Group #14565893 — subgroups

Subgroups — #14565893

Order 2432.

184 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 53 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×Dic₁₅₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597284	C₂	1	2	yes	maximal, complemented
3	#11926927	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
6	C₂×D₈×C₁₉	C₂²	1	2	yes	—
7	#10597382	—	2	2	no	—
8	C₂×#64526	—	2	2	no	—
9	C₂×Dic₇₆	C₂²	1	2	yes	—
10	C₁₉×D₁₆	—	2	2	no	—
11	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	#10597284	—	2	4	no	—
13	C₈×Dic₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉⋊C₁₆	C₂²	1	1	yes	characteristic
15	Dic₁₅₂	—	2	2	no	—
16	C₂×D₄×C₁₉	—	2	2	no	—
17	C₂×Dic₃₈	—	2	2	no	—
18	D₈×C₁₉	—	2	2	no	—
19	D₈×C₁₉	—	2	2	no	—
20	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
21	C₂²⋊Dic₁₉	—	4	4	no	—
22	#64526	—	4	4	no	—
23	C₄×Dic₁₉	D₄	1	1	yes	characteristic
24	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
25	Dic₇₆	—	2	2	no	—
26	Dic₇₆	—	2	2	no	—
27	C₁₆×C₁₉	D₄	1	2	yes	—
28	C₁₉⋊C₁₆	D₄	1	2	yes	—
29	C₂³×C₁₉	—	4	2	no	—
30	D₄×C₁₉	—	4	2	no	—
31	D₄×C₁₉	—	4	2	no	—
32	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
33	C₂×Dic₁₉	—	4	2	no	—
34	C₂×Dic₁₉	D₈	1	2	yes	—
35	Dic₃₈	—	4	2	no	—
36	Dic₃₈	—	4	2	no	—
37	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₁₉⋊C₈	D₈	1	2	yes	—
40	#2249	—	19	1	no	maximal, Sylow
41	C₂²×C₁₉	—	8	2	no	—
42	C₂²×C₁₉	—	8	4	no	—
43	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
44	C₄×C₁₉	#127	1	1	yes	characteristic
45	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
46	Dic₁₉	—	2	2	no	—
47	Dic₁₉	—	8	2	no	—
48	C₂×Q₃₂	—	19	1	no	—
49	C₂×SD₃₂	—	19	2	no	—
50	C₂×D₁₆	D₁₉	1	1	yes	characteristic
51	#495	—	19	2	no	—
52	C₄×C₁₆	—	19	1	no	—
53	C₂×C₁₉	—	16	2	no	—
54	C₂×C₁₉	#493	1	1	yes	characteristic
55	C₂×C₁₉	#508	1	2	yes	—
56	C₂×Q₁₆	—	19	2	no	—
57	C₂×SD₁₆	—	38	2	no	—
58	C₂×D₈	C₂×D₁₉	1	2	yes	—
59	#124	—	38	2	no	—
60	Q₃₂	—	38	2	no	—
61	SD₃₂	—	38	4	no	—
62	D₁₆	—	2	2	no	—
63	C₂×C₁₆	—	19	1	no	—
64	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
65	C₄×C₈	—	19	1	no	—
66	C₁₉	#2249	1	1	yes	characteristic, complemented, Sylow
67	C₂×Q₈	—	38	2	no	—
68	C₂×D₄	—	2	2	no	—
69	Q₁₆	—	38	2	no	—
70	Q₁₆	—	38	2	no	—
71	SD₁₆	—	76	4	no	—
72	D₈	—	2	2	no	—
73	D₈	—	2	2	no	—
74	C₂×C₈	—	19	1	no	—
75	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
76	C₂²⋊C₄	—	76	4	no	—
77	C₄²	—	19	1	no	—
78	C₁₆	—	19	2	no	—
79	C₁₆	C₂²⋊D₁₉	1	2	yes	—
80	C₂³	—	4	2	no	—
81	Q₈	—	76	2	no	—
82	Q₈	—	76	2	no	—
83	D₄	—	4	2	no	—
84	D₄	—	4	2	no	—
85	C₂×C₄	—	19	2	no	—
86	C₂×C₄	—	76	2	no	—
87	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
88	C₈	—	19	2	no	—
89	C₈	D₄×D₁₉	1	1	yes	characteristic
90	C₈	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
91	C₂²	—	8	2	no	—
92	C₂²	—	8	4	no	—
93	C₂²	D₈×D₁₉	1	1	yes	characteristic
94	C₄	—	38	2	no	—
95	C₄	—	152	2	no	—
96	C₄	D₈×D₁₉	1	1	yes	characteristic
97	C₄	#10597386	1	1	yes	characteristic
98	C₂	—	16	2	no	—
99	C₂	#11926919	1	1	yes	characteristic
100	C₂	#11926973	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₁₅₂

