Group #14571904 — subgroups

Subgroups — #14571904

Order 2432.

348 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 133 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	#11926483	C₂	1	3	yes	maximal
2	#11926477	C₂	1	6	yes	maximal
3	#11926464	C₂	1	3	yes	maximal
4	#11926412	C₂	1	2	yes	maximal
5	C₁₉×#384	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
8	C₂×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
9	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₁₉	C₂²	1	3	yes	—
11	C₂×Dic₁₉⋊C₄	C₂²	1	6	yes	—
12	C₁₉⋊#95	C₂²	1	6	yes	—
13	C₁₉⋊#95	C₂²	1	6	yes	—
14	C₁₉⋊#95	C₂²	1	3	yes	—
15	C₁₉⋊#95	C₂²	1	3	yes	—
16	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
17	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
18	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
19	C₂²×Dic₁₉	C₂³	1	2	yes	—
20	C₂²×Dic₁₉	C₂³	1	6	yes	—
21	C₂×Dic₃₈	—	4	3	no	—
22	C₄⋊C₄×C₁₉	—	4	3	no	—
23	C₄⋊C₄×C₁₉	—	4	3	no	—
24	C₄²×C₁₉	Q₈	1	4	yes	complemented
25	C₄⋊Dic₁₉	—	4	3	no	—
26	Dic₁₉⋊C₄	—	4	6	no	—
27	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
28	C₂×C₄×C₁₉	—	2	3	no	—
29	C₂×C₄×C₁₉	—	2	3	no	—
30	C₂×C₄×C₁₉	—	2	6	no	—
31	C₂×C₄×C₁₉	—	2	3	no	—
32	C₂×C₄×C₁₉	—	2	3	no	—
33	C₂×C₄×C₁₉	C₂×Q₈	1	6	yes	—
34	C₂×Dic₁₉	—	2	6	no	—
35	C₂×Dic₁₉	—	2	6	no	—
36	C₂×Dic₁₉	—	2	12	no	—
37	Dic₃₈	—	4	4	no	—
38	#2843	—	19	1	no	maximal, Sylow
39	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
40	C₂²×C₁₉	H(5,𝔽₂)	1	3	yes	—
41	C₂²×C₁₉	2₋¹⁺⁴	1	3	yes	—
42	C₄×C₁₉	—	2	6	no	—
43	C₄×C₁₉	—	4	1	no	—
44	C₄×C₁₉	—	4	3	no	—
45	Dic₁₉	—	4	2	no	—
46	Dic₁₉	—	4	6	no	—
47	#400	—	19	3	no	—
48	#398	—	19	6	no	—
49	#395	—	19	3	no	—
50	#384	D₁₉	1	1	yes	characteristic
51	#383	—	19	2	no	—
52	C₂×C₁₉	#544	1	3	yes	—
53	C₂×C₁₉	#560	1	1	yes	characteristic
54	C₂×C₁₉	#563	1	3	yes	—
55	C₂²×Q₈	—	19	1	no	—
56	C₂×C₄⋊C₄	—	19	6	no	—
57	C₂×C₄⋊C₄	—	19	3	no	—
58	C₂×C₄⋊C₄	C₂×D₁₉	1	3	yes	—
59	C₂×C₄⋊C₄	C₂×D₁₉	1	3	yes	—
60	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
61	#95	—	19	6	no	—
62	#95	—	19	6	no	—
63	#95	—	19	3	no	—
64	#95	—	19	3	no	—
65	C₁₉	#2843	1	1	yes	characteristic, complemented, Sylow
66	C₂×Q₈	—	76	3	no	—
67	C₂²×C₄	—	19	6	no	—
68	C₂²×C₄	—	19	2	no	—
69	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
70	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
71	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
72	C₄⋊C₄	—	4	3	no	—
73	C₄⋊C₄	—	4	3	no	—
74	C₄⋊C₄	—	76	6	no	—
75	C₄⋊C₄	—	76	3	no	—
76	C₄²	Dic₃₈	1	4	yes	complemented
77	C₂³	C₂³×D₁₉	1	1	yes	characteristic
78	Q₈	—	76	4	no	—
79	C₂×C₄	—	2	3	no	—
80	C₂×C₄	—	2	3	no	—
81	C₂×C₄	—	2	6	no	—
82	C₂×C₄	—	2	3	no	—
83	C₂×C₄	—	2	3	no	—
84	C₂×C₄	—	38	6	no	—
85	C₂×C₄	—	38	6	no	—
86	C₂×C₄	—	38	12	no	—
87	C₂×C₄	C₂×Dic₃₈	1	6	yes	—
88	C₂²	C₂²×Dic₃₈	1	1	yes	characteristic
89	C₂²	#10597430	1	3	yes	—
90	C₂²	#10597433	1	3	yes	—
91	C₄	—	2	6	no	—
92	C₄	—	4	1	no	—
93	C₄	—	4	3	no	—
94	C₄	—	76	2	no	—
95	C₄	—	76	6	no	—
96	C₂	#11927175	1	3	yes	—
97	C₂	#11927281	1	1	yes	characteristic
98	C₂	#11927293	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11926483

C₂

yes

maximal

#11926477

C₂

yes

maximal

#11926464

C₂

yes

maximal

#11926412

C₂

yes

maximal

C₁₉×#384

C₂

yes

maximal, characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×Dic₃₈

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

Q₈

yes

complemented

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

#2843

—

maximal, Sylow

C₂²×C₁₉

C₂²×Q₈

yes

characteristic

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

D₁₉

yes

characteristic

#383

—

C₂×C₁₉

#544

yes

—

C₂×C₁₉

#560

yes

characteristic

C₂×C₁₉

#563

yes

—

C₂²×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

C₂×D₁₉

yes

—

—

—

—

C₁₉

#2843

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

Dic₃₈

yes

complemented

C₂³

C₂³×D₁₉

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×Dic₃₈

yes

—

C₂²

C₂²×Dic₃₈

yes

characteristic

C₂²

#10597430

yes

—

C₂²

#10597433

yes

—

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

C₂

#11927175

yes

—

C₂

#11927281

yes

characteristic

C₂

#11927293

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, prime radical, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#384	C₂
hypercenter	#384	D₁₉
hypocenter	C₁₉	#2843
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #384

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, prime radical, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₁₉×#384

C₂

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #384

N	H ≅ G/N	type
24. C₄²×C₁₉	Q₈	semidirect
65. C₁₉	#2843	semidirect
76. C₄²	Dic₃₈	semidirect

H ≅ G/N

type

24. C₄²×C₁₉

Q₈

semidirect

65. C₁₉

#2843

semidirect

76. C₄²

Dic₃₈

semidirect

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

subgroup	index
#11926483	2
#11926477	2
#11926464	2
#11926412	2
C₁₉×#384	2
#2843	19

subgroup

index

C₁₉×#384

Subgroups — #14571904

Conjugacy classes of subgroups

Complements

Maximal subgroups