Group #18069882 — subgroups

Subgroups — #18069882

Order 4864.

170 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 51 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	#14561775	C₂	1	2	yes	maximal, complemented
2	C₁₉×#2112	C₂	1	1	yes	maximal, characteristic
3	#11926378	—	2	2	no	—
4	C₂³×C₈×C₁₉	C₄	1	1	yes	characteristic
5	C₂×C₁₉×M₃₂	C₄	1	1	yes	characteristic
6	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
7	C₁₉×C₂²⋊C₁₆	—	2	2	no	—
8	C₂³×C₄×C₁₉	C₈	1	1	yes	characteristic
9	C₂²×C₈×C₁₉	—	2	1	no	—
10	C₂²×C₈×C₁₉	—	2	1	no	—
11	C₂²×C₈×C₁₉	—	4	1	no	—
12	C₂²×C₈×C₁₉	—	4	1	no	—
13	C₂²×C₈×C₁₉	C₈	1	1	yes	characteristic
14	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₁₉×M₃₂	—	4	1	no	—
16	C₁₉×M₃₂	—	4	1	no	—
17	C₂×C₁₆×C₁₉	—	2	1	no	—
18	C₂×C₁₆×C₁₉	D₄	1	2	yes	—
19	C₁₉⋊C₃₂	—	4	2	no	—
20	C₂⁴×C₁₉	C₁₆	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	—	2	1	no	—
22	C₂²×C₄×C₁₉	—	2	1	no	—
23	C₂²×C₄×C₁₉	—	4	1	no	—
24	C₂²×C₄×C₁₉	—	4	1	no	—
25	C₂²×C₄×C₁₉	C₁₆	1	1	yes	characteristic
26	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
27	C₂×C₈×C₁₉	—	2	1	no	—
28	C₂×C₈×C₁₉	—	2	1	no	—
29	C₂×C₈×C₁₉	—	2	1	no	—
30	C₂×C₈×C₁₉	—	4	2	no	—
31	C₂×C₈×C₁₉	—	4	1	no	—
32	C₂×C₈×C₁₉	—	4	1	no	—
33	C₂×C₈×C₁₉	—	4	1	no	—
34	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
36	C₁₆×C₁₉	—	2	2	no	—
37	C₁₆×C₁₉	—	4	1	no	—
38	#7336	—	19	1	no	maximal, Sylow
39	C₂³×C₁₉	—	2	1	no	—
40	C₂³×C₁₉	—	4	1	no	—
41	C₂³×C₁₉	—	4	2	no	—
42	C₂³×C₁₉	C₂×C₁₆	1	1	yes	characteristic
43	C₂×C₄×C₁₉	—	2	1	no	—
44	C₂×C₄×C₁₉	—	2	1	no	—
45	C₂×C₄×C₁₉	—	2	1	no	—
46	C₂×C₄×C₁₉	—	4	2	no	—
47	C₂×C₄×C₁₉	—	4	1	no	—
48	C₂×C₄×C₁₉	—	4	1	no	—
49	C₂×C₄×C₁₉	—	4	1	no	—
50	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
51	C₂×C₄×C₁₉	M₃₂	1	1	yes	characteristic
52	C₈×C₁₉	—	2	1	no	—
53	C₈×C₁₉	—	4	1	no	—
54	C₈×C₁₉	#99	1	1	yes	characteristic
55	C₈×C₁₉	#100	1	1	yes	characteristic
56	#2112	D₁₉	1	1	yes	characteristic
57	#1400	—	19	2	no	—
58	C₂²×C₁₉	—	2	2	no	—
59	C₂²×C₁₉	—	2	1	no	—
60	C₂²×C₁₉	—	4	1	no	—
61	C₂²×C₁₉	—	4	1	no	—
62	C₂²×C₁₉	—	4	2	no	—
63	C₂²×C₁₉	—	4	2	no	—
64	C₂²×C₁₉	—	4	1	no	—
65	C₂²×C₁₉	C₂²⋊C₁₆	1	1	yes	characteristic
66	C₄×C₁₉	—	2	1	no	—
