Group #18076237 — subgroups

Subgroups — #18076237

Order 4864.

270 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 115 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	#14563807	C₂	1	1	yes	maximal, characteristic
2	#14563766	C₂	1	1	yes	maximal, characteristic
3	#14561494	C₂	1	4	yes	maximal
4	C₁₉×#1452	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597276	—	2	2	no	—
6	#11926568	C₂²	1	2	yes	—
7	#11926410	C₂²	1	2	yes	—
8	#11926307	—	2	2	no	—
9	C₁₉×#431	C₂²	1	2	yes	—
10	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#322	C₄	1	4	yes	complemented
12	C₂²×C₈×C₁₉	D₄	1	2	yes	—
13	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
14	C₂×C₄⋊Dic₁₉	—	2	2	no	—
15	C₂×#64520	—	2	2	no	—
16	C₁₉×C₄⋊C₈	—	2	2	no	—
17	C₁₉×C₂²⋊C₈	—	2	2	no	—
18	C₄×C₈×C₁₉	C₂×C₄	1	4	yes	—
19	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
20	C₄×C₈×C₁₉	Q₈	1	2	yes	—
21	C₁₉⋊#95	—	2	4	no	—
22	#10597276	—	4	4	no	—
23	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
24	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	#41	1	2	yes	—
26	C₂²×Dic₁₉	—	4	2	no	—
27	C₂×C₈×C₁₉	—	2	2	no	—
28	C₂×C₈×C₁₉	—	2	2	no	—
29	C₂×C₈×C₁₉	—	2	4	no	—
30	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
31	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
32	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
33	C₄²×C₁₉	#41	1	2	yes	—
34	C₄⋊Dic₁₉	—	4	2	no	—
35	C₄⋊Dic₁₉	—	4	2	no	—
36	#64520	—	4	4	no	—
37	C₂×C₁₉⋊C₈	—	4	2	no	—
38	#8794	—	19	1	no	maximal, Sylow
39	C₂³×C₁₉	#124	1	1	yes	characteristic
40	C₂×C₄×C₁₉	—	4	2	no	—
41	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₄×C₁₉	#117	1	2	yes	—
43	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
44	C₂×C₄×C₁₉	#125	1	2	yes	—
45	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
46	C₂×C₄×C₁₉	#137	1	2	yes	—
47	C₂×Dic₁₉	—	8	4	no	—
48	C₂×Dic₁₉	—	8	2	no	—
49	C₈×C₁₉	—	2	4	no	—
50	C₈×C₁₉	—	4	4	no	—
51	C₁₉⋊C₈	—	8	2	no	—
52	#1848	—	19	1	no	—
53	#1835	—	19	1	no	—
54	#1452	D₁₉	1	1	yes	characteristic
55	#1286	—	19	4	no	—
56	C₂²×C₁₉	—	2	2	no	—
57	C₂²×C₁₉	#382	1	1	yes	characteristic
58	C₂²×C₁₉	#489	1	2	yes	—
59	C₄×C₁₉	—	2	2	no	—
60	C₄×C₁₉	—	2	2	no	—
61	C₄×C₁₉	#428	1	2	yes	—
62	C₄×C₁₉	#490	1	1	yes	characteristic
63	C₄×C₁₉	#491	1	1	yes	characteristic
64	Dic₁₉	—	16	2	no	—
65	#431	C₂×D₁₉	1	2	yes	—
66	C₂×#108	—	38	2	no	—
67	#423	—	19	2	no	—
68	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
69	#382	—	19	2	no	—
70	#340	—	38	2	no	—
71	#322	Dic₁₉	1	4	yes	complemented
72	C₂×C₁₉	—	2	2	no	—
73	C₂×C₁₉	#1833	1	2	yes	—
74	C₂×C₁₉	#1836	1	1	yes	characteristic
75	C₂×M₁₆	—	38	2	no	—
76	C₂²×C₈	D₇₆	1	2	yes	—
77	C₂×C₄⋊C₄	—	38	2	no	—
78	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
79	#108	—	76	4	no	—
80	C₄⋊C₈	—	2	2	no	—
81	C₄⋊C₈	—	38	4	no	—
82	C₂²⋊C₈	—	2	2	no	—
83	C₄×C₈	Dic₃₈	1	2	yes	—
84	C₄×C₈	C₂×Dic₁₉	1	4	yes	—
85	C₄×C₈	C₂×Dic₁₉	1	2	yes	—
86	#95	—	38	4	no	—
87	C₁₉	#8794	1	1	yes	characteristic, complemented, Sylow
88	C₂²×C₄	—	76	2	no	—
89	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
90	C₂²×C₄	#64541	1	2	yes	—
91	M₁₆	—	76	4	no	—
92	C₂×C₈	—	2	2	no	—
93	C₂×C₈	—	2	2	no	—
94	C₂×C₈	—	2	4	no	—
95	C₂×C₈	—	76	2	no	—
96	C₂×C₈	C₄⋊Dic₁₉	1	4	yes	—
97	C₄⋊C₄	—	76	2	no	—
98	C₄⋊C₄	—	76	2	no	—
99	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
100	C₄²	#64541	1	2	yes	—
101	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
102	C₂³	#10597321	1	1	yes	characteristic
103	C₂×C₄	—	4	2	no	—
104	C₂×C₄	—	152	4	no	—
105	C₂×C₄	—	152	2	no	—
106	C₂×C₄	#10597316	1	2	yes	—
107	C₂×C₄	#10597321	1	1	yes	characteristic
108	C₂×C₄	#10597354	1	2	yes	—
109	C₂×C₄	#10597355	1	2	yes	—
110	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
111	C₂×C₄	#10597372	1	2	yes	—
112	C₈	—	2	4	no	—
113	C₈	—	4	4	no	—
114	C₈	—	152	2	no	—
115	C₂²	—	2	2	no	—
116	C₂²	#11926410	1	1	yes	characteristic
117	C₂²	#11926904	1	2	yes	—
118	C₄	—	2	2	no	—
119	C₄	—	2	2	no	—
120	C₄	—	304	2	no	—
121	C₄	#11926586	1	2	yes	—
122	C₄	#11926909	1	1	yes	characteristic
123	C₄	#11926913	1	1	yes	characteristic
124	C₂	—	2	2	no	—
125	C₂	#14563759	1	2	yes	—
126	C₂	#14563769	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563807

