Subgroups — #18073707

Order 4864.

390 conjugacy classes of subgroups.

The subgroup lattice has 202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10597272	C₂	1	1	yes	maximal, characteristic
2	#14562383	C₂	1	1	yes	maximal, characteristic
3	#14561919	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×#10597272	C₄	1	2	yes	—
8	C₂×#10597272	C₄	1	2	yes	—
9	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
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	C₈×C₁₉⋊C₈	—	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	#10597272	—	2	4	no	—
35	#10597272	C₈	1	8	yes	complemented
36	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	—
37	C₄×C₁₉⋊C₈	—	2	2	no	—
38	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
39	C₄×C₁₉⋊C₈	Q₈	1	2	yes	—
40	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
43	C₂²×Dic₁₉	—	2	2	no	—
44	C₂×C₈×C₁₉	—	2	2	no	—
45	C₂×C₈×C₁₉	—	2	4	no	—
46	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
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	C₂×C₈	1	4	yes	—
51	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
52	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
53	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
55	C₄×Dic₁₉	—	2	2	no	—
56	C₄×Dic₁₉	—	4	2	no	—
57	C₄×Dic₁₉	—	4	2	no	—
58	C₄×Dic₁₉	C₂×C₈	1	4	yes	—
59	C₂×C₁₉⋊C₈	—	2	4	no	—
60	C₂×C₁₉⋊C₈	C₄⋊C₄	1	4	yes	—
61	C₂×C₁₉⋊C₈	C₂×C₈	1	4	yes	—
62	C₂×C₁₉⋊C₈	M₁₆	1	4	yes	—
63	#8268	—	19	1	no	maximal, Sylow
64	C₂³×C₁₉	#117	1	1	yes	characteristic
65	C₂×C₄×C₁₉	—	2	2	no	—
66	C₂×C₄×C₁₉	—	2	2	no	—
67	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
68	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
69	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
70	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
71	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
72	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
73	C₂×C₄×C₁₉	C₂²×C₈	1	2	yes	—
74	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
75	C₂×Dic₁₉	—	2	4	no	—
76	C₂×Dic₁₉	—	4	2	no	—
77	C₂×Dic₁₉	—	4	2	no	—
78	C₈×C₁₉	—	2	1	no	—
79	C₈×C₁₉	—	2	1	no	—
80	C₈×C₁₉	—	4	4	no	—
81	C₈×C₁₉	C₄×C₈	1	2	yes	—
82	C₈×C₁₉	C₄×C₈	1	2	yes	—
83	C₁₉⋊C₈	—	4	4	no	—
84	C₁₉⋊C₈	C₄⋊C₈	1	8	yes	—
85	C₄×#97	—	19	1	no	—
86	#1564	—	19	1	no	—
87	#1564	D₁₉	1	1	yes	characteristic
88	#1450	—	19	2	no	—
89	#1276	—	19	2	no	—
90	C₂²×C₁₉	—	2	1	no	—
91	C₂²×C₁₉	—	2	1	no	—
92	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
93	C₂²×C₁₉	#431	1	2	yes	—
94	C₄×C₁₉	—	2	1	no	—
95	C₄×C₁₉	—	2	1	no	—
96	C₄×C₁₉	C₂×C₄×C₈	1	1	yes	characteristic
97	C₄×C₁₉	C₄×M₁₆	1	1	yes	characteristic
98	C₄×C₁₉	C₂×C₄⋊C₈	1	2	yes	—
99	C₄×C₁₉	#444	1	2	yes	—
100	C₄×C₁₉	#444	1	2	yes	—
101	Dic₁₉	—	4	4	no	—
102	#431	—	19	2	no	—
103	#431	C₂×D₁₉	1	2	yes	—
104	C₂×#97	—	19	2	no	—
105	C₂×#97	—	19	2	no	—
106	C₂×C₄×C₈	—	19	1	no	—
107	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
108	C₄³	—	19	1	no	—
109	#335	—	19	2	no	—
110	#335	Dic₁₉	1	2	yes	complemented
111	#334	—	19	2	no	—
112	#334	Dic₁₉	1	2	yes	complemented
113	#322	—	38	2	no	—
114	C₈²	—	38	2	no	—
115	C₂×C₁₉	—	2	2	no	—
116	C₂×C₁₉	C₄×C₄⋊C₈	1	1	yes	characteristic
117	C₂×C₁₉	#1773	1	1	yes	characteristic
118	C₂×C₁₉	#1773	1	1	yes	characteristic
119	C₂²×C₈	—	19	2	no	—
