Subgroups — #18076293

Order 4864.

402 conjugacy classes of subgroups.

The subgroup lattice has 194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563786	C₂	1	2	yes	maximal
2	#14563380	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926297	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926296	C₂	1	2	yes	maximal
5	C₂×C₁₉×#335	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
7	C₂×Dic₁₉⋊C₈	—	2	4	no	—
8	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
10	#11926298	C₄	1	2	yes	—
11	#11926298	C₄	1	2	yes	—
12	#11926297	—	2	2	no	—
13	#11926296	—	2	4	no	—
14	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#335	—	2	2	no	—
17	C₂²×C₈×C₁₉	—	2	2	no	—
18	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
21	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
22	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
23	C₂×C₄×Dic₁₉	Q₈	1	2	yes	—
24	C₂²×C₁₉⋊C₈	—	2	2	no	—
25	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
26	C₁₉×C₄⋊C₈	—	2	2	no	—
27	C₁₉×C₄⋊C₈	—	2	2	no	—
28	C₄×C₈×C₁₉	D₄	1	2	yes	—
29	C₄×C₈×C₁₉	Q₈	1	2	yes	—
30	Dic₁₉⋊C₈	—	4	8	no	—
31	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
32	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
33	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
34	C₄×C₁₉⋊C₈	Q₈	1	2	yes	—
35	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
36	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
38	C₂²×Dic₁₉	C₄⋊C₄	1	4	yes	—
39	C₂×C₈×C₁₉	—	2	2	no	—
40	C₂×C₈×C₁₉	—	2	2	no	—
41	C₂×C₈×C₁₉	—	4	2	no	—
42	C₂×C₈×C₁₉	—	4	4	no	—
43	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
44	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
45	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
47	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
48	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
49	C₄×Dic₁₉	—	2	2	no	—
50	C₄×Dic₁₉	—	2	2	no	—
51	C₄×Dic₁₉	—	4	2	no	—
52	C₄×Dic₁₉	D₈	1	4	yes	—
53	C₄×Dic₁₉	Q₁₆	1	4	yes	—
54	C₂×C₁₉⋊C₈	—	2	2	no	—
55	C₂×C₁₉⋊C₈	—	2	2	no	—
56	C₂×C₁₉⋊C₈	—	4	2	no	—
57	C₂×C₁₉⋊C₈	—	4	4	no	—
58	C₂×C₁₉⋊C₈	C₄⋊C₄	1	4	yes	—
59	#8810	—	19	1	no	maximal, Sylow
60	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
61	C₂×C₄×C₁₉	—	2	2	no	—
62	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
63	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
64	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
65	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
66	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
67	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
68	C₂×C₄×C₁₉	#131	1	2	yes	—
69	C₂×C₄×C₁₉	#131	1	2	yes	—
70	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
71	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
72	C₂×Dic₁₉	—	2	4	no	—
73	C₂×Dic₁₉	—	2	4	no	—
74	C₂×Dic₁₉	#107	1	8	yes	—
75	C₈×C₁₉	—	2	2	no	—
76	C₈×C₁₉	—	2	2	no	—
77	C₈×C₁₉	—	8	2	no	—
78	C₁₉⋊C₈	—	2	4	no	—
79	C₁₉⋊C₈	—	8	2	no	—
80	#1842	—	19	2	no	—
81	#1744	—	19	1	no	—
82	C₂×#335	—	19	2	no	—
83	C₂×#335	—	19	1	no	—
84	C₂×#335	D₁₉	1	1	yes	characteristic
85	C₂²×C₁₉	#384	1	1	yes	characteristic
86	C₂²×C₁₉	#424	1	2	yes	—
87	C₂²×C₁₉	C₂×#107	1	2	yes	—
88	C₂²×C₁₉	#430	1	2	yes	—
89	C₄×C₁₉	—	2	1	no	—
90	C₄×C₁₉	—	2	1	no	—
91	C₄×C₁₉	#424	1	2	yes	—
92	C₄×C₁₉	#424	1	1	yes	characteristic
93	C₄×C₁₉	#424	1	1	yes	characteristic
94	C₄×C₁₉	#493	1	1	yes	characteristic
95	C₄×C₁₉	#494	1	1	yes	characteristic
96	C₄×C₁₉	#500	1	2	yes	—
97	Dic₁₉	—	2	8	no	—
98	C₂×C₄⋊C₈	—	19	2	no	—
99	C₂×C₄⋊C₈	—	38	4	no	—
