Group #18069181 — subgroups

Subgroups — #18069181

Order 4864.

156 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14561575	C₂	1	2	yes	maximal
2	C₁₉×#1832	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊(C₁₉⋊C₁₆)	—	2	2	no	—
4	C₂×C₁₉×C₄⋊C₈	C₄	1	1	yes	characteristic
5	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
6	C₁₉×#376	C₄	1	1	yes	characteristic
7	C₁₉×#336	—	2	2	no	—
8	C₂²×C₈×C₁₉	—	2	1	no	—
9	C₂²×C₈×C₁₉	D₄	1	2	yes	—
10	C₂×C₄²×C₁₉	—	2	1	no	—
11	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₁₉×C₄⋊C₈	—	4	1	no	—
13	C₁₉×C₄⋊C₈	—	4	1	no	—
14	C₁₉×#95	—	2	1	no	—
15	C₁₉×#95	C₈	1	2	yes	—
16	C₂×C₁₉⋊C₁₆	—	4	2	no	—
17	C₂²×C₄×C₁₉	—	2	2	no	—
18	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
20	C₂²×C₄×C₁₉	M₁₆	1	1	yes	characteristic
21	C₂×C₈×C₁₉	—	2	2	no	—
22	C₂×C₈×C₁₉	—	4	2	no	—
23	C₂×C₈×C₁₉	—	4	2	no	—
24	C₂×C₈×C₁₉	—	4	1	no	—
25	C₄²×C₁₉	—	2	1	no	—
26	C₄²×C₁₉	—	2	1	no	—
27	C₄²×C₁₉	—	4	1	no	—
28	C₄²×C₁₉	—	4	1	no	—
29	C₁₉⋊C₁₆	—	8	2	no	—
30	#7065	—	19	1	no	maximal, Sylow
31	C₂³×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
32	C₂×C₄×C₁₉	—	2	1	no	—
33	C₂×C₄×C₁₉	—	2	1	no	—
34	C₂×C₄×C₁₉	—	2	1	no	—
35	C₂×C₄×C₁₉	—	2	1	no	—
36	C₂×C₄×C₁₉	—	2	2	no	—
37	C₂×C₄×C₁₉	—	4	1	no	—
38	C₂×C₄×C₁₉	—	4	2	no	—
39	C₂×C₄×C₁₉	—	4	2	no	—
40	C₂×C₄×C₁₉	—	4	2	no	—
41	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
42	C₂×C₄×C₁₉	#101	1	1	yes	characteristic
43	C₈×C₁₉	—	4	2	no	—
44	C₈×C₁₉	—	8	1	no	—
45	#1832	D₁₉	1	1	yes	characteristic
46	#1322	—	19	2	no	—
47	C₂²×C₁₉	—	2	1	no	—
48	C₂²×C₁₉	—	2	1	no	—
49	C₂²×C₁₉	#324	1	1	yes	characteristic
50	C₂²×C₁₉	#350	1	2	yes	—
51	C₄×C₁₉	—	2	1	no	—
52	C₄×C₁₉	—	4	1	no	—
53	C₄×C₁₉	—	4	1	no	—
54	C₄×C₁₉	—	8	2	no	—
55	C₄×C₁₉	#354	1	1	yes	characteristic
56	C₄×C₁₉	#355	1	1	yes	characteristic
57	C₂×C₄⋊C₈	Dic₁₉	1	1	yes	characteristic
58	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
59	#376	Dic₁₉	1	1	yes	characteristic
60	C₂²⋊C₁₆	—	38	2	no	—
61	#336	—	2	2	no	—
62	C₂×C₁₉	—	2	2	no	—
63	C₂×C₁₉	#1323	1	1	yes	characteristic
64	C₂×C₁₉	#1324	1	1	yes	characteristic
65	C₂×C₁₉	#1328	1	1	yes	characteristic
66	C₂²×C₈	—	2	1	no	—
67	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
68	C₂×C₄²	—	2	1	no	—
69	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
70	C₂×C₁₆	—	76	2	no	—
71	C₄⋊C₈	—	4	1	no	—
72	C₄⋊C₈	—	4	1	no	—
73	#95	—	2	1	no	—
74	#95	C₁₉⋊C₈	1	2	yes	—
75	C₁₉	#7065	1	1	yes	characteristic, complemented, Sylow
76	C₂²×C₄	—	2	2	no	—
77	C₂²×C₄	C₂×C₁₉⋊C₈	1	1	yes	characteristic
78	C₂²×C₄	#64520	1	1	yes	characteristic
79	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
80	C₂×C₈	—	2	2	no	—
81	C₂×C₈	—	4	2	no	—
82	C₂×C₈	—	4	2	no	—
83	C₂×C₈	—	4	1	no	—
84	C₄²	—	2	1	no	—
85	C₄²	—	2	1	no	—
86	C₄²	—	4	1	no	—
87	C₄²	—	4	1	no	—
88	C₁₆	—	152	2	no	—
89	C₂³	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
90	C₂×C₄	—	2	1	no	—
91	C₂×C₄	—	2	1	no	—
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	2	1	no	—
94	C₂×C₄	—	2	1	no	—
95	C₂×C₄	—	4	1	no	—
96	C₂×C₄	—	4	2	no	—
97	C₂×C₄	—	4	2	no	—
98	C₂×C₄	—	4	2	no	—
99	C₂×C₄	#10597291	1	1	yes	characteristic
100	C₂×C₄	#10597293	1	1	yes	characteristic
101	C₈	—	4	2	no	—
102	C₈	—	8	1	no	—
103	C₂²	—	2	1	no	—
104	C₂²	—	2	1	no	—
105	C₂²	#11926270	1	1	yes	characteristic
106	C₂²	#11926328	1	2	yes	—
107	C₄	—	2	1	no	—
108	C₄	—	4	1	no	—
109	C₄	—	4	1	no	—
110	C₄	—	8	2	no	—
111	C₄	#11926339	1	1	yes	characteristic
112	C₄	#11926341	1	1	yes	characteristic
113	C₂	—	2	2	no	—
114	C₂	#14561577	1	1	yes	characteristic
115	C₂	#14561579	1	1	yes	characteristic
116	C₂	#14561588	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561575

