Group #14269633 — subgroups

Subgroups — D₃×C₂²⋊C₄×C₁₉ #14269633

Order 1824.

264 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 98 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	C₂³×D₃×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₃×C₁₉	C₂	1	2	yes	maximal, complemented
3	C₃×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#217	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal, complemented
6	C₂×C₂²⋊C₄×C₁₉	—	3	1	no	maximal, Hall
7	C₂³×C₃×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×D₃×C₁₉	—	2	4	no	—
9	C₂²×D₃×C₁₉	C₄	1	4	yes	complemented
10	C₂²×D₃×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×D₃×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄×C₁₉	C₂²	1	2	yes	complemented
13	C₂×Dic₃×C₁₉	C₂²	1	2	yes	complemented
14	C₄×D₃×C₁₉	—	2	4	no	—
15	C₂⁴×C₁₉	—	3	1	no	—
16	C₂²×C₄×C₁₉	—	3	2	no	—
17	C₂²⋊C₄×C₁₉	—	3	1	no	—
18	C₂²⋊C₄×C₁₉	—	3	2	no	—
19	C₂²⋊C₄×C₁₉	D₃	1	1	yes	characteristic, direct product factor
20	C₂²×C₃×C₁₉	—	2	2	no	—
21	C₂²×C₃×C₁₉	C₂×C₄	1	2	yes	complemented
22	C₂²×C₃×C₁₉	C₂³	1	1	yes	characteristic
23	C₂×D₃×C₁₉	—	2	2	no	—
24	C₂×D₃×C₁₉	—	2	8	no	—
25	C₂×D₃×C₁₉	C₂×C₄	1	2	yes	—
26	C₂×D₃×C₁₉	C₂×C₄	1	2	yes	complemented
27	C₂×D₃×C₁₉	D₄	1	4	yes	—
28	C₃×C₄×C₁₉	—	2	2	no	—
29	Dic₃×C₁₉	—	2	2	no	—
30	C₂³×C₁₉	—	3	1	no	—
31	C₂³×C₁₉	—	3	4	no	—
32	C₂³×C₁₉	—	3	1	no	—
33	C₂³×C₁₉	—	6	4	no	—
34	C₂³×C₁₉	C₂×D₃	1	1	yes	characteristic
35	C₂×C₄×C₁₉	—	3	2	no	—
36	C₂×C₄×C₁₉	—	6	4	no	—
37	C₂×C₄×C₁₉	C₂×D₃	1	2	yes	complemented
38	C₂×C₃×C₁₉	—	2	2	no	—
39	C₂×C₃×C₁₉	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₃×C₁₉	C₂×D₄	1	2	yes	—
41	D₃×C₁₉	—	2	2	no	—
42	D₃×C₁₉	C₂²⋊C₄	1	4	yes	direct product factor
43	D₃×C₂²⋊C₄	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
44	C₂²×C₁₉	—	2	2	no	—
45	C₂²×C₁₉	—	3	2	no	—
46	C₂²×C₁₉	—	3	4	no	—
47	C₂²×C₁₉	—	3	2	no	—
48	C₂²×C₁₉	—	6	8	no	—
49	C₂²×C₁₉	—	6	2	no	—
50	C₂²×C₁₉	C₄×D₃	1	2	yes	complemented
51	C₂²×C₁₉	C₂²×D₃	1	1	yes	characteristic
52	C₄×C₁₉	—	2	2	no	—
53	C₄×C₁₉	—	6	2	no	—
54	C₃×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
