Group #14269255 — subgroups

Subgroups — D₃×#64520 #14269255

Order 1824.

136 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 64 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×C₄×D₃×C₁₉	C₂	1	1	yes	maximal, characteristic
2	#11744885	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#64520	C₂	1	1	yes	maximal, characteristic, complemented
4	#11744816	C₂	1	2	yes	maximal, complemented
5	D₃×C₁₉⋊C₈	C₂	1	2	yes	maximal, complemented
6	C₂×#64520	—	3	1	no	maximal, Hall
7	C₂²×D₃×C₁₉	C₄	1	1	yes	characteristic
8	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×Dic₃×C₁₉	C₄	1	1	yes	characteristic
10	C₄×D₃×C₁₉	C₄	1	1	yes	characteristic
11	C₄×D₃×C₁₉	C₄	1	1	yes	characteristic
12	C₄×D₃×C₁₉	C₂²	1	1	yes	characteristic
13	C₄×D₃×C₁₉	C₂²	1	1	yes	characteristic
14	C₃⋊(C₁₉⋊C₈)	C₂²	1	2	yes	complemented
15	C₃×C₁₉⋊C₈	C₂²	1	2	yes	complemented
16	C₂²×C₄×C₁₉	—	3	1	no	—
17	#64520	—	3	1	no	—
18	#64520	—	3	2	no	—
19	#64520	D₃	1	1	yes	characteristic, direct product factor
20	C₂×C₁₉⋊C₈	—	3	2	no	—
21	C₂²×C₃×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂×D₃×C₁₉	—	2	2	no	—
23	C₂×D₃×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂×D₃×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₃×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₃×C₄×C₁₉	C₂³	1	1	yes	characteristic
27	Dic₃×C₁₉	C₂×C₄	1	1	yes	characteristic
28	Dic₃×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₁₉	—	3	1	no	—
30	C₂×C₄×C₁₉	—	3	1	no	—
31	C₂×C₄×C₁₉	—	3	1	no	—
32	C₂×C₄×C₁₉	—	3	1	no	—
33	C₂×C₄×C₁₉	—	3	1	no	—
34	C₂×C₄×C₁₉	—	3	1	no	—
35	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
36	C₁₉⋊C₈	—	3	2	no	—
37	C₁₉⋊C₈	C₂×D₃	1	2	yes	complemented
38	C₂×C₃×C₁₉	—	2	1	no	—
39	C₂×C₃×C₁₉	C₂²×C₄	1	1	yes	characteristic
40	D₃×C₁₉	—	2	1	no	—
41	D₃×C₁₉	M₁₆	1	2	yes	complemented
42	D₃×M₁₆	—	19	1	no	maximal, Hall
43	C₂²×C₁₉	—	3	1	no	—
44	C₂²×C₁₉	—	3	1	no	—
45	C₂²×C₁₉	—	6	2	no	—
46	C₂²×C₁₉	C₄×D₃	1	1	yes	characteristic
47	C₄×C₁₉	—	3	1	no	—
48	C₄×C₁₉	—	3	1	no	—
49	C₄×C₁₉	C₄×D₃	1	1	yes	characteristic
50	C₄×C₁₉	C₂²×D₃	1	1	yes	characteristic
51	C₃×C₁₉	C₂×M₁₆	1	1	yes	characteristic, complemented, Hall
52	C₂×C₄×D₃	D₁₉	1	1	yes	characteristic
53	C₃×M₁₆	—	19	1	no	—
54	#208	—	19	1	no	—
55	ΓL(1,𝔽₂₅)	—	19	2	no	—
56	D₃×C₈	—	19	2	no	—
57	C₂×C₁₉	—	2	1	no	—
58	C₂×C₁₉	—	3	2	no	—
59	C₂×C₁₉	—	6	1	no	—
60	C₂×C₁₉	C₂×C₄×D₃	1	1	yes	characteristic
61	C₂×M₁₆	—	57	1	no	Sylow
62	C₂²×D₃	Dic₁₉	1	1	yes	characteristic
63	C₂×C₃×C₄	C₂×D₁₉	1	1	yes	characteristic
64	C₂×Dic₃	Dic₁₉	1	1	yes	characteristic
65	C₄×D₃	Dic₁₉	1	1	yes	characteristic
66	C₄×D₃	Dic₁₉	1	1	yes	characteristic
67	C₄×D₃	C₂×D₁₉	1	1	yes	characteristic
68	C₄×D₃	C₂×D₁₉	1	1	yes	characteristic
69	C₃×C₈	—	19	2	no	—
70	C₃⋊C₈	—	19	2	no	—
71	C₁₉	D₃×M₁₆	1	1	yes	characteristic, complemented, Sylow
72	C₂²×C₄	—	3	1	no	—
73	M₁₆	—	19	1	no	—
74	M₁₆	—	57	2	no	—
75	M₁₆	—	57	1	no	—
76	C₂×C₈	—	57	2	no	—
77	C₂²×C₃	C₂×Dic₁₉	1	1	yes	characteristic
78	C₂×D₃	—	2	2	no	—
79	C₂×D₃	C₂×Dic₁₉	1	1	yes	characteristic
80	C₂×D₃	C₂×Dic₁₉	1	1	yes	characteristic
81	C₃×C₄	C₂×Dic₁₉	1	1	yes	characteristic
82	C₃×C₄	C₂²×D₁₉	1	1	yes	characteristic
83	Dic₃	C₂×Dic₁₉	1	1	yes	characteristic
84	Dic₃	C₂×Dic₁₉	1	1	yes	characteristic
85	C₂³	—	3	1	no	—
86	C₂×C₄	—	3	1	no	—
87	C₂×C₄	—	3	1	no	—
88	C₂×C₄	—	3	1	no	—
89	C₂×C₄	—	3	1	no	—
90	C₂×C₄	—	3	1	no	—
91	C₂×C₄	D₃×D₁₉	1	1	yes	characteristic
92	C₈	—	19	2	no	—
93	C₈	—	57	2	no	—
94	C₂×C₃	—	2	1	no	—
95	C₂×C₃	C₂²×Dic₁₉	1	1	yes	characteristic
96	D₃	—	2	1	no	—
97	D₃	#64520	1	2	yes	direct product factor
98	C₂²	—	3	1	no	—
99	C₂²	—	3	1	no	—
100	C₂²	—	6	2	no	—
101	C₂²	D₃×Dic₁₉	1	1	yes	characteristic
102	C₄	—	3	1	no	—
103	C₄	—	3	1	no	—
104	C₄	D₃×Dic₁₉	1	1	yes	characteristic
105	C₄	C₂×D₃×D₁₉	1	1	yes	characteristic
106	C₃	C₂×#64520	1	1	yes	characteristic, complemented, Sylow
107	C₂	—	2	1	no	—
108	C₂	—	3	2	no	—
109	C₂	—	6	1	no	—
110	C₂	C₂×D₃×Dic₁₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×D₃×C₁₉

