Group #18070391 — subgroups

Subgroups — #18070391

Order 4864.

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

normal subgroups only

This group has 164 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	#14561802	C₂	1	1	yes	maximal, characteristic, complemented
2	#14561800	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1721	C₂	1	1	yes	maximal, characteristic
4	#11926343	—	2	1	no	—
5	#11926337	—	2	1	no	—
6	C₁₉×#493	—	2	1	no	—
7	C₁₉×#493	C₄	1	1	yes	characteristic, complemented
8	C₁₉×#492	C₂²	1	1	yes	characteristic
9	C₁₉×#486	—	2	1	no	—
10	C₁₉×#322	C₄	1	1	yes	characteristic, complemented
11	C₂×SD₁₆×C₁₉	—	4	1	no	—
12	C₂×D₈×C₁₉	—	4	2	no	—
13	C₂×D₈×C₁₉	—	4	1	no	—
14	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
15	C₁₉×#127	—	2	1	no	—
16	C₁₉×#127	D₄	1	1	yes	characteristic
17	C₁₉×#102	—	4	2	no	—
18	C₄×C₈×C₁₉	—	2	1	no	—
19	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
20	#10597293	—	4	1	no	—
21	#10597291	—	4	1	no	—
22	C₂×Q₈×C₁₉	—	2	1	no	—
23	C₂×D₄×C₁₉	—	2	1	no	—
24	C₂×D₄×C₁₉	—	4	1	no	—
25	C₂×D₄×C₁₉	—	4	1	no	—
26	C₂×D₄×C₁₉	—	4	1	no	—
27	C₂×D₄×C₁₉	—	4	1	no	—
28	SD₁₆×C₁₉	—	8	2	no	—
29	D₈×C₁₉	—	8	2	no	—
30	D₈×C₁₉	—	8	4	no	—
31	C₂×C₈×C₁₉	—	2	1	no	—
32	C₂×C₈×C₁₉	—	2	2	no	—
33	C₄⋊C₄×C₁₉	—	4	1	no	—
34	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₂²⋊Dic₁₉	—	8	1	no	—
36	#64520	—	8	1	no	—
37	#7527	—	19	1	no	maximal, Sylow
38	C₂³×C₁₉	—	4	1	no	—
39	C₂³×C₁₉	—	8	1	no	—
40	Q₈×C₁₉	—	8	1	no	—
41	D₄×C₁₉	—	8	1	no	—
42	D₄×C₁₉	—	8	2	no	—
43	D₄×C₁₉	—	8	2	no	—
44	D₄×C₁₉	—	8	2	no	—
45	D₄×C₁₉	—	8	2	no	—
46	C₂×C₄×C₁₉	—	2	1	no	—
47	C₂×C₄×C₁₉	—	4	1	no	—
48	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
49	C₂×Dic₁₉	—	16	1	no	—
50	C₈×C₁₉	—	2	2	no	—
51	C₈×C₁₉	—	4	2	no	—
52	C₁₉⋊C₈	—	16	1	no	—
53	#1721	D₁₉	1	1	yes	characteristic
54	#1410	—	19	1	no	—
55	#1409	—	19	1	no	—
56	C₂²×C₁₉	—	8	1	no	—
57	C₂²×C₁₉	—	16	1	no	—
58	C₂²×C₁₉	—	16	1	no	—
59	C₂²×C₁₉	—	16	1	no	—
60	C₂²×C₁₉	—	16	1	no	—
61	C₂²×C₁₉	#353	1	1	yes	characteristic
62	C₄×C₁₉	—	2	2	no	—
63	C₄×C₁₉	—	2	1	no	—
64	C₄×C₁₉	—	8	1	no	—
65	Dic₁₉	—	32	1	no	—
66	#493	—	2	1	no	—
67	#493	Dic₁₉	1	1	yes	characteristic, complemented
68	#492	C₂×D₁₉	1	1	yes	characteristic
69	#486	—	2	1	no	—
70	#356	—	38	1	no	—
71	#353	—	38	1	no	—
72	#322	Dic₁₉	1	1	yes	characteristic, complemented
73	C₂×C₁₉	—	2	1	no	—
74	C₂×C₁₉	—	16	1	no	—
75	C₂×C₁₉	—	32	1	no	—
76	C₂×C₁₉	#1408	1	1	yes	characteristic
77	C₂×SD₁₆	—	4	1	no	—
78	C₂×D₈	—	4	1	no	—
79	C₂×D₈	—	4	2	no	—
80	C₄⋊Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
81	#127	—	2	1	no	—
82	#127	C₂²⋊D₁₉	1	1	yes	characteristic
83	#102	—	4	2	no	—
84	#101	—	76	1	no	—
85	#99	—	76	1	no	—
86	C₄×C₈	—	2	1	no	—
87	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
88	C₁₉	#7527	1	1	yes	characteristic, complemented, Sylow
89	C₂×Q₈	—	2	1	no	—
90	C₂×D₄	—	2	1	no	—
91	C₂×D₄	—	4	1	no	—
92	C₂×D₄	—	4	1	no	—
93	C₂×D₄	—	4	1	no	—
94	C₂×D₄	—	4	1	no	—
95	SD₁₆	—	8	2	no	—
96	D₈	—	8	2	no	—
97	D₈	—	8	4	no	—
98	M₁₆	—	152	1	no	—
99	C₂×C₈	—	2	1	no	—
100	C₂×C₈	—	2	2	no	—
101	C₄⋊C₄	—	4	1	no	—
102	C₂²⋊C₄	—	152	1	no	—
103	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
104	C₂³	—	4	1	no	—
105	C₂³	—	8	1	no	—
106	Q₈	—	8	1	no	—
107	D₄	—	8	1	no	—
108	D₄	—	8	2	no	—
109	D₄	—	8	2	no	—
110	D₄	—	8	2	no	—
111	D₄	—	8	2	no	—
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	4	1	no	—
114	C₂×C₄	—	304	1	no	—
115	C₂×C₄	#10597291	1	1	yes	characteristic
116	C₈	—	2	2	no	—
117	C₈	—	4	2	no	—
118	C₈	—	304	1	no	—
119	C₂²	—	8	1	no	—
120	C₂²	—	16	1	no	—
121	C₂²	—	16	1	no	—
122	C₂²	—	16	1	no	—
123	C₂²	—	16	1	no	—
124	C₂²	#11926337	1	1	yes	characteristic
125	C₄	—	2	2	no	—
126	C₄	—	2	1	no	—
127	C₄	—	8	1	no	—
128	C₄	—	608	1	no	—
129	C₂	—	2	1	no	—
130	C₂	—	16	1	no	—
131	C₂	—	32	1	no	—
132	C₂	#14561798	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561802

