Group #14565652 — subgroups

Subgroups — #14565652

Order 2432.

248 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 45 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	#11926716	C₂	1	3	yes	maximal, complemented
2	#11926341	C₂	1	3	yes	maximal, complemented
3	C₁₉×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic, complemented
4	#10597433	C₂²	1	1	yes	characteristic, complemented
5	C₁₉×#124	—	2	3	no	—
6	C₁₉×#124	C₂²	1	3	yes	—
7	C₁₉×#120	—	2	3	no	—
8	#10597378	—	2	3	no	—
9	#10597293	C₂²	1	3	yes	complemented
10	#10597262	—	2	3	no	—
11	C₂⁴×C₁₉	—	2	1	no	—
12	C₂×Q₈×C₁₉	—	2	1	no	—
13	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
14	C₂×D₄×C₁₉	—	2	3	no	—
15	C₂×D₄×C₁₉	D₄	1	3	yes	—
16	#64545	—	4	1	no	—
17	Q₈×D₁₉	—	4	1	no	—
18	#64541	—	2	3	no	—
19	C₂²⋊C₄×C₁₉	—	2	3	no	—
20	C₂²⋊C₄×C₁₉	—	2	6	no	—
21	C₄²×C₁₉	D₄	1	3	yes	—
22	#64526	—	4	3	no	—
23	#64525	—	4	3	no	—
24	#64520	—	2	3	no	—
25	C₂³×C₁₉	—	2	3	no	—
26	C₂³×C₁₉	—	8	2	no	—
27	C₂³×C₁₉	—	8	1	no	—
28	Q₈×C₁₉	—	4	1	no	—
29	Q₈×C₁₉	—	8	1	no	—
30	D₄×C₁₉	—	4	3	no	—
31	D₄×C₁₉	—	8	3	no	—
32	C₂×C₄×C₁₉	—	2	3	no	—
33	C₂×C₄×C₁₉	C₂×D₄	1	3	yes	—
34	C₂²⋊D₁₉	—	4	1	no	—
35	D₇₆	—	2	3	no	—
36	C₄×D₁₉	—	4	3	no	—
37	Dic₃₈	—	2	3	no	—
38	C₁₉⋊C₈	—	4	3	no	—
39	#2202	—	19	1	no	maximal, Sylow
40	C₂²×C₁₉	—	4	6	no	—
41	C₂²×C₁₉	—	4	3	no	—
42	C₂²×C₁₉	—	8	4	no	—
43	C₂²×C₁₉	#120	1	1	yes	characteristic
44	C₂×D₁₉	—	4	1	no	—
45	C₄×C₁₉	—	2	3	no	—
46	C₄×C₁₉	—	4	3	no	—
47	Dic₁₉	—	4	1	no	—
48	H(3,𝔽₄)	D₁₉	1	1	yes	characteristic, complemented
49	#454	—	19	3	no	—
50	#355	—	19	3	no	—
51	C₂×C₁₉	—	2	1	no	—
52	C₂×C₁₉	—	8	3	no	—
53	C₂×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
54	D₁₉	—	8	1	no	—
55	2₋¹⁺⁴	—	19	1	no	—
56	AGL(1,ℤ/8)	—	38	3	no	—
57	#124	—	2	3	no	—
58	#124	C₂×D₁₉	1	3	yes	—
59	#120	—	2	3	no	—
60	#104	—	38	3	no	—
61	#101	—	19	3	no	—
62	C₁₉	#2202	1	1	yes	characteristic, complemented, Sylow
63	C₂⁴	—	2	1	no	—
64	#41	—	38	3	no	—
65	#41	—	76	1	no	—
66	C₂×Q₈	—	2	1	no	—
67	C₂×Q₈	—	76	1	no	—
68	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
69	C₂×D₄	—	2	3	no	—
70	C₂×D₄	C₂²⋊D₁₉	1	3	yes	—
71	SD₁₆	—	76	3	no	—
72	D₈	—	76	3	no	—
73	M₁₆	—	38	3	no	—
74	C₂²⋊C₄	—	2	3	no	—
75	C₂²⋊C₄	—	2	6	no	—
76	C₄²	C₂²⋊D₁₉	1	3	yes	—
77	C₂³	—	2	3	no	—
78	C₂³	—	8	2	no	—
79	C₂³	—	8	1	no	—
80	Q₈	—	4	1	no	—
81	Q₈	—	8	1	no	—
82	Q₈	—	38	3	no	—
83	D₄	—	4	3	no	—
84	D₄	—	8	3	no	—
85	D₄	—	38	3	no	—
86	D₄	—	76	1	no	—
87	C₂×C₄	—	2	3	no	—
88	C₂×C₄	—	76	3	no	—
89	C₂×C₄	C₂×C₂²⋊D₁₉	1	3	yes	—
90	C₈	—	76	3	no	—
91	C₂²	—	4	6	no	—
92	C₂²	—	4	3	no	—
93	C₂²	—	8	4	no	—
94	C₂²	—	76	1	no	—
95	C₂²	#10597399	1	1	yes	characteristic
96	C₄	—	2	3	no	—
97	C₄	—	4	3	no	—
98	C₄	—	76	1	no	—
99	C₂	—	2	1	no	—
100	C₂	—	8	3	no	—
101	C₂	—	152	1	no	—
102	C₂	#11926731	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926716

