Subgroups — #18073703

Order 4864.

390 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic
2	#14562383	C₂	1	1	yes	maximal, characteristic
3	#14561928	C₂	1	2	yes	maximal
4	#14561467	C₂	1	2	yes	maximal
5	C₁₉×#1564	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	2	yes	—
7	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
8	C₂×C₈×Dic₁₉	C₄	1	2	yes	—
9	C₂×C₈×Dic₁₉	C₄	1	2	yes	—
10	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
11	#11926297	C₄	1	2	yes	complemented
12	#11926295	C₄	1	2	yes	complemented
13	#11926266	—	2	2	no	—
14	#11926265	—	2	2	no	—
15	C₁₉×#431	C₂²	1	2	yes	—
16	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#335	C₄	1	2	yes	complemented
18	C₁₉×#334	C₄	1	2	yes	complemented
19	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
22	C₂×C₄×Dic₁₉	—	2	1	no	—
23	C₂×C₄×Dic₁₉	—	2	1	no	—
24	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
25	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
26	C₁₉×C₄⋊C₈	C₂×C₄	1	4	yes	—
27	C₁₉×C₂²⋊C₈	—	2	2	no	—
28	C₄×C₈×C₁₉	—	2	2	no	—
29	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
34	C₈×Dic₁₉	—	2	4	no	—
35	C₈×Dic₁₉	—	2	4	no	—
36	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	—
37	C₄×C₁₉⋊C₈	—	2	2	no	—
38	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
39	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
40	C₄×C₁₉⋊C₈	Q₈	1	2	yes	—
41	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
43	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
44	C₂²×Dic₁₉	—	2	2	no	—
45	C₂×C₈×C₁₉	—	2	2	no	—
46	C₂×C₈×C₁₉	—	2	4	no	—
47	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
48	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
49	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
50	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
51	C₂×C₈×C₁₉	M₁₆	1	4	yes	—
52	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
53	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
54	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
56	C₄×Dic₁₉	—	2	4	no	—
57	C₄×Dic₁₉	—	2	4	no	—
58	C₄×Dic₁₉	—	2	2	no	—
59	C₄×Dic₁₉	M₁₆	1	4	yes	—
60	C₂×C₁₉⋊C₈	—	2	2	no	—
61	C₂×C₁₉⋊C₈	—	2	2	no	—
62	C₂×C₁₉⋊C₈	—	2	4	no	—
63	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
64	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
65	#8267	—	19	1	no	maximal, Sylow
66	C₂³×C₁₉	#117	1	1	yes	characteristic
67	C₂×C₄×C₁₉	—	2	2	no	—
68	C₂×C₄×C₁₉	—	2	2	no	—
69	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
70	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
71	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
72	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
73	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
74	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
75	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
76	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
77	C₂×Dic₁₉	—	2	4	no	—
78	C₂×Dic₁₉	—	2	4	no	—
79	C₂×Dic₁₉	—	2	4	no	—
80	C₈×C₁₉	—	2	1	no	—
81	C₈×C₁₉	—	2	1	no	—
82	C₈×C₁₉	—	4	4	no	—
83	C₈×C₁₉	#97	1	2	yes	—
84	C₈×C₁₉	#97	1	2	yes	—
85	C₁₉⋊C₈	—	2	2	no	—
86	C₁₉⋊C₈	—	2	2	no	—
87	C₁₉⋊C₈	—	4	4	no	—
88	C₄²×C₈	—	19	1	no	—
89	#1564	—	19	1	no	—
90	#1564	D₁₉	1	1	yes	characteristic
91	#1452	—	19	2	no	—
92	#1276	—	19	2	no	—
93	C₂²×C₁₉	—	2	1	no	—
94	C₂²×C₁₉	—	2	1	no	—
95	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
96	C₂²×C₁₉	#432	1	2	yes	—
97	C₄×C₁₉	—	2	1	no	—
98	C₄×C₁₉	—	2	1	no	—
99	C₄×C₁₉	C₂×#97	1	1	yes	characteristic
100	C₄×C₁₉	C₄×M₁₆	1	1	yes	characteristic
101	C₄×C₁₉	#423	1	2	yes	—
102	C₄×C₁₉	#443	1	2	yes	—
103	C₄×C₁₉	#443	1	2	yes	—
104	Dic₁₉	—	2	8	no	—
105	#431	—	19	2	no	—
106	#431	C₂×D₁₉	1	2	yes	—
107	C₂×C₄×C₈	—	19	1	no	—
108	C₂×C₄×C₈	—	19	2	no	—
109	C₂×C₄×C₈	—	19	2	no	—
