Group #14564455 — subgroups

Subgroups — #14564455

Order 2432.

308 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 109 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×#10597315	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597273	C₂	1	4	yes	maximal
3	#11926410	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#97	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₃₈	C₂²	1	2	yes	—
6	C₂²×C₈×C₁₉	C₂²	1	2	yes	—
7	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₁₉	—	2	2	no	—
9	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
10	#10597315	—	2	2	no	—
11	#10597315	C₄	1	4	yes	complemented
12	C₁₉×#97	—	2	2	no	—
13	C₁₉⋊#95	—	2	2	no	—
14	#10597273	—	2	8	no	—
15	C₂²×C₄×C₁₉	D₄	1	2	yes	—
16	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
17	C₂²×Dic₁₉	—	2	2	no	—
18	C₂²×Dic₁₉	—	2	2	no	—
19	C₂×Dic₃₈	—	2	4	no	—
20	C₂×Dic₃₈	—	2	4	no	—
21	C₂×Dic₃₈	—	2	2	no	—
22	C₂×Dic₃₈	C₂×C₄	1	4	yes	—
23	C₂×C₈×C₁₉	—	2	2	no	—
24	C₂×C₈×C₁₉	—	2	2	no	—
25	C₂×C₈×C₁₉	D₄	1	4	yes	—
26	C₄²×C₁₉	C₂×C₄	1	2	yes	—
27	C₄²×C₁₉	D₄	1	2	yes	—
28	C₄⋊Dic₁₉	—	2	8	no	—
29	C₄⋊Dic₁₉	—	2	4	no	—
30	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₁₉	—	2	4	no	—
32	C₂×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
33	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
35	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₁₉	#41	1	2	yes	—
37	C₂×Dic₁₉	—	2	4	no	—
38	C₂×Dic₁₉	—	4	2	no	—
39	C₂×Dic₁₉	—	4	2	no	—
40	C₂×Dic₁₉	—	4	2	no	—
41	C₂×Dic₁₉	—	4	4	no	—
42	Dic₃₈	—	2	8	no	—
43	Dic₃₈	—	4	4	no	—
44	C₈×C₁₉	—	2	4	no	—
45	#1960	—	19	1	no	maximal, Sylow
46	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
47	C₂²×C₁₉	#124	1	1	yes	characteristic
48	C₂²×C₁₉	#127	1	1	yes	characteristic
49	C₂²×C₁₉	#137	1	4	yes	—
50	C₄×C₁₉	—	2	4	no	—
51	C₄×C₁₉	C₄×D₄	1	2	yes	—
52	C₄×C₁₉	#121	1	2	yes	—
53	Dic₁₉	—	4	4	no	—
54	Dic₁₉	—	8	2	no	—
55	C₂×C₄⋊Q₈	—	19	1	no	—
56	C₂×#103	—	19	4	no	—
57	C₂×#97	D₁₉	1	1	yes	characteristic
58	#382	—	19	1	no	—
59	C₂×C₁₉	#390	1	1	yes	characteristic
60	C₂×C₁₉	#419	1	2	yes	—
61	C₂×C₁₉	#491	1	2	yes	—
62	C₂×C₁₉	#497	1	2	yes	—
63	C₂²×Q₈	—	19	2	no	—
64	C₂²×C₈	C₂×D₁₉	1	2	yes	—
65	C₄⋊Q₈	—	19	4	no	—
66	C₄⋊Q₈	—	38	2	no	—
67	C₂×C₄⋊C₄	—	19	2	no	—
68	C₂×C₄⋊C₄	—	38	2	no	—
69	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
70	#103	—	38	8	no	—
71	#97	—	2	2	no	—
72	#95	—	38	2	no	—
73	C₁₉	#1960	1	1	yes	characteristic, complemented, Sylow
74	C₂×Q₈	—	19	4	no	—
75	C₂×Q₈	—	38	2	no	—
76	C₂×Q₈	—	38	4	no	—
77	C₂×Q₈	—	38	4	no	—
78	C₂²×C₄	—	38	2	no	—
79	C₂²×C₄	—	38	2	no	—
80	C₂²×C₄	D₇₆	1	2	yes	—
81	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
82	C₂×C₈	—	2	2	no	—
83	C₂×C₈	—	2	2	no	—
84	C₂×C₈	D₇₆	1	4	yes	—
85	C₄⋊C₄	—	38	8	no	—
86	C₄⋊C₄	—	38	4	no	—
87	C₄²	C₄×D₁₉	1	2	yes	—
88	C₄²	C₂²⋊D₁₉	1	2	yes	—
89	C₂³	C₂×D₇₆	1	1	yes	characteristic
90	Q₈	—	38	8	no	—
91	Q₈	—	76	4	no	—
92	C₂×C₄	—	2	4	no	—
93	C₂×C₄	—	38	4	no	—
94	C₂×C₄	—	76	2	no	—
95	C₂×C₄	—	76	2	no	—
96	C₂×C₄	—	76	2	no	—
97	C₂×C₄	—	76	4	no	—
98	C₂×C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
99	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
100	C₂×C₄	C₂×D₇₆	1	2	yes	—
101	C₂×C₄	#64541	1	2	yes	—
102	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
103	C₈	—	2	4	no	—
104	C₂²	#10597320	1	1	yes	characteristic
105	C₂²	#10597321	1	1	yes	characteristic
106	C₂²	#10597355	1	4	yes	—
107	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
108	C₄	—	2	4	no	—
109	C₄	—	76	4	no	—
110	C₄	—	152	2	no	—
111	C₄	C₄×D₇₆	1	2	yes	—
112	C₄	#10597376	1	2	yes	—
113	C₂	#11926446	1	1	yes	characteristic
114	C₂	#11926554	1	2	yes	—
115	C₂	#11926913	1	2	yes	—
116	C₂	#11926938	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597315

