Group #14565799 — subgroups

Subgroups — #14565799

Order 2432.

124 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 53 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	#11926946	C₂	1	1	yes	maximal, characteristic
2	#11926371	C₂	1	1	yes	maximal, characteristic
3	#11926369	C₂	1	1	yes	maximal, characteristic
4	C₄⋊(C₁₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
5	#11926348	C₂	1	1	yes	maximal, characteristic
6	#11926348	C₂	1	1	yes	maximal, characteristic
7	C₄×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₄×Q₈×C₁₉	—	2	1	no	—
10	#10597316	—	2	1	no	—
11	C₁₉×#107	C₂²	1	1	yes	characteristic
12	C₁₉×#103	—	2	1	no	—
13	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	#10597275	C₂²	1	1	yes	characteristic
15	#10597275	C₂²	1	1	yes	characteristic
16	#10597274	—	2	1	no	—
17	C₂×C₁₉⋊C₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₁₉⋊C₁₆	C₂²	1	1	yes	characteristic
19	C₂×Q₈×C₁₉	—	2	1	no	—
20	Q₁₆×C₁₉	—	2	1	no	—
21	Q₁₆×C₁₉	Q₈	1	2	yes	—
22	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
24	C₄⋊C₄×C₁₉	—	2	1	no	—
25	C₄⋊C₄×C₁₉	—	4	1	no	—
26	C₄²×C₁₉	—	4	1	no	—
27	C₄²×C₁₉	D₄	1	1	yes	characteristic
28	C₄⋊Dic₁₉	—	2	1	no	—
29	C₄⋊Dic₁₉	—	2	1	no	—
30	Dic₁₉⋊C₄	—	4	1	no	—
31	Dic₁₉⋊C₄	—	4	1	no	—
32	C₁₉⋊C₁₆	—	2	1	no	—
33	C₁₉⋊C₁₆	—	2	1	no	—
34	Q₈×C₁₉	—	2	2	no	—
35	Q₈×C₁₉	—	4	1	no	—
36	C₂×C₄×C₁₉	—	4	1	no	—
37	C₂×C₄×C₁₉	—	4	1	no	—
38	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
39	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
40	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₂×Dic₁₉	—	4	1	no	—
42	C₂×Dic₁₉	—	4	1	no	—
43	C₈×C₁₉	—	2	1	no	—
44	C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
45	C₈×C₁₉	#41	1	1	yes	characteristic
46	#2229	—	19	1	no	maximal, Sylow
47	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
48	C₄×C₁₉	—	2	1	no	—
49	C₄×C₁₉	—	2	1	no	—
50	C₄×C₁₉	—	4	2	no	—
51	C₄×C₁₉	—	8	1	no	—
52	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
53	C₄×C₁₉	#137	1	1	yes	characteristic
54	Dic₁₉	—	8	1	no	—
55	Dic₁₉	—	8	1	no	—
56	#499	—	19	1	no	—
57	C₄×Q₁₆	D₁₉	1	1	yes	characteristic
58	#367	—	19	1	no	—
59	#366	—	19	1	no	—
60	C₄⋊C₁₆	—	19	1	no	—
61	#358	—	19	1	no	—
62	#358	—	19	1	no	—
63	C₂×C₁₉	#474	1	1	yes	characteristic
64	C₂×C₁₉	#508	1	1	yes	characteristic
65	C₂×C₁₉	#510	1	1	yes	characteristic
66	C₂×Q₁₆	C₂×D₁₉	1	1	yes	characteristic
67	#125	—	38	1	no	—
68	C₄×Q₈	—	2	1	no	—
69	C₂×C₁₆	—	19	1	no	—
70	C₂×C₁₆	—	19	1	no	—
71	#107	—	19	1	no	—
72	#107	—	19	1	no	—
73	#107	C₂×D₁₉	1	1	yes	characteristic
74	#106	—	38	1	no	—
75	#103	—	2	1	no	—
76	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
77	C₁₉	#2229	1	1	yes	characteristic, complemented, Sylow
78	C₂×Q₈	—	2	1	no	—
79	Q₁₆	—	2	1	no	—
80	Q₁₆	Dic₃₈	1	2	yes	—
81	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
82	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
83	C₄⋊C₄	—	2	1	no	—
84	C₄⋊C₄	—	4	1	no	—
85	C₄⋊C₄	—	38	1	no	—
86	C₄⋊C₄	—	38	1	no	—
87	C₄⋊C₄	—	76	1	no	—
88	C₄⋊C₄	—	76	1	no	—
89	C₄²	—	4	1	no	—
90	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
91	C₁₆	—	38	1	no	—
92	C₁₆	—	38	1	no	—
93	Q₈	—	2	2	no	—
94	Q₈	—	4	1	no	—
95	C₂×C₄	—	4	1	no	—
96	C₂×C₄	—	4	1	no	—
97	C₂×C₄	—	76	1	no	—
98	C₂×C₄	—	76	1	no	—
99	C₂×C₄	#64525	1	1	yes	characteristic
100	C₂×C₄	#64525	1	1	yes	characteristic
101	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
102	C₈	—	2	1	no	—
103	C₈	C₂×Dic₃₈	1	1	yes	characteristic
104	C₈	#64541	1	1	yes	characteristic
105	C₂²	C₂×#64525	1	1	yes	characteristic
106	C₄	—	2	1	no	—
107	C₄	—	2	1	no	—
108	C₄	—	4	2	no	—
109	C₄	—	8	1	no	—
110	C₄	—	152	1	no	—
111	C₄	—	152	1	no	—
112	C₄	#10597370	1	1	yes	characteristic
113	C₄	#10597397	1	1	yes	characteristic
114	C₂	#11926824	1	1	yes	characteristic
115	C₂	#11926974	1	1	yes	characteristic
116	C₂	#11926985	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926946

