Group #14563759 — subgroups

Subgroups — #14563759

Order 2432.

172 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 89 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×#10597276	C₂	1	1	yes	maximal, characteristic
2	#11926582	C₂	1	1	yes	maximal, characteristic
3	#11926315	C₂	1	2	yes	maximal
4	#11926300	C₂	1	2	yes	maximal
5	C₁₉×#405	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#117	C₂²	1	1	yes	characteristic
9	#10597372	C₂²	1	2	yes	—
10	C₂×#64520	C₂²	1	2	yes	—
11	C₁₉×#97	C₄	1	2	yes	complemented
12	C₄×C₈×C₁₉	C₄	1	2	yes	complemented
13	#10597276	—	2	1	no	—
14	#10597276	—	2	1	no	—
15	#10597275	—	2	1	no	—
16	#10597274	—	2	1	no	—
17	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
18	M₁₆×C₁₉	—	2	1	no	—
19	M₁₆×C₁₉	—	2	1	no	—
20	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
21	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
25	C₂×C₈×C₁₉	Q₈	1	1	yes	characteristic
26	C₂×C₈×C₁₉	Q₈	1	1	yes	characteristic
27	C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₂²⋊C₄×C₁₉	—	2	1	no	—
29	C₄²×C₁₉	C₂×C₄	1	2	yes	—
30	C₂²⋊Dic₁₉	—	2	2	no	—
31	C₄⋊Dic₁₉	—	2	2	no	—
32	C₄×Dic₁₉	—	2	2	no	—
33	#64520	—	2	2	no	—
34	#64520	—	2	2	no	—
35	C₂×C₁₉⋊C₈	—	2	2	no	—
36	C₂³×C₁₉	#41	1	1	yes	characteristic
37	C₂×C₄×C₁₉	—	2	2	no	—
38	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
42	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
43	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
44	C₂×Dic₁₉	—	4	2	no	—
45	C₈×C₁₉	—	2	2	no	—
46	C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
47	C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
48	C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
49	C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
50	C₁₉⋊C₈	—	4	2	no	—
51	#1833	—	19	1	no	maximal, Sylow
52	C₂²×C₁₉	—	4	1	no	—
53	C₂²×C₁₉	#117	1	1	yes	characteristic
54	C₂²×C₁₉	#124	1	1	yes	characteristic
55	C₂²×C₁₉	#125	1	1	yes	characteristic
56	C₄×C₁₉	—	4	2	no	—
57	C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
58	C₄×C₁₉	#117	1	1	yes	characteristic
59	C₄×C₁₉	#124	1	1	yes	characteristic
60	C₄×C₁₉	#125	1	1	yes	characteristic
61	Dic₁₉	—	8	2	no	—
62	C₂×#108	—	19	1	no	—
63	#427	—	19	1	no	—
64	#405	D₁₉	1	1	yes	characteristic
65	#344	—	19	2	no	—
66	H(3,ℤ/4)	—	19	2	no	—
67	C₂×C₁₉	—	2	1	no	—
68	C₂×C₁₉	—	2	1	no	—
69	C₂×C₁₉	—	2	1	no	—
70	C₂×C₁₉	#382	1	1	yes	characteristic
71	C₂×M₁₆	—	19	2	no	—
72	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
73	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
74	#117	—	19	2	no	—
75	#117	C₂×D₁₉	1	1	yes	characteristic
76	#108	—	38	1	no	—
77	#108	—	38	1	no	—
78	#107	—	38	1	no	—
79	#106	—	38	1	no	—
80	#97	Dic₁₉	1	2	yes	complemented
81	C₄×C₈	Dic₁₉	1	2	yes	complemented
82	C₁₉	#1833	1	1	yes	characteristic, complemented, Sylow
83	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
84	M₁₆	—	2	1	no	—
85	M₁₆	—	2	1	no	—
86	M₁₆	—	38	2	no	—
87	M₁₆	—	38	2	no	—
88	C₂×C₈	—	38	2	no	—
89	C₂×C₈	Dic₃₈	1	1	yes	characteristic
90	C₂×C₈	Dic₃₈	1	1	yes	characteristic
91	C₂×C₈	D₇₆	1	1	yes	characteristic
92	C₂×C₈	D₇₆	1	1	yes	characteristic
93	C₂×C₈	C₂×Dic₁₉	1	2	yes	—
94	C₂×C₈	C₂×Dic₁₉	1	1	yes	characteristic
95	C₂×C₈	C₂×Dic₁₉	1	1	yes	characteristic
96	C₄⋊C₄	—	2	1	no	—
97	C₄⋊C₄	—	38	2	no	—
98	C₂²⋊C₄	—	2	1	no	—
99	C₂²⋊C₄	—	38	2	no	—
100	C₄²	—	38	2	no	—
101	C₄²	C₂×Dic₁₉	1	2	yes	—
102	C₂³	#64541	1	1	yes	characteristic
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	76	2	no	—
105	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
106	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
107	C₂×C₄	#64541	1	1	yes	characteristic
108	C₂×C₄	#64541	1	1	yes	characteristic
109	C₂×C₄	#64541	1	1	yes	characteristic
110	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
111	C₈	—	2	2	no	—
112	C₈	—	76	2	no	—
113	C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
114	C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
115	C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
116	C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
117	C₂²	—	4	1	no	—
118	C₂²	#10597316	1	1	yes	characteristic
119	C₂²	#10597321	1	1	yes	characteristic
120	C₂²	#10597372	1	1	yes	characteristic
121	C₄	—	4	2	no	—
122	C₄	—	152	2	no	—
123	C₄	#10597316	1	1	yes	characteristic
124	C₄	#10597321	1	1	yes	characteristic
125	C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
126	C₄	#10597372	1	1	yes	characteristic
127	C₂	—	2	1	no	—
128	C₂	—	2	1	no	—
129	C₂	—	2	1	no	—
130	C₂	#11926410	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597276

