Group #18072971 — subgroups

Subgroups — #18072971

Order 4864.

414 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 187 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	#14563381	C₂	1	1	yes	maximal, characteristic
2	C₄×#10597260	C₂	1	1	yes	maximal, characteristic
3	C₁₉⋊#1273	C₂	1	4	yes	maximal
4	C₁₉×#1744	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597260	C₄	1	4	yes	—
6	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
8	#11926299	C₄	1	4	yes	—
9	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
10	C₄³×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#336	C₄	1	4	yes	—
12	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
13	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
14	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
15	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
16	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
17	C₂²×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
18	C₂²×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
19	C₄×C₈×C₁₉	—	2	4	no	—
20	#10597260	—	2	8	no	—
21	C₄×C₁₉⋊C₈	—	2	4	no	—
22	C₄×C₁₉⋊C₈	—	2	4	no	—
23	C₂²×C₄×C₁₉	C₄²	1	4	yes	—
24	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
26	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₈×C₁₉	—	2	4	no	—
28	C₂×C₈×C₁₉	—	2	8	no	—
29	C₄²×C₁₉	—	2	4	no	—
30	C₄²×C₁₉	—	2	4	no	—
31	C₄²×C₁₉	—	2	4	no	—
32	C₄²×C₁₉	#41	1	4	yes	—
33	C₂×C₁₉⋊C₈	—	2	4	no	—
34	C₂×C₁₉⋊C₈	—	2	4	no	—
35	C₂×C₁₉⋊C₈	—	2	4	no	—
36	C₂×C₁₉⋊C₈	—	2	8	no	—
37	C₂×C₁₉⋊C₈	M₁₆	1	8	yes	—
38	#8134	—	19	1	no	maximal, Sylow
39	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
40	C₂×C₄×C₁₉	—	2	4	no	—
41	C₂×C₄×C₁₉	—	2	4	no	—
42	C₂×C₄×C₁₉	—	2	4	no	—
43	C₂×C₄×C₁₉	#117	1	2	yes	—
44	C₂×C₄×C₁₉	#117	1	2	yes	—
45	C₂×C₄×C₁₉	#117	1	2	yes	—
46	C₂×C₄×C₁₉	C₂×M₁₆	1	4	yes	—
47	C₂×C₄×C₁₉	#131	1	4	yes	—
48	C₂×C₄×C₁₉	#131	1	4	yes	—
49	C₈×C₁₉	—	4	4	no	—
50	C₁₉⋊C₈	—	2	8	no	—
51	C₁₉⋊C₈	—	4	4	no	—
52	#1744	—	19	1	no	—
53	#1744	D₁₉	1	1	yes	characteristic
54	C₄×#97	—	19	1	no	—
55	#1273	—	19	4	no	—
56	C₂²×C₁₉	#376	1	1	yes	characteristic
57	C₂²×C₁₉	C₄×M₁₆	1	2	yes	—
58	C₂²×C₁₉	#405	1	2	yes	—
59	C₂²×C₁₉	#405	1	2	yes	—
60	C₄×C₁₉	—	4	4	no	—
61	C₄×C₁₉	#432	1	4	yes	—
62	C₄×C₁₉	#433	1	4	yes	—
63	C₄×C₁₉	#433	1	4	yes	—
64	C₂×#97	—	19	4	no	—
65	C₂×C₄×C₈	—	19	2	no	—
66	C₂×C₄×C₈	—	19	2	no	—
67	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
68	C₄³	C₂×D₁₉	1	1	yes	characteristic
69	#336	—	19	4	no	—
70	#336	Dic₁₉	1	4	yes	—
71	C₂×C₁₉	#1453	1	4	yes	—
72	C₂×C₁₉	#1745	1	1	yes	characteristic
73	C₂×C₁₉	#1746	1	1	yes	characteristic
74	C₂×C₁₉	#1746	1	1	yes	characteristic
75	C₂²×C₈	—	19	4	no	—
76	C₂²×C₈	—	19	4	no	—
77	C₂²×C₈	C₂×Dic₁₉	1	4	yes	—
78	C₂×C₄²	C₄×D₁₉	1	2	yes	—
79	C₂×C₄²	C₄×D₁₉	1	2	yes	—
80	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
81	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
82	#97	—	38	8	no	—
83	C₄×C₈	—	2	4	no	—
84	C₄×C₈	—	38	4	no	—
85	C₄×C₈	—	38	4	no	—
86	C₁₉	#8134	1	1	yes	characteristic, complemented, Sylow
87	C₂²×C₄	C₄×Dic₁₉	1	4	yes	—
88	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
89	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
90	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
91	C₂×C₈	—	2	8	no	—
92	C₂×C₈	—	2	4	no	—
93	C₂×C₈	—	19	8	no	—
94	C₂×C₈	—	38	4	no	—
95	C₂×C₈	—	38	4	no	—
96	C₂×C₈	—	38	4	no	—
97	C₂×C₈	—	38	8	no	—
98	C₄²	—	2	4	no	—
99	C₄²	—	2	4	no	—
100	C₄²	—	2	4	no	—
101	C₄²	#64541	1	4	yes	—
102	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
103	C₂×C₄	—	2	4	no	—
104	C₂×C₄	—	2	4	no	—
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	#10597318	1	2	yes	—
107	C₂×C₄	#10597318	1	2	yes	—
108	C₂×C₄	#10597347	1	4	yes	—
109	C₂×C₄	M₁₆×D₁₉	1	4	yes	—
110	C₂×C₄	#10597372	1	2	yes	—
111	C₂×C₄	#10597394	1	4	yes	—
112	C₈	—	4	4	no	—
113	C₈	—	38	8	no	—
114	C₈	—	76	4	no	—
115	C₂²	#11926390	1	1	yes	characteristic
116	C₂²	M₁₆×Dic₁₉	1	2	yes	—
117	C₂²	#11926499	1	2	yes	—
118	C₂²	#11926500	1	2	yes	—
119	C₄	—	4	4	no	—
120	C₄	#11926599	1	4	yes	—
121	C₄	#11926603	1	4	yes	—
122	C₄	#11926605	1	4	yes	—
123	C₂	#14561930	1	4	yes	—
124	C₂	#14563383	1	1	yes	characteristic
125	C₂	#14563386	1	1	yes	characteristic
126	C₂	#14563387	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563381

