Subgroups — #18076297

Order 4864.

362 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	#14563752	C₂	1	1	yes	maximal, characteristic
2	#14563381	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926296	C₂	1	2	yes	maximal
4	C₂×#11926294	C₂	1	2	yes	maximal
5	C₁₉×#1831	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
7	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
9	#11926299	—	2	2	no	—
10	#11926299	C₄	1	2	yes	—
11	#11926299	C₄	1	2	yes	—
12	#11926296	—	2	4	no	—
13	#11926294	—	2	4	no	—
14	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
15	C₄³×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#336	—	2	2	no	—
17	C₂²×C₈×C₁₉	—	2	2	no	—
18	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₉	D₄	1	2	yes	—
21	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
22	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
23	C₂²×C₁₉⋊C₈	—	2	2	no	—
24	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
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⋊(C₁₉⋊C₈)	—	2	2	no	—
29	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
30	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
31	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
32	C₄×C₁₉⋊C₈	Q₈	1	2	yes	—
33	C₄×C₁₉⋊C₈	Q₈	1	2	yes	—
34	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
35	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
36	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₈×C₁₉	—	4	2	no	—
40	C₂×C₈×C₁₉	—	4	4	no	—
41	C₄²×C₁₉	—	2	2	no	—
42	C₄²×C₁₉	—	2	2	no	—
43	C₄²×C₁₉	—	2	4	no	—
44	C₄²×C₁₉	—	4	2	no	—
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	C₂×C₁₉⋊C₈	—	2	2	no	—
50	C₂×C₁₉⋊C₈	—	2	2	no	—
51	C₂×C₁₉⋊C₈	—	2	2	no	—
52	C₂×C₁₉⋊C₈	—	2	2	no	—
53	C₂×C₁₉⋊C₈	—	4	2	no	—
54	C₂×C₁₉⋊C₈	—	4	4	no	—
55	C₂×C₁₉⋊C₈	C₄⋊C₄	1	4	yes	—
56	C₂×C₁₉⋊C₈	C₄⋊C₄	1	4	yes	—
57	#8811	—	19	1	no	maximal, Sylow
58	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
59	C₂×C₄×C₁₉	—	2	2	no	—
60	C₂×C₄×C₁₉	—	2	2	no	—
61	C₂×C₄×C₁₉	—	2	2	no	—
62	C₂×C₄×C₁₉	—	2	2	no	—
63	C₂×C₄×C₁₉	—	2	2	no	—
64	C₂×C₄×C₁₉	—	2	2	no	—
65	C₂×C₄×C₁₉	—	2	2	no	—
66	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
67	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
68	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
69	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
70	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
71	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
72	C₂×C₄×C₁₉	#131	1	2	yes	—
73	C₂×C₄×C₁₉	#131	1	2	yes	—
74	C₂×C₄×C₁₉	#135	1	4	yes	—
75	C₈×C₁₉	—	8	2	no	—
76	C₁₉⋊C₈	—	2	4	no	—
77	C₁₉⋊C₈	—	2	4	no	—
78	C₁₉⋊C₈	—	8	2	no	—
79	#1831	—	19	1	no	—
80	#1831	D₁₉	1	1	yes	characteristic
81	#1744	—	19	1	no	—
82	C₂×#335	—	19	2	no	—
83	C₂×#334	—	19	2	no	—
84	C₂²×C₁₉	#384	1	1	yes	characteristic
85	C₂²×C₁₉	#424	1	1	yes	characteristic
86	C₂²×C₁₉	#424	1	1	yes	characteristic
87	C₂²×C₁₉	#427	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	—	4	2	no	—
92	C₄×C₁₉	—	4	2	no	—
93	C₄×C₁₉	#424	1	2	yes	—
94	C₄×C₁₉	#424	1	2	yes	—
95	C₄×C₁₉	#495	1	2	yes	—
96	C₄×C₁₉	#499	1	2	yes	—
97	C₂×C₄⋊C₈	—	19	2	no	—
98	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
99	C₂×C₄×C₈	—	19	1	no	—
100	C₂×C₄×C₈	—	19	1	no	—
101	C₄³	C₂×D₁₉	1	1	yes	characteristic