55	C₂³×D₃	C₂×C₁₉	1	1	yes	characteristic
56	C₂×C₄×D₃	C₂×C₁₉	1	2	yes	complemented
57	C₃×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
58	#217	C₂×C₁₉	1	1	yes	characteristic, complemented
59	(C₂×D₃)⋊C₄	C₂×C₁₉	1	2	yes	complemented
60	C₂×C₁₉	—	2	2	no	—
61	C₂×C₁₉	—	3	4	no	—
62	C₂×C₁₉	—	6	2	no	—
63	C₂×C₁₉	C₂×C₄×D₃	1	1	yes	characteristic
64	C₂×C₁₉	D₃×D₄	1	2	yes	—
65	C₂×C₂²⋊C₄	—	3	1	no	Sylow
66	C₂³×C₃	C₂²×C₁₉	1	1	yes	characteristic
67	C₂²×D₃	—	2	4	no	—
68	C₂²×D₃	C₄×C₁₉	1	4	yes	complemented
69	C₂²×D₃	C₂²×C₁₉	1	1	yes	characteristic
70	C₂²×D₃	C₂²×C₁₉	1	1	yes	characteristic
71	C₂×C₃×C₄	C₂²×C₁₉	1	2	yes	complemented
72	C₂×Dic₃	C₂²×C₁₉	1	2	yes	complemented
73	C₄×D₃	—	2	4	no	—
74	C₁₉	D₃×C₂²⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
75	C₂⁴	—	3	1	no	—
76	C₂²×C₄	—	3	2	no	—
77	C₂²⋊C₄	—	3	1	no	—
78	C₂²⋊C₄	—	3	2	no	—
79	C₂²⋊C₄	D₃×C₁₉	1	1	yes	characteristic, direct product factor
80	C₂²×C₃	—	2	2	no	—
81	C₂²×C₃	C₂×C₄×C₁₉	1	2	yes	complemented
82	C₂²×C₃	C₂³×C₁₉	1	1	yes	characteristic
83	C₂×D₃	—	2	2	no	—
84	C₂×D₃	—	2	8	no	—
85	C₂×D₃	C₂×C₄×C₁₉	1	2	yes	—
86	C₂×D₃	C₂×C₄×C₁₉	1	2	yes	complemented
87	C₂×D₃	D₄×C₁₉	1	4	yes	—
88	C₃×C₄	—	2	2	no	—
89	Dic₃	—	2	2	no	—
90	C₂³	—	3	1	no	—
91	C₂³	—	3	4	no	—
92	C₂³	—	3	1	no	—
93	C₂³	—	6	4	no	—
94	C₂³	C₂×D₃×C₁₉	1	1	yes	characteristic
95	C₂×C₄	—	3	2	no	—
96	C₂×C₄	—	6	4	no	—
97	C₂×C₄	C₂×D₃×C₁₉	1	2	yes	complemented
98	C₂×C₃	—	2	2	no	—
99	C₂×C₃	C₂²×C₄×C₁₉	1	1	yes	characteristic
100	C₂×C₃	C₂×D₄×C₁₉	1	2	yes	—
101	D₃	—	2	2	no	—
102	D₃	C₂²⋊C₄×C₁₉	1	4	yes	direct product factor
103	C₂²	—	2	2	no	—
104	C₂²	—	3	2	no	—
105	C₂²	—	3	4	no	—
106	C₂²	—	3	2	no	—
107	C₂²	—	6	8	no	—
108	C₂²	—	6	2	no	—
109	C₂²	C₄×D₃×C₁₉	1	2	yes	complemented
110	C₂²	C₂²×D₃×C₁₉	1	1	yes	characteristic
111	C₄	—	2	2	no	—
112	C₄	—	6	2	no	—
113	C₃	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic, complemented, Sylow
114	C₂	—	2	2	no	—
115	C₂	—	3	4	no	—
116	C₂	—	6	2	no	—
117	C₂	C₂×C₄×D₃×C₁₉	1	1	yes	characteristic
118	C₂	D₃×D₄×C₁₉	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂³×D₃×C₁₉

