Group #14563352 — subgroups

Subgroups — #14563352

Order 2432.

424 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 205 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×#10597372	C₂	1	2	yes	maximal
2	#11926307	C₂	1	4	yes	maximal, complemented
3	C₂³×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
5	C₂²×C₈×C₁₉	—	2	4	no	—
6	C₂²×C₈×C₁₉	C₄	1	4	yes	complemented
7	C₂²×C₈×C₁₉	C₂²	1	2	yes	—
8	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
9	#10597372	—	2	4	no	—
10	#10597372	C₄	1	8	yes	complemented
11	C₂×C₄⋊Dic₁₉	C₂²	1	4	yes	—
12	C₂×C₄×Dic₁₉	—	2	2	no	—
13	C₂⁴×C₁₉	D₄	1	1	yes	characteristic
14	C₂²×C₄×C₁₉	C₂×C₄	1	4	yes	—
15	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
16	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
17	C₂²×C₄×C₁₉	D₄	1	4	yes	—
18	C₂²×C₄×C₁₉	Q₈	1	2	yes	—
19	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
20	C₂²×Dic₁₉	—	2	4	no	—
21	C₂×C₈×C₁₉	—	2	8	no	—
22	C₂×C₈×C₁₉	—	2	4	no	—
23	C₂×C₈×C₁₉	C₂×C₄	1	4	yes	—
24	C₂²⋊Dic₁₉	—	2	8	no	—
25	C₄⋊Dic₁₉	—	2	4	no	—
26	C₄⋊Dic₁₉	C₂×C₄	1	8	yes	—
27	C₄×Dic₁₉	—	2	8	no	—
28	C₂³×C₁₉	—	2	4	no	—
29	C₂³×C₁₉	C₂²⋊C₄	1	4	yes	—
30	C₂³×C₁₉	C₄⋊C₄	1	2	yes	—
31	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₁₉	C₄²	1	4	yes	—
33	C₂×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
34	C₂×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
35	C₂×C₄×C₁₉	C₄⋊C₄	1	8	yes	—
36	C₂×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
37	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
38	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
40	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
41	C₂×Dic₁₉	—	2	8	no	—
42	C₂×Dic₁₉	—	4	8	no	—
43	C₈×C₁₉	—	2	4	no	—
44	#1735	—	19	1	no	maximal, Sylow
45	C₂²×C₁₉	—	2	8	no	—
46	C₂²×C₁₉	—	2	4	no	—
47	C₂²×C₁₉	#95	1	4	yes	—
48	C₂²×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
49	C₂²×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₂²×C₁₉	#135	1	4	yes	—
51	C₄×C₁₉	#95	1	4	yes	—
52	C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
53	C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
54	C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
55	Dic₁₉	—	4	8	no	—
56	C₂³×C₈	D₁₉	1	1	yes	characteristic
57	C₂×#117	—	19	2	no	—
58	#340	—	19	4	no	—
59	C₂×C₁₉	—	2	4	no	—
60	C₂×C₁₉	C₂×#95	1	1	yes	characteristic
61	C₂×C₁₉	#416	1	4	yes	—
62	C₂×C₁₉	#427	1	2	yes	—
63	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
64	C₂²×C₈	—	2	4	no	—
65	C₂²×C₈	Dic₁₉	1	4	yes	complemented
66	C₂²×C₈	C₂×D₁₉	1	2	yes	—
67	#117	—	19	8	no	—
68	#117	—	38	4	no	—
69	C₂×C₄⋊C₄	—	19	4	no	—
70	C₂×C₂²⋊C₄	—	38	2	no	—
71	C₂×C₄²	—	38	2	no	—
72	C₁₉	#1735	1	1	yes	characteristic, complemented, Sylow
73	C₂⁴	D₇₆	1	1	yes	characteristic
74	C₂²×C₄	—	38	4	no	—
75	C₂²×C₄	Dic₃₈	1	2	yes	—
76	C₂²×C₄	C₄×D₁₉	1	4	yes	—
77	C₂²×C₄	D₇₆	1	1	yes	characteristic
78	C₂²×C₄	C₂×Dic₁₉	1	2	yes	—
79	C₂²×C₄	C₂²⋊D₁₉	1	4	yes	—
80	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
81	C₂×C₈	—	2	8	no	—
82	C₂×C₈	—	2	4	no	—
83	C₂×C₈	C₂×Dic₁₉	1	4	yes	—
84	C₄⋊C₄	—	19	8	no	—
85	C₄⋊C₄	—	38	4	no	—
86	C₂²⋊C₄	—	38	8	no	—
87	C₄²	—	38	8	no	—
88	C₂³	—	2	4	no	—
89	C₂³	C₄⋊Dic₁₉	1	2	yes	—
90	C₂³	(C₂×D₁₉)⋊C₄	1	4	yes	—
91	C₂³	C₂×D₇₆	1	1	yes	characteristic
92	C₂×C₄	—	38	8	no	—
93	C₂×C₄	—	76	8	no	—
94	C₂×C₄	C₄×Dic₁₉	1	4	yes	—
95	C₂×C₄	Dic₁₉⋊C₄	1	8	yes	—
96	C₂×C₄	C₄⋊Dic₁₉	1	2	yes	—
97	C₂×C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
98	C₂×C₄	C₂²⋊Dic₁₉	1	4	yes	—
99	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
100	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
101	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
102	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
103	C₈	—	2	4	no	—
104	C₂²	—	2	8	no	—
105	C₂²	—	2	4	no	—
106	C₂²	C₁₉⋊#95	1	4	yes	—
107	C₂²	#10597350	1	4	yes	—
108	C₂²	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
109	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	2	yes	—
110	C₄	—	76	8	no	—
111	C₄	C₁₉⋊#95	1	4	yes	—
112	C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
113	C₄	C₂×Dic₁₉⋊C₄	1	2	yes	—
114	C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
115	C₂	—	2	4	no	—
116	C₂	C₂×C₁₉⋊#95	1	1	yes	characteristic
117	C₂	#11926541	1	4	yes	—
118	C₂	#11926582	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597372

