Subgroups — C₃₇×#18914 #22640167

Order 9472.

954 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3502	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	C₂×C₃₇×#460	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#1626	C₂	1	4	yes	maximal, complemented
6	C₃₇×#1623	C₂	1	4	yes	maximal, complemented
7	C₃₇×#1542	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1481	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1479	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₃₇	—	2	1	no	—
11	Q₈²×C₃₇	—	2	1	no	—
12	Q₈²×C₃₇	C₂²	1	2	yes	complemented
13	C₃₇×#557	—	2	1	no	—
14	C₃₇×#557	—	2	2	no	—
15	C₃₇×#557	—	2	2	no	—
16	C₃₇×#557	C₂²	1	2	yes	complemented
17	C₃₇×#544	—	2	2	no	—
18	C₃₇×#544	—	2	1	no	—
19	C₃₇×#533	—	2	2	no	—
20	C₃₇×#533	C₂²	1	1	yes	characteristic
21	C₃₇×#533	C₂²	1	1	yes	characteristic
22	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic
23	C₃₇×#519	—	2	1	no	—
24	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
25	C₃₇×#492	—	2	1	no	—
26	C₃₇×#492	C₂²	1	2	yes	—
27	C₃₇×#486	—	2	1	no	—
28	C₃₇×#486	C₂²	1	2	yes	—
29	C₃₇×#460	—	2	2	no	—
30	C₃₇×#460	—	2	2	no	—
31	C₃₇×#460	C₂²	1	4	yes	—
32	C₃₇×#460	C₂²	1	4	yes	—
33	C₃₇×#450	—	2	2	no	—
34	C₃₇×#450	—	2	2	no	—
35	C₃₇×#431	C₂²	1	1	yes	characteristic
36	C₃₇×#431	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
38	C₂×#102×C₃₇	—	2	1	no	—
39	C₃₇×#333	C₂²	1	2	yes	complemented
40	C₃₇×#332	C₂²	1	2	yes	complemented
41	C₃₇×Q₈⋊C₈	C₂²	1	4	yes	complemented
42	C₃₇×Q₈⋊C₈	C₂²	1	4	yes	complemented
43	C₂²×Q₈×C₃₇	D₄	1	1	yes	characteristic
44	C₂²×D₄×C₃₇	—	2	1	no	—
45	C₂²×D₄×C₃₇	—	2	1	no	—
46	C₂²×D₄×C₃₇	—	2	1	no	—
47	C₂×SD₁₆×C₃₇	—	2	4	no	—
48	C₂×SD₁₆×C₃₇	—	2	4	no	—
49	C₂×SD₁₆×C₃₇	—	2	4	no	—
50	C₂×SD₁₆×C₃₇	—	4	4	no	—
51	C₂²×C₈×C₃₇	—	2	1	no	—
52	C₄⋊Q₈×C₃₇	—	2	4	no	—
53	C₄⋊Q₈×C₃₇	—	2	2	no	—
54	C₄⋊Q₈×C₃₇	—	2	2	no	—
55	C₄⋊Q₈×C₃₇	—	2	4	no	—
56	C₄⋊Q₈×C₃₇	—	2	2	no	—
57	C₄⋊Q₈×C₃₇	—	2	2	no	—
58	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
59	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
60	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
61	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
62	#127×C₃₇	—	2	1	no	—
63	#127×C₃₇	—	2	1	no	—
64	#127×C₃₇	—	2	1	no	—
65	#127×C₃₇	C₂³	1	2	yes	—
66	#125×C₃₇	—	2	4	no	—
67	#125×C₃₇	—	2	4	no	—
68	#125×C₃₇	—	2	2	no	—
69	#125×C₃₇	—	2	4	no	—
70	#125×C₃₇	—	2	2	no	—
71	#125×C₃₇	—	2	1	no	—
