	yes	characteristic, complemented
298	#1496	C₂×C₃₇	1	1	yes	characteristic, complemented
299	#1480	C₂×C₃₇	1	1	yes	characteristic, complemented
300	C₂×C₃₇	—	4	1	no	—
301	C₂×C₃₇	—	8	2	no	—
302	C₂×C₃₇	—	8	2	no	—
303	C₂×C₃₇	—	8	2	no	—
304	C₂×C₃₇	—	16	1	no	—
305	C₂×C₃₇	#3008	1	1	yes	characteristic
306	C₂×C₃₇	#3012	1	1	yes	characteristic
307	C₂×C₃₇	#3019	1	1	yes	characteristic
308	H(3,𝔽₄)	—	2	2	no	—
309	#555	—	2	1	no	—
310	#555	—	2	1	no	—
311	#555	C₂²×C₃₇	1	2	yes	—
312	D₄²	—	2	1	no	—
313	D₄²	—	2	1	no	—
314	D₄²	C₂²×C₃₇	1	2	yes	—
315	#535	—	2	2	no	—
316	#535	—	2	2	no	—
317	#535	—	2	2	no	—
318	#532	C₂²×C₃₇	1	1	yes	characteristic
319	#532	C₂²×C₃₇	1	1	yes	characteristic
320	#532	C₂²×C₃₇	1	1	yes	characteristic
321	#532	C₂²×C₃₇	1	1	yes	characteristic, complemented
322	#496	—	2	1	no	—
323	#493	C₂²×C₃₇	1	1	yes	characteristic
324	#492	C₂²×C₃₇	1	1	yes	characteristic, complemented
325	#489	—	2	1	no	—
326	#487	C₂²×C₃₇	1	1	yes	characteristic, complemented
327	#486	C₂²×C₃₇	1	1	yes	characteristic
328	#474	—	2	1	no	—
329	#474	C₂²×C₃₇	1	2	yes	complemented
330	#466	—	2	2	no	—
331	#463	—	2	2	no	—
332	#461	C₂²×C₃₇	1	2	yes	complemented
333	#459	—	2	1	no	—
334	#459	C₂²×C₃₇	1	2	yes	complemented
335	#459	C₂²×C₃₇	1	2	yes	complemented
336	#449	—	2	2	no	—
337	#449	—	2	2	no	—
338	#432	C₂²×C₃₇	1	1	yes	characteristic, complemented
339	#431	C₂²×C₃₇	1	1	yes	characteristic, complemented
340	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic, complemented
341	#333	C₂²×C₃₇	1	2	yes	complemented
342	#331	C₂²×C₃₇	1	2	yes	—
343	D₄⋊C₈	C₂²×C₃₇	1	2	yes	complemented
344	D₄⋊C₈	C₂²×C₃₇	1	2	yes	complemented
345	D₄⋊C₈	C₂²×C₃₇	1	2	yes	complemented
346	D₄⋊C₈	C₂²×C₃₇	1	2	yes	complemented
347	C₃₇	#18934	1	1	yes	characteristic, direct product factor, Sylow
348	C₂×#41	—	2	1	no	—
349	C₂×#41	—	2	1	no	—
350	C₂×#41	—	2	1	no	—
351	C₂×#41	D₄×C₃₇	1	2	yes	—
352	C₂²×D₄	—	2	2	no	—
353	C₂²×D₄	—	2	2	no	—
354	C₂²×D₄	—	2	2	no	—
355	C₂×SD₁₆	—	2	2	no	—
356	C₂×SD₁₆	—	2	2	no	—
357	C₂×D₈	—	2	2	no	—
358	C₂×D₈	—	2	2	no	—
359	C₂×D₈	—	2	2	no	—
360	C₂²×C₈	—	2	1	no	—
361	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
362	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
363	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
364	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
365	#127	—	2	4	no	—
366	#127	D₄×C₃₇	1	1	yes	characteristic
367	#127	D₄×C₃₇	1	1	yes	characteristic
368	#127	C₂³×C₃₇	1	1	yes	characteristic
369	#127	C₂³×C₃₇	1	1	yes	characteristic
370	#124	—	2	4	no	—
371	#124	—	2	4	no	—
372	#124	—	2	4	no	—
373	#124	—	2	1	no	—
374	#124	—	2	1	no	—
375	#124	—	2	1	no	—
376	#124	D₄×C₃₇	1	2	yes	—
377	#121	—	2	2	no	—
378	#121	—	2	2	no	—
379	#121	—	2	2	no	—
380	#121	—	2	2	no	—
381	#121	—	2	1	no	—
382	#121	—	2	1	no	—
383	#121	—	2	1	no	—
384	#121	—	2	1	no	—
385	#121	—	2	2	no	—
386	#121	—	2	2	no	—
387	#121	—	2	1	no	—
388	#121	—	2	1	no	—
389	#121	D₄×C₃₇	1	2	yes	—
390	#121	D₄×C₃₇	1	2	yes	—
391	#120	—	2	4	no	—
392	#120	—	2	4	no	—
393	#120	—	2	4	no	—
394	#120	—	2	4	no	—
395	C₄×D₄	—	2	1	no	—
396	C₄×D₄	—	2	1	no	—
397	C₄×D₄	—	2	1	no	—
398	C₄×D₄	—	2	1	no	—
