Group #14564426 — subgroups

Subgroups — #14564426

Order 2432.

184 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 93 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	#11926593	C₂	1	2	yes	maximal
2	C₂×#10597276	C₂	1	1	yes	maximal, characteristic
3	#11926499	C₂	1	1	yes	maximal, characteristic
4	#11926316	C₂	1	2	yes	maximal
5	C₂×C₁₉×#108	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
7	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	#10597372	C₂²	1	1	yes	characteristic
9	C₂×#64520	C₂²	1	2	yes	—
10	C₂×#64520	C₂²	1	1	yes	characteristic
11	C₁₉×#108	C₄	1	4	yes	complemented
12	#10597276	—	2	1	no	—
13	#10597276	—	2	1	no	—
14	#10597276	—	2	4	no	—
15	#10597272	—	2	1	no	—
16	C₈×Dic₁₉	—	2	1	no	—
17	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
18	M₁₆×C₁₉	—	2	2	no	—
19	M₁₆×C₁₉	C₂×C₄	1	4	yes	—
20	C₂×C₈×C₁₉	—	2	2	no	—
21	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
22	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₂×C₈×C₁₉	Q₈	1	2	yes	—
25	C₂²⋊Dic₁₉	Q₈	1	2	yes	—
26	C₄⋊Dic₁₉	—	2	1	no	—
27	C₄×Dic₁₉	—	2	1	no	—
28	#64520	—	2	1	no	—
29	#64520	—	2	2	no	—
30	#64520	—	2	2	no	—
31	#64520	D₄	1	2	yes	—
32	C₂×C₁₉⋊C₈	—	2	1	no	—
33	C₂×C₁₉⋊C₈	—	2	2	no	—
34	C₂³×C₁₉	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
40	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
41	C₂×Dic₁₉	—	2	2	no	—
42	C₈×C₁₉	—	2	4	no	—
43	C₈×C₁₉	C₄⋊C₄	1	2	yes	—
44	C₈×C₁₉	C₄⋊C₄	1	2	yes	—
45	C₁₉⋊C₈	—	2	2	no	—
46	C₁₉⋊C₈	—	4	2	no	—
47	#1953	—	19	1	no	maximal, Sylow
48	C₂²×C₁₉	—	4	1	no	—
49	C₂²×C₁₉	C₄×Q₈	1	1	yes	characteristic
50	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
51	C₂²×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
52	C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
54	C₄×C₁₉	#121	1	1	yes	characteristic
55	C₄×C₁₉	#125	1	1	yes	characteristic
56	Dic₁₉	—	4	2	no	—
57	#430	—	19	2	no	—
58	C₂×#108	—	19	1	no	—
59	C₂×#108	D₁₉	1	1	yes	characteristic
60	#405	—	19	1	no	—
61	#344	—	19	2	no	—
62	C₂×C₁₉	—	2	1	no	—
63	C₂×C₁₉	—	2	1	no	—
64	C₂×C₁₉	—	2	1	no	—
65	C₂×C₁₉	#389	1	1	yes	characteristic
66	C₂×M₁₆	—	19	1	no	—
67	C₂×M₁₆	—	19	2	no	—
68	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
69	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
70	#117	—	19	1	no	—
71	#108	—	38	4	no	—
72	#108	—	38	1	no	—
73	#108	—	38	1	no	—
74	#108	Dic₁₉	1	4	yes	complemented
75	#97	—	38	1	no	—
76	C₄×C₈	—	38	1	no	—
77	C₁₉	#1953	1	1	yes	characteristic, complemented, Sylow
78	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
79	M₁₆	—	2	2	no	—
80	M₁₆	—	19	2	no	—
81	M₁₆	—	38	1	no	—
82	M₁₆	—	38	2	no	—
83	M₁₆	—	38	2	no	—
84	M₁₆	C₂×Dic₁₉	1	4	yes	—
85	C₂×C₈	—	2	2	no	—
86	C₂×C₈	—	38	1	no	—
87	C₂×C₈	—	38	2	no	—
88	C₂×C₈	Dic₃₈	1	2	yes	—
89	C₂×C₈	D₇₆	1	1	yes	characteristic
90	C₂×C₈	D₇₆	1	1	yes	characteristic
91	C₂×C₈	C₂×Dic₁₉	1	2	yes	—
92	C₄⋊C₄	—	38	1	no	—
93	C₂²⋊C₄	—	19	2	no	—
94	C₄²	—	38	1	no	—
95	C₂³	Q₈×D₁₉	1	1	yes	characteristic
96	C₂×C₄	—	38	2	no	—
97	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
98	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
99	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
100	C₂×C₄	#64543	1	1	yes	characteristic
101	C₂×C₄	#64545	1	1	yes	characteristic
102	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
103	C₈	—	2	4	no	—
104	C₈	—	38	2	no	—
105	C₈	—	76	2	no	—
106	C₈	C₄⋊Dic₁₉	1	2	yes	—
107	C₈	C₄⋊Dic₁₉	1	2	yes	—
108	C₂²	—	4	1	no	—
109	C₂²	#10597334	1	1	yes	characteristic
110	C₂²	#10597343	1	1	yes	characteristic
111	C₂²	Q₈×Dic₁₉	1	1	yes	characteristic
112	C₄	—	76	2	no	—
113	C₄	#10597336	1	1	yes	characteristic
114	C₄	#10597341	1	1	yes	characteristic
115	C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
116	C₄	D₄×Dic₁₉	1	1	yes	characteristic
117	C₂	—	2	1	no	—
118	C₂	—	2	1	no	—
119	C₂	—	2	1	no	—
120	C₂	#11926443	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926593