C₂

yes

maximal, characteristic, complemented

C₂×#10597284

C₂

yes

maximal, complemented

#11926927

C₂

yes

maximal, complemented

C₁₆×Dic₁₉

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×D₁₆

C₂

yes

maximal, characteristic

C₂×D₈×C₁₉

C₂²

yes

—

#10597382

—

C₂×#64526

—

C₂×Dic₇₆

C₂²

yes

—

C₁₉×D₁₆

—

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

#10597284

—

C₈×Dic₁₉

C₂²

yes

characteristic

C₂×C₁₉⋊C₁₆

C₂²

yes

characteristic

Dic₁₅₂

—

C₂×D₄×C₁₉

—

C₂×Dic₃₈

—

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

—

#64526

—

C₄×Dic₁₉

D₄

yes

characteristic

C₂×C₁₉⋊C₈

D₄

yes

characteristic

Dic₇₆

—

Dic₇₆

—

C₁₆×C₁₉

D₄

yes

—

C₁₉⋊C₁₆

D₄

yes

—

C₂³×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

D₈

yes

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

C₂×D₄

yes

characteristic

C₈×C₁₉

C₂×D₄

yes

characteristic

C₁₉⋊C₈

D₈

yes

—

#2249

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

#127

yes

characteristic

C₄×C₁₉

C₂×D₈

yes

characteristic

Dic₁₉

—

Dic₁₉

—

C₂×Q₃₂

—

C₂×SD₃₂

—

C₂×D₁₆

D₁₉

yes

characteristic

#495

—

C₄×C₁₆

—

C₂×C₁₉

—

C₂×C₁₉

#493

yes

characteristic

C₂×C₁₉

#508

yes

—

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×D₈

C₂×D₁₉

yes

—

#124

—

Q₃₂

—

SD₃₂

—

D₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₁₉

yes

characteristic

C₄×C₈

—

C₁₉

#2249

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

Q₁₆

—

Q₁₆

—

SD₁₆

—

D₈

—

D₈

—

C₂×C₈

—

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₂²⋊C₄

—

C₄²

—

C₁₆

—

C₁₆

C₂²⋊D₁₉

yes

—

C₂³

—

Q₈

—

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₄×D₁₉

yes

characteristic

C₈

—

C₈

D₄×D₁₉

yes

characteristic

C₈

C₂×C₂²⋊D₁₉

yes

characteristic

C₂²

—

C₂²

—

C₂²

D₈×D₁₉

yes

characteristic

C₄

—

C₄

—

152

—

C₄

D₈×D₁₉

yes

characteristic

C₄

#10597386

yes

characteristic

C₂

—

C₂

#11926919

yes

characteristic

100

C₂

#11926973

yes

—

	subgroup	G/H
center	C₂²	D₈×D₁₉
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting, prime radical	C₂×C₁₉×D₁₆	C₂
socle	C₂²×C₁₉	C₂×D₈
hypercenter	C₂×D₁₆	D₁₉
hypocenter	C₁₉	#2249
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, prime radical

C₂×C₁₉×D₁₆

C₂

socle

C₂²×C₁₉

C₂×D₈

hypercenter

C₂×D₁₆

D₁₉

hypocenter

C₁₉

#2249

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×Dic₁₅₂	C₂	semidirect
2. C₂×#10597284	C₂	semidirect
3. #11926927	C₂	semidirect
4. C₁₆×Dic₁₉	C₂	semidirect
66. C₁₉	#2249	semidirect

H ≅ G/N

type

1. C₂×Dic₁₅₂

C₂

semidirect

2. C₂×#10597284

C₂

semidirect

3. #11926927

C₂

semidirect

4. C₁₆×Dic₁₉

C₂

semidirect

66. C₁₉

#2249

semidirect

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

subgroup	index
C₂×Dic₁₅₂	2
C₂×#10597284	2
#11926927	2
C₁₆×Dic₁₉	2
C₂×C₁₉×D₁₆	2
#2249	19

subgroup

index

C₂×Dic₁₅₂

C₂×#10597284

#11926927

C₁₆×Dic₁₉

C₂×C₁₉×D₁₆

#2249

Subgroups — #14565893

Conjugacy classes of subgroups

Complements

Maximal subgroups