Subgroups — #18003433

Order 4736.

470 conjugacy classes of subgroups.

The subgroup lattice has 262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924567	C₂	1	1	yes	maximal, characteristic
2	#14558014	C₂	1	1	yes	maximal, characteristic
3	#14558011	C₂	1	1	yes	maximal, characteristic, complemented
4	#14557637	C₂	1	2	yes	maximal, complemented
5	#14557636	C₂	1	2	yes	maximal, complemented
6	#14557625	C₂	1	2	yes	maximal, complemented
7	#14557618	C₂	1	2	yes	maximal, complemented
8	#14557573	C₂	1	1	yes	maximal, characteristic, complemented
9	#14557530	C₂	1	1	yes	maximal, characteristic
10	#14557488	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#103×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#10596962	C₂²	1	1	yes	characteristic
13	#11924567	C₄	1	8	yes	complemented
14	C₂×#10596942	C₂²	1	2	yes	—
15	C₂×#10596941	C₂²	1	2	yes	—
16	C₂×#10596934	C₂²	1	1	yes	characteristic
17	Q₈×Dic₃₇	—	2	1	no	—
18	Q₈×Dic₃₇	—	2	1	no	—
19	Q₈×Dic₃₇	C₂²	1	2	yes	—
20	Q₈×Dic₃₇	C₂²	1	2	yes	—
21	#11924501	C₂²	1	2	yes	—
22	#11924498	C₂²	1	2	yes	—
23	C₄×C₂²⋊D₃₇	—	2	2	no	—
24	#11924495	—	2	2	no	—
25	#11924495	C₂²	1	1	yes	characteristic
26	#11924495	C₂²	1	1	yes	characteristic
27	#11924494	—	2	1	no	—
28	C₄⋊C₄×D₃₇	—	2	1	no	—
29	#11924469	C₂²	1	2	yes	—
30	#11924467	C₂²	1	2	yes	—
31	#11924461	C₂²	1	1	yes	characteristic
32	#11924461	C₂²	1	1	yes	characteristic
33	#11924458	C₂²	1	1	yes	characteristic
34	#11924458	C₂²	1	1	yes	characteristic
35	#11924446	C₂²	1	2	yes	—
36	C₈×Dic₃₇	C₂²	1	2	yes	—
37	C₂²×Q₈×C₃₇	C₂²	1	1	yes	characteristic
38	C₂²×C₈×C₃₇	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
40	#103×C₃₇	C₂²	1	2	yes	—
41	#103×C₃₇	C₂²	1	2	yes	—
42	C₂×Q₈×C₃₇	—	2	1	no	—
43	C₂×Q₈×C₃₇	—	2	2	no	—
44	C₂×Q₈×C₃₇	C₂×C₄	1	4	yes	complemented
45	C₂×Q₈×C₃₇	C₂³	1	2	yes	—
46	C₂²×C₄×C₃₇	—	2	1	no	—
47	C₂²×C₄×C₃₇	—	2	1	no	—
48	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
49	C₂×C₂²⋊D₃₇	—	2	1	no	—
50	#10596962	—	2	2	no	—
51	#10596962	C₂×C₄	1	4	yes	—
52	C₂×D₁₄₈	C₂³	1	1	yes	characteristic
53	C₂×C₄×D₃₇	—	2	1	no	—
54	C₂×C₄×D₃₇	—	2	2	no	—
55	C₂×Dic₇₄	C₂³	1	1	yes	characteristic
56	C₂×C₈×C₃₇	—	2	2	no	—
57	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
