Subgroups — #462×D₃₇ #18004030

Order 4736.

480 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×D₃₇	C₂	1	2	yes	maximal
2	C₄⋊Q₈×D₃₇	C₂	1	1	yes	maximal, characteristic
3	C₄×Q₈×D₃₇	C₂	1	1	yes	maximal, characteristic
4	#14557744	C₂	1	1	yes	maximal, characteristic, complemented
5	#14557743	C₂	1	1	yes	maximal, characteristic, complemented
6	#14557742	C₂	1	2	yes	maximal, complemented
7	#14557741	C₂	1	2	yes	maximal, complemented
8	#14557740	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄⋊C₈×D₃₇	C₂	1	1	yes	maximal, characteristic
10	#103×D₃₇	C₂	1	2	yes	maximal
11	C₃₇×#462	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₈×D₃₇	C₂²	1	2	yes	—
13	C₂×Q₈×D₃₇	C₂²	1	1	yes	characteristic
14	C₂×Dic₁₄₈	C₂²	1	2	yes	—
15	C₂×#10596942	C₂²	1	2	yes	—
16	C₂×#10596942	C₂²	1	2	yes	—
17	Q₁₆×D₃₇	—	2	8	no	—
18	C₂×C₈×D₃₇	C₂²	1	2	yes	—
19	#11924536	C₂²	1	1	yes	characteristic
20	#11924535	—	2	1	no	—
21	#11924535	—	2	1	no	—
22	#11924534	C₂²	1	2	yes	—
23	Q₈×Dic₃₇	C₂²	1	1	yes	characteristic
24	C₄×Dic₇₄	—	2	1	no	—
25	C₄×Dic₇₄	C₂²	1	1	yes	characteristic
26	#11924501	—	2	1	no	—
27	#11924501	C₂²	1	1	yes	characteristic
28	C₄⋊C₄×D₃₇	—	2	1	no	—
29	C₄⋊C₄×D₃₇	—	2	1	no	—
30	C₄⋊C₄×D₃₇	—	2	1	no	—
31	C₄⋊C₄×D₃₇	C₂²	1	1	yes	characteristic
32	C₄²×D₃₇	—	2	1	no	—
33	C₄²×D₃₇	C₂²	1	1	yes	characteristic
34	C₄⋊#64436	C₂²	1	1	yes	characteristic
35	#11924465	C₂²	1	2	yes	—
36	#11924461	C₂²	1	2	yes	—
37	#11924460	C₂²	1	2	yes	—
38	#11924459	C₂²	1	2	yes	—
39	C₂×Q₁₆×C₃₇	C₂²	1	2	yes	—
40	C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
41	C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
42	C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
43	#103×C₃₇	C₂²	1	2	yes	—
44	C₂×Q₈×C₃₇	C₂³	1	2	yes	—
45	C₂×Q₈×C₃₇	C₂³	1	1	yes	characteristic
46	Q₈×D₃₇	—	2	2	no	—
47	Q₈×D₃₇	—	2	4	no	—
48	Q₈×D₃₇	—	2	4	no	—
49	Q₈×D₃₇	D₄	1	4	yes	—
50	C₂×C₄×D₃₇	—	2	1	no	—
51	C₂×C₄×D₃₇	—	2	1	no	—
52	C₂×C₄×D₃₇	—	2	2	no	—
53	C₂×C₄×D₃₇	D₄	1	1	yes	characteristic
54	C₂×C₄×D₃₇	D₄	1	1	yes	characteristic
55	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
56	C₂×Dic₇₄	—	2	1	no	—
57	C₂×Dic₇₄	—	2	2	no	—
58	C₂×Dic₇₄	C₂³	1	2	yes	—
59	C₂×Dic₇₄	C₂³	1	1	yes	characteristic
60	Q₁₆×C₃₇	—	2	4	no	—
61	C₂×C₈×C₃₇	C₂³	1	2	yes	—
62	C₄⋊C₄×C₃₇	—	2	1	no	—
63	C₄⋊C₄×C₃₇	—	2	1	no	—
