Group #14565398 — subgroups

Subgroups — C₂×#11926365 #14565398

Order 2432.

168 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 109 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×#10597269	C₂	1	2	yes	maximal
2	#11926365	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₁₉	C₄	1	1	yes	characteristic
5	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
6	C₂×C₄²×C₁₉	C₄	1	1	yes	characteristic
7	C₄×C₈×C₁₉	C₄	1	2	yes	—
8	C₄×C₈×C₁₉	C₂²	1	2	yes	—
9	#10597269	—	2	2	no	—
10	#10597269	C₂²	1	4	yes	—
11	C₂×C₁₉⋊C₁₆	—	2	2	no	—
12	C₂²×C₄×C₁₉	—	2	1	no	—
13	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₁₉	C₈	1	2	yes	—
15	C₂×C₈×C₁₉	C₈	1	2	yes	—
16	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
19	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
20	C₂×C₈×C₁₉	Q₈	1	1	yes	characteristic
21	C₂×C₈×C₁₉	Q₈	1	1	yes	characteristic
22	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
23	C₄²×C₁₉	—	2	1	no	—
24	C₄²×C₁₉	C₂×C₄	1	2	yes	—
25	C₁₉⋊C₁₆	—	2	4	no	—
26	C₂³×C₁₉	M₁₆	1	1	yes	characteristic
27	C₂×C₄×C₁₉	—	2	4	no	—
28	C₂×C₄×C₁₉	—	2	2	no	—
29	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
33	C₂×C₄×C₁₉	M₁₆	1	1	yes	characteristic
34	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
35	C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
36	C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
37	C₈×C₁₉	C₂×C₈	1	4	yes	—
38	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
40	C₂×#364	—	19	1	no	maximal, Sylow
41	C₂²×C₁₉	—	2	2	no	—
42	C₂²×C₁₉	C₄⋊C₈	1	1	yes	characteristic
43	C₂²×C₁₉	C₄⋊C₈	1	1	yes	characteristic
44	C₂²×C₁₉	C₂×M₁₆	1	1	yes	characteristic
45	C₄×C₁₉	—	2	4	no	—
46	C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
47	C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
48	C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
50	C₂×M₃₂	—	19	2	no	—
51	C₂×C₄×C₈	D₁₉	1	1	yes	characteristic
52	#364	—	19	4	no	—
53	C₂×C₁₉	—	2	1	no	—
54	C₂×C₁₉	—	2	1	no	—
55	C₂×C₁₉	#364	1	2	yes	complemented
56	C₂×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
57	C₂²×C₈	Dic₁₉	1	1	yes	characteristic
58	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
59	C₂×C₄²	Dic₁₉	1	1	yes	characteristic
60	M₃₂	—	19	4	no	—
61	M₃₂	—	38	2	no	—
62	C₂×C₁₆	—	38	2	no	—
63	C₄×C₈	Dic₁₉	1	2	yes	—
64	C₄×C₈	C₂×D₁₉	1	2	yes	—
65	C₁₉	C₂×#364	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₄	—	2	1	no	—
67	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
68	C₂×C₈	C₁₉⋊C₈	1	2	yes	—
69	C₂×C₈	C₁₉⋊C₈	1	2	yes	—
70	C₂×C₈	Dic₃₈	1	1	yes	characteristic
71	C₂×C₈	Dic₃₈	1	1	yes	characteristic
72	C₂×C₈	D₇₆	1	1	yes	characteristic
73	C₂×C₈	D₇₆	1	1	yes	characteristic
74	C₂×C₈	C₂×Dic₁₉	1	2	yes	—
75	C₂×C₈	C₂×Dic₁₉	1	1	yes	characteristic
76	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
77	C₄²	—	2	1	no	—
78	C₄²	C₂×Dic₁₉	1	2	yes	—
79	C₁₆	—	38	4	no	—
80	C₂³	#64520	1	1	yes	characteristic
81	C₂×C₄	—	2	4	no	—
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	C₂×C₁₉⋊C₈	1	1	yes	characteristic
84	C₂×C₄	C₂×C₁₉⋊C₈	1	1	yes	characteristic
85	C₂×C₄	#64520	1	1	yes	characteristic
86	C₂×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
87	C₂×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
88	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
89	C₈	C₂×C₁₉⋊C₈	1	4	yes	—
90	C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
91	C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
92	C₈	C₂×Dic₃₈	1	1	yes	characteristic
93	C₈	C₂×D₇₆	1	1	yes	characteristic
94	C₂²	—	2	2	no	—
95	C₂²	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
96	C₂²	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
97	C₂²	C₂×#64520	1	1	yes	characteristic
98	C₄	—	2	4	no	—
99	C₄	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
100	C₄	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
101	C₄	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
102	C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
103	C₂	—	2	1	no	—
104	C₂	—	2	1	no	—
105	C₂	#11926365	1	2	yes	direct product factor
106	C₂	C₂×C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597269