C₂

yes

maximal

#11926307

C₂

yes

maximal, complemented

C₂³×C₈×C₁₉

C₂

yes

maximal, characteristic

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₄

yes

complemented

C₂²×C₈×C₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

—

#10597372

—

#10597372

C₄

yes

complemented

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

—

C₂⁴×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

Q₈

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

C₄×Dic₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²⋊C₄

yes

—

C₂³×C₁₉

C₄⋊C₄

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₄²

yes

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₄⋊C₄

yes

—

C₂×C₄×C₁₉

C₄⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

#1735

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#95

yes

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

—

C₂²×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₉

#135

yes

—

C₄×C₁₉

#95

yes

—

C₄×C₁₉

C₂×C₄²

yes

characteristic

C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₉

C₂×C₄⋊C₄

yes

—

Dic₁₉

—

C₂³×C₈

D₁₉

yes

characteristic

C₂×#117

—

#340

—

C₂×C₁₉

—

C₂×C₁₉

C₂×#95

yes

characteristic

C₂×C₁₉

#416

yes

—

C₂×C₁₉

#427

yes

—

C₂³×C₄

C₂×D₁₉

yes

characteristic

C₂²×C₈

—

C₂²×C₈

Dic₁₉

yes

complemented

C₂²×C₈

C₂×D₁₉

yes

—

#117

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₁₉

#1735

yes

characteristic, complemented, Sylow

C₂⁴

D₇₆

yes

characteristic

C₂²×C₄

—

C₂²×C₄

Dic₃₈

yes

—

C₂²×C₄

C₄×D₁₉

yes

—

C₂²×C₄

D₇₆

yes

characteristic

C₂²×C₄

C₂×Dic₁₉

yes

—

C₂²×C₄

C₂²⋊D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

—

C₂³

C₄⋊Dic₁₉

yes

—

C₂³

(C₂×D₁₉)⋊C₄

yes

—

C₂³

C₂×D₇₆

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₁₉

yes

—

C₂×C₄

Dic₁₉⋊C₄

yes

—

C₂×C₄

C₄⋊Dic₁₉

yes

—

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

—

C₂×C₄

C₂²⋊Dic₁₉

yes

—

C₂×C₄

C₂×Dic₃₈

yes

characteristic

100

C₂×C₄

C₂×C₄×D₁₉

yes

—

101

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

102

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

103

C₈

—

104

C₂²

—

105

C₂²

—

106

C₂²

C₁₉⋊#95

yes

—

107

C₂²

#10597350

yes

—

108

C₂²

C₂×C₄⋊Dic₁₉

yes

characteristic

109

C₂²

C₂×(C₂×D₁₉)⋊C₄

yes

—

110

C₄

—

111

C₄

C₁₉⋊#95

yes

—

112

C₄

C₂×C₄×Dic₁₉

yes

characteristic

113

C₄

C₂×Dic₁₉⋊C₄

yes

—

114

C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

115

C₂

—

116

C₂

C₂×C₁₉⋊#95

yes

characteristic

117

C₂

#11926541

yes

—

118

C₂

#11926582

yes

—

	subgroup	G/H
center	C₂²×C₄	D₇₆
commutator	C₄×C₁₉	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂³×C₈×C₁₉	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂⁴×C₁₉	D₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂³×C₈	D₁₉
hypocenter	C₁₉	#1735
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈

subgroup

G/H

center

C₂²×C₄

D₇₆

commutator

C₄×C₁₉

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂³×C₈×C₁₉

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂⁴×C₁₉

D₄

cosocle

C₂²×C₄×C₁₉

C₂³

hypercenter

C₂³×C₈

D₁₉

hypocenter

C₁₉

#1735

LCS

G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈

N	H ≅ G/N	type
2. #11926307	C₂	semidirect
6. C₂²×C₈×C₁₉	C₄	semidirect
10. #10597372	C₄	semidirect
65. C₂²×C₈	Dic₁₉	semidirect
72. C₁₉	#1735	semidirect

H ≅ G/N

type

2. #11926307

C₂

semidirect

6. C₂²×C₈×C₁₉

C₄

semidirect

10. #10597372

C₄

semidirect

65. C₂²×C₈

Dic₁₉

semidirect

72. C₁₉

#1735

semidirect

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

subgroup	index
C₂×#10597372	2
#11926307	2
C₂³×C₈×C₁₉	2
#1735	19

subgroup

index

C₂×#10597372

#11926307

C₂³×C₈×C₁₉

#1735

Subgroups — #14563352

Conjugacy classes of subgroups

Complements

Maximal subgroups