Group #14572723 — subgroups

Subgroups — #14572723

Order 2432.

364 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 179 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	C₄×Q₈×D₁₉	C₂	1	1	yes	maximal, characteristic
2	#11926674	C₂	1	3	yes	maximal, complemented
3	#11926671	C₂	1	3	yes	maximal, complemented
4	Q₈×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926600	C₂	1	3	yes	maximal
6	#11926595	C₂	1	3	yes	maximal
7	C₈×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₈×D₁₉	C₄	1	1	yes	characteristic
9	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
10	Q₈×Dic₁₉	C₄	1	1	yes	characteristic
11	C₄⋊C₄×D₁₉	C₄	1	3	yes	—
12	#10597333	C₄	1	3	yes	—
13	C₄²×D₁₉	C₂²	1	3	yes	—
14	C₄×Dic₃₈	C₂²	1	3	yes	—
15	C₁₉×C₄⋊C₈	C₂²	1	3	yes	—
16	C₄×C₈×C₁₉	C₂²	1	3	yes	—
17	(C₂×D₁₉)⋊C₈	C₂²	1	1	yes	characteristic
18	(C₂×D₁₉)⋊C₈	C₂²	1	3	yes	—
19	#10597272	C₂²	1	6	yes	—
20	Dic₁₉⋊C₈	C₂²	1	3	yes	—
21	Dic₁₉⋊C₈	C₂²	1	3	yes	—
22	C₄⋊(C₁₉⋊C₈)	C₂²	1	3	yes	—
23	C₄×C₁₉⋊C₈	C₂²	1	3	yes	—
24	C₂×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
25	Q₈×D₁₉	—	2	4	no	—
26	C₂×C₄×D₁₉	C₂×C₄	1	3	yes	—
27	C₂×C₄×D₁₉	C₂×C₄	1	3	yes	—
28	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
29	C₂×Dic₃₈	C₂×C₄	1	3	yes	—
30	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
31	C₂×C₈×C₁₉	C₂³	1	3	yes	—
32	C₄⋊C₄×C₁₉	C₂×C₄	1	3	yes	—
33	C₄²×C₁₉	C₂³	1	3	yes	—
34	C₄⋊Dic₁₉	C₂×C₄	1	3	yes	—
35	Dic₁₉⋊C₄	C₂×C₄	1	6	yes	—
36	C₄×Dic₁₉	C₂×C₄	1	3	yes	—
37	C₄×Dic₁₉	C₂×C₄	1	3	yes	—
38	C₄×Dic₁₉	C₂³	1	3	yes	—
39	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
40	C₂×C₁₉⋊C₈	C₂³	1	3	yes	—
41	C₂²×D₁₉	C₂²×C₄	1	1	yes	characteristic
42	Q₈×C₁₉	M₁₆	1	4	yes	—
43	C₂×C₄×C₁₉	C₂²×C₄	1	3	yes	—
44	C₂×C₄×C₁₉	C₂²×C₄	1	3	yes	—
45	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
46	C₂×Dic₁₉	C₂²×C₄	1	1	yes	characteristic
47	C₂×Dic₁₉	C₂²×C₄	1	3	yes	—
48	C₂×Dic₁₉	C₂²×C₄	1	3	yes	—
49	C₄×D₁₉	—	2	6	no	—
50	C₄×D₁₉	—	2	6	no	—
51	C₄×D₁₉	—	2	1	no	—
52	C₄×D₁₉	—	2	1	no	—
53	Dic₃₈	—	2	6	no	—
54	C₈×C₁₉	—	2	1	no	—
55	C₈×C₁₉	—	2	3	no	—
56	C₁₉⋊C₈	—	2	3	no	—
57	C₁₉⋊C₈	—	2	1	no	—
58	#2984	—	19	1	no	maximal, Sylow
59	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
60	C₂×D₁₉	—	2	1	no	—
61	C₂×D₁₉	—	2	1	no	—
62	C₂×D₁₉	#131	1	2	yes	—
63	C₄×C₁₉	—	2	3	no	—
64	C₄×C₁₉	C₂×M₁₆	1	6	yes	—