72	#125×C₃₇	—	2	1	no	—
73	C₂²⋊Q₈×C₃₇	—	2	4	no	—
74	C₂²⋊Q₈×C₃₇	—	2	1	no	—
75	C₂²⋊Q₈×C₃₇	—	2	1	no	—
76	C₂²⋊Q₈×C₃₇	D₄	1	2	yes	—
77	C₂²⋊Q₈×C₃₇	D₄	1	2	yes	—
78	C₄×Q₈×C₃₇	—	2	2	no	—
79	C₄×Q₈×C₃₇	—	2	2	no	—
80	C₄×Q₈×C₃₇	—	2	4	no	—
81	C₄×Q₈×C₃₇	—	2	2	no	—
82	C₄×Q₈×C₃₇	—	2	2	no	—
83	C₄×Q₈×C₃₇	—	2	2	no	—
84	C₄×Q₈×C₃₇	—	2	2	no	—
85	C₄×Q₈×C₃₇	—	2	1	no	—
86	C₄×Q₈×C₃₇	—	2	1	no	—
87	C₄×Q₈×C₃₇	—	2	1	no	—
88	C₄×Q₈×C₃₇	—	2	1	no	—
89	C₄×Q₈×C₃₇	D₄	1	2	yes	—
90	C₄×Q₈×C₃₇	D₄	1	2	yes	—
91	C₄×Q₈×C₃₇	C₂³	1	2	yes	—
92	C₄×Q₈×C₃₇	C₂³	1	2	yes	—
93	#117×C₃₇	—	2	4	no	—
94	#117×C₃₇	—	2	1	no	—
95	#117×C₃₇	—	2	1	no	—
96	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
97	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₃₇	—	2	1	no	—
99	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
100	C₄⋊C₈×C₃₇	—	2	1	no	—
101	C₄⋊C₈×C₃₇	—	2	1	no	—
102	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
103	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
104	#102×C₃₇	—	2	4	no	—
105	#102×C₃₇	—	2	4	no	—
106	#102×C₃₇	—	2	4	no	—
107	C₂²⋊C₈×C₃₇	—	2	1	no	—
108	C₂²⋊C₈×C₃₇	—	2	1	no	—
109	C₄×C₈×C₃₇	—	2	1	no	—
110	C₄×C₈×C₃₇	C₂³	1	2	yes	—
111	C₂⁴×C₃₇	—	4	1	no	—
112	C₂×Q₈×C₃₇	—	2	4	no	—
113	C₂×Q₈×C₃₇	—	2	1	no	—
114	C₂×Q₈×C₃₇	—	2	1	no	—
115	C₂×Q₈×C₃₇	—	2	2	no	—
116	C₂×Q₈×C₃₇	—	2	1	no	—
117	C₂×Q₈×C₃₇	SD₁₆	1	4	yes	complemented
118	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
119	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
120	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
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	—	4	1	no	—
125	C₂×D₄×C₃₇	—	4	1	no	—
126	C₂×D₄×C₃₇	—	4	1	no	—
127	C₂×D₄×C₃₇	—	4	2	no	—
128	C₂×D₄×C₃₇	—	4	2	no	—
129	C₂×D₄×C₃₇	—	8	2	no	—
130	C₂×D₄×C₃₇	—	8	2	no	—
131	C₂²×C₄×C₃₇	—	2	1	no	—
132	C₂²×C₄×C₃₇	—	2	1	no	—
133	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
136	SD₁₆×C₃₇	—	4	8	no	—
137	SD₁₆×C₃₇	—	8	4	no	—
138	SD₁₆×C₃₇	—	8	4	no	—
139	C₂×C₈×C₃₇	—	2	2	no	—
140	C₂×C₈×C₃₇	—	2	2	no	—
141	C₂×C₈×C₃₇	—	2	2	no	—
142	C₂×C₈×C₃₇	—	4	2	no	—
143	C₄⋊C₄×C₃₇	—	2	4	no	—
144	C₄⋊C₄×C₃₇	—	2	4	no	—
145	C₄⋊C₄×C₃₇	—	2	4	no	—
146	C₄⋊C₄×C₃₇	—	2	4	no	—
147	C₄⋊C₄×C₃₇	—	2	4	no	—
148	C₄⋊C₄×C₃₇	—	2	2	no	—
149	C₄⋊C₄×C₃₇	—	2	1	no	—
150	C₄⋊C₄×C₃₇	—	2	1	no	—
151	C₄⋊C₄×C₃₇	—	2	1	no	—
152	C₄⋊C₄×C₃₇	—	2	2	no	—
153	C₄⋊C₄×C₃₇	—	2	2	no	—
154	C₄⋊C₄×C₃₇	—	2	1	no	—
155	C₄⋊C₄×C₃₇	—	2	2	no	—
156	C₄⋊C₄×C₃₇	—	2	2	no	—
