Group #14572098 — subgroups

Subgroups — #14572098

Order 2432.

716 conjugacy classes of subgroups; only the 249 normal subgroups are shown.

normal subgroups only

This group has 716 conjugacy classes of subgroups — too many to draw. Only its 249 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×#10597433	C₂	1	1	yes	maximal, characteristic
2	#11927022	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926517	C₂	1	12	yes	maximal, complemented
4	C₁₉×#519	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
6	#10597433	—	2	4	no	—
7	#10597433	—	2	4	no	—
8	C₂×#64545	C₄	1	4	yes	complemented
9	C₂×Q₈×D₁₉	C₄	1	4	yes	complemented
10	C₂×#64541	C₂²	1	6	yes	—
11	C₄×Q₈×C₁₉	—	2	4	no	—
12	C₁₉×#117	C₂²	1	6	yes	—
13	Q₈×Dic₁₉	—	2	4	no	—
14	#10597372	C₂²	1	6	yes	—
15	#10597263	C₂²	1	16	yes	—
16	C₂×Q₈×C₁₉	C₂×C₄	1	4	yes	—
17	C₂×Q₈×C₁₉	D₄	1	4	yes	—
18	C₂×Q₈×C₁₉	D₄	1	4	yes	—
19	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
20	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
21	#64545	—	2	16	no	—
22	Q₈×D₁₉	—	2	16	no	—
23	#64541	—	2	12	no	—
24	#64541	—	2	12	no	—
25	C₂×D₇₆	C₂×C₄	1	6	yes	—
26	C₂×C₄×D₁₉	C₂×C₄	1	12	yes	—
27	C₂×Dic₃₈	C₂×C₄	1	6	yes	—
28	C₄⋊C₄×C₁₉	—	2	6	no	—
29	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
30	C₄²×C₁₉	—	2	6	no	—
31	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
32	C₄⋊Dic₁₉	—	2	6	no	—
33	C₄×Dic₁₉	—	2	6	no	—
34	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
35	C₂²×D₁₉	C₂²×C₄	1	4	yes	—
36	Q₈×C₁₉	C₂²⋊C₄	1	16	yes	—
37	C₂×C₄×C₁₉	—	2	4	no	—
38	C₂×C₄×C₁₉	C₂²×C₄	1	6	yes	—
39	C₂×C₄×C₁₉	C₂×D₄	1	6	yes	—
40	C₂×C₄×C₁₉	C₂×D₄	1	6	yes	—
41	C₂²⋊D₁₉	—	2	4	no	—
42	C₂²⋊D₁₉	—	2	4	no	—
43	C₂×Dic₁₉	—	2	4	no	—
44	C₂×Dic₁₉	C₂²×C₄	1	4	yes	—
45	D₇₆	—	2	12	no	—
46	C₄×D₁₉	—	2	24	no	—
47	Dic₃₈	—	2	12	no	—
48	#2884	—	19	1	no	maximal, Sylow
49	C₂²×C₁₉	—	4	1	no	—
50	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
51	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
52	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
