Group #14575016 — subgroups

Subgroups — #14575016

Order 2432.

430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 125 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	#11927094	C₂	1	2	yes	maximal, complemented
2	#11926835	C₂	1	4	yes	maximal, complemented
3	#11926797	C₂	1	4	yes	maximal, complemented
4	#11926740	C₂	1	4	yes	maximal, complemented
5	C₁₉×#423	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#64541	—	2	2	no	—
7	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
8	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	#10597376	—	2	2	no	—
10	#10597376	C₂²	1	4	yes	—
11	C₂×D₁₅₂	C₂²	1	4	yes	—
12	#10597321	—	2	2	no	—
13	#10597320	C₂²	1	2	yes	—
14	C₄×D₇₆	—	2	2	no	—
15	C₄×D₇₆	C₂²	1	4	yes	—
16	#10597315	C₂²	1	2	yes	—
17	C₁₉×C₄⋊C₈	C₂²	1	4	yes	—
18	#10597278	C₂²	1	8	yes	—
19	#10597274	C₂²	1	4	yes	—
20	C₂²×C₄×C₁₉	D₄	1	2	yes	—
21	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
22	C₂×C₂²⋊D₁₉	—	2	4	no	—
23	#64541	—	4	8	no	—
24	C₂×D₇₆	—	2	2	no	—
25	C₂×D₇₆	—	2	2	no	—
26	C₂×D₇₆	C₂³	1	4	yes	—
27	C₂×C₄×D₁₉	—	2	4	no	—
28	C₂×Dic₃₈	—	2	2	no	—
29	M₁₆×C₁₉	—	4	2	no	—
30	C₂×C₈×C₁₉	C₂³	1	4	yes	—
31	C₄²×C₁₉	D₄	1	1	yes	characteristic
32	C₄²×C₁₉	D₄	1	1	yes	characteristic
33	C₄²×C₁₉	C₂³	1	2	yes	—
34	(C₂×D₁₉)⋊C₄	—	2	4	no	—
35	(C₂×D₁₉)⋊C₄	—	2	4	no	—
36	C₄⋊Dic₁₉	—	2	2	no	—
37	C₄⋊Dic₁₉	C₂³	1	4	yes	—
38	D₁₅₂	—	4	4	no	—
39	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂²×D₁₉	—	2	4	no	—
41	C₂×C₄×C₁₉	—	2	4	no	—
42	C₂×C₄×C₁₉	—	2	1	no	—
43	C₂×C₄×C₁₉	—	2	1	no	—
44	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
46	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
47	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
48	C₂²⋊D₁₉	—	4	8	no	—
49	C₂×Dic₁₉	—	2	4	no	—
50	D₇₆	—	2	4	no	—
51	D₇₆	—	2	4	no	—
52	D₇₆	—	4	4	no	—
53	D₇₆	—	4	4	no	—
54	C₄×D₁₉	—	4	8	no	—
55	Dic₃₈	—	4	4	no	—
56	C₈×C₁₉	—	2	4	no	—
57	#3253	—	19	1	no	maximal, Sylow
58	C₂²×C₁₉	—	2	1	no	—
59	C₂²×C₁₉	—	2	2	no	—
60	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
61	C₂×D₁₉	—	4	4	no	—
62	C₂×D₁₉	—	4	4	no	—
63	C₂×D₁₉	—	4	4	no	—
64	C₄×C₁₉	—	2	1	no	—
65	C₄×C₁₉	—	2	2	no	—
66	C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
67	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
68	C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
69	Dic₁₉	—	4	4	no	—
70	#532	—	19	2	no	—
71	#476	—	19	4	no	—
72	#469	—	19	4	no	—
73	#459	—	19	4	no	—
74	#423	D₁₉	1	1	yes	characteristic, complemented
75	C₂×C₁₉	—	4	1	no	—
76	C₂×C₁₉	#537	1	1	yes	characteristic
77	C₂×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
78	D₁₉	—	8	4	no	—
79	C₂×#41	—	38	2	no	—
80	C₂×D₈	—	19	4	no	—
81	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
82	C₄⋊Q₈	—	19	2	no	—
83	#127	—	19	2	no	—
84	#124	—	38	2	no	—
85	#121	—	19	4	no	—
86	#121	—	38	2	no	—
87	C₄×D₄	—	19	4	no	—
88	C₄×D₄	—	38	2	no	—
89	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
90	#106	—	19	4	no	—
91	C₄⋊C₈	C₂×D₁₉	1	4	yes	—
92	#102	—	19	8	no	—
93	C₁₉	#3253	1	1	yes	characteristic, complemented, Sylow
94	#41	—	76	8	no	—
95	C₂×Q₈	—	38	2	no	—
96	C₂×D₄	—	19	4	no	—
97	C₂×D₄	—	38	4	no	—
98	C₂×D₄	—	38	2	no	—
99	C₂×D₄	—	38	2	no	—
100	C₂²×C₄	—	38	4	no	—
101	C₂²×C₄	D₇₆	1	2	yes	—
102	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
103	D₈	—	76	4	no	—
104	M₁₆	—	4	2	no	—
105	C₂×C₈	C₂²×D₁₉	1	4	yes	—
106	C₄⋊C₄	—	19	4	no	—
107	C₄⋊C₄	—	38	2	no	—
108	C₂²⋊C₄	—	38	4	no	—
109	C₂²⋊C₄	—	38	4	no	—
110	C₄²	D₇₆	1	1	yes	characteristic
111	C₄²	D₇₆	1	1	yes	characteristic
112	C₄²	C₂²×D₁₉	1	2	yes	—
113	C₂³	—	38	4	no	—
114	C₂³	C₂×D₇₆	1	1	yes	characteristic
115	Q₈	—	76	4	no	—
116	D₄	—	38	4	no	—
117	D₄	—	38	4	no	—
118	D₄	—	76	4	no	—
119	D₄	—	76	8	no	—
120	D₄	—	76	4	no	—
121	C₂×C₄	—	2	1	no	—
122	C₂×C₄	—	2	1	no	—
123	C₂×C₄	—	2	4	no	—
124	C₂×C₄	—	38	4	no	—
125	C₂×C₄	—	76	8	no	—
126	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
127	C₂×C₄	C₂×D₇₆	1	2	yes	—
128	C₂×C₄	C₂×D₇₆	1	2	yes	—
129	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
130	C₈	—	2	4	no	—
131	C₂²	—	2	2	no	—
132	C₂²	—	2	1	no	—
133	C₂²	—	76	4	no	—
134	C₂²	—	76	4	no	—
135	C₂²	—	76	4	no	—
136	C₂²	C₂²×D₇₆	1	1	yes	characteristic
137	C₄	—	2	2	no	—
138	C₄	—	2	1	no	—
139	C₄	—	76	4	no	—
140	C₄	#10597354	1	4	yes	—
141	C₄	#10597430	1	1	yes	characteristic
142	C₄	#10597433	1	1	yes	characteristic
143	C₂	—	4	1	no	—
144	C₂	—	152	4	no	—
145	C₂	#11927125	1	1	yes	characteristic
146	C₂	C₂×#10597354	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11927094