C₂

yes

maximal

#11926365

C₂

yes

maximal, direct product factor

C₂×C₄×C₈×C₁₉

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₉

C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₄

yes

characteristic

C₄×C₈×C₁₉

C₄

yes

—

C₄×C₈×C₁₉

C₂²

yes

—

#10597269

—

#10597269

C₂²

yes

—

C₂×C₁₉⋊C₁₆

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₈

yes

—

C₂×C₈×C₁₉

C₈

yes

—

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

Q₈

yes

characteristic

C₂×C₈×C₁₉

Q₈

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

—

C₁₉⋊C₁₆

—

C₂³×C₁₉

M₁₆

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂×C₄×C₁₉

M₁₆

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₈×C₁₉

C₂×C₈

yes

—

C₈×C₁₉

C₂×D₄

yes

characteristic

C₈×C₁₉

C₂×Q₈

yes

characteristic

C₂×#364

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₄⋊C₈

yes

characteristic

C₂²×C₁₉

C₄⋊C₈

yes

characteristic

C₂²×C₁₉

C₂×M₁₆

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

C₄⋊C₈

yes

characteristic

C₄×C₁₉

C₄⋊C₈

yes

characteristic

C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₉

C₂²×C₈

yes

characteristic

C₂×M₃₂

—

C₂×C₄×C₈

D₁₉

yes

characteristic

#364

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#364

yes

complemented

C₂×C₁₉

C₂×C₄⋊C₈

yes

characteristic

C₂²×C₈

Dic₁₉

yes

characteristic

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₂×C₄²

Dic₁₉

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₄×C₈

Dic₁₉

yes

—

C₄×C₈

C₂×D₁₉

yes

—

C₁₉

C₂×#364

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂×Dic₁₉

yes

characteristic

C₂×C₈

C₁₉⋊C₈

yes

—

C₂×C₈

C₁₉⋊C₈

yes

—

C₂×C₈

Dic₃₈

yes

characteristic

C₂×C₈

Dic₃₈

yes

characteristic

C₂×C₈

D₇₆

yes

characteristic

C₂×C₈

D₇₆

yes

characteristic

C₂×C₈

C₂×Dic₁₉

yes

—

C₂×C₈

C₂×Dic₁₉

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄²

—

C₄²

C₂×Dic₁₉

yes

—

C₁₆

—

C₂³

#64520

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₁₉⋊C₈

yes

characteristic

C₂×C₄

C₂×C₁₉⋊C₈

yes

characteristic

C₂×C₄

#64520

yes

characteristic

C₂×C₄

C₄⋊Dic₁₉

yes

characteristic

C₂×C₄

C₄⋊Dic₁₉

yes

characteristic

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

C₈

C₂×C₁₉⋊C₈

yes

—

C₈

C₄⋊Dic₁₉

yes

characteristic

C₈

C₄⋊Dic₁₉

yes

characteristic

C₈

C₂×Dic₃₈

yes

characteristic

C₈

C₂×D₇₆

yes

characteristic

C₂²

—

C₂²

C₄⋊(C₁₉⋊C₈)

yes

characteristic

C₂²

C₄⋊(C₁₉⋊C₈)

yes

characteristic

C₂²

C₂×#64520

yes

characteristic

C₄

—

C₄

C₄⋊(C₁₉⋊C₈)

yes

characteristic

100

C₄

C₄⋊(C₁₉⋊C₈)

yes

characteristic

101

C₄

C₂²×C₁₉⋊C₈

yes

characteristic

102

C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

103

C₂

—

104

C₂

—

105

C₂

#11926365

yes

direct product factor

106

C₂

C₂×C₄⋊(C₁₉⋊C₈)

yes

characteristic

	subgroup	G/H
center	C₂×C₈	D₇₆
commutator	C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₂×C₄×C₈×C₁₉	C₂
socle	C₂²×C₁₉	C₄⋊C₈
prime radical	C₂³×C₁₉	M₁₆
cosocle	C₂×C₈×C₁₉	C₂³
hypercenter	C₂×C₄×C₈	D₁₉
hypocenter	C₁₉	C₂×#364
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂×C₈

D₇₆

commutator

C₄×C₁₉

C₂²×C₈

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₂×C₄×C₈×C₁₉

C₂

socle

C₂²×C₁₉

C₄⋊C₈

prime radical

C₂³×C₁₉

M₁₆

cosocle

C₂×C₈×C₁₉

C₂³

hypercenter

C₂×C₄×C₈

D₁₉

hypocenter

C₁₉

C₂×#364

LCS

G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

N	H ≅ G/N	type
2. #11926365	C₂	direct (N × H)
55. C₂×C₁₉	#364	semidirect
65. C₁₉	C₂×#364	semidirect
105. C₂	#11926365	direct (N × H)

H ≅ G/N

type

2. #11926365

C₂

direct (N × H)

55. C₂×C₁₉

#364

semidirect

65. C₁₉

C₂×#364

semidirect

105. C₂

#11926365

direct (N × H)

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

subgroup	index
C₂×#10597269	2
#11926365	2
C₂×C₄×C₈×C₁₉	2
C₂×#364	19

subgroup

index

C₂×#10597269

#11926365

C₂×C₄×C₈×C₁₉

C₂×#364

Subgroups — C₂×#11926365 #14565398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#11926365 #14565398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11926365 #14565398