Group #14565883 — subgroups

Subgroups — #14565883

Order 2432.

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

normal subgroups only

This group has 216 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×D₃₀₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597283	C₂	1	2	yes	maximal, complemented
3	#11926919	C₂	1	2	yes	maximal, complemented
4	C₁₆×Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₈×C₁₉	C₂²	1	2	yes	—
7	#10597386	—	2	2	no	—
8	C₂×#64525	—	2	2	no	—
9	C₂×D₁₅₂	C₂²	1	2	yes	—
10	C₁₉×D₁₆	—	2	2	no	—
11	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	#10597283	—	2	4	no	—
13	C₈×Dic₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉⋊C₁₆	C₂²	1	1	yes	characteristic
15	D₃₀₄	—	2	2	no	—
16	C₂×D₄×C₁₉	—	2	2	no	—
17	C₂×C₂²⋊D₁₉	—	4	4	no	—
18	C₂×D₇₆	—	2	2	no	—
19	D₈×C₁₉	—	2	2	no	—
20	D₈×C₁₉	—	2	2	no	—
21	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
22	#64525	—	4	4	no	—
23	C₄×Dic₁₉	D₄	1	1	yes	characteristic
24	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
25	D₁₅₂	—	2	2	no	—
26	D₁₅₂	—	2	2	no	—
27	C₁₆×C₁₉	D₄	1	2	yes	complemented
28	C₁₉⋊C₁₆	D₄	1	2	yes	complemented
29	C₂³×C₁₉	—	4	2	no	—
30	C₂²×D₁₉	—	4	2	no	—
31	D₄×C₁₉	—	4	2	no	—
32	D₄×C₁₉	—	4	2	no	—
33	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₂²⋊D₁₉	—	8	8	no	—
35	C₂×Dic₁₉	D₈	1	2	yes	—
36	D₇₆	—	4	2	no	—
37	D₇₆	—	4	2	no	—
38	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₁₉⋊C₈	D₈	1	2	yes	—
41	#2246	—	19	1	no	maximal, Sylow
42	C₂²×C₁₉	—	8	2	no	—
43	C₂²×C₁₉	—	8	4	no	—
44	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
45	C₂×D₁₉	—	8	2	no	—
46	C₂×D₁₉	—	8	4	no	—
47	C₄×C₁₉	#127	1	1	yes	characteristic
48	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
49	Dic₁₉	D₁₆	1	4	yes	complemented
50	C₂×D₁₆	—	19	2	no	—
51	C₂×D₁₆	—	19	1	no	—
52	C₂×D₁₆	D₁₉	1	1	yes	characteristic, complemented
53	#493	—	19	2	no	—
54	C₄×C₁₆	—	19	1	no	—
55	C₂×C₁₉	—	16	2	no	—
56	C₂×C₁₉	#493	1	1	yes	characteristic
57	C₂×C₁₉	C₂×D₁₆	1	2	yes	—
58	D₁₉	—	16	2	no	—
59	C₂×D₈	—	19	2	no	—
60	C₂×D₈	—	38	2	no	—
61	C₂×D₈	C₂×D₁₉	1	2	yes	—
62	#127	—	38	2	no	—
63	D₁₆	—	2	2	no	—
64	D₁₆	—	38	4	no	—
65	D₁₆	—	38	2	no	—
66	C₂×C₁₆	—	19	1	no	—
67	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
68	C₄×C₈	—	19	1	no	—
69	C₁₉	#2246	1	1	yes	characteristic, complemented, Sylow
70	C₂×D₄	—	2	2	no	—
71	C₂×D₄	—	38	2	no	—
72	C₂×D₄	—	76	4	no	—
73	D₈	—	2	2	no	—
74	D₈	—	2	2	no	—
75	D₈	—	38	2	no	—
76	D₈	—	38	2	no	—
77	D₈	—	76	4	no	—
78	C₂×C₈	—	19	1	no	—
79	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
80	C₄²	—	19	1	no	—
81	C₁₆	—	19	2	no	—
82	C₁₆	C₂²⋊D₁₉	1	2	yes	complemented
83	C₂³	—	4	2	no	—
84	C₂³	—	76	2	no	—
85	D₄	—	4	2	no	—
86	D₄	—	4	2	no	—
87	D₄	—	76	2	no	—
88	D₄	—	76	2	no	—
89	D₄	—	152	8	no	—
90	C₂×C₄	—	19	2	no	—
91	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
92	C₈	—	19	2	no	—
93	C₈	D₄×D₁₉	1	1	yes	characteristic
94	C₈	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
95	C₂²	—	8	2	no	—
96	C₂²	—	8	4	no	—
97	C₂²	—	152	2	no	—
98	C₂²	—	152	4	no	—
99	C₂²	D₈×D₁₉	1	1	yes	characteristic
100	C₄	—	19	4	no	—
101	C₄	D₈×D₁₉	1	1	yes	characteristic
102	C₄	#10597386	1	1	yes	characteristic
103	C₂	—	16	2	no	—
104	C₂	—	304	2	no	—
105	C₂	#11926919	1	1	yes	characteristic
106	C₂	D₁₆×D₁₉	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₃₀₄

