Group #14269420 — subgroups

Subgroups — D₃×#64527 #14269420

Order 1824.

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

normal subgroups only

This group has 136 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, complemented
2	D₃×D₇₆	C₂	1	1	yes	maximal, characteristic
3	#11744892	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64527	C₂	1	1	yes	maximal, characteristic, complemented
5	#11744826	C₂	1	1	yes	maximal, characteristic, complemented
6	#11744821	C₂	1	1	yes	maximal, characteristic, complemented
7	D₃×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#64527	—	3	1	no	maximal, Hall
9	C₂×D₃×D₁₉	—	2	1	no	—
10	C₃×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
11	D₂₂₈	C₂²	1	1	yes	characteristic
12	C₄×D₃×C₁₉	—	2	1	no	—
13	C₄×D₃×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×Dic₆	—	2	1	no	—
15	C₁₉×Dic₆	C₂²	1	1	yes	characteristic, complemented
16	C₃×D₇₆	C₂²	1	1	yes	characteristic
17	#90696	—	2	1	no	—
18	C₃⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
19	C₃×C₁₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
20	C₂×Q₈×C₁₉	—	3	1	no	—
21	C₂×D₇₆	—	3	1	no	—
22	#64527	—	3	1	no	—
23	#64527	—	3	1	no	—
24	#64527	—	3	1	no	—
25	#64527	D₃	1	1	yes	characteristic, direct product factor
26	C₂×C₁₉⋊C₈	—	3	1	no	—
27	C₂×D₅₇	—	2	1	no	—
28	C₂×D₃×C₁₉	D₄	1	1	yes	characteristic
29	C₂×C₃×D₁₉	—	2	1	no	—
30	D₃×D₁₉	—	4	2	no	—
31	C₃×C₄×C₁₉	—	2	1	no	—
32	C₃×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	Dic₃×C₁₉	—	2	1	no	—
34	Dic₃×C₁₉	D₄	1	1	yes	characteristic
35	C₂²×D₁₉	—	6	1	no	—
36	Q₈×C₁₉	—	3	1	no	—
37	Q₈×C₁₉	—	6	1	no	—
38	Q₈×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented
39	C₂×C₄×C₁₉	—	3	1	no	—
40	C₂×C₄×C₁₉	—	6	1	no	—
41	D₇₆	—	3	1	no	—
42	D₇₆	—	6	1	no	—
43	D₇₆	C₂×D₃	1	1	yes	characteristic
44	C₁₉⋊C₈	—	3	1	no	—
45	C₁₉⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
46	C₂×C₃×C₁₉	C₂×D₄	1	1	yes	characteristic
47	D₅₇	—	4	1	no	—
48	C₃×D₁₉	—	4	1	no	—
49	D₃×C₁₉	SD₁₆	1	2	yes	complemented
50	D₃×SD₁₆	—	19	1	no	maximal, Hall
51	C₂²×C₁₉	—	3	1	no	—
52	C₂×D₁₉	—	2	1	no	—
53	C₂×D₁₉	—	6	1	no	—
54	C₂×D₁₉	—	12	2	no	—
55	C₄×C₁₉	—	2	1	no	—
56	C₄×C₁₉	—	3	1	no	—
57	C₄×C₁₉	—	6	1	no	—
58	C₄×C₁₉	C₂²×D₃	1	1	yes	characteristic
59	C₃×C₁₉	C₂×SD₁₆	1	1	yes	characteristic, complemented, Hall
60	D₃×Q₈	D₁₉	1	1	yes	characteristic, complemented
61	D₃×D₄	—	19	1	no	—
62	C₃×SD₁₆	—	19	1	no	—
63	#215	—	19	1	no	—
64	#214	—	19	1	no	—
65	#204	—	19	1	no	—
66	D₃×C₈	—	19	1	no	—
67	C₂×C₁₉	—	3	2	no	—
68	C₂×C₁₉	D₃×D₄	1	1	yes	characteristic
69	D₁₉	—	4	1	no	—
70	D₁₉	—	12	1	no	—
71	C₂×SD₁₆	—	57	1	no	Sylow
72	C₂²×D₃	—	38	1	no	—
73	C₃×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
74	C₃×D₄	—	19	1	no	—
75	#67	—	38	1	no	—
76	D₁₂	—	19	1	no	—
77	C₄×D₃	—	2	1	no	—
78	C₄×D₃	C₂×D₁₉	1	1	yes	characteristic
79	Dic₆	—	2	1	no	—
80	Dic₆	C₂×D₁₉	1	1	yes	characteristic, complemented
81	C₃×C₈	—	19	1	no	—
82	C₃⋊C₈	—	19	1	no	—
83	C₁₉	D₃×SD₁₆	1	1	yes	characteristic, complemented, Sylow
84	C₂×Q₈	—	3	1	no	—
85	C₂×D₄	—	57	1	no	—
86	SD₁₆	—	19	1	no	—
87	SD₁₆	—	57	1	no	—
88	SD₁₆	—	57	1	no	—
89	SD₁₆	—	57	1	no	—
90	C₂×C₈	—	57	1	no	—
91	C₂²×C₃	—	38	1	no	—
92	C₂×D₃	—	38	1	no	—
93	C₂×D₃	—	76	2	no	—
94	C₂×D₃	C₂²⋊D₁₉	1	1	yes	characteristic
95	C₃×C₄	—	2	1	no	—
96	C₃×C₄	C₂²×D₁₉	1	1	yes	characteristic
97	Dic₃	—	2	1	no	—
98	Dic₃	C₂²⋊D₁₉	1	1	yes	characteristic
99	C₂³	—	114	1	no	—
100	Q₈	—	3	1	no	—
101	Q₈	—	6	1	no	—
102	Q₈	D₃×D₁₉	1	1	yes	characteristic, complemented
103	D₄	—	19	1	no	—
104	D₄	—	57	1	no	—
105	D₄	—	114	1	no	—
106	C₂×C₄	—	3	1	no	—
107	C₂×C₄	—	6	1	no	—
108	C₈	—	19	1	no	—
109	C₈	—	57	1	no	—
110	C₂×C₃	—	76	1	no	—
111	C₂×C₃	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
112	D₃	—	76	1	no	—
113	D₃	#64527	1	2	yes	direct product factor
114	C₂²	—	3	1	no	—
115	C₂²	—	38	1	no	—
116	C₂²	—	114	1	no	—
117	C₂²	—	228	2	no	—
118	C₄	—	2	1	no	—
119	C₄	—	3	1	no	—
120	C₄	—	6	1	no	—
121	C₄	C₂×D₃×D₁₉	1	1	yes	characteristic
122	C₃	C₂×#64527	1	1	yes	characteristic, complemented, Sylow
123	C₂	—	3	2	no	—
124	C₂	—	76	1	no	—
125	C₂	—	228	1	no	—
126	C₂	D₃×C₂²⋊D₁₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₃×Q₈×C₁₉