C₂

yes

maximal, characteristic

C₄×#10597260

C₂

yes

maximal, characteristic

C₁₉⋊#1273

C₂

yes

maximal

C₁₉×#1744

C₂

yes

maximal, characteristic

C₂×#10597260

C₄

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

#11926299

C₄

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#336

C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

—

C₄×C₈×C₁₉

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₄²

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

#41

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

M₁₆

yes

—

#8134

—

maximal, Sylow

C₂³×C₁₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1744

—

#1744

D₁₉

yes

characteristic

C₄×#97

—

#1273

—

C₂²×C₁₉

#376

yes

characteristic

C₂²×C₁₉

C₄×M₁₆

yes

—

C₂²×C₁₉

#405

yes

—

C₂²×C₁₉

#405

yes

—

C₄×C₁₉

—

C₄×C₁₉

#432

yes

—

C₄×C₁₉

#433

yes

—

C₄×C₁₉

#433

yes

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

C₄³

C₂×D₁₉

yes

characteristic

#336

—

#336

Dic₁₉

yes

—

C₂×C₁₉

#1453

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×Dic₁₉

yes

—

C₂×C₄²

C₄×D₁₉

yes

—

C₂×C₄²

C₄×D₁₉

yes

—

C₂×C₄²

C₂×Dic₁₉

yes

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₁₉

#8134

yes

characteristic, complemented, Sylow

C₂²×C₄

C₄×Dic₁₉

yes

—

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

100

C₄²

—

101

C₄²

#64541

yes

—

102

C₂³

C₂×C₄×Dic₁₉

yes

characteristic

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

#10597318

yes

—

107

C₂×C₄

#10597318

yes

—

108

C₂×C₄

#10597347

yes

—

109

C₂×C₄

M₁₆×D₁₉

yes

—

110

C₂×C₄

#10597372

yes

—

111

C₂×C₄

#10597394

yes

—

112

C₈

—

113

C₈

—

114

C₈

—

115

C₂²

#11926390

yes

characteristic

116

C₂²

M₁₆×Dic₁₉

yes

—

117

C₂²

#11926499

yes

—

118

C₂²

#11926500

yes

—

119

C₄

—

120

C₄

#11926599

yes

—

121

C₄

#11926603

yes

—

122

C₄

#11926605

yes

—

123

C₂

#14561930

yes

—

124

C₂

#14563383

yes

characteristic

125

C₂

#14563386

yes

characteristic

126

C₂

#14563387

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₉
commutator, socle, prime radical	C₂³×C₁₉	C₂×C₄²
Fitting	C₁₉×#1744	C₂
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1744	D₁₉
hypocenter	C₁₉	#8134
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄² ◁ #1744

subgroup

G/H

center, Frattini

C₂×C₄²

C₂²×D₁₉

commutator, socle, prime radical

C₂³×C₁₉

C₂×C₄²

Fitting

C₁₉×#1744

C₂

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂×C₄² ◁ #1744

N	H ≅ G/N	type
86. C₁₉	#8134	semidirect

H ≅ G/N

type

86. C₁₉

#8134

semidirect

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

subgroup	index
#14563381	2
C₄×#10597260	2
C₁₉⋊#1273	2
C₁₉×#1744	2
#8134	19

subgroup

index

#14563381

C₄×#10597260

C₁₉⋊#1273

C₁₉×#1744

#8134

Subgroups — #18072971

Conjugacy classes of subgroups

Complements

Maximal subgroups