Group #18069183 — subgroups

Subgroups — #18069183

Order 4864.

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

normal subgroups only

This group has 176 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×#1843	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊(C₁₉⋊C₁₆)	—	2	2	no	—
4	C₂×C₁₉×C₄⋊C₈	—	2	2	no	—
5	C₂×C₁₉×C₄⋊C₈	C₄	1	1	yes	characteristic
6	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
7	C₁₉×#376	C₄	1	1	yes	characteristic
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	4	no	—
14	C₁₉×C₄⋊C₈	—	4	1	no	—
15	C₁₉×#95	—	2	1	no	—
16	C₁₉×#95	C₈	1	2	yes	—
17	C₂×C₁₉⋊C₁₆	—	4	2	no	—
18	C₂²×C₄×C₁₉	—	2	2	no	—
19	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
20	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	M₁₆	1	1	yes	characteristic
22	C₂×C₈×C₁₉	—	2	2	no	—
23	C₂×C₈×C₁₉	—	4	2	no	—
24	C₂×C₈×C₁₉	—	4	2	no	—
25	C₂×C₈×C₁₉	—	4	1	no	—
26	C₄²×C₁₉	—	2	2	no	—
27	C₄²×C₁₉	—	2	2	no	—
28	C₄²×C₁₉	—	2	1	no	—
29	C₄²×C₁₉	—	2	1	no	—
30	C₁₉⋊C₁₆	—	8	2	no	—
31	#7066	—	19	1	no	maximal, Sylow
32	C₂³×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
33	C₂×C₄×C₁₉	—	2	1	no	—
34	C₂×C₄×C₁₉	—	2	1	no	—
35	C₂×C₄×C₁₉	—	2	4	no	—
36	C₂×C₄×C₁₉	—	2	1	no	—
37	C₂×C₄×C₁₉	—	2	1	no	—
38	C₂×C₄×C₁₉	—	2	2	no	—
39	C₂×C₄×C₁₉	—	4	2	no	—
40	C₂×C₄×C₁₉	—	4	2	no	—
41	C₂×C₄×C₁₉	—	4	1	no	—
42	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
43	C₂×C₄×C₁₉	#101	1	1	yes	characteristic
44	C₈×C₁₉	—	4	2	no	—
45	C₈×C₁₉	—	8	1	no	—
46	#1843	D₁₉	1	1	yes	characteristic
47	#1322	—	19	2	no	—
48	C₂²×C₁₉	—	2	1	no	—
49	C₂²×C₁₉	—	2	1	no	—
50	C₂²×C₁₉	#324	1	1	yes	characteristic
51	C₂²×C₁₉	#350	1	2	yes	—
52	C₄×C₁₉	—	2	1	no	—
53	C₄×C₁₉	—	4	4	no	—
54	C₄×C₁₉	—	4	1	no	—
55	C₄×C₁₉	—	4	1	no	—
56	C₄×C₁₉	#353	1	1	yes	characteristic
57	C₄×C₁₉	#356	1	1	yes	characteristic
58	C₂×C₄⋊C₈	—	2	2	no	—
59	C₂×C₄⋊C₈	Dic₁₉	1	1	yes	characteristic
60	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
61	#376	Dic₁₉	1	1	yes	characteristic
62	C₂²⋊C₁₆	—	38	2	no	—
63	C₂×C₁₉	—	2	2	no	—
64	C₂×C₁₉	#1323	1	1	yes	characteristic
65	C₂×C₁₉	#1325	1	1	yes	characteristic
66	C₂×C₁₉	#1328	1	1	yes	characteristic
67	C₂²×C₈	—	2	1	no	—
68	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
69	C₂×C₄²	—	2	1	no	—
70	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
71	C₂×C₁₆	—	76	2	no	—
72	C₄⋊C₈	—	4	1	no	—
73	C₄⋊C₈	—	4	1	no	—
74	C₄⋊C₈	—	4	4	no	—
75	#95	—	2	1	no	—
76	#95	C₁₉⋊C₈	1	2	yes	—
77	C₁₉	#7066	1	1	yes	characteristic, complemented, Sylow
78	C₂²×C₄	—	2	2	no	—
79	C₂²×C₄	C₂×C₁₉⋊C₈	1	1	yes	characteristic
80	C₂²×C₄	#64520	1	1	yes	characteristic
81	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
82	C₂×C₈	—	2	2	no	—
83	C₂×C₈	—	4	2	no	—
84	C₂×C₈	—	4	2	no	—
85	C₂×C₈	—	4	1	no	—
86	C₄²	—	2	2	no	—
87	C₄²	—	2	2	no	—
88	C₄²	—	2	1	no	—
89	C₄²	—	2	1	no	—
90	C₁₆	—	152	2	no	—
91	C₂³	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
92	C₂×C₄	—	2	1	no	—
93	C₂×C₄	—	2	1	no	—
94	C₂×C₄	—	2	4	no	—
95	C₂×C₄	—	2	2	no	—
96	C₂×C₄	—	2	1	no	—
97	C₂×C₄	—	2	1	no	—
98	C₂×C₄	—	4	2	no	—
99	C₂×C₄	—	4	2	no	—
100	C₂×C₄	—	4	1	no	—
101	C₂×C₄	#10597291	1	1	yes	characteristic
102	C₂×C₄	#10597293	1	1	yes	characteristic
103	C₈	—	4	2	no	—
104	C₈	—	8	1	no	—
105	C₂²	—	2	1	no	—
106	C₂²	—	2	1	no	—
107	C₂²	#11926270	1	1	yes	characteristic
108	C₂²	#11926328	1	2	yes	—
109	C₄	—	2	1	no	—
110	C₄	—	4	4	no	—
111	C₄	—	4	1	no	—
112	C₄	—	4	1	no	—
113	C₄	#11926337	1	1	yes	characteristic
114	C₄	#11926343	1	1	yes	characteristic
115	C₂	—	2	2	no	—
116	C₂	#14561577	1	1	yes	characteristic
117	C₂	#14561581	1	1	yes	characteristic
118	C₂	#14561588	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561575