C₂

yes

maximal, characteristic, complemented

D₃×D₇₆

C₂

yes

maximal, characteristic

#11744892

C₂

yes

maximal, characteristic, complemented

C₃×#64527

C₂

yes

maximal, characteristic, complemented

#11744826

C₂

yes

maximal, characteristic, complemented

#11744821

C₂

yes

maximal, characteristic, complemented

D₃×C₁₉⋊C₈

C₂

yes

maximal, characteristic, complemented

C₂×#64527

—

maximal, Hall

C₂×D₃×D₁₉

—

C₃×Q₈×C₁₉

C₂²

yes

characteristic, complemented

D₂₂₈

C₂²

yes

characteristic

C₄×D₃×C₁₉

—

C₄×D₃×C₁₉

C₂²

yes

characteristic

C₁₉×Dic₆

—

C₁₉×Dic₆

C₂²

yes

characteristic, complemented

C₃×D₇₆

C₂²

yes

characteristic

#90696

—

C₃⋊(C₁₉⋊C₈)

C₂²

yes

characteristic, complemented

C₃×C₁₉⋊C₈

C₂²

yes

characteristic, complemented

C₂×Q₈×C₁₉

—

C₂×D₇₆

—

—

—

—

D₃

yes

characteristic, direct product factor

C₂×C₁₉⋊C₈

—

C₂×D₅₇

—

C₂×D₃×C₁₉

D₄

yes

characteristic

C₂×C₃×D₁₉

—

D₃×D₁₉

—

C₃×C₄×C₁₉

—

C₃×C₄×C₁₉

C₂³

yes

characteristic

Dic₃×C₁₉

—

Dic₃×C₁₉

D₄

yes

characteristic

C₂²×D₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

C₂×D₃

yes

characteristic, complemented

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

D₇₆

—

D₇₆

—

D₇₆

C₂×D₃

yes

characteristic

C₁₉⋊C₈

—

C₁₉⋊C₈

C₂×D₃

yes

characteristic, complemented

C₂×C₃×C₁₉

C₂×D₄

yes

characteristic

D₅₇

—

C₃×D₁₉

—

D₃×C₁₉

SD₁₆

yes

complemented

D₃×SD₁₆

—

maximal, Hall

C₂²×C₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²×D₃

yes

characteristic

C₃×C₁₉

C₂×SD₁₆

yes

characteristic, complemented, Hall

D₃×Q₈

D₁₉

yes

characteristic, complemented

D₃×D₄

—

C₃×SD₁₆

—

#215

—

#214

—

#204

—

D₃×C₈

—

C₂×C₁₉

—

C₂×C₁₉

D₃×D₄

yes

characteristic

D₁₉

—

D₁₉

—

C₂×SD₁₆

—

Sylow

C₂²×D₃

—

C₃×Q₈

C₂×D₁₉

yes

characteristic, complemented

C₃×D₄

—

#67

—

D₁₂

—

C₄×D₃

—

C₄×D₃

C₂×D₁₉

yes

characteristic

Dic₆

—

Dic₆

C₂×D₁₉

yes

characteristic, complemented

C₃×C₈

—

C₃⋊C₈

—

C₁₉

D₃×SD₁₆

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

SD₁₆

—

SD₁₆

—

SD₁₆

—

SD₁₆

—

C₂×C₈

—

C₂²×C₃

—

C₂×D₃

—

C₂×D₃

—

C₂×D₃

C₂²⋊D₁₉

yes

characteristic

C₃×C₄

—

C₃×C₄

C₂²×D₁₉

yes

characteristic

Dic₃

—

Dic₃

C₂²⋊D₁₉

yes

characteristic

C₂³

—

114

—

100

Q₈

—

101

Q₈

—

102

Q₈

D₃×D₁₉

yes

characteristic, complemented

103

D₄

—

104

D₄

—

105

D₄

—

114

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₈

