Group #14565907 — subgroups

Subgroups — #14565907

Order 2432.

178 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 57 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×#10597286	C₂	1	2	yes	maximal, complemented
2	C₂×#10597284	C₂	1	2	yes	maximal
3	#11926924	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926320	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#495	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×SD₁₆×C₁₉	—	2	1	no	—
8	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#124	—	2	1	no	—
10	C₂×Dic₇₆	—	2	1	no	—
11	C₂×Dic₇₆	C₂²	1	2	yes	—
12	#10597315	—	2	1	no	—
13	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	#10597286	—	2	4	no	—
15	#10597284	—	2	4	no	—
16	C₂×C₁₉⋊C₁₆	C₂²	1	2	yes	—
17	C₂×Q₈×C₁₉	—	2	1	no	—
18	C₂×D₄×C₁₉	—	2	1	no	—
19	C₂×Dic₃₈	—	2	2	no	—
20	Q₁₆×C₁₉	—	2	2	no	—
21	SD₁₆×C₁₉	—	4	2	no	—
22	D₈×C₁₉	—	2	2	no	—
23	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
25	C₂²⋊C₄×C₁₉	—	4	2	no	—
26	C₄²×C₁₉	D₄	1	1	yes	characteristic
27	C₄⋊Dic₁₉	—	4	2	no	—
28	Dic₇₆	—	2	2	no	—
29	Dic₇₆	—	2	2	no	—
30	Dic₇₆	—	4	2	no	—
31	C₁₉⋊C₁₆	D₄	1	4	yes	—
32	C₂³×C₁₉	—	4	1	no	—
33	Q₈×C₁₉	—	4	1	no	—
34	Q₈×C₁₉	—	4	1	no	—
35	D₄×C₁₉	—	4	1	no	—
36	D₄×C₁₉	—	4	1	no	—
37	C₂×C₄×C₁₉	—	4	1	no	—
38	C₂×C₄×C₁₉	D₈	1	2	yes	—
39	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂×Dic₁₉	—	4	2	no	—
41	Dic₃₈	—	4	2	no	—
42	Dic₃₈	—	4	2	no	—
43	C₈×C₁₉	D₈	1	2	yes	—
44	C₈×C₁₉	C₂×D₄	1	2	yes	—
45	#2251	—	19	1	no	maximal, Sylow
46	C₂²×C₁₉	—	8	1	no	—
47	C₂²×C₁₉	—	8	2	no	—
48	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
49	C₄×C₁₉	—	2	2	no	—
50	C₄×C₁₉	—	8	1	no	—
51	C₄×C₁₉	#127	1	1	yes	characteristic
52	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
53	Dic₁₉	—	8	2	no	—
54	C₂×Q₃₂	—	19	2	no	—
55	C₂×SD₃₂	—	19	2	no	—
56	#495	D₁₉	1	1	yes	characteristic
57	#494	—	19	1	no	—
58	#346	—	19	1	no	—
59	C₂×C₁₉	—	16	1	no	—
60	C₂×C₁₉	#493	1	1	yes	characteristic
61	C₂×C₁₉	#510	1	2	yes	—
62	C₂×Q₁₆	—	19	2	no	—
63	C₂×Q₁₆	—	38	1	no	—
64	C₂×Q₁₆	C₂×D₁₉	1	1	yes	characteristic
65	C₂×SD₁₆	—	2	1	no	—
66	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic
67	C₄⋊Q₈	—	38	1	no	—
68	#124	—	2	1	no	—
69	Q₃₂	—	38	4	no	—
70	SD₃₂	—	38	4	no	—
71	C₂×C₁₆	—	19	2	no	—
72	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
73	C₁₉	#2251	1	1	yes	characteristic, complemented, Sylow
74	C₂×Q₈	—	2	1	no	—
75	C₂×Q₈	—	38	2	no	—
76	C₂×D₄	—	2	1	no	—
77	Q₁₆	—	2	2	no	—
78	Q₁₆	—	38	2	no	—
79	Q₁₆	—	38	2	no	—
80	Q₁₆	—	76	2	no	—
81	SD₁₆	—	4	2	no	—
82	D₈	—	2	2	no	—
83	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
84	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
85	C₄⋊C₄	—	76	2	no	—
86	C₂²⋊C₄	—	4	2	no	—
87	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
88	C₁₆	—	19	4	no	—
89	C₂³	—	4	1	no	—
90	Q₈	—	4	1	no	—
91	Q₈	—	4	1	no	—
92	Q₈	—	76	2	no	—
93	Q₈	—	76	2	no	—
94	D₄	—	4	1	no	—
95	D₄	—	4	1	no	—
96	C₂×C₄	—	4	1	no	—
97	C₂×C₄	—	76	2	no	—
98	C₂×C₄	#64525	1	2	yes	—
99	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
100	C₈	#64525	1	2	yes	—
101	C₈	D₄×D₁₉	1	2	yes	—
102	C₂²	—	8	1	no	—
103	C₂²	—	8	2	no	—
104	C₂²	C₂×#64525	1	1	yes	characteristic
105	C₄	—	2	2	no	—
106	C₄	—	8	1	no	—
107	C₄	—	152	2	no	—
108	C₄	C₂×#64525	1	1	yes	characteristic
109	C₄	#10597386	1	1	yes	characteristic
110	C₂	—	16	1	no	—
111	C₂	#11926920	1	1	yes	characteristic
112	C₂	#11926984	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597286