C₂

yes

maximal, characteristic

C₂×C₄×D₃×C₁₉

C₂

yes

maximal, complemented

C₃×C₂²⋊C₄×C₁₉

C₂

yes

maximal, characteristic, complemented

C₁₉×#217

C₂

yes

maximal, characteristic, complemented

C₁₉×(C₂×D₃)⋊C₄

C₂

yes

maximal, complemented

C₂×C₂²⋊C₄×C₁₉

—

maximal, Hall

C₂³×C₃×C₁₉

C₂²

yes

characteristic

C₂²×D₃×C₁₉

—

C₂²×D₃×C₁₉

C₄

yes

complemented

C₂²×D₃×C₁₉

C₂²

yes

characteristic

C₂²×D₃×C₁₉

C₂²

yes

characteristic

C₂×C₃×C₄×C₁₉

C₂²

yes

complemented

C₂×Dic₃×C₁₉

C₂²

yes

complemented

C₄×D₃×C₁₉

—

C₂⁴×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

D₃

yes

characteristic, direct product factor

C₂²×C₃×C₁₉

—

C₂²×C₃×C₁₉

C₂×C₄

yes

complemented

C₂²×C₃×C₁₉

C₂³

yes

characteristic

C₂×D₃×C₁₉

—

C₂×D₃×C₁₉

—

C₂×D₃×C₁₉

C₂×C₄

yes

—

C₂×D₃×C₁₉

C₂×C₄

yes

complemented

C₂×D₃×C₁₉

D₄

yes

—

C₃×C₄×C₁₉

—

Dic₃×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₃

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₃

yes

complemented

C₂×C₃×C₁₉

—

C₂×C₃×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₃×C₁₉

C₂×D₄

yes

—

D₃×C₁₉

—

D₃×C₁₉

C₂²⋊C₄

yes

direct product factor

D₃×C₂²⋊C₄

C₁₉

yes

maximal, characteristic, direct product factor, Hall

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₄×D₃

yes

complemented

C₂²×C₁₉

C₂²×D₃

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₃×C₁₉

C₂×C₂²⋊C₄

yes

characteristic, complemented, Hall

C₂³×D₃

C₂×C₁₉

yes

characteristic

C₂×C₄×D₃

C₂×C₁₉

yes

complemented

C₃×C₂²⋊C₄

C₂×C₁₉

yes

characteristic, complemented

#217

C₂×C₁₉

yes

characteristic, complemented

(C₂×D₃)⋊C₄

C₂×C₁₉

yes

complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

C₂×C₄×D₃

yes

characteristic

C₂×C₁₉

D₃×D₄

yes

—

C₂×C₂²⋊C₄

—

Sylow

C₂³×C₃

C₂²×C₁₉

yes

characteristic

C₂²×D₃

—

C₂²×D₃

C₄×C₁₉

yes

complemented

C₂²×D₃

C₂²×C₁₉

yes

characteristic

C₂²×D₃

C₂²×C₁₉

yes

characteristic

C₂×C₃×C₄

C₂²×C₁₉

yes

complemented

C₂×Dic₃

C₂²×C₁₉

yes

complemented

C₄×D₃

—

C₁₉

D₃×C₂²⋊C₄

yes

characteristic, direct product factor, Sylow

C₂⁴

—

C₂²×C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

D₃×C₁₉

yes

characteristic, direct product factor

C₂²×C₃

—

C₂²×C₃

C₂×C₄×C₁₉

yes

complemented

C₂²×C₃

C₂³×C₁₉

yes

characteristic

C₂×D₃

—

C₂×D₃

—

C₂×D₃

C₂×C₄×C₁₉

yes

—

C₂×D₃

C₂×C₄×C₁₉

yes

complemented

C₂×D₃

D₄×C₁₉

yes

—

C₃×C₄

—

Dic₃

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂×D₃×C₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₃×C₁₉