58	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
59	C₄⋊C₄×C₃₇	—	2	1	no	—
60	C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
61	C₂²⋊Dic₃₇	—	2	1	no	—
62	C₂²⋊Dic₃₇	D₄	1	2	yes	—
63	#10596942	C₂×C₄	1	8	yes	complemented
64	#10596941	C₂×C₄	1	8	yes	complemented
65	#10596938	—	2	2	no	—
66	C₄⋊Dic₃₇	—	2	2	no	—
67	C₄⋊Dic₃₇	—	2	2	no	—
68	C₄⋊Dic₃₇	D₄	1	1	yes	characteristic
69	C₄⋊Dic₃₇	D₄	1	1	yes	characteristic
70	C₄⋊Dic₃₇	C₂³	1	1	yes	characteristic
71	C₄⋊Dic₃₇	C₂³	1	1	yes	characteristic
72	#10596936	—	2	2	no	—
73	C₄×Dic₃₇	—	2	1	no	—
74	C₄×Dic₃₇	—	2	2	no	—
75	C₄×Dic₃₇	—	2	2	no	—
76	C₄×Dic₃₇	—	2	2	no	—
77	C₄×Dic₃₇	C₂³	1	2	yes	—
78	#10596934	C₂×C₄	1	4	yes	complemented
79	C₂×#64436	C₂³	1	2	yes	—
80	C₂³×C₃₇	C₂×D₄	1	1	yes	characteristic
81	C₂²×D₃₇	—	2	1	no	—
82	Q₈×C₃₇	—	2	4	no	—
83	Q₈×C₃₇	—	2	2	no	—
84	Q₈×C₃₇	C₂²×C₄	1	4	yes	—
85	C₂×C₄×C₃₇	—	2	4	no	—
86	C₂×C₄×C₃₇	—	2	2	no	—
87	C₂×C₄×C₃₇	—	2	2	no	—
88	C₂×C₄×C₃₇	—	8	1	no	—
89	C₂×C₄×C₃₇	C₂²×C₄	1	2	yes	—
90	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
91	C₂×C₄×C₃₇	#41	1	2	yes	—
92	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
93	C₂²⋊D₃₇	—	2	4	no	—
94	C₂×Dic₃₇	—	2	1	no	—
95	C₂×Dic₃₇	—	2	1	no	—
96	C₂×Dic₃₇	—	2	1	no	—
97	C₂×Dic₃₇	C₂×D₄	1	2	yes	—
98	C₂×Dic₃₇	C₂×D₄	1	2	yes	—
99	D₁₄₈	—	2	1	no	—
100	D₁₄₈	C₂²×C₄	1	2	yes	—
101	C₄×D₃₇	—	2	4	no	—
102	C₄×D₃₇	—	8	2	no	—
103	Dic₇₄	—	2	1	no	—
104	Dic₇₄	C₂²×C₄	1	2	yes	—
105	C₈×C₃₇	—	2	1	no	—
106	C₈×C₃₇	—	2	1	no	—
107	#64436	C₂²×C₄	1	4	yes	—
108	C₂²×C₃₇	—	2	1	no	—
109	C₂²×C₃₇	—	2	1	no	—
110	C₂²×C₃₇	C₄×D₄	1	2	yes	—
111	C₂²×C₃₇	C₂²×D₄	1	1	yes	characteristic
112	C₂×D₃₇	—	2	2	no	—
113	C₂×D₃₇	—	4	1	no	—
114	C₂×D₃₇	—	4	1	no	—
115	C₄×C₃₇	—	2	4	no	—
116	C₄×C₃₇	—	4	2	no	—
117	C₄×C₃₇	C₄×D₄	1	2	yes	—
118	C₄×C₃₇	C₂³×C₄	1	1	yes	characteristic
119	C₄×C₃₇	C₂×#41	1	1	yes	characteristic
120	Dic₃₇	—	2	2	no	—
121	Dic₃₇	—	2	2	no	—
122	Dic₃₇	—	2	2	no	—
123	Dic₃₇	—	4	1	no	—
124	Dic₃₇	—	4	1	no	—
125	#2947	—	37	1	no	maximal, Sylow
126	C₂×C₃₇	—	2	2	no	—
127	C₂×C₃₇	C₂×C₄×D₄	1	1	yes	characteristic
128	C₂×C₃₇	#577	1	1	yes	characteristic
129	C₂×C₃₇	#578	1	1	yes	characteristic
130	D₃₇	—	4	2	no	—
131	C₂×#137	—	37	1	no	—
