Group #18070159 — subgroups

Subgroups — #18070159

Order 4864.

144 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 37 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	#14565210	C₂	1	1	yes	maximal, characteristic
2	#14561586	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1309	C₂	1	1	yes	maximal, characteristic
4	#11926593	C₄	1	1	yes	characteristic
5	#11926326	—	2	1	no	—
6	#11926316	—	2	1	no	—
7	#11926304	—	2	1	no	—
8	#11926301	C₄	1	1	yes	characteristic
9	C₁₉×#423	—	2	1	no	—
10	C₁₉×#423	C₂²	1	1	yes	characteristic
11	C₂×M₁₆×C₁₉	—	2	2	no	—
12	C₂×M₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
13	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
14	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
15	#10597372	—	2	1	no	—
16	C₂×#64520	—	2	1	no	—
17	C₁₉×C₄⋊C₈	—	4	1	no	—
18	C₁₉×C₄⋊C₈	—	4	1	no	—
19	C₁₉×C₄⋊C₈	—	4	1	no	—
20	#10597276	—	4	1	no	—
21	#10597269	—	4	1	no	—
22	C₂²×C₄×C₁₉	—	2	1	no	—
23	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
24	M₁₆×C₁₉	—	4	1	no	—
25	M₁₆×C₁₉	—	4	1	no	—
26	M₁₆×C₁₉	—	8	2	no	—
27	C₂×C₈×C₁₉	—	2	1	no	—
28	C₂×C₈×C₁₉	—	2	1	no	—
29	C₂×C₈×C₁₉	—	4	2	no	—
30	C₄²×C₁₉	—	2	1	no	—
31	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
32	C₄²×C₁₉	Q₁₆	1	1	yes	characteristic
33	C₂²⋊Dic₁₉	—	4	1	no	—
34	C₄⋊Dic₁₉	—	4	1	no	—
35	C₄×Dic₁₉	—	4	1	no	—
36	#64520	—	4	1	no	—
37	#64520	—	4	1	no	—
38	C₂×C₁₉⋊C₈	—	4	1	no	—
39	C₁₉⋊C₁₆	—	8	1	no	—
40	#7440	—	19	1	no	maximal, Sylow
41	C₂³×C₁₉	#104	1	1	yes	characteristic
42	C₂×C₄×C₁₉	—	2	1	no	—
43	C₂×C₄×C₁₉	—	2	1	no	—
44	C₂×C₄×C₁₉	—	2	1	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	#99	1	1	yes	characteristic
49	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
50	C₂×Dic₁₉	—	8	1	no	—
51	C₈×C₁₉	—	4	1	no	—
52	C₈×C₁₉	—	4	1	no	—
53	C₈×C₁₉	—	8	2	no	—
54	C₁₉⋊C₈	—	8	1	no	—
55	#2102	—	19	1	no	—
56	#1327	—	19	1	no	—
57	#1309	D₁₉	1	1	yes	characteristic
58	C₂²×C₁₉	—	2	1	no	—
59	C₂²×C₁₉	—	4	1	no	—
60	C₂²×C₁₉	#328	1	1	yes	characteristic
61	C₄×C₁₉	—	2	1	no	—
62	C₄×C₁₉	—	2	1	no	—
63	C₄×C₁₉	—	2	1	no	—
64	C₄×C₁₉	—	4	1	no	—
65	C₄×C₁₉	#352	1	1	yes	characteristic
66	C₄×C₁₉	#355	1	1	yes	characteristic
67	Dic₁₉	—	16	1	no	—
68	#430	—	19	1	no	—
69	#423	—	2	1	no	—
70	#423	C₂×D₁₉	1	1	yes	characteristic
71	#349	—	38	1	no	—
72	#344	—	38	1	no	—
73	#339	—	38	1	no	—
74	H(3,ℤ/4)	—	19	1	no	—
75	C₂×C₁₉	—	2	1	no	—
76	C₂×C₁₉	—	4	1	no	—
77	C₂×C₁₉	#1353	1	1	yes	characteristic
78	C₂×M₁₆	—	2	2	no	—
79	C₂×M₁₆	—	38	1	no	—
80	C₂×M₁₆	C₄×D₁₉	1	1	yes	characteristic
81	C₂×M₁₆	D₇₆	1	1	yes	characteristic
82	#117	—	38	1	no	—
83	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
84	M₃₂	—	76	1	no	—
85	#108	—	76	1	no	—
86	C₄⋊C₈	—	4	1	no	—
87	C₄⋊C₈	—	4	1	no	—
88	C₄⋊C₈	—	4	1	no	—
89	C₁₉	#7440	1	1	yes	characteristic, complemented, Sylow
90	C₂²×C₄	—	2	1	no	—
91	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
92	M₁₆	—	4	1	no	—
93	M₁₆	—	4	1	no	—
94	M₁₆	—	8	2	no	—
95	M₁₆	—	76	1	no	—
96	M₁₆	—	76	1	no	—
97	C₂×C₈	—	2	1	no	—
98	C₂×C₈	—	2	1	no	—
99	C₂×C₈	—	4	2	no	—
100	C₂×C₈	—	76	1	no	—
101	C₄⋊C₄	—	76	1	no	—
102	C₂²⋊C₄	—	76	1	no	—
103	C₄²	—	2	1	no	—
104	C₄²	—	76	1	no	—
105	C₄²	#64526	1	1	yes	characteristic
106	C₄²	#64528	1	1	yes	characteristic
107	C₁₆	—	152	1	no	—
108	C₂³	#10597262	1	1	yes	characteristic
109	C₂×C₄	—	2	1	no	—
110	C₂×C₄	—	2	1	no	—
111	C₂×C₄	—	2	1	no	—
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	4	1	no	—
114	C₂×C₄	—	4	1	no	—
115	C₂×C₄	—	152	1	no	—
116	C₂×C₄	#10597263	1	1	yes	characteristic
117	C₂×C₄	#10597267	1	1	yes	characteristic
118	C₈	—	4	1	no	—
119	C₈	—	4	1	no	—
120	C₈	—	8	2	no	—
121	C₈	—	152	1	no	—
122	C₂²	—	2	1	no	—
123	C₂²	—	4	1	no	—
124	C₂²	#11926280	1	1	yes	characteristic
125	C₄	—	2	1	no	—
126	C₄	—	2	1	no	—
127	C₄	—	2	1	no	—
128	C₄	—	4	1	no	—
129	C₄	—	304	1	no	—
130	C₄	#11926335	1	1	yes	characteristic
131	C₄	#11926340	1	1	yes	characteristic
132	C₂	—	2	1	no	—
133	C₂	—	4	1	no	—
134	C₂	#14561661	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565210