64	C₄⋊C₄×C₃₇	—	2	1	no	—
65	C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
66	C₄²×C₃₇	—	2	1	no	—
67	C₄²×C₃₇	C₂³	1	1	yes	characteristic
68	#10596942	—	2	4	no	—
69	#10596942	—	2	4	no	—
70	C₄⋊Dic₃₇	—	2	1	no	—
71	C₄⋊Dic₃₇	—	2	1	no	—
72	C₄⋊Dic₃₇	—	2	1	no	—
73	C₄⋊Dic₃₇	C₂³	1	1	yes	characteristic
74	#10596936	—	2	1	no	—
75	#10596936	—	2	1	no	—
76	#10596936	—	2	2	no	—
77	#10596936	—	2	2	no	—
78	#10596936	—	2	1	no	—
79	C₄×Dic₃₇	—	2	1	no	—
80	C₄×Dic₃₇	—	2	1	no	—
81	C₄×Dic₃₇	—	2	1	no	—
82	C₄×Dic₃₇	D₄	1	1	yes	characteristic
83	C₄×Dic₃₇	D₄	1	1	yes	characteristic
84	C₄×Dic₃₇	C₂³	1	1	yes	characteristic
85	C₂×#64436	C₂³	1	2	yes	—
86	Dic₁₄₈	—	2	4	no	—
87	C₈×D₃₇	—	2	4	no	—
88	C₂²×D₃₇	C₂×D₄	1	1	yes	characteristic
89	Q₈×C₃₇	—	2	1	no	—
90	Q₈×C₃₇	—	2	2	no	—
91	Q₈×C₃₇	—	2	2	no	—
92	Q₈×C₃₇	C₂×D₄	1	2	yes	—
93	C₂×C₄×C₃₇	—	2	1	no	—
94	C₂×C₄×C₃₇	—	2	1	no	—
95	C₂×C₄×C₃₇	—	2	2	no	—
96	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
97	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
98	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
99	C₂×Dic₃₇	—	2	1	no	—
100	C₂×Dic₃₇	—	2	1	no	—
101	C₂×Dic₃₇	—	2	2	no	—
102	C₂×Dic₃₇	C₂×D₄	1	1	yes	characteristic
103	C₂×Dic₃₇	C₂×D₄	1	1	yes	characteristic
104	C₂×Dic₃₇	C₂×D₄	1	1	yes	characteristic
105	C₄×D₃₇	—	2	4	no	—
106	C₄×D₃₇	—	2	2	no	—
107	C₄×D₃₇	—	4	4	no	—
108	C₄×D₃₇	—	4	2	no	—
109	C₄×D₃₇	Q₁₆	1	4	yes	complemented
110	C₄×D₃₇	C₂×D₄	1	2	yes	—
111	C₄×D₃₇	#41	1	2	yes	—
112	Dic₇₄	—	2	1	no	—
113	Dic₇₄	—	2	4	no	—
114	Dic₇₄	—	2	2	no	—
115	Dic₇₄	—	2	2	no	—
116	Dic₇₄	—	4	4	no	—
117	Dic₇₄	C₂×D₄	1	2	yes	—
118	C₈×C₃₇	—	2	2	no	—
119	#64436	—	2	2	no	—
120	C₂²×C₃₇	C₂²×D₄	1	1	yes	characteristic
121	C₂×D₃₇	#121	1	2	yes	—
122	C₂×D₃₇	C₂×Q₁₆	1	2	yes	—
123	C₂×D₃₇	#137	1	2	yes	—
124	C₄×C₃₇	—	2	2	no	—
125	C₄×C₃₇	—	2	1	no	—
126	C₄×C₃₇	—	4	2	no	—
127	C₄×C₃₇	—	4	1	no	—
128	C₄×C₃₇	C₂×Q₁₆	1	2	yes	complemented
129	C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
130	C₄×C₃₇	C₂×#41	1	1	yes	characteristic
131	Dic₃₇	—	2	2	no	—
132	Dic₃₇	—	2	1	no	—
133	Dic₃₇	—	4	2	no	—
134	Dic₃₇	—	4	1	no	—
135	Dic₃₇	#121	1	2	yes	—
136	Dic₃₇	C₂×Q₁₆	1	2	yes	complemented
137	C₂×#462	—	37	1	no	maximal, Sylow
138	C₂×C₃₇	C₂×#121	1	1	yes	characteristic
139	C₂×C₃₇	C₂²×Q₁₆	1	1	yes	characteristic
140	C₂×C₃₇	C₂×#137	1	1	yes	characteristic
