Group #14575074 — subgroups

Subgroups — #14575074

Order 2432.

370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 117 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	#11927149	C₂	1	2	yes	maximal, complemented
2	#11926845	C₂	1	4	yes	maximal, complemented
3	#11926797	C₂	1	2	yes	maximal, complemented
4	#11926780	C₂	1	2	yes	maximal, complemented
5	#11926740	C₂	1	4	yes	maximal, complemented
6	C₁₉×#424	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#117	C₂²	1	1	yes	characteristic
10	#10597376	C₂²	1	4	yes	—
11	C₂×D₁₅₂	C₂²	1	2	yes	—
12	C₂×D₁₅₂	C₂²	1	2	yes	—
13	#10597340	—	2	4	no	—
14	#10597330	—	2	4	no	—
15	#10597320	C₂²	1	2	yes	—
16	C₄×D₇₆	C₂²	1	4	yes	—
17	#10597316	C₂²	1	2	yes	—
18	C₁₉×C₄⋊C₈	C₂²	1	4	yes	—
19	#10597278	C₂²	1	4	yes	—
20	#10597278	C₂²	1	4	yes	—
21	#10597275	C₂²	1	2	yes	—
22	#10597274	C₂²	1	2	yes	—
23	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₂×C₂²⋊D₁₉	—	2	4	no	—
25	C₂×D₇₆	—	2	4	no	—
26	C₂×D₇₆	C₂³	1	4	yes	—
27	C₂×C₄×D₁₉	—	2	4	no	—
28	M₁₆×C₁₉	—	4	1	no	—
29	C₂×C₈×C₁₉	—	4	1	no	—
30	C₂×C₈×C₁₉	C₂³	1	2	yes	—
31	C₂×C₈×C₁₉	C₂³	1	2	yes	—
32	C₄⋊C₄×C₁₉	D₄	1	2	yes	—
33	C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
34	C₄²×C₁₉	C₂³	1	2	yes	—
35	(C₂×D₁₉)⋊C₄	—	2	4	no	—
36	(C₂×D₁₉)⋊C₄	—	2	4	no	—
37	C₄⋊Dic₁₉	C₂³	1	4	yes	—
38	Dic₁₉⋊C₄	—	2	4	no	—
39	D₁₅₂	—	4	2	no	—
40	D₁₅₂	—	4	2	no	—
41	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂²×D₁₉	—	2	4	no	—
43	C₂×C₄×C₁₉	—	2	1	no	—
44	C₂×C₄×C₁₉	—	2	1	no	—
45	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
46	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
48	C₂²⋊D₁₉	—	8	4	no	—
49	C₂×Dic₁₉	—	2	4	no	—
50	D₇₆	—	2	4	no	—
51	D₇₆	—	2	4	no	—
52	D₇₆	—	8	4	no	—
53	C₄×D₁₉	—	8	4	no	—
54	C₈×C₁₉	—	2	2	no	—
55	C₈×C₁₉	—	2	2	no	—
56	#3259	—	19	1	no	maximal, Sylow
57	C₂²×C₁₉	—	2	1	no	—
58	C₂²×C₁₉	—	2	2	no	—
59	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
60	C₂×D₁₉	—	4	4	no	—
61	C₂×D₁₉	—	4	4	no	—
62	C₂×D₁₉	—	4	4	no	—
63	C₄×C₁₉	—	2	1	no	—
64	C₄×C₁₉	—	2	4	no	—
65	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
66	C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
67	Dic₁₉	—	4	4	no	—
68	#540	—	19	2	no	—
69	#478	—	19	4	no	—
70	#469	—	19	2	no	—
71	#466	—	19	2	no	—
72	#459	—	19	4	no	—
73	#424	D₁₉	1	1	yes	characteristic, complemented
74	C₂×C₁₉	—	4	1	no	—
75	C₂×C₁₉	#537	1	1	yes	characteristic
76	C₂×C₁₉	#576	1	2	yes	—
77	D₁₉	—	8	4	no	—
78	C₂×D₈	—	19	2	no	—
79	C₂×D₈	—	19	2	no	—
80	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
81	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
82	#127	—	19	2	no	—
83	#125	—	19	2	no	—
84	#123	—	38	4	no	—
85	#121	—	19	4	no	—
86	#121	—	38	4	no	—
87	C₄×D₄	—	19	4	no	—
88	#117	C₂×D₁₉	1	1	yes	characteristic
89	#107	—	19	2	no	—
90	#106	—	19	2	no	—
91	C₄⋊C₈	C₂×D₁₉	1	4	yes	—
92	#102	—	19	4	no	—
93	#102	—	19	4	no	—
94	C₁₉	#3259	1	1	yes	characteristic, complemented, Sylow
95	C₂×D₄	—	19	4	no	—
96	C₂×D₄	—	38	4	no	—
97	C₂×D₄	—	38	4	no	—
98	C₂²×C₄	—	38	4	no	—
99	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
100	D₈	—	76	2	no	—
101	D₈	—	76	2	no	—
102	M₁₆	—	4	1	no	—
103	C₂×C₈	—	4	1	no	—
104	C₂×C₈	C₂²×D₁₉	1	2	yes	—
105	C₂×C₈	C₂²×D₁₉	1	2	yes	—
106	C₄⋊C₄	—	19	4	no	—
107	C₄⋊C₄	—	38	4	no	—
108	C₄⋊C₄	D₇₆	1	2	yes	—
109	C₂²⋊C₄	—	38	4	no	—
110	C₂²⋊C₄	—	38	4	no	—
111	C₂²⋊C₄	D₇₆	1	2	yes	—
112	C₄²	C₂²×D₁₉	1	2	yes	—
113	C₂³	—	38	4	no	—
114	C₂³	C₂×D₇₆	1	1	yes	characteristic
115	D₄	—	38	4	no	—
116	D₄	—	38	4	no	—
117	D₄	—	152	4	no	—
118	D₄	—	152	4	no	—
119	C₂×C₄	—	2	1	no	—
120	C₂×C₄	—	2	1	no	—
121	C₂×C₄	—	38	4	no	—
122	C₂×C₄	—	152	4	no	—
123	C₂×C₄	C₂×D₇₆	1	4	yes	—
124	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
125	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
126	C₈	—	2	2	no	—
127	C₈	—	2	2	no	—
128	C₂²	—	2	2	no	—
129	C₂²	—	2	1	no	—
130	C₂²	—	76	4	no	—
131	C₂²	—	76	4	no	—
132	C₂²	—	76	4	no	—
133	C₂²	C₂²×D₇₆	1	1	yes	characteristic
134	C₄	—	2	4	no	—
135	C₄	—	2	1	no	—
136	C₄	—	76	4	no	—
137	C₄	#10597430	1	1	yes	characteristic
138	C₄	#10597433	1	1	yes	characteristic
139	C₂	—	4	1	no	—
140	C₂	—	152	4	no	—
141	C₂	#11927125	1	1	yes	characteristic
142	C₂	#11927349	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11927149