53	C₂×D₁₉	—	2	4	no	—
54	C₂×D₁₉	—	4	4	no	—
55	C₄×C₁₉	—	4	4	no	—
56	C₄×C₁₉	C₂×C₂²⋊C₄	1	12	yes	—
57	Dic₁₉	—	2	4	no	—
58	Dic₁₉	—	4	4	no	—
59	C₂×2₋¹⁺⁴	—	19	1	no	—
60	#519	—	19	1	no	—
61	#519	D₁₉	1	1	yes	characteristic, complemented
62	#410	—	19	12	no	—
63	C₂×C₁₉	—	2	1	no	—
64	C₂×C₁₉	—	2	1	no	—
65	C₂×C₁₉	—	2	1	no	—
66	C₂×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
67	D₁₉	—	4	4	no	—
68	2₋¹⁺⁴	—	38	4	no	—
69	2₋¹⁺⁴	—	38	4	no	—
70	C₂×#41	—	19	4	no	—
71	C₂×#41	—	19	6	no	—
72	C₂²×Q₈	—	19	4	no	—
73	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
74	C₄×Q₈	—	2	4	no	—
75	C₄×Q₈	—	38	4	no	—
76	#117	—	19	6	no	—
77	#117	C₂×D₁₉	1	6	yes	—
78	#99	—	19	16	no	—
79	C₁₉	#2884	1	1	yes	characteristic, complemented, Sylow
80	#41	—	38	16	no	—
81	#41	—	38	12	no	—
82	#41	—	38	12	no	—
83	C₂×Q₈	—	19	6	no	—
84	C₂×Q₈	—	38	16	no	—
85	C₂×Q₈	C₄×D₁₉	1	4	yes	—
86	C₂×Q₈	D₇₆	1	4	yes	—
87	C₂×Q₈	C₂²⋊D₁₉	1	4	yes	—
88	C₂×D₄	—	19	4	no	—
89	C₂×D₄	—	19	6	no	—
90	C₂²×C₄	—	19	12	no	—
91	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
92	C₄⋊C₄	—	2	6	no	—
93	C₄⋊C₄	—	38	6	no	—
94	C₂²⋊C₄	—	19	4	no	—
95	C₂²⋊C₄	C₂²×D₁₉	1	4	yes	—
96	C₄²	—	2	6	no	—
97	C₄²	—	38	6	no	—
98	C₂³	—	19	4	no	—
99	C₂³	C₂³×D₁₉	1	1	yes	characteristic
100	Q₈	—	38	12	no	—
101	Q₈	(C₂×D₁₉)⋊C₄	1	16	yes	—
102	D₄	—	38	4	no	—
103	D₄	—	38	4	no	—
104	D₄	—	38	12	no	—
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	—	19	4	no	—
107	C₂×C₄	—	38	24	no	—
108	C₂×C₄	—	38	4	no	—
109	C₂×C₄	C₂×C₄×D₁₉	1	6	yes	—
110	C₂×C₄	C₂×D₇₆	1	6	yes	—
111	C₂×C₄	C₂×C₂²⋊D₁₉	1	6	yes	—
112	C₂²	—	4	1	no	—
113	C₂²	—	38	4	no	—
114	C₂²	—	76	4	no	—
115	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
116	C₂²	C₂²×D₇₆	1	1	yes	characteristic
117	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
118	C₄	—	4	4	no	—
119	C₄	—	38	4	no	—
120	C₄	—	76	4	no	—
121	C₄	C₂×(C₂×D₁₉)⋊C₄	1	12	yes	—
122	C₂	—	2	1	no	—
123	C₂	—	2	1	no	—
124	C₂	—	2	1	no	—
125	C₂	—	76	4	no	—
126	C₂	C₂²×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597433

