Group #14564476 — subgroups

Subgroups — #14564476

Order 2432.

396 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 105 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	#11926568	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597290	C₂	1	4	yes	maximal, complemented
3	C₄×#64520	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#127	C₂	1	1	yes	maximal, characteristic
5	C₂²×D₄×C₁₉	C₄	1	4	yes	—
6	C₂²×D₄×C₁₉	C₂²	1	2	yes	—
7	C₁₉×#127	—	2	1	no	—
8	C₁₉×#127	—	2	1	no	—
9	C₁₉×#127	—	2	2	no	—
10	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×#64520	C₂²	1	2	yes	—
12	C₂×#64520	C₂²	1	2	yes	—
13	#10597290	—	2	8	no	—
14	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
15	#10597260	—	2	1	no	—
16	C₄×C₁₉⋊C₈	—	2	1	no	—
17	C₂⁴×C₁₉	C₂×C₄	1	4	yes	—
18	C₂×D₄×C₁₉	—	2	4	no	—
19	C₂×D₄×C₁₉	—	2	4	no	—
20	C₂×D₄×C₁₉	—	2	2	no	—
21	C₂×D₄×C₁₉	—	2	2	no	—
22	C₂×D₄×C₁₉	—	2	4	no	—
23	C₂×D₄×C₁₉	—	2	4	no	—
24	C₂×D₄×C₁₉	—	4	8	no	—
25	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
26	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
27	C₄²×C₁₉	D₄	1	1	yes	characteristic
28	C₄²×C₁₉	D₄	1	1	yes	characteristic
29	C₄²×C₁₉	D₄	1	2	yes	—
30	#64520	—	2	2	no	—
31	#64520	—	2	4	no	—
32	#64520	D₄	1	4	yes	complemented
33	C₂×C₁₉⋊C₈	—	2	2	no	—
34	C₂×C₁₉⋊C₈	—	2	2	no	—
35	C₂³×C₁₉	—	2	4	no	—
36	C₂³×C₁₉	—	2	8	no	—
37	C₂³×C₁₉	—	4	8	no	—
38	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
39	D₄×C₁₉	—	4	8	no	—
40	D₄×C₁₉	—	4	8	no	—
41	D₄×C₁₉	—	4	4	no	—
42	D₄×C₁₉	—	4	2	no	—
43	D₄×C₁₉	—	4	2	no	—
44	C₂×C₄×C₁₉	—	2	4	no	—
45	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
46	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
47	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
48	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₁₉	#41	1	2	yes	—
51	C₁₉⋊C₈	—	2	4	no	—
52	C₁₉⋊C₈	—	4	2	no	—
53	#1965	—	19	1	no	maximal, Sylow
54	C₂²×C₁₉	—	2	2	no	—
55	C₂²×C₁₉	—	4	4	no	—
56	C₂²×C₁₉	—	4	8	no	—
57	C₂²×C₁₉	—	8	8	no	—
58	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
59	C₂²×C₁₉	C₄×D₄	1	2	yes	—
60	C₄×C₁₉	—	2	2	no	—
61	C₄×C₁₉	#100	1	4	yes	complemented
62	C₄×C₁₉	#121	1	2	yes	—
63	C₄×C₁₉	#124	1	1	yes	characteristic
64	C₄×C₁₉	#127	1	1	yes	characteristic
65	C₂×#127	D₁₉	1	1	yes	characteristic
66	#423	—	19	1	no	—
67	C₂×#100	—	19	4	no	—
68	C₄×M₁₆	—	19	1	no	—
69	C₂×C₁₉	—	2	2	no	—
70	C₂×C₁₉	—	8	4	no	—
71	C₂×C₁₉	#390	1	1	yes	characteristic
72	C₂×C₁₉	C₂×#100	1	2	yes	—
73	C₂²×D₄	Dic₁₉	1	4	yes	—
74	C₂²×D₄	C₂×D₁₉	1	2	yes	—
75	C₂×M₁₆	—	19	2	no	—
76	C₂×M₁₆	—	19	2	no	—
77	#127	—	2	1	no	—
78	#127	—	2	1	no	—
79	#127	—	2	2	no	—
80	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
81	C₄⋊C₈	—	38	2	no	—
82	#100	—	38	8	no	—
83	#97	—	38	1	no	—
84	C₄×C₈	—	38	1	no	—
85	C₁₉	#1965	1	1	yes	characteristic, complemented, Sylow
86	C₂⁴	C₂×Dic₁₉	1	4	yes	—
87	C₂×D₄	—	2	4	no	—
88	C₂×D₄	—	2	4	no	—
89	C₂×D₄	—	2	4	no	—
90	C₂×D₄	—	2	4	no	—
91	C₂×D₄	—	2	2	no	—
92	C₂×D₄	—	2	2	no	—
93	C₂×D₄	—	4	8	no	—
94	C₂²×C₄	C₂×Dic₁₉	1	2	yes	—
95	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
96	M₁₆	—	19	4	no	—
97	M₁₆	—	38	2	no	—
98	M₁₆	—	38	4	no	—
99	C₂×C₈	—	38	2	no	—
100	C₂×C₈	—	38	2	no	—
101	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
102	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
103	C₄²	C₂²⋊D₁₉	1	2	yes	—
104	C₂³	—	2	4	no	—
105	C₂³	—	2	8	no	—
106	C₂³	—	4	8	no	—
107	C₂³	C₂²×Dic₁₉	1	1	yes	characteristic
108	D₄	—	4	8	no	—
109	D₄	—	4	2	no	—
110	D₄	—	4	4	no	—
111	D₄	—	4	2	no	—
112	D₄	—	4	8	no	—
113	C₂×C₄	—	2	4	no	—
114	C₂×C₄	C₂²⋊Dic₁₉	1	2	yes	—
115	C₂×C₄	C₂²⋊Dic₁₉	1	2	yes	—
116	C₂×C₄	D₄×D₁₉	1	2	yes	—
117	C₂×C₄	#64543	1	2	yes	—
118	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
119	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
120	C₈	—	38	4	no	—
121	C₈	—	76	2	no	—
122	C₂²	—	2	2	no	—
123	C₂²	—	4	4	no	—
124	C₂²	—	4	8	no	—
125	C₂²	—	8	8	no	—
126	C₂²	D₄×Dic₁₉	1	2	yes	—
127	C₂²	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
128	C₄	—	2	2	no	—
129	C₄	#10597290	1	4	yes	complemented
130	C₄	#10597382	1	1	yes	characteristic
131	C₄	#10597384	1	2	yes	—
132	C₄	#10597386	1	1	yes	characteristic
133	C₂	—	2	2	no	—
134	C₂	—	8	4	no	—
135	C₂	#11926447	1	1	yes	characteristic
136	C₂	C₂×#10597290	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11926568