399	C₄×D₄	—	2	1	no	—
400	C₄×D₄	—	2	1	no	—
401	C₄×D₄	C₂³×C₃₇	1	2	yes	—
402	C₄×D₄	C₂³×C₃₇	1	2	yes	—
403	#117	—	2	2	no	—
404	#117	—	2	2	no	—
405	#117	—	2	2	no	—
406	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
407	#107	—	2	2	no	—
408	C₄⋊C₈	—	2	1	no	—
409	C₄⋊C₈	—	2	1	no	—
410	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
411	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
412	#103	—	2	2	no	—
413	#103	—	2	2	no	—
414	#102	—	2	2	no	—
415	#102	—	2	2	no	—
416	#102	—	2	2	no	—
417	#102	—	2	2	no	—
418	C₂²⋊C₈	—	2	1	no	—
419	C₂²⋊C₈	—	2	1	no	—
420	#97	—	2	1	no	—
421	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
422	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
423	C₂⁴	—	2	4	no	—
424	#41	—	8	1	no	—
425	#41	—	8	2	no	—
426	#41	—	8	1	no	—
427	#41	—	8	2	no	—
428	#41	—	8	2	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
433	C₂×D₄	—	2	4	no	—
434	C₂×D₄	—	2	4	no	—
435	C₂×D₄	—	2	4	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	4	1	no	—
449	C₂×D₄	—	8	2	no	—
450	C₂×D₄	—	8	2	no	—
451	C₂×D₄	—	8	2	no	—
452	C₂×D₄	—	8	2	no	—
453	C₂×D₄	—	8	4	no	—
454	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
455	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
456	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	4	1	no	—
461	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
462	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
463	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
464	SD₁₆	—	8	2	no	—
465	SD₁₆	—	8	2	no	—
466	D₈	—	8	2	no	—
467	D₈	—	8	2	no	—
468	D₈	—	8	2	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	—	8	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
481	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
482	C₂²⋊C₄	—	2	4	no	—
483	C₂²⋊C₄	—	2	4	no	—
484	C₂²⋊C₄	—	2	4	no	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	—	2	2	no	—
487	C₂²⋊C₄	—	2	2	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	4	1	no	—
492	C₂²⋊C₄	—	4	1	no	—
493	C₄²	—	2	4	no	—
494	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
495	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
496	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
497	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
498	C₂³	—	2	2	no	—
499	C₂³	—	2	2	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	4	1	no	—
502	C₂³	—	8	4	no	—
503	C₂³	—	8	4	no	—
504	C₂³	—	8	4	no	—
505	C₂³	#120×C₃₇	1	1	yes	characteristic
506	Q₈	—	4	2	no	—
507	Q₈	—	4	2	no	—
508	Q₈	—	8	1	no	—
509	Q₈	—	8	1	no	—
510	D₄	—	2	2	no	—
511	D₄	—	2	2	no	—
512	D₄	—	2	2	no	—
513	D₄	—	2	2	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	2	no	—
518	D₄	—	4	2	no	—
519	D₄	—	4	1	no	—
520	D₄	—	4	1	no	—
521	D₄	—	4	2	no	—
522	D₄	—	4	1	no	—
523	D₄	—	4	1	no	—
524	D₄	—	8	1	no	—
525	D₄	—	8	1	no	—
526	D₄	—	8	2	no	—
527	D₄	—	8	2	no	—
528	D₄	—	8	2	no	—
529	D₄	—	8	4	no	—
530	D₄	—	8	4	no	—
531	D₄	—	8	4	no	—
532	D₄	—	8	2	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	4	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	8	2	no	—
547	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
548	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
