Group #18069916 — subgroups

Subgroups — #18069916

Order 4864.

178 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 43 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	#14561571	C₂	1	2	yes	maximal
2	C₁₉×#1822	C₂	1	1	yes	maximal, characteristic
3	#11926326	—	2	2	no	—
4	C₂×C₁₉×#117	C₄	1	1	yes	characteristic
5	C₁₉×#407	C₄	1	1	yes	characteristic
6	C₁₉×#407	C₂²	1	1	yes	characteristic
7	C₁₉×#343	—	2	2	no	—
8	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
9	C₂×M₁₆×C₁₉	—	2	1	no	—
10	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
11	C₁₉×#117	—	4	1	no	—
12	C₁₉×#117	—	4	1	no	—
13	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
14	C₂×C₂²⋊C₄×C₁₉	C₈	1	2	yes	—
15	C₂×C₄²×C₁₉	—	2	1	no	—
16	C₁₉×C₂²⋊C₈	—	4	1	no	—
17	C₁₉×C₂²⋊C₈	—	4	1	no	—
18	#10597269	—	4	2	no	—
19	C₂⁴×C₁₉	C₂×C₈	1	1	yes	characteristic
20	C₂²×C₄×C₁₉	—	2	1	no	—
21	C₂²×C₄×C₁₉	—	2	1	no	—
22	C₂²×C₄×C₁₉	—	2	2	no	—
23	C₂²×C₄×C₁₉	—	4	2	no	—
24	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	M₁₆	1	1	yes	characteristic
26	M₁₆×C₁₉	—	4	2	no	—
27	M₁₆×C₁₉	—	4	2	no	—
28	C₂×C₈×C₁₉	—	2	2	no	—
29	C₂×C₈×C₁₉	—	4	1	no	—
30	C₄⋊C₄×C₁₉	—	4	1	no	—
31	C₄⋊C₄×C₁₉	—	4	1	no	—
32	C₂²⋊C₄×C₁₉	—	4	2	no	—
33	C₄²×C₁₉	—	4	2	no	—
34	C₁₉⋊C₁₆	—	8	2	no	—
35	#7351	—	19	1	no	maximal, Sylow
36	C₂³×C₁₉	—	2	1	no	—
37	C₂³×C₁₉	—	4	1	no	—
38	C₂³×C₁₉	—	8	1	no	—
39	C₂³×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
40	C₂×C₄×C₁₉	—	2	2	no	—
41	C₂×C₄×C₁₉	—	2	1	no	—
42	C₂×C₄×C₁₉	—	4	2	no	—
43	C₂×C₄×C₁₉	—	4	2	no	—
44	C₂×C₄×C₁₉	—	4	1	no	—
45	C₂×C₄×C₁₉	—	4	2	no	—
46	C₂×C₄×C₁₉	—	8	2	no	—
47	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
48	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
49	C₈×C₁₉	—	4	2	no	—
50	C₈×C₁₉	—	8	1	no	—
51	#1822	D₁₉	1	1	yes	characteristic
52	#1320	—	19	2	no	—
53	C₂²×C₁₉	—	2	1	no	—
54	C₂²×C₁₉	—	4	1	no	—
55	C₂²×C₁₉	—	4	2	no	—
56	C₂²×C₁₉	—	4	1	no	—
57	C₂²×C₁₉	—	8	2	no	—
58	C₂²×C₁₉	#323	1	1	yes	characteristic
59	C₄×C₁₉	—	2	1	no	—
60	C₄×C₁₉	—	4	1	no	—
61	C₄×C₁₉	—	8	2	no	—
62	C₄×C₁₉	#352	1	2	yes	—
63	C₂×#117	Dic₁₉	1	1	yes	characteristic
64	#407	Dic₁₉	1	1	yes	characteristic
65	#407	C₂×D₁₉	1	1	yes	characteristic
66	#349	—	38	2	no	—
67	#343	—	2	2	no	—
68	C₂×C₁₉	—	2	1	no	—
69	C₂×C₁₉	—	4	1	no	—
70	C₂×C₁₉	—	8	1	no	—
71	C₂×C₁₉	#1317	1	1	yes	characteristic
72	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
73	C₂×M₁₆	—	2	1	no	—
74	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
75	#117	—	4	1	no	—
76	#117	—	4	1	no	—
77	C₂×C₄⋊C₄	—	2	1	no	—
78	C₂×C₂²⋊C₄	C₁₉⋊C₈	1	2	yes	—
79	C₂×C₄²	—	2	1	no	—
80	M₃₂	—	76	2	no	—
81	C₂²⋊C₈	—	4	1	no	—
82	C₂²⋊C₈	—	4	1	no	—
83	C₁₉	#7351	1	1	yes	characteristic, complemented, Sylow
84	C₂⁴	C₂×C₁₉⋊C₈	1	1	yes	characteristic
85	C₂²×C₄	—	2	1	no	—
86	C₂²×C₄	—	2	1	no	—
87	C₂²×C₄	—	2	2	no	—
88	C₂²×C₄	—	4	2	no	—
89	C₂²×C₄	#64520	1	1	yes	characteristic
90	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
91	M₁₆	—	4	2	no	—
92	M₁₆	—	4	2	no	—
93	C₂×C₈	—	2	2	no	—
94	C₂×C₈	—	4	1	no	—
95	C₄⋊C₄	—	4	1	no	—
96	C₄⋊C₄	—	4	1	no	—
97	C₂²⋊C₄	—	4	2	no	—
98	C₄²	—	4	2	no	—
99	C₁₆	—	152	2	no	—
100	C₂³	—	2	1	no	—
101	C₂³	—	4	1	no	—
102	C₂³	—	8	1	no	—
103	C₂³	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	2	1	no	—
106	C₂×C₄	—	4	2	no	—
107	C₂×C₄	—	4	2	no	—
108	C₂×C₄	—	4	1	no	—
109	C₂×C₄	—	4	2	no	—
110	C₂×C₄	—	8	2	no	—
111	C₂×C₄	#10597290	1	1	yes	characteristic
112	C₂×C₄	#10597291	1	1	yes	characteristic
113	C₈	—	4	2	no	—
114	C₈	—	8	1	no	—
115	C₂²	—	2	1	no	—
116	C₂²	—	4	1	no	—
117	C₂²	—	4	2	no	—
118	C₂²	—	4	1	no	—
119	C₂²	—	8	2	no	—
120	C₂²	#11926268	1	1	yes	characteristic
121	C₄	—	2	1	no	—
122	C₄	—	4	1	no	—
123	C₄	—	8	2	no	—
124	C₄	#11926334	1	2	yes	—
125	C₂	—	2	1	no	—
126	C₂	—	4	1	no	—
127	C₂	—	8	1	no	—
128	C₂	#14561565	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561571