C₂

yes

maximal, complemented

#11926341

C₂

yes

maximal, complemented

C₁₉×H(3,𝔽₄)

C₂

yes

maximal, characteristic, complemented

#10597433

C₂²

yes

characteristic, complemented

C₁₉×#124

—

C₁₉×#124

C₂²

yes

—

C₁₉×#120

—

#10597378

—

#10597293

C₂²

yes

complemented

#10597262

—

C₂⁴×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂³

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

D₄

yes

—

#64545

—

Q₈×D₁₉

—

#64541

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

—

#64526

—

#64525

—

#64520

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂²⋊D₁₉

—

D₇₆

—

C₄×D₁₉

—

Dic₃₈

—

C₁₉⋊C₈

—

#2202

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#120

yes

characteristic

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

H(3,𝔽₄)

D₁₉

yes

characteristic, complemented

#454

—

#355

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

B(4,𝔽₂)

yes

characteristic

D₁₉

—

2₋¹⁺⁴

—

AGL(1,ℤ/8)

—

#124

—

#124

C₂×D₁₉

yes

—

#120

—

#104

—

#101

—

C₁₉

#2202

yes

characteristic, complemented, Sylow

C₂⁴

—

#41

—

#41

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂²×D₁₉

yes

characteristic

C₂×D₄

—

C₂×D₄

C₂²⋊D₁₉

yes

—

SD₁₆

—

D₈

—

M₁₆

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

C₂²⋊D₁₉

yes

—

C₂³

—

C₂³

—

C₂³

—

Q₈

—

Q₈

—

Q₈

—

D₄

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

C₈

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

#10597399

yes

characteristic

C₄

—

C₄

—

C₄

—

C₂

—

100

C₂

—

101

C₂

—

152

—

102

C₂

#11926731

yes

characteristic

	subgroup	G/H
center	C₂	#11926731
commutator, cosocle	C₂×Q₈×C₁₉	C₂³
Frattini	C₂×Q₈	C₂²×D₁₉
Fitting	C₁₉×H(3,𝔽₄)	C₂
socle	C₂×C₁₉	B(4,𝔽₂)
hypercenter	H(3,𝔽₄)	D₁₉
hypocenter	C₁₉	#2202
LCS	G ▷ C₂×Q₈×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×Q₈ ◁ H(3,𝔽₄)

subgroup

G/H

center

C₂

#11926731

commutator, cosocle

C₂×Q₈×C₁₉

C₂³

Frattini

C₂×Q₈

C₂²×D₁₉

Fitting

C₁₉×H(3,𝔽₄)

C₂

C₂×C₁₉

D₁₉

C₁₉

G ▷ C₂×Q₈×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×Q₈ ◁ H(3,𝔽₄)

N	H ≅ G/N	type
1. #11926716	C₂	semidirect
2. #11926341	C₂	semidirect
3. C₁₉×H(3,𝔽₄)	C₂	semidirect
4. #10597433	C₂²	semidirect
9. #10597293	C₂²	semidirect
48. H(3,𝔽₄)	D₁₉	semidirect
62. C₁₉	#2202	semidirect

H ≅ G/N

type

1. #11926716

C₂

semidirect

2. #11926341

C₂

semidirect

3. C₁₉×H(3,𝔽₄)

C₂

semidirect

4. #10597433

C₂²

semidirect

9. #10597293

C₂²

semidirect

48. H(3,𝔽₄)

D₁₉

semidirect

62. C₁₉

#2202

semidirect

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

subgroup	index
#11926716	2
#11926341	2
C₁₉×H(3,𝔽₄)	2
#2202	19

subgroup

index

#11926716

#11926341

C₁₉×H(3,𝔽₄)

#2202

Subgroups — #14565652

Conjugacy classes of subgroups

Complements

Maximal subgroups