C₂

yes

maximal, complemented

#11926835

C₂

yes

maximal, complemented

#11926797

C₂

yes

maximal, complemented

#11926740

C₂

yes

maximal, complemented

C₁₉×#423

C₂

yes

maximal, characteristic, complemented

C₂×#64541

—

C₂×M₁₆×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

#10597376

—

#10597376

C₂²

yes

—

C₂×D₁₅₂

C₂²

yes

—

#10597321

—

#10597320

C₂²

yes

—

C₄×D₇₆

—

C₄×D₇₆

C₂²

yes

—

#10597315

C₂²

yes

—

C₁₉×C₄⋊C₈

C₂²

yes

—

#10597278

C₂²

yes

—

#10597274

C₂²

yes

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

C₂³

yes

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

—

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

C₂³

yes

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

—

D₁₅₂

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

—

#3253

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₄×C₁₉

H(5,𝔽₂)

yes

characteristic

C₄×C₁₉

2₋¹⁺⁴

yes

characteristic

Dic₁₉

—

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

#537

yes

characteristic

C₂×C₁₉

C₂×AGL(1,ℤ/8)

yes

—

D₁₉

—

C₂×#41

—

C₂×D₈

—

C₂×M₁₆

C₂×D₁₉

yes

—

C₄⋊Q₈

—

—

—

—

—

C₄×D₄

—

C₄×D₄

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

#106

—

C₄⋊C₈

C₂×D₁₉

yes

—

#102

—

C₁₉

#3253

yes

characteristic, complemented, Sylow

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

100

C₂²×C₄

—

101

C₂²×C₄

D₇₆

yes

—

102

C₂²×C₄

C₂²×D₁₉

yes

characteristic

103

D₈

—

104

M₁₆

—

105

C₂×C₈

C₂²×D₁₉

yes

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₂²⋊C₄

—

109

C₂²⋊C₄

—

110

C₄²

D₇₆

yes

characteristic

111

C₄²

D₇₆

yes

characteristic

112

C₄²

C₂²×D₁₉

yes

—

113

C₂³

—

114

C₂³

C₂×D₇₆

yes

characteristic

115

Q₈

—

116

D₄

—

117

D₄

—

118

D₄

—

119

D₄

—

120

D₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

C₂×D₇₆

yes

characteristic

127

C₂×C₄

C₂×D₇₆

yes

—

128

C₂×C₄

C₂×D₇₆

yes

—

129

C₂×C₄

C₂³×D₁₉

yes

characteristic

130

C₈

—

131

C₂²

—

132

C₂²

—

133

C₂²

—

134

C₂²

—

135

C₂²

—

136

C₂²

C₂²×D₇₆

yes

characteristic

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

#10597354

yes

—

141

C₄

#10597430

yes

characteristic

142

C₄

#10597433

yes

characteristic

143

C₂

—

144

C₂

—

152

—

145

C₂

#11927125

yes

characteristic

146

C₂

C₂×#10597354

yes

—

	subgroup	G/H
center	C₂²	C₂²×D₇₆
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#423	C₂
socle	C₂²×C₁₉	C₂²×D₄
hypercenter	#423	D₁₉
hypocenter	C₁₉	#3253
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

subgroup

G/H

center

C₂²

C₂²×D₇₆

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#423

C₂

socle

C₂²×C₁₉

C₂²×D₄

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

N	H ≅ G/N	type
1. #11927094	C₂	semidirect
2. #11926835	C₂	semidirect
3. #11926797	C₂	semidirect
4. #11926740	C₂	semidirect
5. C₁₉×#423	C₂	semidirect
74. #423	D₁₉	semidirect
93. C₁₉	#3253	semidirect

H ≅ G/N

type

1. #11927094

C₂

semidirect

2. #11926835

C₂

semidirect

3. #11926797

C₂

semidirect

4. #11926740

C₂

semidirect

5. C₁₉×#423

C₂

semidirect

74. #423

D₁₉

semidirect

93. C₁₉

#3253

semidirect

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

subgroup	index
#11927094	2
#11926835	2
#11926797	2
#11926740	2
C₁₉×#423	2
#3253	19

subgroup

index

C₁₉×#423

Subgroups — #14575016

Conjugacy classes of subgroups

Complements

Maximal subgroups