C₂

yes

maximal

C₂×#10597276

C₂

yes

maximal, characteristic

#11926499

C₂

yes

maximal, characteristic

#11926316

C₂

yes

maximal

C₂×C₁₉×#108

C₂

yes

maximal, characteristic

C₂×M₁₆×C₁₉

C₂²

yes

—

C₂²×C₈×C₁₉

C₂²

yes

characteristic

#10597372

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

—

C₂×#64520

C₂²

yes

characteristic

C₁₉×#108

C₄

yes

—

—

—

—

C₈×Dic₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

Q₈

yes

—

C₂²⋊Dic₁₉

Q₈

yes

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

—

—

—

D₄

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

C₄⋊C₄

yes

—

C₈×C₁₉

C₄⋊C₄

yes

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1953

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₄×Q₈

yes

characteristic

C₂²×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₁₉

C₄⋊Q₈

yes

characteristic

C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₉

C₄×D₄

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

#430

—

C₂×#108

—

C₂×#108

D₁₉

yes

characteristic

#405

—

#344

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#389

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

—

C₂²×C₈

C₂×D₁₉

yes

—

—

—

—

Dic₁₉

yes

complemented

#97

—

C₄×C₈

—

C₁₉

#1953

yes

characteristic, complemented, Sylow

C₂²×C₄

C₂²×D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

C₂×Dic₁₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₃₈

yes

—

C₂×C₈

D₇₆

yes

characteristic

C₂×C₈

D₇₆

yes

characteristic

C₂×C₈

C₂×Dic₁₉

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

Q₈×D₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

C₂×Dic₃₈

yes

characteristic

C₂×C₄

C₂×D₇₆

yes

characteristic

C₂×C₄

D₄×D₁₉

yes

characteristic

100

C₂×C₄

#64543

yes

characteristic

101

C₂×C₄

#64545

yes

characteristic

102

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

103

C₈

—

104

C₈

—

105

C₈

—

106

C₈

C₄⋊Dic₁₉

yes

—

107

C₈

C₄⋊Dic₁₉

yes

—

108

C₂²

—

109

C₂²

#10597334

yes

characteristic

110

C₂²

#10597343

yes

characteristic

111

C₂²

Q₈×Dic₁₉

yes

characteristic

112

C₄

—

113

C₄

#10597336

yes

characteristic

114

C₄

#10597341

yes

characteristic

115

C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

116

C₄

D₄×Dic₁₉

yes

characteristic

117

C₂

—

118

C₂

—

119

C₂

—

120

C₂

#11926443

yes

characteristic

	subgroup	G/H
center	C₄	#10597341
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#108	C₂
socle	C₂×C₁₉	#389
prime radical	C₂³×C₁₉	C₂×Q₈
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#108	D₁₉
hypocenter	C₁₉	#1953
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₄

#10597341

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#108

C₂

socle

C₂×C₁₉

#389

prime radical

C₂³×C₁₉

C₂×Q₈

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
11. C₁₉×#108	C₄	semidirect
74. #108	Dic₁₉	semidirect
77. C₁₉	#1953	semidirect

H ≅ G/N

type

11. C₁₉×#108

C₄

semidirect

74. #108

Dic₁₉

semidirect

77. C₁₉

#1953

semidirect

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

subgroup	index
#11926593	2
C₂×#10597276	2
#11926499	2
#11926316	2
C₂×C₁₉×#108	2
#1953	19

subgroup

index

C₂×C₁₉×#108

Subgroups — #14564426

Conjugacy classes of subgroups

Complements

Maximal subgroups