C₂

yes

maximal, characteristic

#14563766

C₂

yes

maximal, characteristic

#14561494

C₂

yes

maximal

C₁₉×#1452

C₂

yes

maximal, characteristic

C₂×#10597276

—

#11926568

C₂²

yes

—

#11926410

C₂²

yes

—

#11926307

—

C₁₉×#431

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#322

C₄

yes

complemented

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×#64520

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

Q₈

yes

—

C₁₉⋊#95

—

#10597276

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

#124

yes

characteristic

C₂×C₄×C₁₉

#125

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1848

—

#1835

—

#1452

D₁₉

yes

characteristic

#1286

—

C₂²×C₁₉

—

C₂²×C₁₉

#382

yes

characteristic

C₂²×C₁₉

#489

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#428

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

#431

C₂×D₁₉

yes

—

C₂×#108

—

#423

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

—

Dic₁₉

yes

complemented

C₂×C₁₉

—

C₂×C₁₉

#1833

yes

—

C₂×C₁₉

#1836

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

D₇₆

yes

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

#108

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

Dic₃₈

yes

—

C₄×C₈

C₂×Dic₁₉

yes

—

C₄×C₈

C₂×Dic₁₉

yes

—

#95

—

C₁₉

#8794

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂×D₇₆

yes

characteristic

C₂²×C₄

#64541

yes

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄⋊Dic₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂×Dic₃₈

yes

characteristic

100

C₄²

#64541

yes

—

101

C₄²

C₂²×Dic₁₉

yes

characteristic

102

C₂³

#10597321

yes

characteristic

103

C₂×C₄

—

104

C₂×C₄

—

152

—

105

C₂×C₄

—

152

—

106

C₂×C₄

#10597316

yes

—

107

C₂×C₄

#10597321

yes

characteristic

108

C₂×C₄

#10597354

yes

—

109

C₂×C₄

#10597355

yes

—

110

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

111

C₂×C₄

#10597372

yes

—

112

C₈

—

113

C₈

—

114

C₈

—

152

—

115

C₂²

—

116

C₂²

#11926410

yes

characteristic

117

C₂²

#11926904

yes

—

118

C₄

—

119

C₄

—

120

C₄

—

304

—

121

C₄

#11926586

yes

—

122

C₄

#11926909

yes

characteristic

123

C₄

#11926913

yes

characteristic

124

C₂

—

125

C₂

#14563759

yes

—

126

C₂

#14563769

yes

characteristic

	subgroup	G/H
center	C₂²	#11926410
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1452	C₂
socle	C₂²×C₁₉	#382
prime radical	C₂³×C₁₉	#124
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1452	D₁₉
hypocenter	C₁₉	#8794
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1452

subgroup

G/H

center

C₂²

#11926410

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1452

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1452

N	H ≅ G/N	type
11. C₁₉×#322	C₄	semidirect
71. #322	Dic₁₉	semidirect
87. C₁₉	#8794	semidirect

H ≅ G/N

type

11. C₁₉×#322

C₄

semidirect

71. #322

Dic₁₉

semidirect

87. C₁₉

#8794

semidirect

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

subgroup	index
#14563807	2
#14563766	2
#14561494	2
C₁₉×#1452	2
#8794	19

subgroup

index

C₁₉×#1452

Subgroups — #18076237

Conjugacy classes of subgroups

Complements

Maximal subgroups