157	C₄⋊C₄×C₃₇	—	2	1	no	—
158	C₄⋊C₄×C₃₇	—	2	1	no	—
159	C₄⋊C₄×C₃₇	—	2	1	no	—
160	C₄⋊C₄×C₃₇	—	2	2	no	—
161	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
162	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
163	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
164	C₂²⋊C₄×C₃₇	—	2	2	no	—
165	C₂²⋊C₄×C₃₇	—	2	2	no	—
166	C₄²×C₃₇	—	2	4	no	—
167	C₄²×C₃₇	—	2	4	no	—
168	C₄²×C₃₇	—	2	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	1	yes	characteristic
174	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
176	C₂³×C₃₇	—	4	2	no	—
177	C₂³×C₃₇	—	8	2	no	—
178	C₂³×C₃₇	—	8	2	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	4	no	—
183	Q₈×C₃₇	—	2	4	no	—
184	Q₈×C₃₇	—	4	2	no	—
185	Q₈×C₃₇	—	4	2	no	—
186	Q₈×C₃₇	—	8	1	no	—
187	Q₈×C₃₇	—	8	4	no	—
188	Q₈×C₃₇	C₂×SD₁₆	1	4	yes	—
189	D₄×C₃₇	—	4	4	no	—
190	D₄×C₃₇	—	4	2	no	—
191	D₄×C₃₇	—	4	2	no	—
192	D₄×C₃₇	—	4	4	no	—
193	D₄×C₃₇	—	8	2	no	—
194	D₄×C₃₇	—	8	2	no	—
195	D₄×C₃₇	—	8	2	no	—
196	C₂×C₄×C₃₇	—	2	2	no	—
197	C₂×C₄×C₃₇	—	2	4	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	1	no	—
205	C₂×C₄×C₃₇	—	8	1	no	—
206	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
207	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
208	C₂×C₄×C₃₇	#120	1	1	yes	characteristic
209	C₂×C₄×C₃₇	C₂×SD₁₆	1	2	yes	—
210	C₂×C₄×C₃₇	#137	1	2	yes	—
211	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
214	C₈×C₃₇	—	4	2	no	—
215	C₈×C₃₇	—	4	2	no	—
216	C₈×C₃₇	—	4	2	no	—
217	#18914	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂²×C₃₇	—	2	1	no	—
219	C₂²×C₃₇	—	2	1	no	—
220	C₂²×C₃₇	—	8	2	no	—
221	C₂²×C₃₇	—	8	2	no	—
222	C₂²×C₃₇	—	8	2	no	—
223	C₂²×C₃₇	—	16	4	no	—
224	C₂²×C₃₇	#448	1	2	yes	—
225	C₂²×C₃₇	C₂×#120	1	1	yes	characteristic
226	C₄×C₃₇	—	2	4	no	—
227	C₄×C₃₇	—	2	1	no	—
228	C₄×C₃₇	—	2	1	no	—
229	C₄×C₃₇	—	2	1	no	—
230	C₄×C₃₇	—	4	2	no	—
231	C₄×C₃₇	—	4	2	no	—
232	C₄×C₃₇	—	4	2	no	—
233	C₄×C₃₇	—	4	2	no	—
234	C₄×C₃₇	—	4	2	no	—
235	C₄×C₃₇	#448	1	2	yes	—
236	C₄×C₃₇	C₂²×SD₁₆	1	1	yes	characteristic
237	C₄×C₃₇	C₂×#137	1	1	yes	characteristic
238	C₄×C₃₇	#577	1	2	yes	—
239	#3502	C₂×C₃₇	1	1	yes	characteristic, complemented
240	#3208	C₂×C₃₇	1	1	yes	characteristic
241	#3208	C₂×C₃₇	1	1	yes	characteristic
242	C₂×#460	C₂×C₃₇	1	1	yes	characteristic
243	#1626	C₂×C₃₇	1	4	yes	complemented
244	#1623	C₂×C₃₇	1	4	yes	complemented
245	#1542	C₂×C₃₇	1	1	yes	characteristic, complemented
