Group #18070364 — subgroups

Subgroups — #18070364

Order 4864.

148 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 27 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	#14561802	C₂	1	1	yes	maximal, characteristic
2	#14561676	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1630	C₂	1	1	yes	maximal, characteristic
4	#11926365	—	2	1	no	—
5	#11926343	—	2	1	no	—
6	C₁₉×#559	C₄	1	1	yes	characteristic
7	C₁₉×#492	C₂²	1	1	yes	characteristic
8	C₁₉×#477	—	2	1	no	—
9	C₁₉×#331	C₄	1	1	yes	characteristic
10	C₁₉×Q₈⋊C₈	—	2	1	no	—
11	C₂×SD₁₆×C₁₉	—	4	1	no	—
12	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
13	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
14	C₁₉×#124	—	4	1	no	—
15	C₁₉×#123	—	4	1	no	—
16	C₄×Q₈×C₁₉	—	2	1	no	—
17	C₄×D₄×C₁₉	—	4	1	no	—
18	C₁₉×#107	—	4	1	no	—
19	C₁₉×C₄⋊C₈	—	2	1	no	—
20	C₁₉×#103	—	4	1	no	—
21	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
22	#10597293	—	4	1	no	—
23	#10597269	—	4	1	no	—
24	C₂×Q₈×C₁₉	—	2	1	no	—
25	C₂×Q₈×C₁₉	—	2	1	no	—
26	C₂×D₄×C₁₉	—	2	1	no	—
27	C₂×D₄×C₁₉	—	4	1	no	—
28	C₂²×C₄×C₁₉	—	4	1	no	—
29	SD₁₆×C₁₉	—	8	1	no	—
30	SD₁₆×C₁₉	—	8	1	no	—
31	C₂×C₈×C₁₉	—	2	1	no	—
32	C₂×C₈×C₁₉	—	4	1	no	—
33	C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₄⋊C₄×C₁₉	—	4	1	no	—
35	C₄⋊C₄×C₁₉	—	4	1	no	—
36	C₂²⋊C₄×C₁₉	—	4	2	no	—
37	C₂²⋊C₄×C₁₉	—	4	1	no	—
38	C₄²×C₁₉	—	4	1	no	—
39	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
40	#64520	—	8	1	no	—
41	C₁₉⋊C₁₆	—	8	1	no	—
42	#7518	—	19	1	no	maximal, Sylow
43	C₂³×C₁₉	—	4	1	no	—
44	Q₈×C₁₉	—	4	1	no	—
45	Q₈×C₁₉	—	4	1	no	—
46	Q₈×C₁₉	—	8	1	no	—
47	D₄×C₁₉	—	8	1	no	—
48	D₄×C₁₉	—	8	1	no	—
49	D₄×C₁₉	—	8	1	no	—
50	C₂×C₄×C₁₉	—	2	1	no	—
51	C₂×C₄×C₁₉	—	4	1	no	—
52	C₂×C₄×C₁₉	—	4	1	no	—
53	C₂×C₄×C₁₉	—	4	1	no	—
54	C₂×C₄×C₁₉	—	16	1	no	—
55	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
56	C₈×C₁₉	—	2	1	no	—
57	C₈×C₁₉	—	2	1	no	—
58	C₈×C₁₉	—	8	1	no	—
59	C₁₉⋊C₈	—	16	1	no	—
60	#1630	D₁₉	1	1	yes	characteristic
61	#1410	—	19	1	no	—
62	#1359	—	19	1	no	—
63	C₂²×C₁₉	—	8	2	no	—
64	C₂²×C₁₉	—	8	1	no	—
65	C₂²×C₁₉	AΣL(1,𝔽₁₆)	1	1	yes	characteristic
66	C₄×C₁₉	—	2	1	no	—
67	C₄×C₁₉	—	2	1	no	—
68	C₄×C₁₉	—	2	1	no	—
69	C₄×C₁₉	—	8	1	no	—
70	C₄×C₁₉	—	8	1	no	—
71	C₄×C₁₉	—	8	1	no	—
72	#559	Dic₁₉	1	1	yes	characteristic
73	#492	C₂×D₁₉	1	1	yes	characteristic
74	#477	—	2	1	no	—
75	#364	—	38	1	no	—
76	#356	—	38	1	no	—
77	#331	Dic₁₉	1	1	yes	characteristic
78	Q₈⋊C₈	—	2	1	no	—
79	C₂×C₁₉	—	2	1	no	—
80	C₂×C₁₉	—	16	1	no	—
81	C₂×C₁₉	#1402	1	1	yes	characteristic
82	C₂×SD₁₆	—	4	1	no	—
83	C₄⋊Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
84	#127	C₂×Dic₁₉	1	1	yes	characteristic
85	#124	—	4	1	no	—
86	#123	—	4	1	no	—
87	C₄×Q₈	—	2	1	no	—
88	C₄×D₄	—	4	1	no	—
89	M₃₂	—	76	1	no	—
90	#107	—	4	1	no	—
91	C₄⋊C₈	—	2	1	no	—
92	#103	—	4	1	no	—
93	#101	—	76	1	no	—
94	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
95	C₁₉	#7518	1	1	yes	characteristic, complemented, Sylow
96	C₂×Q₈	—	2	1	no	—
97	C₂×Q₈	—	2	1	no	—
98	C₂×D₄	—	2	1	no	—
99	C₂×D₄	—	4	1	no	—
100	C₂²×C₄	—	4	1	no	—
101	SD₁₆	—	8	1	no	—
102	SD₁₆	—	8	1	no	—
103	M₁₆	—	152	1	no	—
104	C₂×C₈	—	2	1	no	—
105	C₂×C₈	—	4	1	no	—
106	C₄⋊C₄	—	2	1	no	—
107	C₄⋊C₄	—	4	1	no	—
108	C₄⋊C₄	—	4	1	no	—
109	C₂²⋊C₄	—	4	2	no	—
110	C₂²⋊C₄	—	4	1	no	—
111	C₄²	—	4	1	no	—
112	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
113	C₁₆	—	152	1	no	—
114	C₂³	—	4	1	no	—
115	Q₈	—	4	1	no	—
116	Q₈	—	4	1	no	—
117	Q₈	—	8	1	no	—
118	D₄	—	8	1	no	—
119	D₄	—	8	1	no	—
120	D₄	—	8	1	no	—
121	C₂×C₄	—	2	1	no	—
122	C₂×C₄	—	4	1	no	—
123	C₂×C₄	—	4	1	no	—
124	C₂×C₄	—	4	1	no	—
125	C₂×C₄	—	16	1	no	—
126	C₂×C₄	#10597291	1	1	yes	characteristic
127	C₈	—	2	1	no	—
128	C₈	—	2	1	no	—
129	C₈	—	8	1	no	—
130	C₈	—	304	1	no	—
131	C₂²	—	8	2	no	—
132	C₂²	—	8	1	no	—
133	C₂²	#11926331	1	1	yes	characteristic
134	C₄	—	2	1	no	—
135	C₄	—	2	1	no	—
136	C₄	—	2	1	no	—
137	C₄	—	8	1	no	—
138	C₄	—	8	1	no	—
139	C₄	—	8	1	no	—
140	C₂	—	2	1	no	—
141	C₂	—	16	1	no	—
142	C₂	#14561780	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561802