C₂

yes

maximal, characteristic

#11927022

C₂

yes

maximal, characteristic, complemented

#11926517

C₂

yes

maximal, complemented

C₁₉×#519

C₂

yes

maximal, characteristic, complemented

C₂²×Q₈×C₁₉

C₂²

yes

—

—

C₄

yes

complemented

C₂×Q₈×D₁₉

C₄

yes

complemented

C₂×#64541

C₂²

yes

—

C₄×Q₈×C₁₉

—

C₁₉×#117

C₂²

yes

—

Q₈×Dic₁₉

—

#10597372

C₂²

yes

—

#10597263

C₂²

yes

—

C₂×Q₈×C₁₉

C₂×C₄

yes

—

C₂×Q₈×C₁₉

D₄

yes

—

C₂×Q₈×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂×C₂²⋊D₁₉

C₂³

yes

—

#64545

—

Q₈×D₁₉

—

#64541

—

#64541

—

C₂×D₇₆

C₂×C₄

yes

—

C₂×C₄×D₁₉

C₂×C₄

yes

—

C₂×Dic₃₈

C₂×C₄

yes

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

C₂³

yes

—

C₄²×C₁₉

—

C₂²⋊Dic₁₉

C₂³

yes

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

C₂²×C₄

yes

—

Q₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂²⋊D₁₉

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂²×C₄

yes

—

D₇₆

—

C₄×D₁₉

—

Dic₃₈

—

#2884

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₂³×C₄

yes

characteristic

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×C₂²⋊C₄

yes

—

Dic₁₉

—

Dic₁₉

—

C₂×2₋¹⁺⁴

—

#519

—

#519

D₁₉

yes

characteristic, complemented

#410

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

C₂²×C₂²⋊C₄

yes

characteristic

D₁₉

—

2₋¹⁺⁴

—

2₋¹⁺⁴

—

C₂×#41

—

C₂×#41

—

C₂²×Q₈

—

C₂²×Q₈

C₂×D₁₉

yes

characteristic

C₄×Q₈

—

C₄×Q₈

—

#117

—

#117

C₂×D₁₉

yes

—

#99

—

C₁₉

#2884

yes

characteristic, complemented, Sylow

#41

—

#41

—

#41

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₄×D₁₉

yes

—

C₂×Q₈

D₇₆

yes

—

C₂×Q₈

C₂²⋊D₁₉

yes

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

C₂²×D₁₉

yes

—

C₄²

—

C₄²

—

C₂³

—

C₂³

C₂³×D₁₉

yes

characteristic

100

Q₈

—

101

Q₈

(C₂×D₁₉)⋊C₄

yes

—

102

D₄

—

103

D₄

—

104

D₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

C₂×C₄×D₁₉

yes

—

110

C₂×C₄

C₂×D₇₆

yes

—

111

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

112

C₂²

—

113

C₂²

—

114

C₂²

—

115

C₂²

C₂²×C₄×D₁₉

yes

characteristic

116

C₂²

C₂²×D₇₆

yes

characteristic

117

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

C₂×(C₂×D₁₉)⋊C₄

yes

—

122

C₂

—

123

C₂

—

124

C₂

—

125

C₂

—

126

C₂

C₂²×(C₂×D₁₉)⋊C₄

yes

characteristic

	subgroup	G/H
center	C₂	C₂²×(C₂×D₁₉)⋊C₄
commutator	C₂²×C₁₉	C₂³×C₄
Frattini	C₂³	C₂³×D₁₉
Fitting	C₁₉×#519	C₂
socle	C₂×C₁₉	C₂²×C₂²⋊C₄
prime radical	C₂×#10597433	C₂
cosocle	C₂³×C₁₉	C₂⁴
hypercenter	#519	D₁₉
hypocenter	C₁₉	#2884
LCS	G ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂²×Q₈ ◁ #519

subgroup

G/H

center

C₂

C₂²×(C₂×D₁₉)⋊C₄

commutator

C₂²×C₁₉

C₂³×C₄

Frattini

C₂³

C₂³×D₁₉

Fitting

C₁₉×#519

C₂

socle

C₂×C₁₉

C₂²×C₂²⋊C₄

prime radical

C₂×#10597433

C₂

cosocle

C₂³×C₁₉

C₂⁴

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂²×Q₈ ◁ #519

N	H ≅ G/N	type
2. #11927022	C₂	semidirect
3. #11926517	C₂	semidirect
4. C₁₉×#519	C₂	semidirect
8. C₂×#64545	C₄	semidirect
9. C₂×Q₈×D₁₉	C₄	semidirect
61. #519	D₁₉	semidirect
79. C₁₉	#2884	semidirect

H ≅ G/N

type

2. #11927022

C₂

semidirect

3. #11926517

C₂

semidirect

4. C₁₉×#519

C₂

semidirect

8. C₂×#64545

C₄

semidirect

9. C₂×Q₈×D₁₉

C₄

semidirect

61. #519

D₁₉

semidirect

79. C₁₉

#2884

semidirect

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

subgroup	index
C₂×#10597433	2
#11927022	2
#11926517	2
C₁₉×#519	2
#2884	19

subgroup

index

C₁₉×#519

Subgroups — #14572098

Conjugacy classes of subgroups

Complements

Maximal subgroups