141	D₃₇	#462	1	4	yes	direct product factor
142	C₂²×Q₁₆	—	37	2	no	—
143	C₂×C₄⋊Q₈	—	37	1	no	—
144	C₂×C₄×Q₈	—	37	1	no	—
145	#462	—	37	2	no	—
146	#462	—	37	1	no	—
147	#462	—	37	1	no	—
148	#462	—	37	1	no	—
149	#462	—	37	2	no	—
150	#462	D₃₇	1	1	yes	characteristic, direct product factor
151	C₂×C₄⋊C₈	—	37	1	no	—
152	C₂×#103	—	37	2	no	—
153	C₃₇	C₂×#462	1	1	yes	characteristic, complemented, Sylow
154	C₂²×Q₈	—	37	1	no	—
155	C₂²×Q₈	—	37	2	no	—
156	C₂×Q₁₆	—	37	2	no	—
157	C₂×Q₁₆	—	37	2	no	—
158	C₂×Q₁₆	—	37	2	no	—
159	C₂×Q₁₆	—	74	8	no	—
160	C₂×Q₁₆	C₂×D₃₇	1	2	yes	—
161	C₂²×C₈	—	37	2	no	—
162	C₄⋊Q₈	—	37	2	no	—
163	C₄⋊Q₈	—	37	1	no	—
164	C₄⋊Q₈	—	74	1	no	—
165	C₄⋊Q₈	—	74	1	no	—
166	C₄⋊Q₈	C₂×D₃₇	1	1	yes	characteristic
167	C₄×Q₈	—	37	1	no	—
168	C₄×Q₈	—	37	1	no	—
169	C₄×Q₈	—	37	1	no	—
170	C₄×Q₈	—	74	1	no	—
171	C₄×Q₈	—	74	1	no	—
172	C₄×Q₈	C₂×D₃₇	1	1	yes	characteristic
173	C₂×C₄⋊C₄	—	37	1	no	—
174	C₂×C₄⋊C₄	—	74	1	no	—
175	C₂×C₄⋊C₄	—	74	1	no	—
176	C₂×C₄⋊C₄	—	74	1	no	—
177	C₂×C₄²	—	37	1	no	—
178	C₂×C₄²	—	74	1	no	—
179	C₄⋊C₈	—	37	2	no	—
180	C₄⋊C₈	—	37	1	no	—
181	C₄⋊C₈	C₂×D₃₇	1	1	yes	characteristic
182	#103	—	37	2	no	—
183	#103	—	37	2	no	—
184	#103	—	37	2	no	—
185	#103	C₂×D₃₇	1	2	yes	—
186	C₂×Q₈	—	37	4	no	—
187	C₂×Q₈	—	37	1	no	—
188	C₂×Q₈	—	37	2	no	—
189	C₂×Q₈	—	74	1	no	—
190	C₂×Q₈	—	74	2	no	—
191	C₂×Q₈	—	74	2	no	—
192	C₂×Q₈	—	74	4	no	—
193	C₂×Q₈	—	74	4	no	—
194	C₂×Q₈	C₂²×D₃₇	1	2	yes	—
195	C₂×Q₈	C₂²×D₃₇	1	1	yes	characteristic
196	C₂²×C₄	—	37	1	no	—
197	C₂²×C₄	—	37	1	no	—
198	C₂²×C₄	—	37	1	no	—
199	C₂²×C₄	—	74	1	no	—
200	C₂²×C₄	—	74	1	no	—
201	C₂²×C₄	—	74	2	no	—
202	Q₁₆	—	2	4	no	—
203	Q₁₆	—	74	4	no	—
204	Q₁₆	—	74	4	no	—
205	Q₁₆	—	74	4	no	—
206	C₂×C₈	—	37	2	no	—
207	C₂×C₈	—	74	4	no	—
208	C₂×C₈	C₂²×D₃₇	1	2	yes	—
209	C₄⋊C₄	—	2	1	no	—
210	C₄⋊C₄	—	2	1	no	—
211	C₄⋊C₄	—	2	1	no	—
212	C₄⋊C₄	—	37	1	no	—
213	C₄⋊C₄	—	74	1	no	—
214	C₄⋊C₄	—	74	1	no	—
215	C₄⋊C₄	—	74	2	no	—
216	C₄⋊C₄	—	74	2	no	—
217	C₄⋊C₄	—	74	1	no	—
218	C₄⋊C₄	—	74	1	no	—
219	C₄⋊C₄	—	74	1	no	—
220	C₄⋊C₄	—	74	1	no	—
221	C₄⋊C₄	C₂²×D₃₇	1	1	yes	characteristic
222	C₄²	—	2	1	no	—
223	C₄²	—	37	1	no	—
224	C₄²	—	37	1	no	—
225	C₄²	—	37	1	no	—
226	C₄²	—	74	1	no	—
227	C₄²	—	74	1	no	—
228	C₄²	—	74	1	no	—
229	C₄²	C₂²×D₃₇	1	1	yes	characteristic
230	C₂³	—	37	1	no	—
231	Q₈	—	2	1	no	—
232	Q₈	—	2	2	no	—