C₂

yes

maximal

C₁₉×#1822

C₂

yes

maximal, characteristic

#11926326

—

C₂×C₁₉×#117

C₄

yes

characteristic

C₁₉×#407

C₄

yes

characteristic

C₁₉×#407

C₂²

yes

characteristic

C₁₉×#343

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

D₄

yes

—

C₁₉×#117

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

C₈

yes

—

C₂×C₄²×C₁₉

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

#10597269

—

C₂⁴×C₁₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

M₁₆

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₁₉⋊C₁₆

—

#7351

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

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

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₈×C₁₉

—

#1822

D₁₉

yes

characteristic

#1320

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#323

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#352

yes

—

C₂×#117

Dic₁₉

yes

characteristic

#407

Dic₁₉

yes

characteristic

#407

C₂×D₁₉

yes

characteristic

#349

—

#343

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1317

yes

characteristic

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂²⋊D₁₉

yes

—

#117

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

C₁₉⋊C₈

yes

—

C₂×C₄²

—

M₃₂

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₁₉

#7351

yes

characteristic, complemented, Sylow

C₂⁴

C₂×C₁₉⋊C₈

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

#64520

yes

characteristic

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₁₆

—

152

—

100

C₂³

—

101

C₂³

—

102

C₂³

—

103

C₂³

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

#10597290

yes

characteristic

112

C₂×C₄

#10597291

yes

characteristic

113

C₈

—

114

C₈

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

#11926268

yes

characteristic

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

#11926334

yes

—

125

C₂

—

126

C₂

—

127

C₂

—

128

C₂

#14561565

yes

characteristic

	subgroup	G/H
center	C₂	#14561565
commutator, prime radical	C₂⁴×C₁₉	C₂×C₈
Frattini	#407	C₂×D₁₉
Fitting	C₁₉×#1822	C₂
socle	C₂×C₁₉	#1317
cosocle	C₁₉×#407	C₂²
hypercenter	#1822	D₁₉
hypocenter	C₁₉	#7351
LCS	G ▷ C₂⁴×C₁₉ ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #407 ◁ #1822

subgroup

G/H

center

C₂

#14561565

commutator, prime radical

C₂⁴×C₁₉

C₂×C₈

Frattini

#407

C₂×D₁₉

Fitting

C₁₉×#1822

C₂

socle

C₂×C₁₉

#1317

cosocle

C₁₉×#407

C₂²

D₁₉

C₁₉

G ▷ C₂⁴×C₁₉ ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #407 ◁ #1822

N	H ≅ G/N	type
83. C₁₉	#7351	semidirect

H ≅ G/N

type

83. C₁₉

#7351

semidirect

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

subgroup	index
#14561571	2
C₁₉×#1822	2
#7351	19

subgroup

index

#14561571

C₁₉×#1822

#7351

Subgroups — #18069916

Conjugacy classes of subgroups

Complements

Maximal subgroups