Group #14562270 — subgroups

Subgroups — #14562270

Order 2432.

238 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 77 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	#11926601	C₂	1	2	yes	maximal, complemented
2	#11926284	C₂	1	4	yes	maximal, complemented
3	C₁₉×#532	C₂	1	1	yes	maximal, characteristic
4	C₂×#41×C₁₉	C₄	1	2	yes	—
5	C₁₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
6	C₁₉×#127	C₄	1	1	yes	characteristic
7	C₁₉×#124	C₂²	1	2	yes	—
8	C₁₉×#121	—	2	2	no	—
9	C₄×D₄×C₁₉	—	2	2	no	—
10	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
12	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
13	#10597260	C₂²	1	4	yes	—
14	#41×C₁₉	—	4	4	no	—
15	C₂×Q₈×C₁₉	C₂×C₄	1	2	yes	—
16	C₂×D₄×C₁₉	—	2	2	no	—
17	C₂×D₄×C₁₉	—	2	2	no	—
18	C₂×D₄×C₁₉	C₂×C₄	1	2	yes	—
19	C₂²×C₄×C₁₉	—	2	2	no	—
20	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	D₄	1	2	yes	—
22	C₄⋊C₄×C₁₉	—	2	2	no	—
23	C₂²⋊C₄×C₁₉	—	2	4	no	—
24	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₄²×C₁₉	D₄	1	2	yes	—
26	C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	C₂×C₁₉⋊C₈	—	2	4	no	—
28	C₂³×C₁₉	—	2	2	no	—
29	C₂³×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
30	Q₈×C₁₉	—	4	2	no	—
31	D₄×C₁₉	—	4	2	no	—
32	D₄×C₁₉	—	4	4	no	—
33	D₄×C₁₉	—	4	4	no	—
34	C₂×C₄×C₁₉	—	2	2	no	—
35	C₂×C₄×C₁₉	—	2	2	no	—
36	C₂×C₄×C₁₉	—	4	2	no	—
37	C₂×C₄×C₁₉	—	4	4	no	—
38	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
39	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
42	C₁₉⋊C₈	—	4	4	no	—
43	#1536	—	19	1	no	maximal, Sylow
44	C₂²×C₁₉	—	2	1	no	—
45	C₂²×C₁₉	—	2	2	no	—
46	C₂²×C₁₉	—	4	2	no	—
47	C₂²×C₁₉	—	4	4	no	—
48	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
49	C₄×C₁₉	—	2	1	no	—
50	C₄×C₁₉	—	2	2	no	—
51	C₄×C₁₉	—	2	2	no	—
52	C₄×C₁₉	—	4	2	no	—
53	C₄×C₁₉	#100	1	2	yes	—
54	#532	D₁₉	1	1	yes	characteristic
55	#432	—	19	2	no	—
56	#329	—	19	4	no	—
57	C₂×C₁₉	—	4	1	no	—
58	C₂×C₁₉	—	8	2	no	—
59	C₂×C₁₉	C₂×#100	1	1	yes	characteristic
60	C₂×C₁₉	#421	1	2	yes	—
61	C₂×#41	Dic₁₉	1	2	yes	—
62	C₄⋊Q₈	Dic₁₉	1	1	yes	characteristic
63	#127	Dic₁₉	1	1	yes	characteristic
64	#124	C₂×D₁₉	1	2	yes	—
65	#121	—	2	2	no	—
66	C₄×D₄	—	2	2	no	—
67	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
68	C₄⋊C₈	—	38	2	no	—
69	C₂²⋊C₈	—	38	2	no	—
70	#97	—	19	4	no	—
71	C₁₉	#1536	1	1	yes	characteristic, complemented, Sylow
72	#41	—	4	4	no	—
73	C₂×Q₈	C₂×Dic₁₉	1	2	yes	—
74	C₂×D₄	—	2	2	no	—
75	C₂×D₄	—	2	2	no	—
76	C₂×D₄	C₂×Dic₁₉	1	2	yes	—
77	C₂²×C₄	—	2	2	no	—
78	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
79	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
80	C₂×C₈	—	38	4	no	—
81	C₄⋊C₄	—	2	2	no	—
82	C₂²⋊C₄	—	2	4	no	—
83	C₄²	C₂×Dic₁₉	1	1	yes	characteristic
84	C₄²	C₂²⋊D₁₉	1	2	yes	—
85	C₄²	C₂²×D₁₉	1	1	yes	characteristic
86	C₂³	—	2	2	no	—
87	C₂³	C₂²⋊Dic₁₉	1	1	yes	characteristic
88	Q₈	—	4	2	no	—
89	D₄	—	4	2	no	—
90	D₄	—	4	4	no	—
91	D₄	—	4	4	no	—
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	4	2	no	—
95	C₂×C₄	—	4	4	no	—
96	C₂×C₄	C₂²⋊Dic₁₉	1	2	yes	—
97	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
98	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
99	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
100	C₈	—	76	4	no	—
101	C₂²	—	2	2	no	—
102	C₂²	—	2	1	no	—
103	C₂²	—	4	4	no	—
104	C₂²	—	4	2	no	—
105	C₂²	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
106	C₄	—	2	2	no	—
107	C₄	—	2	2	no	—
108	C₄	—	2	1	no	—
109	C₄	—	4	2	no	—
110	C₄	#10597290	1	2	yes	—
111	C₂	—	4	1	no	—
112	C₂	—	8	2	no	—
113	C₂	C₂×#10597290	1	1	yes	characteristic
114	C₂	#11926561	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11926601