C₂

yes

maximal, characteristic

#11926582

C₂

yes

maximal, characteristic

#11926315

C₂

yes

maximal

#11926300

C₂

yes

maximal

C₁₉×#405

C₂

yes

maximal, characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

characteristic

#10597372

C₂²

yes

—

C₂×#64520

C₂²

yes

—

C₁₉×#97

C₄

yes

complemented

C₄×C₈×C₁₉

C₄

yes

—

—

—

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

Q₈

yes

characteristic

C₂×C₈×C₁₉

Q₈

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

#41

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₁₉⋊C₈

—

#1833

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

C₂×C₄⋊C₄

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

C₂×#108

—

#427

—

#405

D₁₉

yes

characteristic

#344

—

H(3,ℤ/4)

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#382

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

characteristic

C₂²×C₈

C₂×D₁₉

yes

characteristic

#117

—

#117

C₂×D₁₉

yes

—

—

—

—

Dic₁₉

yes

complemented

C₄×C₈

Dic₁₉

yes

complemented

C₁₉

#1833

yes

characteristic, complemented, Sylow

C₂²×C₄

C₂²×D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

Dic₃₈

yes

characteristic

C₂×C₈

Dic₃₈

yes

characteristic

C₂×C₈

D₇₆

yes

characteristic

C₂×C₈

D₇₆

yes

characteristic

C₂×C₈

C₂×Dic₁₉

yes

—

C₂×C₈

C₂×Dic₁₉

yes

characteristic

C₂×C₈

C₂×Dic₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

100

C₄²

—

101

C₄²

C₂×Dic₁₉

yes

—

102

C₂³

#64541

yes

characteristic

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

C₂×Dic₃₈

yes

characteristic

106

C₂×C₄

C₂×D₇₆

yes

characteristic

107

C₂×C₄

#64541

yes

characteristic

108

C₂×C₄

#64541

yes

characteristic

109

C₂×C₄

#64541

yes

characteristic

110

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

111

C₈

—

112

C₈

—

113

C₈

C₄⋊Dic₁₉

yes

characteristic

114

C₈

C₄⋊Dic₁₉

yes

characteristic

115

C₈

C₄⋊Dic₁₉

yes

characteristic

116

C₈

C₄⋊Dic₁₉

yes

characteristic

117

C₂²

—

118

C₂²

#10597316

yes

characteristic

119

C₂²

#10597321

yes

characteristic

120

C₂²

#10597372

yes

characteristic

121

C₄

—

122

C₄

—

152

—

123

C₄

#10597316

yes

characteristic

124

C₄

#10597321

yes

characteristic

125

C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

126

C₄

#10597372

yes

characteristic

127

C₂

—

128

C₂

—

129

C₂

—

130

C₂

#11926410

yes

characteristic

	subgroup	G/H
center	C₄	#10597372
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#405	C₂
socle	C₂×C₁₉	#382
prime radical	C₂³×C₁₉	#41
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#405	D₁₉
hypocenter	C₁₉	#1833
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ #117 ◁ #405

subgroup

G/H

center

C₄

#10597372

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#405

C₂

C₂×C₁₉

C₂³×C₁₉

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄ ◁ #117 ◁ #405

N	H ≅ G/N	type
11. C₁₉×#97	C₄	semidirect
12. C₄×C₈×C₁₉	C₄	semidirect
80. #97	Dic₁₉	semidirect
81. C₄×C₈	Dic₁₉	semidirect
82. C₁₉	#1833	semidirect

H ≅ G/N

type

11. C₁₉×#97

C₄

semidirect

12. C₄×C₈×C₁₉

C₄

semidirect

80. #97

Dic₁₉

semidirect

81. C₄×C₈

Dic₁₉

semidirect

82. C₁₉

#1833

semidirect

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

subgroup	index
C₂×#10597276	2
#11926582	2
#11926315	2
#11926300	2
C₁₉×#405	2
#1833	19

subgroup

index

C₁₉×#405

Subgroups — #14563759

Conjugacy classes of subgroups

Complements

Maximal subgroups