Group #14565672 — subgroups

Subgroups — #14565672

Order 2432.

174 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 55 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×#10597284	C₂	1	2	yes	maximal, complemented
2	C₄×Dic₇₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊(C₁₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926345	C₂	1	2	yes	maximal, complemented
5	C₁₉×#493	C₂	1	1	yes	maximal, characteristic
6	C₂×D₈×C₁₉	—	2	1	no	—
7	C₂×D₈×C₁₉	C₂²	1	2	yes	—
8	C₁₉×#127	—	2	1	no	—
9	C₂×Dic₇₆	C₂²	1	1	yes	characteristic
10	C₄×Dic₃₈	—	2	1	no	—
11	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	#10597284	—	2	4	no	—
13	#10597275	C₂²	1	1	yes	characteristic
14	#10597273	—	2	1	no	—
15	C₂×C₁₉⋊C₁₆	C₂²	1	2	yes	—
16	C₂×D₄×C₁₉	—	2	2	no	—
17	C₂×D₄×C₁₉	—	4	1	no	—
18	C₂×D₄×C₁₉	—	4	1	no	—
19	C₂×Dic₃₈	—	2	1	no	—
20	D₈×C₁₉	—	2	2	no	—
21	D₈×C₁₉	—	2	2	no	—
22	D₈×C₁₉	—	4	2	no	—
23	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
25	C₄²×C₁₉	D₄	1	1	yes	characteristic
26	C₄⋊Dic₁₉	—	2	1	no	—
27	Dic₁₉⋊C₄	—	4	1	no	—
28	C₄×Dic₁₉	—	4	1	no	—
29	Dic₇₆	—	2	1	no	—
30	Dic₇₆	D₄	1	2	yes	complemented
31	C₁₉⋊C₁₆	—	2	2	no	—
32	C₂³×C₁₉	—	4	2	no	—
33	D₄×C₁₉	—	4	2	no	—
34	D₄×C₁₉	—	4	2	no	—
35	D₄×C₁₉	—	8	2	no	—
36	D₄×C₁₉	—	8	2	no	—
37	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
38	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
39	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂×Dic₁₉	—	4	1	no	—
41	C₂×Dic₁₉	—	4	1	no	—
42	Dic₃₈	—	2	2	no	—
43	Dic₃₈	—	4	1	no	—
44	C₈×C₁₉	—	2	1	no	—
45	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₈×C₁₉	#41	1	1	yes	characteristic
47	#2207	—	19	1	no	maximal, Sylow
48	C₂²×C₁₉	—	8	2	no	—
49	C₂²×C₁₉	—	8	2	no	—
50	C₂²×C₁₉	—	8	2	no	—
51	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
52	C₄×C₁₉	—	2	1	no	—
53	C₄×C₁₉	SD₃₂	1	2	yes	complemented
54	C₄×C₁₉	#121	1	1	yes	characteristic
55	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
56	Dic₁₉	—	4	2	no	—
57	Dic₁₉	—	8	1	no	—
58	C₂×SD₃₂	—	19	2	no	—
59	#493	D₁₉	1	1	yes	characteristic
60	C₄×Q₁₆	—	19	1	no	—
61	C₄⋊C₁₆	—	19	1	no	—
62	#357	—	19	2	no	—
63	C₂×C₁₉	—	16	2	no	—
64	C₂×C₁₉	#459	1	1	yes	characteristic
65	C₂×C₁₉	C₂×SD₃₂	1	1	yes	characteristic
66	C₂×C₁₉	#509	1	1	yes	characteristic
67	C₂×Q₁₆	—	19	1	no	—
68	C₂×D₈	—	2	1	no	—
69	C₂×D₈	C₂×D₁₉	1	2	yes	—
70	#127	—	2	1	no	—
71	C₄×Q₈	—	38	1	no	—
72	SD₃₂	—	38	4	no	—
73	C₂×C₁₆	—	19	2	no	—
74	#107	—	19	1	no	—
75	#103	—	38	1	no	—
76	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
77	C₁₉	#2207	1	1	yes	characteristic, complemented, Sylow
78	C₂×Q₈	—	38	1	no	—
79	C₂×D₄	—	2	2	no	—
80	C₂×D₄	—	4	1	no	—
81	C₂×D₄	—	4	1	no	—
82	Q₁₆	—	19	2	no	—
83	Q₁₆	—	38	1	no	—
84	D₈	—	2	2	no	—
85	D₈	—	2	2	no	—
86	D₈	—	4	2	no	—
87	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
88	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
89	C₄⋊C₄	—	38	1	no	—
90	C₄⋊C₄	—	76	1	no	—
91	C₄²	—	76	1	no	—
92	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
93	C₁₆	—	38	2	no	—
94	C₂³	—	4	2	no	—
95	Q₈	—	38	2	no	—
96	Q₈	—	76	1	no	—
97	D₄	—	4	2	no	—
98	D₄	—	4	2	no	—
99	D₄	—	8	2	no	—
100	D₄	—	8	2	no	—
101	C₂×C₄	—	76	1	no	—
102	C₂×C₄	—	76	1	no	—
103	C₂×C₄	#64525	1	1	yes	characteristic
104	C₂×C₄	#64525	1	1	yes	characteristic
105	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
106	C₈	—	2	1	no	—
107	C₈	D₄×D₁₉	1	1	yes	characteristic
108	C₈	#64543	1	1	yes	characteristic
109	C₂²	—	8	2	no	—
110	C₂²	—	8	2	no	—
111	C₂²	—	8	2	no	—
112	C₂²	C₂×#64525	1	1	yes	characteristic
113	C₄	—	2	1	no	—
114	C₄	—	76	2	no	—
115	C₄	—	152	1	no	—
116	C₄	#10597284	1	2	yes	complemented
117	C₄	#10597378	1	1	yes	characteristic
118	C₄	#10597384	1	1	yes	characteristic
119	C₂	—	16	2	no	—
120	C₂	#11926736	1	1	yes	characteristic
121	C₂	C₂×#10597284	1	1	yes	characteristic
122	C₂	#11926980	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597284