65	C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
66	C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
67	Dic₁₉	—	2	1	no	—
68	Dic₁₉	—	2	3	no	—
69	Dic₁₉	—	2	3	no	—
70	C₂×C₄×Q₈	—	19	1	no	—
71	#446	—	19	3	no	—
72	#446	—	19	3	no	—
73	C₈×Q₈	—	19	1	no	—
74	C₈×Q₈	D₁₉	1	1	yes	characteristic, complemented
75	#432	—	19	3	no	—
76	#431	—	19	3	no	—
77	C₂×C₁₉	#519	1	1	yes	characteristic
78	C₂×C₁₉	C₂²×M₁₆	1	1	yes	characteristic
79	C₂×C₁₉	C₂×#131	1	1	yes	characteristic
80	D₁₉	—	2	2	no	—
81	C₂²×Q₈	—	19	1	no	—
82	C₄×Q₈	—	19	1	no	—
83	C₄×Q₈	—	19	3	no	—
84	C₄×Q₈	—	19	3	no	—
85	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
86	C₂×C₄⋊C₄	—	19	3	no	—
87	C₂×C₄²	—	19	3	no	—
88	C₄⋊C₈	—	19	3	no	—
89	C₄⋊C₈	—	19	3	no	—
90	C₄⋊C₈	—	19	3	no	—
91	C₄⋊C₈	C₂×D₁₉	1	3	yes	—
92	C₂²⋊C₈	—	19	1	no	—
93	C₂²⋊C₈	—	19	3	no	—
94	#97	—	19	6	no	—
95	C₄×C₈	—	19	3	no	—
96	C₄×C₈	C₂×D₁₉	1	3	yes	—
97	C₁₉	#2984	1	1	yes	characteristic, complemented, Sylow
98	C₂×Q₈	—	19	3	no	—
99	C₂×Q₈	—	38	4	no	—
100	C₂×Q₈	C₄×D₁₉	1	1	yes	characteristic
101	C₂²×C₄	—	19	3	no	—
102	C₂²×C₄	—	19	3	no	—
103	C₂²×C₄	—	19	1	no	—
104	C₂×C₈	—	19	1	no	—
105	C₂×C₈	—	19	3	no	—
106	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
107	C₂×C₈	C₂²×D₁₉	1	3	yes	—
108	C₄⋊C₄	—	19	6	no	—
109	C₄⋊C₄	—	19	3	no	—
110	C₄⋊C₄	C₄×D₁₉	1	3	yes	—
111	C₄²	—	19	3	no	—
112	C₄²	—	19	3	no	—
113	C₄²	—	19	3	no	—
114	C₄²	C₂²×D₁₉	1	3	yes	—
115	C₂³	—	19	1	no	—
116	Q₈	—	38	6	no	—
117	Q₈	#64515	1	4	yes	—
118	C₂×C₄	—	19	1	no	—
119	C₂×C₄	—	19	3	no	—
120	C₂×C₄	—	19	3	no	—
121	C₂×C₄	—	38	6	no	—
122	C₂×C₄	—	38	1	no	—
123	C₂×C₄	—	38	1	no	—
124	C₂×C₄	—	38	6	no	—
125	C₂×C₄	C₂×C₄×D₁₉	1	3	yes	—
126	C₂×C₄	C₂×C₄×D₁₉	1	3	yes	—
127	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
128	C₈	—	2	1	no	—
129	C₈	—	2	3	no	—
130	C₈	—	38	3	no	—
131	C₈	—	38	1	no	—
132	C₂²	—	19	2	no	—
133	C₂²	—	38	1	no	—
134	C₂²	—	38	1	no	—
135	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
136	C₄	—	2	3	no	—
137	C₄	—	38	3	no	—
138	C₄	—	38	3	no	—
139	C₄	—	38	1	no	—
140	C₄	C₂×#64515	1	6	yes	—
141	C₄	#10597433	1	1	yes	characteristic
142	C₄	#10597436	1	1	yes	characteristic
143	C₂	—	38	2	no	—
144	C₂	#11927020	1	1	yes	characteristic
145	C₂	C₂²×#64515	1	1	yes	characteristic
146	C₂	#131×D₁₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×Q₈×D₁₉

