Group #14564458 — subgroups

Subgroups — #14564458

Order 2432.

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

normal subgroups only

This group has 412 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	C₂×#10597320	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597266	C₂	1	4	yes	maximal, complemented
3	C₂×#10597260	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#382	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₇₆	—	2	2	no	—
6	C₂²×D₇₆	C₂²	1	2	yes	—
7	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
8	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
10	#10597320	—	2	2	no	—
11	#10597320	C₄	1	4	yes	complemented
12	C₁₉×#95	—	2	2	no	—
13	#10597266	—	2	8	no	—
14	#10597260	—	2	2	no	—
15	C₂³×D₁₉	—	2	2	no	—
16	C₂²×C₄×C₁₉	—	2	2	no	—
17	C₂²×C₄×C₁₉	D₄	1	2	yes	—
18	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
19	C₂×D₇₆	—	2	4	no	—
20	C₂×D₇₆	—	2	4	no	—
21	C₂×D₇₆	—	2	8	no	—
22	C₂×D₇₆	—	2	2	no	—
23	C₂×D₇₆	—	4	8	no	—
24	C₂×D₇₆	C₂×C₄	1	4	yes	—
25	C₄⋊C₄×C₁₉	—	2	4	no	—
26	C₄²×C₁₉	C₂×C₄	1	2	yes	—
27	C₄²×C₁₉	D₄	1	2	yes	—
28	C₂×C₁₉⋊C₈	—	2	2	no	—
29	C₂×C₁₉⋊C₈	—	2	2	no	—
30	C₂×C₁₉⋊C₈	D₄	1	4	yes	complemented
31	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
32	C₂²×D₁₉	—	2	4	no	—
33	C₂²×D₁₉	—	4	2	no	—
34	C₂²×D₁₉	—	4	2	no	—
35	C₂²×D₁₉	—	4	8	no	—
36	C₂×C₄×C₁₉	—	2	4	no	—
37	C₂×C₄×C₁₉	—	4	2	no	—
38	C₂×C₄×C₁₉	—	4	4	no	—
39	C₂×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
40	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
43	C₂×C₄×C₁₉	#41	1	2	yes	—
44	D₇₆	—	2	8	no	—
45	D₇₆	—	4	16	no	—
46	D₇₆	—	4	4	no	—
47	C₁₉⋊C₈	—	2	4	no	—
48	#1961	—	19	1	no	maximal, Sylow
49	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
50	C₂²×C₁₉	#124	1	1	yes	characteristic
51	C₂²×C₁₉	#127	1	1	yes	characteristic
52	C₂²×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
53	C₂×D₁₉	—	4	4	no	—
54	C₂×D₁₉	—	4	8	no	—
55	C₂×D₁₉	—	8	4	no	—
56	C₂×D₁₉	—	8	4	no	—
57	C₄×C₁₉	—	2	4	no	—
58	C₄×C₁₉	—	8	2	no	—
59	C₄×C₁₉	C₄×D₄	1	2	yes	—
60	C₄×C₁₉	#121	1	2	yes	—
61	C₂×#127	—	19	1	no	—
62	C₂×#102	—	19	4	no	—
63	C₂×#97	—	19	1	no	—
64	#382	D₁₉	1	1	yes	characteristic, complemented
65	C₂×C₁₉	#390	1	1	yes	characteristic
66	C₂×C₁₉	#418	1	2	yes	—
67	C₂×C₁₉	#490	1	2	yes	—
68	C₂×C₁₉	#496	1	2	yes	—
69	D₁₉	—	8	4	no	—
70	C₂²×D₄	—	19	2	no	—
71	C₂²×D₄	—	38	2	no	—
72	C₂²×C₈	—	19	2	no	—
73	#127	—	19	4	no	—
74	#127	—	38	2	no	—
75	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
76	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
77	#102	—	38	8	no	—
78	#97	—	38	2	no	—
79	#95	—	2	2	no	—
80	C₁₉	#1961	1	1	yes	characteristic, complemented, Sylow
81	C₂⁴	—	38	2	no	—
82	C₂×D₄	—	19	4	no	—
83	C₂×D₄	—	38	8	no	—
84	C₂×D₄	—	38	2	no	—
85	C₂×D₄	—	38	4	no	—
86	C₂×D₄	—	38	4	no	—
87	C₂×D₄	—	76	8	no	—
88	C₂²×C₄	—	2	2	no	—
89	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
90	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
91	C₂×C₈	—	19	4	no	—
92	C₂×C₈	—	38	2	no	—
93	C₂×C₈	—	38	2	no	—
94	C₄⋊C₄	—	2	4	no	—
95	C₄²	C₄×D₁₉	1	2	yes	—
96	C₄²	D₇₆	1	2	yes	—
97	C₂³	—	38	4	no	—
98	C₂³	—	76	2	no	—
99	C₂³	—	76	2	no	—
100	C₂³	—	76	8	no	—
101	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
102	D₄	—	38	8	no	—
103	D₄	—	76	16	no	—
104	D₄	—	76	4	no	—
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	—	4	2	no	—
107	C₂×C₄	—	4	4	no	—
108	C₂×C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
109	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
110	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
111	C₂×C₄	D₄×D₁₉	1	2	yes	—
112	C₂×C₄	#64545	1	2	yes	—
113	C₈	—	38	4	no	—
114	C₂²	—	76	8	no	—
115	C₂²	—	76	4	no	—
116	C₂²	—	152	4	no	—
117	C₂²	—	152	4	no	—
118	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
119	C₂²	#10597386	1	1	yes	characteristic
120	C₂²	#10597393	1	1	yes	characteristic
121	C₂²	#10597395	1	4	yes	—
122	C₄	—	2	4	no	—
123	C₄	—	8	2	no	—
124	C₄	#10597339	1	2	yes	—
125	C₄	#10597341	1	2	yes	—
126	C₂	—	152	4	no	—
127	C₂	#11926445	1	1	yes	characteristic
128	C₂	#11926548	1	2	yes	—
129	C₂	#11926910	1	2	yes	—
130	C₂	#11926934	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597320