246	#1481	C₂×C₃₇	1	1	yes	characteristic, complemented
247	#1479	C₂×C₃₇	1	1	yes	characteristic, complemented
248	C₂×C₃₇	—	2	2	no	—
249	C₂×C₃₇	—	16	2	no	—
250	C₂×C₃₇	C₂×#448	1	1	yes	characteristic
251	C₂×C₃₇	#3010	1	1	yes	characteristic
252	C₂×C₃₇	#3021	1	1	yes	characteristic
253	C₂²×SD₁₆	—	2	1	no	—
254	Q₈²	—	2	1	no	—
255	Q₈²	C₂²×C₃₇	1	2	yes	complemented
256	#557	—	2	1	no	—
257	#557	—	2	2	no	—
258	#557	—	2	2	no	—
259	#557	C₂²×C₃₇	1	2	yes	complemented
260	#544	—	2	2	no	—
261	#544	—	2	1	no	—
262	#533	—	2	2	no	—
263	#533	C₂²×C₃₇	1	1	yes	characteristic
264	#533	C₂²×C₃₇	1	1	yes	characteristic
265	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic
266	#519	—	2	1	no	—
267	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
268	#492	—	2	1	no	—
269	#492	C₂²×C₃₇	1	2	yes	—
270	#486	—	2	1	no	—
271	#486	C₂²×C₃₇	1	2	yes	—
272	#460	—	2	2	no	—
273	#460	—	2	2	no	—
274	#460	C₂²×C₃₇	1	4	yes	—
275	#460	C₂²×C₃₇	1	4	yes	—
276	#450	—	2	2	no	—
277	#450	—	2	2	no	—
278	#431	C₂²×C₃₇	1	1	yes	characteristic
279	#431	C₂²×C₃₇	1	1	yes	characteristic
280	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
281	C₂×#102	—	2	1	no	—
282	#333	C₂²×C₃₇	1	2	yes	complemented
283	#332	C₂²×C₃₇	1	2	yes	complemented
284	Q₈⋊C₈	C₂²×C₃₇	1	4	yes	complemented
285	Q₈⋊C₈	C₂²×C₃₇	1	4	yes	complemented
286	C₃₇	#18914	1	1	yes	characteristic, direct product factor, Sylow
287	C₂²×Q₈	D₄×C₃₇	1	1	yes	characteristic
288	C₂²×D₄	—	2	1	no	—
289	C₂²×D₄	—	2	1	no	—
290	C₂²×D₄	—	2	1	no	—
291	C₂×SD₁₆	—	2	4	no	—
292	C₂×SD₁₆	—	2	4	no	—
293	C₂×SD₁₆	—	2	4	no	—
294	C₂×SD₁₆	—	4	4	no	—
295	C₂²×C₈	—	2	1	no	—
296	C₄⋊Q₈	—	2	4	no	—
297	C₄⋊Q₈	—	2	2	no	—
298	C₄⋊Q₈	—	2	2	no	—
299	C₄⋊Q₈	—	2	4	no	—
300	C₄⋊Q₈	—	2	2	no	—
301	C₄⋊Q₈	—	2	2	no	—
302	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
303	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
304	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
305	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
306	#127	—	2	1	no	—
307	#127	—	2	1	no	—
308	#127	—	2	1	no	—
309	#127	C₂³×C₃₇	1	2	yes	—
310	#125	—	2	4	no	—
311	#125	—	2	4	no	—
312	#125	—	2	2	no	—
313	#125	—	2	4	no	—
314	#125	—	2	2	no	—
315	#125	—	2	1	no	—
316	#125	—	2	1	no	—
317	C₂²⋊Q₈	—	2	4	no	—
318	C₂²⋊Q₈	—	2	1	no	—
319	C₂²⋊Q₈	—	2	1	no	—
320	C₂²⋊Q₈	D₄×C₃₇	1	2	yes	—
321	C₂²⋊Q₈	D₄×C₃₇	1	2	yes	—
322	C₄×Q₈	—	2	2	no	—
323	C₄×Q₈	—	2	2	no	—
324	C₄×Q₈	—	2	4	no	—
325	C₄×Q₈	—	2	2	no	—