132	#520	—	37	1	no	—
133	#519	—	37	1	no	—
134	#441	—	37	2	no	—
135	#440	—	37	2	no	—
136	C₄×Q₁₆	—	37	2	no	—
137	C₄×SD₁₆	—	37	2	no	—
138	#428	—	37	1	no	—
139	#416	—	37	1	no	—
140	C₂×#103	D₃₇	1	1	yes	characteristic, complemented
141	#405	—	37	1	no	—
142	C₃₇	#2947	1	1	yes	characteristic, complemented, Sylow
143	C₂×#41	—	37	1	no	—
144	C₂²×Q₈	C₂×D₃₇	1	1	yes	characteristic
145	#137	—	37	8	no	—
146	C₂×Q₁₆	—	37	2	no	—
147	C₂×SD₁₆	—	37	2	no	—
148	C₂×M₁₆	—	37	1	no	—
149	C₂²×C₈	C₂×D₃₇	1	1	yes	characteristic
150	C₄×Q₈	—	37	2	no	—
151	C₄×Q₈	—	37	2	no	—
152	C₄×Q₈	—	37	2	no	—
153	C₄×Q₈	—	74	1	no	—
154	C₄×Q₈	—	74	1	no	—
155	C₄×D₄	—	37	2	no	—
156	C₄×D₄	—	74	2	no	—
157	#117	—	37	1	no	—
158	#117	—	37	1	no	—
159	#117	—	74	2	no	—
160	#117	—	74	1	no	—
161	C₂×C₄⋊C₄	—	74	1	no	—
162	C₂×C₄⋊C₄	C₂×D₃₇	1	1	yes	characteristic
163	#107	—	37	2	no	—
164	#106	—	37	2	no	—
165	#103	—	37	1	no	—
166	#103	—	37	1	no	—
167	#103	C₂×D₃₇	1	2	yes	—
168	#103	C₂×D₃₇	1	2	yes	—
169	#102	—	37	1	no	—
170	#102	—	37	1	no	—
171	#97	—	37	2	no	—
172	C₄×C₈	—	37	2	no	—
173	#41	—	37	4	no	—
174	#41	—	74	2	no	—
175	C₂×Q₈	—	2	1	no	—
176	C₂×Q₈	—	2	2	no	—
177	C₂×Q₈	—	37	1	no	—
178	C₂×Q₈	C₄×D₃₇	1	4	yes	complemented
179	C₂×Q₈	C₂²×D₃₇	1	2	yes	—
180	C₂×D₄	—	37	1	no	—
181	C₂×D₄	—	74	1	no	—
182	C₂²×C₄	—	2	1	no	—
183	C₂²×C₄	—	2	1	no	—
184	C₂²×C₄	—	74	2	no	—
185	C₂²×C₄	—	74	1	no	—
186	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
187	Q₁₆	—	37	8	no	—
188	SD₁₆	—	37	8	no	—
189	M₁₆	—	37	4	no	—
190	C₂×C₈	—	2	2	no	—
191	C₂×C₈	—	37	2	no	—
192	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
193	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
194	C₄⋊C₄	—	2	1	no	—
195	C₄⋊C₄	—	37	1	no	—
196	C₄⋊C₄	—	37	1	no	—
197	C₄⋊C₄	—	37	1	no	—
198	C₄⋊C₄	—	37	1	no	—
199	C₄⋊C₄	—	74	2	no	—
200	C₄⋊C₄	—	74	2	no	—
201	C₄⋊C₄	—	74	2	no	—
202	C₄⋊C₄	C₂²×D₃₇	1	2	yes	—
203	C₂²⋊C₄	—	37	2	no	—
204	C₂²⋊C₄	—	74	2	no	—
205	C₂²⋊C₄	—	74	1	no	—
206	C₄²	—	37	2	no	—
207	C₄²	—	74	2	no	—
208	C₄²	—	74	2	no	—
209	C₄²	—	74	2	no	—
210	C₄²	—	74	1	no	—
211	C₂³	—	74	1	no	—
212	C₂³	D₄×D₃₇	1	1	yes	characteristic
213	Q₈	—	2	4	no	—
214	Q₈	—	2	2	no	—
215	Q₈	—	37	2	no	—
216	Q₈	—	74	1	no	—
