Group #14269426 — subgroups

Subgroups — D₃×#64528 #14269426

Order 1824.

120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 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	D₃×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
2	D₃×Dic₃₈	C₂	1	1	yes	maximal, characteristic
3	#11744893	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64528	C₂	1	1	yes	maximal, characteristic, complemented
5	#11744829	C₂	1	1	yes	maximal, characteristic, complemented
6	#11744827	C₂	1	1	yes	maximal, characteristic, complemented
7	D₃×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
8	C₂×#64528	—	3	1	no	maximal, Hall
9	C₃×Q₈×C₁₉	C₂²	1	1	yes	characteristic
10	Dic₁₁₄	C₂²	1	1	yes	characteristic
11	C₄×D₃×C₁₉	—	2	1	no	—
12	C₄×D₃×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×Dic₆	—	2	1	no	—
14	C₁₉×Dic₆	C₂²	1	1	yes	characteristic
15	C₃×Dic₃₈	C₂²	1	1	yes	characteristic
16	#90698	—	2	1	no	—
17	D₃×Dic₁₉	—	2	1	no	—
18	C₃⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
19	C₃×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×Q₈×C₁₉	—	3	1	no	—
21	C₂×Dic₃₈	—	3	1	no	—
22	#64528	—	3	1	no	—
23	#64528	—	3	1	no	—
24	#64528	—	3	1	no	—
25	#64528	D₃	1	1	yes	characteristic, direct product factor
26	C₂×C₁₉⋊C₈	—	3	1	no	—
27	C₂×D₃×C₁₉	D₄	1	1	yes	characteristic
28	C₃×C₄×C₁₉	—	2	1	no	—
29	C₃×C₄×C₁₉	C₂³	1	1	yes	characteristic
30	Dic₅₇	—	2	1	no	—
31	C₃×Dic₁₉	—	2	1	no	—
32	Dic₃×C₁₉	—	2	1	no	—
33	Dic₃×C₁₉	D₄	1	1	yes	characteristic
34	Q₈×C₁₉	—	3	1	no	—
35	Q₈×C₁₉	—	6	1	no	—
36	Q₈×C₁₉	C₂×D₃	1	1	yes	characteristic
37	C₂×C₄×C₁₉	—	3	1	no	—
38	C₂×C₄×C₁₉	—	6	1	no	—
39	C₂×Dic₁₉	—	6	1	no	—
40	Dic₃₈	—	3	1	no	—
41	Dic₃₈	—	6	1	no	—
42	Dic₃₈	C₂×D₃	1	1	yes	characteristic
43	C₁₉⋊C₈	—	3	1	no	—
44	C₁₉⋊C₈	C₂×D₃	1	1	yes	characteristic
45	C₂×C₃×C₁₉	C₂×D₄	1	1	yes	characteristic
46	D₃×C₁₉	Q₁₆	1	2	yes	complemented