C₂

yes

maximal, characteristic

#11744885

C₂

yes

maximal, characteristic, complemented

C₃×#64520

C₂

yes

maximal, characteristic, complemented

#11744816

C₂

yes

maximal, complemented

D₃×C₁₉⋊C₈

C₂

yes

maximal, complemented

C₂×#64520

—

maximal, Hall

C₂²×D₃×C₁₉

C₄

yes

characteristic

C₂×C₃×C₄×C₁₉

C₂²

yes

characteristic

C₂×Dic₃×C₁₉

C₄

yes

characteristic

C₄×D₃×C₁₉

C₄

yes

characteristic

C₄×D₃×C₁₉

C₄

yes

characteristic

C₄×D₃×C₁₉

C₂²

yes

characteristic

C₄×D₃×C₁₉

C₂²

yes

characteristic

C₃⋊(C₁₉⋊C₈)

C₂²

yes

complemented

C₃×C₁₉⋊C₈

C₂²

yes

complemented

C₂²×C₄×C₁₉

—

#64520

—

#64520

—

#64520

D₃

yes

characteristic, direct product factor

C₂×C₁₉⋊C₈

—

C₂²×C₃×C₁₉

C₂×C₄

yes

characteristic

C₂×D₃×C₁₉

—

C₂×D₃×C₁₉

C₂×C₄

yes

characteristic

C₂×D₃×C₁₉

C₂×C₄

yes

characteristic

C₃×C₄×C₁₉

C₂×C₄

yes

characteristic

C₃×C₄×C₁₉

C₂³

yes

characteristic

Dic₃×C₁₉

C₂×C₄

yes

characteristic

Dic₃×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₃

yes

characteristic

C₁₉⋊C₈

—

C₁₉⋊C₈

C₂×D₃

yes

complemented

C₂×C₃×C₁₉

—

C₂×C₃×C₁₉

C₂²×C₄

yes

characteristic

D₃×C₁₉

—

D₃×C₁₉

M₁₆

yes

complemented

D₃×M₁₆

—

maximal, Hall

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₄×D₃

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×D₃

yes

characteristic

C₄×C₁₉

C₂²×D₃

yes

characteristic

C₃×C₁₉

C₂×M₁₆

yes

characteristic, complemented, Hall

C₂×C₄×D₃

D₁₉

yes

characteristic

C₃×M₁₆

—

#208

—

ΓL(1,𝔽₂₅)