549	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
550	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
551	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
552	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
553	C₈	—	4	1	no	—
554	C₈	—	4	1	no	—
555	C₈	—	4	2	no	—
556	C₈	—	4	2	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	4	2	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	4	2	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	4	2	no	—
566	C₂²	—	4	2	no	—
567	C₂²	—	4	2	no	—
568	C₂²	—	4	2	no	—
569	C₂²	—	8	1	no	—
570	C₂²	—	8	1	no	—
571	C₂²	—	8	1	no	—
572	C₂²	—	16	8	no	—
573	C₂²	C₂×#120×C₃₇	1	1	yes	characteristic
574	C₄	—	2	1	no	—
575	C₄	—	2	1	no	—
576	C₄	—	2	1	no	—
577	C₄	—	2	1	no	—
578	C₄	—	4	2	no	—
579	C₄	—	4	2	no	—
580	C₄	—	4	2	no	—
581	C₄	—	8	1	no	—
582	C₄	C₃₇×#576	1	2	yes	—
583	C₄	C₃₇×#576	1	1	yes	characteristic
584	C₄	C₃₇×#577	1	1	yes	characteristic
585	C₂	—	4	1	no	—
586	C₂	—	8	2	no	—
587	C₂	—	8	2	no	—
588	C₂	—	8	2	no	—
589	C₂	—	16	1	no	—
590	C₂	C₃₇×#3008	1	1	yes	characteristic
591	C₂	C₃₇×#3012	1	1	yes	characteristic
592	C₂	C₃₇×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₇
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×#3549	C₂	semidirect
2. C₃₇×#3245	C₂	semidirect
3. C₃₇×#3214	C₂	semidirect
4. C₃₇×#3207	C₂	semidirect
5. C₃₇×#1646	C₂	semidirect
6. C₃₇×#1639	C₂	semidirect
7. C₃₇×#1624	C₂	semidirect
8. C₃₇×#1619	C₂	semidirect
9. C₃₇×#1551	C₂	semidirect
10. C₃₇×#1496	C₂	semidirect
11. C₃₇×#1480	C₂	semidirect
25. C₃₇×#532	C₂²	semidirect
28. C₃₇×#492	C₂²	semidirect
30. C₃₇×#487	C₂²	semidirect
33. C₃₇×#474	C₂²	semidirect
36. C₃₇×#461	C₂²	semidirect
38. C₃₇×#459	C₂²	semidirect
39. C₃₇×#459	C₂²	semidirect
42. C₃₇×#432	C₂²	semidirect
43. C₃₇×#431	C₂²	semidirect
44. C₂×C₄⋊C₈×C₃₇	C₂²	semidirect
45. C₃₇×#333	C₂²	semidirect
47. C₃₇×D₄⋊C₈	C₂²	semidirect
48. C₃₇×D₄⋊C₈	C₂²	semidirect
49. C₃₇×D₄⋊C₈	C₂²	semidirect
50. C₃₇×D₄⋊C₈	C₂²	semidirect
260. #18934	C₃₇	direct (N × H)
289. #3549	C₂×C₃₇	semidirect
290. #3245	C₂×C₃₇	semidirect
291. #3214	C₂×C₃₇	semidirect
292. #3207	C₂×C₃₇	semidirect
293. #1646	C₂×C₃₇	semidirect
294. #1639	C₂×C₃₇	semidirect
295. #1624	C₂×C₃₇	semidirect
296. #1619	C₂×C₃₇	semidirect
297. #1551	C₂×C₃₇	semidirect
298. #1496	C₂×C₃₇	semidirect
299. #1480	C₂×C₃₇	semidirect
321. #532	C₂²×C₃₇	semidirect
324. #492	C₂²×C₃₇	semidirect
326. #487	C₂²×C₃₇	semidirect
329. #474	C₂²×C₃₇	semidirect
332. #461	C₂²×C₃₇	semidirect
334. #459	C₂²×C₃₇	semidirect
335. #459	C₂²×C₃₇	semidirect
338. #432	C₂²×C₃₇	semidirect
339. #431	C₂²×C₃₇	semidirect
340. C₂×C₄⋊C₈	C₂²×C₃₇	semidirect
341. #333	C₂²×C₃₇	semidirect
343. D₄⋊C₈	C₂²×C₃₇	semidirect
344. D₄⋊C₈	C₂²×C₃₇	semidirect
345. D₄⋊C₈	C₂²×C₃₇	semidirect
346. D₄⋊C₈	C₂²×C₃₇	semidirect
347. C₃₇	#18934	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×#3549	2
C₃₇×#3245	2
C₃₇×#3214	2
C₃₇×#3207	2
C₃₇×#1646	2
C₃₇×#1639	2
C₃₇×#1624	2
C₃₇×#1619	2
C₃₇×#1551	2
C₃₇×#1496	2
C₃₇×#1480	2
#18934	37

Subgroups — C37×#18934 #22640187

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#18934 #22640187