C₂

yes

maximal, characteristic

#11926371

C₂

yes

maximal, characteristic

#11926369

C₂

yes

maximal, characteristic

C₄⋊(C₁₉⋊C₁₆)

C₂

yes

maximal, characteristic

#11926348

C₂

yes

maximal, characteristic

#11926348

C₂

yes

maximal, characteristic

C₄×Q₁₆×C₁₉

C₂

yes

maximal, characteristic

C₂×Q₁₆×C₁₉

C₂²

yes

characteristic

C₄×Q₈×C₁₉

—

#10597316

—

C₁₉×#107

C₂²

yes

characteristic

C₁₉×#103

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597275

C₂²

yes

characteristic

#10597275

C₂²

yes

characteristic

#10597274

—

C₂×C₁₉⋊C₁₆

C₂²

yes

characteristic

C₂×C₁₉⋊C₁₆

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

Q₈

yes

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₁₉⋊C₁₆

—

C₁₉⋊C₁₆

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

C₂×Q₈

yes

C₈×C₁₉

yes

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

#137

yes

characteristic

Dic₁₉

—

Dic₁₉

—

#499

—

C₄×Q₁₆

D₁₉

yes

characteristic

#367

—

#366

—

C₄⋊C₁₆

—

#358

—

#358

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

C₂×D₁₉

yes

characteristic

#125

—

C₄×Q₈

—

C₂×C₁₆

—

C₂×C₁₆

—

#107

—

#107

—

#107

C₂×D₁₉

yes

characteristic

#106

—

#103

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#2229

yes

characteristic, complemented, Sylow

C₂×Q₈

—

Q₁₆

—

Q₁₆

Dic₃₈

yes

—

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂²⋊D₁₉

yes

characteristic

C₁₆

—

C₁₆

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#64525

yes

characteristic

100

C₂×C₄

#64525

yes

characteristic

101

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

102

C₈

—

103

C₈

C₂×Dic₃₈

yes

characteristic

104

C₈

#64541

yes

characteristic

105

C₂²

C₂×#64525

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

152

—

111

C₄

—

152

—

112

C₄

#10597370

yes

characteristic

113

C₄

#10597397

yes

characteristic

114

C₂

#11926824

yes

characteristic

115

C₂

#11926974

yes

characteristic

116

C₂

#11926985

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#64525
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₄×Q₁₆×C₁₉	C₂
socle, prime radical	C₂²×C₁₉	C₂×D₈
hypercenter	C₄×Q₁₆	D₁₉
hypocenter	C₁₉	#2229
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×Q₁₆

subgroup

G/H

center

C₂²

C₂×#64525

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₄×Q₁₆×C₁₉

C₂

socle, prime radical

C₂²×C₁₉

C₂×D₈

hypercenter

C₄×Q₁₆

D₁₉

hypocenter

C₁₉

#2229

LCS

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×Q₁₆

N	H ≅ G/N	type
77. C₁₉	#2229	semidirect

H ≅ G/N

type

77. C₁₉

#2229

semidirect

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

subgroup	index
#11926946	2
#11926371	2
#11926369	2
C₄⋊(C₁₉⋊C₁₆)	2
#11926348	2
C₄×Q₁₆×C₁₉	2
#2229	19

subgroup

index

C₄⋊(C₁₉⋊C₁₆)

C₄×Q₁₆×C₁₉

Subgroups — #14565799

Conjugacy classes of subgroups

Complements

Maximal subgroups