—

D₃×C₈

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

C₂×C₄×D₃

yes

characteristic

C₂×M₁₆

—

Sylow

C₂²×D₃

Dic₁₉

yes

characteristic

C₂×C₃×C₄

C₂×D₁₉

yes

characteristic

C₂×Dic₃

Dic₁₉

yes

characteristic

C₄×D₃

Dic₁₉

yes

characteristic

C₄×D₃

Dic₁₉

yes

characteristic

C₄×D₃

C₂×D₁₉

yes

characteristic

C₄×D₃

C₂×D₁₉

yes

characteristic

C₃×C₈

—

C₃⋊C₈

—

C₁₉

D₃×M₁₆

yes

characteristic, complemented, Sylow

C₂²×C₄

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂²×C₃

C₂×Dic₁₉

yes

characteristic

C₂×D₃

—

C₂×D₃

C₂×Dic₁₉

yes

characteristic

C₂×D₃

C₂×Dic₁₉

yes

characteristic

C₃×C₄

C₂×Dic₁₉

yes

characteristic

C₃×C₄

C₂²×D₁₉

yes

characteristic

Dic₃

C₂×Dic₁₉

yes

characteristic

Dic₃

C₂×Dic₁₉

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₃×D₁₉

yes

characteristic

C₈

—

C₈

—

C₂×C₃

—

C₂×C₃

C₂²×Dic₁₉

yes

characteristic

D₃

—

D₃

#64520

yes

direct product factor

C₂²

—

C₂²

—

100

C₂²

—

101

C₂²

D₃×Dic₁₉

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

D₃×Dic₁₉

yes

characteristic

105

C₄

C₂×D₃×D₁₉

yes

characteristic

106

C₃

C₂×#64520

yes

characteristic, complemented, Sylow

107

C₂

—

108

C₂

—

109

C₂

—

110

C₂

C₂×D₃×Dic₁₉

yes

characteristic

	subgroup	G/H
center, Frattini	C₄	C₂×D₃×D₁₉
commutator, socle	C₂×C₃×C₁₉	C₂²×C₄
Fitting	C₂×C₃×C₄×C₁₉	C₂²
prime radical	C₂²×D₃×C₁₉	C₄
cosocle	C₃×C₄×C₁₉	C₂³
hypercenter	C₂×C₄	D₃×D₁₉
hypocenter	C₃×C₁₉	C₂×M₁₆
LCS	G ▷ C₂×C₃×C₁₉ ▷ C₃×C₁₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄

subgroup

G/H

center, Frattini

C₄

C₂×D₃×D₁₉

commutator, socle

C₂×C₃×C₁₉

C₂²×C₄

Fitting

C₂×C₃×C₄×C₁₉

C₂²

prime radical

C₂²×D₃×C₁₉

C₄

cosocle

C₃×C₄×C₁₉

C₂³

hypercenter

C₂×C₄

D₃×D₁₉

hypocenter

C₃×C₁₉

C₂×M₁₆

LCS

G ▷ C₂×C₃×C₁₉ ▷ C₃×C₁₉

UCS

C₁ ◁ C₄ ◁ C₂×C₄

N	H ≅ G/N	type
2. #11744885	C₂	semidirect
3. C₃×#64520	C₂	semidirect
4. #11744816	C₂	semidirect
5. D₃×C₁₉⋊C₈	C₂	semidirect
14. C₃⋊(C₁₉⋊C₈)	C₂²	semidirect
15. C₃×C₁₉⋊C₈	C₂²	semidirect
19. #64520	D₃	direct (N × H)
37. C₁₉⋊C₈	C₂×D₃	semidirect
41. D₃×C₁₉	M₁₆	semidirect
51. C₃×C₁₉	C₂×M₁₆	semidirect
71. C₁₉	D₃×M₁₆	semidirect
97. D₃	#64520	direct (N × H)
106. C₃	C₂×#64520	semidirect

H ≅ G/N

type

2. #11744885

C₂

semidirect

3. C₃×#64520

C₂

semidirect

4. #11744816

C₂

semidirect

5. D₃×C₁₉⋊C₈

C₂

semidirect

14. C₃⋊(C₁₉⋊C₈)

C₂²

semidirect

15. C₃×C₁₉⋊C₈

C₂²

semidirect

19. #64520

D₃

direct (N × H)

37. C₁₉⋊C₈

C₂×D₃

semidirect

41. D₃×C₁₉

M₁₆

semidirect

51. C₃×C₁₉

C₂×M₁₆

semidirect

71. C₁₉

D₃×M₁₆

semidirect

97. D₃

#64520

direct (N × H)

106. C₃

C₂×#64520

semidirect

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

subgroup	index
C₂×C₄×D₃×C₁₉	2
#11744885	2
C₃×#64520	2
#11744816	2
D₃×C₁₉⋊C₈	2
C₂×#64520	3
D₃×M₁₆	19

subgroup

index

C₂×C₄×D₃×C₁₉

D₃×C₁₉⋊C₈

D₃×M₁₆

Subgroups — D₃×#64520 #14269255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D3×#64520 #14269255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#64520 #14269255