Group #14561678 — subgroups

Subgroups — #14561678

Order 2432.

102 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 102 conjugacy classes of subgroups — too many to draw. Only its 41 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	C₄⋊(C₁₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926295	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#495	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆×C₁₉	C₄	1	1	yes	characteristic
5	C₂×SD₁₆×C₁₉	—	2	1	no	—
6	C₂×D₈×C₁₉	C₄	1	1	yes	characteristic
7	C₁₉×#124	—	2	1	no	—
8	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₁₉⋊C₁₆	—	2	1	no	—
10	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
11	C₂×Q₈×C₁₉	—	2	1	no	—
12	C₂×D₄×C₁₉	—	2	1	no	—
13	Q₁₆×C₁₉	—	4	1	no	—
14	SD₁₆×C₁₉	—	4	1	no	—
15	SD₁₆×C₁₉	—	4	1	no	—
16	D₈×C₁₉	—	4	1	no	—
17	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
19	C₂²⋊C₄×C₁₉	—	4	1	no	—
20	C₂²⋊C₄×C₁₉	—	4	1	no	—
21	C₄²×C₁₉	D₄	1	1	yes	characteristic
22	C₂×C₁₉⋊C₈	—	4	1	no	—
23	C₁₉⋊C₁₆	—	4	1	no	—
24	C₂³×C₁₉	—	4	1	no	—
25	Q₈×C₁₉	—	4	1	no	—
26	Q₈×C₁₉	—	4	1	no	—
27	D₄×C₁₉	—	4	1	no	—
28	D₄×C₁₉	—	4	1	no	—
29	C₂×C₄×C₁₉	—	4	1	no	—
30	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
32	C₂×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
33	C₈×C₁₉	—	2	1	no	—
34	C₈×C₁₉	D₈	1	1	yes	characteristic
35	C₈×C₁₉	SD₁₆	1	1	yes	characteristic
36	C₁₉⋊C₈	—	8	1	no	—
37	#1360	—	19	1	no	maximal, Sylow
38	C₂²×C₁₉	—	8	1	no	—
39	C₂²×C₁₉	—	8	1	no	—
40	C₂²×C₁₉	—	8	1	no	—
41	C₂²×C₁₉	#102	1	1	yes	characteristic
42	C₄×C₁₉	—	2	1	no	—
43	C₄×C₁₉	—	2	1	no	—
44	C₄×C₁₉	—	8	1	no	—
45	C₄×C₁₉	#100	1	1	yes	characteristic
46	C₄×C₁₉	#102	1	1	yes	characteristic
47	#495	D₁₉	1	1	yes	characteristic
48	C₄⋊C₁₆	—	19	1	no	—
49	#334	—	19	1	no	—
50	C₂×C₁₉	—	16	1	no	—
51	C₂×C₁₉	#331	1	1	yes	characteristic
52	C₂×C₁₉	#359	1	1	yes	characteristic
53	C₂×C₁₉	#360	1	1	yes	characteristic
54	C₂×Q₁₆	Dic₁₉	1	1	yes	characteristic
55	C₂×SD₁₆	—	2	1	no	—
56	C₂×D₈	Dic₁₉	1	1	yes	characteristic
57	#124	—	2	1	no	—
58	C₂×C₁₆	—	38	1	no	—
59	C₄⋊C₈	—	38	1	no	—
60	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
61	C₁₉	#1360	1	1	yes	characteristic, complemented, Sylow
62	C₂×Q₈	—	2	1	no	—
63	C₂×D₄	—	2	1	no	—
64	Q₁₆	—	4	1	no	—
65	SD₁₆	—	4	1	no	—
66	SD₁₆	—	4	1	no	—
67	D₈	—	4	1	no	—
68	C₂×C₈	—	76	1	no	—
69	C₂×C₈	C₂×Dic₁₉	1	1	yes	characteristic
70	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
71	C₂²⋊C₄	—	4	1	no	—
72	C₂²⋊C₄	—	4	1	no	—
73	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
74	C₁₆	—	76	1	no	—
75	C₂³	—	4	1	no	—
76	Q₈	—	4	1	no	—
77	Q₈	—	4	1	no	—
78	D₄	—	4	1	no	—
79	D₄	—	4	1	no	—
80	C₂×C₄	—	4	1	no	—
81	C₂×C₄	#64525	1	1	yes	characteristic
82	C₂×C₄	#64526	1	1	yes	characteristic
83	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
84	C₈	—	2	1	no	—
85	C₈	—	152	1	no	—
86	C₈	#64525	1	1	yes	characteristic
87	C₈	#64526	1	1	yes	characteristic
88	C₂²	—	8	1	no	—
89	C₂²	—	8	1	no	—
90	C₂²	—	8	1	no	—
91	C₂²	#10597289	1	1	yes	characteristic
92	C₄	—	2	1	no	—
93	C₄	—	2	1	no	—
94	C₄	—	8	1	no	—
95	C₄	#10597289	1	1	yes	characteristic
96	C₄	#10597290	1	1	yes	characteristic
97	C₂	—	16	1	no	—
98	C₂	#11926288	1	1	yes	characteristic
99	C₂	#11926351	1	1	yes	characteristic
100	C₂	#11926354	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊(C₁₉⋊C₁₆)