C₂

yes

maximal, characteristic, complemented

#14561800

C₂

yes

maximal, characteristic, complemented

C₁₉×#1721

C₂

yes

maximal, characteristic

#11926343

—

#11926337

—

C₁₉×#493

—

C₁₉×#493

C₄

yes

characteristic, complemented

C₁₉×#492

C₂²

yes

characteristic

C₁₉×#486

—

C₁₉×#322

C₄

yes

characteristic, complemented

C₂×SD₁₆×C₁₉

—

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

—

C₁₉×C₄⋊Q₈

D₄

yes

characteristic

C₁₉×#127

—

C₁₉×#127

D₄

yes

characteristic

C₁₉×#102

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

#10597293

—

#10597291

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

SD₁₆×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²⋊Dic₁₉

—

#64520

—

#7527

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#99

yes

characteristic

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1721

D₁₉

yes

characteristic

#1410

—

#1409

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#353

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

#493

—

#493

Dic₁₉

yes

characteristic, complemented

#492

C₂×D₁₉

yes

—

—

—

Dic₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1408

yes

characteristic

C₂×SD₁₆

—

C₂×D₈

—

C₂×D₈

—

C₄⋊Q₈

C₂²⋊D₁₉

yes

characteristic

#127

—

#127

C₂²⋊D₁₉

yes

—

—

—

C₄×C₈

—

C₄×C₈

C₂×Dic₁₉

yes

characteristic

C₁₉

#7527

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

SD₁₆

—

D₈

—

D₈

—

M₁₆

—

152

—

C₂×C₈

—

100

C₂×C₈

—

101

C₄⋊C₄

—

102

C₂²⋊C₄

—

152

—

103

C₄²

C₂²⋊Dic₁₉

yes

characteristic

104

C₂³

—

105

C₂³

—

106

Q₈

—

107

D₄

—

108

D₄

—

109

D₄

—

110

D₄

—

111

D₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

304

—

115

C₂×C₄

#10597291

yes

characteristic

116

C₈

—

117

C₈

—

118

C₈

—

304

—

119

C₂²

—

120

C₂²

—

121

C₂²

—

122

C₂²

—

123

C₂²

—

124

C₂²

#11926337

yes

characteristic

125

C₄

—

126

C₄

—

127

C₄

—

128

C₄

—

608

—

129

C₂

—

130

C₂

—

131

C₂

—

132

C₂

#14561798

yes

characteristic

	subgroup	G/H
center	C₂	#14561798
commutator	C₄×C₈×C₁₉	C₂×C₄
Frattini	#492	C₂×D₁₉
Fitting, prime radical	C₁₉×#1721	C₂
socle	C₂×C₁₉	#1408
cosocle	C₁₉×#492	C₂²
hypercenter	#1721	D₁₉
hypocenter	C₁₉	#7527
LCS	G ▷ C₄×C₈×C₁₉ ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #492 ◁ #1721

subgroup

G/H

center

C₂

#14561798

commutator

C₄×C₈×C₁₉

C₂×C₄

Frattini

#492

C₂×D₁₉

Fitting, prime radical

C₁₉×#1721

C₂

socle

C₂×C₁₉

#1408

cosocle

C₁₉×#492

C₂²

D₁₉

C₁₉

G ▷ C₄×C₈×C₁₉ ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #492 ◁ #1721

N	H ≅ G/N	type
1. #14561802	C₂	semidirect
2. #14561800	C₂	semidirect
7. C₁₉×#493	C₄	semidirect
10. C₁₉×#322	C₄	semidirect
67. #493	Dic₁₉	semidirect
72. #322	Dic₁₉	semidirect
88. C₁₉	#7527	semidirect

H ≅ G/N

type

1. #14561802

C₂

semidirect

2. #14561800

C₂

semidirect

7. C₁₉×#493

C₄

semidirect

10. C₁₉×#322

C₄

semidirect

67. #493

Dic₁₉

semidirect

72. #322

Dic₁₉

semidirect

88. C₁₉

#7527

semidirect

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

subgroup	index
#14561802	2
#14561800	2
C₁₉×#1721	2
#7527	19

subgroup

index

#14561802

#14561800

C₁₉×#1721

#7527

Subgroups — #18070391

Conjugacy classes of subgroups

Complements

Maximal subgroups