67	C₄×C₁₉	—	4	1	no	—
68	C₄×C₁₉	#323	1	1	yes	characteristic
69	C₄×C₁₉	#349	1	1	yes	characteristic
70	C₂³×C₈	Dic₁₉	1	1	yes	characteristic
71	C₂×M₃₂	Dic₁₉	1	1	yes	characteristic
72	C₂×M₃₂	C₂×D₁₉	1	1	yes	characteristic
73	M₆₄	—	38	2	no	—
74	C₂²⋊C₁₆	—	2	2	no	—
75	C₂×C₁₉	—	2	1	no	—
76	C₂×C₁₉	—	4	2	no	—
77	C₂×C₁₉	—	4	1	no	—
78	C₂×C₁₉	#1314	1	1	yes	characteristic
79	C₂³×C₄	C₁₉⋊C₈	1	1	yes	characteristic
80	C₂²×C₈	—	2	1	no	—
81	C₂²×C₈	—	2	1	no	—
82	C₂²×C₈	—	4	1	no	—
83	C₂²×C₈	—	4	1	no	—
84	C₂²×C₈	C₁₉⋊C₈	1	1	yes	characteristic
85	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
86	M₃₂	—	4	1	no	—
87	M₃₂	—	4	1	no	—
88	C₂×C₁₆	—	2	1	no	—
89	C₂×C₁₆	C₂²⋊D₁₉	1	2	yes	—
90	C₃₂	—	76	2	no	—
91	C₁₉	#7336	1	1	yes	characteristic, complemented, Sylow
92	C₂⁴	C₁₉⋊C₁₆	1	1	yes	characteristic
93	C₂²×C₄	—	2	1	no	—
94	C₂²×C₄	—	2	1	no	—
95	C₂²×C₄	—	4	1	no	—
96	C₂²×C₄	—	4	1	no	—
97	C₂²×C₄	C₁₉⋊C₁₆	1	1	yes	characteristic
98	C₂²×C₄	C₂×C₁₉⋊C₈	1	1	yes	characteristic
99	C₂×C₈	—	2	1	no	—
100	C₂×C₈	—	2	1	no	—
101	C₂×C₈	—	2	1	no	—
102	C₂×C₈	—	4	2	no	—
103	C₂×C₈	—	4	1	no	—
104	C₂×C₈	—	4	1	no	—
105	C₂×C₈	—	4	1	no	—
106	C₂×C₈	#64520	1	1	yes	characteristic
107	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
108	C₁₆	—	2	2	no	—
109	C₁₆	—	4	1	no	—
110	C₂³	—	2	1	no	—
111	C₂³	—	4	1	no	—
112	C₂³	—	4	2	no	—
113	C₂³	C₂×C₁₉⋊C₁₆	1	1	yes	characteristic
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	2	1	no	—
117	C₂×C₄	—	4	2	no	—
118	C₂×C₄	—	4	1	no	—
119	C₂×C₄	—	4	1	no	—
120	C₂×C₄	—	4	1	no	—
121	C₂×C₄	#10597269	1	1	yes	characteristic
122	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
123	C₈	—	2	1	no	—
124	C₈	—	4	1	no	—
125	C₈	#10597290	1	1	yes	characteristic
126	C₈	#10597291	1	1	yes	characteristic
127	C₂²	—	2	2	no	—
128	C₂²	—	2	1	no	—
129	C₂²	—	4	1	no	—
130	C₂²	—	4	1	no	—
131	C₂²	—	4	2	no	—
132	C₂²	—	4	2	no	—
133	C₂²	—	4	1	no	—
134	C₂²	C₂²⋊(C₁₉⋊C₁₆)	1	1	yes	characteristic
135	C₄	—	2	1	no	—
136	C₄	—	4	1	no	—
137	C₄	#11926268	1	1	yes	characteristic
138	C₄	#11926326	1	1	yes	characteristic
139	C₂	—	2	1	no	—
140	C₂	—	4	2	no	—
141	C₂	—	4	1	no	—
142	C₂	#14561559	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561775