C₂

yes

maximal, characteristic, complemented

#11926295

C₂

yes

maximal, characteristic, complemented

C₁₉×#495

C₂

yes

maximal, characteristic

C₂×Q₁₆×C₁₉

C₄

yes

characteristic

C₂×SD₁₆×C₁₉

—

C₂×D₈×C₁₉

C₄

yes

characteristic

C₁₉×#124

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₁₉⋊C₁₆

—

C₄⋊(C₁₉⋊C₈)

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

Q₁₆×C₁₉

—

SD₁₆×C₁₉

—

SD₁₆×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₂×C₁₉⋊C₈

—

C₁₉⋊C₁₆

—

C₂³×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

SD₁₆

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

D₈

yes

characteristic

C₈×C₁₉

SD₁₆

yes

characteristic

C₁₉⋊C₈

—

#1360

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#102

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

D₁₉

yes

characteristic

C₄⋊C₁₆

—

#334

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

Dic₁₉

yes

characteristic

C₂×SD₁₆

—

C₂×D₈

Dic₁₉

yes

characteristic

#124

—

C₂×C₁₆

—

C₄⋊C₈

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#1360

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

Q₁₆

—

SD₁₆

—

SD₁₆

—

D₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₁₉

yes

characteristic

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

C₂²⋊D₁₉

yes

characteristic

C₁₆

—

C₂³

—

Q₈

—

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

C₈

—

C₈

—

152

—

C₈

yes

C₈

yes

C₂²

—

C₂²

—

C₂²

—

C₂²

#10597289

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

yes

C₄

yes

C₂

—

C₂

yes

C₂

yes

100

C₂

#11926354

yes

characteristic

	subgroup	G/H
center	C₂²	#10597289
commutator	C₂×C₈×C₁₉	C₂×C₄
Frattini	C₄×C₈	C₂×D₁₉
Fitting	C₁₉×#495	C₂
socle	C₂²×C₁₉	#102
prime radical	C₂×D₈×C₁₉	C₄
cosocle	C₄×C₈×C₁₉	C₂²
hypercenter	#495	D₁₉
hypocenter	C₁₉	#1360
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #495

subgroup

G/H

center

C₂²

#10597289

commutator

C₂×C₈×C₁₉

C₂×C₄

Frattini

C₄×C₈

C₂×D₁₉

Fitting

C₁₉×#495

C₂

socle

C₂²×C₁₉

#102

prime radical

C₂×D₈×C₁₉

C₄

cosocle

C₄×C₈×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #495

N	H ≅ G/N	type
1. C₄⋊(C₁₉⋊C₁₆)	C₂	semidirect
2. #11926295	C₂	semidirect
61. C₁₉	#1360	semidirect

H ≅ G/N

type

1. C₄⋊(C₁₉⋊C₁₆)

C₂

semidirect

2. #11926295

C₂

semidirect

61. C₁₉

#1360

semidirect

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

subgroup	index
C₄⋊(C₁₉⋊C₁₆)	2
#11926295	2
C₁₉×#495	2
#1360	19

subgroup

index

C₄⋊(C₁₉⋊C₁₆)

#11926295

C₁₉×#495

#1360

Subgroups — #14561678

Conjugacy classes of subgroups

Complements

Maximal subgroups