Group #18069415 — subgroups

Subgroups — #18069415

Order 4864.

214 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 119 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	#14562383	C₂	1	2	yes	maximal
2	C₂×C₁₉×#346	C₂	1	1	yes	maximal, characteristic
3	#11926597	—	2	2	no	—
4	#11926297	—	2	2	no	—
5	#11926295	C₄	1	4	yes	—
6	C₂²×C₁₆×C₁₉	C₄	1	2	yes	—
7	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#346	—	2	2	no	—
9	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₈×C₁₉	Q₈	1	1	yes	characteristic
11	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
12	C₂×C₁₆×C₁₉	—	2	2	no	—
13	C₂×C₁₆×C₁₉	—	2	2	no	—
14	C₂×C₁₆×C₁₉	C₈	1	4	yes	complemented
15	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
16	C₄×C₈×C₁₉	D₄	1	2	yes	—
17	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
18	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
19	C₄×C₁₉⋊C₈	—	4	2	no	—
20	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
22	C₂²×C₄×C₁₉	Q₁₆	1	1	yes	characteristic
23	C₂×C₈×C₁₉	—	2	2	no	—
24	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
25	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
27	C₂×C₈×C₁₉	C₂×C₈	1	2	yes	—
28	C₂×C₈×C₁₉	M₁₆	1	2	yes	—
29	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
30	C₄²×C₁₉	SD₁₆	1	2	yes	—
31	C₂×C₁₉⋊C₈	—	4	4	no	—
32	C₁₆×C₁₉	—	2	4	no	—
33	#7157	—	19	1	no	maximal, Sylow
34	C₂³×C₁₉	#107	1	1	yes	characteristic
35	C₂×C₄×C₁₉	—	4	1	no	—
36	C₂×C₄×C₁₉	—	4	1	no	—
37	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
38	C₂×C₄×C₁₉	#102	1	2	yes	—
39	C₂×C₄×C₁₉	#103	1	2	yes	—
40	C₂×C₄×C₁₉	C₄⋊C₈	1	2	yes	—
41	C₂×C₄×C₁₉	#106	1	1	yes	characteristic
42	C₂×C₄×C₁₉	#108	1	2	yes	—
43	C₈×C₁₉	—	2	2	no	—
44	C₈×C₁₉	C₄×C₈	1	1	yes	characteristic
45	C₈×C₁₉	#97	1	1	yes	characteristic
46	C₈×C₁₉	C₂²⋊C₈	1	2	yes	—
47	C₁₉⋊C₈	—	8	4	no	—
48	C₂×#346	D₁₉	1	1	yes	characteristic
49	#1564	—	19	2	no	—
50	C₂²×C₁₉	—	2	1	no	—
51	C₂²×C₁₉	—	2	1	no	—
52	C₂²×C₁₉	#335	1	2	yes	—
53	C₂²×C₁₉	#340	1	1	yes	characteristic
54	C₄×C₁₉	—	2	2	no	—
55	C₄×C₁₉	—	2	2	no	—
56	C₄×C₁₉	#334	1	2	yes	—
57	C₄×C₁₉	#336	1	1	yes	characteristic
58	C₄×C₁₉	#341	1	1	yes	characteristic
59	C₂²×C₁₆	Dic₁₉	1	2	yes	—
60	#431	—	38	2	no	—
61	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
62	#346	—	2	2	no	—
63	#335	—	38	2	no	—
64	#334	—	19	4	no	—
65	C₂×C₁₉	—	2	2	no	—
66	C₂×C₁₉	#1277	1	1	yes	characteristic
67	C₂×C₁₉	#1384	1	1	yes	characteristic
68	C₂×C₁₉	#1385	1	1	yes	characteristic
69	C₂²×C₈	Dic₃₈	1	1	yes	characteristic
70	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
71	C₂×C₄²	D₇₆	1	1	yes	characteristic
72	C₂×C₁₆	—	2	2	no	—
73	C₂×C₁₆	—	2	2	no	—
74	C₂×C₁₆	C₁₉⋊C₈	1	4	yes	complemented
75	C₄⋊C₈	—	38	4	no	—
76	C₂²⋊C₈	—	76	2	no	—
77	C₄×C₈	—	76	2	no	—
78	C₄×C₈	C₄×D₁₉	1	2	yes	—
79	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
80	C₁₉	#7157	1	1	yes	characteristic, complemented, Sylow
81	C₂²×C₄	D₁₅₂	1	1	yes	characteristic
82	C₂²×C₄	Dic₇₆	1	1	yes	characteristic
83	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
84	C₂×C₈	—	2	2	no	—
85	C₂×C₈	—	76	4	no	—
86	C₂×C₈	C₂×C₁₉⋊C₈	1	2	yes	—
87	C₂×C₈	#64520	1	2	yes	—
88	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
89	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
90	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
91	C₄²	#64516	1	2	yes	—
92	C₄²	(C₂×D₁₉)⋊C₄	1	2	yes	—
93	C₁₆	—	2	4	no	—
94	C₂³	#10597275	1	1	yes	characteristic
95	C₂×C₄	—	4	1	no	—
96	C₂×C₄	—	4	1	no	—
97	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	2	yes	—
98	C₂×C₄	#10597273	1	2	yes	—
99	C₂×C₄	#10597274	1	1	yes	characteristic
100	C₂×C₄	#10597276	1	2	yes	—
101	C₂×C₄	#10597278	1	2	yes	—
102	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
103	C₈	—	2	2	no	—
104	C₈	—	152	4	no	—
105	C₈	C₄×C₁₉⋊C₈	1	1	yes	characteristic
106	C₈	#10597260	1	1	yes	characteristic
107	C₈	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
108	C₂²	—	2	1	no	—
109	C₂²	—	2	1	no	—
110	C₂²	#11926297	1	2	yes	—
111	C₂²	#11926307	1	1	yes	characteristic
112	C₄	—	2	2	no	—
113	C₄	—	2	2	no	—
114	C₄	#11926295	1	2	yes	—
115	C₄	#11926299	1	1	yes	characteristic
116	C₄	#11926309	1	1	yes	characteristic
117	C₂	—	2	2	no	—
118	C₂	#14561470	1	1	yes	characteristic
119	C₂	#14561737	1	1	yes	characteristic
120	C₂	#14561739	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14562383