C₂

yes

maximal, complemented

C₁₉×#2112

C₂

yes

maximal, characteristic

#11926378

—

C₂³×C₈×C₁₉

C₄

yes

characteristic

C₂×C₁₉×M₃₂

C₄

yes

characteristic

C₂×C₁₉×M₃₂

C₂²

yes

characteristic

C₁₉×C₂²⋊C₁₆

—

C₂³×C₄×C₁₉

C₈

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₈

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₁₉×M₃₂

—

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

D₄

yes

—

C₁₉⋊C₃₂

—

C₂⁴×C₁₉

C₁₆

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₁₆

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

M₁₆

yes

characteristic

C₁₆×C₁₉

—

C₁₆×C₁₉

—

#7336

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₁₆

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

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

M₃₂

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

yes

C₈×C₁₉

yes

D₁₉

yes

characteristic

#1400

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²⋊C₁₆

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂³×C₈

Dic₁₉

yes

characteristic

C₂×M₃₂

Dic₁₉

yes

characteristic

C₂×M₃₂

C₂×D₁₉

yes

characteristic

M₆₄

—

C₂²⋊C₁₆

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1314

yes

characteristic

C₂³×C₄

C₁₉⋊C₈

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₁₉⋊C₈

yes

characteristic

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂²⋊D₁₉

yes

—

C₃₂

—

C₁₉

#7336

yes

characteristic, complemented, Sylow

C₂⁴

C₁₉⋊C₁₆

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₁₉⋊C₁₆

yes

characteristic

C₂²×C₄

C₂×C₁₉⋊C₈

yes

characteristic

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

#64520

yes

characteristic

107

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

108

C₁₆

—

109

C₁₆

—

110

C₂³

—

111

C₂³

—

112

C₂³

—

113

C₂³

C₂×C₁₉⋊C₁₆

yes

characteristic

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

#10597269

yes

characteristic

122

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

123

C₈

—

124

C₈

—

125

C₈

#10597290

yes

characteristic

126

C₈

#10597291

yes

characteristic

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

—

134

C₂²

C₂²⋊(C₁₉⋊C₁₆)

yes

characteristic

135

C₄

—

136

C₄

—

137

C₄

#11926268

yes

characteristic

138

C₄

#11926326

yes

characteristic

139

C₂

—

140

C₂

—

141

C₂

—

142

C₂

#14561559

yes

characteristic

	subgroup	G/H
center	C₈	#10597291
commutator	C₂³×C₁₉	C₂×C₁₆
Frattini	C₂×M₃₂	C₂×D₁₉
Fitting	C₁₉×#2112	C₂
socle	C₂×C₁₉	#1314
prime radical	C₂⁴×C₁₉	C₁₆
cosocle	C₂×C₁₉×M₃₂	C₂²
hypercenter	#2112	D₁₉
hypocenter	C₁₉	#7336
LCS	G ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×M₃₂ ◁ #2112

subgroup

G/H

center

C₈

#10597291

commutator

C₂³×C₁₉

C₂×C₁₆

Frattini

C₂×M₃₂

C₂×D₁₉

Fitting

C₁₉×#2112

C₂

socle

C₂×C₁₉

#1314

prime radical

C₂⁴×C₁₉

C₁₆

cosocle

C₂×C₁₉×M₃₂

C₂²

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×M₃₂ ◁ #2112

N	H ≅ G/N	type
1. #14561775	C₂	semidirect
91. C₁₉	#7336	semidirect

H ≅ G/N

type

1. #14561775

C₂

semidirect

91. C₁₉

#7336

semidirect

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

subgroup	index
#14561775	2
C₁₉×#2112	2
#7336	19

subgroup

index

#14561775

C₁₉×#2112

#7336

Subgroups — #18069882

Conjugacy classes of subgroups

Complements

Maximal subgroups