Subgroups — #18076205

Order 4864.

378 conjugacy classes of subgroups.

The subgroup lattice has 190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563787	C₂	1	1	yes	maximal, characteristic
2	C₄×#10597260	C₂	1	1	yes	maximal, characteristic
3	#14561469	C₂	1	4	yes	maximal
4	C₁₉×#1831	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
6	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
7	C₂×#10597260	C₄	1	2	yes	—
8	C₂×#10597260	C₄	1	1	yes	characteristic
9	C₂×#10597260	C₄	1	1	yes	characteristic
10	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
11	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
12	C₄³×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#336	—	2	2	no	—
14	C₂²×C₈×C₁₉	—	2	2	no	—
15	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₉	D₄	1	2	yes	—
18	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
19	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
20	C₂²×C₁₉⋊C₈	—	2	2	no	—
21	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
22	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
23	C₁₉×C₄⋊C₈	—	2	4	no	—
24	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
25	C₄⋊(C₁₉⋊C₈)	—	4	4	no	—
26	#10597260	—	2	2	no	—
27	#10597260	—	2	4	no	—
28	#10597260	C₈	1	4	yes	complemented
29	C₄×C₁₉⋊C₈	—	2	2	no	—
30	C₄×C₁₉⋊C₈	—	2	2	no	—
31	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
32	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
33	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
34	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
36	C₂×C₈×C₁₉	—	4	2	no	—
37	C₂×C₈×C₁₉	—	4	2	no	—
38	C₂×C₈×C₁₉	—	4	2	no	—
39	C₄²×C₁₉	—	2	2	no	—
40	C₄²×C₁₉	—	2	2	no	—
41	C₄²×C₁₉	—	2	2	no	—
42	C₄²×C₁₉	—	4	2	no	—
43	C₄²×C₁₉	C₂×C₈	1	2	yes	—
44	C₄²×C₁₉	M₁₆	1	2	yes	—
45	C₄²×C₁₉	#41	1	2	yes	—
46	C₄²×C₁₉	#41	1	2	yes	—
47	C₂×C₁₉⋊C₈	—	2	2	no	—
48	C₂×C₁₉⋊C₈	—	2	2	no	—
49	C₂×C₁₉⋊C₈	—	2	2	no	—
50	C₂×C₁₉⋊C₈	—	2	2	no	—
51	C₂×C₁₉⋊C₈	—	4	2	no	—
52	C₂×C₁₉⋊C₈	—	4	4	no	—
53	C₂×C₁₉⋊C₈	C₂×C₈	1	4	yes	—
54	C₂×C₁₉⋊C₈	M₁₆	1	4	yes	—
55	#8786	—	19	1	no	maximal, Sylow
56	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₂×C₄×C₁₉	—	2	2	no	—
58	C₂×C₄×C₁₉	—	2	2	no	—
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	C₄⋊C₈	1	4	yes	—
64	C₂×C₄×C₁₉	#117	1	2	yes	—
65	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
66	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
67	C₂×C₄×C₁₉	#125	1	2	yes	—
68	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
69	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
70	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
71	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
72	C₂×C₄×C₁₉	#137	1	2	yes	—
73	C₈×C₁₉	—	8	2	no	—
74	C₁₉⋊C₈	—	2	4	no	—
75	C₁₉⋊C₈	—	2	4	no	—
76	C₁₉⋊C₈	—	8	2	no	—
77	#1842	—	19	1	no	—
78	#1831	D₁₉	1	1	yes	characteristic
79	C₄×#97	—	19	1	no	—
80	#1277	—	19	4	no	—
81	C₂²×C₁₉	#382	1	1	yes	characteristic
82	C₂²×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
83	C₂²×C₁₉	#423	1	1	yes	characteristic
84	C₂²×C₁₉	#428	1	2	yes	—
85	C₂²×C₁₉	#430	1	2	yes	—
86	C₄×C₁₉	—	2	4	no	—
87	C₄×C₁₉	—	2	2	no	—
88	C₄×C₁₉	—	4	2	no	—
89	C₄×C₁₉	#431	1	2	yes	—
90	C₄×C₁₉	#432	1	2	yes	—
91	C₄×C₁₉	#489	1	2	yes	—
92	C₄×C₁₉	#490	1	1	yes	characteristic
93	C₄×C₁₉	#491	1	1	yes	characteristic
94	C₂×C₄⋊C₈	—	19	2	no	—
95	C₂×C₄⋊C₈	—	38	2	no	—