326	C₄×Q₈	—	2	2	no	—
327	C₄×Q₈	—	2	2	no	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	—	2	1	no	—
330	C₄×Q₈	—	2	1	no	—
331	C₄×Q₈	—	2	1	no	—
332	C₄×Q₈	—	2	1	no	—
333	C₄×Q₈	D₄×C₃₇	1	2	yes	—
334	C₄×Q₈	D₄×C₃₇	1	2	yes	—
335	C₄×Q₈	C₂³×C₃₇	1	2	yes	—
336	C₄×Q₈	C₂³×C₃₇	1	2	yes	—
337	#117	—	2	4	no	—
338	#117	—	2	1	no	—
339	#117	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
342	C₂×C₄²	—	2	1	no	—
343	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
344	C₄⋊C₈	—	2	1	no	—
345	C₄⋊C₈	—	2	1	no	—
346	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
347	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
348	#102	—	2	4	no	—
349	#102	—	2	4	no	—
350	#102	—	2	4	no	—
351	C₂²⋊C₈	—	2	1	no	—
352	C₂²⋊C₈	—	2	1	no	—
353	C₄×C₈	—	2	1	no	—
354	C₄×C₈	C₂³×C₃₇	1	2	yes	—
355	C₂⁴	—	4	1	no	—
356	C₂×Q₈	—	2	4	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	SD₁₆×C₃₇	1	4	yes	complemented
362	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
363	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
364	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	4	1	no	—
369	C₂×D₄	—	4	1	no	—
370	C₂×D₄	—	4	1	no	—
371	C₂×D₄	—	4	2	no	—
372	C₂×D₄	—	4	2	no	—
373	C₂×D₄	—	8	2	no	—
374	C₂×D₄	—	8	2	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
380	SD₁₆	—	4	8	no	—
381	SD₁₆	—	8	4	no	—
382	SD₁₆	—	8	4	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	4	2	no	—
387	C₄⋊C₄	—	2	4	no	—
388	C₄⋊C₄	—	2	4	no	—
389	C₄⋊C₄	—	2	4	no	—
390	C₄⋊C₄	—	2	4	no	—
391	C₄⋊C₄	—	2	4	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
406	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
407	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
408	C₂²⋊C₄	—	2	2	no	—
409	C₂²⋊C₄	—	2	2	no	—
410	C₄²	—	2	4	no	—
411	C₄²	—	2	4	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	2	2	no	—
415	C₄²	—	2	2	no	—
416	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
417	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
418	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
419	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
420	C₂³	—	4	2	no	—
421	C₂³	—	8	2	no	—
422	C₂³	—	8	2	no	—
423	C₂³	—	8	2	no	—
424	C₂³	#120×C₃₇	1	1	yes	characteristic
425	Q₈	—	2	2	no	—
426	Q₈	—	2	4	no	—
427	Q₈	—	2	4	no	—
428	Q₈	—	4	2	no	—
429	Q₈	—	4	2	no	—
430	Q₈	—	8	1	no	—
431	Q₈	—	8	4	no	—
432	Q₈	C₂×SD₁₆×C₃₇	1	4	yes	—
433	D₄	—	4	4	no	—
434	D₄	—	4	2	no	—