C₂

yes

maximal, characteristic

#14561586

C₂

yes

maximal, characteristic

C₁₉×#1309

C₂

yes

maximal, characteristic

#11926593

C₄

yes

—

—

—

C₄

yes

characteristic

C₁₉×#423

—

C₁₉×#423

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×M₁₆×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

#10597372

—

C₂×#64520

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

#10597276

—

#10597269

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

SD₁₆

yes

characteristic

C₄²×C₁₉

Q₁₆

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₁₉⋊C₁₆

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2102

—

#1327

—

#1309

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#328

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

#430

—

#423

—

#423

C₂×D₁₉

yes

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1353

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₄×D₁₉

yes

characteristic

C₂×M₁₆

D₇₆

yes

characteristic

#117

—

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

M₃₂

—

#108

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₁₉

#7440

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₄⋊C₄

—

102

C₂²⋊C₄

—

103

C₄²

—

104

C₄²

—

105

C₄²

#64526

yes

characteristic

106

C₄²

#64528

yes

characteristic

107

C₁₆

—

152

—

108

C₂³

#10597262

yes

characteristic

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

152

—

116

C₂×C₄

#10597263

yes

characteristic

117

C₂×C₄

#10597267

yes

characteristic

118

C₈

—

119

C₈

—

120

C₈

—

121

C₈

—

152

—

122

C₂²

—

123

C₂²

—

124

C₂²

#11926280

yes

characteristic

125

C₄

—

126

C₄

—

127

C₄

—

128

C₄

—

129

C₄

—

304

—

130

C₄

#11926335

yes

characteristic

131

C₄

#11926340

yes

characteristic

132

C₂

—

133

C₂

—

134

C₂

#14561661

yes

characteristic

	subgroup	G/H
center	C₂	#14561661
commutator	C₂×M₁₆×C₁₉	C₂×C₄
Frattini	#423	C₂×D₁₉
Fitting	C₁₉×#1309	C₂
socle	C₂×C₁₉	#1353
prime radical	C₂³×C₁₉	#104
cosocle	C₁₉×#423	C₂²
hypercenter	#1309	D₁₉
hypocenter	C₁₉	#7440
LCS	G ▷ C₂×M₁₆×C₁₉ ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #423 ◁ #1309

subgroup

G/H

center

C₂

#14561661

commutator

C₂×M₁₆×C₁₉

C₂×C₄

Frattini

#423

C₂×D₁₉

Fitting

C₁₉×#1309

C₂

C₂×C₁₉

C₂³×C₁₉

C₁₉×#423

C₂²

D₁₉

C₁₉

G ▷ C₂×M₁₆×C₁₉ ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #423 ◁ #1309

N	H ≅ G/N	type
89. C₁₉	#7440	semidirect

H ≅ G/N

type

89. C₁₉

#7440

semidirect

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

subgroup	index
#14565210	2
#14561586	2
C₁₉×#1309	2
#7440	19

subgroup

index

#14565210

#14561586

C₁₉×#1309

#7440

Subgroups — #18070159

Conjugacy classes of subgroups

Complements

Maximal subgroups