217	Q₈	C₂×C₄×D₃₇	1	4	yes	—
218	D₄	—	37	2	no	—
219	D₄	—	74	4	no	—
220	D₄	—	74	1	no	—
221	C₂×C₄	—	2	4	no	—
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	8	1	no	—
225	C₂×C₄	—	37	2	no	—
226	C₂×C₄	—	37	2	no	—
227	C₂×C₄	—	296	2	no	—
228	C₂×C₄	—	74	1	no	—
229	C₂×C₄	—	74	4	no	—
230	C₂×C₄	—	74	1	no	—
231	C₂×C₄	—	74	1	no	—
232	C₂×C₄	C₂×C₄×D₃₇	1	2	yes	—
233	C₂×C₄	D₄×D₃₇	1	1	yes	characteristic
234	C₂×C₄	#10596964	1	2	yes	—
235	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
236	C₈	—	2	1	no	—
237	C₈	—	2	1	no	—
238	C₈	—	37	4	no	—
239	C₂²	—	2	1	no	—
240	C₂²	—	2	1	no	—
241	C₂²	—	74	2	no	—
242	C₂²	—	148	1	no	—
243	C₂²	—	148	1	no	—
244	C₂²	#11924496	1	2	yes	—
245	C₂²	C₂×D₄×D₃₇	1	1	yes	characteristic
246	C₄	—	2	4	no	—
247	C₄	—	4	2	no	—
248	C₄	—	74	2	no	—
249	C₄	—	74	2	no	—
250	C₄	—	74	2	no	—
251	C₄	—	148	1	no	—
252	C₄	—	148	1	no	—
253	C₄	#11924496	1	2	yes	—
254	C₄	C₂²×C₄×D₃₇	1	1	yes	characteristic
255	C₄	C₂×#10596964	1	1	yes	characteristic
256	C₂	—	2	2	no	—
257	C₂	—	148	2	no	—
258	C₂	C₂×#11924496	1	1	yes	characteristic
259	C₂	#14558339	1	1	yes	characteristic
260	C₂	#14558346	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₃₇
commutator	C₄×C₃₇	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₃₇
Fitting	C₂×#103×C₃₇	C₂
socle	C₂²×C₃₇	C₂²×D₄
prime radical	C₂×#10596962	C₂²
cosocle	C₂×C₄×C₃₇	C₂⁴
hypercenter	C₂×#103	D₃₇
hypocenter	C₃₇	#2947
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#103

Complements

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

N	H ≅ G/N	type
3. #14558011	C₂	semidirect
4. #14557637	C₂	semidirect
5. #14557636	C₂	semidirect
6. #14557625	C₂	semidirect
7. #14557618	C₂	semidirect
8. #14557573	C₂	semidirect
10. #14557488	C₂	semidirect
11. C₂×#103×C₃₇	C₂	semidirect
13. #11924567	C₄	semidirect
44. C₂×Q₈×C₃₇	C₂×C₄	semidirect
63. #10596942	C₂×C₄	semidirect
64. #10596941	C₂×C₄	semidirect
78. #10596934	C₂×C₄	semidirect
140. C₂×#103	D₃₇	semidirect
142. C₃₇	#2947	semidirect
178. C₂×Q₈	C₄×D₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11924567	2
#14558014	2
#14558011	2
#14557637	2
#14557636	2
#14557625	2
#14557618	2
#14557573	2
#14557530	2
#14557488	2
C₂×#103×C₃₇	2
#2947	37