C₂

yes

maximal, characteristic, complemented

C₂×#10597290

C₂

yes

maximal, complemented

C₄×#64520

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#127

C₂

yes

maximal, characteristic

C₂²×D₄×C₁₉

C₄

yes

—

C₂²×D₄×C₁₉

C₂²

yes

—

C₁₉×#127

—

C₁₉×#127

—

C₁₉×#127

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

—

C₂×#64520

C₂²

yes

—

#10597290

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₂⁴×C₁₉

C₂×C₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

—

#64520

—

#64520

—

#64520

D₄

yes

complemented

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1965

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

C₄×D₄

yes

—

C₄×C₁₉

—

C₄×C₁₉

#100

yes

complemented

C₄×C₁₉

#121

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

D₁₉

yes

characteristic

#423

—

C₂×#100

—

C₄×M₁₆

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#390

yes

characteristic

C₂×C₁₉

C₂×#100

yes

—

C₂²×D₄

Dic₁₉

yes

—

C₂²×D₄

C₂×D₁₉

yes

—

C₂×M₁₆

—

C₂×M₁₆

—

#127

—

#127

—

#127

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

#100

—

#97

—

C₄×C₈

—

C₁₉

#1965

yes

characteristic, complemented, Sylow

C₂⁴

C₂×Dic₁₉

yes

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

C₂×Dic₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

100

C₂×C₈

—

101

C₄²

C₂²⋊D₁₉

yes

characteristic

102

C₄²

C₂²⋊D₁₉

yes

characteristic

103

C₄²

C₂²⋊D₁₉

yes

—

104

C₂³

—

105

C₂³

—

106

C₂³

—

107

C₂³

C₂²×Dic₁₉

yes

characteristic

108

D₄

—

109

D₄

—

110

D₄

—

111

D₄

—

112

D₄

—

113

C₂×C₄

—

114

C₂×C₄

C₂²⋊Dic₁₉

yes

—

115

C₂×C₄

C₂²⋊Dic₁₉

yes

—

116

C₂×C₄

D₄×D₁₉

yes

—

117

C₂×C₄

#64543

yes

—

118

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

119

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

120

C₈

—

121

C₈

—

122

C₂²

—

123

C₂²

—

124

C₂²

—

125

C₂²

—

126

C₂²

D₄×Dic₁₉

yes

—

127

C₂²

C₂×C₂²⋊Dic₁₉

yes

characteristic

128

C₄

—

129

C₄

#10597290

yes

complemented

130

C₄

#10597382

yes

characteristic

131

C₄

#10597384

yes

—

132

C₄

#10597386

yes

characteristic

133

C₂

—

134

C₂

—

135

C₂

#11926447

yes

characteristic

136

C₂

C₂×#10597290

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊Dic₁₉
commutator	C₂³×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting, prime radical	C₂×C₁₉×#127	C₂
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#127	D₁₉
hypocenter	C₁₉	#1965
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#127

subgroup

G/H

center

C₂²

C₂×C₂²⋊Dic₁₉

commutator

C₂³×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting, prime radical

C₂×C₁₉×#127

C₂

socle

C₂²×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#127

N	H ≅ G/N	type
1. #11926568	C₂	semidirect
2. C₂×#10597290	C₂	semidirect
3. C₄×#64520	C₂	semidirect
32. #64520	D₄	semidirect
61. C₄×C₁₉	#100	semidirect
85. C₁₉	#1965	semidirect
129. C₄	#10597290	semidirect

H ≅ G/N

type

1. #11926568

C₂

semidirect

2. C₂×#10597290

C₂

semidirect

3. C₄×#64520

C₂

semidirect

32. #64520

D₄

semidirect

61. C₄×C₁₉

#100

semidirect

85. C₁₉

#1965

semidirect

129. C₄

#10597290

semidirect

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

subgroup	index
#11926568	2
C₂×#10597290	2
C₄×#64520	2
C₂×C₁₉×#127	2
#1965	19

subgroup

index

C₂×C₁₉×#127

Subgroups — #14564476

Conjugacy classes of subgroups

Complements

Maximal subgroups