102	#336	—	2	2	no	—
103	#336	—	19	2	no	—
104	#336	—	19	2	no	—
105	#336	—	38	2	no	—
106	#335	—	38	4	no	—
107	#334	—	38	4	no	—
108	C₂×C₁₉	#1572	1	2	yes	—
109	C₂×C₁₉	#1572	1	2	yes	—
110	C₂×C₁₉	#1843	1	1	yes	characteristic
111	C₂×C₁₉	#1846	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	—	19	2	no	—
116	C₂²×C₈	—	38	2	no	—
117	C₂×C₄²	Dic₃₈	1	2	yes	—
118	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
119	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
120	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
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	—	19	2	no	—
127	C₄×C₈	—	19	2	no	—
128	C₄×C₈	—	19	2	no	—
129	C₄×C₈	—	19	2	no	—
130	C₁₉	#8811	1	1	yes	characteristic, complemented, Sylow
131	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
132	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
133	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
134	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
135	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
136	C₂×C₈	—	4	2	no	—
137	C₂×C₈	—	4	4	no	—
138	C₂×C₈	—	19	4	no	—
139	C₂×C₈	—	19	4	no	—
140	C₂×C₈	—	38	2	no	—
141	C₂×C₈	—	38	2	no	—
142	C₂×C₈	—	38	2	no	—
143	C₂×C₈	—	38	2	no	—
144	C₂×C₈	—	76	2	no	—
145	C₂×C₈	—	76	4	no	—
146	C₄²	—	2	4	no	—
147	C₄²	—	2	2	no	—
148	C₄²	—	2	2	no	—
149	C₄²	—	4	2	no	—
150	C₄²	D₄×D₁₉	1	1	yes	characteristic
151	C₄²	D₄×D₁₉	1	1	yes	characteristic
152	C₄²	Q₈×D₁₉	1	1	yes	characteristic
153	C₄²	Q₈×D₁₉	1	1	yes	characteristic
154	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
155	C₂×C₄	—	2	2	no	—
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	—	2	2	no	—
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	2	no	—
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	#10597334	1	1	yes	characteristic
163	C₂×C₄	#10597334	1	1	yes	characteristic
164	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
165	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
166	C₂×C₄	#10597347	1	2	yes	—
167	C₂×C₄	#10597353	1	2	yes	—
168	C₂×C₄	#10597386	1	1	yes	characteristic
169	C₂×C₄	#10597390	1	1	yes	characteristic
170	C₂×C₄	#10597396	1	4	yes	—
171	C₈	—	8	2	no	—
172	C₈	—	38	4	no	—
173	C₈	—	38	4	no	—
174	C₈	—	152	2	no	—
175	C₂²	#11926413	1	1	yes	characteristic
176	C₂²	#11926570	1	1	yes	characteristic
177	C₂²	#11926572	1	1	yes	characteristic
178	C₂²	#11926580	1	2	yes	—
179	C₂²	#11926592	1	2	yes	—
180	C₄	—	2	1	no	—
181	C₄	—	2	1	no	—
182	C₄	—	4	2	no	—
183	C₄	—	4	2	no	—
184	C₄	#11926569	1	2	yes	—
185	C₄	#11926569	1	2	yes	—
186	C₄	#11926926	1	2	yes	—
187	C₄	#11926943	1	2	yes	—
188	C₂	#14562413	1	2	yes	—
189	C₂	#14562416	1	2	yes	—
190	C₂	#14563788	1	1	yes	characteristic
191	C₂	#14563797	1	1	yes	characteristic
192	C₂	#14563809	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1831	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1831	D₁₉
hypocenter	C₁₉	#8811
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1831

Complements

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

N	H ≅ G/N	type
130. C₁₉	#8811	semidirect

Maximal subgroups

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

subgroup	index
#14563752	2
#14563381	2
C₂×#11926296	2
C₂×#11926294	2
C₁₉×#1831	2
#8811	19