C₂

yes

maximal, characteristic

C₂×#10597273

C₂

yes

maximal

#11926410

C₂

yes

maximal, characteristic

C₂×C₁₉×#97

C₂

yes

maximal, characteristic

C₂²×Dic₃₈

C₂²

yes

—

C₂²×C₈×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

#10597315

—

#10597315

C₄

yes

complemented

C₁₉×#97

—

C₁₉⋊#95

—

#10597273

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂×C₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄²×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

D₄

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

#1960

—

maximal, Sylow

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₄×C₁₉

—

C₄×C₁₉

C₄×D₄

yes

—

C₄×C₁₉

#121

yes

—

Dic₁₉

—

Dic₁₉

—

C₂×C₄⋊Q₈

—

C₂×#103

—

C₂×#97

D₁₉

yes

characteristic

#382

—

C₂×C₁₉

#390

yes

characteristic

C₂×C₁₉

#419

yes

—

C₂×C₁₉

#491

yes

—

C₂×C₁₉

#497

yes

—

C₂²×Q₈

—

C₂²×C₈

C₂×D₁₉

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₁₉

yes

—

—

—

C₁₉

#1960

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₇₆

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₇₆

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₄×D₁₉

yes

—

C₄²

C₂²⋊D₁₉

yes

—

C₂³

C₂×D₇₆

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

—

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

100

C₂×C₄

C₂×D₇₆

yes

—

101

C₂×C₄

#64541

yes

—

102

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

103

C₈

—

104

C₂²

#10597320

yes

characteristic

105

C₂²

#10597321

yes

characteristic

106

C₂²

#10597355

yes

—

107

C₂²

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

152

—

111

C₄

C₄×D₇₆

yes

—

112

C₄

#10597376

yes

—

113

C₂

#11926446

yes

characteristic

114

C₂

#11926554

yes

—

115

C₂

#11926913

yes

—

116

C₂

#11926938

yes

—

	subgroup	G/H
center	C₂³	C₂×D₇₆
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#97	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#97	D₁₉
hypocenter	C₁₉	#1960
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

subgroup

G/H

center

C₂³

C₂×D₇₆

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#97

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

cosocle

C₂²×C₄×C₁₉

C₂³

hypercenter

C₂×#97

D₁₉

hypocenter

C₁₉

#1960

LCS

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

N	H ≅ G/N	type
11. #10597315	C₄	semidirect
73. C₁₉	#1960	semidirect

H ≅ G/N

type

11. #10597315

C₄

semidirect

73. C₁₉

#1960

semidirect

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

subgroup	index
C₂×#10597315	2
C₂×#10597273	2
#11926410	2
C₂×C₁₉×#97	2
#1960	19

subgroup

index

C₂×C₁₉×#97

Subgroups — #14564455

Conjugacy classes of subgroups

Complements

Maximal subgroups