233	Q₈	—	2	2	no	—
234	Q₈	—	37	2	no	—
235	Q₈	—	74	4	no	—
236	Q₈	—	74	1	no	—
237	Q₈	—	74	2	no	—
238	Q₈	—	74	2	no	—
239	Q₈	—	148	4	no	—
240	Q₈	D₄×D₃₇	1	2	yes	—
241	C₂×C₄	—	2	1	no	—
242	C₂×C₄	—	2	1	no	—
243	C₂×C₄	—	2	2	no	—
244	C₂×C₄	—	37	1	no	—
245	C₂×C₄	—	37	1	no	—
246	C₂×C₄	—	37	4	no	—
247	C₂×C₄	—	37	2	no	—
248	C₂×C₄	—	37	2	no	—
249	C₂×C₄	—	37	1	no	—
250	C₂×C₄	—	74	2	no	—
251	C₂×C₄	—	74	4	no	—
252	C₂×C₄	—	74	1	no	—
253	C₂×C₄	—	74	1	no	—
254	C₂×C₄	—	74	2	no	—
255	C₂×C₄	—	148	4	no	—
256	C₂×C₄	—	148	2	no	—
257	C₂×C₄	D₄×D₃₇	1	1	yes	characteristic
258	C₂×C₄	D₄×D₃₇	1	1	yes	characteristic
259	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
260	C₈	—	2	2	no	—
261	C₈	—	74	2	no	—
262	C₂²	—	37	2	no	—
263	C₂²	—	37	2	no	—
264	C₂²	—	37	2	no	—
265	C₂²	C₂×D₄×D₃₇	1	1	yes	characteristic
266	C₄	—	2	2	no	—
267	C₄	—	2	1	no	—
268	C₄	—	4	2	no	—
269	C₄	—	4	1	no	—
270	C₄	—	37	2	no	—
271	C₄	—	37	2	no	—
272	C₄	—	74	2	no	—
273	C₄	—	74	1	no	—
274	C₄	—	148	2	no	—
275	C₄	—	148	1	no	—
276	C₄	Q₁₆×D₃₇	1	2	yes	complemented
277	C₄	C₂×D₄×D₃₇	1	1	yes	characteristic
278	C₄	#41×D₃₇	1	1	yes	characteristic
279	C₂	—	37	4	no	—
280	C₂	#121×D₃₇	1	1	yes	characteristic
281	C₂	C₂×Q₁₆×D₃₇	1	1	yes	characteristic
282	C₂	#137×D₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₃₇
commutator, cosocle	C₂×C₄×C₃₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₃₇
Fitting	C₃₇×#462	C₂
socle	C₂²×C₃₇	C₂²×D₄
prime radical	C₂²×D₃₇	C₂×D₄
hypercenter	#462	D₃₇
hypocenter	C₃₇	C₂×#462
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #462

Complements

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

N	H ≅ G/N	type
4. #14557744	C₂	semidirect
5. #14557743	C₂	semidirect
6. #14557742	C₂	semidirect
7. #14557741	C₂	semidirect
8. #14557740	C₂	semidirect
11. C₃₇×#462	C₂	semidirect
109. C₄×D₃₇	Q₁₆	semidirect
128. C₄×C₃₇	C₂×Q₁₆	semidirect
136. Dic₃₇	C₂×Q₁₆	semidirect
141. D₃₇	#462	direct (N × H)
150. #462	D₃₇	direct (N × H)
153. C₃₇	C₂×#462	semidirect
276. C₄	Q₁₆×D₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₁₆×D₃₇	2
C₄⋊Q₈×D₃₇	2
C₄×Q₈×D₃₇	2
#14557744	2
#14557743	2
#14557742	2
#14557741	2
#14557740	2
C₄⋊C₈×D₃₇	2
#103×D₃₇	2
C₃₇×#462	2
C₂×#462	37

Subgroups — #462×D37 #18004030

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #462×D₃₇ #18004030