Group #18070382 — subgroups

Subgroups — #18070382

Order 4864.

134 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 27 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	#14561806	C₂	1	1	yes	maximal, characteristic
2	#14561668	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1658	C₂	1	1	yes	maximal, characteristic
4	#11926337	—	2	1	no	—
5	#11926322	—	2	1	no	—
6	C₁₉×#564	C₄	1	1	yes	characteristic, complemented
7	C₁₉×#490	—	2	1	no	—
8	C₁₉×#490	C₂²	1	1	yes	characteristic
9	C₁₉×#330	—	2	1	no	—
10	C₁₉×#330	C₄	1	1	yes	characteristic, complemented
11	C₁₉×#127	D₄	1	1	yes	characteristic
12	C₁₉×#125	—	2	1	no	—
13	C₁₉×#125	—	4	1	no	—
14	C₁₉×#125	—	4	1	no	—
15	C₁₉×#125	—	4	1	no	—
16	C₁₉×#125	C₂×C₄	1	1	yes	characteristic
17	C₁₉×#102	—	4	1	no	—
18	C₁₉×#102	—	4	1	no	—
19	C₁₉×#102	—	4	1	no	—
20	C₁₉×#97	—	2	1	no	—
21	C₁₉×#97	D₄	1	1	yes	characteristic
22	#10597291	—	4	1	no	—
23	#10597269	—	4	1	no	—
24	C₂×D₄×C₁₉	—	2	1	no	—
25	C₂×D₄×C₁₉	—	4	1	no	—
26	C₂×C₈×C₁₉	—	2	1	no	—
27	C₂×C₈×C₁₉	—	4	1	no	—
28	C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₄⋊C₄×C₁₉	—	4	1	no	—
32	C₄⋊C₄×C₁₉	—	4	1	no	—
33	C₄⋊C₄×C₁₉	—	4	1	no	—
34	C₄⋊C₄×C₁₉	—	4	1	no	—
35	C₄⋊C₄×C₁₉	—	4	1	no	—
36	C₄⋊C₄×C₁₉	—	4	1	no	—
37	C₄²×C₁₉	—	4	1	no	—
38	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
39	C₂²⋊Dic₁₉	—	8	1	no	—
40	C₁₉⋊C₁₆	—	4	2	no	—
41	#7524	—	19	1	no	maximal, Sylow
42	C₂³×C₁₉	—	4	1	no	—
43	D₄×C₁₉	—	8	1	no	—
44	D₄×C₁₉	—	8	2	no	—
45	C₂×C₄×C₁₉	—	2	1	no	—
46	C₂×C₄×C₁₉	—	4	1	no	—
47	C₂×C₄×C₁₉	—	4	1	no	—
48	C₂×C₄×C₁₉	—	4	1	no	—
49	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
50	C₂×Dic₁₉	—	16	1	no	—
51	C₈×C₁₉	—	4	1	no	—
52	C₈×C₁₉	—	8	1	no	—
53	#1658	D₁₉	1	1	yes	characteristic
54	#1412	—	19	1	no	—
55	#1355	—	19	1	no	—
56	C₂²×C₁₉	—	8	1	no	—
57	C₂²×C₁₉	—	16	1	no	—
58	C₂²×C₁₉	AΣL(1,𝔽₁₆)	1	1	yes	characteristic
59	C₄×C₁₉	—	2	1	no	—
60	C₄×C₁₉	—	4	1	no	—
61	C₄×C₁₉	—	8	1	no	—
62	C₄×C₁₉	—	8	1	no	—
63	C₄×C₁₉	—	8	1	no	—
64	Dic₁₉	—	32	1	no	—
65	#564	Dic₁₉	1	1	yes	characteristic, complemented
66	#490	—	2	1	no	—
67	#490	C₂×D₁₉	1	1	yes	characteristic
68	#353	—	38	1	no	—
69	#347	—	38	1	no	—
70	#330	—	2	1	no	—
71	#330	Dic₁₉	1	1	yes	characteristic, complemented
72	C₂×C₁₉	—	2	1	no	—
73	C₂×C₁₉	—	16	1	no	—
74	C₂×C₁₉	#1404	1	1	yes	characteristic
75	#127	C₂²⋊D₁₉	1	1	yes	characteristic
76	#125	—	2	1	no	—
77	#125	—	4	1	no	—
78	#125	—	4	1	no	—
79	#125	—	4	1	no	—
80	#125	C₂×Dic₁₉	1	1	yes	characteristic
81	M₃₂	—	76	1	no	—
82	#102	—	4	1	no	—
83	#102	—	4	1	no	—
84	#102	—	4	1	no	—
85	#99	—	76	1	no	—
86	#97	—	2	1	no	—
87	#97	C₂²⋊D₁₉	1	1	yes	characteristic
88	C₁₉	#7524	1	1	yes	characteristic, complemented, Sylow
89	C₂×D₄	—	2	1	no	—
90	C₂×D₄	—	4	1	no	—
91	C₂×C₈	—	2	1	no	—
92	C₂×C₈	—	4	1	no	—
93	C₄⋊C₄	—	2	1	no	—
94	C₄⋊C₄	—	2	1	no	—
95	C₄⋊C₄	—	2	1	no	—
96	C₄⋊C₄	—	4	1	no	—
97	C₄⋊C₄	—	4	1	no	—
98	C₄⋊C₄	—	4	1	no	—
99	C₄⋊C₄	—	4	1	no	—
100	C₄⋊C₄	—	4	1	no	—
101	C₄⋊C₄	—	4	1	no	—
102	C₂²⋊C₄	—	152	1	no	—
103	C₄²	—	4	1	no	—
104	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
105	C₁₆	—	76	2	no	—
106	C₂³	—	4	1	no	—
107	D₄	—	8	1	no	—
108	D₄	—	8	2	no	—
109	C₂×C₄	—	2	1	no	—
110	C₂×C₄	—	4	1	no	—
111	C₂×C₄	—	4	1	no	—
112	C₂×C₄	—	4	1	no	—
113	C₂×C₄	—	304	1	no	—
114	C₂×C₄	#10597291	1	1	yes	characteristic
115	C₈	—	4	1	no	—
116	C₈	—	8	1	no	—
117	C₂²	—	8	1	no	—
118	C₂²	—	16	1	no	—
119	C₂²	#11926331	1	1	yes	characteristic
120	C₄	—	2	1	no	—
121	C₄	—	4	1	no	—
122	C₄	—	8	1	no	—
123	C₄	—	8	1	no	—
124	C₄	—	8	1	no	—
125	C₄	—	608	1	no	—
126	C₂	—	2	1	no	—
127	C₂	—	16	1	no	—
128	C₂	#14561786	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561806