C₂

yes

maximal, characteristic

#11926674

C₂

yes

maximal, complemented

#11926671

C₂

yes

maximal, complemented

Q₈×C₁₉⋊C₈

C₂

yes

maximal, characteristic, complemented

#11926600

C₂

yes

maximal

#11926595

C₂

yes

maximal

C₈×Q₈×C₁₉

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×D₁₉

C₄

yes

characteristic

C₄×Q₈×C₁₉

C₂²

yes

characteristic

Q₈×Dic₁₉

C₄

yes

characteristic

C₄⋊C₄×D₁₉

C₄

yes

—

#10597333

C₄

yes

—

C₄²×D₁₉

C₂²

yes

—

C₄×Dic₃₈

C₂²

yes

—

C₁₉×C₄⋊C₈

C₂²

yes

—

C₄×C₈×C₁₉

C₂²

yes

—

(C₂×D₁₉)⋊C₈

C₂²

yes

characteristic

(C₂×D₁₉)⋊C₈

C₂²

yes

—

#10597272

C₂²

yes

—

Dic₁₉⋊C₈

C₂²

yes

—

Dic₁₉⋊C₈

C₂²

yes

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₄×C₁₉⋊C₈

C₂²

yes

—

C₂×Q₈×C₁₉

C₂×C₄

yes

characteristic

Q₈×D₁₉

—

C₂×C₄×D₁₉

C₂×C₄

yes

—

C₂×C₄×D₁₉

C₂×C₄

yes

—

C₂×C₄×D₁₉

C₂³

yes

characteristic

C₂×Dic₃₈

C₂×C₄

yes

—

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

C₂³

yes

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

Dic₁₉⋊C₄

C₂×C₄

yes

—

C₄×Dic₁₉

C₂×C₄

yes

—

C₄×Dic₁₉

C₂×C₄

yes

—

C₄×Dic₁₉

C₂³

yes

—

C₂×C₁₉⋊C₈

C₂³

yes

characteristic

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂²×D₁₉

C₂²×C₄

yes

characteristic

Q₈×C₁₉

M₁₆

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

C₂²×C₄

yes

characteristic

C₂×Dic₁₉

C₂²×C₄

yes

—

C₂×Dic₁₉

C₂²×C₄

yes

—

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2984

—

maximal, Sylow

C₂²×C₁₉

C₂³×C₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

#131

yes

—

C₄×C₁₉

—

C₄×C₁₉

C₂×M₁₆

yes

—

C₄×C₁₉

2₋¹⁺⁴

yes

characteristic

C₄×C₁₉

2₋¹⁺⁴

yes

characteristic

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×C₄×Q₈

—

#446

—

#446

—

C₈×Q₈

—

C₈×Q₈

D₁₉

yes

characteristic, complemented

#432

—

#431

—

C₂×C₁₉

#519

yes

characteristic

C₂×C₁₉

C₂²×M₁₆

yes

characteristic

C₂×C₁₉

C₂×#131

yes

characteristic

D₁₉

—

C₂²×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

C₂×D₁₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₁₉

yes

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₄×C₈

C₂×D₁₉

yes

—

C₁₉

#2984

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

100

C₂×Q₈

C₄×D₁₉

yes

characteristic

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

C₂²×D₁₉

yes

characteristic

107

C₂×C₈

C₂²×D₁₉

yes

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄⋊C₄

C₄×D₁₉

yes

—

111

C₄²

—

112

C₄²

—

113

C₄²

—

114

C₄²

C₂²×D₁₉

yes

—

115

C₂³

—

116

Q₈

—

117

Q₈

#64515

yes

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

C₂×C₄×D₁₉

yes

—

126

C₂×C₄

C₂×C₄×D₁₉

yes

—

127

C₂×C₄

C₂³×D₁₉

yes

characteristic

128

C₈

—

129

C₈

—

130

C₈

—

131

C₈

—

132

C₂²

—

133

C₂²

—

134

C₂²

—

135

C₂²

C₂²×C₄×D₁₉

yes

characteristic

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

C₂×#64515

yes

—

141

C₄

#10597433

yes

characteristic

142

C₄

#10597436

yes

characteristic

143

C₂

—

144

C₂

#11927020

yes

characteristic

145

C₂

C₂²×#64515

yes

characteristic

146

C₂

#131×D₁₉

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₉
commutator, socle	C₂²×C₁₉	C₂³×C₄
Fitting	C₈×Q₈×C₁₉	C₂
prime radical	C₂²×D₁₉	C₂²×C₄
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	C₈×Q₈	D₁₉
hypocenter	C₁₉	#2984
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₈×Q₈

subgroup

G/H

center, Frattini

C₂×C₄

C₂³×D₁₉

commutator, socle

C₂²×C₁₉

C₂³×C₄

Fitting

C₈×Q₈×C₁₉

C₂

prime radical

C₂²×D₁₉

C₂²×C₄

cosocle

C₂×C₄×C₁₉

C₂⁴

hypercenter

C₈×Q₈

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂×C₄ ◁ C₈×Q₈

N	H ≅ G/N	type
2. #11926674	C₂	semidirect
3. #11926671	C₂	semidirect
4. Q₈×C₁₉⋊C₈	C₂	semidirect
7. C₈×Q₈×C₁₉	C₂	semidirect
74. C₈×Q₈	D₁₉	semidirect
97. C₁₉	#2984	semidirect

H ≅ G/N

type

2. #11926674

C₂

semidirect

3. #11926671

C₂

semidirect

4. Q₈×C₁₉⋊C₈

C₂

semidirect

7. C₈×Q₈×C₁₉

C₂

semidirect

74. C₈×Q₈

D₁₉

semidirect

97. C₁₉

#2984

semidirect

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

subgroup	index
C₄×Q₈×D₁₉	2
#11926674	2
#11926671	2
Q₈×C₁₉⋊C₈	2
#11926600	2
#11926595	2
C₈×Q₈×C₁₉	2
#2984	19

subgroup

index

C₄×Q₈×D₁₉

Q₈×C₁₉⋊C₈

C₈×Q₈×C₁₉

Subgroups — #14572723

Conjugacy classes of subgroups

Complements

Maximal subgroups