C₂

yes

maximal, complemented

C₂×#10597284

C₂

yes

maximal

#11926924

C₂

yes

maximal, characteristic, complemented

#11926320

C₂

yes

maximal, characteristic, complemented

C₁₉×#495

C₂

yes

maximal, characteristic

C₂×Q₁₆×C₁₉

C₂²

yes

characteristic

C₂×SD₁₆×C₁₉

—

C₂×D₈×C₁₉

C₂²

yes

characteristic

C₁₉×#124

—

C₂×Dic₇₆

—

C₂×Dic₇₆

C₂²

yes

—

#10597315

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597286

—

#10597284

—

C₂×C₁₉⋊C₁₆

C₂²

yes

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×Dic₃₈

—

Q₁₆×C₁₉

—

SD₁₆×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₄⋊Dic₁₉

—

Dic₇₆

—

Dic₇₆

—

Dic₇₆

—

C₁₉⋊C₁₆

D₄

yes

—

C₂³×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₈

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

D₈

yes

—

C₈×C₁₉

C₂×D₄

yes

—

#2251

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#127

yes

characteristic

C₄×C₁₉

C₂×D₈

yes

characteristic

Dic₁₉

—

C₂×Q₃₂

—

C₂×SD₃₂

—

#495

D₁₉

yes

characteristic

#494

—

#346

—

C₂×C₁₉

—

C₂×C₁₉

#493

yes

characteristic

C₂×C₁₉

#510

yes

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₁₉

yes

characteristic

C₂×SD₁₆

—

C₂×D₈

C₂×D₁₉

yes

characteristic

C₄⋊Q₈

—

#124

—

Q₃₂

—

SD₃₂

—

C₂×C₁₆

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#2251

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

SD₁₆

—

D₈

—

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

C₂²⋊D₁₉

yes

characteristic

C₁₆

—

C₂³

—

Q₈

—

Q₈

—

Q₈

—

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#64525

yes

—

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

100

C₈

#64525

yes

—

101

C₈

D₄×D₁₉

yes

—

102

C₂²

—

103

C₂²

—

104

C₂²

C₂×#64525

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

—

152

—

108

C₄

C₂×#64525

yes

characteristic

109

C₄

#10597386

yes

characteristic

110

C₂

—

111

C₂

#11926920

yes

characteristic

112

C₂

#11926984

yes

—

	subgroup	G/H
center	C₂²	C₂×#64525
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#495	C₂
socle	C₂²×C₁₉	C₂×D₈
prime radical	C₂×D₈×C₁₉	C₂²
hypercenter	#495	D₁₉
hypocenter	C₁₉	#2251
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #495

subgroup

G/H

center

C₂²

C₂×#64525

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₁₉×#495

C₂

socle

C₂²×C₁₉

C₂×D₈

prime radical

C₂×D₈×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #495

N	H ≅ G/N	type
1. C₂×#10597286	C₂	semidirect
3. #11926924	C₂	semidirect
4. #11926320	C₂	semidirect
73. C₁₉	#2251	semidirect

H ≅ G/N

type

1. C₂×#10597286

C₂

semidirect

3. #11926924

C₂

semidirect

4. #11926320

C₂

semidirect

73. C₁₉

#2251

semidirect

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

subgroup	index
C₂×#10597286	2
C₂×#10597284	2
#11926924	2
#11926320	2
C₁₉×#495	2
#2251	19

subgroup

index

C₁₉×#495

Subgroups — #14565907

Conjugacy classes of subgroups

Complements

Maximal subgroups