C₂

yes

maximal, complemented

#11926284

C₂

yes

maximal, complemented

C₁₉×#532

C₂

yes

maximal, characteristic

C₂×#41×C₁₉

C₄

yes

—

C₁₉×C₄⋊Q₈

C₄

yes

characteristic

C₁₉×#127

C₄

yes

characteristic

C₁₉×#124

C₂²

yes

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

C₂²

yes

—

#41×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

D₄

yes

—

C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₁₉⋊C₈

—

#1536

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#100

yes

—

#532

D₁₉

yes

characteristic

#432

—

#329

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

C₂×#100

yes

characteristic

C₂×C₁₉

#421

yes

—

C₂×#41

Dic₁₉

yes

—

C₄⋊Q₈

Dic₁₉

yes

characteristic

#127

Dic₁₉

yes

characteristic

#124

C₂×D₁₉

yes

—

#121

—

C₄×D₄

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₁₉

#1536

yes

characteristic, complemented, Sylow

#41

—

C₂×Q₈

C₂×Dic₁₉

yes

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

C₂×Dic₁₉

yes

—

C₂²×C₄

—

C₂²×C₄

C₂×Dic₁₉

yes

characteristic

C₂²×C₄

C₂²⋊D₁₉

yes

—

C₂×C₈

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

C₂×Dic₁₉

yes

characteristic

C₄²

C₂²⋊D₁₉

yes

—

C₄²

C₂²×D₁₉

yes

characteristic

C₂³

—

C₂³

C₂²⋊Dic₁₉

yes

characteristic

Q₈

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊Dic₁₉

yes

—

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

100

C₈

—

101

C₂²

—

102

C₂²

—

103

C₂²

—

104

C₂²

—

105

C₂²

C₂×C₂²⋊Dic₁₉

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

#10597290

yes

—

111

C₂

—

112

C₂

—

113

C₂

C₂×#10597290

yes

characteristic

114

C₂

#11926561

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊Dic₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#532	C₂
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
cosocle	C₄²×C₁₉	C₂³
hypercenter	#532	D₁₉
hypocenter	C₁₉	#1536
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #532

subgroup

G/H

center

C₂²

C₂×C₂²⋊Dic₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₄²

C₂²×D₁₉

Fitting, prime radical

C₁₉×#532

C₂

socle

C₂²×C₁₉

C₂×C₂²⋊C₄

cosocle

C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #532

N	H ≅ G/N	type
1. #11926601	C₂	semidirect
2. #11926284	C₂	semidirect
71. C₁₉	#1536	semidirect

H ≅ G/N

type

1. #11926601

C₂

semidirect

2. #11926284

C₂

semidirect

71. C₁₉

#1536

semidirect

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

subgroup	index
#11926601	2
#11926284	2
C₁₉×#532	2
#1536	19

subgroup

index

#11926601

#11926284

C₁₉×#532

#1536

Subgroups — #14562270

Conjugacy classes of subgroups

Complements

Maximal subgroups