C₂

yes

maximal

C₁₉×#1832

C₂

yes

maximal, characteristic

C₂²⋊(C₁₉⋊C₁₆)

—

C₂×C₁₉×C₄⋊C₈

C₄

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×#376

C₄

yes

characteristic

C₁₉×#336

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#95

—

C₁₉×#95

C₈

yes

—

C₂×C₁₉⋊C₁₆

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₉

M₁₆

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₁₉⋊C₁₆

—

#7065

—

maximal, Sylow

C₂³×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₈×C₁₉

—

#1832

D₁₉

yes

characteristic

#1322

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#324

yes

characteristic

C₂²×C₁₉

#350

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×C₄⋊C₈

Dic₁₉

yes

characteristic

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

#376

Dic₁₉

yes

characteristic

C₂²⋊C₁₆

—

#336

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

—

C₂²×C₈

C₂²⋊D₁₉

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

C₂×C₁₆

—

C₄⋊C₈

—

C₄⋊C₈

—

#95

—

#95

C₁₉⋊C₈

yes

—

C₁₉

#7065

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂×C₁₉⋊C₈

yes

characteristic

C₂²×C₄

#64520

yes

characteristic

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₁₆

—

152

—

C₂³

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#10597291

yes

characteristic

100

C₂×C₄

#10597293

yes

characteristic

101

C₈

—

102

C₈

—

103

C₂²

—

104

C₂²

—

105

C₂²

#11926270

yes

characteristic

106

C₂²

#11926328

yes

—

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

#11926339

yes

characteristic

112

C₄

#11926341

yes

characteristic

113

C₂

—

114

C₂

#14561577

yes

characteristic

115

C₂

#14561579

yes

characteristic

116

C₂

#14561588

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597291
commutator	C₂²×C₄×C₁₉	C₂×C₈
Frattini	C₂×C₄⋊C₈	C₂×D₁₉
Fitting	C₁₉×#1832	C₂
socle	C₂²×C₁₉	#324
prime radical	C₂³×C₁₉	C₂²⋊C₈
cosocle	C₂×C₁₉×C₄⋊C₈	C₂²
hypercenter	#1832	D₁₉
hypocenter	C₁₉	#7065
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈ ◁ #1832

subgroup

G/H

center

C₂×C₄

#10597291

commutator

C₂²×C₄×C₁₉

C₂×C₈

Frattini

C₂×C₄⋊C₈

C₂×D₁₉

Fitting

C₁₉×#1832

C₂

socle

C₂²×C₁₉

#324

prime radical

C₂³×C₁₉

C₂²⋊C₈

cosocle

C₂×C₁₉×C₄⋊C₈

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈ ◁ #1832

N	H ≅ G/N	type
75. C₁₉	#7065	semidirect

H ≅ G/N

type

75. C₁₉

#7065

semidirect

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

subgroup	index
#14561575	2
C₁₉×#1832	2
#7065	19

subgroup

index

#14561575

C₁₉×#1832

#7065

Subgroups — #18069181

Conjugacy classes of subgroups

Complements

Maximal subgroups