C₂

yes

maximal, complemented

C₄×Dic₇₆

C₂

yes

maximal, characteristic, complemented

C₄⋊(C₁₉⋊C₁₆)

C₂

yes

maximal, characteristic, complemented

#11926345

C₂

yes

maximal, complemented

C₁₉×#493

C₂

yes

maximal, characteristic

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

C₂²

yes

—

C₁₉×#127

—

C₂×Dic₇₆

C₂²

yes

characteristic

C₄×Dic₃₈

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597284

—

#10597275

C₂²

yes

characteristic

#10597273

—

C₂×C₁₉⋊C₁₆

C₂²

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×Dic₃₈

—

D₈×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

Dic₇₆

—

Dic₇₆

D₄

yes

complemented

C₁₉⋊C₁₆

—

C₂³×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

C₂×D₄

yes

C₈×C₁₉

yes

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

SD₃₂

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

C₂×SD₃₂

—

#493

D₁₉

yes

characteristic

C₄×Q₁₆

—

C₄⋊C₁₆

—

#357

—

C₂×C₁₉

—

C₂×C₁₉

#459

yes

characteristic

C₂×C₁₉

C₂×SD₃₂

yes

characteristic

C₂×C₁₉

#509

yes

characteristic

C₂×Q₁₆

—

C₂×D₈

—

C₂×D₈

C₂×D₁₉

yes

—

#127

—

C₄×Q₈

—

SD₃₂

—

C₂×C₁₆

—

#107

—

#103

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#2207

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

Q₁₆

—

Q₁₆

—

D₈

—

D₈

—

D₈

—

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂²⋊D₁₉

yes

characteristic

C₁₆

—

C₂³

—

Q₈

—

Q₈

—

D₄

—

D₄

—

D₄

—

100

D₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

#64525

yes

characteristic

104

C₂×C₄

#64525

yes

characteristic

105

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

106

C₈

—

107

C₈

D₄×D₁₉

yes

characteristic

108

C₈

#64543

yes

characteristic

109

C₂²

—

110

C₂²

—

111

C₂²

—

112

C₂²

C₂×#64525

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

152

—

116

C₄

#10597284

yes

complemented

117

C₄

#10597378

yes

characteristic

118

C₄

#10597384

yes

characteristic

119

C₂

—

120

C₂

#11926736

yes

characteristic

121

C₂

C₂×#10597284

yes

characteristic

122

C₂

#11926980

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#64525
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting, prime radical	C₁₉×#493	C₂
socle	C₂²×C₁₉	C₂×D₈
hypercenter	#493	D₁₉
hypocenter	C₁₉	#2207
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #493

subgroup

G/H

center

C₂²

C₂×#64525

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting, prime radical

C₁₉×#493

C₂

socle

C₂²×C₁₉

C₂×D₈

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #493

N	H ≅ G/N	type
1. C₂×#10597284	C₂	semidirect
2. C₄×Dic₇₆	C₂	semidirect
3. C₄⋊(C₁₉⋊C₁₆)	C₂	semidirect
4. #11926345	C₂	semidirect
30. Dic₇₆	D₄	semidirect
53. C₄×C₁₉	SD₃₂	semidirect
77. C₁₉	#2207	semidirect
116. C₄	#10597284	semidirect

H ≅ G/N

type

1. C₂×#10597284

C₂

semidirect

2. C₄×Dic₇₆

C₂

semidirect

3. C₄⋊(C₁₉⋊C₁₆)

C₂

semidirect

4. #11926345

C₂

semidirect

30. Dic₇₆

D₄

semidirect

53. C₄×C₁₉

SD₃₂

semidirect

77. C₁₉

#2207

semidirect

116. C₄

#10597284

semidirect

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

subgroup	index
C₂×#10597284	2
C₄×Dic₇₆	2
C₄⋊(C₁₉⋊C₁₆)	2
#11926345	2
C₁₉×#493	2
#2207	19

subgroup

index

C₂×#10597284

C₄×Dic₇₆

C₄⋊(C₁₉⋊C₁₆)

#11926345

C₁₉×#493

#2207

Subgroups — #14565672

Conjugacy classes of subgroups

Complements

Maximal subgroups