yes

complemented

C₂×C₃

—

C₂×C₃

C₂²×C₄×C₁₉

yes

characteristic

100

C₂×C₃

C₂×D₄×C₁₉

yes

—

101

D₃

—

102

D₃

C₂²⋊C₄×C₁₉

yes

direct product factor

103

C₂²

—

104

C₂²

—

105

C₂²

—

106

C₂²

—

107

C₂²

—

108

C₂²

—

109

C₂²

C₄×D₃×C₁₉

yes

complemented

110

C₂²

C₂²×D₃×C₁₉

yes

characteristic

111

C₄

—

112

C₄

—

113

C₃

C₂×C₂²⋊C₄×C₁₉

yes

characteristic, complemented, Sylow

114

C₂

—

115

C₂

—

116

C₂

—

117

C₂

C₂×C₄×D₃×C₁₉

yes

characteristic

118

C₂

D₃×D₄×C₁₉

yes

—

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

subgroup

G/H

center

C₂²×C₁₉

C₂²×D₃

commutator

C₂×C₃

C₂²×C₄×C₁₉

Frattini

C₂²

C₂²×D₃×C₁₉

Fitting

C₃×C₂²⋊C₄×C₁₉

C₂

socle

C₂²×C₃×C₁₉

C₂³

prime radical

C₂³×D₃×C₁₉

C₂

cosocle

C₂²×C₃

C₂³×C₁₉

hypercenter

C₂²⋊C₄×C₁₉

D₃

hypocenter

C₃

C₂×C₂²⋊C₄×C₁₉

LCS

G ▷ C₂×C₃ ▷ C₃

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂²⋊C₄×C₁₉

N	H ≅ G/N	type
2. C₂×C₄×D₃×C₁₉	C₂	semidirect
3. C₃×C₂²⋊C₄×C₁₉	C₂	semidirect
4. C₁₉×#217	C₂	semidirect
5. C₁₉×(C₂×D₃)⋊C₄	C₂	semidirect
9. C₂²×D₃×C₁₉	C₄	semidirect
12. C₂×C₃×C₄×C₁₉	C₂²	semidirect
13. C₂×Dic₃×C₁₉	C₂²	semidirect
19. C₂²⋊C₄×C₁₉	D₃	direct (N × H)
21. C₂²×C₃×C₁₉	C₂×C₄	semidirect
26. C₂×D₃×C₁₉	C₂×C₄	semidirect
37. C₂×C₄×C₁₉	C₂×D₃	semidirect
42. D₃×C₁₉	C₂²⋊C₄	direct (N × H)
43. D₃×C₂²⋊C₄	C₁₉	direct (N × H)
50. C₂²×C₁₉	C₄×D₃	semidirect
54. C₃×C₁₉	C₂×C₂²⋊C₄	semidirect
56. C₂×C₄×D₃	C₂×C₁₉	semidirect
57. C₃×C₂²⋊C₄	C₂×C₁₉	semidirect
58. #217	C₂×C₁₉	semidirect
59. (C₂×D₃)⋊C₄	C₂×C₁₉	semidirect
68. C₂²×D₃	C₄×C₁₉	semidirect
71. C₂×C₃×C₄	C₂²×C₁₉	semidirect
72. C₂×Dic₃	C₂²×C₁₉	semidirect
74. C₁₉	D₃×C₂²⋊C₄	direct (N × H)
79. C₂²⋊C₄	D₃×C₁₉	direct (N × H)
81. C₂²×C₃	C₂×C₄×C₁₉	semidirect
86. C₂×D₃	C₂×C₄×C₁₉	semidirect
97. C₂×C₄	C₂×D₃×C₁₉	semidirect
102. D₃	C₂²⋊C₄×C₁₉	direct (N × H)
109. C₂²	C₄×D₃×C₁₉	semidirect
113. C₃	C₂×C₂²⋊C₄×C₁₉	semidirect

H ≅ G/N

type

2. C₂×C₄×D₃×C₁₉

C₂

semidirect

3. C₃×C₂²⋊C₄×C₁₉

C₂

semidirect

4. C₁₉×#217

C₂

semidirect

5. C₁₉×(C₂×D₃)⋊C₄

C₂

semidirect

9. C₂²×D₃×C₁₉

C₄

semidirect

12. C₂×C₃×C₄×C₁₉

C₂²

semidirect

13. C₂×Dic₃×C₁₉

C₂²

semidirect

19. C₂²⋊C₄×C₁₉

D₃

direct (N × H)

21. C₂²×C₃×C₁₉

C₂×C₄

semidirect

26. C₂×D₃×C₁₉

C₂×C₄

semidirect

37. C₂×C₄×C₁₉

C₂×D₃

semidirect

42. D₃×C₁₉

C₂²⋊C₄

direct (N × H)

43. D₃×C₂²⋊C₄

C₁₉

direct (N × H)

50. C₂²×C₁₉

C₄×D₃

semidirect

54. C₃×C₁₉

C₂×C₂²⋊C₄

semidirect

56. C₂×C₄×D₃

C₂×C₁₉

semidirect

57. C₃×C₂²⋊C₄

C₂×C₁₉

semidirect

58. #217

C₂×C₁₉

semidirect

59. (C₂×D₃)⋊C₄

C₂×C₁₉

semidirect

68. C₂²×D₃

C₄×C₁₉

semidirect

71. C₂×C₃×C₄

C₂²×C₁₉

semidirect

72. C₂×Dic₃

C₂²×C₁₉

semidirect

74. C₁₉

D₃×C₂²⋊C₄

direct (N × H)

79. C₂²⋊C₄

D₃×C₁₉

direct (N × H)

81. C₂²×C₃

C₂×C₄×C₁₉

semidirect

86. C₂×D₃

C₂×C₄×C₁₉

semidirect

97. C₂×C₄

C₂×D₃×C₁₉

semidirect

102. D₃

C₂²⋊C₄×C₁₉

direct (N × H)

109. C₂²

C₄×D₃×C₁₉

semidirect

113. C₃

C₂×C₂²⋊C₄×C₁₉

semidirect

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

subgroup	index
C₂³×D₃×C₁₉	2
C₂×C₄×D₃×C₁₉	2
C₃×C₂²⋊C₄×C₁₉	2
C₁₉×#217	2
C₁₉×(C₂×D₃)⋊C₄	2
C₂×C₂²⋊C₄×C₁₉	3
D₃×C₂²⋊C₄	19

subgroup

index

C₂³×D₃×C₁₉

C₂×C₄×D₃×C₁₉

C₃×C₂²⋊C₄×C₁₉

C₁₉×#217

C₁₉×(C₂×D₃)⋊C₄

C₂×C₂²⋊C₄×C₁₉

D₃×C₂²⋊C₄

Subgroups — D₃×C₂²⋊C₄×C₁₉ #14269633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D3×C22⋊C4×C19 #14269633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₂²⋊C₄×C₁₉ #14269633