435	D₄	—	4	2	no	—
436	D₄	—	4	4	no	—
437	D₄	—	8	2	no	—
438	D₄	—	8	2	no	—
439	D₄	—	8	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	8	1	no	—
450	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
451	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
452	C₂×C₄	#120×C₃₇	1	1	yes	characteristic
453	C₂×C₄	C₂×SD₁₆×C₃₇	1	2	yes	—
454	C₂×C₄	#137×C₃₇	1	2	yes	—
455	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
456	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
457	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
458	C₈	—	4	2	no	—
459	C₈	—	4	2	no	—
460	C₈	—	4	2	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	8	2	no	—
464	C₂²	—	8	2	no	—
465	C₂²	—	8	2	no	—
466	C₂²	—	16	4	no	—
467	C₂²	C₃₇×#448	1	2	yes	—
468	C₂²	C₂×#120×C₃₇	1	1	yes	characteristic
469	C₄	—	2	4	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	1	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	2	no	—
478	C₄	C₃₇×#448	1	2	yes	—
479	C₄	C₂²×SD₁₆×C₃₇	1	1	yes	characteristic
480	C₄	C₂×#137×C₃₇	1	1	yes	characteristic
481	C₄	C₃₇×#577	1	2	yes	—
482	C₂	—	2	2	no	—
483	C₂	—	16	2	no	—
484	C₂	C₂×C₃₇×#448	1	1	yes	characteristic
485	C₂	C₃₇×#3010	1	1	yes	characteristic
486	C₂	C₃₇×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×#120
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×#3502	C₂	semidirect
5. C₃₇×#1626	C₂	semidirect
6. C₃₇×#1623	C₂	semidirect
7. C₃₇×#1542	C₂	semidirect
8. C₃₇×#1481	C₂	semidirect
9. C₃₇×#1479	C₂	semidirect
12. Q₈²×C₃₇	C₂²	semidirect
16. C₃₇×#557	C₂²	semidirect
39. C₃₇×#333	C₂²	semidirect
40. C₃₇×#332	C₂²	semidirect
41. C₃₇×Q₈⋊C₈	C₂²	semidirect
42. C₃₇×Q₈⋊C₈	C₂²	semidirect
117. C₂×Q₈×C₃₇	SD₁₆	semidirect
217. #18914	C₃₇	direct (N × H)
239. #3502	C₂×C₃₇	semidirect
243. #1626	C₂×C₃₇	semidirect
244. #1623	C₂×C₃₇	semidirect
245. #1542	C₂×C₃₇	semidirect
246. #1481	C₂×C₃₇	semidirect
247. #1479	C₂×C₃₇	semidirect
255. Q₈²	C₂²×C₃₇	semidirect
259. #557	C₂²×C₃₇	semidirect
282. #333	C₂²×C₃₇	semidirect
283. #332	C₂²×C₃₇	semidirect
284. Q₈⋊C₈	C₂²×C₃₇	semidirect
285. Q₈⋊C₈	C₂²×C₃₇	semidirect
286. C₃₇	#18914	direct (N × H)
361. C₂×Q₈	SD₁₆×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₃₇×#3502	2
C₃₇×#3208	2
C₂×C₃₇×#460	2
C₃₇×#1626	2
C₃₇×#1623	2
C₃₇×#1542	2
C₃₇×#1481	2
C₃₇×#1479	2
#18914	37

Subgroups — C37×#18914 #22640167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#18914 #22640167