C₂

yes

maximal

C₁₉×#1843

C₂

yes

maximal, characteristic

C₂²⋊(C₁₉⋊C₁₆)

—

C₂×C₁₉×C₄⋊C₈

—

C₂×C₁₉×C₄⋊C₈

C₄

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×#376

C₄

yes

characteristic

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×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

—

#7066

—

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

—

#1843

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

—

C₂×C₄⋊C₈

Dic₁₉

yes

characteristic

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

#376

Dic₁₉

yes

characteristic

C₂²⋊C₁₆

—

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

—

C₄⋊C₈

—

#95

—

#95

C₁₉⋊C₈

yes

—

C₁₉

#7066

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

—

100

C₂×C₄

—

101

C₂×C₄

#10597291

yes

characteristic

102

C₂×C₄

#10597293

yes

characteristic

103

C₈

—

104

C₈

—

105

C₂²

—

106

C₂²

—

107

C₂²

#11926270

yes

characteristic

108

C₂²

#11926328

yes

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

#11926337

yes

characteristic

114

C₄

#11926343

yes

characteristic

115

C₂

—

116

C₂

#14561577

yes

characteristic

117

C₂

#14561581

yes

characteristic

118

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×#1843	C₂
socle	C₂²×C₁₉	#324
prime radical	C₂³×C₁₉	C₂²⋊C₈
cosocle	C₂×C₁₉×C₄⋊C₈	C₂²
hypercenter	#1843	D₁₉
hypocenter	C₁₉	#7066
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈ ◁ #1843

subgroup

G/H

center

C₂×C₄

#10597291

commutator

C₂²×C₄×C₁₉

C₂×C₈

Frattini

C₂×C₄⋊C₈

C₂×D₁₉

Fitting

C₁₉×#1843

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 ◁ #1843

N	H ≅ G/N	type
77. C₁₉	#7066	semidirect

H ≅ G/N

type

77. C₁₉

#7066

semidirect

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

subgroup	index
#14561575	2
C₁₉×#1843	2
#7066	19

subgroup

index

#14561575

C₁₉×#1843

#7066

Subgroups — #18069183

Conjugacy classes of subgroups

Complements

Maximal subgroups