47	D₃×Q₁₆	—	19	1	no	maximal, Hall
48	C₂²×C₁₉	—	3	1	no	—
49	C₄×C₁₉	—	2	1	no	—
50	C₄×C₁₉	—	3	1	no	—
51	C₄×C₁₉	—	6	1	no	—
52	C₄×C₁₉	C₂²×D₃	1	1	yes	characteristic
53	Dic₁₉	—	2	1	no	—
54	Dic₁₉	—	6	1	no	—
55	C₃×C₁₉	C₂×Q₁₆	1	1	yes	characteristic, complemented, Hall
56	D₃×Q₈	—	19	1	no	—
57	D₃×Q₈	D₁₉	1	1	yes	characteristic
58	C₃×Q₁₆	—	19	1	no	—
59	#216	—	19	1	no	—
60	#216	—	19	1	no	—
61	Dic₁₂	—	19	1	no	—
62	D₃×C₈	—	19	1	no	—
63	C₂×C₁₉	—	3	2	no	—
64	C₂×C₁₉	D₃×D₄	1	1	yes	characteristic
65	C₂×Q₁₆	—	57	1	no	Sylow
66	C₃×Q₈	—	19	1	no	—
67	C₃×Q₈	C₂×D₁₉	1	1	yes	characteristic
68	C₄×D₃	—	2	1	no	—
69	C₄×D₃	—	38	1	no	—
70	C₄×D₃	C₂×D₁₉	1	1	yes	characteristic
71	Dic₆	—	2	1	no	—
72	Dic₆	—	19	1	no	—
73	Dic₆	—	38	1	no	—
74	Dic₆	C₂×D₁₉	1	1	yes	characteristic
75	C₃×C₈	—	19	1	no	—
76	C₃⋊C₈	—	19	1	no	—
77	C₁₉	D₃×Q₁₆	1	1	yes	characteristic, complemented, Sylow
78	C₂×Q₈	—	3	1	no	—
79	C₂×Q₈	—	57	1	no	—
80	Q₁₆	—	19	1	no	—
81	Q₁₆	—	57	1	no	—
82	Q₁₆	—	57	1	no	—
83	Q₁₆	—	57	1	no	—
84	C₂×C₈	—	57	1	no	—
85	C₂×D₃	C₂²⋊D₁₉	1	1	yes	characteristic
86	C₃×C₄	—	2	1	no	—
87	C₃×C₄	—	38	1	no	—
88	C₃×C₄	C₂²×D₁₉	1	1	yes	characteristic
89	Dic₃	—	2	1	no	—
90	Dic₃	—	38	1	no	—
91	Dic₃	C₂²⋊D₁₉	1	1	yes	characteristic
92	Q₈	—	3	1	no	—
93	Q₈	—	6	1	no	—
94	Q₈	—	19	1	no	—
95	Q₈	—	57	1	no	—
96	Q₈	—	114	1	no	—
97	Q₈	D₃×D₁₉	1	1	yes	characteristic
98	C₂×C₄	—	3	1	no	—
99	C₂×C₄	—	6	1	no	—
100	C₂×C₄	—	114	1	no	—
101	C₈	—	19	1	no	—
102	C₈	—	57	1	no	—
103	C₂×C₃	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
104	D₃	#64528	1	2	yes	direct product factor
105	C₂²	—	3	1	no	—
106	C₄	—	2	1	no	—
107	C₄	—	3	1	no	—
108	C₄	—	6	1	no	—
109	C₄	—	38	1	no	—
110	C₄	—	114	1	no	—
111	C₄	C₂×D₃×D₁₉	1	1	yes	characteristic
112	C₃	C₂×#64528	1	1	yes	characteristic, complemented, Sylow
113	C₂	—	3	2	no	—
114	C₂	D₃×C₂²⋊D₁₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₃×Q₈×C₁₉

