Group #14561523 — subgroups

Subgroups — #14561523

Order 2432.

190 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 65 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	#11926508	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂²⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
5	C₂²×C₈×C₁₉	—	2	1	no	—
6	C₂×#64520	C₄	1	2	yes	—
7	C₂²×C₁₉⋊C₈	—	2	1	no	—
8	C₁₉×C₂²⋊C₈	—	2	1	no	—
9	C₁₉×C₂²⋊C₈	C₄	1	2	yes	—
10	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
11	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
12	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
13	C₂²⋊(C₁₉⋊C₈)	C₄	1	2	yes	—
14	C₂⁴×C₁₉	Q₈	1	1	yes	characteristic
15	C₂²×C₄×C₁₉	—	4	2	no	—
16	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
20	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂×C₈×C₁₉	—	2	2	no	—
23	C₂×C₈×C₁₉	—	4	2	no	—
24	#64520	—	4	2	no	—
25	C₂×C₁₉⋊C₈	—	2	2	no	—
26	C₂×C₁₉⋊C₈	—	2	2	no	—
27	C₂×C₁₉⋊C₈	—	4	2	no	—
28	C₂³×C₁₉	—	2	2	no	—
29	C₂³×C₁₉	—	2	2	no	—
30	C₂³×C₁₉	—	4	1	no	—
31	C₂³×C₁₉	C₄⋊C₄	1	1	yes	characteristic
32	C₂³×C₁₉	C₄⋊C₄	1	1	yes	characteristic
33	C₂³×C₁₉	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₁₉	—	2	2	no	—
35	C₂×C₄×C₁₉	—	2	2	no	—
36	C₂×C₄×C₁₉	—	2	2	no	—
37	C₂×C₄×C₁₉	—	4	1	no	—
38	C₂×C₄×C₁₉	—	4	1	no	—
39	C₂×C₄×C₁₉	—	4	1	no	—
40	C₂×C₄×C₁₉	C₄²	1	1	yes	characteristic
41	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
42	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
43	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
44	C₈×C₁₉	—	4	2	no	—
45	C₁₉⋊C₈	—	4	2	no	—
46	C₁₉⋊C₈	—	4	2	no	—
47	#1298	—	19	1	no	maximal, Sylow
48	C₂²×C₁₉	—	2	1	no	—
49	C₂²×C₁₉	—	2	1	no	—
50	C₂²×C₁₉	—	2	1	no	—
51	C₂²×C₁₉	—	2	1	no	—
52	C₂²×C₁₉	—	2	1	no	—
53	C₂²×C₁₉	—	2	1	no	—
54	C₂²×C₁₉	—	2	1	no	—
55	C₂²×C₁₉	—	4	4	no	—
56	C₂²×C₁₉	#95	1	1	yes	characteristic
57	C₂²×C₁₉	#108	1	2	yes	—
58	C₂²×C₁₉	#108	1	2	yes	—
59	C₄×C₁₉	—	2	1	no	—
60	C₄×C₁₉	—	2	1	no	—
61	C₄×C₁₉	—	2	1	no	—
62	C₄×C₁₉	#99	1	2	yes	—
63	#407	—	19	1	no	—
64	C₂×C₂²⋊C₈	—	19	1	no	—
65	C₂×C₂²⋊C₈	D₁₉	1	1	yes	characteristic
66	C₂×C₁₉	—	2	2	no	—
67	C₂×C₁₉	—	2	2	no	—
68	C₂×C₁₉	—	4	1	no	—
69	C₂×C₁₉	#341	1	1	yes	characteristic
70	C₂×C₁₉	#341	1	1	yes	characteristic
71	C₂×C₁₉	#342	1	1	yes	characteristic
72	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
73	C₂×M₁₆	—	19	2	no	—
74	C₂²×C₈	—	2	1	no	—
75	C₂²×C₈	—	38	1	no	—
76	C₂²⋊C₈	—	2	1	no	—
77	C₂²⋊C₈	—	19	2	no	—
78	C₂²⋊C₈	—	38	1	no	—
79	C₂²⋊C₈	—	38	1	no	—
80	C₂²⋊C₈	—	38	1	no	—
81	C₂²⋊C₈	Dic₁₉	1	2	yes	—
82	C₁₉	#1298	1	1	yes	characteristic, complemented, Sylow
83	C₂⁴	Dic₃₈	1	1	yes	characteristic
84	C₂²×C₄	—	4	2	no	—
85	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
86	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
87	C₂²×C₄	D₇₆	1	1	yes	characteristic
88	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
89	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
90	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
91	M₁₆	—	76	2	no	—
92	C₂×C₈	—	2	2	no	—
93	C₂×C₈	—	4	2	no	—
94	C₂×C₈	—	38	2	no	—
95	C₂×C₈	—	38	2	no	—
96	C₂×C₈	—	76	2	no	—
97	C₂³	—	2	2	no	—
98	C₂³	—	2	2	no	—
99	C₂³	—	4	1	no	—
100	C₂³	Dic₁₉⋊C₄	1	1	yes	characteristic
101	C₂³	Dic₁₉⋊C₄	1	1	yes	characteristic
102	C₂³	C₄⋊Dic₁₉	1	1	yes	characteristic
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	2	2	no	—
106	C₂×C₄	—	4	1	no	—
107	C₂×C₄	—	4	1	no	—
108	C₂×C₄	—	4	1	no	—
109	C₂×C₄	C₄×Dic₁₉	1	1	yes	characteristic
110	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
111	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
112	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
113	C₈	—	4	2	no	—
114	C₈	—	76	2	no	—
115	C₈	—	76	2	no	—
116	C₂²	—	2	1	no	—
117	C₂²	—	2	1	no	—
118	C₂²	—	2	1	no	—
119	C₂²	—	2	1	no	—
120	C₂²	—	2	1	no	—
121	C₂²	—	2	1	no	—
122	C₂²	—	2	1	no	—
123	C₂²	—	4	4	no	—
124	C₂²	#10597276	1	2	yes	—
125	C₂²	#10597279	1	2	yes	—
126	C₂²	C₁₉⋊#95	1	1	yes	characteristic
127	C₄	—	2	1	no	—
128	C₄	—	2	1	no	—
129	C₄	—	2	1	no	—
130	C₄	#10597263	1	2	yes	—
131	C₂	—	2	2	no	—
132	C₂	—	2	2	no	—
133	C₂	—	4	1	no	—
134	C₂	#11926308	1	1	yes	characteristic
135	C₂	#11926309	1	1	yes	characteristic
136	C₂	#11926310	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926508