C₂

yes

maximal, characteristic

C₂×#10597266

C₂

yes

maximal, complemented

C₂×#10597260

C₂

yes

maximal, characteristic, complemented

C₁₉×#382

C₂

yes

maximal, characteristic, complemented

C₂²×D₇₆

—

C₂²×D₇₆

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

—

#10597320

—

#10597320

C₄

yes

complemented

C₁₉×#95

—

#10597266

—

#10597260

—

C₂³×D₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

C₂×C₄

yes

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

D₄

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

complemented

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

—

D₇₆

—

D₇₆

—

D₇₆

—

C₁₉⋊C₈

—

#1961

—

maximal, Sylow

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×D₄

yes

—

C₄×C₁₉

#121

yes

—

C₂×#127

—

C₂×#102

—

C₂×#97

—

#382

D₁₉

yes

characteristic, complemented

C₂×C₁₉

#390

yes

characteristic

C₂×C₁₉

#418

yes

—

C₂×C₁₉

#490

yes

—

C₂×C₁₉

#496

yes

—

D₁₉

—

C₂²×D₄

—

C₂²×D₄

—

C₂²×C₈

—

#127

—

#127

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

C₂×D₁₉

yes

—

—

—

C₁₉

#1961

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄²

C₄×D₁₉

yes

—

C₄²

D₇₆

yes

—

C₂³

—

C₂³

—

C₂³

—

100

C₂³

—

101

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

102

D₄

—

103

D₄

—

104

D₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

—

109

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

110

C₂×C₄

C₂×D₇₆

yes

characteristic

111

C₂×C₄

D₄×D₁₉

yes

—

112

C₂×C₄

#64545

yes

—

113

C₈

—

114

C₂²

—

115

C₂²

—

116

C₂²

—

152

—

117

C₂²

—

152

—

118

C₂²

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

119

C₂²

#10597386

yes

characteristic

120

C₂²

#10597393

yes

characteristic

121

C₂²

#10597395

yes

—

122

C₄

—

123

C₄

—

124

C₄

#10597339

yes

—

125

C₄

#10597341

yes

—

126

C₂

—

152

—

127

C₂

#11926445

yes

characteristic

128

C₂

#11926548

yes

—

129

C₂

#11926910

yes

—

130

C₂

#11926934

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#382	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂×#10597320	C₂
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#382	D₁₉
hypocenter	C₁₉	#1961
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #382

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#382

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂×#10597320

C₂

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #382

N	H ≅ G/N	type
2. C₂×#10597266	C₂	semidirect
3. C₂×#10597260	C₂	semidirect
4. C₁₉×#382	C₂	semidirect
11. #10597320	C₄	semidirect
30. C₂×C₁₉⋊C₈	D₄	semidirect
64. #382	D₁₉	semidirect
80. C₁₉	#1961	semidirect

H ≅ G/N

type

2. C₂×#10597266

C₂

semidirect

3. C₂×#10597260

C₂

semidirect

4. C₁₉×#382

C₂

semidirect

11. #10597320

C₄

semidirect

30. C₂×C₁₉⋊C₈

D₄

semidirect

64. #382

D₁₉

semidirect

80. C₁₉

#1961

semidirect

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

subgroup	index
C₂×#10597320	2
C₂×#10597266	2
C₂×#10597260	2
C₁₉×#382	2
#1961	19

subgroup

index

C₁₉×#382

Subgroups — #14564458

Conjugacy classes of subgroups

Complements

Maximal subgroups