100	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
101	C₂×C₄×C₈	—	19	1	no	—
102	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
103	C₄³	—	19	1	no	—
104	#336	—	19	2	no	—
105	#336	—	19	2	no	—
106	#335	—	2	2	no	—
107	#335	—	38	4	no	—
108	#335	—	38	2	no	—
109	C₂×C₁₉	#1571	1	4	yes	—
110	C₂×C₁₉	#1843	1	1	yes	characteristic
111	C₂×C₁₉	#1845	1	1	yes	characteristic
112	C₂×C₁₉	#1849	1	1	yes	characteristic
113	C₂²×C₈	—	2	2	no	—
114	C₂²×C₈	—	19	2	no	—
115	C₂²×C₈	—	38	2	no	—
116	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
117	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
118	C₂×C₄²	—	19	2	no	—
119	C₂×C₄²	—	19	2	no	—
120	C₂×C₄²	—	19	2	no	—
121	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
122	C₄⋊C₈	—	2	2	no	—
123	C₄⋊C₈	—	2	2	no	—
124	C₄⋊C₈	—	38	2	no	—
125	C₄⋊C₈	—	38	2	no	—
126	C₄⋊C₈	—	76	8	no	—
127	C₄×C₈	—	19	2	no	—
128	C₄×C₈	—	19	2	no	—
129	C₄×C₈	Dic₃₈	1	2	yes	—
130	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
131	C₁₉	#8810	1	1	yes	characteristic, complemented, Sylow
132	C₂²×C₄	—	19	4	no	—
133	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
134	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
135	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
136	C₂×C₈	—	2	2	no	—
137	C₂×C₈	—	2	2	no	—
138	C₂×C₈	—	4	2	no	—
139	C₂×C₈	—	4	4	no	—
140	C₂×C₈	—	19	4	no	—
141	C₂×C₈	—	38	2	no	—
142	C₂×C₈	—	38	2	no	—
143	C₂×C₈	—	76	2	no	—
144	C₂×C₈	—	76	4	no	—
145	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
146	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
147	C₄²	—	19	4	no	—
148	C₄²	—	19	4	no	—
149	C₄²	—	38	2	no	—
150	C₄²	—	38	2	no	—
151	C₄²	—	76	2	no	—
152	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
153	C₄²	D₄×D₁₉	1	1	yes	characteristic
154	C₄²	Q₈×D₁₉	1	1	yes	characteristic
155	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
156	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
157	C₂×C₄	—	2	2	no	—
158	C₂×C₄	—	19	8	no	—
159	C₂×C₄	—	38	4	no	—
160	C₂×C₄	—	38	4	no	—
161	C₂×C₄	#10597334	1	1	yes	characteristic
162	C₂×C₄	#10597334	1	1	yes	characteristic
163	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
164	C₂×C₄	#10597347	1	2	yes	—
165	C₂×C₄	#10597353	1	2	yes	—
166	C₂×C₄	D₈×D₁₉	1	2	yes	—
167	C₂×C₄	Q₁₆×D₁₉	1	2	yes	—
168	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
169	C₂×C₄	#10597386	1	1	yes	characteristic
170	C₂×C₄	#10597390	1	1	yes	characteristic
171	C₈	—	2	2	no	—
172	C₈	—	2	2	no	—
173	C₈	—	8	2	no	—
174	C₈	—	38	4	no	—
175	C₈	—	152	2	no	—
176	C₂²	#11926413	1	1	yes	characteristic
177	C₂²	#11926569	1	2	yes	—
178	C₂²	#107×D₁₉	1	2	yes	—
179	C₂²	#11926591	1	2	yes	—
180	C₄	—	2	1	no	—
181	C₄	—	2	1	no	—
182	C₄	—	38	8	no	—
183	C₄	#11926569	1	2	yes	—
184	C₄	#11926570	1	1	yes	characteristic
185	C₄	#11926572	1	1	yes	characteristic
186	C₄	#11926919	1	1	yes	characteristic
187	C₄	#11926922	1	1	yes	characteristic
188	C₄	#11926948	1	2	yes	—
189	C₂	#14562408	1	4	yes	—
190	C₂	#14563788	1	1	yes	characteristic
191	C₂	#14563793	1	1	yes	characteristic
192	C₂	#14563808	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#335	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#335	D₁₉
hypocenter	C₁₉	#8810
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#335

Complements

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

N	H ≅ G/N	type
131. C₁₉	#8810	semidirect

Maximal subgroups

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

subgroup	index
#14563786	2
#14563380	2
C₂×#11926297	2
C₂×#11926296	2
C₂×C₁₉×#335	2
#8810	19