C₂

yes

maximal, characteristic

#14561668

C₂

yes

maximal, characteristic

C₁₉×#1658

C₂

yes

maximal, characteristic

#11926337

—

#11926322

—

C₁₉×#564

C₄

yes

characteristic, complemented

C₁₉×#490

—

C₁₉×#490

C₂²

yes

characteristic

C₁₉×#330

—

C₁₉×#330

C₄

yes

characteristic, complemented

C₁₉×#127

D₄

yes

characteristic

C₁₉×#125

—

C₁₉×#125

—

C₁₉×#125

—

C₁₉×#125

—

C₁₉×#125

C₂×C₄

yes

characteristic

C₁₉×#102

—

C₁₉×#102

—

C₁₉×#102

—

C₁₉×#97

—

C₁₉×#97

D₄

yes

characteristic

#10597291

—

#10597269

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²⋊Dic₁₉

—

C₁₉⋊C₁₆

—

#7524

—

maximal, Sylow

C₂³×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#99

yes

characteristic

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

#1658

D₁₉

yes

characteristic

#1412

—

#1355

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

AΣL(1,𝔽₁₆)

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

#564

Dic₁₉

yes

characteristic, complemented

#490

—

#490

C₂×D₁₉

yes

—

—

—

Dic₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1404

yes

characteristic

#127

C₂²⋊D₁₉

yes

—

—

—

—

C₂×Dic₁₉

yes

characteristic

M₃₂

—

—

—

—

—

—

C₂²⋊D₁₉

yes

characteristic

C₁₉

#7524

yes

characteristic, complemented, Sylow

C₂×D₄

—

C₂×D₄

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₂²⋊C₄

—

152

—

103

C₄²

—

104

C₄²

C₂²⋊Dic₁₉

yes

characteristic

105

C₁₆

—

106

C₂³

—

107

D₄

—

108

D₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

304

—

114

C₂×C₄

#10597291

yes

characteristic

115

C₈

—

116

C₈

—

117

C₂²

—

118

C₂²

—

119

C₂²

#11926331

yes

characteristic

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

—

608

—

126

C₂

—

127

C₂

—

128

C₂

#14561786

yes

characteristic

	subgroup	G/H
center	C₂	#14561786
commutator	C₁₉×#125	C₂×C₄
Frattini	#490	C₂×D₁₉
Fitting	C₁₉×#1658	C₂
socle	C₂×C₁₉	#1404
prime radical	C₁₉×#127	D₄
cosocle	C₁₉×#490	C₂²
hypercenter	#1658	D₁₉
hypocenter	C₁₉	#7524
LCS	G ▷ C₁₉×#125 ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #490 ◁ #1658

subgroup

G/H

center

C₂

#14561786

commutator

C₁₉×#125

C₂×C₄

Frattini

#490

C₂×D₁₉

Fitting

C₁₉×#1658

C₂

socle

C₂×C₁₉

#1404

prime radical

C₁₉×#127

D₄

cosocle

C₁₉×#490

C₂²

D₁₉

C₁₉

G ▷ C₁₉×#125 ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #490 ◁ #1658

N	H ≅ G/N	type
6. C₁₉×#564	C₄	semidirect
10. C₁₉×#330	C₄	semidirect
65. #564	Dic₁₉	semidirect
71. #330	Dic₁₉	semidirect
88. C₁₉	#7524	semidirect

H ≅ G/N

type

6. C₁₉×#564

C₄

semidirect

10. C₁₉×#330

C₄

semidirect

65. #564

Dic₁₉

semidirect

71. #330

Dic₁₉

semidirect

88. C₁₉

#7524

semidirect

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

subgroup	index
#14561806	2
#14561668	2
C₁₉×#1658	2
#7524	19

subgroup

index

#14561806

#14561668

C₁₉×#1658

#7524

Subgroups — #18070382

Conjugacy classes of subgroups

Complements

Maximal subgroups