96	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
97	C₂×#97	—	19	1	no	—
98	C₂×#97	—	19	2	no	—
99	C₂×#97	—	19	1	no	—
100	C₂×C₄×C₈	—	19	2	no	—
101	C₄³	C₂×D₁₉	1	1	yes	characteristic
102	#336	—	2	2	no	—
103	C₂×C₁₉	#1565	1	2	yes	—
104	C₂×C₁₉	#1569	1	2	yes	—
105	C₂×C₁₉	#1831	1	1	yes	characteristic
106	C₂×C₁₉	#1836	1	1	yes	characteristic
107	C₂×C₁₉	#1838	1	1	yes	characteristic
108	C₂²×C₈	—	2	2	no	—
109	C₂²×C₈	—	19	2	no	—
110	C₂²×C₈	—	19	2	no	—
111	C₂²×C₈	—	38	2	no	—
112	C₂×C₄²	Dic₃₈	1	2	yes	—
113	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
114	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
115	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
116	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
117	C₄⋊C₈	—	2	4	no	—
118	C₄⋊C₈	—	38	4	no	—
119	C₄⋊C₈	—	76	4	no	—
120	#97	—	19	4	no	—
121	#97	—	38	4	no	—
122	#97	—	38	2	no	—
123	C₄×C₈	—	38	2	no	—
124	C₄×C₈	—	38	2	no	—
125	C₁₉	#8786	1	1	yes	characteristic, complemented, Sylow
126	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
127	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
128	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
129	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
130	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
131	C₂×C₈	—	4	2	no	—
132	C₂×C₈	—	4	2	no	—
133	C₂×C₈	—	4	2	no	—
134	C₂×C₈	—	19	4	no	—
135	C₂×C₈	—	19	4	no	—
136	C₂×C₈	—	38	2	no	—
137	C₂×C₈	—	38	2	no	—
138	C₂×C₈	—	38	2	no	—
139	C₂×C₈	—	38	2	no	—
140	C₂×C₈	—	76	2	no	—
141	C₂×C₈	—	76	4	no	—
142	C₄²	—	2	2	no	—
143	C₄²	—	2	2	no	—
144	C₄²	—	2	2	no	—
145	C₄²	—	4	2	no	—
146	C₄²	C₈×D₁₉	1	2	yes	—
147	C₄²	#64515	1	2	yes	—
148	C₄²	#64543	1	2	yes	—
149	C₄²	#64545	1	2	yes	—
150	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
151	C₂×C₄	—	2	2	no	—
152	C₂×C₄	—	2	2	no	—
153	C₂×C₄	—	2	2	no	—
154	C₂×C₄	—	2	2	no	—
155	C₂×C₄	—	2	2	no	—
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	Dic₁₉⋊C₈	1	4	yes	—
158	C₂×C₄	#10597336	1	2	yes	—
159	C₂×C₄	#10597338	1	2	yes	—
160	C₂×C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
161	C₂×C₄	C₂×#64515	1	1	yes	characteristic
162	C₂×C₄	M₁₆×D₁₉	1	2	yes	—
163	C₂×C₄	#10597382	1	1	yes	characteristic
164	C₂×C₄	#10597393	1	1	yes	characteristic
165	C₂×C₄	#10597395	1	2	yes	—
166	C₂×C₄	#10597397	1	2	yes	—
167	C₈	—	8	2	no	—
168	C₈	—	38	4	no	—
169	C₈	—	38	4	no	—
170	C₈	—	152	2	no	—
171	C₂²	#11926409	1	1	yes	characteristic
172	C₂²	C₂×Dic₁₉⋊C₈	1	1	yes	characteristic
173	C₂²	#11926567	1	1	yes	characteristic
174	C₂²	#11926587	1	2	yes	—
175	C₂²	#11926592	1	2	yes	—
176	C₄	—	2	4	no	—
177	C₄	—	2	2	no	—
178	C₄	—	4	2	no	—
179	C₄	#11926596	1	2	yes	—
180	C₄	#11926600	1	2	yes	—
181	C₄	#11926903	1	2	yes	—
182	C₄	#11926910	1	1	yes	characteristic
183	C₄	#11926914	1	1	yes	characteristic
184	C₂	#14562388	1	2	yes	—
185	C₂	#14562403	1	2	yes	—
186	C₂	#14563751	1	1	yes	characteristic
187	C₂	#14563768	1	1	yes	characteristic
188	C₂	#14563775	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₈
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	#8786
LCS	G ▷ C₂×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
28. #10597260	C₈	semidirect
125. C₁₉	#8786	semidirect

Maximal subgroups

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

subgroup	index
#14563787	2
C₄×#10597260	2
#14561469	2
C₁₉×#1831	2
#8786	19