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

C₂

yes

maximal, characteristic

C₂×C₁₉×C₂²⋊C₈

C₂

yes

maximal, characteristic

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

—

C₂×#64520

C₄

yes

—

C₂²×C₁₉⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

C₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

C₄

yes

—

C₂⁴×C₁₉

Q₈

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₄⋊C₄

yes

characteristic

C₂³×C₁₉

C₄⋊C₄

yes

characteristic

C₂³×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₄²

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1298

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#95

yes

characteristic

C₂²×C₁₉

#108

yes

—

C₂²×C₁₉

#108

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#99

yes

—

#407

—

C₂×C₂²⋊C₈

—

C₂×C₂²⋊C₈

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂³×C₄

C₂×D₁₉

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

Dic₁₉

yes

—

C₁₉

#1298

yes

characteristic, complemented, Sylow

C₂⁴

Dic₃₈

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₄×D₁₉

yes

characteristic

C₂²×C₄

C₄×D₁₉

yes

characteristic

C₂²×C₄

D₇₆

yes

characteristic

C₂²×C₄

C₂×Dic₁₉

yes

characteristic

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂³

—

C₂³

—

C₂³

—

100

C₂³

Dic₁₉⋊C₄

yes

characteristic

101

C₂³

Dic₁₉⋊C₄

yes

characteristic

102

C₂³

C₄⋊Dic₁₉

yes

characteristic

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

C₄×Dic₁₉

yes

characteristic

110

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

111

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

112

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

113

C₈

—

114

C₈

—

115

C₈

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

—

122

C₂²

—

123

C₂²

—

124

C₂²

#10597276

yes

—

125

C₂²

#10597279

yes

—

126

C₂²

C₁₉⋊#95

yes

characteristic

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

#10597263

yes

—

131

C₂

—

132

C₂

—

133

C₂

—

134

C₂

#11926308

yes

characteristic

135

C₂

#11926309

yes

characteristic

136

C₂

#11926310

yes

characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×D₁₉)⋊C₄
commutator	C₂×C₄×C₁₉	C₄²
Frattini	C₂³×C₄	C₂×D₁₉
Fitting	C₂×C₁₉×C₂²⋊C₈	C₂
socle	C₂²×C₁₉	#95
prime radical	C₂⁴×C₁₉	Q₈
cosocle	C₂³×C₄×C₁₉	C₂²
hypercenter	C₂×C₂²⋊C₈	D₁₉
hypocenter	C₁₉	#1298
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×C₂²⋊C₈

subgroup

G/H

center

C₂×C₄

(C₂×D₁₉)⋊C₄

commutator

C₂×C₄×C₁₉

C₄²

Frattini

C₂³×C₄

C₂×D₁₉

Fitting

C₂×C₁₉×C₂²⋊C₈

C₂

socle

C₂²×C₁₉

#95

prime radical

C₂⁴×C₁₉

Q₈

cosocle

C₂³×C₄×C₁₉

C₂²

hypercenter

C₂×C₂²⋊C₈

D₁₉

hypocenter

C₁₉

#1298

LCS

G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×C₂²⋊C₈

N	H ≅ G/N	type
82. C₁₉	#1298	semidirect

H ≅ G/N

type

82. C₁₉

#1298

semidirect

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

subgroup	index
#11926508	2
C₂×C₂²⋊(C₁₉⋊C₈)	2
C₂×C₁₉×C₂²⋊C₈	2
#1298	19

subgroup

index

#11926508

C₂×C₂²⋊(C₁₉⋊C₈)

C₂×C₁₉×C₂²⋊C₈

#1298

Subgroups — #14561523

Conjugacy classes of subgroups

Complements

Maximal subgroups