C₂

yes

maximal, characteristic

D₃×Dic₃₈

C₂

yes

maximal, characteristic

#11744893

C₂

yes

maximal, characteristic, complemented

C₃×#64528

C₂

yes

maximal, characteristic, complemented

#11744829

C₂

yes

maximal, characteristic, complemented

#11744827

C₂

yes

maximal, characteristic, complemented

D₃×C₁₉⋊C₈

C₂

yes

maximal, characteristic

C₂×#64528

—

maximal, Hall

C₃×Q₈×C₁₉

C₂²

yes

characteristic

Dic₁₁₄

C₂²

yes

characteristic

C₄×D₃×C₁₉

—

C₄×D₃×C₁₉

C₂²

yes

characteristic

C₁₉×Dic₆

—

C₁₉×Dic₆

C₂²

yes

characteristic

C₃×Dic₃₈

C₂²

yes

characteristic

#90698

—

D₃×Dic₁₉

—

C₃⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₃×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Dic₃₈

—

—

—

—

D₃

yes

characteristic, direct product factor

C₂×C₁₉⋊C₈

—

C₂×D₃×C₁₉

D₄

yes

characteristic

C₃×C₄×C₁₉

—

C₃×C₄×C₁₉

C₂³

yes

characteristic

Dic₅₇

—

C₃×Dic₁₉

—

Dic₃×C₁₉

—

Dic₃×C₁₉

D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

C₂×D₃

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

C₂×D₃

yes

characteristic

C₁₉⋊C₈

—

C₁₉⋊C₈

C₂×D₃

yes

characteristic

C₂×C₃×C₁₉

C₂×D₄

yes

characteristic

D₃×C₁₉

Q₁₆

yes

complemented

D₃×Q₁₆

—

maximal, Hall

C₂²×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²×D₃

yes

characteristic

Dic₁₉

—

Dic₁₉

—

C₃×C₁₉

C₂×Q₁₆

yes

characteristic, complemented, Hall

D₃×Q₈

—

D₃×Q₈

D₁₉

yes

characteristic

C₃×Q₁₆

—

#216

—

#216

—

Dic₁₂

—

D₃×C₈

—

C₂×C₁₉

—

C₂×C₁₉

D₃×D₄

yes

characteristic

C₂×Q₁₆

—

Sylow

C₃×Q₈

—

C₃×Q₈

C₂×D₁₉

yes

characteristic

C₄×D₃

—

C₄×D₃

—

C₄×D₃

C₂×D₁₉

yes

characteristic

Dic₆

—

Dic₆

—

Dic₆

—

Dic₆

C₂×D₁₉

yes

characteristic

C₃×C₈

—

C₃⋊C₈

—

C₁₉

D₃×Q₁₆

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

C₂×C₈

—

C₂×D₃

C₂²⋊D₁₉

yes

characteristic

C₃×C₄

—

C₃×C₄

—

C₃×C₄

C₂²×D₁₉

yes

characteristic

Dic₃

—

Dic₃

—

Dic₃

C₂²⋊D₁₉

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

Q₈

—

Q₈

—

114

—

Q₈

D₃×D₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

114

—

101

C₈

—

102

C₈

—

103

C₂×C₃

C₂×C₂²⋊D₁₉

yes

characteristic

104

D₃

#64528

yes

direct product factor

105

C₂²

—

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

114

—

111

C₄

C₂×D₃×D₁₉

yes

characteristic

112

C₃

C₂×#64528

yes

characteristic, complemented, Sylow

113

C₂

—

114

C₂

D₃×C₂²⋊D₁₉

yes

characteristic

	subgroup	G/H
center	C₂	D₃×C₂²⋊D₁₉
commutator, cosocle	C₃×C₄×C₁₉	C₂³
Frattini	C₄	C₂×D₃×D₁₉
Fitting	C₃×Q₈×C₁₉	C₂²
socle	C₂×C₃×C₁₉	C₂×D₄
prime radical	C₂×D₃×C₁₉	D₄
hypercenter	Q₈	D₃×D₁₉
hypocenter	C₃×C₁₉	C₂×Q₁₆
LCS	G ▷ C₃×C₄×C₁₉ ▷ C₂×C₃×C₁₉ ▷ C₃×C₁₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₈

subgroup

G/H

center

C₂

D₃×C₂²⋊D₁₉

commutator, cosocle

C₃×C₄×C₁₉

C₂³

Frattini

C₄

C₂×D₃×D₁₉

Fitting

C₃×Q₈×C₁₉

C₂²

socle

C₂×C₃×C₁₉

C₂×D₄

prime radical

C₂×D₃×C₁₉

D₄

hypercenter

Q₈

D₃×D₁₉

hypocenter

C₃×C₁₉

C₂×Q₁₆

LCS

G ▷ C₃×C₄×C₁₉ ▷ C₂×C₃×C₁₉ ▷ C₃×C₁₉

UCS

C₁ ◁ C₂ ◁ C₄ ◁ Q₈

N	H ≅ G/N	type
3. #11744893	C₂	semidirect
4. C₃×#64528	C₂	semidirect
5. #11744829	C₂	semidirect
6. #11744827	C₂	semidirect
25. #64528	D₃	direct (N × H)
46. D₃×C₁₉	Q₁₆	semidirect
55. C₃×C₁₉	C₂×Q₁₆	semidirect
77. C₁₉	D₃×Q₁₆	semidirect
104. D₃	#64528	direct (N × H)
112. C₃	C₂×#64528	semidirect

H ≅ G/N

type

3. #11744893

C₂

semidirect

4. C₃×#64528

C₂

semidirect

5. #11744829

C₂

semidirect

6. #11744827

C₂

semidirect

25. #64528

D₃

direct (N × H)

46. D₃×C₁₉

Q₁₆

semidirect

55. C₃×C₁₉

C₂×Q₁₆

semidirect

77. C₁₉

D₃×Q₁₆

semidirect

104. D₃

#64528

direct (N × H)

112. C₃

C₂×#64528

semidirect

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

subgroup	index
D₃×Q₈×C₁₉	2
D₃×Dic₃₈	2
#11744893	2
C₃×#64528	2
#11744829	2
#11744827	2
D₃×C₁₉⋊C₈	2
C₂×#64528	3
D₃×Q₁₆	19

subgroup

index

D₃×Q₈×C₁₉

D₃×Dic₃₈

D₃×C₁₉⋊C₈

D₃×Q₁₆

Subgroups — D₃×#64528 #14269426

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D3×#64528 #14269426

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#64528 #14269426