C₂

yes

maximal, complemented

#11926845

C₂

yes

maximal, complemented

#11926797

C₂

yes

maximal, complemented

#11926780

C₂

yes

maximal, complemented

#11926740

C₂

yes

maximal, complemented

C₁₉×#424

C₂

yes

maximal, characteristic, complemented

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

characteristic

#10597376

C₂²

yes

—

C₂×D₁₅₂

C₂²

yes

—

C₂×D₁₅₂

C₂²

yes

—

#10597340

—

#10597330

—

#10597320

C₂²

yes

—

C₄×D₇₆

C₂²

yes

—

#10597316

C₂²

yes

—

C₁₉×C₄⋊C₈

C₂²

yes

—

#10597278

C₂²

yes

—

#10597278

C₂²

yes

—

#10597275

C₂²

yes

—

#10597274

C₂²

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂×D₇₆

—

C₂×D₇₆

C₂³

yes

—

C₂×C₄×D₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

—

C₂×C₈×C₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

D₄

yes

—

C₂²⋊C₄×C₁₉

D₄

yes

—

C₄²×C₁₉

C₂³

yes

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

D₁₅₂

—

D₁₅₂

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

#3259

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

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

#576

yes

—

D₁₉

—

C₂×D₈

—

C₂×D₈

—

C₂×M₁₆

C₂×D₁₉

yes

characteristic

C₂²×C₈

C₂×D₁₉

yes

—

—

—

—

—

C₄×D₄

—

#117

C₂×D₁₉

yes

characteristic

#107

—

#106

—

C₄⋊C₈

C₂×D₁₉

yes

—

#102

—

#102

—

C₁₉

#3259

yes

characteristic, complemented, Sylow

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

100

D₈

—

101

D₈

—

102

M₁₆

—

103

C₂×C₈

—

104

C₂×C₈

C₂²×D₁₉

yes

—

105

C₂×C₈

C₂²×D₁₉

yes

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

D₇₆

yes

—

109

C₂²⋊C₄

—

110

C₂²⋊C₄

—

111

C₂²⋊C₄

D₇₆

yes

—

112

C₄²

C₂²×D₁₉

yes

—

113

C₂³

—

114

C₂³

C₂×D₇₆

yes

characteristic

115

D₄

—

116

D₄

—

117

D₄

—

152

—

118

D₄

—

152

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

152

—

123

C₂×C₄

C₂×D₇₆

yes

—

124

C₂×C₄

C₂×D₇₆

yes

characteristic

125

C₂×C₄

C₂³×D₁₉

yes

characteristic

126

C₈

—

127

C₈

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

C₂²×D₇₆

yes

characteristic

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

#10597430

yes

characteristic

138

C₄

#10597433

yes

characteristic

139

C₂

—

140

C₂

—

152

—

141

C₂

#11927125

yes

characteristic

142

C₂

#11927349

yes

—

	subgroup	G/H
center	C₂²	C₂²×D₇₆
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#424	C₂
socle	C₂²×C₁₉	C₂²×D₄
hypercenter	#424	D₁₉
hypocenter	C₁₉	#3259
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #117 ◁ #424

subgroup

G/H

center

C₂²

C₂²×D₇₆

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#424

C₂

socle

C₂²×C₁₉

C₂²×D₄

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ #117 ◁ #424

N	H ≅ G/N	type
1. #11927149	C₂	semidirect
2. #11926845	C₂	semidirect
3. #11926797	C₂	semidirect
4. #11926780	C₂	semidirect
5. #11926740	C₂	semidirect
6. C₁₉×#424	C₂	semidirect
73. #424	D₁₉	semidirect
94. C₁₉	#3259	semidirect

H ≅ G/N

type

1. #11927149

C₂

semidirect

2. #11926845

C₂

semidirect

3. #11926797

C₂

semidirect

4. #11926780

C₂

semidirect

5. #11926740

C₂

semidirect

6. C₁₉×#424

C₂

semidirect

73. #424

D₁₉

semidirect

94. C₁₉

#3259

semidirect

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

subgroup	index
#11927149	2
#11926845	2
#11926797	2
#11926780	2
#11926740	2
C₁₉×#424	2
#3259	19

subgroup

index

C₁₉×#424

Subgroups — #14575074

Conjugacy classes of subgroups

Complements

Maximal subgroups