110	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
111	C₄³	—	19	1	no	—
112	#335	—	19	2	no	—
113	#335	Dic₁₉	1	2	yes	complemented
114	#334	—	19	2	no	—
115	#334	Dic₁₉	1	2	yes	complemented
116	#322	—	38	2	no	—
117	#322	—	38	2	no	—
118	C₂×C₁₉	—	2	2	no	—
119	C₂×C₁₉	#1767	1	1	yes	characteristic
120	C₂×C₁₉	#1772	1	1	yes	characteristic
121	C₂×C₁₉	#1772	1	1	yes	characteristic
122	C₂²×C₈	—	19	2	no	—
123	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
124	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
125	C₂×C₄²	—	19	2	no	—
126	C₂×C₄²	—	38	1	no	—
127	C₂×C₄²	—	38	1	no	—
128	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
129	C₄⋊C₈	—	19	4	no	—
130	C₄⋊C₈	C₂×Dic₁₉	1	4	yes	—
131	C₂²⋊C₈	—	2	2	no	—
132	C₂²⋊C₈	—	38	2	no	—
133	C₄×C₈	—	2	2	no	—
134	C₄×C₈	—	19	1	no	—
135	C₄×C₈	—	19	1	no	—
136	C₄×C₈	—	19	2	no	—
137	C₄×C₈	—	38	4	no	—
138	C₄×C₈	—	38	4	no	—
139	C₄×C₈	—	38	2	no	—
140	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
141	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
142	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
143	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
144	C₁₉	#8267	1	1	yes	characteristic, complemented, Sylow
145	C₂²×C₄	—	38	2	no	—
146	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
147	C₂²×C₄	#64543	1	1	yes	characteristic
148	C₂²×C₄	#64545	1	1	yes	characteristic
149	C₂×C₈	—	2	2	no	—
150	C₂×C₈	—	2	4	no	—
151	C₂×C₈	—	19	2	no	—
152	C₂×C₈	—	19	2	no	—
153	C₂×C₈	—	38	2	no	—
154	C₂×C₈	—	38	2	no	—
155	C₂×C₈	—	38	4	no	—
156	C₂×C₈	#64515	1	4	yes	—
157	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
158	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
159	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
160	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
161	C₄²	—	19	4	no	—
162	C₄²	—	38	4	no	—
163	C₄²	—	38	4	no	—
164	C₄²	—	38	2	no	—
165	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
166	C₄²	D₄×D₁₉	1	1	yes	characteristic
167	C₄²	Q₈×D₁₉	1	1	yes	characteristic
168	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
169	C₂³	#10597338	1	1	yes	characteristic
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	38	4	no	—
173	C₂×C₄	—	38	4	no	—
174	C₂×C₄	—	38	4	no	—
175	C₂×C₄	#10597333	1	1	yes	characteristic
176	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
177	C₂×C₄	#10597339	1	1	yes	characteristic
178	C₂×C₄	C₂×#64515	1	2	yes	—
179	C₂×C₄	M₁₆×D₁₉	1	2	yes	—
180	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
181	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
182	C₂×C₄	Q₈×Dic₁₉	1	1	yes	characteristic
183	C₈	—	2	1	no	—
184	C₈	—	2	1	no	—
185	C₈	—	4	4	no	—
186	C₈	—	38	2	no	—
187	C₈	—	38	2	no	—
188	C₈	—	76	4	no	—
189	C₈	#10597272	1	2	yes	—
190	C₈	#10597272	1	2	yes	—
191	C₂²	—	2	1	no	—
192	C₂²	—	2	1	no	—
193	C₂²	C₄⋊C₄×Dic₁₉	1	1	yes	characteristic
194	C₂²	#11926600	1	2	yes	—
195	C₄	—	2	1	no	—
196	C₄	—	2	1	no	—
197	C₄	—	38	8	no	—
198	C₄	C₂×#10597272	1	1	yes	characteristic
199	C₄	M₁₆×Dic₁₉	1	1	yes	characteristic
200	C₄	#11926566	1	2	yes	—
201	C₄	#11926660	1	2	yes	—
202	C₄	#11926661	1	2	yes	—
203	C₂	—	2	2	no	—
204	C₂	#14563490	1	1	yes	characteristic
205	C₂	#14563516	1	1	yes	characteristic
206	C₂	#14563517	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1564	C₂
socle	C₂²×C₁₉	C₄×C₄⋊C₄
prime radical	C₂³×C₁₉	#117
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1564	D₁₉
hypocenter	C₁₉	#8267
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
11. #11926297	C₄	semidirect
12. #11926295	C₄	semidirect
17. C₁₉×#335	C₄	semidirect
18. C₁₉×#334	C₄	semidirect
113. #335	Dic₁₉	semidirect
115. #334	Dic₁₉	semidirect
144. C₁₉	#8267	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₈×Dic₁₉	2
#14562383	2
#14561928	2
#14561467	2
C₁₉×#1564	2
#8267	19