120	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
121	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
122	C₂×C₄²	—	19	2	no	—
123	C₂×C₄²	—	38	1	no	—
124	C₂×C₄²	—	38	1	no	—
125	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
126	C₄⋊C₈	—	19	4	no	—
127	C₄⋊C₈	C₂×Dic₁₉	1	4	yes	—
128	C₂²⋊C₈	—	2	2	no	—
129	C₂²⋊C₈	—	38	2	no	—
130	#97	—	19	8	no	—
131	#97	—	38	4	no	—
132	C₄×C₈	—	2	2	no	—
133	C₄×C₈	—	19	2	no	—
134	C₄×C₈	—	19	2	no	—
135	C₄×C₈	—	38	2	no	—
136	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
137	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
138	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
139	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
140	C₁₉	#8268	1	1	yes	characteristic, complemented, Sylow
141	C₂²×C₄	—	38	2	no	—
142	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
143	C₂²×C₄	#64543	1	1	yes	characteristic
144	C₂²×C₄	#64545	1	1	yes	characteristic
145	C₂×C₈	—	2	2	no	—
146	C₂×C₈	—	2	4	no	—
147	C₂×C₈	—	19	4	no	—
148	C₂×C₈	—	19	4	no	—
149	C₂×C₈	—	19	4	no	—
150	C₂×C₈	—	38	4	no	—
151	C₂×C₈	C₈×D₁₉	1	4	yes	—
152	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
153	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
154	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
155	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
156	C₄²	—	19	4	no	—
157	C₄²	—	38	2	no	—
158	C₄²	—	76	2	no	—
159	C₄²	—	76	2	no	—
160	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
161	C₄²	D₄×D₁₉	1	1	yes	characteristic
162	C₄²	Q₈×D₁₉	1	1	yes	characteristic
163	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
164	C₂³	#10597338	1	1	yes	characteristic
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	38	4	no	—
168	C₂×C₄	—	76	2	no	—
169	C₂×C₄	—	76	2	no	—
170	C₂×C₄	#10597333	1	1	yes	characteristic
171	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
172	C₂×C₄	#10597339	1	1	yes	characteristic
173	C₂×C₄	C₂×C₈×D₁₉	1	2	yes	—
174	C₂×C₄	M₁₆×D₁₉	1	2	yes	—
175	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
176	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
177	C₂×C₄	Q₈×Dic₁₉	1	1	yes	characteristic
178	C₈	—	2	1	no	—
179	C₈	—	2	1	no	—
180	C₈	—	4	4	no	—
181	C₈	—	19	8	no	—
182	C₈	—	76	4	no	—
183	C₈	C₈×Dic₁₉	1	2	yes	—
184	C₈	C₈×Dic₁₉	1	2	yes	—
185	C₂²	—	2	1	no	—
186	C₂²	—	2	1	no	—
187	C₂²	C₄⋊C₄×Dic₁₉	1	1	yes	characteristic
188	C₂²	#11926596	1	2	yes	—
189	C₄	—	2	1	no	—
190	C₄	—	2	1	no	—
191	C₄	—	76	4	no	—
192	C₄	C₂×C₈×Dic₁₉	1	1	yes	characteristic
193	C₄	M₁₆×Dic₁₉	1	1	yes	characteristic
194	C₄	C₄⋊C₈×D₁₉	1	2	yes	—
195	C₄	#11926665	1	2	yes	—
196	C₄	#11926666	1	2	yes	—
197	C₂	—	2	2	no	—
198	C₂	C₄⋊C₈×Dic₁₉	1	1	yes	characteristic
199	C₂	#14563521	1	1	yes	characteristic
200	C₂	#14563522	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	D₄×D₁₉
commutator	C₄×C₁₉	C₂×C₄×C₈
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	#8268
LCS	G ▷ 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
35. #10597272	C₈	semidirect
110. #335	Dic₁₉	semidirect
112. #334	Dic₁₉	semidirect
140. C₁₉	#8268	semidirect

Maximal subgroups

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

subgroup	index
C₄×#10597272	2
#14562383	2
#14561919	2
#14561467	2
C₁₉×#1564	2
#8268	19