C₂

yes

maximal, characteristic

#14561676

C₂

yes

maximal, characteristic

C₁₉×#1630

C₂

yes

maximal, characteristic

#11926365

—

#11926343

—

C₁₉×#559

C₄

yes

characteristic

C₁₉×#492

C₂²

yes

characteristic

C₁₉×#477

—

C₁₉×#331

C₄

yes

characteristic

C₁₉×Q₈⋊C₈

—

C₂×SD₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

D₄

yes

characteristic

C₁₉×#127

C₂×C₄

yes

characteristic

C₁₉×#124

—

C₁₉×#123

—

C₄×Q₈×C₁₉

—

C₄×D₄×C₁₉

—

C₁₉×#107

—

C₁₉×C₄⋊C₈

—

C₁₉×#103

—

C₄×C₈×C₁₉

D₄

yes

characteristic

#10597293

—

#10597269

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

SD₁₆×C₁₉

—

SD₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

#64520

—

C₁₉⋊C₁₆

—

#7518

—

maximal, Sylow

C₂³×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#99

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1630

D₁₉

yes

characteristic

#1410

—

#1359

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

AΣL(1,𝔽₁₆)

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

#559

Dic₁₉

yes

characteristic

#492

C₂×D₁₉

yes

—

—

—

Dic₁₉

yes

characteristic

Q₈⋊C₈

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1402

yes

characteristic

C₂×SD₁₆

—

C₄⋊Q₈

C₂²⋊D₁₉

yes

characteristic

#127

C₂×Dic₁₉

yes

characteristic

#124

—

#123

—

C₄×Q₈

—

C₄×D₄

—

M₃₂

—

#107

—

C₄⋊C₈

—

#103

—

#101

—

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

C₁₉

#7518

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

100

C₂²×C₄

—

101

SD₁₆

—

102

SD₁₆

—

103

M₁₆

—

152

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₂²⋊C₄

—

110

C₂²⋊C₄

—

111

C₄²

—

112

C₄²

C₂²⋊Dic₁₉

yes

characteristic

113

C₁₆

—

152

—

114

C₂³

—

115

Q₈

—

116

Q₈

—

117

Q₈

—

118

D₄

—

119

D₄

—

120

D₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

#10597291

yes

characteristic

127

C₈

—

128

C₈

—

129

C₈

—

130

C₈

—

304

—

131

C₂²

—

132

C₂²

—

133

C₂²

#11926331

yes

characteristic

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₂

—

141

C₂

—

142

C₂

#14561780

yes

characteristic

	subgroup	G/H
center	C₂	#14561780
commutator, prime radical	C₁₉×#127	C₂×C₄
Frattini	#492	C₂×D₁₉
Fitting	C₁₉×#1630	C₂
socle	C₂×C₁₉	#1402
cosocle	C₁₉×#492	C₂²
hypercenter	#1630	D₁₉
hypocenter	C₁₉	#7518
LCS	G ▷ C₁₉×#127 ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #492 ◁ #1630

subgroup

G/H

center

C₂

#14561780

commutator, prime radical

C₁₉×#127

C₂×C₄

Frattini

#492

C₂×D₁₉

Fitting

C₁₉×#1630

C₂

socle

C₂×C₁₉

#1402

cosocle

C₁₉×#492

C₂²

D₁₉

C₁₉

G ▷ C₁₉×#127 ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #492 ◁ #1630

N	H ≅ G/N	type
95. C₁₉	#7518	semidirect

H ≅ G/N

type

95. C₁₉

#7518

semidirect

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

subgroup	index
#14561802	2
#14561676	2
C₁₉×#1630	2
#7518	19

subgroup

index

#14561802

#14561676

C₁₉×#1630

#7518

Subgroups — #18070364

Conjugacy classes of subgroups

Complements

Maximal subgroups