C₂

yes

maximal

C₂×C₁₉×#346

C₂

yes

maximal, characteristic

#11926597

—

#11926297

—

#11926295

C₄

yes

—

C₂²×C₁₆×C₁₉

C₄

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#346

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

C₈

yes

complemented

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

D₈

yes

characteristic

C₂²×C₄×C₁₉

Q₁₆

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄²

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

C₂×C₈

yes

—

C₂×C₈×C₁₉

M₁₆

yes

—

C₄²×C₁₉

C₂²⋊C₄

yes

—

C₄²×C₁₉

SD₁₆

yes

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#95

yes

characteristic

C₂×C₄×C₁₉

#102

yes

—

C₂×C₄×C₁₉

#103

yes

—

C₂×C₄×C₁₉

C₄⋊C₈

yes

—

C₂×C₄×C₁₉

#106

yes

characteristic

C₂×C₄×C₁₉

#108

yes

—

C₈×C₁₉

—

C₈×C₁₉

C₄×C₈

yes

characteristic

C₈×C₁₉

#97

yes

characteristic

C₈×C₁₉

C₂²⋊C₈

yes

—

C₁₉⋊C₈

—

C₂×#346

D₁₉

yes

characteristic

#1564

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#335

yes

—

C₂²×C₁₉

#340

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#334

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂²×C₁₆

Dic₁₉

yes

—

#431

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

—

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

Dic₃₈

yes

characteristic

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

C₂×C₄²

D₇₆

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₁₉⋊C₈

yes

complemented

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

C₄×D₁₉

yes

—

C₄×C₈

C₂²⋊D₁₉

yes

—

C₁₉

#7157

yes

characteristic, complemented, Sylow

C₂²×C₄

D₁₅₂

yes

characteristic

C₂²×C₄

Dic₇₆

yes

characteristic

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×C₁₉⋊C₈

yes

—

C₂×C₈

#64520

yes

—

C₂×C₈

C₄×Dic₁₉

yes

characteristic

C₂×C₈

Dic₁₉⋊C₄

yes

—

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

C₄²

#64516

yes

—

C₄²

(C₂×D₁₉)⋊C₄

yes

—

C₁₆

—

C₂³

#10597275

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄⋊(C₁₉⋊C₈)

yes

—

C₂×C₄

#10597273

yes

—

C₂×C₄

#10597274

yes

characteristic

100

C₂×C₄

#10597276

yes

—

101

C₂×C₄

#10597278

yes

—

102

C₂×C₄

C₁₉⋊#95

yes

characteristic

103

C₈

—

104

C₈

—

152

—

105

C₈

C₄×C₁₉⋊C₈

yes

characteristic

106

C₈

#10597260

yes

characteristic

107

C₈

C₂²⋊(C₁₉⋊C₈)

yes

—

108

C₂²

—

109

C₂²

—

110

C₂²

#11926297

yes

—

111

C₂²

#11926307

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

#11926295

yes

—

115

C₄

#11926299

yes

characteristic

116

C₄

#11926309

yes

characteristic

117

C₂

—

118

C₂

#14561470

yes

characteristic

119

C₂

#14561737

yes

characteristic

120

C₂

#14561739

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597274
commutator	C₈×C₁₉	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₂×C₁₉×#346	C₂
socle	C₂²×C₁₉	#340
prime radical	C₂³×C₁₉	#107
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	C₂×#346	D₁₉
hypocenter	C₁₉	#7157
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

subgroup

G/H

center

C₂×C₄

#10597274

commutator

C₈×C₁₉

C₄×C₈

Frattini

C₂×C₄×C₈

C₂×D₁₉

Fitting

C₂×C₁₉×#346

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄×C₈×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

N	H ≅ G/N	type
14. C₂×C₁₆×C₁₉	C₈	semidirect
74. C₂×C₁₆	C₁₉⋊C₈	semidirect
80. C₁₉	#7157	semidirect

H ≅ G/N

type

14. C₂×C₁₆×C₁₉

C₈

semidirect

74. C₂×C₁₆

C₁₉⋊C₈

semidirect

80. C₁₉

#7157

semidirect

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

subgroup	index
#14562383	2
C₂×C₁₉×#346	2
#7157	19

subgroup

index

#14562383

C₂×C₁₉×#346

#7157

Subgroups — #18069415

Conjugacy classes of subgroups

Complements

Maximal subgroups