—

109

C₈

—

110

C₂×C₃

—

111

C₂×C₃

C₂×C₂²⋊D₁₉

yes

characteristic

112

D₃

—

113

D₃

#64527

yes

direct product factor

114

C₂²

—

115

C₂²

—

116

C₂²

—

114

—

117

C₂²

—

228

—

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

C₂×D₃×D₁₉

yes

characteristic

122

C₃

C₂×#64527

yes

characteristic, complemented, Sylow

123

C₂

—

124

C₂

—

125

C₂

—

228

—

126

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	D₃×D₇₆	C₂
hypercenter	Q₈	D₃×D₁₉
hypocenter	C₃×C₁₉	C₂×SD₁₆
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

D₃×D₇₆

C₂

hypercenter

Q₈

D₃×D₁₉

hypocenter

C₃×C₁₉

C₂×SD₁₆

LCS

G ▷ C₃×C₄×C₁₉ ▷ C₂×C₃×C₁₉ ▷ C₃×C₁₉

UCS

C₁ ◁ C₂ ◁ C₄ ◁ Q₈

N	H ≅ G/N	type
1. D₃×Q₈×C₁₉	C₂	semidirect
3. #11744892	C₂	semidirect
4. C₃×#64527	C₂	semidirect
5. #11744826	C₂	semidirect
6. #11744821	C₂	semidirect
7. D₃×C₁₉⋊C₈	C₂	semidirect
10. C₃×Q₈×C₁₉	C₂²	semidirect
15. C₁₉×Dic₆	C₂²	semidirect
18. C₃⋊(C₁₉⋊C₈)	C₂²	semidirect
19. C₃×C₁₉⋊C₈	C₂²	semidirect
25. #64527	D₃	direct (N × H)
38. Q₈×C₁₉	C₂×D₃	semidirect
45. C₁₉⋊C₈	C₂×D₃	semidirect
49. D₃×C₁₉	SD₁₆	semidirect
59. C₃×C₁₉	C₂×SD₁₆	semidirect
60. D₃×Q₈	D₁₉	semidirect
73. C₃×Q₈	C₂×D₁₉	semidirect
80. Dic₆	C₂×D₁₉	semidirect
83. C₁₉	D₃×SD₁₆	semidirect
102. Q₈	D₃×D₁₉	semidirect
113. D₃	#64527	direct (N × H)
122. C₃	C₂×#64527	semidirect

H ≅ G/N

type

1. D₃×Q₈×C₁₉

C₂

semidirect

3. #11744892

C₂

semidirect

4. C₃×#64527

C₂

semidirect

5. #11744826

C₂

semidirect

6. #11744821

C₂

semidirect

7. D₃×C₁₉⋊C₈

C₂

semidirect

10. C₃×Q₈×C₁₉

C₂²

semidirect

15. C₁₉×Dic₆

C₂²

semidirect

18. C₃⋊(C₁₉⋊C₈)

C₂²

semidirect

19. C₃×C₁₉⋊C₈

C₂²

semidirect

25. #64527

D₃

direct (N × H)

38. Q₈×C₁₉

C₂×D₃

semidirect

45. C₁₉⋊C₈

C₂×D₃

semidirect

49. D₃×C₁₉

SD₁₆

semidirect

59. C₃×C₁₉

C₂×SD₁₆

semidirect

60. D₃×Q₈

D₁₉

semidirect

73. C₃×Q₈

C₂×D₁₉

semidirect

80. Dic₆

C₂×D₁₉

semidirect

83. C₁₉

D₃×SD₁₆

semidirect

102. Q₈

D₃×D₁₉

semidirect

113. D₃

#64527

direct (N × H)

122. C₃

C₂×#64527

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×D₇₆	2
#11744892	2
C₃×#64527	2
#11744826	2
#11744821	2
D₃×C₁₉⋊C₈	2
C₂×#64527	3
D₃×SD₁₆	19

subgroup

index

D₃×Q₈×C₁₉

D₃×D₇₆

D₃×C₁₉⋊C₈

D₃×SD₁₆

Subgroups — D₃×#64527 #14269420

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D3×#64527 #14269420

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#64527 #14269420