C₂

yes

maximal, characteristic, complemented

C₂×#10597283

C₂

yes

maximal, complemented

#11926919

C₂

yes

maximal, complemented

C₁₆×Dic₁₉

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×D₁₆

C₂

yes

maximal, characteristic, complemented

C₂×D₈×C₁₉

C₂²

yes

—

#10597386

—

C₂×#64525

—

C₂×D₁₅₂

C₂²

yes

—

C₁₉×D₁₆

—

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

#10597283

—

C₈×Dic₁₉

C₂²

yes

characteristic

C₂×C₁₉⋊C₁₆

C₂²

yes

characteristic

D₃₀₄

—

C₂×D₄×C₁₉

—

C₂×C₂²⋊D₁₉

—

C₂×D₇₆

—

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

characteristic

#64525

—

C₄×Dic₁₉

D₄

yes

characteristic

C₂×C₁₉⋊C₈

D₄

yes

characteristic

D₁₅₂

—

D₁₅₂

—

C₁₆×C₁₉

D₄

yes

complemented

C₁₉⋊C₁₆

D₄

yes

complemented

C₂³×C₁₉

—

C₂²×D₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

D₈

yes

—

D₇₆

—

D₇₆

—

C₈×C₁₉

C₂×D₄

yes

characteristic

C₈×C₁₉

C₂×D₄

yes

characteristic

C₁₉⋊C₈

D₈

yes

—

#2246

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

#127

yes

characteristic

C₄×C₁₉

C₂×D₈

yes

characteristic

Dic₁₉

D₁₆

yes

complemented

C₂×D₁₆

—

C₂×D₁₆

—

C₂×D₁₆

D₁₉

yes

characteristic, complemented

#493

—

C₄×C₁₆

—

C₂×C₁₉

—

C₂×C₁₉

#493

yes

characteristic

C₂×C₁₉

C₂×D₁₆

yes

—

D₁₉

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

C₂×D₁₉

yes

—

#127

—

D₁₆

—

D₁₆

—

D₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₁₉

yes

characteristic

C₄×C₈

—

C₁₉

#2246

yes

characteristic, complemented, Sylow

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

D₈

—

D₈

—

D₈

—

D₈

—

D₈

—

C₂×C₈

—

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄²

—

C₁₆

—

C₁₆

C₂²⋊D₁₉

yes

complemented

C₂³

—

C₂³

—

D₄

—

D₄

—

D₄

—

D₄

—

D₄

—

152

—

C₂×C₄

—

C₂×C₄

D₄×D₁₉

yes

characteristic

C₈

—

C₈

D₄×D₁₉

yes

characteristic

C₈

C₂×C₂²⋊D₁₉

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

152

—

C₂²

—

152

—

C₂²

D₈×D₁₉

yes

characteristic

100

C₄

—

101

C₄

D₈×D₁₉

yes

characteristic

102

C₄

#10597386

yes

characteristic

103

C₂

—

104

C₂

—

304

—

105

C₂

#11926919

yes

characteristic

106

C₂

D₁₆×D₁₉

yes

—

	subgroup	G/H
center	C₂²	D₈×D₁₉
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₂×C₁₉×D₁₆	C₂
socle	C₂²×C₁₉	C₂×D₈
hypercenter	C₂×D₁₆	D₁₉
hypocenter	C₁₉	#2246
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

subgroup

G/H

center

C₂²

D₈×D₁₉

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₂×C₁₉×D₁₆

C₂

socle

C₂²×C₁₉

C₂×D₈

hypercenter

C₂×D₁₆

D₁₉

hypocenter

C₁₉

#2246

LCS

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

N	H ≅ G/N	type
1. C₂×D₃₀₄	C₂	semidirect
2. C₂×#10597283	C₂	semidirect
3. #11926919	C₂	semidirect
4. C₁₆×Dic₁₉	C₂	semidirect
5. C₂×C₁₉×D₁₆	C₂	semidirect
27. C₁₆×C₁₉	D₄	semidirect
28. C₁₉⋊C₁₆	D₄	semidirect
49. Dic₁₉	D₁₆	semidirect
52. C₂×D₁₆	D₁₉	semidirect
69. C₁₉	#2246	semidirect
82. C₁₆	C₂²⋊D₁₉	semidirect

H ≅ G/N

type

1. C₂×D₃₀₄

C₂

semidirect

2. C₂×#10597283

C₂

semidirect

3. #11926919

C₂

semidirect

4. C₁₆×Dic₁₉

C₂

semidirect

5. C₂×C₁₉×D₁₆

C₂

semidirect

27. C₁₆×C₁₉

D₄

semidirect

28. C₁₉⋊C₁₆

D₄

semidirect

49. Dic₁₉

D₁₆

semidirect

52. C₂×D₁₆

D₁₉

semidirect

69. C₁₉

#2246

semidirect

82. C₁₆

C₂²⋊D₁₉

semidirect

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

subgroup	index
C₂×D₃₀₄	2
C₂×#10597283	2
#11926919	2
C₁₆×Dic₁₉	2
C₂×C₁₉×D₁₆	2
#2246	19

subgroup

index

C₂×D₃₀₄

C₂×#10597283

#11926919

C₁₆×Dic₁₉

C₂×C₁₉×D₁₆

#2246

Subgroups — #14565883

Conjugacy classes of subgroups

Complements

Maximal subgroups